Semiconductors and Semimetals, Volume 18 Mercury Cadmium Telluride

SEMICONDUCTORS AND SEMIMETALS VOLUME 18 Mercury Cadmium Telluride

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SEMICONDUCTORS AND SEMIMETALS Edited b y R . K . WILLARDSON ELECTRONIC MATERIALS DIVISION COMINCO AMERICAN INCORPORATED SPOKANE, WASHINGTON

ALBERT C . BEER BAlTELLE COLUMBUS LABORATORIES COLUMBUS, OHIO

VOLUME 18 Mercury Cadmium Telluride

1981

ACADEMIC PRESS A Suhsidia ry o j Harco iirt Bruce Jovunovic h , Pu hl is hers

N e w York London Puris Sun Diego Sun Fruncisco Siio Puulo Sydney Tokyo Toronto

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L'OPYRICHI' 198 1 , ItY ACADEMIC PRESS, I N r . AI.1. RIGHTS RESERVED. NO PART 01: THIS I'UBI.ICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCI.UI)INC; PHOTOCOPY, RECORDING, OR ANY INI~ORMATIONSTORAGE AND RETRIEVAL SYSI'EM, WITHOUT PERMISSlON i N WRITING FROM THE PUBLISHER.

ACADEMIC PRESS, INC.

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Uniied Kirigiloni Ediiiori published h y ACADEMIC PRESS, INC. (LONDON) LTD.

24/28 O v a l Road, London N W l

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Library o f Congress Cataloging i n Publication Data Main entry under t i t l e : Saniconductors and semimetals. Includes hiblioqraphical references and index. Contents: v. 1-2 Physics o f 111-V cmpounds-v . 3. Optical properties o f 111-V cmpounds--[etc.l --v. 18. Mercury cadmim t e l l u r i d e . 1. Semiconductors--Collected works. 2. S m i m e t a l s --Collected works. I . Willardson, Robert K . 11. Beer, Albert C . , j o i n t ed. 111. Title. G610.9.547 537.6'22 65-26048 ISBN 0-12-752118-6 ( V . 18) AACR2

PRINTED IN THE UNITED S I A I t S OF AMERICA 81 82 83 84

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Contents LISTOF CONTRIBUTORS . PREFACE. . . . . NOMENCLATURE.

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Chapter 1 The Emergence of (Hg.-.Cd. )Te as a Modern Infrared Sensitive Material Paul W. Kruse I . Historical Overview . . . . . . . . I1. Review of the Electrical. Optical. and Structural Properties References . . . . . . . . . .

Chapter 2 Preparation of High-Purity Cadmium. Mercury. and Tellurium H . E . Hirsch. S . C . Liang. and A . G . White I . Introduction . . . . . . I1 . Purification Processes . . . . . I11. Purification of Cadmium . . . . IV . Purification of Mercury . . . . V . Purification of Tellurium . . . . VI . Special Products for (CdHg)Te Preparation References . . . . . . .

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Chapter 3 The Crystal Growth of Cadmium Mercury Telluride W . F . H . Micklethwaite I . Introduction . . . . . . . . . . I1. I11. IV . V.

Crystal Growth by the QuencWRecrystallization Method Liquid/Solid Growth . . . . . . . Epitaxial Growth . . . . . . . Other Considerations . . . . . . . References . . . . . . . . . V

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CONTENTS

Chapter 4 Auger Recombination in Mercury Cadmium Telluride

Paul E . Peterscri I . Introduction . . I1 . 111. IV . V.

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Auger Lifetime in Nondegenerate Material . Auger Lifetime in Degenerate Material . Experimental Results . . . . . Summary . . . . . . . Appendix . . . . . . . References . . . . . . .

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Chapter 5 (HgCd)Te Photoconductive Detectors R . M . Broudy cind V . J . Mazurczyck I . Introduction . . . . . . . . I1 . Performance Parameters . . . . . . 111. Simple Photoconductivity . . . . . . IV . Photoconductive Device Analyses . . . . V . Photoconductive Device Design . . . . . VI . Technology of (HgCd)Te Detectors . . . . References . . . . . . . . .

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Chapter 6 Photovoltaic Infrared Detectors M . B . Reine. A . K . Sood. und T . J . Tridwell I. I1. 111. IV .

Introduction . . . . . . Theory of p-n Junction Photodiodes . . Hg,-,Cd, Te Junction Photodiode Technology Summary and Conclusions . . . . References . . . . . . .

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Chapter 7 Metal-Insulator-Semiconductor Infrared Detectors M . A . Kinch I . Introduction

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I11 . (HgCd)Te MIS Experimental Data . . . IV . (HgCd)Te MIS Photodiode Technology . . V . (HgCd)Te Charge Transfer Device Technology . VI . Summary . . . . . . . . References . . . . . . . .

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List of Contributors Numbers in parentheses indicate the pages on which the authors’ contributions begin.

R. M. BROUDY, Honeywell Electro-Optics Operations, Lexington, Massachusetts 02173 (157) H. E. HIRSCH, Technical Research, Cominco Ltd., Trail, British Columbia V l R 4L8, Canada (21) M. A. KINCH,Texas Instruments Znc., Dallas, Texas 75265 (313) PAULW. KRUSE,Honeywell Corporate Technology Center, Bloomington, Minnesota 55420 (1) S. C. LIANG,Electronic Materials Division, Cominco American Zncorporated, Spokane, Washington 99216 (21) V . J . MAZURCZYCK,* Honeywell Electro-Optics Operations, Lexington, Massachusetts 02173 (157) W. F. H. MICKLETHWAITE, Electronic Materials, Cominco Ltd., Trail, British Columbia V l R 4L8, Canada (47) PAUL E. PETERSEN, Honeywell Corporate Technology Center, Bloomington, Minnesota 55420 (12 1) M. B. REINE,Honeywell Electro-Optics Operations, Lexington, Massachusetts 02173 (201) A. K. SOOD,Honeywell Electro-Optics Operations, Lexington, Massachusetts 02173 (201) T. J. TREDWELL,? Honeywell Electro-Optics Operations, Lexington, Massachusetts 02173 (201) A. G. WHITE,Technical Research, Cominco Ltd., Trail, British Columbia V l R 4 L 8 , Canada (21)

* Present address: Bell Telephone Laboratories, Holmdel, New Jersey 07733. t Present address: Research Laboratories, Eastman Kodak Company, Rochester, New York 14650.

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Preface A fascinating chapter in compound semiconductor alloys was opened in 1958 when W . D. Lawson and co-workers at the Royal Radar Establishment at Malvern, England discovered that Hg,-,Cd,Te alloys were semiconductors with bandgaps that could be varied from 0.0 to 1.605 eV as x increased from 0.17 to 1 .O. The demonstration of long-wavelength photoconductivity in these alloys led the way for subsequent development of infrared detectors. Studies of the basic properties of this alloy were carried out at various laboratories such as the Laboratoire de Magnetisme et le Physique des Solides in France and the Honeywell Corporate Research Center and Lincoln Laboratory in the United States. Now, work on this alloy system and devices made from it has expanded to over 60 laboratories and production facilities ranging from the Ioffe Institute in the USSR and the Academy of Sciences in Poland to Technion in Israel and Fujitsu in Japan. During the past two decades (HgCd)Te alloys have found widespread applications as infrared detectors, which are vital in a variety of military, space, and industrial systems. Although these alloys are not as well known to the commercial market as silicon, GaAs, Gap, InP, (GaAl)As, and Ga(AsP), the dollar volume now is actually comparable to the total for the latter five compounds. “Semiconductors and Semimetals” first summarized the accumulated knowledge of (HgCd)Te and closely related alloys in Volume 5. More recently (HgCd)Te and the closely related alloy (HgCd)Se were treated in a majority of the chapters in Volume 16. For example, Chapter 2 was devoted to the crystal growth and electrical and physical properties of (HgCd)Se, while Chapter 3 concentrated on magnetooptical properties of (HgCd)Te, including a review of the most accurate determinations of band parameters and transport properties. The subject of Chapter 4 was nonlinear optical effects-mostly those arising from large values of the third-order electric susceptibility in (HgCd)Te. A great variety of useful devices results from phenomena such as resonant four-photon mixing, optical phase conjugation, and the spin-flip Raman laser, with its useful tuning capabilities. The present volume, devoted entirely to (HgCd)Te, deals with the practical production and use of these alloys in photoconductive and photovolix

X

PREFACE

taic infrared detectors and arrays. The first chapter provides a historical overview as well as a review ofthe electrical, optical, and structural properties. For the convenience of the reader, a number of figures from Volume 5 of this treatise are reproduced. An especially useful feature is the information on carrier mobilities and on the longitudinal and transverse phonon frequencies. The second chapter is concerned with techniques for purifying cadmium, mercury, and tellurium. While the technology for preparing these elements with individual impurities less than one part per billion is known, doing it reproducibly for all impurities has not been possible. An associated problem is quantitative analysis at the one-part-per-billion level. Spark source mass spectrometry can provide a semiquantitative analysis for many impurities, but numerous interferences preclude some. Flameless atomic absorption is excellent for some individual impurities, but cannot help with the important group V and VII elements, which are acceptors and donors, respectively, in (HgCd)Te. In Chapter 3, the phase diagram and its implications regarding crystal growth are discussed. Each of the various methods of crystal growth and the results of many investigators are reviewed. Most of the photoconductive devices currently in production utilize crystals grown by a recrystallization method, because it is cost effective in providing the required uniformity of composition. On the other hand, materials with the best purity have been obtained from melt-grown crystals due to the additional purification obtained by impurity segregation during crystal growth. In both photoconductive and photovoltaic detectors, the device performance depends critically on the lifetime of the photoexited carriers. Chapter 4 contains a detailed discussion of carrier lifetime, recombination mechanisms, and the effects of the light-hole and nonparabolic bands, as well as degeneracy. Excellent agreement is shown between experiment and theory using an electron-electron Auger process in which an electron recombines with a heavy hole as being dominant in rz-type (Hg,.,Cd,.,)Te. It is important to note that in characterizing a sample, some investigators refer to experimental data obtained at about 110 K or the peak lifetime, while others are using measurements at 78 K where the lifetime is approaching a minimum. In p-type (HgCd)Te it is expected that the lighthole band will be a major factor in Auger recombination, but more and better experimental data are required to clarify its role. The present generation of (HgCd)Te detectors are photoconductive with linear arrays up to 180 elements. They are the eyes of practical and widely used infrared systems involved in thermal imaging, surveillance and other military, space, and commercial applications. The objective of Chapter 5 is to present an up-to-date description of the theory and basic

PREFACE

xi

principles as applied to these detectors in a form suitable to aid designers and engineers. The next generation of (HgCd)Te detectors will be photovoltaic with two-dimensional focal plane arrays containing thousands of detector elements. Apropos of this, Chapter 6 is a review of the present status ofp-n junctions and Schottky barrier photodiodes, including the theory of operation as well as the fundamental and practical performance limits. Fabrication of arrays utilizing both diffusion and ion implantation' is treated, with emphasis on the latter. Especially valuable is a summary of the electrical and optical properties, including those of minority carriers derived from measurements on p - n junctions. Future generations of focal plane arrays may utilize the technologically challenging intrinsic monolithic approach, where the focal plane contains not only tens of thousands of detectors, but also signal processing functions such as time delay and integration, multiplexing, array staring mode operation, antiblooming, and background subtraction. Detection and signal processing in (HgCd)Te are the subjects of Chapter 7, where the general theory of metal-insulator-semiconductor devices is reviewed and compared with experimental data. The extension of single-level (HgCd)Te technology into the multilevel capability required for charge transfer device operation is discussed. Specific consideration is given (HgCd)Te infrared sensitive charge-coupled shift register performance. The metal-insulator-semiconductor photodiode is relatively easy to fabricate since it does not involve processing extremes. Device quality is determined almost completely by the properties of the substrate material. Charge-coupled-device and charge-injection-device technologies in (HgCd)Te are practical now, and the development of monolithic infrared sensitive integrated circuits to perform advanced signal processing is proceeding. The editors are indebted to the many contributors and their employers who make this treatise possible. They wish to express their appreciation to Corninco American Incorporated and Battelle Memorial Institute for providing the facilities and environment necessary for such an endeavor. Special thanks are also due the editors' wives for their patience and understanding.

R. K . WILLARDSON ALBERT c. BEER

Nomenclature It should be noted that Chapters 2 and 3 as well as current Canadian and European literature follow the older European nomenclature [Report of the German Commission for Nomenclature, Meyer, H e f v . Chim. Acta 20, 159-175 (1937)], where the names of the elements of the inorganic compound with two cations are arranged with the more electropositive cation first, or in the case of two anions they are given in alphabetical order, e.g., (CdHg)Te, (GaAl)As, In(AsP). The other chapters refer to (HgCd)Te following the newer American nomenclature, where according to the American Version of the International Union of Pure and Applied Chemistry Inorganic Rules as published in J . Am. Chem. Soc. 82, 5525 (1960) the following nomenclature for inorganic chemistry is applicable: 1. In formulas the electropositive constituent (cation) should always be placed first, e.g., CdTe. 2. Cations shall be arranged in order of increasing valence. 3. The cations of each valence group shall be arranged in order of decreasing atomic number, e.g., (HgCd)Te, (PbSn)Te. 4. Anions containing the smallest number of atoms shall be cited first. 5 . In the case of two ions containing the same number of atoms they shall be cited in order of decreasing atomic number, e.g., Ga(AsP).

xii

SEMICONDUCTORS A N D SEMIMETALS, VOL. 18

CHAPTER 1

The Emergence of Hg,-,Cd,Te Infrared Sensitive Material

as a Modern

Paul W . Kruse I. HISTORICAL OVERVIEW . . . . . . . . . . . 11. REVIEWOF THE ELECTRICAL, OPTICAL, A N D STRUCTURAL

PROPERTIES.

. . . . . . . . . . . . . . . Effective Muss Ratio . .

1. Energy-Band Siructure 2. Forbidden Energy Gap

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3 . Electron 4. Fermi Energy and Intrinsic Concentruiion 5 . Electron Mobility . . . . . . . 6 . Hole Mobiliiy . . . . . . . . 7. Optical Absorption Edge . . . . . 8. Phonon Frequencies . . . . . . 9. Lattice Constunt and Density . . . REFERENCES. . . . . . . . .

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I. Historical Overview? The usual course of development of a new semiconductor material begins with university research and ends with industrial exploitation. Such has not been the case with Hg,-,Cd,Te. From the outset development has occurred largely within industry and at national laboratories. It is only recently that university research has taken place. The basis for this anomaly lies in the unique role which Hg,-,Cd,Te plays in infrared detection for military applications. Although radar technology came of age during World War 11, infrared technology was in its infancy, consisting principally of active infrared image converters and single element PbS cells (Cashman, 1946). Neither was capable of passive thermal imaging, an emerging military need. In the decade following the war, the lead salt family, including PbS, PbSe, and PbTe, was exploited (Cashman, 1959). In addition to their use in missile guidance, PbSe and PbTe, with absorption edges at 77 K near 5 p m , were potentially useful for 3-5 pm thermal imaging. During the latter part of the period it was determined that InSb, a member of the newly discovered 111-V compound 1- As viewed from the limited perspective of the author.

1 Copyright 0 1981 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-7.52118-6

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PAUL W. KRUSE

semiconductor family, held promise as a material useful for thermal imaging (Reike et ul., 1959). Dopants for Ge were also discovered which had excitation energies useful for thermal imaging; those of greatest interest for military applications were Ge: Au and Ge: Hg (Levinstein, 1959). As the 1950s ended, those materials under active investigation for military thermal imaging systems were Ge: Hg and InSb. The former had the virtue of responding throughout the 8-12 pm atmospheric window, but required cooling to around 30 K. The latter operated at 77 K but operated only in the 3-5 Frn interval. Thus, the need existed for a new material which would combine 8-12 pm response and 77 K operation. A search therefore began for such a material. One candidate was gray Sn, which was thought to be a narrow-gap (i.e., 0.1 eV) semiconductor. It turned out that gray tin was semimetallic and unstable at room temperature. HgSe, another candidate in the late 1950s, was believed to be a semiconductor, but studies showed that it too was semimetallic (Blue and Kruse, 1962b). HgTe, a third candidate, was thought to be a narrow-gap semiconductor, but it also turned out to be semimetallic (Harman et al., 1958). What was really needed was an “InSb-like” material whose properties were similar to InSb but whose energy gap was about half as large. It was realized that an intrinsic photoconductor was better than an extrinsic one in terms of reduced cooling requirements, and that a direct-gap material was superior to an indirect one in terms of free-carrier lifetime, and thus speed of response. The sought-for material should be radiative lifetime limited in order to minimize the cooling needed to attain the photon noise, or BLIP, limit (Kruse er a / . , 1962b). All of these characteristics were sought in the as-yet undiscovered material. In 1959, Lawson, Nielsen, Putley, and Young published a paper reporting that the alloy system Hg,-,Cd,Te exhibited semiconducting properties over much of the composition range (Lawson et a/., 1959). The forbidden energy gap was found to be dependent on the composition variable x, ranging from a wide-gap semiconductor for x = 1 to a semimetal at x = 0. This was widely recognized as an InSb-like material which appeared promising, and it was therefore selected for investigation. Studies began at laboratories in the U.S. (Kruse et af., 1962b; Harman et al., 19611, France (Bailly et al., 1963; Rodot and Henoc, 1963), Poland (Galazka, 1963), and the Soviet Union (Kolomiets and Mal’kova, 1963). Because of the potential military application, secrecy surrounded some of these efforts. Early investigations, from 1961- 1965, were concerned with determining a method for preparing crystals of Hg,-,Cd,Te having the proper x value to have an absorption edge at 12 pm at the temperature of opera-

1. Hg,-,Cd,Te

AS A MODERN INFRARED SENSITIVE MATERIAL

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tion. This was the optimum; if the edge were too short or too long, then the BLIP-limited value of D*(300 K) would be too 1ow.t It was realized that the optimum spectral response was obtained by convoluting the atmospheric transmission spectrum with the thermal emission spectrum of the earth (Kruse et al., 1962b). The initial problem to be faced was one of determining accurately the energy gap as a function of composition and temperature. This was not at all easy to do. There was the difficulty of determining the composition itself. Determining the composition by measuring the density was sufficiently accurate for a large sample, but it assumed that the composition was uniform throughout the measured volume. The x value of very small volumes could be measured with an electron beam microprobe, but the accuracy was poor. Measurement calibration data were also insufficient. Crystal growth was a major problem, especially because of explosions. Because of the high vapor pressure of free Hg, open-tube methods were not employed. The initial approach was the Bridgman technique, in which the elements were sealed within a quartz ampoule that was heated above the liquidus temperature appropriate to the composition, then lowered through a temperature gradient (Woolley and Ray, 1960; Blair and Newnham, 1961). The quality of the thick-walled quartz from which ampoules were constructed was inconsistent, and explosions were frequent. A sidearm at a lower temperature to establish the Hg vapor pressure was sometimes employed (Harman, 1967). Because of the health hazard, it was necessary to seal the tubes and furnaces in steel liners, with proper venting to remove Hg vapor in case of an explosion. It was soon realized that constitutional supercooling gave rise to a dendritic growth pattern within the crystal, in which there was a microscopic web of high-x material within a low-x surrounding. The initial attempts to avoid this employed a rocking furnace to thoroughly mix the melt. The ampoule was then lowered through a very large temperature gradient at a very slow rate. Such attempts were only partially successful. It was then discovered that a high-temperature anneal (just below the solidus temperature) would remove the dendritic structure. Electrical defects that resulted from deviations from stoichiometry were another problem. It was discovered that they could be controlled by a low-temperature anneal. Optical and galvanomagnetic studies were underway from the very beginning. The optical studies were directed toward determining the energy gap by measuring the energy of the absorption edge. The early edges t D*(300 K) is the signal-to-noise ratio measured in a I-Hz bandwidth in response to 1 W of radiant power from a 300-K blackbody incident on a detector normalized to 1 cm2 sensitive area.

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P A U L W . KRUSE

were soft, and often of unusual shape, because the relatively large samples employed in the spectrometers incorporated composition gradients (Kruse and Blue, 1963; Blue, 1964). Even so, such measurements revealed that at 77 K, the desired temperature of detector operation, the required x value for a 12-pm absorption edge was about 0.20 (Scott, 1969; Schmit and Stelzer, 1969). The galvanomagnetic studies were mostly measurements of the Hall coefficient and resistivity as functions of temperature for a given composition (Blue and Kruse, 1962b; Galazka, 1963); thus energy gap, carrier concentration, and mobility could be determined. The early studies concentrated on n-type samples. It was found that Hg in excess of that required for stoichiometry needed to be loaded into the ampoule. Too much excess resulted in droplets and voids in the crystal. Too little resulted in p-type samples. The electron density of n-type ~ . samples of x = 0.20 material was usually about 1-2 x loi5 ~ m - Very unusual shapes were found in some of the Hall curves, e.g., double crossovers, and Hall coefficients that showed a dip at low temperatures. Some of these anomalies were later determined to arise from an n-type surface on lightly doped p-type material (Scott and Hager, 1971). The preparation and evaluation of infrared detectors made from the crystals was carried out in parallel with these studies. Attention was directed toward photoconductivity in n-type samples. Here too, spurious effects showed up early. Composition and purity gradients in the individual detector elements gave rise to the bulk photovoltaic effect (Kruse, 1965). These spurious effects confused the interpretation of the spectral response and responsivity measurements of the early detectors. Despite all of these obstacles, progress was rapid. By 1965 Hg,-,Cd,Te photoconductive infrared detector technology had advanced sufficiently so that prototype detectors could be made for thermal imaging systems. Photoconductivity continued to be of major interest; lifetime studies were undertaken (Ayache and Marfaing, 1967). Airborne thermal mappers based upon single elements or small linear arrays of InSb and Ge: Hg had been developed earlier and placed into limited production in the U.S. New mappers were forthcoming based upon small arrays of Hgo.,,,Cdo.20,Te detectors. Yield of high performance detectors was a problem; even today there are yield problems. During the second half of the 1960s much interest was devoted to the preparation of epitaxial layers of Hg,-,Cd,Te. A close-spaced method utilizing evaporation of HgTe upon a CdTe substrate was reported (Cohen-Solal et d.,1965). Another employed a temperature gradient between source and substrate (Tufte and Stelzer, 1969). Thin films of Hg,-,Cd,Te were also prepared by sputtering (Kraus ef al., 1967). The 1970s were a period in which (Hg,Cd)Te technology made rapid ad-

1 . Hg,-,Cd,Te

AS A MODERN INFRARED SENSITIVE MATERIAL

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vances. Photoconductive detector technology matured, especially that for Hg,,,,Cd,,,,,Te used in 8-12 p m airborne mappers and in 8-12 p m FLIRs (forward looking infrared systems) (Kinch and Borrello, 1975). Other compositions suitable for use in the 1-3, 3-5, and 15-30 p m range were also investigated (Reine and Broudy, 1977). Photovoltaic detector development also advanced rapidly, including those types suitable for optical heterodyne receivers for CO, laser communications systems operating at 10.6 pm. During the early 1970s, (Pb,Sn)Te detector technology was also rapidly advancing (Melngailis and Harman, 1970). However, interest in (Pb,Sn)Te waned for various reasons, including its high dielectric constant and relatively large thermal expansion coefficient, and it is no longer a viable competitor for military infrared systems. Today (Hg,Cd)Te ranks as one of the most thoroughly studied semiconductors (Long and Schmit, 1970; Harman and Melngailis, 1974; Dornhaus and Nimtz, 1976). From an investment point of view, it is the third most important semiconductor, outranked only by Si and GaAs. Mercury cadmium telluride detector linear arrays of 60- 180 elements are in mass production in the U.S. for the common modular FLIR. It is the preferred material for second generation FLIRs, in the form of a (Hg,Cd)Te photovoltaic detector array bonded to a Si CCD chip. Hg,-,Cd,Te PV detector/% CCD hybrid matrix arrays are also under investigation for terminal homing missile seekers. In other military applications, arrays having spectral responses as short as 2-3 p m for detecting missile plumes, and as long as 15-30 p m for detecting spaceborne objects are under development. Civilian applications of Hg,-,Cd,Te thermal imaging systems are also being explored, including thermography for early detection of breast cancer. During the 198Os, Hg,-,Cd,Te technology, including research development and production, will continue to expand. Infrared detector development and production will increase rapidly. New phenomena and applications will emerge; recent examples are CCD shift registers (Chapman et ul., 1978), injection lasers (Harman, 1979), and nonlinear optics (Kruse et al., 1979). This trend will clearly continue; by the end of the 1980s, Hg,-,Cd,Te will be established as one of the most useful of all semiconductors. 11. Review of the Electrical, Optical, and Structural Properties

There exists a wealth of published data concerning the properties of Hg,-,Cd,Te (Dornhaus and Nimtz, 1976). Because of compositional nonuniformities and measurement inaccuracies, some of the early data

6

PAUL W . K R U S E

have been superseded by better values. The following brief overview includes data which are believed accurately to represent the compositional dependence of selected parameters. 1. ENERGY-BAND STRUCTURE The band structure near the r point for three different values of forbidden energy gap is illustrated in Fig. 1 (Overhof, 1971). The left-hand part illustrates the semimetallic behavior found in HgTe and Hg,-,Cd,Te for which x is less than -0.16 at 0 K. The re state, which is the conduction-band minimum in CdTe and other zinc-blende semiconductors, lies at a lower energy than the restate, which is the valence-band maximum in CdTe. Thus the energy gap Eo is negative in HgTe. The usual light-hole valence band becomes the conduction band and the conduction band becopes the light-hole valence band. Because of the k p interaction (Kane, 1966) the conduction band and light-hole valence bands are nonparabolic. The central part of Fig. 1 illustrates the region near the r point when the forbidden energy gap is slightly positive. Here the light-hole valence band is the normal Ts state and the conduction band, the normal re.The conduction and light-hole valence bands are nonparabolic and symmetric, with the free-electron and light-hole masses at the re and Tspoints very small and equal. The right-hand part of Fig. 1 illustrates the region near the r point when

1. Hg,-,Cd,Te

AS A MODERN INFRARED SENSITIVE MATERIAL

7

the energy gap is relatively wide. The band structure is very similar to that of InSb, with a small amount of conduction-band nonparabolicity, which decreases and ultimately vanishes as the energy gap widens with increasing x value.

2. FORBIDDEN ENERGY GAP The dependence of the forbidden energy gap, i.e., the Ta-Ts transition, upon composition at 0 and 300 K is illustrated in Fig. 2 (Long, 1968). The temperature coefficient of the energy gap for CdTe is negative, which is

I. 6

1.4

1.2

1.0 c

-2,

a 0.8 Q

W

0.6 lr

w

z W

0.4

0.2 0 -0.2 -0.4

I HgTe

I

I

1

X

I

CdTe

FIG.2. Energy gap as a function of composition in Hg,-,Cd,Te. 0, interband magnetoreflection at 77 K; x , interband magnetoreflection at 4 K; f , optical absorption at 300 K; A,A, photovoltaic studies at 77 and 300 K; V, photoluminescence at 12 K. [From Long (1968).]

8

PAUL W . KRUSE

0.50 0.4 5

0.40 0.35

0.30 0.25 m

w

0.20

0.15 0.10

0.05 0 T (K)

FIG. 3. Dependences of the energy gap E , and the long wavelength limit A,, of Hg,,Cd,Te as functions of temperature and composition. [From J . L. Schmit and E. L. Stelzer ( I 969).]

the usual case for most semiconductors, but is positive for compositions rich in HgTe. Figure 3 illustrates the compositional and temperature dependences in more detail for x values equal to or less than 0.40, the region of most interest (Schmit and Stelzer, 1969). The left-hand ordinate is the forbidden energy gap expressed in electron volts, whereas the right-hand one is the corresponding absorption edge wavelength or photodetector long-wavelength limit. The data illustrate that the composition Hgo.,esCdo.sosTe is the proper choice for an infrared detector operating at 77 K having an energy gap of 0.10 eV (long-wavelength limit of 12.4 pm). The analytic expression for the data illustrated is

E, (eV)

=

1 . 5 9 ~- 0.25

+ 5.233(10-4)T(1-2.08x) + 0 . 3 2 7 ~ ~ (1)

1. Hg,-,Cd,Te

AS A MODERN INFRARED SENSITIVE MATERIAL

9

where Eg is the energy gap in electron volts, x is the composition variable, and T is the absolute temperature.

3. ELECTRON EFFECTIVE MASSRATIO The dependence of the electron effective mass ratio upon composition is illustrated in Fig. 4 (Long, 1968). The values illustrated are at the conduction band edge. The ratio goes to zero at the semiconductorsemimetal transition. In the region of most interest, the right-hand half of the figure, the effective mass is small and directly proportional to the gap, as predicted by the Kane model (Kane, 1966). More detailed data concerning the effective mass is illustrated in Fig. 5 (Schmit, 1970). The values shown have been calculated based upon the I

I

0.025

0.020

mz -

0.015

m0

0.010

0.005

0

0 HgTe

0.I

X

0.2

0.3

FIG.4. Dependence of conduction band edge effective mass ratio upon composition at 0 K in Hg,-,Cd,Te. 0, interband magnetoreflection at 77 K; X, interband magnetoreflection at 4 K; cyclotron resonance at 4 and 77 K; A,oscillatory magnetoresistance at 4 K . [From D. Long (1968).]

+,

10

PAUL W . KRUSE X

0.07

0.70 w

2

0.65

0.06

0.60

0.05

0.55 0.50

0.04

0.45 0.40

0.03

0.35

0.30 0.28

0.26 0.24

0.02

0.22

0.20 0.IB

0.16

0.0I

0

0

50

100

150 200 TEMPERATURE ( K )

250

300

350

FIG.5 . Temperature dependence of the electron effective mass ratio of Hg,-,Cd,Te. [From J. L. Schmit (1970).]

Kane model and the measured dependence of energy gap upon composition illustrated in Fig. 3. The electron effective mass values illustrated in Fig. 5 are referred to by Schmit as the parabolic equivalent effective mass, i.e., the electron effective mass which would have to be employed in the standard expression for the intrinsic concentration in order to give the intrinsic concentration value predicted by the Kane model. 4. FERMI ENERGYA N D INTRINSIC CONCENTRATION

The temperature dependences of the reduced Fermi energy and intrinsic concentration with composition as an independent parameter are illustrated in Figs. 6 and 7 (Schmit, 1970). The calculations upon which the figures are based employ the measured dependence of the energy gap upon composition and temperature illustrated in Fig. 3 and expressed in Eq. (1). A nonparabolic conduction band was used. The valence band was approximated by a single parabolic band with hole effective mass equal to 0.55 m, (free-electron mass).

1. Hg,-,Cd,Te

AS A MODERN INFRARED SENSITIVE MATERIAL

11

+3

F

0

-15 TEMPERATURE ( K )

FIG.6. Temperature dependence of the intrinsic reduced Fermi energy (measured from the conduction-band edge) of Hg,-,Cd,Te. [From J. L. Schmit (1970).]

5 . ELECTRON MOBILITY

Figure 8 illustrates the dependence of the free-electron mobility upon composition at 4 K (Long and Schmit, 1970). The parameter ,uIis the Hall mobility, i.e., the Hall coefficient divided by the resistivity. The curves are theoretical, with account taken of the dependence of free-electron mass upon concentration (Fig. 4); the scattering is assumed to be by singly ionized impurity or defect centers of density equal to the extrinsic electric concentration. Measured data points are also shown in the figure. Extremely high values of mobility for high-purity samples are observed near the semiconductor-semimetal transition. The dependence of the free-electron mobility at 4.2 K upon composition and free-electron concentration is illustrated in Fig. 9 (Scott, 1971). At this temperature, the mobility is determined by scattering from ionized impurities or defect centers, as has been seen in the calculations of Fig. 8. The values illustrated were calculated from the known dependence of electron effective mass upon composition (Fig. 4). The dependence of the electron Hall mobility upon composition and temperature, determined experimentally for n-type samples in which the free-electron concentration was less than 2 x 1015 cmP3, is illustrated in

12

P A U L W . KRUSE X

10'

lo1'

*-

10'6

E v

z

50

1015

w

I-

z u

0

z a 0

1014

0 m

2 a I-

z

10':

1012

10"

50

100

150

200

250

300

350

TEMPERATURE ( K )

FIG.7. Temperature dependence of the intrinsic carrier concentration in Hg,-,Cd,Te. [From J . L. Schmit, Honeywell Corporate Technology Center, personal communication, based upon revised data from J . L. Schmit. (1970).]

Fig. 10 (Scott, 1972). Below about 30 K, the value for Hp0.80Cd0.20Te is about 3 x 105 cm2/V sec, which is extremely high for semiconductors. The room-temperature mobility of Hgo.aoCdo.20Te is about 1 X lo4 cm2/V sec. As the x value increases, the mobility decreases monotonically. For x 2 0.25, the mobility increases as the temperature increases between 4 and 20 K. Over this composition and temperature range, singly ionized donor impurity scattering dominates.

1. Hg,-,Cd,Te

5 3

AS A MODERN INFRARED SENSITIVE MATERIAL

13

r

2

I o6

7

5

Y

:

3

c

0

-

0 u) 0

2

>

5

" 10

5

-

7

4

I

FIG.8. Hall mobility of electrons as a function of composition in Hg,-,Cd,Te at approximately 4 K.[From D. Long and J. L. Schmit (1970).]

Figure 11 illustrates the dependence of free electron Hall mobility upon composition at 300 K for n-type Hg,-,Cd,Te samples in which the freeelectron concentration was less than 2 x lOI5 (Scott, 1972). The highest value, about 3.5 x lo4 cm2/V sec, is obtained near x = 0.08, i.e., near the semiconductor-semimetal transition at room temperature, where the electron effective mass has its minimum value. 6. HOLE MOBILITY Most of the mobility data are for n-type samples. Figure 12 illustrates some data on the hole mobility determined from Hall effect and resistivity measurements on p-type samples (Schmit and Scott, 1971; Scott et af., 1976). The hole mobility at room temperature ranges from

I

14

PAUL W . KRUSE

I

I

I l l

I

15

I0

I

I

l

i

l

I

16

I0

l

i I'

7

CONDUCTION-ELECTRON CONCENTRATION ( c m V 3 )

FIG.9. Electron mobility at 4.2 K as afunction of composition in Hg,-,Cd,Te. [From M. w. Scott (1971).]

40-80 cm2/V sec. The temperature dependence is relatively small. As indicated, the p-type samples are relatively impure compared to the n-type ones of Fies. 10 and 11.

'"F

J W

CdTe

HgTe

MOLE

FRACTION CdTe

FIG.1 1 . Electron mobility at 300 K as afunction of composition. [From M. W. Scott (1972).]

T (K) FIG. 10. Temperature dependence of the electron Hall mobility in Hg,-,Cd,Te as a function of composition. [From M. W. Scott (1972).]

lo3

c

I00 TEMPERATURE ( K )

10

FIG. 12. Temperature dependence of the hole Hall mobility in Hg,,Cd,Te as a function of composition. [From J . L. Schmit and M. W. Scott (1971); M. W. Scott, E. L. Stelzer, and R. J . Hager (1976). Numbers (1)-(6) identify the samples.]

X

:

0.21 0.23 0.25 0 0

0

0 0

9

o 0 0 0

L

w

o o

0 0

o o

0

oo 0

ooo

a

0

1

0

0

0

0

0

0

:

0

0

0

I

I

01

0 2

0

0

0

l

0 3

o

n

0 0

0 0

0 0

0

0 0

0

O

0

0

0

0

,"

o

O 0

0

0

0 0

0

x

d x x x x

0

0

0 0 0

x x x

0

0 0

0 0

:,"

z

00

0

x o x x o x o x o x

O

o

0

0

0 0

0

0

I

0 4 ENERGY ( e V )

0

0 0

1-

0 5

0 6

0 7

FIG. 13. Optical absorption coefficient as a function of composition in Hg,-,Cd,Te.at room temperature. [From M. W. Scott (1969).]

1 . Hg,-,Cd,Te

I10

AS A MODERN INFRARED SENSITIVE MATERIAL

0

0.2

HgTe

04

06 X

0.0

17

I CdTe

FIG. 14. Longitudinal and transverse phonon frequencies in Hg,-,Cd,Te at 71 (+,O) and 300 K (@,a). [From R . Dornhaus and G. Nimtz (1976).]

7. OPTICALABSORPTION EDGE Figure 13 illustrates the dependence of the optical absorption coefficient upon photon energy for various compositions (Scott, 1969). The edges are steep, as expected for a direct-gap semiconductor. Early results (Blue, 1964) showing edges with a more shallow dependence upon energy probably were obtained from samples of nonuniform composition.

.

8. PHONONFREQUENCIES

Figure 14 depicts longitudinal and transverse phonon frequencies as functions of composition at 77 and 300 K (Dornhaus and Nimtz, 1976). Most of the data illustrated were originally published by Baars and Sorger (Baars and Sorger, 1972). The LO and TO frequencies were deduced by Kramers -Kronig analysis of reflectivity measurements.

PAUL W . KRUSE

18 I

\ 5

t

i

I

1

I

- 6.0

I

-

,DENSITY

7.5

* ,i

-1.0

6.475

0

l I-n

z

>

- 6.5 t9

0 V 6.470

n t J

-

0

6.465

ATTIC€ 6.460

0

6.0

CONSTANT

I

1

I

I

1

I

I

I

I

0I

02

03

0.4

0.5

06

0.7 0.7

0.8

09

5.5

1.0

X

FIG.15. Lattice constant and density of Hg,_,Cd,Te as a function of composition. [From D. Long and J. L . Schmit (1970).]

9. LATTICE CONSTANT AND DENSITY Figure 15 illustrates the dependence of lattice constant and density upon composition in Hg,-,Cd,Te (Long and Schmit, 1970; Woolley and Ray, 1960; Blair and Newnham, 1961). There is a small deviation from Vegard's law, i.e., the lattice constant is not quite linear with composition. ACKNOWLEDGEMENT Many colleagues at the Honeywell Corporate Technology Center and the Honeywell Electro-Optics Operation have worked for almost two decades in Hg,-,Cd,Te technology. Among them are Dr. Donald Long, Mr. Joseph L. Schmit, Dr. M. Walter Scott, Dr. Obert N . Tufte, Mr. Ernest L. Stelzer, Mr. Robert J. Hager, Dr. Marion Reine, Dr. Robert Broudy, and Mr. Robert Lancaster. Thanks to Darlene Rue for typing the manuscript.

REFERENCES Ayache. J. C., and Marfaing, Y. (1967). C . R. Acad. Sci. Paris B265,568. Baars, J., and Sorger, R. (1972). Solid Sfare Cornmutt. 10, 875. Bailly, F., Cohen-Salal, G., and Marfaing, Y.(1963). C. R . A m d . Sci. Paris 257, 103. Blair, J., and Newnham, R. (1961). "Metallurgy of Elemental and Compound Semiconductors," Vol. 12, p. 393. Wiley (Interscience), New York.

1 . Hg,-,Cd,Te

AS A MODERN I N F R A R E D SENSITIVE MATERIAL

19

Blue, M. D. (1964). Phys. Rev. 134, A226; in Phys. Semicond. 1, 233. Blue, M. D., and Kruse, P. W. (1962a). Bull. A m . Phys. Soc. Ser. I1 7, 202. Blue, M. D., and Kruse, P. W. (1962b). J . Phys. Chem. Solids 23, 577. Cashman, R. J . (1946). J . O p t . So(..A m . 36, 356. Cashman, R. J . (1959). Proc. Inst. Radio Eng. 41, 1471. Chapman, R . A. et a / . (1978). Appl. Phys. L e t f . 32, 434. Cohen-Solal, G., Marfaing, Y., Bailly, F . , and Rodot, M. (1965). C. R. Acad. Sci. Paris 261, 931. Dornhaus, R., and Nimtz, G. (1976). The properties and applications of the Hg,-,Cd,Te alloy system. In “Springer Tracts in Modem Physics, Solid State Physics” (G. Hohler, ed.), Vol. 78. Springer-Verlag, Berlin. Galazka, R. R. (1963). A d a Phys. Pulon. 24, 791. Harman, T. C. (1967). In “Physics and Chemistry of 11-VI Compounds” (M. Aven and J. S. Prener, eds.), p. 784. Wiley, New York. Harman, T. C. (1979). J . Elecrron. Muter. 8, 191. Harman, T . C., and Melngailis, I. (1974). Narrow gap semiconductors, Appl. Solid Sfrite Sci. 4. Harman, T. C., Logan, M. J., and Goering, H. L. (1958). J . Phys. Chrm. Solids 7, 228. Harman, T . C., Strauss, A. J., Dickey, D. H., Dresselhaus, M. S . , Wright, G. B., and Mavroides, J. G. (1961). Phys. Rev. Lett. 7 , 403. Kane, E. 0. (1966). The k p method, Semicund. Srmimer. 1. Khan, M. A., Kruse, P. W., and Ready, J . F. (1980). Optics L e f t . 5, 261. Kinch, M. A., and Borello, S. R. (1975). Infrared Phys. 15, 1 1 1 . Kolomiets, B. T., and Mal’kova, A. A. (1963). Fiz. Tverd. Tele 5 , 1219 [English Transl.: Sov. Phys. Solid State 5, 8891. Kraus, H. , Parker, S . G., and Smith, J. P. (1967). J . Electrochem. Soc. 114, 616. Kruse, P. W. (1965). Appl. O p t . 4, 687. Kruse, P. W., and Blue, M. D. (1963). Bull. A m . Phys. SOC. Ser. I1 8, 246. Kruse, P. W., Blue, M. D., Garfunkel, J. H., and Saur, W. D. (1962a). Injrured Phys. 2,53. Kruse, P. W., McGlauchlin, L. D., and McQuistan, R. 9 . (1962b). “Elements of Infrared Technology,” Chapter 9. Wiley, New York. Kmse, P. W . , Ready, J . F . , and Khan, M. A. (1979). Injrured Phys. 19, 497. Lawson, W. D., Nielsen, S. , Putley, E. H., and Young, A. S. (1959). .I. Phys. Chem. Solids 9, 325. Levinstein, H. (1959). Proc. Inst. Radio Eng. 47, 1478. Long, D. (1968). “Energy Bands in Semiconductors.” Wiley, New York. Long, D., and Schmit, J. L. (1970). Mercury cadmium telluride and closely related alloys, Semicond. Semimet. 5 . Melngailis, I., and Harman, T. C. (1970). Single crystal lead-tin chalcogenides, Semicond. Semimet. 5 . Overhof, H. (1971). Phys. Sturus Solidi B45, 315. Reine, M. B., and Broudy, R. M. (1977). A review of (Hg,Cd)Te infrared detector technology. In Proc. SPIE Tech. Symp., 2/st, Sun Diego, Culifortliu, August. SPIE, Bellingham, Washington. Rieke, F. F., DeVaux, L. H. and Tuzzolino, A . J. (1959). Proc. Inst. Rudiu Eng. 47, 1475. Rodot, H., and Henoc, J. (1963). C. R . A c a d . Sci. Paris 256, 1954. Schmit, 3. L., (1970). J . Appl. Phys. 41, 2876. Schmit, J. L., and Scott, M. W. (1971). Honeywell Corporate Technology Center, unpublished data. Schmit, J. L., and Stelzer, E. L. (1969). J . Appl. Phys. 40,4865.

20

P A U L W . KRUSE

Scott, M. W. (1969). J . Appl. Phys. 40, 4077. Scott, M. W. (1971). Honeywell Corporate Technology Center, unpublished data. Scott, M. W. (1972). J . Appl. Phys. 43, 1055. Scott, M. W., and Hager, R. J . (1971). J . App'pl. Phys. 42, 803. Scott, M. W., Stelzer, E. L . , and Hager, R. J. (1976). J . Appl. Phys. 47, 1408. Tufte, 0. N . , and Stelzer, E. L. (1969).J . Appl. Phys. 40, 4559. Woolley, J . C., and Ray, B. (1960).J . Phys. C h m . Solid.\- 13, 151.

SEMICONDUCTORS A N D SEMIMETALS, VOL. 18

CHAPTER 2

Preparation of High-Purity Cadmium, Mercury, and Tellurium H . E . Hirsch, S. C . Liang, and A . G . White I. INTRODUCTION. . . . . . . . . . . . . . . . . . .

. . .

. . . . . . . . . . . . . . . . . . . . . . . . 1 . Electrolysis . . . . . . . . . . . . . . . . . . . . 2. Distillation . . . . . . . . . . . . . . . . . . . . 3. Zone Refining. . . . . . . . . . . . . . . . . . . Iv. P U R I F I C A T I O N OF M E R C U R Y . . . . . . . . . . . . . . 4. Chemical Methods . . . . . . . . . . . . . . . . V. PURIFICATION OF TELLURIUM . . . . . . . . . . . . . 5. Introduction . . . . . . . . . . . . . . . . . . . 6. Chemical Refining: Crystullization und Precipitation . I . Hydride Process . . . . . . . . . . . . . . . . . 8. Chloride Refining . . . . . . . . . . . . . . . . . 9. Solvent Extruction. . . . . . . . . . . . . . . . . 10. Electrolytic Purification . . . . . . . . . . . . . . 11. Distillation . . . . . . . . . . . . . . . . . . . . 12. Zone Refining. . . . . . . . . . . . . . . . . . . VI. SPECIAL PRODUCTS FOR (CdHg)Te PREPARATION . . . . 13. Mercury . . . . . . . . . . . . . . . . . . . . . 14. Cadmium and Tellurium . . . . . . . . . . . . . . 15. General . . . . . . . . . . . . . . . . . . . . . REFERENCES. . . . . . . . . . . . . . . . . . . . . 11. PURIFICATION PROCESSES . . . 111. PURIFICATION OF CADMIUM..

. .

. . . .

. .

. . . . . .

. .

. . . . . .

. .

. .

. .

. .

. . . .

. .

. .

. .

. .

21 23 24 25 25 29 32 33 34 34 36 36 36 36 37 37 31 38 39 41 43 45

I. Introduction

The term “high purity” can mean different things. In this chapter, it is defined to mean a purity of 69 (99.9999%)o r better, and in any case, not less than 59 (99.999%), as is commonly understood in the high-purity metal trade. Purity cannot be defined without defining the method of analysis. Indeed, even analysis is meaningless without regard for the end use, and realistically, end use is a method of analysis. For instance, where high-purity metals, e.g., aluminum, copper, etc., are used in low-temperature (4 K) magnet applications, the residual resistivity reflecting the transition-element impurities becomes important, whereas the total impurity content is not. In the case of indium used for 21

Copyright 0 1981 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-752118-6

22

H . E . HIRSCH, S. C . LIANG, A N D A . G . WHITE

doping silicon to make high-performance infrared detectors, the shallow-level impurities affect detector performance even though undetectable by other analytical means (lO-'Orange). In preparing compound semiconductors, often the isoelectronic impurities can be tolerated well above 1 ppm, whereas the carrier-generating impurities must be reduced to a level that would give less than l O I 3 carriers/cm3 in the final semiconductor. The identification of such impurities is difficult, if possible at all. The only analytical method is the determination of the extrinsic carrier concentration; where such measurements indicate no harmful effect or the concentration is at such a low level as not to affect the end use, the material is judged good. Thus, the only useful method of analysis, when dealing with truly high-purity materials, is the measurement of the factors or parameters which affect the end use. The material suppliers do not claim to be able to determine the precise amount of all the low-level impurities. The designations 59 or 69 have been chosen because it is believed that the metals processed and supplied to customers are essentially that pure. For routine quality control, the emission spectrometric method is the principal analytical tool. To assure consistency, at Cominco when establishing the production process all methods appropriate to the subject are used periodically on a continuing basis. These include emission and spark mass spectrographic analyses, chemical analysis, polarographic analysis, atomic absorption, residual resistivity, and other electrical measurements. The 69 purity allows a total impurity concentration of 1 ppm, as measured by emission spectrograph. While this requirement is demanding, for semiconductor applications it is not a very high purity. Specifically, the n-type cadmium mercury telluride (CdHg)Te single crystal used for making high-performance photoconductive infrared detectors peaking around 12 km must routinely exhibit fewer than 1015carriers/cm3 and preferably approaching 1014carriers/cm3. Such a carrier concentration corresponds to one part in 300 million, or 3 x lo+'. With regard to the net carrier concentration one might therefore designate the purity of the (CdHg)Te as 89. For such a product, it is important that the starting metals Cd, Hg, and Te have a purity better than 69. To deliver metals of adequate purity to allow production of (CdHg)Te routinely having a total concentration of active elements of less than lo-* is no simple matter, particularly in view of the added complication that oxygen is an active element in (CdHg)Te. Users must also possess and deploy adequately sophisticated technology. Since metal purity for such applications cannot be assured by any of the conventional analytical techniques, a direct but lengthy and costly approach is used. A portion of each production lot is taken and processed to (CdHg)Te single crystals. The

2.

PREPARATION OF HIGH-PURITY

Cd, Hg,

AND

Te

23

crystals must exhibit fewer than 1015carriers/cm3. While this method as closely as possible guarantees product quality, it does not always assure the desired quality because at such high purity the metals are inordinately active as collectors and scavengers. Packaging processes must also be observed to the most minute detail. A user who is unwilling to take an equal amount of care after receiving the metals will obviously not receive the benefit of the manufacturer’s efforts. When designing a purification process, one principal concept is followed. Because all purification processes are based on the difference in response of the host metal and the impurities to a given treatment and no element in the periodic table is so unique that no other elements will respond in the same way to the treatment, free energy consideration dictates that no single treatment can remove all impurities to less than level and still leave the host metal mostly unaffected, i.e., to give a reasonable yield. On the other hand, it is not difficult to find a treatment method based on one physicochemical principle to remove one group of elements, and another method based on a different principle to remove a different group. The two groups may overlap and include all impurities of concern, yet both groups will exclude the host metal. Thus, as a rule at least two processes based on significantly different prinCiples are used-for instance, electrolysis and zone refining-to complement each other. The combination is also chosen to take advantage of the primary metallurgy. A knowledge of the origin and processing history of the metal is a great advantage, which can accrue to the producer who has control of primary metals sources. Short of this, a reliable source of primary metal is absolutely necessary in order to obtain the specified purity on a routine basis. A detailed discussion of primary metallurgy is outside the scope of this paper. In the following descriptions, therefore, we shall present only the different methods used for purifying Cd, Hg, and Te. Combinations of these methods are used in various laboratories to obtain high-purity materials. 11. Purification Processes

Strange as it may seem, the preparation of high-purity metals is relatively simple. The only knowledge required is that of the basic chemical and physical properties of the subject metal. Processes mentioned here include distillation (including sublimation), electrolysis (including chemical displacement), wet chemical treatment, and zone refining. The processes are basically simple and the methods of application are straightforward. The specified purity is readily obtained if all necessary care against con-

24

H . E . H I R S H , S . C . L I A N G , A N D A . G. WHITE

tamination is taken. For instance, the human hand can be a source of contamination. Finger marks on high-purity metal surfaces are virtually indelible. The choice of gloves must be made with care. While baby powder will greatly reduce the discomfort of the wearer, if used it also introduces many elements foreign to the metal. Less noticeably, if the gloved hands, while processing the metal, should pick up a work tool in between motions, such actions may transfer contaminants from the tool to the metal. Undoubtedly, such constraints will slow down the work. In fact, they are some of the reasons why high-purity metals are costly. However, ignoring such requirements can be disastrous. No less important is the technique of comminuting a high-purity metal into a form which can be used in a practical manner without sacrificing purity. The most common technique is melting and casting. Materials for the melting and casting vessels must be chosen to cause no recontamination. High-density, high-purity graphite (such as UC grade ECL or equivalent), pyrolytic graphite, and quartz (sometimes Vycor) vessels, if properly cleaned, have all been successfully used. Melting and casting of cadmium and tellurium for (CdHg)Te semiconductor applications must be done in protective atmospheres such as argon, hydrogen, nitrogen, or vacuum. Mechanical cutting tools may also be used if the knowledge of avoiding contamination is properly applied. An instructive review of the requirements for maintaining purity during handling and exposure has been given by Zief ( 1978). 111. Purification of Cadmium

Cadmium occurs in nature as a minor constituent of zinc and zincbearing polymetallic ores. Production in the western world from 1967 to 1977 has been in the range of 10,000-14,000 metric ton per year. Virtually all cadmium is recovered as a coproduct in zinc plants, which may also treat zinc- and cadmium-bearing fumes and dusts from lead and copper smelters. The efficiency of cadmium recovery in electrolytic zinc plants has already reached a realistically high level ( 270%), and the future growth in the supply of cadmium will be tied to the demand for zinc. Recycling of cadmium is relatively insignificant now and will likely remain so in the foreseeable future. The purification practice for commercial grade cadmium has been surveyed by Lund and Sheppard (1964). The purity of current commercial cadmium metal is generally 99.96% or better. A typical analysis of Cominco commercial grade cadmium is shown in Table I. The relatively high purity of the commercial'grade metal reflects the significant differences in certain physical and chemical properties between

2.

PREPARATION OF HIGH-PURITY

Cd, Hg, AND Te

25

TABLE I TYPICAL ANALYSIS OF COMINCO COMMERCIAL GRADECADMIUM

Pb cu Ni Zn Al

TI Fe

co Mg Cd by difference

0.0025% 0.0025% 0.0010% 0.0002% 0.0003% 0.000 1% 0.0002%
cadmium and the accompanying metals. More specifically, commercial refining operations make use of the differences in electrochemical potentials (cementation with zinc, electrowinning of cadmium), in boiling points (the normal boiling point of cadmium of 767°C is 141°C below that of zinc, the impurity with the next lowest boiling point), and in the solvent characteristics of liquid cadmium. Further purification of the commercial grade cadmium to 59 and better purity is based on the same chemical and physical properties. 1. ELECTROLYSIS Electrowinning from highly purified solutions or soluble anode refining in sulfate, chloride, cyanide, acetate, perchlorate, and likely several other aqueous as well as fused electrolytes and amalgam electrolysis can be used with success to reject impurities. The state of the art was reviewed by Chizhikov in 1966 and summarized by Zanio in 1978. Although electrolytic methods in general have been advanced appreciably since Chizhikov’s review, in particular with regard to anode stability (Kuhn and Wright, 1971), addition agents, and current control (programmed or periodic reversal, Liekens and Charles, 1973; Biswas and Davenport, 1976; Krauss, 1977), and would yield high-purity cadmium directly or in combination with other methods, there are practically no indications that these more recent developments have been applied to cadmium purification. It appears that other methods to produce cadmium of equal or better purity, which are less costly and less demanding in technical skills, have relegated electrolysis to a lower rank. 2. DISTILLATION The low boiling point of cadmium of 767°C at one atmosphere pressure has prompted many investigations of its purification by distillation. An

26

H . E . HIRSCH, S . C . L I A N G , A N D A . G . WHITE

inert atmosphere is necessary to avoid oxidation of the cadmium vapor. Some benefits have been claimed from the reduced oxide content obtained when the distillation is conducted under hydrogen. Single or mulTorr and at 450-500°C has tiple distillation under a vacuum of lo+been reported by several investigators to result in 69 grade or better purity (Zanio, 1978). The efficient elimination of the prominent impurities results from the significant differentials in vapor pressure as exemplified in Table 11. TABLE I1 V A P O R P R E S S U R E S OF C A D M I U M AND

COMMON IMPURITIES A T 400°C'

1.2

Cd Zn

8 x

Mg

4 8 2 2 7

TI Pb

cu A1 Fe,

Co,

Ni

x

10-3

x 10-6 x 10-7 x 10-11 x 10-15

.=

10-15

Selected from Nesmeyanov ( 1963).

The impurities ranking highest in volatility and expected to distill in part together with cadmium, i.e., Zn, Mg, TI, and Pb, do not form compounds with and are sufficiently soluble in molten cadmium at 400°C and above to have their activities reduced in the first order according to their concentrations. Thus, for instance, the partial pressures of cadmium and zinc above a cadmium melt held at 400°C and containing 2 ppm zinc by weight have a ratio of about 3 x lo6. A vapor of this composition upon total condensation will yield a product containing less than 0.2 ppm by weight of zinc provided evaporation and condensation conditions are practically close to equilibrium. Similarly, lead should be reduced from 25 ppm by weight to a few parts per trillion. In practice the results achieved by distillation can deviate by orders of magnitude from those predicted from simple ratios of concentrations and equilibrium vapor pressures of the elements. The following factors contribute to the observed deviation. Activity caeficient. This can differ from unity in a positive or negative direction for various impurities in elemental solution.

2.

PREPARATION OF HIGH-PURITY

Cd, Hg,

AND

Te

27

Rate of evaporation. True metallic impurities evaporate from the melt as monoatomic gases with the rate defined by the Knudsen-Langmuir equation,

where

w = rate of evaporation, a = Langmuir coefficient (close to unity for many metals), y = activity coefficient, N = mole fraction, Po = normal vapor pressure of the evaporating element, M = molecular weight of species, in the vapor phase, and T = temperature in Kelvin. The evaporation rates can be much lower, however, at a given temperature for impurities which are in monoatomic solution in the melt but form multiatomic molecules in the vapor phase, e.g., arsenic: 4As (melt) + As, (vapor).

The evaporation of arsenic from its monoatomic solutions appears to be preceded by the formation of As, molecules at the evaporating surface by rapid equilibration 2

qAsdtsso~ved7 As, surfare.

As,

K[Asl'. K = concentration equilibrium constant.

surface =

The probability of such activity is not to be construed as an argument for a true fourth-order reaction but this kind of evaporation rate dependency on concentration in systems containing arsenic and antimony has been observed (Hirsch, 1969). Contrary to the results expected by this postulate and our experience, arsenic contamination in distilled cadmium has been reported (Alexandrov and Udovikov, 1973). The reasons for this are likely to be found among the factors below. Compound formation. This can either retard or enhance the evaporation of impurities. The formation of intermetallic compounds would normally reduce both the vapor pressure and the evaporation rate while the formation of sulfides and halides tends to produce the opposite effect particularly if the compounds are insoluble in the molten host metal and accumulate at the surface. Pressure gradienr of vapor. This determines the rate of vapor transfer from the evaporating surface to the condensing surface. The effective distance between the two surfaces is increased by equipment features such

28

H . E. HIRSCH, S. C. LIANG, A N D A . G . W H I T E

as baffles and orifices designed to increase selectivity by creating a shallow gradient in the proximity of the evaporating surface. Selective condenstition. The condenser is designed with one section operating at a higher temperature than the main product condenser. A fraction of the vapor condenses in the hotter section with preferential condensation of the less volatile impurities, thereby increasing the purity of the vapor entering the main product condenser. Quiescent melt. As cadmium distills, the surface layer becomes depleted in cadmium and enriched in the less volatile impurities, and possibly also arsenic for the reasons outlined before. The surface layer is being replenished in cadmium by diffusion from the body of the melt and by agitation of the melt. The rate of distillation can surpass the rate of replenishment through diffusion by orders of magnitude, and the resultant composition of the surface layer inevitably causes poorer separations. These factors have to be taken into account in the design and operation of cadmium distillation equipment by matching the distillation rate and yield to heater arrangement and melt geometry (induced thermal convection) and by providing a clean melt surface at the start of a distillation run. Equipment of refined yet relatively simple design has evolved with particular attention devoted to induced melt agitation, the vapor paths, and the condenser arrangement for optimal separation of impurities. Highpurity graphite, quartz, glass, and mild steel are adequate materials of construction. Electric heating is the preferred method. In industrial practice, distillation under vacuum has been developed into an efficient method of producing 59 and 69 grade cadmium. One stage of distillation is adequate for 59 grade provided the feed is commercial grade metal of the typical qua!ity quoted in Table I, and distillation conditions, rate, and yield are combined in an appropriate manner. Repeated distillation results in a 69 grade product. This should not be construed as a departure from the two-principle process design, because the metallurgical processing for the 49 commercial grade cadmium (Table I) is an integral part of the 69 grade production. The vacuum distillation process is normally conducted as a batch operation. At Cominco, equipment has been scaled up from laboratory size to approach the one ton per batch scale which is large enough to satisfy the foreseeable demand for high-purity cadmium to be used as a starting material for further purification by zone refining. On this scale of operation there is no justification for the development of continuously operating equipment. The type of equipment that can be used for large-scale vacuum distilla-

2.

PREPARATION OF HIGH-PURITY

Cd, Hg,

29

Te

AND

-7 -

Connection to cold trap and vacuum pump

Baffle arrangement

-1%

I

Air-cooled zone

Heoting elements

)ooooooooooooo/

FIG. 1 . Vacuum retort for distillation of cadmium.

tion is sketched in Fig. 1. Some typical industrial results are listed in Table 111. The above products find uses in areas where their respective purity is appropriate. The distillation crops are melted under inert atmosphere or vacuum and then cast into pore-free rods and bars or shotted to yield a convenient form for handling by the user. The melting crucible and mold materials can be steel, graphite, pyrolytic carbon, glass, and quartz. Potential contamination at the product surface is removed by etching with high-purity nitric acid, followed quickly by thorough rinsing with deionized water, alcohol, and acetone, and drying under vacuum.

3. ZONE REFINING Although appropriately conducted and repeated vacuum distillation of selected commercial grade cadmium will result in 69 grade purity, experienc.e has shown that zone refining of the distillate can lead to significant benefits in critical semiconductor applications-where for instance cadmium containing 100 ppb at. of a singly ionized electrically active impuTABLE I11 PURITY OF VACUUM DISTILLED CADMIUM

Impurities in pprn

Feed Single distillation Double distillation a

Pb

Cu

Ni

Zn

A1

TI

Fe

Co

Mg

As

35 0.5

15 0.5

3

<0.1

3 0.1 0.1

1


0.1

10 NDn ND"

ND" ND"

2 0.1 0.1




ND denotes not detected.

ND"

30

H . E. HIRSCH, S . C. LIANG, A N D A. G . WHITE

rity may translate into 1.6 x 1015 carriers/cm3 in cadmium telluride or 3 X 1014 carriers/cm3 in Cd,Hg,-,Te of composition x = 0.2. The effectiveness of zone refining vacuum-distilled 69 grade cadmium is difficult to assess on the basis of published information. The ratio of electrical resistivity at 4.2 K and room temperature has been interpreted as indicative of further purity improvements (Aleksandrov, 1961; Wernick and Thomas, 1960), but this type of measurement is not likely to be specific or precise enough to be used to control the purity of cadmium for (CdHg)Te synthesis. In designing an effective approach to zone refining, one route that can be considered involves using a combination of segregation coefficients and characteristic general process parameters as presented by Loechtermann et al. (1977). Zanio’s recent compilation shows large differences in experimentally determined segregation coefficients, and the uncertainty about the correct value combined with the inferred nature of segregation coefficients deduced from phase diagrams makes zone refining process design and operation initially nothing more than a speculative effort. Emission and mass spectrographic determination of s l lected impurities in intentionally doped cadmium bars after zone refining revealed the following distribution coefficients: copper 0.6, zinc 0.7, tin 0.2, lead 0.2. See Figs. 2 and 3 (Willardson, 1980, private communication). Using the end use criterion of low carrier concentration in single-crystal

DISTANCE IN ZONE LENGTHS

FIG.2. Distribution of copper in zone refined cadmium. Emission spectrometric data: D,doped; 0, zone refined. Mass spectrometric data: 0 ,doped; 0, zone refined. ---, theoretical (6 pass).

2.

PREPARATION OF HIGH-PURITY

1

2

3

4

5

6

7

Cd, Hg,

8

9

AND

Te

31

10

DISTANCE IN ZONE LENGTHS ( I n )

FIG.3. Distribution of Zn, Sn, and Pb (C, = 2.4 ppm for Zn, 50 ppm for Sn and Pb) in zone refined cadmium. Emission spectrometric data: A, Zn; 0 , Sn; 0, Pb. Mass spectrometric data. A,Zn; H, Sn; 8, Pb.

(CdHg)Te is not only expensive and requires long periods of time per determination, but also carries an inherent element of uncertainty in the assumption that the impurities are evenly distributed not only through the lot of cadmium used, but also through the tellurium and mercury. In the end, however, it is the accumulated long term experience that proves to be the master of the results. Among the low-melting metals, cadmium is one of the more difficult to zone refine. The combination of the low melting point (321°C) with high thermal conductivity (0.9 W/cm-' K-I) and volume expansion on melting requires careful equipment design and installation to achieve the required close temperature and zone control. Resistance heating is the preferred method in industrial practice. Boats fabricated from suitable grades of graphite, boron nitride, and

32

H . E. HIRSCH, S . C . L.IANG, A N D A . G . WHITE

even high-temperature plastics have been used experimentally with some success. For production, Cominco uses quartz or Vycor boats having a semicircular cross section up to 100 mm wide and 1500 mm long. Although the process is conducted under an atmosphere of dry highpurity hydrogen to reduce the oxygen content and aid in the volatilization of some impurities, application of a carbon coating to the inside of the boat is necessary to avoid a reaction between cadmium and the silica and avoid sticking of the charge which could break the boat. The zone travel speed is around 1 mm/min, and a total of 30-50 zone passes are performed to obtain a near-equilibrium impurity distribution. The zone refined bar is sampled at predetermined intervals along the main axis and profiled analytically. This analysis determines the lengths of the leading and trailing ends which show elevated impurity levels and are cut from the bar. The remaining center section of the bar, after careful etching, represents the best purity at this stage. It is the most desirable product for users who can use it at the given size. For others the ingot will require remelting and casting into smaller shapes, e.g., thin rods or pellets. If these operations are conducted in air, the product will inevitably have a high oxygen content, and pellets more so than rods. It is possible, however, to drip melt the bar into pellets by inductive heating in an oxygen-free atmosphere, thereby avoiding oxygen contamination. For the purpose of preparing the special grade for (CdHg)Te synthesis the center section of the zone refined bar is processed further as described in Section 6. IV. Purification of Mercury

More than 20 mercury-containing minerals are known in nature but the red sulfide cinnabar is the only significant ore mineral. Cinnabar ore bodies are usually single metal deposits, i.e., mercury is the only valuable constituent, but some ores may contain a n appreciable fraction of the total mercury in metallic form. The recovery method consists of highly efficient roasting of the ore (or of a concentrate in some locations) followed by condensation of the resulting mercury vapor and hoeing for the separation of solids to yield “prime virgin” mercury. The estimated production of mercury from primary and secondary sources from 1965 to 1975 worldwide has ranged from 8,800-11,400 ton per year with recycling contributing 10-20% of the total. Production has declined in the more recent years as consumption receded in the wake of environmental and health concerns. Known mine reserves are large enough for significant production increases and, because it is based on single metal deposits, the supply is adaptable to the scale of demand.

2.

PREPARATION OF HIGH-PURITY

Cd, Hg,

AND

Te

33

There are few major uses of mercury which do not require or specify a purity of 59 grade or better as determined by emission spectrographic analysis. Consequently, most of the virgin as well as the recycled mercury is supplied to the market with that degree of purity. The scale of operation and the ease of purifying and determining the purity of mercury account for the relatively modest price premium for 59 grade metal over prime virgin metal. Simple ways of judging the purity of mercury deserve mention. A bright mirrorlike surface, particularly after shaking the metal for some time in a previously scoured container, or after slowly evaporating most of the mercury, reflects the absence of all metallic impurities at levels of more than 1 ppm except for the precious metals. Any contamination by gold in excess of 10 ppm becomes visible as a dark particle after dissolution of a 10-g sample in nitric acid. In mercury, chemical and physical properties combine to permit the removal of metallic and other impurities to extremely low levels. Mercury has been called “The Purest Metal” (Lawrence, 1952). The U.S. National Bureau of Standards, based upon the ease and reliability with which mercury can be ultrapurified, has designated the triple point of mercury of 234.3082(2) K as a thermometric standard (Furukawa and Bigge, 1976). 4. CHEMICAL METHODS Mercury is a good solvent for many metals, both reactive and noble, and the successive application of two purification methods utilizing different properties is required to achieve the desired high degree of purity. The reactive metals, e.g., magnesium, zinc, lead, copper, etc., are readily removed by oxidation, which can be accomplished either by aeration of the metal or by acids and other oxidizing substances in an aqueous environment. The solid oxides formed during dry aeration are insoluble in and normally not wetted by mercury and rise to the surface because of the high buoyancy force. They can be separated from the mercury by skimming, filtration, or simple under-(bottom-)pouring. Wet oxidation is usually accomplished at or moderately above the room temperature with nitric, hydrochloric, or sulfuric acid and may be augmented by additions of dichromate, permanganate, or peroxide as appropriate. Achieving thorough dispersion of the mercury in the purifying medium is of key importance. Repeated displacement washing with deionized water is advisable. The separation of the mercury from the aqueous solutions is usually accomplished by decantation or underpouring. If present, traces of water can be removed by agitating the mercury with calcium oxide followed by another underpour, or by simple filtration through paper.

34

H . E . HIRSCH, S. C . LIANG, A N D A . G. WHITE

Simple oxidative procedures, of course, do not remove impurity metals more noble than mercury. Wet methods have been claimed for the removal of more noble metals, e.g., gold by cyanidation in the presence of peroxide, but distillation and rectification under normal pressure or under vacuum have become the preeminent separation methods. Distilled mercury is supplied commercially as redistilled, double, and triple distilled, and instrument grade. The distillation is usually carried out in batches or semicontinuously at atmospheric pressure in simple steel or glass equipment. The products frequently develop surface scums during storage which probably result from the presence of oxygen during distillation and the pickup of minor quantities of organics, water, and other impurities. However, the purity of the underpoured mercury with respect to metallic contaminants is excellent as shown in Table IV for typical triple-distilled product. TABLE 1V EMISSION SPECTROGRAPHIC ANALYSIS OF TRIPLE-DISTILLED MERCURY" A1

Ca

cu Fe

Mg

0.001 <0.001 <0.001 0.001 0.001

Si Ag Ti AU

Bi

0.002 0.002

0.003 0.01 <0.01

In ppm by weight.

Although not clearly understood, it is well known that gold, and to a lesser extent silver and platinum, can accompany the mercury vapor during distillation, particularly at atmospheric pressure and high distillation rates, and contaminate the product. Traces of both gold and silver are of no consequence in many uses for high-purity mercury, but they cannot be tolerated for obvious reasons in mercury used in the synthesis of cadmium mercury telluride. The triple distilled product is therefore distilled at least once more under carefully controlled conditions as described in Section 6. V. Purification of Tellurium 5 . INTRODUCTION

Tellurium is widely distributed over the earth's crust. Large quantities are found in small concentrations in the copper porphyries, copper sul-

2.

PREPARATION OF HIGH-PURITY

Cd, Hg,

AND

Te

35

phide, nickel sulphide, and lead sulphide deposits (Kirk-Othmer 1969). There are no deposits mined specifically for their tellurium content. The overall percentage recovery of tellurium during processing of the heavy metal ores is very small. In the free world, about 500,000 pounds of tellurium is produced annually (Hampel and Hawley 1973), most of which is recovered from electrolytic copper refinery slimes. After the removal of copper and selenium from the slimes, tellurium is extracted by leaching with caustic and neutralizing the leach liquor. The resulting impure tellurous acid precipitate can be purified by repeatedly dissolving it in caustic solution and neutralizing to reprecipitate it. Acceptably pure tellurous acid precipitate is reduced to metal either by direct reduction with flour, or by sulphur dioxide from hydrochloric acid solution, or (most commonly) by electrolytic deposition from an alkaline solution, usually onto stainless steel plates (Kirk-Othmer 1969). In the commercial grades, the purity of the recovered tellurium may range from 96-99.99% (see Table V).

TABLE Y COMMERCIAL

TELLURIUM ANALYSES Impurity content (%)

Nominal Te (%)

Se

Pb

Cu

S

Na

Si

A1

Fe

99.99 99.9 99.0 96.0

0.002 0.01 0.1

0.0001 0.GQI 0.2 1.0

0.002 0.002 0.05 0.3

NR"

0.001 0.01 0.05 0.3

0.0001 0.001 0.05 0.2

0.0001

0.0001 0.001

1.5

0.05 0.05 0.2

0.001 0.1 0.1

0.15 0. I5

NR = not reported.

The tellurium used in the semiconductor industry must meet more stringent purity specifications. A variety of chemical and physical techniques have been developed for the further refining of commercial grades. The chemical refining methods usually involve the recrystallization or precipitation of tellurium or its compounds from solution. Examples of such processes include fractional reduction of tellurium metal from acidic solutions using sulphur dioxide, and reprecipitation of tellurous acid from alkaline solutions. Other methods such as thermal dissociation of the hydride, purification of the chloride followed by reduction, solvent extraction, and electrolytic purification are also employed.

36

H. E.

HIRSCH,

S.

C. LIANG,

A N D A. G . WHITE

Physical refining techniques include vacuum distillation and zone refining. Typically, some form of physical refining is used as a final step following preliminary chemical purification. 6. CHEMICAL REFINING: A N D PRECIPITATION CRYSTALLIZATION

The fractional reduction of tellurium from an acidic solution is a commonly used technique for separating it from its impurities (Bagnall, 1966; Chizhikov and Schastlivyi, 1970). The separation of selenium from tellurium is based upon the difference in redox potential of their tetravalent compounds and upon the pH dependence of those potentials. Commercial grade tellurium or tellurium dioxide is dissolved in excess hydrochloric acid to greater than 8.8 N. Under these conditions, selenium is precipitated as the element by sulphur dioxide, while tellurium remains in solution. Following selenium precipitation and separation, pure water is added to the solution to lower the acidity to 2 N , and the tellurium is precipitated by reduction with sulphur dioxide. A major proportion of heavy metal impurities remains in solution. Their concentrations in the tellurium fraction can be decreased by repeated dissolving and precipitation. Tellurium can be obtained in pure form by recrystallizing compounds such as basic tellurium nitrate or telluric acid, or by purifying the dioxide in an alkaline or acidic solution (Chizhikov and Schastlivyi, 1970). 7. HYDRIDE PROCESS Relatively low yields (25-30%) of very pure tellurium have been obtained from processes involving the thermal decomposition of hydrogen telluride (Bagnall, 1966; Chizhikov and Schastlivyi, 1970). 8. CHLORIDE REFINING

The chloride process for tellurium refining is based upon the preparation in two stages of stable tellurium tetrachloride, its purification by distillation or rectification, and reduction of the purified chloride to metal (Chizhikov and Schastlivyi, 1970). 9. SOLVENT EXTRACTION

In this process, tellurium is extracted from an aqueous hydrochloric acid solution of the tetrachloride, using a mixture of diethyl ether and 10-5076 n-amyl alcohol. Washing with hydrochloric acid removes the tellurium from the organic fraction. The resulting tellurium-rich acid solution is neutralized to precipitate the dioxide, which is then reduced to the metal for further refining by sublimation (Chizhikov and Schastlivyi, 1970).

2.

PREPARATION OF HIGH-PURITY

Cd, Hg,

AND

Te

37

10. ELECTROLYTIC PURIFICATION Electrolytic processes to recover or separate tellurium are based on the use of acid (hydrochloric or nitric) or alkaline solutions. Acid solutions require the use of titanium anodes and platinum cathodes. The product is usually powdery in form. When alkaline solutions are electrolyzed, stainless steel electrodes are frequently used, and the cathode deposit is usually dense and adherent (Chizhikov and Schastlivyi, 1970; KirkOthmer, 1969). 1 1 . DISTILLATION

Tellurium has a vapor pressure of 760 mm at 990"C, which precludes any practical application of atmospheric pressure distillation (KirkOthmer, 1969). Vacuum distillation at temperatures of 450-550°C allows the use of conventional construction materials. At those temperatures, separation of tellurium from antimony, lead, bismuth, aluminum, silver, copper, silicon, iron, and gold is readily achieved. Selenium, arsenic, sodium, potassium, magnesium, and sulphur are more difficult to remove using vacuum distillation. Overall yields of up to 93% can be achieved at distillation rates of 6-58 g/cm2 h (Chizhikov and Schastlivyi, 1970). 12. ZONEREFINING Zone refining is an effective purification technique for tellurium because of the favorable values of the segregation coefficients for most impurities, as shown in Table VI. TABLE VI DISTRIBUTION COEFFICIENTS OF

IMPURITIESI N T E ~

-

K

Impurity element

10-5 10-4 10-3

Cu, Ag, Au As, Sn, Mg, A1 Bi, Ge, Ca, TI, Ni Sb, In, Ge, 1 Hg, Se, C r , Na Cd

10-2 10-1

2

Schaub and Potard (1970).

All impurities listed have segregation coefficients much less than 1 except Cd, Se, Hg, Cr, and Na. The dependency of these coefficients on zone travel rates has been demonstrated for copper and silver (Chizhikov and

38

H . E. HIRSCH, S . C . LIANG, AND A . G . WHITE

Schastlivyi, 1970). Rates of up to 60 mm/h are used for most effective refining. Although inert gas cover may be used during zone refining, the removal of selenium from tellurium has been found to be more effective if hydrogen is present. A vapor transport mechanism has been postulated as a reason for the improvement (Chizhikov and Schastlivyi, 1970; Schaub and Potard, 1971). Tellurium intended for (CdHg)Te manufacture is further zone refined, as discussed in Section 6.

VI. Special Products €or (CdHg)Te Preparation Detailed production technology of (CdHg)Te is not discussed in this chapter, but certain significant points affecting the feed metals used to prepare the compound follow. (CdHg)Te can be made by single- or two-stage synthesis. The former involves the direct combination of the three metals while in the latter the binary compounds cadmium telluride and mercury telluride are first prepared separately and then combined to give (CdHg)Te. As usual, various tradeoffs exist between the two methods. For example, the two-stage method offers the possibility of further purification of the binary compounds by zone refining, growth from solution, and sublimation. Purification methods for cadmium telluride have been reviewed by Zanio (1978). Information on mercury telluride preparation and purification has been given by Dziuba (1964), Vanyukov er al. (1967), and Ivanov-Omskii cf af. (1969). Single-stage synthesis, however, requires far fewer handling steps and has become the preferred method given the availability of the starting metals in appropriate purity. The required purity is obtained by further special processing of the 69 grade metals with proper safeguards against contamination. Because Cd,Hg,-,Te forms a continuous spectrum of compounds (not solution or alloy), and because an as-synthesized ingot invariably has a range of x values, it is not practical to refine the (CdHg)Te ingot by the zone melting technique. The final product, therefore, contains substantially all the impurities in the starting metals. As was discussed earlier, the desired carrier concentration (< 1015/cm3)is considerably lower than the impurity content in the 69 metals. For such use specially prepared grades of the metals are now available, with the ordinary 69 metals used as the crude feed.

2.

PREPARATION OF HIGH-PURITY

Cd, Hg,

AND

Te

39

13. MERCURY

Triple-distilled mercury is usually of reliable quality to serve directly as feed for the final distillation operation. However, it is a justified precaution to devote some specific attention to feed preparation. Accidental contamination can result from the solvent properties of the metal and the number of relatively small containers for triple-distilled mercury involved in preparing a 50-100 kg batch of feed. The individual containers are emptied into a Pyrex container and thoroughly mixed. Any dispersed impurities will rise to the surface over a period of a few days. The mercury is then bottom poured into a second Pyrex container and an analysis sample is taken during the transfer. Emission spectrography is used to confirm the purity listed in Table IV. In order to detect impurities at the low levels quoted there, it has been necessary to develop special sample preparation methods. A sample distillation procedure has evolved which retains and concentrates essentially all metallic impurities in a residue amounting to 1% of the original sample weight. By analyzing this residue and projecting the results to the initial sample, the equivalent of a hundredfold increase in sensitivity is achieved. The validity and internal consistency of this approach has been confirmed and the results are in agreement with those obtained by other suitable analytical methods which may also determine nonmetallic elements not detected by emission spectrography. A portion of the feed batch is then transferred to the reservoir of an all quartz vacuum distillation apparatus. An example of the design of suitable equipment is shown in Fig. 4. Various other versions are possible. It is advisable to scour new or reassembled equipment by distilling several kilograms of mercury and then draining it completely. This procedure removes surface contaminants including organics and water. Most of the mercury used for scouring can be returned to the triple-distilled stock. The equipment shown in Fig. 4 operates semicontinuously , requiring practically no operator attention except for periodic product removal and refilling of the feed reservoir. It is most important to conduct the distillation at a rate compatible with quiescent evaporation from the surface of the mercury in the boiler so as to avoid bumping and splashing, which could result in carryover of impurities. A practical distillation rate is readily obtained at a system pressure of 7- 14 Pa (5- 10pm) so long as the evaporating surface remains clean. Dissolved impurities obviously build up in the boiler and are controlled by bleeding from the boiler at appropriate intervals. Infrequently the boiler needs to be shut down and drained, followed by flushing with mer-

40

H . E . HIRSCH, S . C . LIANG, A N D A . G . W H I T E To cold trap and vacuum pump

Drain valve

FIG.4. Mercury distillation apparatus.

cury from the feed reservoir to remove heterogenous surface films. The few joints and stopcocks in the system are vacuum sealed with Teflon sleeves or by judicious use of Apiezon grease (in preference to silicone grease). The batches of finished product are accumulated in a Pyrex vessel under cover, blended, and sampled for analysis. The samples are processed as described earlier and the residues subjected to emission spectrographic analysis for routine quality control. At periodic intervals samples of product are analyzed directly by mass spectrography to confirm the results obtained by emission spectrographic analysis of distillation residues. A typical product analysis is shown in Table VII. Vacuum-distilled mercury for (CdHg)Te production is packed in Pyrex or flint glass bottles or ampoules under dry high-purity argon. The containers and caps are carefully acid cleaned, rinsed repeatedly with distilled, deionized water and dried in vacuum or by infrared radiation. The work station at which clean mercury is processed and handled must be well ventilated for the protection of the operators. In normal laboratory or industrial practice any mercury used or spilled will quickly collect a surface film which drastically reduces the rate of evaporation, often

2.

PREPARATION OF HIGH-PURITY

Cd, Hg,

AND

Te

41

TABLE VII O F VACUUM TYPICAL ANALYSIS DISTILLED MERCURY

ppm by weight

A1 Bi Cd Ca cu Cr In Fe K Mg

0.001 (0.01)" (0.0l)n 0.001 <0.001 (0.01)"

(0.01)" <0.01

0.04 <0.001

Mn Ni Pb Si Ag Na Sn Ti CI S

(0.01)" (0.01)~ (0.1)" <0.001 <0.001 0.02 (0.0l)a (0.0l)a 0.04 0.06

( ), not detected with detection limits given in parenthesis.

to negligible values. Clean high-purity mercury at room temperature has a calculated unrestricted evaporation rate of approximately 3 mg/cm2 min. Although the actual rate of evaporation into slow moving air is lower by a factor of lo3- 105 due to the high atomic weight of mercury, giving rise to a high mercury concentration localized immediately above the mercury surface, the rate is still sufficiently fast to establish potentially dangerous levels of mercury even in adequately ventilated areas in a relatively short time. Obviously, all containers should be kept closed or at least covered to reduce not only the potential for contamination but also health hazards. 14. CADMIUM A N D TELLURIUM

Cadmium and tellurium are available in what is known as double zone refined (DZR), triple zone refined (TZR), and quadruple zone refined (QZR) grades. Normal 99.9999% cadmium and tellurium are zone refined products. Feed material is zone refined until the impurity equilibrium is established. The section which meets the 99.9999% specification is collected as the product, and the leading and trailing ends where the impurities are conentrated are rejected as scrap. The 69 pure metal is subjected to the same zone refining operation, and an impurity equilibrium established for a second time. The gradient on the normalized logarithmic scale is the same as before, but the actual impurity level is reduced. Metal obtained from this second zone-refining operation is referred to as double zone refined (DZR) grade.

42

H . E. HIRSCH, S . C. LIANG, A N D A. G . WHITE

Similarly, the DZR metal is refined a third time to give triple zone refined (TZR) grade and the TZR is treated to yield quadruple zone refined (QZR) grade. Since essentially all of the impurities of concern in tellurium have distribution coefficients less than unity, a distribution of those impurities in the host metal after zone refining can be depicted graphically as in Fig. 5.

FIG.5. Impurity distribution in zone refined cadmium and tellurium.

0

Bar Length

iZone Travel -)

Control of purity at each successive stage of zone refining is monitored by sampling the bar at a control point, determined on the basis of experience to be near the trailing extremity of the ‘‘level’’ section of the impurity distribution curve (see Fig. 5). Typical analyses of control-point samples for the various zone refined tellurium products are shown in Table VIII. The control-point analyses in Table VIII show only slight evidence of the purity improvement that actually takes place during each successive stage of zone refining. Interpretation of the analytical information in relation to actual use becomes very difficult. The control-point analyses in Table VIII show only slight or perhaps even questionable improvements from DZR through TZR to QZR. The actual improvement is amplified when the analyses of the trailing ends, where the impurities accumulate to higher concentrations, are compared (Table IX). Even here, only selected impurities (Cu, As, Se, Sb, and 02)show observable improvements. To illustrate that effect, Table IX shows the analysis of samples from the extreme trailing end section of comparable zone refined bars. In high purity metal production operation, therefore, analytical information as shown in Tables VIII and IX is collected primarily to guard against accidental product contamination. The data collected routinely are judged to be inadequate to provide conclusive evidence of the im-

2.

PREPARATION OF HIGH-PURITY

Cd, Hg,

AND

43

Te

TABLE VlIl MASSSPECTROGRAPH ANALYSES OF REFINED TELLURIUM (ppmw)

Impurity

99.9999%

C N2 OP H 2

Na Mg A1 Si P C1

K Cr Fe Ni

cu Ga As Se

0.9 0.04

1

X"

0.02 0.04 0.1 0.04 Int.b 0.02 0.02 0.04 0.2 0.05 Int.b.c 0.01 0.01 2

Double zone refined

Triple zone refined

Quadruple zone refined

0.9 0.02 4 X" 0.02 0.04 0.09 0.03 Int.b 0.02 0.02 0.04 0.2 0.04 Int.b.c 0.003 0.01 0.8

0.1 0.02 3 X" 0.02 0.03 0.09 0.02 Int.b 0.02 0.02 0.04 0.1 0.01 Int.b.c NDd NDd 0.3

0.8 0.02 3 X" 0.02 0.03 0.08 0.02 Int.b 0.02 0.02 0.03 0.1 0.01 Int . NDd NDd 0.1

X, not looked for. Int. =line interference. Determined at less that 0.1 ppmw hy emission spectrograph. N D = not detected.

provements in purity resulting from multiple zone refining, particularly for (CdHg)Te production use. The final test of the value of the purity attained must of necessity be the quality of the semiconductor material prepared from it. It is now generally agreed that the metals (Cd, Hg, and Te) produced in the manners described in this chapter will consistently yield n-type Cd,Hg,-,Te of the composition x = 0.20 with carrier concentrations in the 1014- 1015 range. Although further improvements are desirable, such concentrations are adequate for most current detector manufacture requirements. On the basis of the experience from the authors' laboratory, it is believed the DZR Cd-QZR Te combination is adequate. As yet, further gains by using QZR Cd have not been seen.

15. GENERAL Current knowledge suggests that oxygen is a shallow donor in the (CdHg)Te system, and all three metals will pick up oxygen from air readily.

44

H . E. HIRSCH, S. C . L I A N G , A N D A. G . WHITE

TABLE IX MASS SPECTROGRAPHIC ANALYSES O F TELLURIUM BARTRAILING ENDS @pmw) Impurity

Single zone refining

C

1

N,

0.03 7

Oe

H*

X R

Na Mg Al

10

Si P S CI K

In th Int*

Ca Ti V Cr

Mn Fe

co Ni

cu Zn Ga As Se

Rb Sr A&! Cd

In Sn Sb TI Pb Bi

0.08 0.2

0.1

0.03

2 2 0.03 0.08 40 3 400 0.5 500 Int*(100)' 3 0.4

8 10

0.02 0.02 60 0.2 0.08 0.9 2 0.3 300 30

Double zone refining 0.7 0.04 2 X" 0.02 0.06 0.1

0.4 Intb

Triple zone refining

0.006 0.02

X"

lntb -

0.003 0.02

-

-

0.01

Intb(0.2)C 0.06 2 -

-

-

X"

0.01 0.05 0.1 0.04

-

0.03 0. I -

0.7 0.09 0.9

0.7 0.02 I

-d

-

0.02

0.1

0.1

-

Intb(
-

0.006 0.4

-

-

-

-

X, not looked for. Int. = line interference. Determined by emission spectrograph. - (dash) indicates not detected.

-

0.02 -

-

-

0.02 0.05 0.1 0.04 Intb 0.008 0.02

-

-

0.3

Quadruple zone refining

-

0.1

Inth(
-

0.2

-

-

-

2.

PREPARATION OF HIGH-PURITY

Cd, Hg,

AND

Te

45

To obtain the maximum benefit offered by the pure metals, it is very important to minimize the exposure of such metals to oxygen. The physical form and shape of the metals desired of course depends on the facilities available to users. Pellet form is not recommended for (CdHg)Te production because of the oxygen problem. REFERENCES Aleksandrov, B. N. (1961).Fiz. M e t . M e t u l l o ~ w i .11, 588 [English trunsl.: Phyhys. Met. Mrtullogr. 11, 991. Alexandrov, B. V., and Udovikov, V. E. (1973).N P W SA c u d . Sci. USSR M e t . No. 2, 17-25. Bagnall, K. W. (1966).“The Chemistry of Selenium, Tellurium, and Polonium.” Elsevier, Amsterdam. Biswas, A. K., and Davenport, W. G. (1976).“Extractive Metallurgy of Copper,” Vol. 20, Chapter IS. Pergamon, Oxford. Chizhikov, D. M.(1966).“Cadmium” (translated by D. E. Hayler). Pergamon, Oxford. Chizhikov, D. M., and Schastlivyi, V. P. (1970).“Tellurium and the Tellurides.” Collet’s Wellingborough, England. Dziuba, 2. (1964).Actu Phys. Pol. 26, 897-903. Furukawa, G. T.,and Bigge, W. R. (1976). Cum. Int. Poids M e s . C o m . Consult. Thermom. Sess. 11, 138-144. Hampel, C. A., and Hawley, G. G. (1973).“The Encyclopedia of Chemistry,” 3rd ed. Van Nostrand-Reinhold, Princeton, New Jersey. Hirsch, H. E. (1969).Cominco internal communication. Ivanov-Omskii, V. I., Kolomiets, B. T., Ogorodnikov, V. K . , and Smekalova, K. P. ( 1969). Izv. Akad Nauk SSSR Ser. Fiz. 5(3),487-491. Kirk-Othmer(l969). “Kirk-Othmer Encyclopediaof Chemical Technology,” Vol. 19,2nd ed. Wiley, New York. Krauss, C. J . (1977).Can. Patent 1020491. Kuhn, A. T., and Wright, P. M. (1971).I n “Industrial Electrochemical Processes,” Chapter 14,Electrodes for Industrial Processes. Elsevier, Amsterdam. Lawrence, J. B. (1952).lnstrumentution 2543). Liekens, H . A., and Charles, P. D. (1973).World Min. U . S . E d . 26(4), 40-43. Loechtermann, E., Hein, K., and Buhrig, E . (1977).Metullwiss. Tech. 31(1), 39-42. Lund, R. E., and Sheppard, R. E. (1964).J. Met. 16(9), 724-730. Nesmeyanov, A. N. (1963).“Vapor Pressure of the Chemical Elements” (R. Gary, ed.), Elsevier, Amsterdam. Schaub, B., and Potard, C. (1971).Proc. Int. S y m p . Cudrnium Telluride, Muter. Gummu Ruy Detectors. Strasbourg, France, June 29-30. Vanyukov, A . V., Schastlivy, V. P., Polisar, E . L., and Indenbaum, G. V. (1967).Izv. Ahad. Nuuk Neorg. Muter. 3(7), 1271-1272. Wernick, J. H., and Thomas, E. E. (1960).Truns. Metall. Soc. AIME 218, 763. Willardson, R. K. (1980).Private communication. Zanio, K. (1978).Semicond. Semimet. 13, 39-43. Zief, M. (1978).Chomtech 8, 610-614.

This Page Intentionaiiy Left Blank

.

SEMICONDUCTORS AND SEMIMETALS VOL . 18

CHAPTER 3

The Crystal Growth of Cadmium Mercury Telluride W . F . H . Micklethwaite I . INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . 1.General . . . . . . . . . . . . . . . . . . . . . . . 2 . The Pseudobinary Phase Diagram . . . . . . . . . . . 3 . The Ternary Phase Diagram . . . . . . . . . . . . . . 4 . Consequences of the Phase Diagrams . . . . . . . . . . 5.Purity . . . . . . . . . . . . . . . . . . . . . . . . 6 . Furnace Considerations . . . . . . . . . . . . . . . . 7. Crystal-Growth Theory . . . . . . . . . . . . . . . . . 11. CRYSTAL GROWTHBY THE QUENCH/ RECRYSTALLIZATION METHOD. . . . . . . . . . . . . . . 8 . Introduction . . . . . . . . . . . . . . . . . . . . . 9 . Preparation . . . . . . . . . . . . . . . . . . . . . . 10.Quench . . . . . . . . . . . . . . . . . . . . . . . 11. Recrystallization . . . . . . . . . . . . . . . . . . . 111. L I Q U t D / S O L l D GROWTH . . . . . . . . . . . . . . . . . . 12. General . . . . . . . . . . . . . . . . . . . . . . . 13 . Bridgman Growth . . . . . . . . . . . . . . . . . . . 14. Zone Melting . . . . . . . . . . . . . . . . . . . . . 15 . Traveling Solvent Zone Melting . . . . . . . . . . . . . 16 . The Czochralski Method . . . . . . . . . . . . . . . . 17. Slush Growth . . . . . . . . . . . . . . . . . . . . . 18. Replenished Solution Growth . . . . . . . . . . . . . . IV . EPITAXIAL GROWTH. . . . . . . . . . . . . . . . . . . 19. Introduction . . . . . . . . . . . . . . . . . . . . . 20 . Liquid Phase Epitaxy ( L P E ) . . . . . . . . . . . . . . 21 . Vapor Phase Epitaxy ( V P E ) . . . . . . . . . . . . . . V . OTHERCONSIDERATIONS . . . . . . . . . . . . . . . . . 22 . General . . . . . . . . . . . . . . . . . . . . . . . 23 . Homogeneity (the Unkindest Cut of All) . . . . . . . . . 24. Dislocations and Etch Pits . . . . . . . . . . . . . . . 25 . X-Ray Topography . . . . . . . . . . . . . . . . . . 26 . Optical Imaging . . . . . . . . . . . . . . . . . . . . 21. Ordering . . . . . . . . . . . . . . . . . . . . . . . REFERENCES. . . . . . . . . . . . . . . . . . . . . . .

48 48 48 55 59 60 62 62 63 63 63 65 68 70 70 71 76 78 80 80 84 85 85 86 92 106 106 107 110 112 114 114 116

47 Copyright @ 1981 by Academic Press. Inc . All rights of reproduction in any form reserved . ISBN 0- 12-752 118-6

48

W . F . H . MICKLETHWAITE

I. Introduction 1. GENERAL

Cadmium mercury telluride (Cd,Hg,-,Te, or CMT) has the desirable feature of possessing an approximately linear variation of bandgap with composition across the pseudobinary range from mercury telluride to cadmium telluride. This behavior implies complete miscibility of the two compounds in the solid state and a relatively simple phase diagram.

2. THE PSEUDOBINARY PHASEDIAGRAM Rather than discuss at this point the full ternary phase diagram, which is very complicated in this system, let us consider first the pseudobinary phase diagram between the two binary compounds mercury telluride and cadmium telluride. If one considers only the liquid/solid phase diagram for a two-component system, where the vapor pressures of all constituents are low, there is only one degree of freedom; hence the phase boundaries are fixed. However, in the present case the vapor pressure of one component, mercury, is very high. There are therefore two degrees of freedom in this phase diagram, namely pressure and temperature, when x is specified. The early work by Blair and Newnham (1961) and Ray and Spencer (1967) on the liquidus curve, the work by Harman and Strauss in 1964 (reI

loo1

t 6001 0

,

'

01

,

'

02

,

1

,

'

0.3

0.4

,

1

05

,

,

"

O I 0.7

,

'

08

,

1

0s

1.0

Mole froction CdTe

FIG. 1. Early ( T J ) phase diagram for Cd,Hg,-,Te. (19681.1

[From Schmit and Speerschneider

3.

T H E CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

49

ported by Harman in 1967), along with further studies by Ray and Spencer (1967) on the solidus generally seem to disagree. This early work was summarized by Schmit and Speerschneider (1968) and is shown in Fig. 1. These authors explained the discrepancy as due to the differing mercury pressure imposed on the systems, with the upper curves in both cases corresponding to about 2.5 atm mercury overpressure and the lower data corresponding to about 0.4 atm mercury overpressure. Steininger (1970) was able to calculate the solidus lines from the two sets of liquidus data above, finding general agreement for both the high and the low mercury pressure cases. In 1976, Steininger used the high-pressure reflux technique to redetermine the phase diagram at the high mercury partial pressures over the pseudobinary. He found general confirmation of the Blair and Newnham liquidus data and the Harman and Strauss solidus. His phase diagram is reproduced in Fig. 2 and is in general agreement with Balagurowa (1974). 1100

1000

-

900

e c

i

:BOO

t-

700

€001 HgTe

I

I

I

0.2

I

0.4

I

I

I

I

0.6

0.8

I

Cdle

Mole trarrion x

FIG.2. High pressure ( T , x ) phase diagram for Cd,Hg,-,Te. [From Steininger (1976).] 0 , this investigation; 0, liquidus data-Blair and Newnham, 1961; V,solidus data-Harman, 1967; 0, solidus data-Schmit and Speerschneider, 1968.

The phase lines of Fig. 2 were fitted by the author to the hyperbolic relations of Eqs. (1)-(3) to the accuracy of Steininger's data (&2"C). For 0 < x < 0.5, Tsolidus (OC) =

+

looox 668. 5.72 - 2 . 9 2 ~

50

W. F. H . MICKLETHWAITE

For 0.6 < x < 1.0,

For 0 < x < 1.0, THquidusrC)

+ 668.

= 1.37looox 0 . 9 7 ~

+

(3)

An alternate choice for limiting degrees of freedom in the phase diagram is to fix composition and then examine the pressure-temperature phase diagram. A first work of this type was done on mercury telluride, or x = 0.0, by Brebrick and Strauss (1965). Schmit and Speerschneider (1968) reported data for x of 0.20 as shown in Fig. 3. Several features of this diagram are noteworthy, particularly the very steep pressure/temperature relationship on the liquidus and solidus lines and also the zone

1 0 ~( K1) ~

Fic. 3. (PJ)phase diagram for Cd,,,Hg,,,Te. [From Schmit and Speerschneider (1968).]

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

51

where there is solid cadmium mercury telluride dissolved in mercury just below the mercury vapor pressure line at moderate temperatures. The broad range of pressures over a single initial melt indicates a widely varying mercury activity, suggesting that the metal/nonmetal ratio (y) of the more general formula (Cd,Hg,-,),Te,-, is also varying. Another interesting feature which has a bearing on the conversion of cadmium mercury telluride from p-type to n-type is the partitioning of the solid phase with p-type prevailing at lower pressures and higher temperatures, and n-type prevailing at higher mercury pressures and generally lower temperatures. Steininger (1976) explored the variation of mercury pressure and the phase lines for various compositions (x,y ) while varying and measuring the metal/nonmetal mole fraction (y). Several rather interesting conclusions were reached. First, he confirmed the work of Brebrick and Strauss (1965) on the mercury telluride high-pressure liquidus as the metal/telTemperature ( O C )

Reciprocoi temperature (104T K )

FIG.4. ( P , T )phase diagram for (Cd,Hg,_,),Te,-, melts showing liquidus data for HgTe and C$,,H&,,Te and the Hg vapor pressure line. [From Steininger (19761.1

52

W . F . H . MICKLETHWAITE

lurium ratio was allowed to vary. He also examined in detail the liquidus relationship of mercury pressure versus temperature for constant x at 0.30 while the metal mole fraction y was allowed to vary between 0.4 and 0.7. These data are shown in Fig. 4. Note particularly the very steep pressure/temperature relationship on the liquidus curves at y of approximately 0.5. The steep slopes of these curves underscore the fact that good mercury vapor pressure control is absolutely mandatory during crystal growth in order to avoid the formation of second-phase inclusions caused by mercury or tellurium excess. Steininger also examined the pseudobinary system, that is, y = 0.5 for the composition range 0 < x < 0.6, to determine the temperature variation of mercury pressure over this system. Over pseudobinary Cd,Hg,-,Te melts the mercury partial pressure was parallel to that for elemental mercury, but lay below it. The average PHgvalue over the pseudobinary melts is approximately 35% of that over the element at the same temperature, and this ratio seemed to be independent of both composition (x) and temperature. He inferred that mercury maintains approximately constant activity of 35% over cadmium-mercury-telluride melts. He also took the constancy of mercury activity rather than activity coefficient over these melts as an indication that the melt should be considered as a binary mercury-tellurium solution, rather than a ternary cadmiummercury-tellurium one. He suggested that this was due to the strong binding energy of cadmium and tellurium atoms in the solution compared to the relatively weaker binding between mercury and tellurium. The solution should then be considered rather as a mixture of associated, relatively neutral cadmium telluride molecules and disassociated mercury and tellurium atoms. The vapor pressure of mercury over the solution would then be a function only of the relative concentration of the unassociated mercury and tellurium governed by y and not affected by the relative concentration of the more neutral cadmium telluride given by x. This rather unexpected constancy of mercury vapor pressure with temperature is one of the very few simplifying factors in the growth of cadmiummercury -telluride crystals. Vanyukov et al. (1977, 1978) report vapor pressure data over solid CMT varying with x as shown in Fig. 5 . The activity coefficient over the solid varies strong between 1.7 and 5.0 for x = 0.0-0.6 as shown in Fig. 6. The activity coefficient over the liquid varies from 0.7 -1.0 for x = 0.0- I .O, contradicting Steininger’s constant value of 0.35,which has been explained by an association model. Krotov er ul. (1979) report the partial pressure of Tez and Hg over solid Cd,Hg,-,Te at 500-600°C as measured by optical vapor density. The mercury data contradict those of Vanyukov et ul. (1978).

3.

T H E CRYSTAL GROWTH O F CADMIUM MERCURY TELLURIDE

53

4. :

4.c

3.:

-E 0

2 3.C I

FIG. 5. Mercury equilibrium ( P , T ) relations over Cd,Hg,-,Te solids. Curves 1 to 4: x = 0.2, 0.35, 0.56, 0.77. Curve 5: Vapor

pressure of Hg over HgTe. [From Brebrick and Strauss (1965).] Curve 6: Vapor pressure of pure Hg. [From Vanyukov et a/.(1978).]

2.5

2.c

I

I

I .4

1.5 IOYT (K-')

Schwartz (1977) was able to determine the solidus loop forx of 0.416 by monitoring the composition of the equilibrium gases using an optical absorption technique. His data are shown in Fig. 7. Others, such as Bailly et al. (1973, have established confirmatory evidence of this type of phase diagram without actually examining it in detail. In their case, they monitored the actual mercury pressure as a function in time over samples either of mercury telluride or mercury telluride in the presence of a proximate cadmium telluride wafer. Gillham and Farrar (1977) have examined the existence region of the sphalerite pseudobinary phase about y = 0.5. They noted that tellurium precipitation during cooling is rarely seen except in materials rich to the extent of 1-3 at. % in tellurium and they have also established the width of the existence region to be of the order of 1 at. %. They suggested the existence region as a

54

2

i-

0

I

0.2

I

I

0.6

0.4

I

0.6

I I .o

xCdTe

FIG.6. Mercury activity coefficient over Cd,Hg,-,Te phases. [From Vanyukov et al. (1978).]

over the ( 1 ) solid and (2) liquid

IO?’T ( K )

FIG. 7. Mercury partial pressure over ( 1 ) metal-saturated and (2) Te saturated C&,,,Hh.,Te. [From Schwartz (1977).]

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE 55

t

t

-

a+

a+ Atomic o/o Te

FIG.8. Schematic ( T , y ) phase diagram for (Cd,Hg,-,),Te,-, and Farrar (1977).]

for fixed x . [From Gilharn

function of tellurium atomic percent would be in the form as shown in Fig. 8. They have also examined a number of cadmium-mercury-telluride slices nominally stoichiometric and annealed under conditions corresponding to the loop of the phase diagram in Fig. 3 labeled “Solid Dissolved in Mercury.” They discovered that a layer was deposited at the surface of such slices and postulated that it was caused by the loss of either tellurium or both tellurium and cadmium. They also determined that this phase resembled the o phase of the cadmium-mercury binary phase diagram.

3. THE TERNARY PHASEDIAGRAM a . Te Corner

Data on the full ternary phase diagram of cadmium mercury telluride have been very restricted to date because of commercial and military secrecy relating to the growth of epitaxial films. However, Harman (1979a,b, 1980) has reported on some of his continuing work on the tellurium corner of the phase diagram. His data for the temperature of formation of the first solid to form from various x melts as a function of y are shown in Fig. 9. There will be a further discussion of his results in Part IV. Harman’s data agree well with the data of Brebrick and Strauss (1965) and Bowers et al. (1979) (being some 5°C lower than the data by these authors for x = 0.0 and 0.10, respectively) but disagree with the earlier work by Ueda et al. (1972), being some 60-100°C higher than the liquidus data they reported. It is probable that the void space in Ueda’s system resulted in mercury loss from the charge, causing Te levels higher than those of the charge and lower Hg pressures, i.e., giving less controlled experimental conditions than those reported by the later authors.

56

W. F . H . MICKLETHWAITE

.. -..', '\

1 .

750'L--+,

\

\

\

FIG. 9. Partial ( T , y ) liquidus diagram for (Cd,Hgl-,)l-,Tey solutions. [From Harman (1980).] .-Harman (1980); A, 0,0, V-Ueda (1972) (x = 0.05, 0.10, 0.15, 0.20); 0 , *-Bowers cr a / . 1979 (x = 0.067. 0.10).

Figure 10 shows the relationship between the liquidus data determined by Harman (1979a,b, 1980) using differential thermal analysis and the solidus compositions determined from LPE layers. For example, to obtain x = 0.4 layers (Cd,Hg,-,Te) from solutions [(Cd,Hg,-,),-,Te,] at 525°C would require liquid atomic fractions of Cd and Hg of -0.02 and -0.15, respectively. The balance, Te, would have an atomic fraction of -0.83 in the LPE solution. b . Hg Corner

There are few reported results for work on the mercury corner of the ternary phase diagram, apparently became of its unsuitability for liquid phase epitaxy. The mercury corner of the diagram involves very high mercury pressures, suffers from a low solubility of tellurium, and also the tendency of cadmium-mercury amalgams to oxidize during handling, all of which are difficult technical problems during epitaxy. Wong and Eck (1980) report their preliminary work on the Hg corner of the Cd-Hg-Te ternary. They determined the solubility of Te and CdTe in Hg and the cosolubility of CdTe in Hg[Te]. Te is approximately 30 times

3.

-

0.02

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE 57

425

I

I

1

1

I

I

I

I

I

FIG. 10. Interrelationships between MDO liquidus(-) for (Cd,Hg,-,),-,Te, and LPE solidus (---); for Cd,Hg,+,Te for crystal growth from Te-rich melts. [From Harman (1980).]

more soluble, and the presence of Te or CdTe decreases the solubility of the other. They determined the ternary liquidus data of Fig. 11 and were able to estimate some solidus data as shown in Fig. 12. These authors also give their calculation of the ternary diagram based on the regular associated solution (RAS) model. The RAS model adequately predicted the experimental liquidus data in both the Hg and Te corners of the Gibb’s triangle. Solidus predictions gave agreement with measured data only in the Te corner. Vanyukov et al. (1977) determined the solubility of cadmium telluride in mercury in the range 350-580°C by phase separation and dew-point methods, finding a solubility of up to 1.5% at about 600°C. From the agreement between the calculated heat of fusion of CdTe into Hg and that for the formation of pure compound CdTe, they concluded that solutions of CdTe in Hg were nearly ideal. The solubility of cadmium mercury telluride in mercury depends strongly on the mole fraction cadmium telluride (x) and increases as x decreases. They also determined the liquidus isotherms for the Hg corner as shown in Fig. 13.

i

58

W. F . H . MICKLETHWAITE

r

g s .-

0.01

0 0

5

F

0.001

0.0001 0.01

0.I

10

I Atomic O/O To

FIG,11. Cd,Hg,-,Te liquidus in the Hg corner of the Gibb's triangle. [From Wong and Eck (1980).]

5000-

I

8

I

1

1

I

I

-

I

.

L

,

1

4> \

'.

c

-\

Q

u

\

I-" I00

\

50 ' : ; z l

\.

10'

'

'

'

'

I

'

'

'

'

FIG.12. Cd,Hg,-,Te solidus in the Hg comer of the Gibb’s triangle. 395°C; AT 5°C; - A T 0.5”C. [From Wong and Eck (1980).]

-

-

t

- 5-8

pm; T =

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

59

FIG. 13. Liquidus isotherms for Hg comer of the Cd-Hg-Te ternary at ( 1 ) 404°C. (2) 435"C, and (3) 454°C. [From Vanyukov et al. (1977).]

Atomic '/c,Cd

4.

CONSEQUENCES OF THE PHASE

DIAGRAMS

Consider first the case of a perfect pseudobinary melt. From the wide separation of the liquidus and solidus curves in Fig. 2 along any given isotherm, it is apparent that directional freezing of the liquid alloy will result in the formation of solid alloy solutions varying continuously in composition along the growth axis. Tiller (1963) has given Eq. (4) as the condition for the avoidance of constitutional supercooling in the course of freezing such an alloy:

C, = initial melt composition, k = segregation coefficient, m = slope of the liquidus at C,, D = diffusion constant in the liquid, V = solidification velocity, and G = temperature gradient ahead of the interface.

From Fig. 2 the liquidus slope can be estimated to be about 600 K/moie fraction. Schmit and Speerschneider (1968) have reported the segregation

60

W . F. H. MICKLETHWAITE

coefficient k to be 2-4 for initial cadmium telluride mole fractions of 0.02-0.10. Bartlett et ul. (1969) consider the case where the pseudobinary stoichiometry is not preserved. Because of the very high mercury partial pressure in this system, it is very difficult to control the stoichiometry exactly, and frequently the melts are metal deficient immediately before freezing. These authors suggest that for the case of tellurium segregation, the liquidus slope is approximately - 1000 K/mole fraction and considering a typical case of 1 mole % tellurium excess, k is approximately 0.1. Comparing these numbers with those earlier numbers for cadmium telluride segregation in the pseudobinary case, it seems reasonable that tellurium might cause constitutional supercooling before cadmium telluride would. These authors show several results which support this. The criticality of the metal/tellurium balance cannot, therefore, be overemphasized. For acceptable crystal growth, it is absolutely mandatory that this be controlled during all phases of the growth situation. 5.

PURl7-Y

Because of the very strong divergence of the liquidus/solidus lines in the phase diagram, little or no purification is possible by a normal freeze. The classical purification technique of zone refining is made doubly difficult by pronounced segregation into the two binary constituents and the simultaneous, very high mercury overpressure. Some workers have resorted to the expedient of zone refining the two binary subcompounds mercury telluride and cadmium telluride in their own separate furnaces and then combining them in the cadmium-mercury-telluride growth ampoule. Because of the technical difficulties of charging the precise stoichiometric amounts of the two binaries while simultaneously maintaining purity, most laboratories have resorted to directly combining the three elements taken from the purest sources available made usually by repeated distillation or zone refining. Kruse and Schmit (1973) give typical analyses of materials charged to a growth ampoule. Mercury typically contains about 8 ppb of impurities, mainly copper, silver, and gold. The cadmium used contains a total of about 200 ppb, mainly magnesium and silver, while the tellurium used contains perhaps 7 ppm of impurities, mainly excess oxygen and selenium. Since the subject of purification of these elements is discussed in Chapter 2 of this book, it will not be treated further here. Lin (1975) has given analyses typical of the resulting ternary compound for cadmium telluride mole fractions between 0.2 and 0.4. His data are reproduced in Table I. Steininger (1977) lists similar data for material grown by three methods: solid-state recrystallization method, solution-slush

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61

TABLE I DETERMINATION OF TRACE IMPURITIES IN TYPE AND n-TYPE (HgCd)Te BY EMISSION SPECTROMETRY A N D ATOMIC ABSORPTION Concentration (ppm) Impurity

P-tYPe

n-type

Weight of impurity barely detectable (ppm)

cu

0.13-0.61 0.39-0.77 1.2 -1.0 0.8 -1.5 1.3 -1.0

0.1-<0.05

0.05 0.05 1.o

Pb Si Sn

0.1-<0.05

1.0 0.8-1.5 1.o

0.5 1 .O

technique, and the high-pressure reflux technique. His data are listed in Table 11. He suggests that the high-pressure reflux technique is capable of reducing the more volatile impurities; nitrogen, oxygen, chlorine, and potassium, because of the distillation effects in the reflux column. Note that the detection limits given in Tables I and I1 are much higher than those of present analytic techniques and could not adequately define current detector grade material. Bartlett et af. (1980) give data clearly relating the ultimate electrical characteristics to the starting material purity. TABLE I1 MASSSPECTROGRAPHIC ANALYSIS OF (HgCd)Te CRYSTALS GROWN BY DIFFERENT TECHNIQUES Sealed quartz ampoule Element C N

0 F Na A1 S

K Ca

c1

Detection limit (PPm)

Solid-state recrystallization

Solution slush technique

High-pressure reflux technique

0.1

6.6 1.3 2.7 0.3 0.62 ND" ND"

7.5

4.5

1.4

0.58 1.8 0.2 0.78 0.48 ND" 0.29 ND" 0.5

0.1 0. I 0.1 0.05 0.3 5 0.07 0.5 0.3

N D = not detectable.

0.45

ND"

-

7.1 0.3 0.69 N D" ND" 0.72 N Da

62

W.

F.

H. MICKLETHWAITE

6. FURNACE CONSIDERATIONS The technical details of the furnaces required for the various means of crystal growth of cadmium mercury telluride discussed later in this chapter are obviously very specialized and are designed to optimize processing conditions for each application. From the phase diagram, it is evident that it is necessary to contain a very corrosive melt composed of mercury and tellurium, both of which are excellent solvents, at high temperatures (800-900°C) without either contaminating the melt or endangering the experiment and operators. Without exception, the literature reports quartz ampoules as the material of choice in all laboratories. The use of this material which is brittle and not particularly strong at the melt-in temperatures requires that the ampoule diameter be limited, the walls of the ampoule be supported, or the entire ampoule be placed in a pressurized container. The purity and mechanical characteristics of the quartz from each supplier must also be carefully considered, with each laboratory having its preferred source. Bartlett et a / . (1969) reported various surface treatments, for instance, carbon coating, flaming, and so on, but concluded that the original surface of the silica “as supplied” was the best for the growth of cadmium mercury telluride. The ampoule must not be scratched. When the crystal grower profiles his furnace, he is obliged to take into consideration thermal transfer inside the semiinsulating walls of the quartz ampoule. Since excess mercury is present, in any furnace which is not isothermal there must be heat transfer in the mercury vapor column. In some cases, this may take on heat pipe proportions. Bartlett et a / . (1979b) indicate that the 3-mm quartz walls used were a major limitation on heat transfer and caused nonflat freezing interfaces. Another consideration during the compounding of the ternary is the reaction between the elements which takes place exothermically around 400°C.The sudden rise in temperature of the order of 100-200°C can lead to very large mercury pressure excursions unless at least one point in the ampoule is kept cool enough to reflux this mercury through this critical period. Formation of high-melting Cd-Hg-Te compounds begins at quite low temperatures and may seal in unreacted Hg with explosive consequences. This problem is best avoided by inclining the ampoule to maintain a large melt-gas interface as was first described by Harman (1967). 7. CRYSTAL-GROWTH THEORY

No attempt will be made to elaborate on the theoretical aspects of crystal growth here since they have been well described by other authors. The author has found Hannay (1975) to be a useful reference for many of the techniques described here, with chapters dealing with the theory of

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T H E CRYSTAL GROWTH OF C A D M I U M MERCURY TELLURIDE

63

crystal growth, growth from the melt, growth from the vapor, and solution growth. 11. Crystal Growth by the Quench/Recrystallization Method

8. INTRODUCTION As discussed in Part I, the pseudobinary phase diagram for cadmium mercury telluride dictates that there must be severe segregation of the two constituents unless the freezing proceeds very quickly. Bartlett et al. (1969) give data suggesting that the freezing interface should move well in excess of 2.5 mm/h (see Fig. 14). These high freezing rates imply two problems. First, the thermal gradient ahead of the interface must be very high in order to suppress constitutional supercooling as discussed previously, and second, the compound will always freeze as a polycrystalline mass, with or without voids and inclusions depending on quenching conditions.

E

0 0

I

10

20

30

40

Ingot length (mm)

FIG. 14. Effect of crystallization rate on Cd,Hg,-,Te

segregation [From Bartlett ef a/.

( 1969).]

Properly executed, this method can potentially yield single-crystal ingots 1-2 cm in diameter and 2-5 crn in length, having transverse homogeneity better than x &0.005 with a small axial gradient. To obtain these results the metal/nonmetal balance must be precise to avoid precipitates. The recrystallization must be carefully controlled to yield single crystals of random orientation, and a high lattice defect density must be expected. 9. PREPARATION

The three constituent elements are cleaned of all surface oxides and contaminants and stoichiometric amounts are charged to a heavy wall

64

W. F. H . MICKLETHWAITE

quartz ampoule. In addition to the stoichiometric amount of mercury for the compound itself, it is also necessary to compensate for the amount of mercury required to saturate the gas phase. Achieving this compensation is not easy because the thermal conditions in the gas phase are usually different during the melting and quenching procedures. Mercury must then be balanced for either of these or compromised between the two. During either the quench or the melting procedures, stoichiometry of the compound melt will be disturbed, being generally mercury poor and tellurium rich; that is, havingx somewhat greater than the initial charge and y somewhat less than 0.50. The magnitude of these deviations from stoichiometry obviously depends on the free volume of the ampoule. This problem has been addressed by Diet1 and Jarosch (1976) in their patent for a very low free-volume ampoule. In their case, the ampoule was charged by distillation through a very narrow capillary and was filled almost to the top of that capillary before being sealed. As noted by Nelson et uf. (1980), the inevitable minor deviation from stoichiometry will lead to the formation of a second-phase precipitate of either Hg or Te. The former is more readily removed during recrystallization and is less troublesome mechanically. The resorption of Hg droplets has been discussed by Shakhnazarov (1979). The presence of dissolved gases in the charge must be minimized as they result in the formation of voids caused by the trapping of exsolved gases in interdendritic spaces during freezing. A prepared charge is sealed in its quartz ampoule and then placed in a suitable furnace for melt-in. This furnace may be either horizontal or vertical and may consist of one or more thermal zones, depending on the temperature profile and quench means desired. Kruse and Schmit (1973) refer to the use of a gentle rocking motion of this furnace from the vertical to within 15" of the horizontal to maintain agitation and compositional uniformity in the melt during the compounding period. Riley (1977) cautions that the temperature of the melt should be raised slowly through the zone at about 420°C, reporting first an endothermic peak related to the formation of tellurium-mercury telluride eutectic, followed by an exothermic peak as the cadmium -mercury -telluride compound begins to form. There is a considerable danger at this point because of the cooling which tends to freeze higher melting compounds, trapping lower melting ones, particularly mercury, which in turn boil during the exothermic reactions occurring shortly thereafter. This sequence can lead to very dangerous explosions. The molten alloy is commonly raised to 20°C above the liquidus and held at this temperature for 1-24 h for diffusional mixing. Mixing is assisted, if practical, by rocking the furnace.

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65

Immediately prior to quenching, the ampoule and furnace containing it are brought into the desired orientation [usually vertical but on some occasions, as, for example, Schmit (1969), on a shallow angle with the horizontal]. Most workers prefer to use an automated quench sequence in order to adequately control and make reproducible the quenching process. 10. QUENCH Some of the earliest work on the cadmium-mercury-telluride ternary system was done by quenching melts from above the liquidus, out of the furnace into room temperature air. These workers quite quickly learned that this led to to very severe solidification problems, particularly when stoichiometry was not under adequate control. More recently, several authors report moving the charge from the hot zone to a cooler zone in the furnace. This is technically more difficult but it permits much better control. Kruse and Schmit (1973) give some typical details. Their preferred solidification procedure using a three-zone furnace is as follows: Initially, the zone heater at one end of the melt is turned off to establish a temperature gradient along the melt. Subsequently, the temperature in the middle zone is increased for a time and then turned off. Finally, the other end zone is allowed to cool. The exact times used in a particular instance will, of course, depend on the particular furnace arrangement and the amount of the material being prepared. However, it is preferable that the ingot be solidified rapidly enough to minimize long-range segregation. Kruse and Schmit suggest that for a 200-g ingot, a total solidification time of about 2 h is preferred. As a compromise between suppression of macroscopic segregation and the avoidance of a very fine grain size, and other crystalline problems, Parker and Kraus (1969) and Brau (1972) both suggest the use of quenching baths: water and ice baths, various electrolytes, and, in some cases, oil to achieve various quenching rates. These authors also point out that the very high quenching rates associated with liquid cooling media invariably lead to serious or even insurmountable defects in the crystalline structure. In the most severe case, this can be a void pipe running a large fraction of the length of the ingot along the ingot axis, or in a lesser case, the presence of blow holes or other intergranular precipitates along grain boundaries -particularly towards the core of the ingot. These same authors and Schubert et al. (1978) have proposed that complete control over the quenching rate can best be achieved by impinging the flow of a suitable gas such as nitrogen onto one end of the ampoule after mixing. Riley (1977) suggests cooling rates can be controlled easily in the range from 1-8"C/sec for 100-g charges. This can be compared to cooling rates of the order of 70"C/sec when quenching into a water bath.

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W . F. H . MICKLETHWAITE

The low thermal conductivity of solid CMT (Aliev et al., 1978) restricts heat flow along the ingot while the removal of heat from the ampoule is severely limited by the low thermal conductivity of the quartz wall and low emissivity of the shiny CMT surface. Kotsur et al. (1978) and Nelson et ul. (1980) have discussed the rate of solidification as a function of ampoule wall thickness and diameter. Both Parker and Kraus (1969) and Brau (1972), in their respective patents, mention the necessity of avoiding condensing the mercury from the gas phase prior to or during the quenching of the molten alloy itself. By maintaining a high temperature in the gas phase with an insulating jacket, the high mercury pressure necessary to suppress boiling of the alloy can be maintained in the ampoule. By so doing, they avoid disruptive boiling which would otherwise destroy the ingot's soundness during quenching. Their suggested apparatus for maintaining the hot top and using nitrogen cooling is shown in Fig. 15. The general form of the crystalline macrostructure to be expected from a solidification such as this has been discussed by many authors; for instance, Winegard (1964). There are three possible regions: usually a chill cast region with a very fine grain structure around the outer wall of the

FIG.15. Furnace for Bridgman growth of CMT-note lating cap (22). [From Brau (1972).]

gas induction tube (32) and insu-

3. THE

CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

67

ingot at the end which was coldest at quench initiation; an intermediate region of more or less radially oriented columnar crystals; and finally a central core of medium-sized equiaxed grains. The depth of the chill-cast band at the ingot's surface depends strongly on the quenching rate and may be absent completely for relatively slow cooling rates. In this case, the columnar structure will predominate throughout the ingot. If the cooling is exceptionally slow, the central zone will freeze very, very slowly, leaving a more or less equiaxed grain structure of material with very low x . Riley (1977) suggests that an ingot cooled at about S"C/sec will have a predominantly columnar grain structure, with grains typically a few millimeters on a side, whereas an ingot cooled at approximately l"C/sec lacks the columnar structure and has only an equiaxed structure. He also correlates the quench rate with the ultimate grain size of recrystallized ingot with the more rapidly quenched ingots having smaller grain diameters. In a compound semiconductor such as this, there is a tendency for the formation of dendrite arms in the course of freezing [see, for instance, Winegard (1964)l. These are caused by constitutional supercooling, in turn brought on by an insufficient thermal gradient ahead of the moving interface. Schubert et al. (1978) give typical dendritic microstructures for freezing rates of the order of 0.06-0.20 mm/sec and interface gradients of 1-3"C/mm. Bartlett et al. (1979b) give dendrite lengths of 0.5-8 mm for solidification at rates of 2.5 to 3000 mm/h. Vere (1978) discussed the interface type and segregation as the ratio of interfacial thermal gradient/speed (G/R)was varied. As the ratio increases, the interface changes from planar to cellular and the segregation decreases. He reported that as the cooling rate decreased from 10 to approximatley O.Ol"C/sec the dendrite major arm spacing increased from 10 to about 1,000 pm. The interdendritic material is a lamellar eutectic type structure which has one of its phases continuous with dendrite arms. Bartlett et al. (1979b) found the dendrite arms to be CdTe rich while the interdendritic material was richer in HgTe. These reported results have so far dealt only with the stoichiometric case where the material of the dendrite arms will be rich in cadmium telluride. As discussed by Bartlett et al. (1969), in the event of nonstoichiometry where there is tellurium in excess, the constitutional supercooling for tellurium would be substantially greater and the interdendritic material could be expected to be very rich in tellurium, possibly having a second-phase tellurium precipitate. This was reported by Bartlett et al. (1979a). All of the foregoing are with reference to a radially symmetric, cylindrical system chosen because of the optimum burst-strength-to-wall-

68

W . F. H. MICKLETHWAITE

thickness ratio for this geometry. If the wall strength constraint were relaxed, as, for example, when operating within a chamber pressurized to balance the internal mercury pressure, alternate geometries may be advantageous. Merely thinning the quartz walls will alleviate the gross segregation and leave a finer macrostructure. If the geometry is changed to rectangular, the surface-to-volume ratio, hence rate of heat extraction, would be greatly increased. Further, successfully recrystallized material could be economically sawn to the plank form required for second generation device arrays. Such an accelerated quench will make the requirements for perfect stoichiometry even more exacting if second-phase precipitates are to be avoided. 11. RECRYSTALLIZATION

Once quenched to a fine grain, reasonably homogeneous alloy free of voids and other mechanical problems, it is necessary to cause this ingot to recrystallize into a more or less single-crystal boule from which useful slices and fabrications can be taken. Some authors report doing this in the original compounding ampoule, while others such as Riley (1977) report transferring it to a second ampoule for the recrystallization process. In either case, it is necessary that sufficient mercury be provided in the ampoule to maintain at least the cadmium -mercury-telluride decomposition pressure over the soiid during the recrystallization process. Aust (1972) has given the general principles for solid-state recrystallization. He indicates that the controlling factors consist first of the type and amount of driving energy for interfacial motion; second, the presence or absence of any stabilization of the matrix by orientation, texture, inclusions, solutes, or grain boundary grooving; and third, such other variables as prior treatment of the specimen, the overall purity of the starting material, and the annealing conditions, including both temperature and thermal gradient. The first factor is largely controlled by the average grain size, since the disappearance of grain boundary or removal of dendrite interface comprises the driving force for recrystallization. A fine grain size then favors recrystallization and also minimizes the distances across which a boundary must travel in order to completely eliminate the grain or dendrite. The crystallographic orientation of the grains may also have a bearing on recrystallization, since certain orientations will grow preferentially in a thermal gradient. Those of preferred orientations with respect to the gradient would be expected to ultimately dominate the recrystallized structure. The presence of impurity or dopant atoms dissolved in the matrix will slow the process of recrystallization, as will the presence of second phases which tend to pin the boundaries at their junctures. In the event

3.

T H E CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

69

FIG.16. Low-angle grain boundary in CMT. (From Cominco Ltd.)

that the ingot has been transferred from one ampoule to another prior to recrystallization, it is necessary to avoid grooving the grain boundaries by etch cleaning, since this too will pin grain boundaries. An example of the stabilizing effect of orientation is shown in Fig. 16, a photograph showing a low-angle grain boundary, very stable in the axial thermal gradient resulting in a bicrystal ingot. Camp et al. (1976) and Kuwaka et al. (1976) give the general conditions for the recrystallization of a polycrystalline cadmium-mercury -telluride ingot with or without dendritic substructure. In both cases, the initial ingot is cooled very rapidly from above the liquidus by quenching to a solid. It is then held at a temperature just below the solidus temperature (typically 650-700°C) for periods of five to ten days. Riley (1977) has discussed recrystallization thermal conditions for CMT with x of 0.2 in much greater detail and indicated that the optimum recrystallization conditions occurred in a very narrow band of temperatures and pressures. This zone is indicated as an open circle in Fig. 3 for temperatures just below the solidus curve and for mercury pressures just below the zone marked “Solid Dissolved in Mercury.” Schmit and Scott (1976) suggest that the recrystallization rate is improved if the mercury vapor pressure within the ampoule is maintained at a value lower than the equilibrium vapor pressure of the compound at that temperature. Their argument is based on the belief that the interdiffusion of mercury telluride and cadmium telluride occurs by means of mercury vacancies, and that the mercury vacancy concentration in the crystal is determined in turn by mercury pressure. Mercury vacancies increase as the mercury pressure is lowered; therefore, the recrystallization anneal

70

W . F. H . MICKLETHWAITE

proceeds faster under a mercury pressure somewhat reduced from the decomposition pressure. These same authors show data for the microscopic inhomogeneity resulting from the dendritic substructure. On an x = 0.2 slice they reported an inhomogeneity across a 15-mm wafer of x kO.10 in the material as quenched. After the anneal these irregularities have been reduced to about kO.02 and the overall trend variation in x from edge to edge becomes much more apparent. From this it can be seen that a recrystallization anneal not only causes the ingot to become more or less single crystal, but also removes detrimental local inhomogeneities. Several authors have suggested stratagems for improving the efficiency of the recrystallization process. Johnson (1971) has suggested that the polycrystalline ingot should be very slowly drawn through a thermal gradient to a final temperature just below the solidus temperature in order to induce directional recrystallization. In this case, the grain boundaries are caused to migrate from one end of the ingot to the other, leaving a substantially single-crystal ingot of high perfection. Brau and Reynolds (1974) suggest that a single crystal can be nucleated at one end of the polycrystalline ingot by locally raising the temperature above the solidus, slowly cooling to nucleate a single crystal at the solid interface and then using any of the other solid-state recrystallization techniques to propagate the single crystal through the polycrystalline matrix. Schmit (1971) has suggested a variation of this in which the recrystallization temperature is chosen to lie between the liquidus and solidus loops of the phase diagram. This process could be expected to leave behind material of steadily varying composition and is essentially the Harman slush growth process to be described in Section 17.

III. Liquid/Solid Growth 12. GENERAL

The liquid/solid quasiequilibrium methods of crystal growth have always been considered for high-quality semiconductor compounds because of their potentially better crystal structure. However, for a ternary compound such as cadmium mercury telluride with a large difference in liquidus and solidus compositions along a given thermal tie line, the slow moving interface of these equilibrium processes invariably results in a steady variation in the composition of the crystal. In order to find slices of a desired composition, it is then necessary to have a foreknowledge of the inhomogeneity pattern in the crystal and do very detailed mapping. This results in a rather low yield of slices having the target composition and never yields substantial volumes of constant composition bulk material.

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THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

71

These methods have generally been limited to research establishments where a low yield is acceptable and the steady variation in composition can be used to provide test quantities of slices of slightly different compositions. 13. BRIDGMAN GROWTH

The vertical Bridgman (Stockbarger) method of crystal growth was one of the first used for cadmium mercury telluride. In many respects this differs from the quench/recrystallization method only in the rate of freezing utilized. Capper and Harris (1979) have recently published details of a Bridgman furnace system dealing specifically with the problems associated with handling highly toxic and/or volatile compounds in sealed ampoules. They emphasize the problems associated with thermal cycling of the charge, rapid heating or cooling, and many other problems which can lead to the fracture of the ampoule and subsequent explosions. They have accordingly designed a furnace with elaborate temperature controls to avoid thermal cycling or sharp pressure rises caused by rapid temperature increases, while also providing adequate control of the ramping of the furnace for cooling. They have taken elaborate precautions to interlock the furnace controls to protect the operator and the environment in the event of an explosion. Their furnace, which is typical of all Bridgman furnaces, Explosion detector Metallic caniste

Metal guard plotes

Stainless steel tube

Ceramic blanket

Crucible +charge

Adjusting screws

Lower heater section (4 zones)

u

Rototion and lift mechanism

FIG.17. Bridgman growth furnace. [From Capper and Harris (1979).]

72

W . F. H. MICKLETHWAITE

is shown in Fig. 17. It resembles in many ways the furnaces used for the quench/recrystallization method mentioned in Section 1 1 . Boinykh et ul. (1974a,b) report their work on crystals 6-20 mm in diameter for compositions in the 20-24 mole % range. They achieved a crystallization rate (R) of 0.8-8 mm/h by withdrawing an ampoule slowly from an oven which had an interfacial thermal gradient (G) of 50-70 K/cm. For withdrawal rates of the order of 7-8 mm/h they discovered a dendritic structure, frequently with voids or porosity on the order of 3- 100 p m in diameter. The material between the dendrite arms was a lamellar eutectic comprising alternating cadmium mercury telluride and tellurium lamellae. This suggests that their mercury pressure was not under adequate control during the compounding and cooling phases. They report a very high dislocation density of the order of 107/cm2for this material. For slow withdrawal rates on the order of 1-5 mm/h, the material crystallized in relatively large ( 5 - 8 mm diameter) crystals with an internal subgrain structure. These subgrains were misoriented with respect to each other by 0.3-1.5 arc min. For this material, the dislocation density was reported to be substantially worse, by 1-2 orders of magnitude or so, at the circumference of the crystal when compared with that of the center. They also report "rosettes" of dislocations which they attribute to invisible tellurium microprecipitates. At still lower recrystallization rates (less than l mm/h), they report a typical 6-mm grain size with a subgrain structure on the order of 200-700 pm in diameter, having misorientations of the order of 1-3 arc sec. The dislocation density in this material was around 2 x 104/cm2at the leading end of the material and increased steadily towards the tail end where it reached 6 X lo6. They concluded that the optimum crystallization rate was of the order of 1 mm/h in crystals 10-20 mm in diameter, using a furnace with an interface gradient on the order of 50-70 K/cm, but further, that this gave a relatively poor crystal structure and that other .methods might yield better, detector-type material. Dittmar (1978) notes the effect of the phase diagram causing the first material to freeze to be cadmium telluride rich. While the equilibrium partition coefficient for cadmium telluride is approximately 2.5, he shows that it is desirable to take the effective partition coefficient as close as possible to unity using the classical equations for normal freezing. For ingots ofx = 0.2 material having a diameter of about 10 mm and a length of some 100 mm, he worked with freezing rates of 1-40 mm/h in thermal gradients of 25-60 K/mm. He was also careful to control the mercury pressure over the melt in order to avoid tellurium precipitation from offstoichiometry effects. His data for the axial variation of composition in typical ingots are shown in Fig. 18. For a relatively shallow thermal gradient and a freezing rate of 1 mm/h, the effective partition coefficient is

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THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

73

-

XL

FIG.18. Compositional (x) variation with distance for Bridgman crystallization rates of (1) 38, (2) 30, and (3) 1 mm/h. [From Dittmar (1978).]

approximately 1.5 and the homogeneity leaves a great deal t o be desired. However, for higher crystallization rates in correspondingly higher thermal gradients the effective partition coefficient falls as low as 1.13 and there is a long zone of relatively constant composition. Dittmar er a!. (1978) report further work on material with x of about 0.21 caused to crystallize in a gradient of 30-50 K/cm by being transported in a thermal gradient in an oven. They indicate that for adequate homogeneity, thermal control must be held within k O . 1 5 K. For freezing rates less than 10 mm/h, they were able to achieve 30 of 100 mm of the bar length as single crystal, but both radial and longitudinal segregation caused the material to be “not useful for detectors.” For crystallization rates exceeding 100 mm/h there were severe faults in the columnar structure which again negated the material for detector uses. Therefore, they indicate that 25-75 mm/h is the desired crystallization rate, with 40 mm/h being about optimum. For this case they report a radial segregation lying between k0.015 with a best homogeneity of k0.0035 being achieved. Galazka er al. (1979) have reported much lower permissible growth rates for homogeneous material. They give 3 mm/h as the maximum rate under strictly diffusion-controlled growth where gravity (convection) is absent. The thermal gradient was 5-50 K/cm. Homogeneity was found better and Te precipitates fewer in this material (Auleytner et al., 1979). Bartlett et al. (1979b) have considered the effects of growth speed on the compositional variations in x = 0.2 crystals of cadmium mercury telluride. They report results from crystals grown between 0.25 and 300

74

W. F. H. MICKLETHWAITE

mm/h in a vertical furnace using an axial temperature gradient of 100 K/cm at the freezing isotherm. They note that radial composition variations are introduced if the growth takes place with a curved solid/liquid interface and they have attempted to minimize this by operating on a flat freezing isotherm. They also note that the effective partition coefficient of cadmium mercury telluride with respect to the melt can be made to approach unity at relatively high freezing rates as the boundary layer becomes first enriched and then stably saturated with mercury telluride. At higher crystallization speeds, they found that the material was polycrystalline requiring a later recrystallization step as discussed in Part 11. These authors have also discussed in great detail the form and origin of radial composition variation. Two typical results are shown in Fig. 19. Here composition, as indicated by variation in the cut-on wavelengths of the material with distance across the slice, is both greater in degree and more sharply peaked in the case of a rather rapid freezing rate than it is in

Dirtancr across slice (mm)

( a

i

Dirtoncr across slice (mm)

( b )

FIG.19. Variation in IR cut-on wavelength across slice grown at (a) 0.5 rnrn/h, (b) 3000 mrn/h. [From Bartlett e l ul. (19791.1

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

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FIG.20. Change in radial composition variations along crystals grown at (1) 0.25, (2) 0.3, and (3) 0.5 mm/h. [From Bartlett et a / . (1979).]

the case of a much slower freeze. They suggested the variations in radial composition that they observed cannot be fully explained by simply the curvature of the growth interface, since there was a discrepancy between the curvature of the composition variation and that of the interfaces found by suddenly freezing crystals growing at various speeds. They suggest that this discrepancy may be explained by an argument first proposed by Bardsley in a private communication. He suggested that the growth of cadmium mercury telluride in a vertical system was both temperature stable, as the top of the crystal is hotter than the bottom, and also density stable, with an almost planar horizontal interface due to the rejected component (mercury telluride) being denser than the melt and sinking to the bottom of the liquid column. If the freezing interface is slightly concave, this mercury telluride will tend to segregate not only to the bottom, but also towards the center of that interface. This, added to the normal segregation of the low melting point mercury telluride away from the circumferential freezing interface, leads to the large variations observed. They further report the change in radial compositional variation along crystals grown at various speeds as shown in Fig. 20. Note particularly the relatively large increase in the compositional variation for the small increase in freezing rate from 0.3-0.5 mm/h. Figure 21 shows the variation of cut-on wavelengths and corresponding compositions ( x ) across slices from a crystal grown at 0.25 mm/h. The changing form of the radial composition variation is quite evident, as is the overall shift in composition from leading to trailing end of the ingot. Fu and Wilcox (1980) have addressed the problem of achieving a rela-

76

W . F. H . M I C K L E T H W A I T E 17.6

18.6

19.5

-? 0

20.8

$

-m

-E" C

22.3 ._ .;" d

n

., - . . ..

-.

... ....

. r - .. *

4

24.4

~

6 6 1 0 1 2 Distonce ocross slice ( m m )

2

5

0

27.4

31.7

FIG.21. Variation in IR cut-on wavelength across representative slices from several positions on a Bridgman ingot at 0.25 mrn/h-top curve last to freeze, bottom curve first to freeze. [From Bartlett rt a / . (1979).]

tively flat freezing interface mathematically. They investigated a furnace system in which heated and cooled sections of a Bridgman furnace were separated by an insulating section. They found that a judicious choice of insulated length markedly flattened the isotherms (freezing interface) in the radial direction, stabilized the interface shape against system perturbations, and reduced the tendency for convective mixing. The presence of the insulating region had little effect on the interfacial thermal gradient. No papers have yet been published testing their predictions in the practical growth of CMT. 14. ZONEMELTING

Dziuba (1969) reports results for zone melting of crystals 7 mrn in diameter 120 mm long having various xs between 0.2 and 0.8. He used a

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

77

20-mm long, hot zone with the quartz ampoule lowered at approximately 5 mm/h. In this vertical configuration it is interesting to note that there is

a void space between the two liquids in the hot zone. This is due to the initial void necessary for torch clearance when originally filling the ampoule, and could be expected to be filled with a high-pressure mercury vapor during the zone refining process. He reported “several large single crystals” in a typical ingot and apparently good homogeneity over 60-80 9% of the length, but the density method of compositional estimation across entire transverse slices which he used is insensitive to radial variation or local axial variations. His basic method could possibly be improved by repeated inversion to give zone leveling effects. Takase (1974) examined zone leveling in x = 0.2 material. He used crystals 7 mm in diameter, approximately 80 mm long drawn at 0.17 or 2.7 mm/h through a gradient of approximately 40 K/cm. When he found unexpectedly high radial composition variations, he examined the shape of the frozen liquid/solid interfaces at various points along the bar. At 2.7 mm/h he found a strongly curved interface, which was approximately 12 mm convex towards the liquid. Measuring the cadmium telluride concentration across this interface, he found a very sharp drop from solid to liquid. At 1.7 mm/h the curvature of the interface was much less; on the order of 2 mm. His explanation for this was that there was a wide and anomalous diffusion layer of segregating mercury telluride ahead of the interface. This in turn forced interface curvature, which caused radial inhomogeneity. This radial inhomogeneity would, of course, add to the axial variation expected because of the normal freeze situation in this wide phase separation ternary. Nishizawa and Suto (1976) worked with crystals 7- 15 mm in diameter by 80-100 mm long. They used a 30-mm zone width moving at 0.15 mm/h. They report the radial variation in x of less than 0.005, which is very good, although the longitudinal variation is not reported. Steininger and Strauss (1972) suggest the possibility of applying temperature gradient solution zoning. A zone charge about 1 cm long with a composition corresponding to the liquidus and a feed charge about 5 cm long with a composition corresponding to the solidus are sealed in a quartz ampoule. The ampoule is placed in a vertical furnace with small temperature gradient of about 10 K/cm at the temperature corresponding to the selected equilibrium liquidus and solidus compositions. After a period of several days, typically 10, the zone charge is found to have migrated upward through the feed charge, leaving behind crystals having a composition of the feed. These authors caution that success depends on precise knowledge of the equilbrium liquidus and solidus compositions and on good control of the temperature and temperature gradient in the system. They do not report any results specifically for cadmium mercury telluride.

78

W . F . H . MICKLETHWAITE

15. TRAVELING SOLVENT ZONE MELTING In the traveling solvent zone melting method the molten zone consists of an element or compound with a lower melting point than the matrix. This may be either a homosolvent (one of the elements of the compound) or heterosolvent [some other element(s)]. The former are utilized for high-purity, intrinsic semiconductors while the latter can be used for controlled doping purposes. The solvent should have good solubility for the matrix at the operating temperatures which are normally chosen to be as low as possible. This lower solidification temperature has the potential to deposit a more perfect semiconductor with fewer stacking faults and vacancies. There is an additional benefit in the potential purification of the compound by rejection of ko < 1 solutes preferentially to the solvent zone. The major problem with the process is the possibility of constitutional supercooling through too rapid or jerky interface motion. If this occurs, the solvent will tend to be incorporated in second phase precipitates in the semiconductor matrix. Very good control of growth rate and interface thermal gradient are mandatory. Ueda et nf. (1972) report the solution growth of cadmium mercury telluride using the vertical zone melting technique with tellurium as the solvent. The initial charge of CMT was prepared by compounding previously purified mercury telluride and cadmium telluride in an 8-18 mm ampoule and then quenching it to a solid. After this the ampoule was opened, the ingot was cut and a mixture of pure tellurium and cadmium-mercurytelluride alloy was placed between the two portions of the ingot. This mixture forms a liquid zone during a crystal growth when it is raised in a zone furnace to approximately 750°C.The mixture was allowed to soak for a sufficient period to establish equilibrium between the quenched ingot and the molten materials and then the ampoule was lowered through the hot zone at a rate of 0.2-0.3 mm/h. After the first zone pass, the ampoule was removed from the furnace, inverted, and then again run through the furnace in the opposite direction after a preliminary soak to reestablish a compositional equilibrium. They found that the compositional uniformity of cross sections of ingots was significantly improved by reducing the volume of the liquid zone and also by flattening the shape of the liquid-solid interface. The former assists the latter. For a slice taken longitudinally through a diameter of an x = 0.2 crystal, they report lateral variations in composition of -.0.15-r0.25%. These authors also note the effect of purification by the liquid tellurium, making the crystal lower in carrier concentration than material made by conventional zone melting methods, and also the avoidance of explosions caused by the high mercury vapor pressure over pseudobinary melts.

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

79

Itoh et al. (1980) and Ueda (1980) confirm that radial homogeneity is dominated by the shape of the liquid-solid interface. They have improved the method of Ueda et af. (1972) by adding a nuclear grade graphite rod to the lower end of the ampoule to act as a heat sink and maintain an axial heat flow in the system. This flattens the freezing interface and results in a radial inhomogeneity of less than 0.2%. Only a single pass is used with this modified system. Triboulet (1977) reports the preparation of cadmium mercury telluride with x = 0.9 using the traveling solvent zone method with tellurium as the solvent. His source material was a cylinder 15 mm in diameter consisting of two cylindrical sectors. The inner (small diameter) one being mercury telluride and the outer (annular) one cadmium telluride, whose cross sections were in a ratio corresponding to the desired x. This method of combining, purifying, and growing single crystals from previously prepared binaries has been patented by Gallet et al. (1977). He reports that for the x = 0.9 composition with a liquidus point of about 1,062”Cthe principal growth parameters were a 700” growth temperature and a growth rate of approximately 3 mm per day. The growth direction did not correspond to any low index crystallographic axis, but homogeneity was very good when measured with an electron microprobe. He reports “no composition variation has been found in sections cut normal to the growth axis and the greatest part of the ingot presents a very satisfactory homogeneity.’’ The longitudinal variation of composition is shown in Fig. 22. Note particularly the transients at the leading and trailing ends while equilibrium is being established. He also suggests this method is useful for the introduction of dopants such as chlorine to the crystal during growth. In the same paper he mentions the presence of tellurium precipitates in growth of cadmium telluride by a similar process. These might also be expected

0.85 I 0 1 Heod

2

3

4

5

6

7 End

Distance along ingot (cm)

FIG. 22. Dependence of composition on position along the growth axis for a Te solution-grown ingot of C&.pHh.,Te.[From Triboulet (1977).]

80

W. F . H. MICKLETHWAITE

in cadmium mercury telluride, although they are not reported in this paper. The solvent zone may also be made to migrate in the charge using a stationary thermal gradient rather than a moving ampoule or furnace. Because of the very low crystallization velocity during the diffusioncontrolled traveling solvent zone process, constitutional supercooling and other thermal disturbances can be effectively suppressed. Therefore, this method has poteitial for greater success in growing solid solution alloys in nonstoichiometric systems. Bansaragtschin et ul. (1976) have reported the use of this system in lead-tin telluride using a lead-tin alloy lamella as the solvent zone. 16. THE CZOCHRALSKI METHOD

The Czochralski method, which has proved so useful for elemental and binary semiconductors, generally gives a great deal of trouble with ternary semiconductors such as cadmium mercury telluride. Here there is a very high mercury pressure that must be controlled and contained in order to avoid problems with stoichiometry and explosions. There will be vision problems and, of course, the radical segregation along the axis of the crystal caused by the phase line separation. The use of a floating crucible to limit natural segregation or nonconservative modes of crystal growth [see Carruthers in Hannay (1975) in which the charge composition is altered steadily by additions during growth] might limit segregation to tolerable values. Parry (1976) reports the growth of CMT in a highpressure furnace under inert gas. The 25-mm, 200-g charges were solidified under programmed cooling to give homogeneity in x of 20.015 both axially and radially. This equipment tends to be very expensive and requires critical pressure control over all of the growth period if stoichiometry is to be preserved, but does simplify the manipulation of the charge materials. Wagner and Willardson (1968) report the growth of lead-tin telluride under boric oxide and atmospheric pressure. Even in the low vapor pressure system of Pb-SnTe it was still necessary to operate metal-rich in order to suppress tellurium loss, so it seems improbable that a flux covered atmospheric system would be practical for the much higher pressure (CdHg)Te system. In general, it seems that the Czochralski technique is not suited to high-pressure systems such as those necessary to produce CMT. 17. SLUSH GROWTH

Harman (1970, 1972) proposed a new method of growing pseudobinary alloys. A charge of the alloy is prepared by conventional methods and lowered quickly to a new position in a vertical furnace so that the bottom

3.

T H E CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

81

part of the liquid is quickly frozen. A temperature gradient of approximately 10 K/cm is imposed along the material in the vicinity of the solid/liquid interface. After a long period of crystal growth and annealing, the ampoule and its contents are finally cooled to room temperature by turning off the furnaces. He reports that a high-quality single crystal is found in the solid region adjacent to the portion of the solid/liquid interface just prior to cooling. The proposed mechanism for crystal growth can be explained with the help of Figs. 23a and 23b showing the phase diagram of the Cd,Hg,-,Te system and a schematic temperature profile of the vertical furnace in which temperatures rise with increasing distance from bottom of the furnace. An ampoule containing an alloy charge of overall composition x = b is placed in the furnace in position 1 . The charge will be entirely molten since the temperatures along the ampoule are all greater than T A , the liquidus temperature for x = b. If the ampoule is quickly lowered to position 2, the charge will divide into three different regions. In region A, the top of the ampoule, where the temperatures still exceeds T A , the charge will remain liquid with x = 6 . In the intermediate region B, where the temperature increases from TBto T A ,there will be a two-phase mixture or ''slush'' of liquid and solid whose overall composition is x = b. In region C, at the bottom of the ampoule, the liquid will freeze very rapidly because temperatures are less than TB, the solidus temperature for x = b. Because of the high freezing rate, the solid formed will be of essentially uniform composition x = b as described in Part 11. The driving force for crystal growth in this method is supplied entirely by the chemical potential difference between the Cd,Hg,-,Te at the B-A interface and at the C-B interface. Thus, due to the potential gradients across the slush region, both cadmium telluride and mercury telluride will

I,

MOLE FRACTION OF NT

DISTANCE FROM BOTTOM OF FURNACE-

( 0 )

(b)

FIG.23. (a) Schematic pseudobinary MT-NT phase diagram. (b) Schematic temperature profile of the growth furnace showing charge position, liquid fraction (region A), and solid fractions (regions B and C ) after achievement of steady state. [From Harrnan (1972).]

82

W. F. H . MICKLETHWAITE

diffuse across the slush region: cadmium telluride diffusing from the B-A interface to the C-B interface. As cadmium mercury telluride content of the slush increases at the solid-slush interface, CMT solid with x greater than h must freeze out at this boundary forcing the interface to move; that is, crystal growth occurs. The interface will continue to move upward and finally the composition of the freezing material approaches x = a as the overall steady state for the system is approached. Harman proposes certain unique advantages to crystal growth by this system; first, that equilibrium growth may be approached more closely for a system involving a mixture of solid in intimate contact with the liquid, and second, thermal and hydrodynamic stability may be enhanced at the crystal-growing interface as convective flow is minimized. A third advantage which may contribute to high-quality crystals is the fact that the material is solidifiedjust below the solidus temperature-a condition that favors single-crystal growth by recrystallization as discussed earlier. A fourth advantage is that solidification occurs in the presence of an equilibrium liquid to which excess constituents can be rejected rather than forming inclusions or precipitates. Should such inclusions or precipitates happen to form they will tend to migrate out of the solid by the principle of temperature gradient zone melting as discussed earlier. Harman reports results on a 200-g CMT crystal grown in a quartz ampoule 18 mm in diameter and 1 I5 mm long. The elements were reacted, allowed to stabilize, and then the bottom of the ampoule was lowered in a fraction of a second by about 200 mm to a new position in the furnace where part of the charge was converted to the slush and part to a quickly frozen solid. The larger fraction of the charge remained in a slush state. The temperature gradient in the vicinity of the solid slush interface was about 10"C/cm. The ampoule remained in this position for approximately 44 days at which point the power was turned off and the material was examined to reveal the composition profile shown in Fig. 24. The starting charge had an overall composition of x = 0.06. In region C, electron microprobe measurements showed that the cadmium telluride content varied randomly about x = 0.06 and much free tellurium was present. Region B was a high-quality single crystal with a uniform (r0.005) composition in the direction normal to the crystal-growth direction. This method was adapted by Cominco for the production of bulk, detector grade CMT. Riley (1977) reports similar results in his work. Fiorito et ul. (1978) proposed an improvement on this technique. They suggested that a third zone containing feed liquid should be added to the arrangement used by Harman. Provided the crystallization rate does not exceed the diffusion rate through the slush zone, the liquid of the slush

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

O

0

L

02

I 04

I

06

I

00

I 10

83

I

y. FRACTIONAL DISTANCE ALONG INGOT

FIG.24. Composition profile along a 11.5-cm Cd,Hg,-,Te ingot grown by the Harman technique. 0, electron microprobe analysis; 0, density measurements. [From Harman (1973.1

zone will not be depleted during crystallization. There would then be an initial Harman-like transient followed by a long period of steady state with constant composition freezing onto the solid, the slush zone remaining constant and the liquid phase decreasing. Once the liquid zone is depleted, normal Harman growth kinetics will continue. In their method, Fiorito and co-workers proceed by compounding the alloys conventionally in a quartz ampoule and then quenching to room temperature. The ampoule is then reversed vertically so that the void formerly at the top of the ampoule now is at the bottom and this zone is raised to a temperature above the liquidus. The top of the furnace is profiled to maintain a small fraction of the original charge as a solid while the large central zone is held at temperatures in the liquid-solid loop. They claim that this geometry, which is the inversion of that used by Harman, leads to thermohydrodynamic stability in the melt and better mixing. They have reported results for charges of the order of 12- 13 mm in diameter and up to 250 mm in length. They found that the solidification interface under experimental conditions was substantially flat and radially symmetric, giving an inhomogeneity transverse to the growth axis less

84

W. F. H. MlCKLETHWAlTE

than 0.01 inx over 80% of the interface. The rate of change of composition reported in the axial direction is very much less than that reported by Harman, being of the order of 5 mole % in approximately 100 mm of length.

18. REPLENISHEDSOLUTION GROWTH Rodot and Fumeron (1979) have patented a method of solution growth for binary compounds in which three temperature zones are established along a vertical quartz ampoule with steep gradients between them. A liquid is first saturated with a second constituent by control of a vapor source. When one end of the ampoule is cooled, the saturating species tends to crystallize out as an equilibrium solid. The patent refers to binary compounds, but the author believes that the technique could be modified for use with the pseudobinary CdTe and HgTe. The pseudobinary crystallizing will be of constant composition, all other conditions being maintained constant. A seed of CdTe could be introduced in the cool zone to cause bulk epitaxial crystallization of controlled orientation. The pseudobinary case might best be tested using the lower melting compound HgTe as the solvent and feeding Cd and Te or CdTe at a controlled rate. The vapor pressures of Cd and Te are somewhat closer than the other pair (Hg and Te), hence problems of congruency of vaporization would be reduced. Prereaction of the elements in the vapor space need not be avoided if the resultant particles dissolve readily. The density gradient in the melt would be stable, inhibiting rollover but limiting the growth rate to the diffustion rate of Cd and Te through the melt. This will be a high-pressure system. A better choice might be continuous feed of Cd and Hg vapors from separate sources to a Te solvent using the solubility data of Section 3 for guidance. This would be a low-pressure system. Density gradients would require a jucidious choice of the points of introduction of Hg and Cd or even baffling to avoid unstable or cyclic melt convection with attendant compositional variations. If convection could be stabilized under steady flow conditions the growth limitation of the diffusion rate could be eliminated. This condition would favor the use of a large melt which would be more self-stabilizing against perturbations than would the “thinner” system required for adequate growth rate in the diffusion limited case. The convective case would probably result in worse radial composition variations in the solid than the diffusion case. One benefit of these systems would be the tendency to purify the starting materials both by an in-process distillation step and also the normal liquid- solid partitioning of impurities at the freezing interface.

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURlDE

85

IV. Epitaxial Growth 19.

INTRODUCTlON

The growing popularity of epitaxial means of growing cadmium mercury telluride stems not so much from the ease of growing material this way, but rather from the difficulties in achieving the desired ends by the other means of crystal growth discussed earlier. With the exception of seeded Bridgman growth (which has not yet been reported for CMT to the author’s knowledge) the growth direction of a CMT single crystal grown by the quench/recrystallization method or the liquid/solid methods cannot be controlled to those orientations desired for device fabrication. The crystal perfection is at the mercy of the growth kinetics, and the homogeneity suffers from the segregation inherent in these two means of crystal growth. However, the greatest present impetus towards the epitaxial growth techniques is that the previously mentioned methods are unable to achieve the minimum dimensions required by presently projected electrooptical device array sizes. The prospects for epitaxial growth are favored by the availability of next-to-ideal substrates in the form of cadmium telluride or mercury telluride. In the entire mercury telluride-cadmium telluride pseudobinary system there is only a 0.3% variation in the lattice parameter. This leaves the choice open between cadmium telluride and mercury telluride, although cadmium telluride is generally preferred because of its higher melting point and ready availability as single crystals of reasonable size (15-30 mm in diameter). CdTe is also a semiinsulator and transparent to infrared radiation, which makes it an excellent substrate for CCD and other detectors. For epitaxially deposited working layers there are no epoxy or other mounting problems so the device can be fabricated directly from the CMT/CdTe structure. As mentioned earlier, the choice of epitaxial growth is merely the choice of the least of several evils. There are still a great number of problems with epitaxial growth, one of which is the fact that there are three degrees of freedom with the (Cd,Hg,-,),Te,-, system which in turn insist that very rigorous controls be imposed on the system during growth. Generally, there are high pressures under melt conditions, and simultaneously containment-purity problems associated with these three elements, which are excellent solvents. Perhaps the most difficult problem to conquer has been the persistent and radical variation in composition (x) with depth in the epitaxial layer. If such a steep gradient is present, it becomes very difficult to fabricate a device in the chosen layer in order to have response at a chosen wavelength.

86

W . F . H . MICKLEIHWAITE

20. LIQUIDPHASEEPITAXY (LPE) a. Pseudobinary Melts Maciolek and Speerschneider (1975) report the epitaxial growth of cadmium mercury telluride onto various substrates from pseudobinary melts. The melt was formed and stabilized just above the liquidus temperature within a closed quartz ampoule with a CdTe substrate 7.5 mm in diameter mounted at the opposite end. Provision was made to cool the substrate by either impinging a cooling gas on the outside of the ampoule or alternatively by cooling the entire ampoule assembly. Once thermal stability had been achieved, the entire assembly was inverted, causing the melt to first flow and then to crystallize onto the substrate surface. After a desired interval the ampoule was inverted back to its original position decanting the remaining melt. From the phase diagram it is evident that the first solid to form from a given composition has a substantially higher x. For example, from a starting melt of x = 0.1 the first solid to freeze will have a composition of approximately x = 0.4. In the liquid-solid bulk growth methods discussed in Part 111 a substantial fraction of the liquid freezes, while in this epitaxial system only a small volume of solid freezes from a large volume of melt so the composition of the melt does not change substantially during growth. As a result, the epitaxial layer should show very little compositional variation throughout the thickness of the film. However, results show that the epitaxial layer is far from constant composition and instead varies from an x of 1.0 on the substrate to approximately x = 0.20 some 100 pm into the epitaxial layer. This is shown in Fig. 25. These authors report results for several modes of crystallization. In the simplest mode the

x Cd -re 0 40 0

a

'0

20

SUBSTRATE

0 1

V

10 0

20

40

60

80

100

DISTANCE ( F m )

FIG. 25. Composition profile as a function of depth Cd,Hg,-,Te deposited epitaxially CdTe from a pseudobinary melt. [From Maciolek and Speerschneider (1979.1

onto

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

87

melt is undercooled approximately 100°C when it strikes an externally cooled substrate. Other results are given for the slow cooling of the entire melt-substrate combination at various rates. The authors report that the more rapid the cooling rate, the steeper the compositional gradient ahead of the cadmium telluride interface into the epitaxial layer. The compositional gradient is attributed in part to diffusion between the cadmium telluride substrate and the CMT layer after its growth. In one experiment a CMT layer was quenched from the growth temperature (about 700°C) to room temperature shortly after decantation of the excess solution. In this case the compositional profile showed a steeper compositional gradient than a sister layer grown under similar conditions but not quenched after growth. Note, however, that the compositional gradient is still present. Part of the gradient may be due to dissolution of some of the substrate on the initial solution contact followed by x higher than that expected from the solution charged to the system. Maciolek and Speerschneider also report their results on attempts to grow epitaxial CMT layers on other substrates. Germanium was unsatisfactory as it dissolved and no growth was possible. Silicon substrates gave problems with nucleation which they attributed to the formation of surface oxides, however, growth was possible on a silicon substrate precoated by a sputtered coating of cadmium telluride. Similarly, growth was possible on magnesium aluminum spinels and sapphire substrates after a sputter coating of cadmium telluride. Metallographic observation of layers deposited on cadmium telluride substrates showed an excellent bond between the as-grown film and the substrate. Additionally, structural characteristics of the cadmium telluride substrates were observed to continue into the CMT layer. This behavior is, of course, indicative of excellent bonding and true epitaxial growth. Similar results are reported for spinel and sapphire substrates which had been sputter cleaned and precoated with cadmium telluride. Generally poor results were recorded for silicon substrates. Substrates other than cadmium telluride are desirable for epitaxy in that they avoid the worst of the cross diffusion caused composition gradient problems shown in Fig. 25. Bowers et al. (1980b) recently reported further work on the pseudobinary system indicating that for layers grown 30-50 pm thick onto CdTe substrates it was possible to achieve constant composition layers of x = 0.4 material. In-plane homogeneity was said to be inferior to similar Te solvent grown layers. They also established that part of the gradient of Fig. 25 was due to Hg transport onto and diffusion into the CdTe substrate during the equilibration stage preceding the submersion of the substrate into the melt. The above authors also claim that as grown n-type orp-type

88

W . F . H . MICKLETHWAITE

layers are possible with this technique using Hg pressure control and the rapid diffusion occuring at the high growth temperatures. The Te and Hg solvent systems were said to yield only p-type layers.

b. Solvent Systems Of the two most promising solvent systems, tellurium and mercury based, the former has received most of the attention to date because of the lower operating pressures and relative ease of manipulation.

I . Tellurium-Based Harman ( I 979a,h) Harman and Finn (1978), and Harman (1980) have recorded their experiments with tellurium solutions. Their LPE growth was carried out in a horizontal slider system using tellurium-rich cadmium-mercurytelluride solutions prepared by saturating tellurium-rich Hg,-,Te, melts by preequilibration with a cadmium telluride source seed at temperatures some 25°C higher than the ultimate growth temperature. For the initial melt compositions used, the equilibrium mercury vapor pressures are in the range of 0.15-0.6 atm for the melt equilibration temperatures of 500-550°C. In order to avoid unacceptable mercury losses associated with a conventional open tube system, they employed a modified open tube, horizontal slider-type system with an externally generated mercury pressure over the solution well. The substrates for this growth were cadmium telluride-selenide, oriented ( 1 1 1) B. This material was originally chosen for its ability to precisely lattice match the epitaxial layers. However, they claim that two other advantages later became apparent. First, it was found that small cadmium selenide additions to cadmium telluride resulted in the growth of larger and more frequently single-crystal seed material and second, the LPE films of CMT on cadmium tellurideselenide appeared to be of higher quality than those grown on cadmium telluride substrates. Harman also reported his determinations of the lattice constants of both cadmium mercury telluride and cadmium selenide-telluride as shown together in Fig. 26 for lattice matching purposes. An initial melt of 1.5 g and a 9-mm well were used. A melt was first equilibrated for a period of about 50 min with a CdTe source wafer, which was then removed. The Cd(Te,Se) substrate was then slid under the melt which was cooled for about 52 sec at 8"C/min, causing growth. Layers of approximately 3 p m in thickness were grown having a triaxial surface morphology with features approximately 1000 A high. This surface morphology is typical of good quality single-crystal film grown on (1 1 1) substrates. Results are reported for the growth of CMT films with x in the range of 0.44-0.82. These papers also report pulsed laser emission for samples of all these compositions and continuous emission for x = 0.44.

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE

89

w, MOLE F R A C T I O N CdSe 5

6.482 6.480

-

6.478

+

6.476

2 v,

6.474

$

6.472

oa

z

L

6.464 6.462

6 460

05

I(

x , MOLE FRACTION CdTe

Fic. 26. Lattice constant versus composition for Cd,Hg,-,Te and CdTe,-,Sew experimental points based on (444) plane x-ray data. [From Harman (19791.1

.@

Harman suggests that this first report of cw laser emission can be attributed to the low-temperature LPE growth from a tellurium-rich CMT solution, yielding material with a reduced density of nonradiative centers. Wang (1978) and Lanir et al. (1979) report the growth of CMT epitaxially onto cadmium telluride substrates of either (111) or (100) orientation. A tellurium-rich solution is used as source and the growth temperatures vary around 500°C depending on the composition. The depth of mercury penetration into the cadmium telluride substrate by cross diffusion is reported at less than 3 pm as measured by electron microprobe analysis. x constancy across the wafer is reported at 20.004. The material is reported suitable for photovoltaic devices but too high in carrier concentration (2 x 1015/cm3at 77 K) for photoconductive devices. Bowers et af. (1979) and Schmit and Bowers (1979) report results for the epitaxial growth of CMT layers onto cadmium telluride substrates from both pseudobinary and tellurium-rich melts. The first system was as described earlier in Section 2 0 4 requiring closed ampoules to contain the mercury pressure of several atmospheres at typical growth temperatures of 750°C. The second system was an open tube, slider-type system made possible by the lower mercury vapor pressure over tellurium-rich solutions. Using the open tube and slider system may make possible the growth of multiple layers of different compositions by using several wells under different conditions and also the manipulation of large-area layers. The above investigators first determined the liquidus temperature data

W. F. H. MICKLETHWAITE

90

for the tellurium-rich ternary compositions as reported earlier in Section 3. With this they were able to grow epitaxial CMT layers having x in the range of 0.2-0.4 on substrates of several orientations. Closely oriented ( 1 1 1) A and (1 1 1) B orientations and slightly misorientated ( I 11) A, (111) B, and (100) substrates were all found to be suitable. The layers were found to be microscopically smooth but displayed gentle undulations of less than 1 pm in amplitude. Typical layers displayed pinhole densities of less than 100/cm2. The transverse homogeneity of layers in the 0.34-0.4 range are reported as kO.01 in x. Figure 27 gives the variation in composition as a function of distance from the substrate. The profile of a typical layer grown from mercury -telluride-rich solution at 700°C shows a much broader profile with deeper diffusion depth than that for growth from tellurium-rich solutions at 500°C at which temperature interdiffusion is maximized. Their x = 0.40 material was p-type as grown, with 77-K carrier concentration of 1 x 101'/cm3,and could be annealed to n-type with a camer concentration of 4 x 1015/cm3at 77 K. The mobility of the n-type material was approximately 4.7 x lo3 cmZ/V sec at 77 K, roughly a quarter of that found for bulk material grown by the quench-anneal method.

0.a -

5

OBINARY (700. C)

0.6-

P kV

a LL

0.4 J

-

-

0

z 0.2

0

,

\"

,

I

I

FIG.27. Comparison of composition profiles vs. distance from substrate for Cd,Hg,..,Te deposited epitaxially onto CdTe from pseudobinary Te-rich and Hg-rich melts. [From Bowers el a / . (1979).]

3.

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Lanir et al. (1979), Wang et al. (1980a,b), and Chu and Wang (1980) used a pressurized (15-20 atm of H,) vertical dipping system using Te solvent and CdTe substrates. The (111) A face was found optimum for growth of material 0.2 < x < 0.5. The surface morphology showed the wavy texture mentioned by other authors but was specular, indicating good epitaxy. The material was p-type as grown with values similar to bulk grown material. It was successfully annealed to good n-type or low carrier p-type material. In-doping was demonstrated using In-doped CdTe substrates or doped growth solutions. Possible limitations to this vertical system include pressure limitations on the containment and variation in epilayer thickness (center is thinner than the edges) but homogeneity at a0.002 in x was exceptionally good. 2 . Mercury Bases Schmit and Bowers (1979) report a private communication of work by R. Maciolek for the growth of CMT layers epitaxially from mercury solutions. They reported mercury pressure is typically 8 atm for growth temperatures of about 500°C which makes open tube growth impossible. This mercury pressure can be lowered by reducing the growth temperatures, but temperatures below 240°C are required to keep the pressure below the 0.1 atm considered the maximum acceptable for open systems. No details are given of the quality or size of the layers grown by this technique. This work was elaborated upon by Bowers et al. (1980a) giving detail that the layers were grown at 460°C by immersion of 8-mm CdTe substrates. From Fig. 27 it is apparent that there is no constant composition region for Hg solvent systems. The diffusion constants necessary to explain this steep gradient solely by diffusion exceed those of Baley (1975) by orders of magnitude indicating that this is not the governing mechanism. Bowers et al. (1980a) attribute the rapid composition change to Cd depletion of the melt due to the low initial Cd content of high Hg melts. Wong and Eck (1980) report their work in a large system using Hg solvent and (111) B CdTe substrates. The melt is first saturated with Cd and Te to achieve the desired Te: CdTe ratio (typically 500: 1-1200: 1) necessary to yield the target epilayer composition. The temperature is then ramped down to cause layer growth by supersaturation. The optimum rate was established to be - 0.1 K/min with faster rates degrading morphology while slower ones reduced compositional uniformity through thickness. These authors also report considerable detail regarding the quality of the substrate and control of growth parameters on the quality of the epilayer. Details are given of a computer controlled furnace system suitable for kO.1 K control said necessary for LPE.

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Pollack (1979) and Vanier et al. (1980) report the epitaxial deposition of cadmium mercury telluride onto a CMT substrate from a CMT source pellet utilizing the electromigration in a mercury bath. The source and substrate were immersed in a mercury bath at approximately 250°C with mercury reflux condenser above. Using a current density of 28 A/cm*, a layer 50- 100 pm in thickness was deposited in 45 h of operation. The x of the deposited layer was substantially less than that of the source layer and the deposit on ( I I I) substrates gave a surface morphology with tetrahedral pyramids.

21. VAPOR PHASEEPITAXY (VPE) The VPE methods of epitaxially depositing CMT have been under active investigation for more than a decade because of the potential for very large and/or multiple substrates and the tendency to purify the source materials by distillation. However, because of the much lower deposition rate and greater tendency for interdiffusion in the deposited layer in VPE than LPE and the tendency for prereaction of constituents in VPE systems, current emphasis seems to be concentrated on the LPE systems. a . Reactive

There have been several reports of methods to directly combine the three constituent elements to form the ternary in a vapor phase system. Such systems tend to be technologically complex with at least four temperature zones, all of which need to be precisely controlled. There are difficulties in suppressing prereaction of the constituents before they arrive at the substrate and also controlling homogeneity across the surface of the substrate due to lateral thermal variations. Manley et ul. (1971) obtained a patent for a hydrogen transport system with independent furnaces for elemental cadmium, tellurium, and mercury sources. The constituent gases in their carrier streams were thoroughly mixed and maintained at a temperature sufficient to prevent the formation of binary combinations. In the immediate vicinity of the substrate there was a very steep thermal gradient having equithermal lines substantially parallel to the growth surface of the substrate in order to promote uniform deposition. The substrate of their example was cadmium telluride with (100) orientation. It was retained by a spring clip against a thin quartz wall, in turn cooled by a large silver heat sink whose cooling could be controlled by adjusting the cooling air flow. The growth sequence was initiated by first evacuating the system and then heating the substrate preferentially, driving off surface contaminants and a small amount of the constituent elements to further clean the surface of the substrate. Following this, the mercury and cadmium furnaces were energized, and when the source temperatures were reached the hy-

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drogen gas flow was commenced. Lastly, the tellurium source furnace was energized to volatilize tellurium into the hydrogen gas. Simultaneously, cooling air was supplied to the heat sink to drop the temperature of the substrate to the desired film growing temperature. Composition in this system is said to be controlled by fixing the cadmium source temperature (and thus Cd partial pressure) and then varying the amount of tellurium in the gas stream. When the amount of tellurium is stoichiometric with the amount of cadmium, only cadmium telluride will be formed and there is little tellurium available for the reaction with mercury. By adding tellurium in excess of the cadmium stoichiometric amount some free tellurium is available to react with and incorporate mercury into the growing crystal lattice. With the substrate temperature sufficiently low, the supersaturation of tellurium and mercury in the gas is sufficient to cause a complete reaction on the substrate. Under operating conditions, the substrate temperature tends to rise 20-50 K, which does not appreciably affect the cadmium tellurium reaction but does modify the mercury tellurium reaction. Thus, chemical composition can be controlled by adjusting the ratio of constituents in the gas phase and by controlling the substrate temperautre. Growth times were approximately 2 h. Carpenter et al. (1971) have patented a variation of this system in which mercury vapor acts as the carrier gas as well as being one of the reagents. Again there are independent cadmium and tellurium sources under individual temperature control, each contributing to the gas phase which is maintained at a high temperature until it reaches the immediate vicinity of the substrate, as in the previous example. Once again the substrate is cadmium telluride of ( l l l ) , (110), or (100) orientation held by a clip to a quartz plate which is in turn heat sinked by a large mass of silver cooled by an adjustable air flow. A steep thermal gradient is maintained near the substrate so that the reagents do not react to form binaries beforehand but are quench cooled to supersaturation adjacent to the substrate. Any mercury in the system is recondensed and cycled back through the furnace in much the same manner as a mercury diffusion pump. Typical operating conditions are cadmium source temperature of 440"C, tellurium source temperature of 520"C, and the presubstrate gas phase maintained at 460°C. The substrate temperature is maintained at a temperature of 280°C. For a typical run time of 1.25-250 p m thick was produced having a composition of x = 0.2. No data are given for the uniformity of the layer across the substrate. Vohl and Wolfe (1978) give an example of another hydrogen transport system which was said to be able to give compositions covering the entire alloy range of 0 < x < 1.0. The substrate temperature is controlled in the range of 400-550°C and the partial pressures of the three constituent elements are independently controlled using separate elemental sources.

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F. H . MICKLETHWAITE

Those authors have considered in some detail the dependence of layer compositions on these gross parameters. Because of the high mercury vapor pressure, the dissociation constant for mercury telluride is many orders of magnitude greater than the corresponding constant for cadmium telluride. If a constant mercury to cadmium ratio is maintained and tellurium partial pressure is slowly increased, the cadmium telluride reaction quickly becomes quantitative, followed by an increasing and eventually quantitative reaction forming mercury telluride (Fig. 28). By choosing the

a, c

e

f

3

e

a

FIG.28. Schematic plot of the growth rates of CdTe, HgTe, and their sum as functions of PTe. [From Vohl ei al. (1978).]

appropriate tellurium partial pressure it is then possible to control the x if all other factors are held constant. At a given substrate temperature, increasing the mercury to cadmium pressure ratio causes an increase in x . The dependence of x on substrate temperature T , is rather more complicated because of the tendency of cadmium telluride to condense upstream of the substrate; however, this makes it possible to obtain alloys closer to the mercury telluride end of the composition range than would otherwise be possible. The authors also note that in the temperature range wherex is changing with the substrate temperature, a slight variation of temperature across the substrate results in a lateral variation of the alloy composition. Epitaxial growth was carried out in a cross-shaped, vertically mounted, fused silica reactor. Elemental cadmium and tellurium sources occupy the two horizontal arms, mercury the vertical, each being independently heated. The substrate is mounted on an air-cooled quartz finger in the bottom arm. The tubes connecting the three source reservoirs to the reaction chamber were carefully sized to avoid excess pressure drop in the mercury arm and back streaming with the attendant reaction in the tellurium arm. The gas exit from the system is constricted to maintain the highest possible mercury pressure at the substrate, the temperature of the mixing

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zone is maintained at approximately 720°C while the substrate is maintained at 400-550°C. Growth was continued for 4-5 h and then the temperatures of the layer and gaseous reagents were carefully lowered together to maintain stoichiometric balance in order to prevent layer dissociation. Growth rates of 1.2-3 pm/h were reported. The authors report that layers grown on (100) oriented substrates were quite smooth and specularly reflecting, while those grown on (1 10) and (1 11) substrates were significantly rougher. Figure 29 shows an electron microprobe scan across a cleaved epitaxial

r

H

0.4

0.2

+

'0

2

4

6

8

10

12

14

Distance (pm)

FIG.29. Composition variation with depth as determined by electron microprobe for a VPE layer of Cd,Hg,-,Te. [From Vohl er ul. (1978).]

layer. The last 5 pm to form have a relatively constant composition at approximately x = 0.3 while the 7 pm adjacent to the substrate show a graded composition. The authors attributed these graded regions, which were observed for all the layers analyzed, to interdiffusion between the growth layer and the cadmium telluride substrate. The composition was said to be uniform 20.004 across the surface of a 5-cm2layer. Electrically, all layers were found to be n-type, with carrier concentrations of loi6- 101'/cm3 at 77 K. The authors attempted annealing of these layers to restore the metal-to-tellurium ratio but in all cases there was a significant increase in x in the epitaxial layer and an increase in the width of the graded composition region because of interdiffusion between the layer and the substrate. At this point it should be mentioned that both the solvent and the reactive vapor phase epitaxial systems have the potential of depositing layers of rapidly varying composition by design. Schulman and McGill (1979) have proposed that a number of interesting infrared optoelectronic devices could be made by alternating layers of cadmium telluride and mercury telluride. This would be best achieved by one of these two means.

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b. With Controlled Diffusion Cd,Hg,-,Te may also be grown by means of controlled diffusion in which either mercury or mercury telluride is transported to the surface of a cadmium telluride substrate and cross diffusion of the two metallic elements results in an epitaxial graded composition layer of CMT. With this method it is impossible to make epitaxial layers of constant composition; consequently it has only been used for the manufacture of graded energy gap structures. The interdiffusion of mercury telluride and cadmium telluride placed in contact was investigated by Rodot and Henoc (1963) and this work led to the development of a closed-spaced method for epitaxial deposition of HgTe onto CdTe by Cohen-Solal et (11. (1967). In this method the mercury telluride sample is held in close proximity to the cadmium telluride substrate, with mercury telluride being transferred by an evaporationcondensation mechanism. Epitaxial growth is achieved under isothermal conditions, giving layers of high crystalline perfection. During the deposition process, interdiffusion occurs between the mercury telluride and cadmium telluride substrate and results in compositional variation with depth in the epitaxial layer. Tufte and Stelzer (1969) continued and elaborated on this work using the closed-space technique under both isothermal and temperature gradient conditions. The substrates used were cadmium telluride, carefully lapped and polished in bromine methanol solution. The mercury telluride source was in the form of a loose powder, a pressed powder pellet or a slice from a single or polycrystal ingot. The rate of deposition and quality of the epitaxial layer were said to be comparable for all types of sources. The mercury telluride source and the cadmium telluride substrate were separated by an annular quartz spacer with the spacing varying between 1.7 and 15 mm. The entire assembly was placed in an ampoule consisting of two concentric flat-bottomed quartz tubes having minimum volume, which was evacuated to a hard vacuum prior to sealing. For isothermal growth, the temperature profile along the furnace was maintained flat to within 0.5"C over a length of some 15 cm. It was important that the source and substrate be at the same temperature, since a temperature difference of a few degrees between source and substrate produced significant differences in crystalline perfection. The temperature range from 500-600°C was investigated, with the highest degree of crystal imperfection obtained at the higher temperatures. Below 550°C the epitaxial layer became faceted and did not have the mirror surface characteristic of the higher growth temperature. The epitaxial growth rate was dependent on the mercury pressure in the ampoule, and the mercury tel-

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X

0

0

'

I

40

'

'

'

00

'

8

I

' ' 'I' ' 160 2 0 0 240 260 I

I '

120

'

'

8

Thickness (prnl

FIG. 30. Variation in compositional profiles for epitaxial layers grown under the same isothermal conditions for different durations. HgTe powder source: T = 600°C; 5-mm spacing; 3 atm mercury pressure. [From Tufte and Stelzer (1969).]

luride source decomposed unless some excess mercury were added to the ampoule. Approximately 1.5 atm of mercury overpressure were required to suppress surface melting of the mercury telluride source at 600°C. The epitaxial growth achieved by Tufte and Stelzer was similar to that obtained by Cohen-Solal et ul. (1967). Typical composition profiles for three epitaxially grown layers are shown in Fig. 30. The composition of the surface of the epitaxial layer is completely determined by growth conditions. Under different conditions of spacing and deposition time, the surface composition reported by Tufte and Stelzer varied between x = 0.02 and x = 0.40. Cohen-Solal et al. (1976) report being able to achieve pure mercury telluride (x = 0) at the surface. The thickness of the epitaxial layer as measured from the CMTcadmium telluride interface is proportional to the square root of the deposition time. The effect of increasing the deposition time is to increase the thickness of the layer without changing the relative composition profile within the layer. If the three curves of Fig. 30 are replotted in terms of fractional distance through the layer rather than distance, it will be seen that the composition profiles overlap completely. The constancy of the x value at the surface of the epitaxial layer can be explained by the establishment of an equilibrium between the cross diffusion of the two metallic components and the arrival rate of mercury telluride on the surface of the wafer as controlled by the growth conditions. The thickness of the growing layer under these conditions is limited by the diffusion rate and, consequently, is proportional to the square root of deposition time. For a given deposition time, the thickness of the epitaxial layer and

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W . F . H . MICKLETHWAITE

Or igina I stir face

X

(0atm) 11

-100

0

100

200

300

400

Thickness (pm)

Fic. 31. Variation in composition for epitaxial layers grown under the same isothermal conditions except for mercury overpressure. HgTe powder source: 88 h; 600°C; 5-mm spacing. [From Hager et 01. (1973).]

consequently the composition of the material at the surface of the layer can be controlled by means of the excess pressure in the ampoule over the system. Figure 3 1 shows compositional profiles within four epitaxial layers grown under identical conditions except for the amount of the mercury overpressure. Note that these layers grown under identical conditions of time and pressure but at different mercury pressures have the interesting property that the slope of each curve is identical at a given x value regardless of the mercury pressure in the ampoule during growth. This can again be seen by superimposition of the curves normalized to the point where x = 1. The effect of increasing mercury pressure is to reduce the layer thickness, but the compositional profile within the thin layer is identical to the truncated profile of the thicker layer grown at lower pressure. Increased mercury overpressure also reduces both the Cd-Hg interdiffusion constants and the rate of transport of material from the source to the substrate. The reduction in interdiffusion of mercury and cadmium is attributed to the reduction in the number of mercury vacancies. Since diffusion at these temperatures is by a vacancy mechanism, increasing the mercury pressure will reduce the interdiffusion. The source to substrate spacing can also be used to control the deposition rate of mercury telluride and consequently the layer thickness. For spacings greater than approximately 2 mm, the layer thickness and surface composition are slowly varying functions of spacing, but for spacings less than 1 mm the layer thickness depends much more strongly on spacing as discussed by Cohen-Solal et al. (1967, 1976). His results suggest that the composition of the surface layer is unambiguously related to the thickness of the layer, consequently the problem of compositional control becomes a problem of thickness control and re-

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producibility. Tufte and Stelzer were able to control thickness within 1% on 10-mm diameter wafers resulting in a surface composition predicted to vary laterally by at most 0.25 mole %. These authors also investigated the use of CMT alloys as the source material with cadmium telluride as the substrate. The transport mechanism and epitaxial growth process were identical to those described for mercury telluride alone, and their results indicated that cadmium was being transported from the source to the substrate. The presence of cadmium in the source material tends to decrease the epitaxial layer growth rate. The transport rate is also decreased with increasing mercury overpressure as with the mercury telluride source. These authors have also investigated the epitaxial growth of CMT in the presence of a temperature gradient between the source and substrate. A temperature difference of the order of 20°C provides an additional driving force for the transfer of material from the source to the substrate and results in an approximately linear increase in the epitaxial layer thickness with deposition time as shown in Fig. 32. Note that for the isothermal case the deposition rate falls off steadily with time. When the gradient growth technique was used with CMT sources (rather than HgTe), cadmium was not transported and the surface composition of the epitaxial layer always approached x = 0 (that is, HgTe). This was believed due to the enrichment of the source material in cadmium resulting in surface melting. In the case of the ternary compound source it appeared that the presence of two different temperatures in the system prevents the system from coming to equilibrium at any single mercury pressure. The gradient

Time ( h )

FIG.32. Rate of growth for epitaxial layers of C&.2Hg,,.,Te grown with (solid line) and without (dashed line) a 20°C temperature gradient. Substrate temperature = 600°C. [From Tufte and Stelzer (1969).]

100

W . F. H . MICKLETHWAITE

growth technique therefore appears to be suitable for epitaxial growth of mercury telluride on cadmium telluride but not the deposition of the ternary compound. This process has been patented by Hager et al. (1973). Svob et al. (1975) have investigated in detail the influence of mercury vapor pressure on the isothermal growth of mercury telluride on cadmium telluride substrates. Their results clearly showed that the surface composition depends on the mercury overpressure in the system. The diffusion constant decreased with increasing mercury overpressure varying from 0.5 pm2/h for cadmium-rich alloys to 100 pm2/h for mercury-rich alloys. Again, the phenomenon is qualitatively explained by a decrease in the number of vacancies by increasing the mercury overpressure with the subsequent reduction in the diffusion rate. At a given mercury overpressure the diffusion profiles can be uniquely expressed as a function of the layer thickness reduced by the square root of time. These authors deduced that the interdiffusion constant does not explicitly depend on time, suggesting the existence of some vacancy balance mechanism. The compositional gradient in pairs of epitaxial layers was examined after deposition and also after deposition with a post deposition anneal under a saturated mercury pressure. The constancy of the compositional variation of the interdiffusion coefficient between samples simply grown and grown then annealed was confirmation of this time independence, and is shown in Fig. 33. These authors also reported the dependence of layer thickness and surface composition on excess mercury pressure, and the dependence of epitaxial layer thickness on the substrate-to-source spacing. They have also computed the vacancy balance in the epitaxial layer, and have been able to predict the form of the compositional profile. Becla ei al. (1977) have contributed further information to this work, substantially confirming the results of the previous authors. They found that a decrease in epitaxy temperature or a greatly reduced epitaxy time resulted in the formation of a pure mercury telluride surface layer due to the slow diffusion of cadmium into the growing layer. Their x-ray examinations have shown that the epitaxial CMT layers grown on cadmium telluride substrates by this means had a high degree of crystal imperfection and accurately reflected the crystallographic character of the substrate. They have also examined the heterogeneity of the surface composition due to the misalignment of the substrate and the impinging mercury telluride vapors. The surface composition (x) was found to be somewhat higher at the edges of a 1-cm2sample due to the reduced mercury telluride deposition rate at the perimeter. Nowak ef uf. (1978) investigated a slight variation of the previous systems, They vacuum evaporated cadmium telluride films onto suitable

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Relative cadmium content, xCd

FIG.33. Compositional variation of the interdiffusion coefficient in two samples: as grown growth: temperature = 550°C; time = 72 h; and after heat treatment-both at 550°C. 0, 1 atm Hg in excess. 0, annealing: temperature = 550°C; time = 72 h; 8.3 atm Hg. [From Svob et al. (1975).]

substrates, deposited mercury telluride onto these and then caused cross diffusion to equilibrium. Their investigations showed that the structure of films prepared on crystalline substrates such as mica and sapphire were epitaxial while those prepared on amorphous substrates were polycrystalline or textured with large grains. The objective of their studies was to provide a predetermined layer thickness of cadmium telluride onto which a predetermined amount of mercury telluride could be deposited resulting in a relatively uniform final layer of controlled x . Cadmium telluride was first vacuum evaporated onto properly treated substrates using the hot channel method. They sought a substrate which had a suitable crystalline structure, orientation, thermal expansion coefficient, high electrical resistivity, high thermal conductivity, and good adhesion, and which would not react with cadmium, mercury, or tellurium at temperatures up to 600°C. Silicon and germanium are too reactive and therefore had to be oxidized prior to use. Mica has many advantages, being available in thin plates of high mechanical strength and high elec-

102

W. F. H . MICKLETHWAITE

trical resistivity, but it suffers from a low thermal conductivity. The epitaxial CMT layer was grown under isothermal conditions at temperatures of 500-600°C in a sealed quartz ampoule with additions of mercury telluride for deposition and excess mercury to provide the necessary mercury overpressure. For epitaxial films grown on crystalline substrates (mica, sapphire, and lithium niobate), the film quality improved as the deposition temperature increased, and the composition of the films tended towards mercury telluride. Layers grown at temperatures above 500°C had a shiny smooth surface. Films deposited on amorphous substrates such as glass and alumina ceramics coated with amorphous carbon films were polycrystalline and their grain size increased at raised deposition temperatures. At high temperatures, films with grain sizes (tens of microns) far exceeding the film thickness were obtained. Electron diffraction investigation showed a texture with ( 1 11) cadmium-mercury-telluride planes parallel to the substrate. Investigation of films grown on thermally oxidized silicon showed that for thin (- 30 nm) SiOzcoatings these CMT films were epitaxial while for thicker coatings (- 0.5 pm) the CMT films were polycrystalline with the (111) CMT planes parallel to the substrate. The films were found to be very uniform in x over the surface of a 10 x 40-mm2 area for x values in the range of 0.26. c . Direct Deposition

Methods

One of the potentially simplest methods is evaporation/condensation or sublimation. Bradford and Wentworth (1975) applied this technique to the sublimation of lead-tin telluride onto (1 11) oriented (PbSn)Te seeds. The crushed charge material was sealed into a quartz ampoule with the oriented seed. The seed was bonded to a flat at one end of the ampoule to which was connected a length of quartz rod which served as a radiative window from the isothermal heat pipe furnace. They were able to grow 20-mm diameter crystals weighing 40-50 g in a period of 3-4 weeks. The quality of the crystal was improved by a reduction of oxygen in the ampoule: this was attributed to the reduction in attack of the quartz tube, reducing silicon contamination. Golacki et al. (1979) were able to grow mercury telluride by selfnucleation in a system with a rather large temperature differential. The two control parameters were the temperature of the crystallization zone and the temperature difference between the crystallization zone and the sublimation zone. At sublimation temperatures near 450°C with the source material approximately 100°C hotter, they were able to grow crystals 7 mm on a side in a few weeks. In order to get large crystals it was necessary to carefully control the nucleation of the original crystals in the

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condensation zone. The dislocation density reported was approximately 106/cm3,which is relatively good for this type of material. Petty and Juhasz (1976) reported on the growth of 1-pm films of zinc mercury telluride by coevaporation of zinc telluride and mercury telluride. The zinc telluride sublimed in a well-controlled manner at approximately 9 W C , while at 500°C the mercury telluride lost mercury preferentially, causing the source material to first become tellurium saturated and eventually form a tellurium-rich second phase. The deposition rate was of the order of 20 A/sec onto a mica substrate held at 120°C. Films deposited at higher temperatures contained a second phase of tellurium. Piotrowski (1976) reported on the vacuum deposition of cadmiummercury-telluride thin films having thicknesses of 0.5-12 p m andx in the range of 0-0.22. She remarked the distinct feature of the AII-BVIcompound evaporation process that the vapor phase is composed of atomic or molecular beams of the components rather than the compound molecules. The large difference in vapor pressures of the individual components makes it difficult to obtain stoichiometric films of the compound, and the high volatility of mercury results first in an excess and later in a deficiency of mercury in the vapor beam. A s a result, a compound of different composition than the source is formed and tends to contain tellurium as a second phase. There is a further complication in that unless the substrate temperature is kept low, mercury tends to reevaporate from the deposited layer. On the other hand, a high substrate temperature is required for a good film structure. Piotrowski reported a marked deviation in the tellurium balance by as much as 2 5 % from the stoichiometric level. The mean grain size of the polycrystalline film was approximately the film thickness with increasing structural order in thicker films. The grain boundaries had a composition markedly different from the interior of the grains, tending to be enriched with tellurium and depleted in mercury. The cadmium content was approximately the same at grain boundaries and inside the grains. A nonuniform distribution of tellurium inclusions within the grains was also observed in some cases. The relatively low mobility found in these films was attributed to point defects and ionized impurity scattering, which became more pronounced in films of composition close to x = 0.2. Farrow et al. (1979) report a study of the incongruent vaporization of CMT which confirms Piotrowski’s findings. The species emerging from a Knudsen cell varied according to three temperature regimes. Below 2WC, Hg was the only significant dissociation species. Between 200 and 450°C both Hg and Te, were present, Tez steadily increasing in relative proportion to 320°C. Between 320 and 450°C the molecular effusion rate of Hg and Te, was 2 : 1 (corresponding to HgTe) and the surface composi-

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W . F . H. MICKLETHWAITE

tion x approach 1.O. In the third regime above 450°C, Cd and Te2 were the predominant species as the residual CdTe decomposed. Ludeke and Paul (1966) report on the flash evaporation of C&.2Hg,,.,Te onto substrates at temperatures between 27 and 177°C. The layers were CMT with the same composition as the source material, which they interpreted to mean that no mercury was lost from the deposited layers. Hohnke et al. (1971) report different results. In their work, 100-pm diameter granules of C&.2Hgo.8Tewere fed continuously into a tantalum boat at 900°C giving a deposition rate of about 5 A/min. At higher temperatures, preferential mercury evolution ejected the granules from the boat causing them to adhere to the substrate. Deposition onto substrates at 30-60°C gave layers that appeared to be single phase CMT having well-crystallized layers with a ( 1 11) texture. As the substrate temperature was increased through the range 60- 180*C, the mercury content of the layer decreased to zero and there was a corresponding increase in the content of a second phase of unreacted tellurium. They interpreted these results as due to reevaporation of mercury from the deposited layer. This dependence of the composition of the deposit on the substrate temperature is shown in Fig. 34. They found that they were able to compensate for mercury losses from the deposited layers by the use of a mercury-rich incident flux. Operating with substrate temperatures of up to 150"C, they were able to achieve a growth rate of up to 100 A/min but found that this required a mercury flux with greater than an order of magnitude more mercury than was incorporated into the layer. Polycrystalline films grown onto cleaved barium fluoride had (1 11) textures and relatively poor mobility (an order of magnitude less than that typical of good bulk crystal).

0.7 0.6

0.3

=

0.2

Substrote temperature (OC)

FIG.34. Dependence of composition of Cd,Hg,-,Te layers on substrate temperatureexperimental points and curves calculated using two estimates (solid and dashed curves) of PH,overHgTe. Curve 1,5 A/rnin; curve 2 , 5 A/rnin; curve 3.50 &mi"; curve 4,500 A/min. [From Hohnke rf ul. (19711.1

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Kraus et al. (1967) described the deposition of x = 0.05-0.15 CMT by cathodic sputtering in an argon plasma. The sputtering was performed at 1500 V , 0.4 mA/cm2 current density in an oxygen-free argon atmosphere at 0.05 Torr, yielding layers 30-50 pm thick in 4 h. Deposits sputtered onto (1 10) NaCl and (1 11) Ge were not adherent, while those on randomly oriented sapphire were adherent and amorphous as deposited at 25°C but became polycrystalline with a (1 1 1) texture after annealing at 300°C. The amorphous character of the deposits was aggravated by cooling the substrates below 25°C. These authors also indicate that CdTe can be successfully sputtered but HgTe cannot because of decomposition. Chemical analysis of the deposits indicated that the overall composition of the deposit closely approximates the source but there are lateral variations in x and deviations in y about the stoichiometric value of 0.05. Zozime et al. (1972) also discuss sputtering in an argon plasma noting parameter degradation (compared to the source) attributed to entrapment of argon atoms, and also the loss of Hg from the substrate due to heating. The Hg loss in the deposit increased with allowed substrate temperature for x = 0.2 source material but was negligible for x = 0.9 source material. To avoid these problems, these authors investigated the use of a Hg plasma employing the apparatus of Fig. 35. All internal surfaces were stainless steel to avoid amalgam formation. Contrary to the argon sputtering case, the Hg plasma prepared films were nearly the same as the source at low temperatures but became notably Hg poor at 260°C for x = 0.2 source material. The homogeneity of the films was x k 0.02. At 50-60°C substrate temperatures the films were randomly polycrystalline but exhibited a ( 1 11) texture at 200°C when deposited on (100) NaCl. Shutter Substrate

2 magnetic c o i l l

FIG.35. Schematic diagram of an RF sputtering system. [From Zozime et al. (1972).]

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This work was continued by Cohen-Solal C t al. (1976) who prepared 1-5 pm polycrystalline films epitaxially onto CdTe and CMT singlecrystal substrates. They cite "a surprisingly high" degree of homogeneity. These authors also demonstrated the cosputtering of Au or A1 to achieve p-type or n-type doping to levels as high as 0.2%-far exceeding the levels attainable by equilibrium methods. Zozime and Cohen-Solal(l979) developed a detailed phenomenological model for the triode sputtering of CMT in a Hg plasma. Films deposited onto (111) Si or CdTe were polycrystalline with a (111) texture and columnar structure typically 5000 A in diameter. The deposit of x = 0.2 material was high carrier (3 x 1016-8 x 101'/cm3) n-type of low mobility (8 x 102-1.5 x 104 cmZ/V sec). The low mobility was attributed to the polycrystalline structure. The material was said to make photovoltaic detectors equivalent to those prepared on single-crystal material when A1 or Au were cosputtered in second layer. Foss (1968) described a method of CMT layer formation by the bombardment of CdTe single-crystal substrates with Hg ions. The ion source was generated by a radio-frequency glow discharge in Hg vapor using a Hg anode. The manipulation of the anode pool temperature regulated the flux incident on the substrate. For 2000-eV bombardment of a (111) substrate at 200"C, a layer approximately 2 p m thick was found to have x < 0.3 after 30 min. This greater-than-predicted penetration depth was explained by a mechanism of localized melting at an impact site, followed by diffusion. Golacki and Makowski (1979) report early results for the formation of free (nonepitaxial) crystallites of CMT with 0.22 < x < 0.96 by chemical transport. A horizontal quartz tube was charged with HgTe and Te in one end heated zone, the other end heated zone received CdTe and NHJ while in the central, somewhat cooler zone the vapors reacted to form the compound from the constituent streams. The zone temperatures and amounts of the Te and NHJ carriers are control variables on the final compound composition. V. Other Considerations 22. GENERAL Regardless of the growth technique employed, the crystal product must be useful for the final devices. In the early days of CMT, the 6-mm-diameter single crystal of x ? 0.02 homogeneity was a prize from which many useful single-element detectors could be fabricated. The present stateof-the-art demands that at least one dimension exceed 18 mm, and devices already projected will require this in at least two dimensions.

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The foregoing limitations, of course, apply only to the dimensions of the single-crystal part of the ingot. Current requirements are that compositional homogeneity be better than 2 0.005 with additional requirements that dislocations and edge pits be kept to a minimum and that the mosaic substructure be kept below a tolerable maximum. It would also be considered useful if there was order in either the metallic sublattice or in the electronic lattice. 23. HOMOGENEITY (the unkindest cut of all) Fripp and Crouch (1979) have examined the compositional control which will be required in second and third generation multielement CMT detector arrays. They predict that this will be a major limitation to the technology. a. Bridgman Growth

Schmit (1969) has reported in great detail on the homogeneity of 13-mmdiameter Bridgman ingots grown 260 mm in length in an almost horizontal

FIG.36. Isocomposition lines on a cross section of a Bridgman grown C$.,,H&.,,Te ingot. [From Schmit (1969).]

position. Figure 36 shows an axial cross section of an x = 0.3 ingot. It is quite apparent that in order to obtain constant composition pieces of reasonable size it is necessary to very carefully map transverse sections beforehand. By interpolating the compositions between the end point compositions it is possible to slice the cylindrical sections along isocomposition lines. Had this ingot been grown in the vertical position with very flat thermoprofiles, the isocomposition lines would have been approximately normal to the growth axis. In practical terms though, this is never achieved, and the form of the interface is approximately cone shaped with its point towards the end which froze first.

6. The QuenchlRecrystallized and Harman Growth Methods Figures 19-21 reveal that the form of compositional variations for quench recrystallized material is centrosymmetric and varies in degree in the axial direction. Micklethwaite and Redden (1978) have reported simi-

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lar results for sections from a Harman grown ingot. Their results are shown in Fig. 37. The central column of this figure shows schematically a cylindrical section of a 15-mm-diameter ingot. At top center there is a map of the x variation across the slice at the leading end of the ingot that is approximately conical in shape and has a depth Ax. Towards the trailing end of this 30-mm section the compositional variation is again a conical plot but with a shallower variation 6x. At the top and bottom of the right-hand side are maps of the compositional variation along a diametric cut through such a slice both at leading and trailing ends while on the left-hand side the variation is shown for a chordal slab. Clearly, the chordal slab intersects a smaller portion of the total compositional variation than does the diametric cut. At right center is a map of isocomposiReference x

X

FIG.37. Schematic representation of composition profiles at two ends of and ingot with isocomposition lines shown for diametric and chordal slabs cut parallel to the axis.

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tion lines as interpolated from the diagrams above and below, while on the left-hand side there are similar isocomposition lines plotted at the same x contour interval but for a chordal slab. Again it is obvious that slices cut approximately tangent to the cylinder surface are substantially more homogeneous than those cut through a diameter. Bartlett et al. (1979b) report similar results for their work on quench/recrystallized material and also suggest that longitudinal planks cut from large crystals might offer the best method of obtaining large uniform areas. Nelson et al. (1980) analyzed the solidification rate in ampoules of various sizes and confirm that gravity segregation of the HgTe-rich interdendritic phase toward the ingot center is additive to the normal (phase diagram) segregation. They claim to be able to independently control radial and axial solidification rates to achieve 2 0.002 compositional homogeneity over 95% of wafers up to 25 mm in diameter. c . Methods of Estimation

The three commonest methods of composition estimation have been reviewed by Long and Schmit (1970). These are the measurement of density, which can be translated to x values with an accuracy of approximately 0.001 mole fraction; measurement of the 300-K band edge by infrared transmission or absorption methods, convertible to an accuracy in x of 4 0.003 mole fraction and electron microprobe measurement giving data on the relative element contents, which can be converted to xs with approximately 0.01 mole fraction accuracy. For mapping purposes one must also consider the spatial resolution of these three measuring techniqiues, which are respectively approximately 500, 200, and 100 pm. Grainger and Gale (1978) have reported on the trace impurity analysis of CMT by a flameless atomic absorption technique. Using a Varian Model 63 flameless atomizer they were able to achieve detection limits of as low as lo9 atoms on samples of approximately 10 mg. While their intent was just to provide an accurate analysis for impurity elements (particularly dopants), this method could undoubtedly be adapted to the accurate measurement of cadmium, mercury, and tellurium by comparing the time integrated absorption curves against standards. The spatial resolution of this technique would be approximately 150 pm. Cominco staff have used a scanning electron micrograph in the x-ray fluorescent mode to map CMT wafers with a spatial resolution of approximately 100 pm and a compositional resolution of approximately 0.02 inx. Dittmar (1977) has published work from his laboratory on SEM x-ray fluoresence and reports a relative error in x of 0.035 at x = 0.2. His standards were calibrated against density measurements. He also shows

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secondary electron emission photographs of the spatial distribution of mercury and tellurium. This latter technique is particularly useful for mapping variations in concentration in the vicinity of grain boundaries, precipitates, and so on. Vanier ut (11. (1980) have developed a means for evaluating the variations in x as a function of position on the surface of crystal slices using electrolyte electroreflectance. The method is nondestructive and can be employed at room temperature. The spatial resolution of this technique is approximately 150 pm and is able to resolve x variations of the order of 2 0.002. This method should complement the band-edge energy gap mapping based on the E, as the electroreflectance technique is based on the El band structure and gives a relatively large signal in the 2-eV range. In the author’s laboratory, large volumes of production material are routinely mapped using the 300-K band edge; however, this technique must be restricted to undoped a-type and p-type withp carrier concentrations less than 3 X IOl5/cm3. If this p carrier concentration is exceeded, there is a shift to higher absorption and a longer wavelength in apparent band edge. These effects are believed due to free-carrier absorption and possibly the Moss-Burstein effect. Doped n-type materials and highly doped p-type materials cannot be evaluated using the band-edge technique. 24. DISLOCATIONS A N D ETCHPITS The presence or absence of second-phase precipitates, dislocation arrays, or other lattice faults is obviously of great interest to the device manufacturer. The presence of any or all of these defects can lead to increased noise in photoconductive devices, uncontrollable diffusion and junction profiles in photovoltaic devices, and increased leakage in MIS devices. Parker and Pinnell(1971) published information on their etchant which develops triangular etch pits or hillocks on (1 11) planes of CMT. The etch solution consisted of 15 volumes of concentrated HNO9, 15 parts of H,O, 1 part of concentrated HCI, and 1 part of a 5% solution of bromine in methanol. The surface can be prepared by lapping to a smooth finish and then chemically polished in 5% bromine methanol prior to development of the etch pits at room temperature in a period of 5-10 min. Sometimes a dark film forms which can be removed by a 1-2 sec treatment in dilute bromine methanol solution followed by a methanol rinse. Parker and Pinnell reported dislocation densities on x = 0.2 CMT varying between 1 X lo4 and 5 x lo6 etch pits/cm2. They indicated that as the cadmium content increased it was necessary to dilute the etch solution with H 2 0 in

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order to obtain well-defined etch patterns; this also required longer etch periods. In the author’s laboratory, it was found that altering the HCI proportion of the Parker and Pinnell etch had only bad effects and caused random attack. Dilution of the Parker and Pinnell etchant with an equal or double volume of water worked very well, giving good triangular etch pits with a few smaller features. Approximately 10 min is required to produce a dark film on the (111) face while the (iii)face takes on a dark “frosted” appearance as a result of a myriad of pits. Our tests indicate that the Parker and Pinnell or modified Parker and Pinnell etchants must be fresh. They should be discarded after about 2 h. The more dilute etchants work more slowly but are more preferential and we were able to define etch pits on or near (100) and (110) planes-these are somewhat more oval, of course. Grain boundaries show as continuous lines of overlapped etch pits, which frequently can just be resolved at 1 0 0 0 ~magnification. The dislocation counts in such grain boundaries can be estimated by counting the points in the fringed appearance of such a grain boundary. Dislocations counted on one such grain boundary exceeded 1000 dislocations per millimeter. We have also found that dislocation densities in bulk material are in the 105-106/cm2 range. Brown (1978) and Brown and Willoughby (1979) have also reported on etching studies in cadmium mercury telluride. They worked with etchants developed by Polisar et al. (1978) for mercury telluride. They found that Polisar etch No. 1 developed pits within 25” of the (111) plane and that Polisar etch No. 2 revealed etch pits on all planes. Both etchants were polar in nature and showed pits on the mercury (111) face but not on the tellurium (1 l l) face. Brown and Willoughby show the form of the etch pits developed by the Polisar etches at various points in the stereographic triangle. These authors were also able to correlate the subgrain misorientation with counts of dislocations along subgrain boundaries and were able to establish that the slip planes in CMT approximate (1 11) planes. Boinykh et al. (1974b) worked with the Parker-Pinnell etchant to develop etch pits on crystals of Bridgman grown CMT. The dislocations in this material are substantially denser at the periphery of 6-mm ingots than at the core. The dislocation density increased from 2 X 104/cm2 in the initial portion to freeze to approximately 6 x 106/cmzat the last end to freeze. As the diameter was increased to 10 mm these numbers became 5 x 103- 1 x lo5. These were dislocation counts for the bulk material and do not include dislocations of the subgrain boundaries. There appear to be few references to the effects of grain boundaries,

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dislocations, and other defects on the detector properties of CMT-most probably because of commercial and military secrecy. However, Hanafi and van der Ziel (1978) have shown that the flicker noise in a photoconductive detector containing a grain boundary was four times as great as a nongrain boundary section of the similar device. 25. X-RAY TOPOGRAPHY The etchants just described are quite suitable for research purposes and assessing the various means of crystal growth, but are not satisfactory for nondestructive high-resolution scanning of large-area material as required for the placement of detectors or detector arrays. For these purposes the electronics industry has been relying more and more heavily upon x-ray topography. Perhaps the simplest form of x-ray topography is the Laue topography first described by Swink and Brau (1970). Their equipment consisted of a Laue back reflection camera without its normal collimator. A broad beam, typically 1 cm in diameter, gave the normal Laue back reflection pattern but with the spots greatly enlarged (typically 1-2 cm in diameter). If the beam is illuminating a uniform, low-deformation, single-crystal volume the spots will be completely uniform and show no shading. If there is severe misorientation, as in the case of the twin or second grain, the elliptical Laue spot will break up into one or more subspots displaced relative to each other by an amount which is proportional to the angle of misorientation. In the case of dense dislocation arrays or slight subgrain misorientations, different portions of the Laue spot on the film will “underlap” or “overlap,” causing lighter or darker regions and giving a mottled appearance. The degree of this underlap or overlap is again proportional to the misorientation of the various portions of the grain illuminated by the beam. In Cominco’s laboratories we have implemented this system by simply removing the collimator tube from a Polaroid Laue camera and then using a Phillips x-ray generator with molybdenum K alpha radiation at 10 kV, 20 mA with a 5-cm spacing for a 45-min exposure. Bonse et al. (1966) have compared the features of several x-ray topographic methods for the revelation of subgrains and dislocations in various semiconductors. Their conclusion was that the Berg-Barrett technique was best because of simplicity, relatively short exposure times, and 1-pm resolution. This method is not normally able to resolve single dislocations but that is not of concern in this case, The equipment, characteristics, and experimental procedures of Berg-Barrett topography have been described by Newkirk (1959) and Austerman and Newkirk (1966). The slice area which can be observed with acceptable contrast and adequate resolution can be greatly expanded using scanning methods as described

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by Ottel(l973). In these methods the crystal and x-ray sensitive plate are moved in concert with respect to fixed primary and diffracted beam limiting slits. This relative motion results in a moving line scan of the wafer and creates a moving line image on the x-ray plate. Rogers (1979) has suggested conditions for such a scan. Copper K alpha radiation is collimated by slits to a beam width of 0.1-0.3 mm, the beam impinges at 20-30" to the wafer and the film is established approximately parallel to this wafer. Using Kodak type M or R film, exposure of a 15-mm slice takes approximately 48 h with this scan technique. Figure 38 shows a topograph made by this technique. There are several features of note, perhaps the most important of which is the clear definition of subgrains. The very clear subgrain boundaries with a minimum amount of overlap or underlap is an indication of very minor misorientations between subgrains. This photograph also demonstrates the imaging of surface damage in the form of the longitudinal scratches of slight curvature on one side

FIG.38. X-ray topograph of a Cdo.lHgo.,Tewafer (15-mmdiameter) made using the scanned slit technique. [From Rogers (1979).]

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and also the effects of surface disruptions such as the ray-shaped marks around the slice circumference caused by irregularities in etching. Other mechanical problems such as cracks, voids, or second-phase precipitates will also be evident in such a topograph. Bye (1979) has reported on the x-ray topographic assessment of CMT crystals grown by both Bridgman and the cast/recrystallize technique. These topographs showed that the Bridgman material consisted of large numbers of relatively small grains (0.05-0.6 mm) with misorientations from 1-9 arc min. The quench/recrystallized material had a substantially larger grain size and somewhat reduced angular misorientations, although the topograph showed a mottling which is consistent with a strained lattice, possibly caused by compositional variations. 26. OPTICAL IMAGING

Feigelson and Route (1980) describe the use of IR wavelength imaging systems based on CMT for the detection of crystal defects using transmitted radiation. Voids, cracks, precipitates, and impurity banding were visible in TlSAsSeSingots. This technique should be extensible to imaging defects in CMT. 27. ORDERING

The cadmium-mercury -telluride crystalline lattice is of a zinc-blende type comprising two interpenetrating face-centered-cubic lattices, one comprising tellurium only and the other comprising the two metallic species, cadmium and mercury. The tellurium sublattice will be fully ordered being one species only. At high temperatures the metallic sublattice will consist of a disordered array of cadmium and mercury atoms in direct proportion to the pseudobinary composition variable x. However, at lower temperatures the possibility exists for an ordered structure to form in this metallic sublattice. Balagurova and Khabarov (1976) investigated the microhardness of a series of CMT alloys. Their results shown in Fig. 39 indicate the presence of three maxima at,x = 0.14, 0.27, and 0.75 mole %. They cite an earlier work by Shneider and Gavrishchak (1963) indicating there is a further maximum at 0.50. They have extended the correlation of microhardness with impurity interaction in solid solutions to infer that these variations in microhardness may correlate with variations in interaction between the components of a solid solution such as CMT. The maximum at x = 0.14 was thought to be associated with a semimetal-semiconductor transition whereas the peaks at 0.25, 0.5, and 0.75 correspond to cadmium to mercury to ratios of 1: 3 , 2 : 2, and 3 : 1, respectively, They have suggested that

3.

THE CRYSTAL GROWTH OF CADMIUM MERCURY TELLURIDE I

1

I'

1

I

115 I

FIG. 39. Microhardness of Cd,Hg,-,Te versus composition. [From Balagurova and Khabarov (1976).]

the proposed model of interactions might explain some of the peculiarities noticed in the crystallization of certain compositions (particularly x = 0.2, as it lies between two more energetically favored compositions, 0.14 and 0.25). Cullity (1956) has discussed the detection of such ordered superlattices by the appearance of normally forbidden x-ray diffraction lines. In the zinc-blende lattice, planes with unmixed indices should have very strong lines and those having mixed indices should have extremely weak lines. A brief but unsuccessful search was made in the author's laboratory to find such a supperlattice line for the (1 10) plane in an x = 0.26 CMT slice after a prolonged anneal at 250°C. There was no sign of the (1 10) plane even with the most sensitive diffractometer settings. Estimations taken from Cullity of the structure factor for the (110) and the (111) planes suggest that a fully ordered x = 0.25 alloy should have a (100) line intensity of approximately 23% of that of the adjacent (1 11) line intensity. Hence, any appreciable degree of ordering should have been detectable. Steininger (1976) suggested that constant activity of mercury, as opposed to constant activity coefficient, over CMT solutions of various compositions indicated that the liquid should be considered more as a binary mercury -tellurium solution than as the ternary mercurycadmium-tellurium. This, he thought, was apparently due to the strong binding energy of cadmium and tellurium atoms in the solution as compared to the weaker binding energy of mercury and tellurium. The model for the liquid would therefore be a mixture of associated neutral cadmium telluride molecules and of disassociated mercury and tellurium atoms. If this model were also to apply to solid solutions, the strong binding energy of cadmium-tellurium pairs might inhibit the reordering of the alloys at lower temperatures. There is obviously much more work to be done on the subject of superlattices and ordering, with considerable possibilities for improved device characteristics as discussed by Schulman and McGill (1979).

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REFERENCES Aliev, M. I . , Aliev, S. A., Arasly, D. G., Ragimov, R. N., and Gadzhiev, T. G. (1978). Dokl. Akad. Nauk. A z . S S S R 34(9), 28-50. Auleytner, J., Liliental, Z., Mizera, E., and Warminski, T . (1979). P h y s . Status Solidi 55, 603. Aust, K. T. (1972). J . Cryst. Growth 13/14, 57-61. Austerman, S. B., and Newkirk, J. B. (1966). A d v . X-Ray Anal. lo(]), 134. Bailly, F., Svob, L.. Cohen-Solal, G . , and Triboulet, R.(1975). J. Appl. Phys. 46(10), 4244. Balagurova, E. A. (1974). Neorgan. Muter. 10(6), 1135 [English transl.: lnorg. Muter. 10(6), 11351. Balagurova, E. A., and Khabarov, E. N. (1976). Izv. Vyssh. Uchebn. Zaved. Fir. 7 , 133 [English transl.: J. Sov. Phys. 71. Banasargtschin, B., Lehman, B., and Link, R. (1976). Phys. Status Solidi 37, K13. Bartlett, B. E., Deans, J., and Ellen, P. C. (1969). J. M a f e r . Sci. 4, 266. Bartlett, B. E., Capper, P., Harris, J. E., and Quelch, M. J. T . (1979a). J. Cryst. Growth 47, 341. Bartlett, B. E., Capper, P., Harris, J. E., and Quelch, M. J. T. (1979b). J. Cryst. Growth 46, 623. Bartlett, B. E., Capper, P., Harris, J. E., and Qulech, M. J. T. (1980). J. Cryst. Growth 49, 600. Becla, P., Dudziak, E., and Pawlikowski, J. M. (1977). Mater. Sci. IIU1-2, 27. Blair, J., and Newnham, R. (1961). “Metal of Elemental and Comp. Semicond.” (R. 0. Grubel, ed.), Vol. 12, p. 393. Wiley (Interscience), New York. Boinykh, N. M., Sokolov, A. M., Indenbaym, G. B., and Banukov, A. B. (1974a). Izv. Akrtd. Nauk S S S R Metall. No. 5, 240 (Russian). Boinykh, N . M., Sokolov, A. M., Indenbaym, G. V., and Banukov, A. B. (1974b). Izv. Akad. Nauk. SSSR No. 5 , 240 [English transl: Russ. Metall. 5 , 195(1974)]. Bonse, U. K., Hart, M., and Newkirk, J. B. (1966). A d v . X-Ray A n d . 10(1), 1. Bowers, J. E., Schmit, J. L., and Mroczkowski, J. A. (1979). Paper to IRIS-DSC 111 (private communication). Bowers, J. E., Schmit, J. L., and Mroczkowski, J. A. (1980a). IRIS-DSGM Conf., June I2. Bowers, J. E., Schmit, J. L., Speerschneider, C. F., and Maciolek, R. B. (1980b). IEEE l r u n s . Electron Devices ED-27,24-28. Bradford, A., and Wentworth, E. (1975). Injrured Phys. 15, 303. Brau, M. J. (1972). U.S. Patent 3 656 944. Brau, M. J., and Reynolds, R. A. (1974). U.S.Patent 3 849 205. Brebrick, R. F., and Straws, A. J. (1965). J. Phys. C h e m . Solids 26, 989. Brown, M. (1978). Private communication. Brown, M., and Willoughby, A. F. W. (1979). J. Phys. Suppl. C6 40, 151. Bye, K. L. (1979). J. Muter. Sci. 14, 619. Camp, R. J., Hitchell, M. L., Schmit, J. L., and Stelzer, L. (1976). U.S. Patent 3 963 540. Capper, P., and Harris, J. E. (1979). J. Cryst. Growth 46, 575. Carpenter, D. R., Manley, G. W., McDermott, P. S., and Riley, R. J . (1971). U.S. Patent 3 619 283. Chu, M., and Wang, C. C. (1980). J . Appl. Phys. 51(4), 2255-2257. Cohen-Solal, G., Marfaing, Y., and Bailly, F. (1967). J. Phys. Chern. Solids Suppl. 1, 549. Cohen-Solal, G., Zozime, A., Motte, C., and Riant, Y.(1976). Infrared Phys. 16, 555. Cullity, B. D. (1956). “The Elements of X-Ray Diffraction.” Addison-Wesley, Reading, Massachusetts.

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Manley, G. W., McDermott, P. S., Pan, E. S., and Riley, R. J. (1971). U.S. Patent 3 619 282. Micklethwaite, W. F. H., and Redden, R. F. (1978). Paper delivered to the N A T O Conf. C M T , Mulvern, United Kingdom. October. Nelson, D. A., Higgins, W. M., and Lancaster, R. A. (1980). Pror. Photo-Opt. Instrum. Eng. 225, 48. Newkirk, J. B. (1959). Trans. Mefull. S o c . A l M E 215, 483. Nishizawa, J., and Suto, K. (1976). J . Phys. C h e m . Solids 37, 33. Nowak, Z., Piotrowski, J., Piotrowski, T., and Sadowski, J. (1978). Thin Solidkilms 52,405. Ottel, H. (1973). Wiss. Z. Hochsch. Ilmenau 19(2), 53 (German). Parker, S. G., and Kraus, H. (1969). U.S. Patent 3 468 363. Parker, S. G., and Pinnell, J. E. (1971).J . Electrochem. Soc. 118(11), 1868. Parry, 3. M. (1976). Technical Rep. AFML-TR-76-157(NTIS AD A036918). Petty, M. C., and Juhaqx, C. (1976). J . Phys. D A p p l . Phys. 9(3/4), 1605. Piotrowski, A. (1976). Electron Techno/. 9(3/4), 83. Polisar, E. L., Boinykh, N. M., Indenbaum, G. V., Vanyukov, A. V., and Schastlivyi, V. P. (1968). IZV. Vyssh. Uchehn. Zaved. Fiz. 11(6), 81 [English trunsl.: J . Sov. Phys. 11,48 (1968)l. Pollack, F. (1979). Final Rep. AFOSR -TR-79-0452. Ray, B., and Spencer, P. M. (1967). Phys. Status Solid; 22, 371. Riley, K . F. (1977). PhD Thesis, Syracuse Univ. Rodot, H., and Henoc, J. (1963). C. R . Acud. Sci. Paris 256, 1954. Rodot, H., and Schneider, M. (1979). U.S. Patent 4 167 436. Rogers, C. J. (1979). Private communication. Schmit, J. L. (1969). Final Technical Rep. to U.S. Night Vision Laboratory Contract DAAB09-68-C-0073,p. 50. Schmit, J. L. (1971). U.S. Patent 3 622 405. Schmit, J. L., and Bowers, J. E. (1979).Appl. Phys. Lett. Schmit, J. L., and Scott, M. W. (1976). U.S. Patent 3 954 518. Schmit, J. L., and Speerschneider, C. J. (1968). Infrared Phys. 8, 247. Schubert, F., Dittmar, G., and Forburg, B. (1978). Krist. Tech. 13, 1203 (German). Schulman, J. N., and McGill, T . C. (1979).Appl. Phys. Letr. 34(10), 663. Schwartz, J. P. (1977). PhD Thesis, Marquette Univ., Milwaukee, Wisconsin. Shakhnazaov, T. A. (1979).Izv. A d u d . Nuuk. S S S R N m r g . M a t . 15( I), 56 [English trunsl.: Inorg. Mater. 15(I)]. Schneider, A. D.. and Gavrishchak, I. V. (1963). U k r . Fiz. Zh. (USSR) 8(9), 1028. Steininger, J. (1970).J . Appl. Phys. 11(6), 2713. Steininger, J. (1976). J . Electron. Muter. 5(3), 299. Steininger, J. (1977). J . C r y s f . Growth 37, 107. Steininger, J., and Strauss, A. J. (1972).J. Cryst. Growth 13/14, 657. Svob, L., Marfaing, Y.,Triboulet, R., Bailly, and Cohen-Solal, G. (1975). J. Appl. Phys. &(lo), 4251. Swink, L. N., and Brau. M. J. (1970). Merull. Truns. 1, 629. Takase, Y. (1974).J . Appl. Phys. 13, 539. Ta-Wei, Fu, and Wilcox, W. R. (1980). J . C r y s f . Gronsrh 48, 416-424. Tiller, W. A. (1963). "The Art and Science of Growing Crystals," p. 294. Wiley, New York. Triboulet, R. (1977). R e v . Phys. A p p l . 12, 123 (French). Tufte, 0. N., and Stelzer, E. L. (1969). J. Appl. Phys. 40(11), 4559. Ueda, R. (1980). Private communication. Ueda, R.. Ohtsuki, J.. Shinohara, K.,and Ueda, Y . (1972). J . C r y s t . Growth 13/14, 668. Vanier, P. E., Pollack, F. H., and Raccah, P. M. (1980). J. Electron. Muter. 9, 153.

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Vanyukov, A. V., Krotov, I. I., and Ermakov, A. I. (1977). Izv. Akad. Nauk. S S S R Neorg. Muter. 13(5), 815 [English trans/.: lnorg. Muter. 13(5)]. Vanyukov, A. V., Krotov, I. I., and Ermakov, A. I. (1978). Izv. Akad. Nauk. SSSR Neorg. Muter. 14(4), 657 [English trunsl.: Inorg. Muter. 14(4)]. Vere, A. W. (1978). Paper delivered to the N A T O Workshop CMTMulvern, United Kingdom, October. Vohl, P., and Wolfe, C. M. (1978). J . Electron. Muter. 7(5), 659. Wagner, J. W., and Willardson, R. K. (1968). Trans. A l M E 242, 366. Wang, C. C. (1978). Paper delivered to N A T O Workshop C M T Malvern, United Kingdom, October. Wang, C. C., Chu, M., Shin, S. H., Tennant, W. E. et a / . (1980a). IEEE Trans. Electron Devices ED-27,154- 160. Wang, C. C., Shin, S. H., Chu, M., Lanir, M., and Vanderwyck, A. H. B. (1980b). J. Electrochem. Soc. 127, 175-178. Winegard, W. C. (1964). “An Introduction to the Solidification of Metals,” p. 1. The Institute of Metals. Wong, J. Y ., and Eck, R. E. (1980). Interim rep., Exploratory Development on the Growth of CMT by LPE (AFML-F33615-78-C-5226). Zozime, A., and Cohen-Solal, G. (1979). Vide Couches Minces Suppl196,145- 154 (French). Zozime, A . , Sella, C., and Cohen-Solal, G. (1972). Thin Solid Films 13, 373.

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SEMICONDUCTORS AND SEMIMETALS. VOL. I8

CHAPTER 4

Auger Recombination in Mercury Cadmium Telluride* Paul E . Petersen I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 1 . Recombination Mechanisms . . . . . . . . . . . . . . . . 2. Dejinition of Lifetime . . . . . . . . . . . . . . . . . . . 11. AUGERLIFETIME I N NONDEGENERATE MATERIAL. . . . . . . 3. The Parabolic Band Approximation . . . . . . . . . . . . . 4. Nonparabolic Bands and k-Dependent Overlap Integrals . . . 5. Calculation of the Threshold Energy for the Auger Transitions . 6. Effects of the Light-Hole Band . . . . . . . . . . . . . . . 111. AUGERLIFETIME I N DEGENERATE MATERIAL. . . . . . . . . IV. EXPERIMENTAL RESULTS. . . . . . . . . . . . . . . . . . . V. SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . APPENDIX.. . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . .

121 121 125 126 126 135 138 139 143 148 151 152 154

I. Introduction The alloy system Hg,-,Cd,Te was initially developed for use as an infrared photon detector material. Research centered initially on the development of intrinsic photoconductive detectors (P. W. Kruse, this volume, Chapter I), but recently much of the work has been directed to the development of photovoltaic detectors (M. B. Reine et al., this volume, Chapter 6). As we discuss in the Appendix, in both of these detection modes the device performance depends critically on the lifetime of the photoexcited carriers. In fact, the ultimate performance of infrared photovoltaic detectors can be limited by the Auger lifetime. 1 . RECOMBINATION MECHANISMS As discussed by Blakemore (1962) and Dornhaus and Nimtz (1976), there are three fundamental recombination mechanisms by which thermo* Supported in part by the Air Force Office of Scientific Research under contract F49629-77-C-0028.The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon. 121

Copyright 0 1981 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-752118-6

122

PAUL E. PETERSEN CONDUCTION BAND

-fT-(a)

VALENCE BAND

(b)

FIG. 1 . Semiconductor equilibrium mechanisms: (a) Shockley-Read recombination, (b) radiative recombination, (c) Auger recombination, and (d) impact ionization.

dynamic equilibrium is established in semiconductors: Shockley -Read recombination, radiative recombination, and Auger recombination. These mechanisms are schematically illustrated in Fig. 1. In the Shockley-Read mechanism, recombination occurs via energy levels within the forbidden energy gap of the semiconductor. These energy levels are due to lattice defects and impurities in the semiconductor and can, in principle, be controlled by the procedure used to grow the material; hence, the Shockley-Read mechanism is not a fundamental limit to the carrier lifetime. The Auger and the radiative mechanisms are fundamental, however, and are determined by the electronic band structure of the semiconductor. In radiative recombination the excess energy which the conduction-band electron gives up as it annihilates a hole in the valence band is converted into a photon. This mechanism is of central importance to light-emitting diode operation. The theory of radiative recombination in semiconductors has been well developed by van Roosbroeck and Shockley (1954) and reviewed by Hall (1959). It turns out that to a good approximation the radiative lifetime is inversely proportional to the total concentration of free electrons and holes. The Appendix shows that the maximum performance of infrared photon detectors is achieved in those materials that are limited by the radiative lifetime. Consequently, it is desirable to have the Auger mechanism weaker than the radiative mechanism. Whereas radiative recombination is a two-particle (electron and hole) mechanism, Auger recombination is a three-particle interaction. Figure lc shows one of the Auger transitions for a simple two-band model of a semi-

4.

AUGER RECOMBINATION IN MERCURY CADMIUM TELLURIDE

123

conductor. In this mechanism an electron in the conduction band recombines with a hole in the valence band. The energy lost by the electron which falls to the valence band is transferred to a second conduction-band electron by the electron-electron interaction. This “second” electron is excited higher into the conduction band. (Note the similarity between this transition and the familiar Auger transition of atomic physics in which an inner core electron falls to a lower orbital state and in the process ejects an electron from the atom. The Auger transition in semiconductors derives its name from this similarity.) The second electron does not stay in the excited state, but returns to is initial state by phonon emission via the electron-lattice interaction. Here we are only interested in the first part of the transition, i.e., the electron-electron interaction. Figure Id shows the electron transitions for impact ionization, in which a high-energy conduction-band electron falls to the bottom of the conduction band and in the process gives up its excess energy to a valence-band electron, thereby creating an electron-hole pair. Auger recombination is the reciprocal process of impact ionization in the same way that radiative recombination is the reciprocal process of optical absorption. In impact ionization the initial state consists of a single high-energy electron and the E

7

HEAVY-HOLE BAND

k

LIGHT-HOLE

A

LL SPLITOFF

FIG. 2. Schematic of the band structure of (HgCd)Te showing the energy bands around the r point that are involved in Auger transitions. The features are exaggerated to illustrate the characteristics of the different bands.

PAUL E. PETERSEN

124

final state two low-energy electrons and a hole. Analogously, in Auger recombination the initial state has three particles and the final state but one electron. Since these are reciprocal processes, the principle of detailed balance requires that in thermal equilibrium the rate at which electronhole pairs are created by impact ionization must exactly equal the rate at which they are annihilated by Auger recombination. The band structure of (HgCd)Te (Kane, 1957; Overhof, 1971; Katsuki and Kunimune, 1971) is more complicated than that of the simple twoband model depicted in Fig. 1. As shown in Fig. 2, there are four bands of interest around the r point where the direct bandgap occurs in (HgCd)Te. The splitoff band in (HgCd)Te is approximately 1.O eV below the heavyand light-hole maxima, which are degenerate at the r point. Hence, for Auger recombination the splitoff band can be ignored in calculating the transition rates but the light-hole band may well be important, especially for p-type (HgCd)Te. Beattie (1962) has determined all of the possible phononless transitions that result in pair production in a semiconductor with a single conduction band and heavy- and light-hole valence bands. In Fig. 3 we show the reciprocal or Auger recombination mechanisms for each of these ten transitions. For ease of comparison to Beattie’s work we maintain a similar numbering system. For example, in this paper AM-7 is the same as Beattie’s mechanism 7. It can be shown that AM-1 is the dominant mechanism in n-type (HgCd)Te, so this mechanism has received the most attention thus far.

AM-1

AM6

AM-2

AM-7

AM-3

AM4

AM-5

AM%

AM-9

AM-1 0

FIG.3. The ten types of phononless Auger recombination mechanisms which are possible in (HgCd)Te. The arrows indicate electron transitions. [From Beattie (1962).]

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AUGER RECOMBINATION IN MERCURY CADMIUM TELLURIDE

125

AM-3, and to a lesser extent AM-7, have received some consideration in p-type material. The relative importance of these mechanisms to recombination in (HgCd)Te will be discussed in Part 11. 2. DEFINITION OF LIFETIME The study of physical processes in semiconductors has led to several definitions and concepts of lifetime. To avoid misinterpretation, we define at the outset the concept of lifetime which is used in this review. We begin with the continuity equations for electrons and holes (Blakemore, 1962; Many et al., 1965):

an _ - [g" at

- r"] + UEXl+ - V * P,

_ ap - [g"

- P]+ U&

at

1 e

1 v * Jp. e

--

The electron and hole concentrations are given by n and p, respectively; g and r denote respectively the generation and recombination rates per unit volume due to "natural" processes, i.e., those processes which exist in the absence of an external perturbation. Uextdenotes the generation rate due to external sources, e.g., radiation, and J is the particle current density which in general consists of both drift and diffusion terms. The superscripts n and p denote electron and hole processes, respectively. Equations (la) and (1b) form the basis for the calculation of the current in a p - n junction. The relaxation lifetime 7" is defined for electrons by g n - r" = - A n / r " ,

(2)

and is the definition we will employ. A similar definition exists for the hole lifetime 9.An and Ap give the difference between the electron and hole concentrations and their respective equilibrium values. Note that when the divergence of the particle current vanishes the continuity equation for electrons becomes simply abn = UEx1- An at

7"

(3)

'

and that if 7" is independent of time this results in a simple exponential decay of An when the external perturbation is removed. Hence the name relaxation lifetime. Generally 7" and r p are dependent on the carrier concentrations; nevertheless Eq. (2) is still used to define 7. There are several mechanisms which can contribute to 7" and but here we are concerned only with Auger processes. We define the Auger

+',

126

PAUL E . PETERSEN

lifetime, ~;1,for electrons by

( n - neq)/(rA - &?A)? (4) where the subscript A denotes an Auger transition and eq implies an equilibrium process or condition. Note that the lifetime defined above relates to the relaxation of the carrier distribution to equilibrium. It is not necessarily equal to the microscopic lifetime which is defined as the average time an electron (hole) remains in the conduction (valence) band. The microscopic lifetime is defined by (Ryvkin, 1964)

6

=

where N k is the density of capturing centers of the kth type, a; is the cross section for capture of an electron by these centers, and v ; is the relative velocity. In the steady state with V * J , = 0 the rate of generation should equal the rate of capture, or

This leads to Gicm

=

(neq

+ An)/(g” +

E x J .

(7)

Hence, only for high levels of excitation when An >> nep and U;xt>> g ” does the microscopic relaxation time equal the relaxation lifetime. Here we discuss only the relaxation lifetime since that is the lifetime parameter generally of interest for infrared detectors. 11. Auger Lifetime in Nondegenerate Material

3. THE PARABOLIC BAND APPROXIMATION

To determine the Auger lifetime it is first necessary to calculate the transition rates; hence, one must determine whether the electron states involved are degenerate or nondegenerate. The assumption of nondegeneracy is usually valid for the valence-band states, but there are practical cases of interest when the states in the conduction band become degenerate. The general solution for the Auger lifetime for a fully degenerate semiconductor has not been completely solved; furthermore, the analytical complexities of the degenerate solution tend to bury the physics in mathematical detail. Therefore, we shall defer to Part 111 a discussion of the effects of degeneracy on the Auger lifetime and first discuss the calculation when both bands are nondegenerate.

4.

AUGER RECOMBINATION IN MERCURY CADMIUM TELLURIDE

127

The Auger transition involves electron states over a broad range of electron energies. The lowest-lying states are near the conduction band edge, but the high-energy states lie at least an energy bandgap above the band edge. Hence, a rigorous calculation of the Auger lifetime must include the effects of nonparabolicity in the energy-band structure. However, as we shall see later, including the nonparabolic nature of the energy bands increases the complexity of the calculation and in fact prohibits one from obtaining a reasonably simple analytical expression for the lifetime. In order to obtain insight into the physical mechanisms and to identify those parameters which play a major role in determining the lifetime it is helpful to first calculate the Auger lifetime in the parabolic band approximation. Much of the work reported in the literature ignores the effects of nonparabolicity . We therefore proceed with a discussion of the Auger lifetime in nondegenerate n-type material. Of the ten Auger mechanisms shown in Fig. 3, ,4M-1 is the controlling Auger mechanism in n-type (HgCd)Te. We will discuss the reasons for this in more detail later on, but for now we present only an intuitive argument. From Fig. 3 we see that there are two different types of Auger recombination mechanisms: (1) the electron-electron (e-e) mechanism in which two conduction-band electrons interact with a valence-band hole resulting in electron-hole pair annihilation with the remaining electron excited higher into the conduction band; (2) the holehole mechanism in which two holes in the valence band(s) interact with a conduction-band electron resulting in the excitation of a deep valenceband electron to a higher energy state as the electron-hole pair recombines. Transitions 1 and 2 in Fig. 3 are e-e processes while all the others are h-h processes. Intuitively, in n-type material due to the predominance of electrons the e-e processes will dominate over the h-h processes; therefore eight of the ten mechanisms can immediately be dropped from consideration. The threshold for AM-I is lower than for AM-2, because for AM-1 the large mass and hence small curvature of the heavy-hole band permits transitions in which electrons very near the conduction-band edge recombine with valence-band holes. In AM-2, on the other hand, transitions in which a near band-edge electron recombines with a hole are not allowed, since for this transition energy and momentum cannot be simultaneously conserved. Owing to the conservation of energy and momentum, it turns out that the threshold for AM- 1 is approximately equal to the energy bandgap E , , while for AM-2 the threshold is approximately (#)E,. Hence, for n-type (HgCd)Te the light-hole band does not play a major role in the Auger recombination process, and we need only consider AM- 1. Auger mechanism 1 was first analyzed in detail by Beattie and Landsberg (1959) in a classic paper on the Auger effect in semiconductors. Their

128

P A U L E. PETERSEN

work forms the basis for much of the existing theory of Auger processes in semiconductors. The lifetime defined by Eq. (4) is determined primarily by the net rate of recombination. [g“’ - @]. In general the generation and recombination rates per unit volume V for an Auger process are given by

k space

x

spin states

Tif d3k1d3kz d’k; d3k;,

(8)

where Ti, is the probability of a transition from the initial to final state in time r . B(k,k,;k;k;) = O(k,)O($)O(k;)O(k;)t where O(kJ is the appropriate probability of electron occupancy or vacancy of the state with wave vector k,; e.g., for AM-1: Wkikz ;k;kL) = [f(ki)I[f(kdI[1 - f(ki)I[l - f(k;)I,

(9)

wheref(k,) is the Fermi-Dirac distribution function. For a nondegenerate system in which the excess carrier density is small enough so that the distribution function is adequately described by a quasi-Fermi level one can, with a little algebraic manipulation, show that the probability factors may be expressed in terms of the equilibrium occupancy factor and the carrier densities, i.e.,

where n = n,, + An is the electron density. It follows that for this case the generation and recombination rates are given by

In equilibrium the generation rate must equal the recombination rate; therefore, with the aid of Eqs. (4) and (11) we can write

where we have assumed An = Ap. The problem is now reduced to calculating the equilibrium generation rate. t Our notation is that k, and kz are initial states for electrons in the conduction band or valence band, respectively, while k; and k4 are the final states for similar electrons.

4.

AUGER RECOMBINATION IN MERCURY CADMIUM TELLURIDE

129

The generation rate, given by Eq. (B), is obtained by integrating the over all possible one electron states. In general transition probability Ti, Ti, is given by (Schiff, 1955)

where x = ( t / f i ) (El - Eil, Ef and Eiare the energies of the initial and final states, and Uifis the matrix element of the interaction. The wave function is a product of a spatial function 4(k,r) and a spin function ~ ( s )Three . of the possible spin states are symmetric (triplet) while the fourth is antisymmetric (singlet). The perturbation H") for the electron-electron interaction is simply the screened Coulomb potential and so is independent of the electron spin. Hence, after summing over the spin states the generation rate reduces to

X

1 - cos x X2

d3k1d3k2d3k; d3k4,

where I UgTl = (cf$,,T~(l)I&,T) electron state is given by

.The perturbation energy of the two-

H(1'(r1,r2)= e 2 exp(-Alr, - r21)/~lrl- r,l, where A is the screening distance and E the dielectric constant. If we neglect umklapp processes, change the summation over reciprocal space to an integration, and utilize the fact that H"' is symmetric in r, and r, , we can obtain the following expression for the matrix elements:

where g = k, - k; and h = k, - k; . The Fit are the so-called overlap integrals; for example, Fl is given by Fdk,

=

1

u3k1, r ) 4 4 ,r) @ r ,

(16)

where u,(kl ,r) is the periodic part of the electron wave function. In order to simplify the problem and to gain insight into the dependence of the Auger lifetime on temperature and energy-band parameters, it is t We use here F, to denote the overlap integrals to be consistent with the notation of the classic Beattie and Landsberg (1959) paper.

130

PAUL E . PETERSEN

convenient for now to assume that IFIF$ = IF3F4I2= constant. We will return later to a more complete discussion of the overlap integrals. If we substitute Eq. (15) into Eq. (14) and assume constant overlap integrals, we find that g$ is the sum of three integrals. With a little algebra one can show that two of these integrals are equal and that the third is less than the first two. Hence, the equilibrium generation rate satisfies the inequality 2[gk','l' < sk: < 3[g"l',

(17)

where

d3kl d3kl, d3k2i.

(18)

Equation (18), a complicated integral, is essentially Eq. (5.3) of Beattie and Landsberg's (1959) original paper. For nondegenerate statistics [92)Ieq= Ae-E(kl)ikT, with A a normalization constant. After some manipulation it is possible to reduce the integral in Eq. (18) to a single integration from kih to 00; kih is the minimum value (i.e., threshold) of the electron which has absorbed the recombination energy. For parabolic bands the threshold energy for impact ionization is &, = h 2 ( k ~ ) * / 2 mBeattie ,. and Landsberg discuss the solution of this integral; neglecting the effects of screening, assuming parabolic bands, and for nondegenerate statistics they find

where [gk:] = 2gL:', and p is the ratio of the conduction band to the heavy-hole valence-band effective mass. Equation (19) is the result which has been widely used in the current literature (Blakemore, 1962) to calculate the generation rate for AM-l. The lifetime, with the above approximations and assumptions, is easily obtained for n-type material by substituting Eq. (19) into Eq. (12). If we wish to extend this calculation to include p-type material, while retaining the two-band approximation (i.e., neglect the light-hole band) we see from Fig. 3 that we must include AM-3. AM-3 is a hole-hole process; note, however, that if the schematic for AM-3 is inverted, it has the same general features as AM- 1. To the same level of approximation,

4.

AUGER RECOMBINATION I N MERCURY CADMIUM TELLURIDE

131

the generation rate for AM-3 may be obtained from Eq. (19) by simply interchanging m, and m, . This yields

By comparing Eqs. (19) and (20) we see that in (HgCd)Te where p << 1, << g:! so AM-1 will dominate AM-3 unless the material is heavily p-type. From the arguments preceeding Eq. (12) it follows that, for nondegenerate statistics gki

By substituting Eqs. (19), (20), (21), and (8) into Eq. (4) we find that the total Auger lifetime in this two-band approximation is given by TA

=

n4 (neq

+ Peq + An)(g'&Peqn + g'i3&neq)

where again we have used An

=

neqgg = (pl")(l = PessL!

Ap and

+ 2p) exp [- (-)

2+P

&]

l + p kT'

(23)

From Eqs. (22) and (23), we see that for intrinsic material with p << 1 the lifetime is given by

where ni is the intrinsic carrier concentration. Note thatg;; varies linearly with neq, so the factor neq/2gL','in the numerator of Eq. (22) is independent of carrier concentration. Equation (22) is in a very convenient form for studying the temperature and carrier concentration dependence of the Auger lifetime. We consider the expression in the limit of small modulation (An << neq) and in Fig. 4 plot T A / T A ~ as a function of neq/ni for various values of p. There are three distinct regions of carrier lifetime. First, in the limit of small modulation in n-type material, the lifetime varies as the inverse square of the carrier concentration, i.e.,

132

PAUL E. PETERSEN

10-4

10-3

10-2

10-1

1

10

lff

neq'n,

FIG.4. Ratio of the extrinsic to Auger lifetime as a function of carrier concentration for various values of the parameter p.

where use is made of the relation2n:~~~ = nfn,,/gLt, which is proportional to exp[(p/( 1 + p)(E,/kT)].The Auger lifetime therefore varies exponentially with the energy bandgap, as expected. The small conduction-band effective mass ( p << 1) in (HgCd)Te significantly reduces the carrier lifetime. For small values of /3 there is a regime where the lifetime is independent of the carrier concentration and equal to the intrinsic lifetime. This regime occurs when peq> n,, and n,, > /3peq, so that the denominator of Eq. (22) is simply n,~,,, = nt. Finally, for sufficiently p-type material so that p e s >> n,,/P the Auger lifetime vanes as the inverse square of the hole

4.

AUGER RECOMBINATION IN MERCURY CADMIUM TELLURIDE

133

concentration. In this regime

The fact that in this simple two-band model the Auger lifetime in n-type material is significantly shorter than in similarly doped p-type material is a direct consequence of the difference in the effective masses of the two bands. For example, when p = 1, p = 1 and the lifetime in similarly doped n- and p-type material is the same. For (HgCd)Te, however, p is always much less than unity. , the carrier concentraAccording to Eq. (22), we need only p, T A ~and tion in order to calculate the Auger lifetime to this level of approximation. In Fig. 5 we plot T~~ = 42s: as a function of reciprocal temperature for

I

/

/ X=0.25

FIG. 5. Intrinsic Auger lifetime (nt/2&3 as a function of reciprocal temperature for various values of alloy compositions.

134

PAUL E . PETERSEN

various values of alloy composition x, and in Fig. 6 we plot the parameter

p as a function of x for several values of the temperature. This allows a computation of the Auger lifetime for arbitrary values of carrier concentration, alloy composition, and temperature. For these calculations we have computed the energy bandgap according to the expression of Schmit and Stelzer (1969). Following Kane (1957) and Schmit (1970) we used m,/m, = 3h2E,/(4P2mo)= 0.O706Eg for the conduction-band effective mass where P is the matrix element

020

025

030

035

0.40

045

X

FIG.6. values.

p [defined

by Eq. (23)] as a function o f alloy composition for various temperature

4. AUGER

RECOMBINATION I N MERCURY C A D M I U M TELLURIDE

135

from k p perturbation theory. For the valence-band effective mass we used m, = 0.55m0(Kinch ef al., 1973). For the intrinsic carrier concentration we used Schmit’s (1970) calculation. A constant value of 0.25 was assumed for the overlap integral and we used Baars and Sorgen’s (1972) expression for the dielectric constant. In order to obtain the relatively simple analytical expression of Eq. (22) and the results of Figs. 4-6 several simplifying assumptions were made; for the completeness we list them below. (1) Only the conduction band and heavy-hole band were considered, i.e., the light and split-off hole bands were ignored. (2) The bands were assumed parabolic. (3) A constant value was assumed for the overlap integrals, i.e., the k dependence was ignored. (4) Nondegenerate statistics were employed for both electrons and holes. The above assumptions are moderately good for lightly doped, n-type (HgCd) Te and result in a good first estimate of the Auger lifetime. However, as we shall show in the remaining sections, improved values of the carrier lifetime can be calculated by removing these four assumptions. This is particularly evident in calculating the lifetime in p-type material where inclusion of the light-hole band significantly reduces the lifetime over that predicted from the two-band model discussed above. 4. NONPARABOLIC BANDSA N D k-DEPENDENT

OVERLAP INTEGRALS The theory of the Auger lifetime presented in Section 3 used several simplifying assumptions. In this section, following the work of Petersen (1970) we remove the assumptions of parabolic bands and constant overlap integrals and calculate the Auger lifetime in nondegenerate n-type (HgCd)Te. The formalism developed in Section 3 is still applicable. Here we are concerned with n-type material, so only AM-1 need be considered since fi << 1. The Auger lifetime for this case then becomes TA

=

2 nfneq/2gk\’ + An)‘ (neg + Peq +

(27)

As before, the equilibrium generation rate determines the lifetime so we outline the calculation of g:: including the effects of nonparabolicity and k-dependent overlap integrals. When calculating the transition probabilities for the Auger transitions, it is necessary to calculate the matrix elements of the screened Coulomb interaction. In so doing it becomes necessary to calculate integrals of the

136

PAUL E. PETERSEN

form of Eq. (16). In general, these integrals will depend on the wave vectors and a rigorous calculation must include this dependence. The wave functions for (HgCd)Te are not sufficiently well known for an exact determination of these integrals, and methods of approximation must be used. The method generally employed to calculate the overlap integrals for the Auger transitions involves finding the wave functions by firstorder perturbation theory. Then by using the so-calledf-sum rule the integrals are reduced to a form which depends only on the energy bandgaps and effective masses of the energy bands. It follows directly from k p perturbation theory (AntonEik and Tauc, 1966) that the overlap integrals can be expressed as

+

+

where n and n ' are the band indices, k q and k q' are the momentum states of the electrons before and after the transition, and a, /3 denote the k vector coordinates. They,,, are the oscillator strengths which satisfy the sum rule (AntonEik and Landsberg, 1963)

where (l/m);{ is the effective mass tensor for the nth band for momentum state k. Summing over the band index in Eq. (29) along with Eq.(28), we obtain the following simplified expression for the sum of the overlap integrals :

where we have assumed spherical energy surfaces. The overlap integral between the conduction band and the heavy-hole band needed to calculate the lifetime in n-type material is easily obtained from Eq. (30). If we let n denote the heavy-hole band and accept the argument of Kittel and Mitchell (1954) that the overlap intergrals between valence bands are small, then for small values of the wave vectors we obtain

4.

AUGER RECOMBINATION IN MERCURY CADMIUM TELLURIDE

137

There are some questions which we will discuss later concerning the use of these assumptions in calculating overlap integrals involving the lighthole band; however, historically Eq. (31) has been used to calculate the heavy-hole overlap integral required to determine the Auger lifetime in n-type (HgCd)Te. According to k p perturbation theory the intraband overlap integrals e.g., F3F4 of Beattie and Landsberg (1959) are approximately unity (AntonEik and Landsberg, 1963). Using this fact and Eq. (31) for the conduction/heavy-hole overlap integral, which now is under the integral in Eq. (18), Petersen finds

kp, the magnitude of the high-energy conduction-band electron at threshold, will be discussed in more detail later:

and 2g&)'< g:.','< 3gLt. The parameter a derives from the Kane (1957) band structure which was used to describe the k dependence of the conduction band. Schmit's (1969) expression was used for the energy bandgap. The expression for the generation rate is now reduced to a single integration in k space which can be evaluated by straightforward nues < 3g"" eq , so the minimum value merical techniques. As before 2gk'," < g"' for the lifetime is given by (7Ai)min

=

ni/6gk',".

The extrinsic lifetime is obtained by direct substitution of the above equation into Eq. (12). Figure 7 shows the temperature dependence of the Auger lifetime in n-type (HgCd)Te for two different alloy compositions when the extrinsic carrier concentration is lOI4 ~ m - Note ~ . that the result obtained is in close agreement with that obtained in Section 3 when the nonparabolicity and k dependence of the overlap integrals were neglected. This agreement is due to the fact that the constant value for the overlap integrals was selected to give results consistent with this more rigorous calculation.

138

P A U L E. PETERSEN

x=o2

10

H I

3

,

I

1

I

1

5

7

9

11

I 13

10311’ (K-’)

FIG.7. Temperature dependence of the Auger lifetime in (HgCd)Te for two alloy cornpositions. [From Petersen (1970).]

5 . CALCULATION OF THE THRESHOLD ENERGY FOR

THE

AUGERTRANSITIONS Hall (1959) has shown from rather general arguments that the Auger lifetime depends exponentially on the threshold energy. The threshold energy is defined as the minimum energy which an electron or hole requires in order to impact ionize, i.e., create an electron-hole pair. Since Auger recombination is the reciprocal process to impact ionization, the thresholds for these two processes are equal, The threshold energy is required for all calculations of the Auger lifetime, and is the single most important parameter used to determine the relative strengths of the various Auger generation rates. For sake of illustration we will calculate the threshold energy for AM-3, but the procedure is equally valid for all of the ten mechanisms. To simplify the calculation we will assume that all bands are parabolic. From the conservation of energy, it is easy to show that kl is the longest wave vector, and for a most probable transition, i.e., least energy, Beattie and Landsberg (1959) show that the four k vectors will be colinear.

4.

AUGER RECOMBINATION I N MERCURY CADMIUM TELLURIDE

139

Conservation of momentum gives

kl

=

k,(k,rk2tk2) = kit

+ k2t

-

k2.

(33)

The problem then is to minimize k, subject to the constraint AE = Ei Ef = 0 where Ei and Ef are the initial and final energies respectively. We use the Lagrange method of multipliers (Courant and Hilbert, 1953) and define

L

=

k,

+ A AE.

(34)

Setting the derivative of L with respect to k , , , k 2 , , k2 = 0 gives the following relationships between the k vectors:

kit

=

k2,, klr

+ 2p)k2. E(k,) + E(k2) = E ( k ; ) + E(k;) gives

= - pk2,

k,

= - (1

Equation (35) along with threshold energy for transition AM-3:

(35) Ethr the

where p = mc/mh and E , is the bandgap energy. In (HgCd)Te since rn, << m h , the threshold energy is approximately twice the energy bandgap. Table I is a tabulation of the threshold energies for each of the ten phononless Auger mechanisms. The threshold energies for the electronelectron transitions are referred to the conduction band edge while the threshold energy for the hole-hole transitions is referred to the valence band edge. The subscripts h and 1 refer to the heavy- and light-hole bands, respectively. The implication of these results is discussed in Section 6, where we consider the relative importance of these transitions in p-type (HgCd)Te.

6. EFFECTSOF

THE

LIGHT-HOLEBAND

When the light-hole band in addition to the heavy-hole band is taken into consideration, all ten of the phononless Auger transitions can contribute to the recombination process. As seen in Section 5 for (HgCd)Te and like materials in which mc/mhand ml/mh<< 1, six of the ten mechanisms have a threshold energy which is greater than Eg while four have a threshold around Eg. Because the lifetime depends exponentially on the threshold energy the six mechanisms with &, >> Eg will not be dominant Auger transitions. Two of the four mechanisms with Eth Eg (AM-5 and AM-8) involve a final state in the light-hole band while the other two mechanisms (AM-1 and AM-7) have both final states in the heavy-hole band. Since the density of states in the heavy-hole band is much greater

-

TABLE I TABULATION OF THE THRESHOLD ENERGIES FOR THE TEN DESCRIBED I N FIG. 3 AUGERMECHANISMS Auger mechanism no.

Threshold energy"

Asymptotic value for p << 1, m, m ,

-

3

-large

-4

-large

10

Transition not allowed for tn,,

m, << mh

The threshold energy is relative to the conduction-band edge for electrons and to the valence-band edge for holes.

4.

AUGER RECOMBINATION IN MERCURY CADMIUM TELLURIDE

141

than in the light-hole band AM-1 and AM-7 will dominate. Earlier we saw that in the two-band model AM-3 is the dominant Auger recombination mechanism in heavily doped p-type (HgCd)Te, but AM-7 must be considered when all three bands are taken into consideration. Beattie and Smith (1967) have calculated the transition rate for AM-7. In this mechanism an electron in the conduction band recombines with a hole in the heavy-hole band; the energy lost in the recombination process is absorbed by exciting an electron from the light-hole band to an empty state in the heavy-hole valence band. In calculating the transition rate Beattie and Smith used the same perturbation theory as did Beattie and Landsberg for their calculation of the lifetime for AM-1, i.e., umklapp processes were neglected and spherical energy surfaces, and nondegenerate statistics were assumed. They did, however, take into consideration the effects of nonparabolicy in the bands and the k dependence of the overlap integrals. The calculation of Beattie and Smith proceeds in a manner similar to that described in Section 3 with the somewhat complicated result

where 7 t h = Eth/kT.D ( E t h ) is a function of the overlap coefficients and the band effective masses evaluated at the threshold energy, and I ( 7 t h ) is a complex integral over energy in the conduction band. In order to put Eq. (37) in a form which permits easier comparison with the lifetime calculated for AM-1, we assume that the quasi-Fermi level for the light- and heavy-hole bands is the same and use a constant effective mass for these two bands. With the above assumptions it readily follows that 7:)

where

T;!

=

{(neq/Peq)/[I

+

(neq/peq)1)27Li

9

(38)

is the intrinsic lifetime for AM-7 and is given by

From Eq. (12) we can in the limit of small modulation write 72’ in the form

72) = 2723/[ 1 + ( n e q / ~ e q ) ] . From this analysis it follows that

In similar manner, we find, for p << 1 ,

142

P A U L E. PETERSEN

Therefore to determine the relative importance of AM-7, we need only calculate the ratio y = T # / T ~ : . To calculate the ratio y of the intrinsic lifetimes we need values for the overlap integral coefficients am&). These coefficients are described in terms of the overlap integrals by

Beattie and Smith discussed three different methods of evaluating the anm and concluded that thef-sum rule approach described in Section 4 is the most accurate; i.e.,

where /3 = 1 for n , a valence-band index and /3 = 2 for n a conductionband index. We evaluate ah!' at the threshold which yields the result obtained earlier by Beattie and Smith:

where mso is the effective mass of the split-off band. The approximation holds since m, <<mh, msu. The coefficients a&) and a:? are found by evaluating the sum rule

at the threshold. Since a l h >> ash,and using Eq. (45) with = - (Ylh we -(h2/2mo)[mo/ml(kth)]. find a x We should point out that if the overlap integrals are evaluated at k = 0 rather than kth different results from those quoted above will be obtained for the amn (Beattie and Smith, 1967; AntonCik and Landsberg, 1963). In fact, if one follows the work of Kittel and Mitchell (1954) on donor states in Si and Ge where the intervalence overlap integrals are zero, (Ylh = 0. This result is valid only near k = 0. Casselman and Petersen (1980) argue that one should be consistent and evaluate all of the overlap coefficients at the threshold. Using the above values for the overlap coefficients and making some simplifying analytical approximations, they find

-

4.

AUGER RECOMBINATION I N MERCURY C A D M I U M T E L L U R I D E

143

-

where Eth= ,!# 6;)is the threshold for the transition. Over the range 0.16 < x < 0.3 and 50 K < T < 300 K, Eq. (47) yields 3 < y < 6. A more rigorous calculation (Casselman, 1980) shows that for the same range of x and T, 0.1 < y < 6. Hence, from Eq. (41), we see that AM-7 will be the dominant Auger mechanism in p-type (HgCd)Te, but that AM- 1 predominates in n-type material.

111. Auger Lifetime in Degenerate Material In our discussion so far, we have assumed that classical rather than degenerate statistics apply and so have used the Boltzmann distribution function to describe the probability of electron occupancy. This approximation is valid only at high temperatures and/or low carrier concentrations. For the opposite case, i.e., low temperature and high carrier concentrations, the Fermi-Dirac distribution function must be used in the calculation of the generation rates and subsequently the lifetime. The use of Fermi-Dirac statistics in no way alters the formalism for the Auger lifetime , but it does greatly increase the computational complexity of the problem. However, when the system becomes degenerate the physics of the recombination process could be greatly altered. For example, in general, the Auger lifetime varies exponentially with the threshold energy, which for the nondegenerate case is proportional to the energy bandgap; the greater the bandgap, the longer the lifetime. As the conduction band becomes degenerate, transitions to the states near the bottom of the band are no longer allowed (see Fig. 8). Haug (1978) points out that if one assumes (1) parabolic bands with isotropic effective masses (2) that the statistical factors are step functions and (3) that the k dependence of the matrix elements can be neglected,

FIG.8. Band schematic showing the transition for AM-I when the conduction-band electrons are degenerate.

144

PAUL E. PETERSEN

then in the limit of high modulation the Auger generation rate should vary as np rather than nzp as in the nondegenerate case. Hence with these assumptions in the degenerate regime T varies as l/n. Haug (1977) also has argued that standard Auger recombination, i.e., without phonon assistance, is not possible in direct-bandgap semiconductors under degenerate conditions because the inequality Ef2 (m,/2mh)E,cannot be satisfied. This argument, as pointed out by Gerhardts et a / . (1978), while valid for GaAs does not apply to (HgCd)Te. For example, for x = 0.2 E, = 75 meV, m c / m h 0.015 and Ef L 1.3 mev, the inequality is easily- satisfied for n 2 lOI4 ~ m - ~In. addition, the inequality was derived by Haug under the assumption that both the electrons and holes were degenerate. In (HgCd)Te, due to the relatively large hole effective mass Boltzmann statistics are usually valid for the hole states. Blakemore (1962) has summarized the conditions under which a semiconductor becomes degenerate. An electron system is nondegenerate when the Fermi energy lies below or very near the conduction-band minimum, i.e., q = ((E, - E , ) / k T ) is negative. For this case the probability of occupacy F ( E ) of the electron states is adequately described by a Boltzmann distribution. The range of temperatures and carrier concentration over which the conditions for nondegeneracy holds can be found from the expression for the equilibrium carrier concentration

-

(48) where g(E) is the density of energy states in the conduction band and

is the effective density of states in the conduction band. Fl,2(q)is one of the class of Fermi -Dirac integrals which have been tabulated by McDougal and Stoner (1938) over the range - 4 < q < 20. Figure 9 is a log-log plot of neq versus Tmc/mofor constant q. For a specific effective mass this graph allows a quick determination of the conditions for which the system is degenerate. For example, in n-type (HgCd)Te at 200°C the conduction-band effective mass is 0.007mofor this temperature degenerate statistics must be utilized when the carrier concentration exceeds 5 X l O I 5 cmP3. The hole effective mass in (HgCd)Te is, however, much larger (-0.55) so effects of degeneracy at 200°C do not set in until the carrier concentration reaches the mid-lO1*regimen. Figure 9 shows that

-

4. AUGER

RECOMBINATION IN ME:RCURY CADMIUM TELLURIDE

1014

01

1.o

10.0

145

I0

Trn,lmo (K)

FIG.9. Variation of the free-electron concentration with temperature and effective mass for various values of the reduced Ferrni level. [From Blakemore (19621.1

as the temperature is lowered while the carrier concentration held constant the system becomes increasingly degenerate, as it does when the temperature is held constant and the carrier concentration increased. For narrow-band semiconductors such as (HgCd)Te the above must be regarded as qualitative for 7 z 5 , since the effects of nonparabolicity in the conduction band become more noticeable as the electron system becomes increasingly degenerate. The formalism for the Auger lifetime for degenerate n-type material was established by Beattie and Landsberg (1959) in their original paper on the Auger effect in semiconductors. In heavily doped n-type material the effects of hole-hole collisions and the light-hole valence band are minimal. Only the electron-electron interactions of Fig. 3 need be considered, and

146

PAUL E . PETERSEN

the Auger lifetime takes the form

) qC = (& where a r = F-1~2(77c)/F1,2(77J and a, = F - ~ , ~ ( W ) / F & ~with E,)/kT and qv = (E, - E,)/kT. The solution of Eq. (50)proceeds in principle in the same manner as that described earlier for nondegenerate statistics with the exception that Fermi-Dirac functions are used for the statistical factors. Recently Gerhardts P[ a / . (1978) have discussed the Auger effect in n-type (HgCd)Te under degenerate conditions. Earlier experimental work (Dornhaus et a / . , 1976; Gerhardts, 1977) by these authors has shown that the Auger effect is important in (HgCd)Te down to He temperatures. They followed the Beattie-Landsberg formalism, assuming Boltzmann statistics for the valence band, but retained Fermi-Dirac statistics for the conduction band. The valence band was assumed parabolic and isotropic, but the conduction band nonparabolicity was included. The energy eigenvalues and the overlap integrals were obtained from a k p calculation. With these assumptions and conditions they find

X X

where N, is the density of states in the valence band, n' = dn/dEf, and q and Epare parameters which arise in calculation of the energy bandgap. M is essentially the matrix element of the interaction which has a very complicated dependence on the k vectors and band parameters of the electrons involved in the transition. Gerhardts rf ul. (1978) have numerically evaluated Eq. (51) over the temperature range from 1-300 K. The details of their numerical procedure were not published, but the results are shown in Fig. 10 where the Auger lifetime is plotted as a function of reciprocal temperature for several values of alloy composition. Note that for the higher n values the lifetime increases as expected, when the temperature is lowered from room

4.

147

AUGER RECOMBINATION I N MERCURY C A D M I U M TELLURIDE I

I

I

I

I

1

I

I 10-

-

u

0,

h

10-

I

10-

5

100

10

400

103/~ (K-?

FIG. 10. Temperature dependence of the lifetime for n-type Hg,,,C&,,Te for three different carrier concentrations. A: n = 1.7 x 1Ols ~ m - A: ~ ,n = 1.3 x I O l 5 ~ m - 0: ~ ,n = 4 x l O I 4 c m 3 . The dashed lines give the theoretical values for two different carrier concentrations. [From Gerhardts er al. (1978).]

temperature. When the intrinsic carrier concentration falls below the extrinsic value the lifetime rolls over and decreases with a further decrease in temperature. Finally, in the region of extreme degeneracy the lifetime again increases as the temperature decreases even more. Gerhardts et al. (1978) offer the following qualitative explanation for

148

PAUL E. PETERSEN

these results. If we keep in Eq. (51) the terms with the strongest temperature dependence and replace the others with a constant, we obtain 7i1 =

[const/N,(T)] exp( - fi2k5/2mhkT) J J

-

where kt = min(k, + kz - k,,)2. We can set [l - f(E,.)] 1; then the integral in Eq. (52) is proportional to n2.At high temperatures the intrinsic carrier concentration dominates the temperature dependence and T a P Z - ~ a exp[E,/kT]. Then at lower temperatures when the material becomes extrinsic, if the temperature is still too large for the exponential terms in Eq. (52) to dominate, the density of states term is dominant and 7 a PI2 and decreases with decreasing temperature. Finally the exponential term in front of the integrals dominates and again increases exponentially with decreasing temperature, but the apparent activation energy is lower by a factor of me/mhof that at the high temperatures. As we shall see in Part IV these results are in qualitative agreement with experimental results. Casselman (to be published) has employed a numerical calculation to determine the lifetime for AM-1 for strongly degenerate (n z 1) n-type (HgCd)Te. He neglected screening, used momentum dependent overlap integrals and an isotropic but nonparabolic conduction band. To make the calculation tractable he replaced the Fermi functions of the initial electron states with ramp functions. Under these conditions in the limit of low modulation he finds that 721

=

c(x7n’&,

where C(x,T) is a complicated function of x and T and h(

(53) 6

1.

IV. Experimental Results The primary intent of this chapter is to review the status of the theory of Auger recombination in (HgCd)Te. There is also ample experimental evidence that Auger transitions are important recombination mechanisms in (HgCd)Te. Space does not permit a comprehensive review of the experimental literature; rather, we present a few key results for n-type material with x 0.2 (the value of interest for 8-14 pm detectors), since much of the experimental data are for this particular x value. As discussed by Kinch et nl. (1973) the major problem in obtaining useful data on carrier lifetime is to reduce experimentally measured quantities to bulk lifetime. The early work of these researchers is perhaps the

-

4.

AUGER RECOMBINATION I N MERCURY CADMIUM TELLURIDE

149

'0

10-5

"

0 )I U

10-6

10-7

-

, -

10-6 3

8

7

5

9

11

13

103rr (K- l )

FIG.11. Temperature dependence of the lifetime for n-type (HgCd)Te for three different 0 : x = 0.205, n = 4.6 x 10" ~ m - [From ~ . samples. 0 : x = 0.205, n = 1.7 x 10'' Kinch ct a / . (1973).] A: x = 0.21, n = 4 x l0l4 ~ m - [From ~ . Baker et al. (1978).]

most thorough study of the lifetime in n-type (HgCd)Te. They used three independent methods: photoconductive response, short-circuit photoelectromagnetic current, and time response to a laser pulse to deduce the lifetime, and only reported those measurements which provided consistent results for all three methods. Some of their lifetime data along with those of Baker et al. (1978) are shown in Fig. 1 1 . Note first of all that for T > 120 K, the experimental lifetime T,,,, varies as exp(-const/T) and that in this region the slope of the semilog plot is in good agreement with the theoretical prediction shown earlier in Fig. 7. The absolute value of the lifetime varies by about a factor of two from the theoretical prediction which, considering the approximations in the theory, is fairly good agreement. At lower temperature the lifetime rolls over, as expected for Auger recombination. Hence, the temperature dependence of T , , ~ (x = 0.2) supports Auger recombination as the limiting mechanism. According to Eq. (Z),when Auger recombination is the limiting mechanism the lifetime in n-type material should vary as n-*. Bartoli el al. (1974) have measured the concentration dependence of T , , ~and, as shown find T cc n-2, as expected. We conclude in Fig. 12 for n > 1.5 x 1015 that Auger recombination does, at least for T 80 K, determine the lifetime in n-type (HgCd)Te with x 0.2.

-

-

150

P A U L E. PETERSEN

CARRIER CONCENTRATION

(~rn-~)

FIG.12. Experimental carrier lifetime as a function of carrier concentration at T = 80 K. [From Bartoli el d.(19741.1

The only experimental lifetime data available for (HgCd)Te in the degenerate regime are those of Gerhardts et al. (1978). These were shown in Fig. 10 along with the theoretical prodictions. We see that as before there is good agreement at high temperatures and that the general shape of the experimental data is consistent with the theory. The experimentally observed minima in the lifetime for all cases occur at a higher temperature than calculated. Gerhardts et ul. (1978) speculate that this discrepancy could result from the assumption of quasiequilibrium which may be invalid at low temperatures where the intraband energy-relaxation time is not much shorter than r A .In addition, it is possible that other than Auger transitions contribute at the very low temperatures. Takeshima (1 973) has calculated the dependence of the Auger lifetime on an’applied magnetic field. The magnetic field can split the energy bands into the so-called Landau levels. Because of this splitting, vertical Auger transitions are possible, since electrons can jump between Landau levels without changing momentum. The Auger lifetime should vary in an oscillatory manner with increasing magnetic field because the Auger transition probability is maximized when the separation between two Landau levels equals the energy bandgap. Gerhardts and co-workers (Dornhaus et ul., 1976; Gerhardts, 1977, 1978) have measured the lifetime in (HgCd)Te in the presence of a strong

4.

151

AUGER RECOMBINATION IN MERCURY CADMIUM TELLURIDE

-

I

“7

._

c 3

FIG.13. Magnetic field dependence of the lifetime for two compositions of n-type (HgCd)Te. [From Dornhaus rt a / . (1976).]

-

,$ f

0

1

2

3

4

5

6

7

MAGNETIC FIELD (lelsa)

magnetic field, and find the predicted magnetic quantum oscillations in the lifetime. In addition to the quantum oscillations (see Fig. 13) they also observed that at low fields the lifetime increased rapidly with the magnitude of the applied field. The experimental data on lifetime in (HgCd)Te clearly show that Auger recombination is an important mechanism in n-type material. Additional experimental work is required for p-type material to verify the importance of the light-hole band and for heavily doped n-type material to aid in a better understanding of the lifetime under degenerate conditions. V. Summary In summary, Auger recombination is an important lifetime limiting mechanism in (HgCd)Te. The theory for the dominant band-to-band phononless Auger transition is well developed for nondegenerate n-type material. Excellent agreement has been obtained between theory and experiment showing that the electron-electron Auger process in which an electron recombines with a heavy-hole is the dominant fundamental recombination mechanism in n-type (Hg,,,Cd,.,)Te. Both theory and experiment are not as well developed in p-type (HgCd)Te, but recent theoretical work shows that the light-hole band could play a significant role in Auger recombination in p-type (HgCd)Te. Some theoretical work has also been recently reported for degenerate n -type (HgCd)Te and there is qualitative agreement between theory and experiment down to 4 K . Additional experimental studies are required for both highly degenerate n -type and p-type (HgCd)Te. This chapter has reviewed only the phononless band-to-band Auger processes. Landsberg and Robbins (1978) have investigated phononassisted Auger processes involving band-to-band, single-trap, and donor-acceptor processes. There are other Auger processes which could

152

P A U L E . PETERSEN

be considered as well, e.g., transitions which involve excitons (Schmid, 1977),recornbination involving pairs of particles bound to the same defect (Bess, 1958), and finally Auger transitions between three different localized states (Glinchuk el al., 1976). It is beyond the scope of this review, but it would be interesting to calculate the lifetime in (HgCd)Te for each of these mechanisms. ACKNOWLEDGMENTS The author is greatly indebted to Don Long, who instigated the Honeywell program in Auger recombination in semiconductors, for his continued support and technical advice. Special thanks are due to Tom Casselman who reviewed the manuscript and made many suggestions for its improvement. Additional thanks are due to Marion Reine for many stimulating conversations on Auger recombination during the past several years. The help of Bette Linson who carefully typed the manuscript and Martha Collier-Brown who prepared the figures is gratefully acknowledged.

Appendix

It is important to establish the fundamental limits to detectivity in infrared photon detectors. For example, prior to 1976 it was generally believed that Auger recombination was weak in (PbSn)Te, since the ratio of the electron to hole effective mass in that material is nearly unity, which as we have seen implies a long Auger lifetime. Hence, a great deal of research was conducted to develop this material for infrared detectors. In 1976 Emtage showed that if in a multivalley semiconductor like (PbSn)Te one takes into consideration intervalley transitions, the Auger lifetime has the form

TAM"

exp(rE,/2kT)/nZ,

(Al)

where r the anisotropy parameter is the ratio of the transverse to longitudinal effective mass in each valley. For (PbSn)Te, r << 1 and so this anisotropy parameter acts to reduce the Auger lifetime in (PbSn)Te in the same way that the effective mass ratio reduces the Auger lifetime in (HgCd)Te. The point here is that if Emtage's theoretical work had been available earlier it is likely that less effort would have been expended in developing (PbSn)Te as an infrared detector material. Beyen and Pagel (1966) and Igras et ul. (1979) have investigated theoretically the effect of lifetime on the detection limits in photoconductors, and Fiorito et ul. (1977) have done the same for photovoltaic detectors. Perhaps the most lucid account of the influence of lifetime on the performance of infrared photon detectors is that of Long er al. (1978). In this appendix we summarize their results for a photovoltaic detector. Long

4.

AUGER RECOMBINATION I N MERCURY CADMIUM TELLURIDE

153

(1977) has shown that the ultimate performance of a photovoltaic detector exceeds that of a photoconductive detector. The spectral detectivity Df is the performance parameter most often used to compare the performance of infrared detectors; it is defined in general by

where is the total noise current, A is the detector area, Af is the bandwidth, and the spectral current responsivity is given by

RA = eqX/hc,

(A31

where q is the internal quantum efficiency and X is the wavelength of the incident radiation. Shot noise is the limiting noise mechanism in an ideal p -n junction; the noise current resulting from shot noise is given by

G = 2e{(ISat/P)[1+ exp(eV/PWI) Afi

(A41

where Isat is the reverse-biased diode saturation current, /3 is the numerical factor in the exponential term of the p-n junction currentvoltage characteristic and V is the applied bias. P lies between 1 and 2, and in an ideal junction where there is only minority-carrier diffusion current is exactly l . Substituting Eqs. (A3) and (A4) into Eq. (A2) we obtain

Therefore the saturation current is the factor which primarily determines the detectivity of an ideal photovoltaic detector. Melngailis and Harman (1970) presented a detailed theoretical analysis of the properties of ap-n junction photovoltaic detector. Long (1977) expanding on their work, showed that when a back reflecting contact is used the saturation current is given by Isat =

(3-

AeDnnp x tanh Ln

b<
Aebn 7n E,

where L, = is the minority-carrier diffusion length, T" is the minority-carrier lifetime, and D, is the diffusion coefficient. The thickness of the p layer is given by b, and n, is the minority-carrier concentration in the p layer. When b << L,, tanh(b/L,) +. b/Ln; hence, in this limit the saturation current is given by a constant times the ratio of the carrier concentration and the minority-carrier lifetime. From the theory of noise in semiconductors van Vliet (1958) we know

154

PAUL E . PETERSEN gth

= ((W2)/7" =

np/T",

(A71

where g t h is the total equilibrium generation rate. When Eq. (A7) is substituted into Eq. (A6) we obtain for V = 0 and p = 1

Dt

= ( v h / 2 h c ) m .

(A81

We assume the detector has an antireflection coating so that the quantum efficiency is given by 17 = 1 - exp(- ab),

(A91 where a! is the absorption coefficient. The thermal generation rate has an Auger g A and radiative gR component. The thickness b of the active region of the detector is chosen to maximize D f . With these additions we find finally Df (max)

=

0 . 3 2 ( X / h c ) d a / ( g A t- gH).

(A 10)

Ultimately, detector performance is limited by the absorption coefficient and the Auger and radiative generation rates. Hence, if the radiative genLong (1978) shows that eration rate dominates, 0;0~ (KR/a)-1'2. g,/a

=

8r(kT/h3c2)EZ,exp(-E,/kT)nf,

(A11 )

where n, is the index of refraction. For a particular cutoff wavelength Egis the same for all materials so g,/a = const x n: and for this case

D f (max)

nT1.

(A13

The optimum detector material is then one in which Auger recombination is weak compared to radiative recombination and one with the lowest possible index of refraction.

REFERENCES AntonEik, E.. and Landsberg, P. T. (1963). Proc. Phys. Snc. London 82, 337. Antonfik, E., and Tauc, J. (1966). In "Semiconductors and Semimetals" (R.K. Willardson and A. C. Beer, eds.), Vol. 2, p. 245. Academic Press, New York. Baars, J . . and Sorgen, F. (1972). Solid State Commun. 10, 875. Baker, I. M., Capocci, F. A., Charlton, D. E., and Wetherspoon, J . T. M. (1978). Solid Srute Ekcrron. 21, 1475. Bartoli, F., Allen, R., Esterowitz, L., and Kruer, M. (1974). J. A p p l . Phys. 45, 2151. Beattie, A. R. (1962). J. Phys. Chem. Solidr 24, 1049. Beattie, A . R., and Landsberg, P. T. (1959). Proc. R. Snc. k i n d u n Ser. A 249, 16. Beattie, A. R., and Smith, G. (1967). Phyc. Status Solidi. 19, 577. Bess, L. (1958). Phys. Rev. 111, 129. Beyen, W. J., and Pagel, B. R. (1966). Infrared Phys. 6 , 161. Blakemore, J. S . (1962)."Semiconductor Statistics." Pergamon, Oxford.

4.

AUGER RECOMBINATION I N MERCURY C A D M I U M TELLURIDE

155

Casselman, T. N. (1980). J . Appl. f h y s . 52, 848. Casselman, T. N., and Peterson, P. E. (1981). Solid State Commun., to be published. Casselman, T. N., and Petersen, P. E. (1980). Solid State Commun. 33, 615. Courant, R.,and Hilbert, D. (1953). “Methods of Mathematical Physics,” Vol. 1 . Wiley (Interscience), New York. Dornhaus, R., and Nimtz, G. (1976). In “Springer Tracts in Modem Physics” (G. Hohler, ed.). Springer-Verlag, Berlin and New York. Dornhaus, R., Muller, K . H., Nimitz, G., and Schifferdecker, M. (1976). f h y s . Rev. Lett. 37, 710. Emtage, P. R. (1976). J . Appl. f h y s . 47, 2565. Fiorito, G., Gasparrini, G., and Svelto, F. (1977). Infrared f h y s . 17, 25. Gerhardts, R. R. (1977). Solid State Commun. 23, 137. Gerhardts, R. R. (1978). f r o c . Int. Con$ f h y s . Narrow Gap Semicond., 3rd (J. Rauluszkiewicz, M. Gorska, and E. Kaczmarek, eds.), p. 103. Elsevier, Amsterdam. Gerhardts, R. R., Dornhaus, R., and Nimtz, G. (1978). Solid State Electron. 21, 1467. Glinchuk, K. D., Prokhorovich, A . V., and Vovnenko, V. I. (1976). f h y s . Status Solid; ( a ) 34, 777. Hall, R. N. (1959). f r o c . Inst. Eng. B . Suppl. 106, 923. Haug, A. (1977). Solid State Commun. 22, 537. Haug, A. (1978). Solid State Electron. 21, 1281. Ignas, E . , Piotrowski, J., and Piotrowski, T. (1979). Infrared f h y s . 19, 143. Kane, E. 0. (1957). J . f h y s . Chem. Solids 1, 249. Katsuki, S.,and Kunimune, M. (1971). J . f h y s . Soc. J p n . 31, 415. Kinch, M. A., Brau, M. J., and Simmons, A. (1973). J . Appl. f h y s . 44, 1649. Kittel, C., and Mitchell, A. H. (1954). f h y s . Rev. 96, 1488. Landsberg, P. T., and Robbins, D. J. (1978). Solid State Electron. 21, 1289. Long, D.(1977). In “Topics in Applied Physics” (R. J. Keyes, ed.). Springer-Verlag. Berlin and New York. Long, D., Tredwell, T. J., and Woodfill, J. R. (1978). Joint Meeting of the IRIS Specialty Groups on Infrared Dectectors and Imaging, Vol. 1, p. 387. June 13-15. Many, A., Goldstein, Y., and Grover, N. B. (1965). “Semiconductor Surfaces.” Wiley (Interscience), New York. Melngailis, I., and Harman, T. C. (1970). In “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 5 , p. l l l . McDougall, and Stoner (1938). Phil. Trans. R. Soc. London A237, 67. Overhof, H. (1971). f h g s . Status Solidi. f b ) 45, 315. Petersen, P. E. (1970). J. Appl. f h y s . 41, 3465. Ryvkin, S. M. (1964). “Photoelectric Effects in Semiconductors.” Consultants Bureau, New York. Schiff, L. (1955). “Quantum Mechanics,” 2nd ed. McGraw Hill, New York. Schmid, W. (1977). f h y s . Status Solidi (b) 84, 529. Schmit, J . (1970). J. Appl. f h y s . 41, 2876. Schmit, J. L., and Stelzer, E . L. (1969). J . Appl . Phys. 40,4865. Takeshima, M. (1973). J . Appl. f h y s . 44, 4717. van Roosbroeck, W., and Shockley, W. (1954). f h y s . Rev. 94, 1558. van Vliet, K. M. (1958). f r o c . IRE 46, 1004.

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SEMICONDUCTORS AND SEMIMETALS. VOL. 18

CHAPTER 5

(HgCd)Te Photoconductive Detectors R. M . Broudy and V . J . Mazurczyk I. INTRODUCTION..

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. . . . . . . . . . . . .

.

. . .. ..

157 159 159

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.

11. PERFORMANCE PARAMETERS. . . . . . . . . . . . . . 1. Figures of Merit. . . . . . . . . . . . . . . . . .

111.

IV.

V.

VI.

2. Fundamental Limit of Performance f o r Photoconductive Detectors . . . . . . . . . . . SIMPLEPHOTOCONDUCTIVITY . . . . . . . . . . . 3. Responsivity . . . . . . . . . . . . . . . . . 4.Noise . . . . . . . . . . . . . . . . . . . . 5 . Detectivity . . . . . . . . . . . . . . . . . . 6. Temperature and Background Dependence . . . . PHOTOCONDUCTIVE DEVICEANALYSES . . . . . . . 7. Power Dissipation . . . . . . . . . . . . . . . 8. Surface Recombination . . . . . . . . . . . . 9. I/f Noise in (HgCd)Te Photoconductors . . . . . 10. Transport Effects-Dr$t and Dgfusion . . . . . 11. Summary of Equations f o r the One-Dimensional Approximation with Ohmic Contacts . . . . . . PHOTOCONDUCTIVE DEVICEDESIGN. . . . . . . . 12. Extended Contacts . . . . . . . . . . . . . . 13. Complex Conjigurations-Geometry and Contacts 14. Transverse Field Effects-Accumulation Layers . 15. Transverse Field Effect--“Trapping Photoconductivity” . . . . . . . . . . . . . . TECHNOLOGY OF (HgCd)Te DETECTORS. . . . . . REFERENCES.. . . . . . . . . . . . . . . . . .

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... . . . . . . . . . . . .. . .

161 162 163 164 167 168 170 170 171 173 175

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187 187 188 189 190

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191 196 198

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I. Introduction

The emergence of practical and widely useful infrared systems has been made possible by advances in infrared sensing components. Because photon detectors approaching theoretical behavior are becoming available, thermal imaging, surveillance, and other military, space, medical, and commercial systems are achieving performance levels that open up new and broader opportunities. The possibility of improved system behavior has in turn supported and encouraged the development of practical infrared detectors. 157 Copyright 0 1981 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0- 12-7521 18-6

158

R. M . BROUDY A N D V. J . MAZURCZYK

(HgCd)Te was recognized early as a promising material for infrared detectors due to a number of uniquely suitable physical, thermal, and electronic characteristics (Long and Schmit, 1970; Levinstein, 1970; Dornhaus and Nimtz, 1976). Since the initial reports of its crystal growth in I959 and infrared detection behavior in 1962, (HgCd)Te has become the most widely used infrared detector material today, and photoconductive detectors of (HgCd)Te have become the accepted standard in the 8-12 pm region. Photon detectors may be made for operation either in the photovoltaic (PV) or photoconductive (PC) mode (Long, 1977; Kinch and Borello, 1975), and the semiconductor properties of (HgCd)Te are suitable for both modes. The present generation of (HgCd)Te detectors are PC, possibly because initial effort was devoted almost exclusively to this mode, for which material was available with the desired low carrier concentration. During the decade since the appearance of the first article in this series on (HgCd)Te (Long and Schmit, 1970), extensive research and development on PC devices has produced a high degree of maturity for this technology. Material characteristics have improved in crystallinity, carrier mobility, and lifetime. Producible device fabrication processes have been developed. Sophisticated device designs have been implemented, based on the recognition that photoconductivity in (HgCd)Te is a majoritycarrier phenomenon that is controlled by minority-carrier properties. In all respects, the behavior of PC (HgCd)Te photodetectors has been found to be qualitatively and quantitatively consistent with fundamental semiconductor theory and technology. The actual PC (HgCd)Te detector used in systems is a complex multielement array requiring a high level of sophistication in analysis, design, and processing. In fact, the fabrication of modern PC detector array components requires techniques similar to those applied in integrated circuit technology. The purpose of this chapter is to present an up-to-date description of the theory and principles of PC (HgCd)Te detectors in a form most suitable for design and application. It is our objective to consider all relevant mechanisms affecting performance in actual devices, making use of the maximum available rigor. In the interests of conciseness we will rely on information already accessible in several excellent treatises and papers (Long and Schmit, 1970; Levinstein, 1970; Dornhaus and Nimtz, 1976; Long, 1977; Kinch and Borello, 1975; Kruse et al., 1962; Kingston, 1978; Eisenman et al., 1977; Kruse, 1979). Most of the original references may also be obtained from these works. The discussion must be limited for the following reasons: first, many details are not openly available due to classification and proprietary limitations; and second, a rigorous theory has

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

159

not yet appeared for some of the fundamental features of device behavior. We begin in Part I1 with a summary of well-known performance parameters for evaluation of photodetectors, concentrating on those aspects most useful for 8- 12 pm PC (HgCd)Te. For heuristic purposes, and to aid in correlation with much of the literature, we have chosen to initiate the detector analysis with Part 111, which is limited to simple photoconductivity. In this section only conductivity modulation in the bulk of the material is considered, and none of the effects associated with the drift, diffusion, and thermal properties have been included. The behavior of actual devices, however, is considerably modified by additional phenomena, including minority and majority-carrier transport effects and other behavior related to practical device structures and application requirements. Part IV includes these effects. Part V presents a brief summary of the principles used in modern photoconductor design, whereby special structures for control of minoritycarrier transport may greatly improve performance. We conclude with a summary of the principal aspects of practical device fabrication.

11. Performance Parameters

The following subsections relate material parameters and external variables (i.e., temperature, background radiation, bias, and frequency) to the detector performance. As a background for these discussions, it is useful to present a brief survey of the principles by which photodetectors are evaluated. Although there are several well-recognized works on infrared detectors which treat this subject in detail and provide references to the original literature, some issues still remain to be resolved. Much of the discussion in this section follows Kruse et al. (1962). 1. FIGURES OF MERIT

Widely used figures of merit for describing detector performance are the spectral detectivity D,*(h,f,Af)and the responsivity 9iA(f).They are defined by

D f = D*(X,f,Af) = (%&/VN)(AAf)”*,

% = V,/P,,

(1) (2)

where V , is the rms signal voltage at the amplifier input, VN is the rms noise voltage at the amplifier input measured within the electrical band-

160

R . M . BROUDY AND V. J . MAZURCZYK

width Af, and PAis the rms optical power in watts incident on the detector active area, A . The optical power considered is in the spectral region , of 3 are between A and A + AA. The units of D* are cm H Z ” ~ / W and

v/w.

The value of ’?PA must be known absolutely. One technique is to use a blackbody source and some means of limiting the optical bandwidth, such as a narrow pass optical filter. Alternatively, Df may be determined by first measuring D&(Tz ,f,Afl, the wideband response due to blackbody radiation from a source at temperature T2. This quantity is defined by the relationship

where P B B ( T 2 ) is the total optical power incident on the detector from a blackbody at temperature T2 and is equal to the integral of PAover all wavelength. The spectral distribution of the blackbody is known, so that the two types of detectivity can be related when the spectral distribution of the quantum efficiency, y ~ ,is known. The ratio g = D?/D&B

(4)

is given by

where v, is the frequency of the signal power ’?PA, and where M(v,TZ)/BB, is the fraction of power per unit optical frequency interval emitted by a radiating body, and %!BB is the total power emitted by an ideal blackbody at temperature T2. The quantity ~ ( v is) the rate at which incident photons (of frequency v and wavelength A = c/v) are converted to electron-hole pairs. For photon detectors the signal is proportional to the absorbed number of photons, and D* increases with wavelength until the incident photon energy, hv, is less than the bandgap of the material, E g ;below this energy the response falls rapidly to zero. The wavelength at which the peak response occurs is denoted by A,. and it is the value at which D* is usually quoted (with the designation DL). The cutoff wavelength, A,, is generally defined by the wavelength or frequency at which the response has fallen to 50% of the peak value. In (HgCd)Te detectors a reasonable approximation is that h,/Ap .- 1.1. For wavelengths greater than A, (i.e., hv < Eg),71 falls rapidly to zero. A useful approximation is to assume that 7) is constant for all wavelengths less than A c , and zero otherwise. The value of g then depends only on T2 and A,. For example, with T2 = 500 K and A, = 12 pm, g = 3.5. When

5 . (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

161

greater accuracy is required, the measured spectral dependence of ~ ( h ) must be used in Eq. ( 5 ) . The electrical spectrum of the detectivity is dominated at low frequencies by llfnoise and at high frequencies by amplifier and Johnson noise. It is therefore useful to specify D* at a mid-range value along with parameters which indicate the frequencies at which D* has decreased by 3 dB at each end of the spectrum. The low end parameter is usually referred to as the llfcorner frequency and the high end parameter is denoted by f*.Both parameters give the frequency at which the total noise power has doubled relative to the signal. The responsivity rolls off at high frequency with the time constant T = f C / 2 7 r wheref, is the frequency at which the signal has decreased by 3 dB. These parameters will be discussed in the following subsections. 2. FUNDAMENTAL LIMITOF PERFORMANCE PHOTOCONDUCTIVE DETECTORS

FOR

The total noise that determines detector performance originates not only from contributions related to the absorption of photons, but also from a number of other factors, including thermal effects in the detector (Johnson noise), thermal and other effects in the associated circuitry, and llfnoise both in the detector and elsewhere. This section is concerned only with ultimate performance possibilities, and therefore does not consider the second class of effects, although, as will be discussed below, the latter often determines practical performance possibilities. The value of D* ( h , f , A f ) under photon limited conditions is given by

where only fluctuations in the arrival rate of the photons have been considered. Exact and approximate solutions for Eq. (6) are presented in Kruse et al. (1962). For detectors operating below 50 pm and for TB not too far from 300 K, the solution reduces to the well-known form

where QB is the total background photon flux incident on the detector and is assumed to be constant for frequencies above vc. Derivations of ultimate D* proceed from apparently quite different viewpoints in theories that are concerned with fluctuations in excess carriers due to absorption of radiation. One well-known approach uses the

162

R. M . BROUDY A N D V. J . MAZUKCZYK

“g-r theorem” of Burgess and Van Vliet (Van Vliet, 1958, 1967; Burgess, 1954, 1955, 1956; Van Vliet and Fassett, 1965; Long, 1970) to derive carrier fluctuations due to both generation and recombination of excess carriers. Theories using this viewpoint result in the familiar expression for D* given by Eq. (6) except for a factor of 2 instead o f d in the denominator: 0%=

& [$I1’”

In spite of the extensive treatments of the subject in the literature, there does not appear to be a completely rigorous description of noise effects in photoconductive detectors. It seems clear that ultimate performance limits must be determined by fluctuations in the arrival rate of photons, as discussed by Kruse et ul. (1962). It is striking that whichever point of view is used, the ultimate performance limit D* (D*BLIP, for background limited infrared photodetector) differs at most by a factor of 4 between the two approaches (perhaps because of the fundamental statistical nature of fluctuations of any type). It is tempting to join both approaches in a conceptually attractive manner which is not rigorous, but may be physically correct: That is, to separate recombination from generation noise and to equate carrier generation fluctuations with those of the photon flux. If this may be done, then the generation and recombination fluctuations contribute equally, and the limiting L)* of Eq. (7) is, in fact, equal to that of a photovoltaic detector, which has no recombination, while a factor of I / d multiplies the ultimate D” of a photoconductor which has both generation and recombination. This approach may conceptually clarify the limiting D* of a photoconductor operating in the sweepout mode (which has been speculated (Milton, 1973; Williams, 1968) to follow Eq. (7) as discussed below) for which recombination noise is negligible since the minority carriers recombine at or beyond the contact regions. 111. Simple Photoconductivity

A typical photoconductive device is thin and rectangular in shape and is bonded to a much thicker block of material, called the substrate. Electrical leads are bonded to pads of metal as shown in Fig. 1 . Initially, it is instructive to consider only photoconductivity due to the influence of bulk properties. Fundamental principles can be illustrated readily, correspondence is more readily achieved with much of the literature, and useful descriptions of device performance may be obtained. Moreover, a semirigorous theory of noise is available only for this condition. The basic parameters of responsivity, noise, and D* are derived in this section from this point of view.

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

163

ELECTRICAL

SUBSTRATE

RESERVOR

FIG.1. Principal elements of a typical photoconductive device.

3. RESPONSIVITY

The conductance G of the detector is

G

=

( q / L 2 ) ( / d+ php),

(9)

where pe is the electron mobility p h is the hole mobility, N is the total number of electrons, and P is the total number of holes. The detector length is L , and q is the electronic charge. The absorption of photons generated by a constant background will change the conductance from its value at thermal equilibrium, G o , to G by changing No to N and Po to P , where thermal equilibrium values have the 0 subscript. For the majority of applications, changes in N produced by background flux will be small compared to No for the typical n-type PC (HgCd)Te photoconductor. The rms signal photon flux per unit area at wavelength A, namely Q,(A), produces a change in the conductance given by

AG = (q/L*)(peAN

+ ph AP),

(10)

where AN and AP are the total number of excess carriers in steady state. Whether or not AN and AP are equal depends on the recombination mechanism involved. However, it appears that the dominant recombination mechanism for good quality (HgCd)Te is Auger, and thus AN = AP. In the remainder of this work it will be assumed that only Auger recombination is important. At sufficiently low background and temperature apparent or real minority-carrier trapping effects are important (see Part V). Defining the quantity 7,which will subsequently be identified with the excess carrier lifetime, by the expression 7

=

AN/[Q,(A)r)(A)Al,

(11)

164

R. M. BROUDY A N D V. J . MAZURCZYK

where Q s is the signal photon flux, the change in conductance becomes

AG

=

( q / ~ ’ ) ~ , ~ [ Q , ( ~ ) ~ r ( ~+ ) A61, ][l

(12)

where

b = Pe/ph * (13) For n-type (HgCd)Te, b >> 1, and in the remainder of the discussion the approximation I + b = b will be used. The device is usually placed in a simple series circuit with a load resistor whose conductance is much smaller than that of the device. A change in the latter’s conductance, G, produced by a change in the arrival rate of photons, will result in a signal voltage across the load resistor given by AVL = Vb AGIG,

(14)

where V , is the dc bias voltage on the detector. Combining Eqs. (2), (9), (12), and (14), and recognizing that PA= Q,Ahv, gives the responsivity in steady state: %A

=

[71(A)/Lwd)(A/hc)v,T/n,,

115)

where no is the average thermal equilibrium carrier density and d is the thickness of the photoconductor. Under the assumptions of no drift or diffusion and equal recombination, the time dependence of the average excess carriers is described by

aP/at = Q J ~= - A P / t .

(16)

Solving for M ( t )gives AP(r) = Q&qTe-‘’’, or in the frequency domain

+ (27”7)’]-’’*.

A P ( f ) = QsAr)T[l

(18)

The frequency dependent responsivity can therefore be written

+ (2flfT)2]-”2,

%!~(f) = %!~(o)[l

(19)

where WA(0)is the steady-state value given by Eq. (15).

4. Noise

(I. Johnson Noisc The conductance of the detector defined by Eq. (9) is of course an average value. The total current in the detector is made up of many individual vector components whose contributions are constantly changing

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

165

even if the number of charge carriers remain constant. The rms noise per unit bandwidth Af, due to thermal fluctuations, is independent of the material and device characteristics, and is given by the well-known expression for Johnson noise =

( 4 k T / @ Af.

(20)

b . Generation -Recombination Noise

The average number of carriers in the detector is determined by the balance between the generation and recombination processes. Fluctuations in these quantities results in another type of noise appropriately called generation-recombination noise. For a semiconductor where direct recombination dominates, the noise per unit bandwidth Af is (Van Vliet, 1958, 1967; Long, 1970)

where ( A N 2 )is the variance in the number of majority carriers and no is the average density. For a two-level system the variance has been evaluated in general and is given by (Long, 1970)

( A N 2 ) = g7,

(22)

where g is the generation rate and 7 is the relaxation time constant defined by Eq. (11). Equation (21) is correct both for steady-state as well as thermal equilibrium conditions. A key and simplifying assumption is often made that thermal and optical generation-recombination processes are independent. The variances are therefore uncorrelated and combine linearly so that (AN2) = (g&lerrn+

(g7)0,t.

(23)

The first variance is given by (Van Vliet, 1958, 1967; Long, 1970)

and the second by (g7)opt =

Ph =

PhLwd,

(25)

where P b represents the optically generated background hole density. Using the above relations, the g-r noise is found to be

166

R. M . B R O U D Y A N D V . J . M A Z U R C Z Y K

The full equation is practically required only over a small range of temperature, where the semiconductor changes from intrinsic to extrinsic. Outside of that range either optical or thermal generation dominates, and Eq. (26) reduces to the g-r noise for one or the other single generation process. Holes generated by the background flux are relatively independent of temperature when the detector is an extrinsic semiconductor and po may often be made negligible by reducing the temperature so that P b dominates. Under these conditions the noise is photon limited since it is determined by fluctuations in the photon arrival rate; then, as discussed in Part 11, computation of D* using Eqs. (l), (2), and (26) yields the BLIP limit given by Eq. (8). c. l / f Noise

The phenomenon of l/f noise will always determine the low frequency limit of device performance, although it is not related to the same fundamental principles that control the other noise mechanisms. At present, there is no rigorous theory of llfnoise. Nevertheless, it is well recognized that it is related to practical device structures, and may be reduced by improved device design and fabrication techniques. For convenience, the existence of l/f noise may be modeled in terms of the “corner frequency” f o , which is defined as the frequency at which the I/f noise power equals the g-r noise power. llfnoise at any frequency can then be modeled from the relation:

G,f= (fo/f)%-r(O),

(27)

where V&O) is the generation-recombination noise at the plateau region at frequencies below the high rolloff and well above the llfcorner frequency. Both V,,, and Vg-r depend on bias, temperature, and background flux in possibly different ways, so that fo may be a function of these parameters. llfnoise is treated in more detail in Part IV.

d . Ampl$er Noise The noise contribution of the amplifier can be modeled by the presence of a voltage noise generator of rms magnitude e, and a current noise generator i, . The voltage generator appears in series with the amplifier input while the current noise generator is in parallel with the input. These are usually considered to be white noise sources. When a detector of resistance r d is placed across the input of the amplifier, the noise (aside from detector Johnson noise) generated will be

Vf; = ef; + if;r:.

(28)

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

167

With typical (HgCd)Te photoconductive detectors the value of rd is usually less than 100 a. This low resistance, combined with an upper usable frequency range of perhaps 10 MHz allows one to ignore capacitance at the input. However, individual cases should be examined carefully to insure the validity of this assumption. e . Total Noise

The individual noise contributions from the detector and amplifier (V,) are uncorrelated and therefore add in quadrature. The total noise of the detector is given by

v: = vq + v;-*+ (Vl,f)Z + v:.

(29)

A characteristic noise spectrum is shown in Fig 2 to illustrate the contribution of the various noise components.

5. DETECTIVITY Combining equations of the previous sections gives the result,

The expression for D* has been put into this form to emphasize the fact that the maximum performance is given by DgUpand to isolate those factors which cause the performance to deviate from that value.

lif NOISE

g-r CORNER FREQUENCY g-r

NOISE

I/f CORNER F R E O U E N C Y

AMPLl F IE R [NOISE

FREQUENCY

FIG. 2. Characteristic noise spectrum of a photoconductive detector.

168

R. M. BROUDY A N D V. J. MAZURCZYK

At higher temperature where the detector is an intrinsic semiconductor (i.e., no = po) the g-r noise is sufficiently large that the condition V&,(f>

>>

v; + v;

(3 1)

can be achieved with moderate bias levels (except at high frequencies). Performance in the midrange frequencies, therefore, is determined entirely by the factor

which is strongly temperature dependent. Since the performance of the detector in this region is relatively poor, it is used under these conditions only when cooling capacity is limited. With decreasing temperature no becomes constant and dominates p o . The detector then becomes an extrinsic semiconductor, and D* is given by

D” = D&,p(l + ~ o / p b ) ~ ” ’ [ l

+ ( f o / f ) + (Vj +

V~)/VPr(f)]-”’.

(33)

It is obvious that maximum performance is achieved when po/pb<< 1

+

<< 1.

(34) The detector performance at frequencies higher than (27TT)-l is affected by the decrease of V&,(f> relative to V; + Vi . Increasing the bias will help maintain performance but eventually (even for an ideal detector) the amplifier and Johnson noise will dominate and the detectivity will be given by [D*]hf

and

(V;

V:)/V:-,

(f)

+ V;)”’.

= %L(A Af)”’/(V;

(35)

The frequency at which the detectivity has decreased by 3 dB from its midband is often designated asf”. Since it is the value at which the noise power has doubled, that frequency is given by 1

f* = ?&

v;-,(o) [v: + v2,

+

,

as derived from Eqs. ( l ) , (19), and (35). Heating effects can cause a superlinear dependence of Vg-r (0) on bias so that f* no longer corresponds to a decrease of fiin D*.Equation (36) must therefore be used with caution. 6. TEMPERATURE A N D BACKGROUND DEPENDENCE

The temperature and background dependence of the detectivity, responsivity and g-r noise is determined by the variation of the majority and

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

169

minority-carrier concentrations as well as the time constant, as discussed by Kinch and Borello (1975). The majority- and minority-carrier mobilities which affect the above performance parameters indirectly do not depend on background flux and have a relatively weak dependence on temperature. For (HgCd)Te, or any n-type semiconductor where the donor activation energy is negligible, the magnitude and temperature dependence of the quantities of interest are given by

where ND - N A is the concentration of uncompensated donors. The minority-carrier concentration is obtained from (38)

Po = $ / n o ,

and the bulk time constant for Auger recombination (Kinch et al., 1973) is given by 5-

= 2d/(no

+ po)(no).

(39)

The value of ri is 71

= CO(Eg/kT)3/2 exp(EglkT),

(40)

where Eg is the energy gap and the constant Co cannot be calculated without making some gross assumptions. Experimentally (Kinch et al., 1973), the value of T has been found to be approximately 1 x sec at 77 K for x = 0.195 and sec for x = 0.205. The temperature dependence and magnitude of these quantities is determined (Kittel, 1961) by the intrinsic carrier concentration n i , which can be determined from empirical relations (Mazurczyk et af., 1974; Finkman and Nemirovsky, 1979; Schmit and Stelzer, 1969; Schmit, 1970) ni = (A

+ B7)C1P8.75T1.5 exp(-

Eg/2kT),

(41)

with A

=

1.093 - 0.296x,

B = 4.42 x lop4,

C = 4.293 x 1014,

and x is the stoichiometric ratio. The energy gap Egis also dependent on composition and temperature and is given with some accuracy for x = 0.2 by (Finkman and Nemirovsky, 1979; Schmit and Stelzer, 1969; Schmit, 1970)

Eg = 1 . 5 9 ~- 0.25

+ 0 . 3 2 7 ~+~5.23 x

10-4(1 - 2.08x)T.

(42)

Incorporation of these equations into the expression for the detectivity

170

R. M . BROUDY A N D V. J. M A Z U R C Z Y K

will give a good description of the temperature dependence when all the parameters are known and the detector is of uniform composition. The background dependence of the detectivity and other quantities depends on the number of steady-state excess carriers Pb that are optically generated. When P b << no in n-type (HgCd)Te, the background dependence of the detectivity is determined in a straightforward manner from Eqs. (38) and (7). At higher levels of Q B the value of the lifetime is affected. If drift and diffusion effects are neglected then the value of 7 is determined from the simultaneous solution of 7

=

2Tinf/(no 4- Po

P d n o 4- Po),

(43)

where background and all minority carrier effects are considered (Kinch et al., 1973) and Pb

= 77Q/d.

(44)

In real devices, drift and diffusion effects are important and must be considered. The complete analyses of photoconductive device behavior including these effects is discussed in Part IV, where expressions will be derived for the case of A p << no and P b << no including the influence of drift and diffusion. IV. Photoconductive Device Analyses In Part I11 only the influence of volume photoresponse was considered. Real photodetectors, however, are subject to a number of additional constraints related to the practical necessity of holding down the photosensitive material and shaping it to a specified configuration in a working device including provision for contacts. The following subsections modify the simple theory to include these effects. Specifically treated are resistive heating effects, surface recombination, l/f noise, and transport effects.

7. POWERDISSIPATION Generally, photodetectors must be maintained at reduced temperatures to achieve optimum performance by eliminating thermally generated noise. Since there are a number of thermal interfaces between the detector and the cooling reservoir, the Joule heating due to bias current will produce a rise in detector temperature. Assuming edge effects can be neglected and that no heat is lost by radiation or thermal shorts, the rise in detector temperature is closely given by the one-dimensional approximation

5. (HgCd)Te

171

PHOTOCONDUCTIVE DETECTORS

where the thickness and thermal conductivities of the various layers are I, and Z , , respectively. The power dissipation is H, and A, is the contact area between layers. However, achieving good thermal interfaces between the various layers is always a problem. Even with the use of materials that have high thermal conductivities, the effective contact area can be very low due to poor physical contact, air bubbles, and other problems. The epoxy bonding layer between detector and substrate might typically have a thickness of 3 X cm and a thermal conductivity near W/cm K. Similar values can exist for a layer between substrate and reservoir. For example, a substrate of sintered alumina has --- 1 W/cm K at 80 K . For a substrate thickness of 0.05 cm, the thermal resistance is negligible and A T is determined by the thermal resistance of the epoxy layers. For a device such as shown in Fig. 1, these values give

(46)

AT = 0,6H/A,,

where A, is the total effective contact area. It includes the area under the bonding pads of the detector. The thermal interface will limit detector performance when heating causes the term (1 + p o / p b ) to increase. The responsivity may also decrease with increasing temperature, but it is usually less important, except in wideband and other applications where the detectivity is limited by amplifier noise. In many applications, however, the thermal resistance between detector and reservoir would be less important if not for the additional complications of surface recombination and sweepout. 8. SURFACE RECOMBINATION

The simple model also does not account for surface recombination which is perhaps the single most important mechanism that limits photoconductor performance. It is well known that the surfaces of a semiconductor are regions where recombination can proceed at a higher rate than in the bulk. Surface recombination reduces the total number of steadystate excess carriers by effectively reducing the average recombination time, T . In modeling this effect, the bulk recombination time T can be re~ (Kruse ef al., 1962, p. 330) placed by T A where A, =

(1

sinh(d/l,) + S2[cosh(d/L,) + S1S2)sinh(d/l,) + (S, + S,)

The parameters S, , S2are defined by

Sf= s ~ T / L , , i

=

1,2

- l)] cosh(d/L,)

'

(47)

172

R. M . BROUDY A N D V. J . MAZURCZYK

where SI, Sz are the surface recombination velocities of the front and rear surfaces, and where La is given by La

=

[Do~]1'2.

(49)

The equilibrium value of the diffusion constant, Do,is appropriate when assuming low excess carrier generation. Since the parameters S, and Sz are difficult to measure directly, Eq. (47) is not immediately useful in modeling performance. It is useful, however, in establishing the degree to which performance can deteriorate. An appreciation of this effect can be obtained by considering a specific example. The parameters of the device to be considered are given in Table I. For convenience in modeling we assume that Sz = 00 at the back surface of the detector (i.e., Ap = 0) and Sl= 0 at the front surface, in keeping with the general recognition that back surfaces may be more difficult to control in real detectors. From the values in Table I, A = 0.026 and T = 80 K. A calculation of the D* for this detector and an ideal detector is shown in Fig. 3. The performance of the ideal detector drops for temperatures above 80 K because thermally generated minority carriers are beginning to dominate. The low bias level of 45 mV, however, is sufficient for the detector g-r noise to dominate the white noise generated by the amplifier and detector resistance. The addition of surface recombination considerably reduces the D*.To restore performance, the bias must be increased to 150 mV [to satisfy Eq. (34)] and the temperature reduced to 60 K [to satisfy Eq. (3311. For large arrays the increased bias and cooling capacity may not be available.

TABLE I PARAMETERS OF A TYPICAL (HgCd)Te DEVICE -

Composition (n-type) Quantum efficiency Cutoff wavelength Carrier concentrations Intrinsic Auger time constant Mobilities Physical dimensions Thermal interface Background flux

x = 0.200 7)=1 A, = 14.2 pm at 80 K N , - N , = 9 x 10" n, = 3.08 x lOI3 ern-$ at 80 T~ =

0.6

X

K

sec at 80 K

p e = 1.6 x 105 crnz/V sec at 80 K p h = 800 cm2/V sec at 80 K

length = 0.015 crn thickness = 0.001 cm (IIZA,) = 3 K/W QB = 1.08 x I017/cm2at 80 K

"1 y\

5 . (HgCd)Te PHOTOCONDUCTIVE DETECTORS

--r

'%

2

* 4

a

173

DETECTOR IDEAL

45-mV BIAS

DETECTOR WITH SURFACE RECOMBINATION 150 mV 45 mV

TEMPERATURE (K)

FIG.3. The influence of surface recombination on detector performance.

9. l/f NOISEI N (HGCD)TEPHOTOCONDUCTORS

The existence of fluctuations varying inversely with frequency has been widely recognized in both electronic and nonelectronic phenomena. Although llfnoise ultimately limits the low-frequency performance of all electronic devices, no satisfactory or rigorous theory exists. a. The Classical Theory

In photoconductors, most of the literature and theory of llfnoise has taken what might be called the classical approach, in which llfnoise is expected to be independent of other sources of noise but behaves similarly except for the inverse frequency dependence. Thus, for this approach, dimensional relations can be derived from the usual approaches which assume that the noise originates from microscopic noise generators distributed throughout the device. Then, from fairly general noise theory arguments (Kruse et al., 1962, p. 255), the Ilfnoise voltage can be written as

where L, w ,and d a r e length, width, and thickness of the detector, E is the dc-bias electric field, Af is the noise bandwidth,fis the frequency, and C , is a coefficient which gives the strength of the llfnoise. In particular, C , is found to depend on carrier concentration but is independent of detector dimensions even though it possesses the dimensions of cm3. The classical corner frequency can be calculated from Eqs. (26), (27), and (50). With the usual assumptions for n-type (HgCd)Te that no >> p o and p B , fo

174

R. M. BROUDY A N D V. J . MAZURCZYK

becomes

fo = C I ~ % / ~-k@PBO

~ Y

(5 1)

where we have assumed that (07)~ << 1. If the temperature is low enough that thermally generated carriers become negligible

fgB‘.IP

= C1n;d/4r2qQB.

(52)

Thus, f o depends on the detector thickness but not on the active area dimensions. In keeping with the classical approach, the coefficient C1 has been calculated from approaches which assume either that the noise generators originate at the surface, or throughout the bulk. McWhorter’s model (Van der Ziel, 1959) for l/f noise in semiconductors is based on the existence of surface traps. Fluctuations in the capture and release of electrons at these surface traps produce fluctuations in the bulk electron concentration and consequently in the conductivity. In this theory, the characteristic l/f frequency dependence of the noise power due to these fluctuations is the result of assuming that electrons are released from the surface traps by tunneling to the bulk. The tunneling probability depends exponentially on the distance over which tunneling must occur. Consequently, a distribution of lifetimes is obtained which leads to the characteristic llffrequency dependence for the noise power. This model leads to the following expression for C,:

C1 = (NT/4ni)l/ad,

(53)

where NT = the concentration of traps in the surface layer and a is a characteristic tunneling constant. Hooge’s (1969) model for llfnoise assumes that it is a universal bulk phenomenon. His theory leads to the following empirical expression for the coefficient C,:

C , = 2 x 10-3/no.

(54)

It is notable that although these theories have received much attention there has been little if any experimental verification of their validity or even usefulness in photoconductors. b. New Phenomenological Theory A useful phenomenological theory (Broudy , 1974) has recently been developed for l/f noise in (HgCd)Te photoconductive detectors. It was arrived at as the result of a survey and analysis of available data from a large number of photoconductive (HgCd)Te detectors operating in many conditions.

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

175

Consideration of these and other data have led to the notable observation that the l/f noise voltage, Vl,f, bears a simple relation to the generation-recombination voltage, Vg-r. Specifically, the following empirical relation has been found to apply:

V/f (Kl/fl VZ-r

9

(55)

where K1 is a constant. Note that this empirical relation holds whatever the source of VgPr(possibly only the recombination noise may cause the effect). In this viewpoint, llfnoise is “current noise” simply because VgVrvaries with the current. Also, l/fnoise decreases inversely with detector resistance simply because Vg-r behaves in this manner. The corner frequency, fo, is readily determined to be Equations (55) and (56) state that l/f noise increases with g-r noise. Therefore, to reduce 1/fnoise, everything else being equal, material with low g-r noise should be selected. This conclusion is a key and new consequence of the empirical theory which does not appear in the classical theory where Vg.-r and Vlv are essentially independent and are related solely through their current dependences. In terms of detector and material parameters criteria for reduction of l/fnoise can be established from Eq. (26) for g-r noise:

(a) (b) (c) (d) (e)

Use lowest feasible bias current. Keep detector temperature below thermal generation range. Reduce detector background as far as possible. Choose semiconductor material with large donor concentration. Develop improved processing methods (to reduce Kl).

This effect is practically illustrated in Fig. 4 which shows the background dependence offo we have measured for a typical (HgCd)Te photoconduction detector. Note that the detector follows a Qi1’2dependence at the higher background but that dependence diminishes for QB below 10’‘ as thermal g-r noise becomes appreciable. Borello et al. (1977) have also reported background dependences of 1/f noise. EFFECTS-DRIFTA N D DIFFUSION 10. TRANSPORT a . The Fundamental Approach

In real devices, drift and diffusion play a significant role and must be considered. In a classic publication Rittner (1956) has provided a unified and broad treatment of photoconductivity. He derived the basic photoconductivity equations beginning from the first principles of continuity

176

R . M . B R O U D Y A N D V. J . MAZURCZYK

10' 10"

1Ol8

BACKGROUND FLUX ( p h o t o n s / c m 2 s e c i

FIG. 4. l/f knee versus background for a (HgCd)Te photoconductor. Ad = 0.004 in. 0.004 in. A,, = 12.1 pm. T = 78 K.

X

equations, carrier currents, and the Poisson equation. His complete analyses included trapping effects and make the physically reasonable assumption for low impedance photoconductors of the (HgCd)Te type that space-charge neutrality exists and that there are negligible ionic currents. Neglecting trapping, the following equation is obtained (Rittner, 1956):

+ + D div grad Ap + p E

aAp/at = - (Ap/Tg) j

*

grad Ap,

(57)

where f is the generation rate ( f = v Q s / d cm-* set)-*, T~ is the generalized lifetime for all levels of carrier excitation, and the generalized diffusion constant D and generalized mobility p are given by

-n =

n I L + PIP.'

where Dh and D, are the hole and electron diffusion coefficients, respectively. This equation is nonlinear in general, since the coefficients D, p , and T~ depend on n and p . However, it may evolve into a usable form for the physically realistic case that Ap << n, which applies for low light intensities: ahplat

=

-(Ap/T)

+ f + Do div grad A p + mE - grad A p ,

(58)

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

177

where T is the lifetime for low excitation levels and Do and poare given by

Do = (no -k PO)/[(nO/Dh)+ (PO/De)l,

(58a)

po = ( P o - no)/[(nO/ph) + (PO/pe)l.

(58b)

Using the Einstein relation D = k T p / q to describe diffusion coefficients in terms of mobilities, these become

Do = (kT/q)PePh(& Po)/(Peno + P h P o ) r

(58c)

Po = (PO - nO)peph/(penO+ phP0)-

(584

Useful solutions may be obtained in terms of the parameters in Eqs. (58), since T, D o , and p,, are constant coefficients. For purposes of comparison with literature, it is useful to recognize that parameters closely related to Do and po have been similarly derived by authors other than Rittner, and are often denoted by the terminology “ambipolar diffusion coefficient” and “ambipolar mobility.” These parameters differ from Do and po only in signs, as would be expected, since they have been correctly derived for the identical physical phenomena. In any case it is required merely to be self-consistent with whatever approach is chosen. In this chapter, we follow Rittner’s analyses, using Do and p,,, and in order to eliminate confusion with other work, we will avoid the ambipolar expressions, while recognizing that one is dealing with the same device principles. In the following section, Rittner’s equations are applied to n-type (HgCd)Te photoconductors under the assumptions of no trapping and of low excess carrier levels. In Rittner’s work the symbol T is meant to imply a composite lifetime that is the product of the bulk lifetime and the surface recombination factor. In the remainder of this work we will also use this same convention.

6 . One-Dimensional Formulation with Ohmic Contacts Specific solutions of the previous equations were obtained by Rittner for the one-dimensional case with the further simplification that the contacts are ohmic. The electric field is in the x direction [-(L/2) < x < (L/2)]. The low-light-level approximation permits n = no + An, and p = po + Ap, and the ohmic contact assumption requires that An = A p = 0 at x = - L/2 and at x = +L/2. The excess minority-carrier density at the position x on a detector extending from L/2 to L/2 is given by

- emx sinh(a,l/2) sinh(al - a2)L/2

ealr sinh(azL/2)

R. M. BROUDY

178

A N D V . J . MAZURCZYK

where -

a1.2 =

2 0 0 -e

[(& 2Do)2+

(594

and

Do = (kT/dPo. The drift length I, of an excess carrier is is It is sometimes convenient to write

a.

=

a1.2

-1 & [($

+

(60) and the diffusion length l2 terms of ll and 12:

al,zin

$1

1/2

Using these results, Rittner (1956) calculated the steady-state photocurrent of a detector

AJ = qhh(b + l)vQsTE5/d,

(62)

(az- a,)sinh(a,L/2) sinh(a21/2) a1az(L/2) sinh(a, - a2)L/2 *

(63)

where 5=1+

Then for b >> 1, the voltage responsivity becomes

9tk = XqqrDp,&&/hcd.

(64)

At high fields where the drift length 1, is greater than the detector length L or the diffusion length 1 2 , the following first-order approximations can be made 1

^-P

then

a L L sinh-?- =2 211’

sinh a 4 / 2 L z - 1 + -. (65b) then sinh(a, - az)L/2 211 Substitution of these approximations into (63) gives the high field limit for -az =

+ LL >> 1, 21;

5: The high field responsivity is therefore %If

= (Uhc)(qqPe/2Po)rd.

(65c)

In (HgCd)Te, the mobility of the electrons are field dependent; thus, to be completely rigorous, the field dependent resistance should be used in Eqs. (65).

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

179

Note that the drift length I , depends on the mobility p o ,which for extrinsic n-type material reduces to the hole mobility. In an intrinsic semiconductor po is zero and there are no sweepout effects. A rigorous calculation of the g-r noise that includes the effects of drift and diffusion is not yet published, although such a theory is reported soon to become available (Smith, 1981). Many discussions of detector performance in the literature (Williams, 1968; Kinch et al., 1977) assume that g-r noise has the same field dependence as the responsivity, and indeed, experimental results verify the accuracy of this assumption. For modeling purposes, a useful approximation for the g-r noise may be obtained from the simple formula by making the substitutions T*&

Pb’Pb,

pO+pO*

(66)

Lacking a rigorous theory, we shall include a strictly empirical field dependent sweepout factor:

F = F(E), which has been introduced from the viewpoint discussed in Part I1 to account for the possible effect of sweepout on minority carrier fluctuations. This parameter, which also has not been rigorously derived, would have a value between l/& and 1. At low fields, sweepout is small, most of the carriers recombine within the bulk, and there is the full complement of g-r noise due to fluctuations in the bulk recombination; therefore F I1. As the field increases, the number of carriers that recombine in the bulk becomes smaller as more holes (for n-type material) are swept to the contact regions to recombine; thus F becomes smaller, and would saturate to the value of l / d at the maximum field strength where recombination noise disappears. In detectors where the ambipolar diffusion length is comparable to the detector length, one would expect F to be less than 1 even at zero field, since an appreciable number of carriers reach the contacts by thermal diffusion. It is important to recognize explicitly that application of the parameter F depends on two hypotheses: First, as discussed in Part 11, in the absence of a fully regorous theory it is assumed that generation and recombination noises may be partially or totally independent and are equal at low field (in the absence of diffusion to the contacts), such that in full sweepout, only half the maximum g-r noise remains (Milton, 1973; Williams, 1968). Second, it is assumed that there is negligible noise due to recombination of minority carriers at the contact regions. The applicability of the latter assumption will depend on the specific type of contactpossibilities include high-low junctions, true metal-semiconductor inter-

180

R. M. BROUDY A N D

V. J .

MAZURCZYK

faces, and low field regions in transverse field devices, such as discussed in Part V. Using the substitutions indicated in Eq. (66) and the F factor, the g-r noise becomes (for frequencies less than 3m)

Comparison with the responsivity shows that for the extrinsic case both are proportional to (r and the ratio can be expected to be at least roughly constant, except for the factor F ( E ) . As implied above, the electric field cannot distinguish between optically and thermally generated holes. But the latter depend on T and (. But because Vg-r as well as the responsivity saturates, there will be a limit to the achievable detectivity even in the absence of heating and surface recombigation effects. This limit occurs when the g-r noise is background dominated and has saturated at a value less than the white noise generated by the detector resistance and the amplifier. The responsivity at this bias has saturated to the maximum value given by Eq. (65), and the sweepout limited detectivity is therefore

ELECTRIC FIELD

FIG. 5 . Field dependent respoiisivity for an (HgCd)Te detector. 0, data; -, theory using the following parameters: 7bulk = 3.4 psec at 80 K; pn = 1.3 x 105 cmP/V sec; pa = 166 cm2/V sec; rd = 59 a.

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

181

20 19 18

-3

77

c1

-

I

1.6

'

1 5

n

14

5

0 I

13

12 1 1

10 0

2

4

6

8

10 12 14 16 18 20

22 24 26 28 30

ELECTRIC FIELD ( V i c r n l

FIG.6. Field-dependentD* for an (HgCd)Te detector.

This limit is independent of the time constant and is therefore also independent of the effects of surface recombination. The value of the field needed to reach this limit, however, increases with surface recombination. Experimental evidence for the reasonableness of this empirical approach to sweepout and diffuse-out may be seen from the data presented in Figs, 5 and 6, which show the field dependent responsivity and D* for an (HgCd)Te photoconductor (Broudy er af., 1975; Broudy, 1976). However, other reported data (Kinch er af., 1977) have not shown this effect. It may be speculated that experimental disagreements are due to differences in contact characteristics for various detectors (see the following discussion on complex device configurations). To illustrate the effect of sweepout on the temperature and field dependences of actual photoconductors, we have calculated the responsivity and g-r noise for conditions which may occur in practice. For convenience in exposition, the sweepout factor, F, has been set to 1. In Figs. 7 and 8 the g-r noise and the responsivity are shown as a function of bias for the following conditions: (1) An ideal detector with the parameters listed in Table 1 (see curve

4. (2)

The same detector as in (1) but with surface recombination param-

eters: sz

(see curve b).

=

00,

s,

=0

182

R . M . BROUDY A N D V. J . MAZURCZYK

CURVE ( a ) IDEAL DETECTOR 15 CURVE ( d ) SURFACE RECOMBINATION, PLUS SWEEPOUT PLUS THERMAL RESISTAKE

\

c-

I 0 SURFACE

r N

P 3 >b

-

5

1.0

Q5

v,

(V)

FIG. 7. Calculated bias-dependent g-r noise for high and low thermal conductivity bonding layers. cr = 1.

(3) The same detector as in (2) but with sweepout present (see curve

C)

.

(4) The same detector as in (3) but with a thermal interface having ~- -

ZA,

3 ~ / ~ c m

(see curve d). Curves b and c in Fig. 7 illustrate how surface recombination and sweepout dramatically reduce g-r noise and so make it much more difficult to satisfy Eq. (34). Increasing the bias will be effective only until it begins to increase the detector temperature. At this point the g-r noise will show a rapid increase. (Fig. 7b). This increase will be beneficial as far as Eq. (34) is concerned but will cause an overall reduction in the detectivity because of Eq. (33). This is illustrated in Fig. 9 where the detectivity as a function of temperature is shown. For an ideal detector a bias of 45 mV is

CURVE ( a 1 IDEAL DETECTOR

PLUS SWEEPUJT

THERMAL RESISTANCE

I

I

0.5

1.0

J

Vb ( V )

FIG. 8. Calculated bias-dependent responsivity for high and low thermal conductivity bonding layers. u = 1 .

r

.-

.-

45- mV BIAS

0.5

Y

DETECTOR WITH DRIFT, DIFFUSION, ANDTHERMAL EFFECTS

* r D

I

I

I

60

70

I

I

I

1

80 90 400 TEMPERATURE (K)

FIG.9. Calculated temperature-dependent D" for high and low thermal conductivity bonding layers, with and without sweepout, at bias voltage levels of 45 and 150 mV. F = 1. QB = 1.08 x 10" cmz.

184

R. M . BROUDY A N D V . J . MAZURCZYK

sufficient to satisfy Eq. (34). But with the addition of surface recombination, sweepout and a thermal interface, the performance drops drastically if the bias is maintained at 45 mV. Increasing the bias to 150 mV might be expected to produce a substantial improvement in the detectivity , but actually the higher levels of bias result in a decrease of performance because of detector heating. A consequence of minority-carrier sweepout is that the excess carriers and therefore the photoresponse are nonuniformly distributed along the length of the detector as shown in Eq. (59). An experimental example (Mazurczyk, unpublished data) is shown in Fig. I0 which is quantitatively in agreement with Rittner's theory as determined from Eq. (59). The detector has been scanned with a 0.001-in. spot for several different fields. The triangular shape of the response at high fields occurs because the life-

3.3

66 13.1 19 7

33 8

I

i

I

//////A

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

185

time of the carrier is determined by the time to reach the negative contact rather than by bulk or surface recombination. Although the responsivity saturates with increasing bias, the time constant does not and continues to decrease; therefore, the detector upper frequency limit f * increases until heating effects or impact ionization cause an abrupt decrease in the responsivity. Again, from the work of Rittner (1956), the time dependence of the excess carrier density may be determined from the following expressions for a detector of length L:

AP(E,f)= APo @X,f),

(69)

where

+ sin2(nr/2)]

(- l)n+'n2 exp( - Dlf/~)[sinh2(DiL/2) n=O

&(Dl

-

The quantities f, and f 2 are the drift and diffusion lengths defined previously. We have performed a sample computer calculation of Eq. (69) as shown in Fig. 11 . A short detector of L = 25 pm was considered for maximizing the influence of drift and diffusion. It is notable that for field strengths below 30 V/cm the theoretical time dependence is almost exponential as is commonly observed experimentally. The values of T calculated using the T[ approximation agree closely with the rigorous calculation as shown in Fig. 12. At higher fields one must use Eqs. (67) and (70). The preceeding discussions have illustrated several important points. ( 1 ) A consideration of the simple model for detectors leads to the requirements for maximum performance, i.e., Eqs. (33) and (34). These conditions remain true when the effects of sweepout, surface recombination, and heating are introduced. (2) Drift and diffusion of minority carriers, surface recombination, and thermal resistance effects cause the actual performance of detectors to seriously deviate from the predictions of the simple model. However, these effects can be approximated by relatively simple substitutions. (3) The drifted diffusion of minority carriers in the detector generally results in the need for more bias power and refrigeration to achieve the same performance as the ideal detector.

10-2 9

'

I

I

30 V/cm

5 0 V/cm

0.5

1.0

1.5

T (fO-'SW)

FIG.11. Calculation of the transient decay of photoconductivity for varying field strength, using Rittner's theory (1956).

T~~

2

lRlGOflCUS C A L C U L A T I O N )

I

roc ( M O D I F I E D EXPONE

z

g '

~-

10

'ri

t-

1

10

50

FIG. 12. Time constant as determined from Rittner's theory and from the exponential approximation.

5 . (HgCd)Te

187

PHOTOCONDUCTIVE DETECTORS

11. SUMMARY OF EQUATIONS FOR THE ONE-DIMENSIONAL APPROXIMATION WITH OHMICCONTACTS

The equations developed in the preceding sections for the onedimensional case are summarized in Table 11. The parameters must be TABLE I1 ANALYTICAL EXPRESSIONS O F DETECTOR PERFORMANCE FOR T H E ONE-DIMENSIONAL CASE W I T H OHMICCONTACTS

=@%L

Responsivity (without sweepout):

Rh

Generation - recombination noise (without sweepout):

"-' = (Lwd)1f2no

fo

Amplifier noise associated with a detector of resistance rd :

=

=

7

~

)

~

'

~

K1Vg-r

VZ, = e',

+ :z

D'L'p

ri - A 11 "= - 2hc (Q,) -112

(without sweepout):

where

~

(4kTrd)lI2Afl"

Maximum D* at wavelength A, (without sweepout): Detectivity

Sweepout factor:

+~

[[1+PO nO ][PbTAf]]1'2 p b p o + no 1 + w2?

2vh

Johnson noise associated with V, the detector resistance: Ilfnoise with comer frequency f,:

hc no Lwd (1

Pb P O

( = 1'+

al,8

=

+

120

(az - a l )sinh(alL/2) sinh(a&/2)

alaa(L/2) sinh(a, - az)L/2

-E f [(A)* + &]I1* 2kT/q

2kT/q

kTpor

carefully chosen for use in these equations, since many of them are interdependent. For example, variations in the fabrication process can modify the thermal resistance, detector thickness, surface recombination velocity, and l/f noise. In addition, calculations of hypothetical detector performance, especially for arrays, must take into account the possible range of variations. For example, one approach would be to assume a distribution of values for each of the parameters and then calculate the range of expected performance using Monte Carlo techniques. V. Photoconductive Device Design Extensive development of (HgCd)Te photoconductive detectors during recent years has led to semiconductor devices of considerable sophistica-

188

R. M . B R O U D Y A N D V. J. MAZURCZYK

tion and complexity. Designs and process techniques have been developed based on recognition and utilization of the fact that photoconductivity is due to majority carriers that are controlled by the behavior of minority carriers. In most cases, the objective has been to increase the minority carrier lifetime and therefore the device responsivity by reduction of minority-carrier recombination in the appropriate area of the device. This part describes several implementations of these principles.

12. EXTENDED CONTACTS Rittner's theory (1956) and the experimental verifications thereof show that the ultimately limiting lifetime of a photoconductor is the transit time of the minority carrier to the opposite polarity contact. Thus, the upper limit for the minority-carrier lifetime of an n-type (HgCd)Te photoconductor is the time required for a hole generated just inside the positive contact to reach the negative contact, a distance away, T = L / p h E . Carriers generated closer to the negative contact will recombine in a shorter time. Thus, the device lifetime may be seriously diminished for a small geometry detector arrays, as shown in Part IV. For example, for (HgCd)Te detector elements in the 0.001-0.002 in. range, the effective lifetime may never be longer than 700 nsec, whatever the bulk lifetime. Kinch et al. (1977) have proposed and demonstrated a device structure which increases the effective lifetime by extending the contacts away from the active area. In this overlap structure, as shown in Fig. 13, the optically active area is defined by a metal overlay of the insulating antireflection coating and not by the contacts. Although there is additional power dissipation from the overlap regions of the detector, Kinch et al. (1977) show that for detector lengths up to about a factor of 5 greater than the hole diffusion length, an increase in

4

LY

I

I

'I' I

I

INSULATOR (ANTIRFFLFCTION FILM)

r*T I

1

i

i

I

I

MFTAL

i

/

/

\ (Hqf d j i e

FIG. 13. Contact overlap structure for geometrical enhancement. (From Kinch et ul., 1977.)

(HgCd)Te

10

189

PHOTOCONDUCTIVE DETECTORS

I02

Io3

I 0“

I05

OETECTOI~BIAS PowEri (UW)

FIG.14. Responsivity versus detector bias power for overlap and standard devices 0.1-eV (HgCd)Te at 77 K and a 55” FOV. (From Kinch et al., 1977.)

length results in an enhancement in responsivity for equal bias power (assuming that the detector lifetime between the contacts is sufficiently long). Figure 14 illustrates the effect for a standard detector and an overlap structure for 0.1-eV n-type (HgCd)Te measured at 77 K and a 55” FOV. The nominal width of the active areas is 0.002 in. and the overlap length is 0.0010 in. 13. COMPLEX CONFIGURATIONS-GEOMETRY A N D CONTACTS

Actual devices are not one dimensional and may have contacts that deviate from ohmicity, either due to intentional or coincidental processing procedures. In this section we present an abbreviated discussion of the influence of these important effects. Inspection of actual device configurations, such as sketched in Fig. 1 to approximate scale, makes it clear that significant deviations from onedimensional field and current distributions are to be expected. Rigorous multidimensional analyses just becoming available (Kolodny and Kidron, 1981) have shown that departures from the predictions of one-dimensional theory for typical devices may lead to an increase in responsivity and time constant by as much as 80%. This occurs because device resistance is greater and because reduction in effective device thickness originates from redirection and compression of field lines. Moreover, detector noise may be reduced when carriers diffuse away and recombine under the contacts.

190

R . M . BROUDY A N D V. J . MAZURCZYK

Contacts may be either ohmic or “blocking” in nature. In the latter case, a more intensely doped region at the contact (n+ for n-type devices) causes a built-in electric field that repels minority carriers, thereby reducing recombination and increasing the effective lifetime and the responsivity (Long, 1977). Shacham-Diamand and Kidron (1981) have presented an analysis of the influence of blocking or partially blocking contacts on photoconductive detectors. They modified the basic theory of Rittner to include the effects of built-in electric fields due to n+-n regions at the contacts and then applied their model to the calculation of current responsivity and time constant of (HgCd)Te photoconductors as a function of a parameter 2 = n + / n , the doping ratio. Comparison with experimental results showed excellent agreement with observed responsivities, which may be as much as 5 times greater than predicted by the simple Rittner theory with ohmic contacts. It is instructive to note that the field dependence and magnitude of responsivity and noise for the more complex configurations follow closely the same functional behavior predicted by the simple Rittner analysis, but the magnitude of a key parameter must be modified from the actual material values to achieve correspondence with theory and experiment. Specifically, use of Rittner’s one-dimensional ohmic contact theory to match experimental responsivities shows excellent agreement over the entire range of electric field if the magnitude of the ambipolar mobility, p a , which is the only adjustable parameter, is reduced by a factor of 2-5 below the known material value (as applied in Fig. 5). 14. TRANSVERSE FIELDEFFECTS-ACCUMULATION LAYERS

As discussed in Part IV, Section 8, a common practical limitation of performance is caused by the reduction of lifetime due to recombination at the surfaces of the device. In fact, much of the technology of present-day device fabrication is designed to minimize the surface recombination of minority carriers that reach the surface by using appropriate chemical and mechanical preparation procedures to reduce the surface recombination velocity. There is, however, a different approach to reducing surface recombination that has been quite successful and may be more controllable. In this method recombination is reduced by preventing the minority carriers from reaching the surface at all by means of a built-in electric field. In the case of n-type (HgCd)Te, a transverse field would be provided by an n+ accumulation layer extending inward from the surface. An accumulation layer in a semiconductor may exist or be intentionally introduced in two ways: The first utilizes external (positive) charge (for

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

191

n-type devices). This effect can result from charge at three locations: (1) in donor or acceptor surface states; (2) the presence of positive or negative ions in the insulator outside the semiconductor; or (3) charge may be produced by metal field plates above the insulator. In the second method for introducing accumulation layers, n-type doping is provided, extending inward from the surface to form an n+n high-low junction (for n-type devices in this approach, electric charge is provided internally by occupied acceptors). Although both methods have been demonstrated in actual devices, detailed information is limited due to the proprietary nature of the techniques. It is probably accurate to estimate that the majority of devices within recent years have some form of surface accumulation layer. It is also noteworthy that the principle of accumulation for reflection of minority carriers is equally applicable at the contacts of semiconductor detectors to increase minority carrier lifetime and reduce sweepout effects as discussed in the preceding section.

15. TRANSVERSE FIELDEFFECTS“TRAPPING PHOTOCONDUCTIVITY’’ a . Background und Older Theories It has been recognized for some time that the lifetime (and therefore responsivity) of photoconductors could be significantly increased at reduced temperature and background if there were some mechanism for trapping of minority carriers in sites with low recombination probability. Evidence for such phenomena had apparently been seen from experimental results on (HgCd)Te photoconductors at low temperature and low background. Typically, there is a strong increase in responsivity as the temperature is reduced, followed by a plateau region, where the responsivity becomes nearly temperature independent, but varies as I/Q” with n varying between 0.5-1.0. The experimental results indicate clearly that some additional mechanism must be operating for reduction of carrier recombination, since photoconductor lifetimes under low temperature and low background conditions have been observed to be much longer than would be possible even for the smallest known bulk recombination process. It was recognized that such behavior could not be explained by any simple trapping mechanism, since for any typical density and distribution of traps, the traps will become fully occupied at reduced temperature leading to a strong reduction in responsivity. To circumvent this limitation, it was proposed (Broudy and Beck, 1976) that a continuum of minority-carrier traps exists within the lower half of the forbidden gap. Theoret-

192

R . M . BROUDY A N D V . J . MAZURCZYK

ical analyses using this model gave promising agreement with experimentation; best results were found for a variable continuum which diminished exponentially with energy separation from the valence band. However, to validate this model, it was found necessary (Broudy, unpublished analyses) to assume recombination probabilities for the trapped holes that were so small that they appeared physically unreasonable and inconsistent with the very high photoconductive gains measured on the best devices. For this and other reasons, an alternate theory was proposed (Broudy, unpublished analyses; Beck, unpublished analyses; Beck and Sanborn, 1979)for trapping photoconductivity that is based on a quite different mechanism in which traps, per se, do not exist.

b . Chlirg e SPp a ru t ion ( I nd 1ra tisve rs e Field Devices It is now clear that the very high responsivities and photoconductive gain observed in (HgCd)Te photoconductors as well as (probably) other semiconductors can be ascribed to the mechanism of charge separation due to built in transverse electric fields. The principle is essentially an expansion of that utilized in the accumulation device. Minority carriers are physically separated from majority carriers by the presence of a transverse electric field which may be generated by any of the mechanisms described above for the accumulation device. The charge separation, or transverse field effect may also be analyzed from a different, but equivalent, point of view, by recognizing that the photoconductor is essentially a field effect device with a floating gate. If the transverse field originates in the surface or insulator, the analog is a MOSFET device, whereas if it originates from a transverse junction, the analog is a JFET. The effect may be modeled as conductivity modulation due to changes of depletion layer width with background illumination. Since the analysis is less complex for the transverse junction case, only this device is discussed below. The results are similar for the transverse MOSFET device. The structural elements of these devices are illustrated in Fig. 15 (Beck and Sanborn, 1979). c. Charge Sepurution Analysis

The correlation with trapping behavior and general photoconductivity may best be illustrated from direct consideration of charge separation. From this viewpoint, greater photoconductive gain occurs because the minority-carrier lifetime is increased, being ultimately limited by thermally generated current across the transverse junction. The basic principles may be illustrated by a simple analysis (Broudy , unpublished analyses) of the basic concepts, beginning with Rbtthe transfer rate of minority carriers (usually holes) from the bulk into the p-type region across the

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

193

NEGAIIVE CHARGE

,/I

h

N CHANNEL I

vDP--Q I\ CHANNEL

(b)

FIG. 15. Structural elements of transverse field photoconductors (a) with negative charge and (b) with p + .

junction Rbt

=

K , AP,

(73)

where Ap is the excess photogenerated minority-carrier concentration and K , is a constant. It is assumed that the bulk lifetime of the excess minority carriers is long enough so that eventually they all diffuse to the junction region. The transfer rate of excess (due to illumination) carriers across the junction into the bulk is obtained from the standard diode current equation: =

Zo(eqVlmkT

- 1)

(74)

We now make the simple assumption that the voltage across the (floating) junction is proportional to Apt, the total density of excess holes in the p-type region (note that these holes reside at the depletion region across the junction). Rtb,the transfer rate of holes back into the main body of the photoconductor, is given by

Rtb =

J&-L;/”(@

@I

lmkT

- 1)

(75)

where K2 is another constant. In the steady state Rtb = Rbt,leading to the

194

R.

M. BROUDY

A N D V . J . MAZURCZYK

expression: An = Ap

+ Apj = & + __ log d lnkT K3

(1 +

@./kT

where K4 is a different constant, and where we have included the dependence of A P on the photon flux Q (qTQ/d = Ap);the first term being simply the bulk photoconductive gain. Then, in the small signal case, the photoconductive gain Gt is given by

where QBis the background photon flux. It can be seen at once that Eq. (77) has the qualitative features of the experimental results. At high background and low temperatures, the second term in the denominator predominates and the photoconductivity goes as QG’. At lower background and higher temperature, the first term predominates and the photoconductive gain goes exponentially with temperature with the activation energy El3

d . JFET Analysis Further physical insight may be gained from the JFET approach (Beck, unpublished analyses; Beck and Sanborn, 1979) which leads to the identical result to the charge transfer analysis. In this approach, the simple expression for the source-to-drain conductance Gsd is given by Gsd

= qpe(d

- xD)nw/L,

(78)

where w = device width, L, the distance between electrodes, and xDis the depletion width. From this viewpoint the change in excess charge, A p t , is directly determined by the change in depletion width. The depletion width can be calculated from the well known expression:

where ND is the donor concentration and where the built in potential = V,, - V,,, the difference between the built-in across the junction T,,, and open circuit potential. The photoconductive gain and voltage responsivity may be calculated from the current responsivity:

w, = arD/as,

(80)

where Inis the detector current (which from the JFET point of view may be considered to flow from drain to source to the device). Then, as in Part

5. (HgCd)Te

I, the expression for

PHOTOCONDUCTIVE DETECTORS

195

becomes

Since Z, = GsdVb,the depletion modulation determined responsivity becomes

It is convenient to relate the latter term to u,, , the open circuit potential of the floating junction:

(ax~/a Qs)

=

(ax~/a vd(avda Qs).

(83)

Thus the performance may be readily calculated by reference to standard photodiode derivations. Under the assumption of realistic bias levels, V,/kT >> 1 , and Vo, takes the simple well-known form for an illuminated floating junction (Beck and Sanborn, 1979)

+ sqQsA/Zo>.

Voc = fkT/q) Using Eqs. (79), (82), (83), and (84),

(84)

takes the convenient form

Alternately, the photoconductive gain G,, may be used in addition to, or in place of %N from Eq. (85) by noting that %N =

(A/hc)sqGw.

(86)

It should be noted that Eq. (85) has essentially the same form as Eq. (77). Beck and Sanborn (1979) have calculated the temperature and background dependence of & and G, from Eq. (85) for the diffusion limited junction case in the low voltage bias limit for x = 0.39 (HgCd)Te detectors with the following set of typical device parameters and operating conditions: QB = lo", 10l2,and 1013 photons/cm2 sec, N A = 6 x 10l6 in transverse junction, N D = 6 x 1014 cm-3 in body of photoconductor, q = 1.0, d =7 x cm, device thickness, E, = 17.2, dielectric constant, 7, = 1 x sec, bulk lifetime.

196

R . M . BROUDY A N D V. J . MAZURCZYK

,-OB =! x 1 0 t 2 photons/sec ,in2

og

photons/sec cmZ

t

t.0

0

"

'

2

1

4

"

"

6

1

"

8

"

~

1 0 4 2 t 4

tOOO/T ( K - 0 FIG. 16. Calculated gain of the transverse junction device versus temperature and background for the diffusion limited case at low bias for an x = 0.39 (HgCd)Te photoconductor.

The results are shown in Fig. 16. It should be pointed out that the above derivations represent only a first-order evaluation, since the unavoidable effects have not been considered of contacts and longitudinal potential variation along the JFET. Inclusion of these effects (Beck and Sanborn, 1979) will modify the background dependences as well as bias dependences. Similar approaches (Beck and Sanborn, 1979) for the externally initiated transverse field devices may be based on MOSFET theory. VI. Technology of (HgCd)Te Detectors

Modern (HgCd)Te photoconductive detectors are generally fabricated in arrays by methods of which many are quite similar to processes used for silicon integrated circuits, including photolithography, etching, vacuum and sputtering metallization, insulator deposition, and wire bonding. In addition, special techniques applicable to (HgCd)Te may be used, such as slab bonding and subsequent lapping and etching. Array performance close to the theoretical limit has been achieved in many cases.

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

197

A typical set of key steps for array fabrication are the following: (1) Start with good material: Develop methods for material evaluation and selection. (2) Obtain the material in slices sufficiently thick for ease of handling: Prepare the backside. (3) Bond the slab to a substrate: Epoxy is generally used. (4) Lap, polish, and etch the material almost to final thickness (usually close to cm) chosen to be thick enough to absorb almost all of the optical radiation and thin enough to minimize bias current. (5) Delineate the array using a photolithographic process with etching. (6) Accumulate the surface: This process will often also be performed between (2) and (3) above. (7) Metallize after further photolithography for contact and possibly active area delineation. (8) Wire bond for external electrical contact.

For similar reasons to those well known in integrated circuit pro-

FIG. 17. Section of a linear (HgCd)Te photoconductive array. Active area dimensions are 0.00125 x 0.002 in. (L x W) for each element.

R. M. BROUDY A N D V. J. MAZURCZYK

198

-

4

-

3 -

-

0

0

X

i.“

2 -

I

1

.. . FIG.18. D*performance under reduced background levels for a 60-element array with the configuration shown in Fig. 17.

cessing, scrupulous attention must be given to process technique, procedures, and cleanliness for all of these steps. Fig. 17 shows a photograph of section of a modern multielement PC array that has been prepared according to this procedure. The D* of this array is presented in Fig. 18, which shows values approaching the theoretical limit for the reduced background of this measurement.

REFERENCES Beck, J. D., and Sanborn, G. S . (1979). Air Force Materials Laboratory Rep. AFML-TR-79. Borello, S., Kinch, M., and Lamont, D. (1977). fnfrared Phys. 17, 21. Broudy, R. M. (1974). NASA Rep. CR-132512. Broudy, R. M. (1976). Frequency characteristics of high performance (HgCd)Te detectors, Proc. Infrared Informar. Symp. Detector Specidly Group. Broudy, R. M., and Beck, J. D. (1976). Pror. Infrured Informar. Symp. Detector Speciulty Group. Broudy, R. M., Mazurczyk, V. J., Aldrich N. C., and Lorenze, R. V. (1975). Advanced (HgCd)Te array technology, Proc. Infrured Informat. Symp. Defector Sperialty Group. Burgess, R. E. (1954). Physica 20, 1007. Burgess, R. E. (1955). Proc. Phys. Soc. London B68, 661. Burgess, R. E. (1956). Proc. Phys. Soc. London B69, 1020. Domhaus, R., and Nimtz, G. (1976). The properties and applications of the Hg,-,Cd,Te alloy system, in “Springer Tracts in Modem Physics,” Vol. 78, pp. 1-119. SpringerVerlag, Berlin and New York. Eisenman, W. L., Meniam, J. D., and Potter, R. F., (1977). Operational characteristics of

5. (HgCd)Te

PHOTOCONDUCTIVE DETECTORS

199

infrared photodetectors, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 12, Chapter 2. Academic Press, New York. Finkman, E., and Nemirovsky, Y. (1979). J. Appl. Phys. 50, 4356. Hooge, F. N. (1969). Phys. Lett. 29A, 129. Kinch, M. A., and Borello, S. R. (1975). Infrared Phys. 15, 11 1. Kinch, M. A., Brau, M. J., and Simmons, A. (1973). J. Appl. Phys. 44, 1649. Kinch, M. A., Borello, S. R., Breazale, B. H., and Simmons, A. (1977). Infrared Phys. 17, 137. Kinch, M. A., Borrello, S. R., and Simmons, A. (1977). Infrared Phys. 17, 127. Kingston, R. H . (1978). “Detection of Optical and Infrared Radiation.” Springer-Verlag, Berlin and New York. Kittel, C. (1961). “Elementary Statistical Physics,” p. 145. Wiley, New York. Kolodny, A., and Kidron, I. (1981). Infrured Phys. (to be published). Kruse, P. W. (1979). The photon detection process, in “Infrared and Optical Detectors,” Chapter 1. Springer-Verlag, Berlin and New York. Kruse, P. W., McGlauchlin, L. D., and McQuistan, R. B. (1962). “Elements of Infrared Technology: Generation, Transmission and Detection.” Wiley, New York. Levinstein, H. (1970). Characterization of infrared detectors, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 5 , Chapter I . Academic Press, New York. Long, D. L. (1970). Infrared Phys. 7 , 169. Long, D. (1977). Private communication, who refers to the work of J. R. Hauser and P. M. Dunbar, Solid State Electron. 18, 716 (1975). Long, D. (1977). Photovoltaic and photoconductive infrared detectors, in “Topics in Applied Physics” (R. J. Keyes, ed.), Vol. 19, Optical and Infrared Detectors. SpringerVerlag, Berlin and New York. Long, D., and Schmit, J. L. (1970). Mercury-cadmium telluride and closely related alloys, in “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 5 , Chapter 5 . Academic Press, New York. Mazurczyk, V. J., Graney, R. N., and McCullough, J. B. (1974). High performance, wide bandwidth (Hg,Cd)Te detectors, Opt. Eng. 13, 307. Milton, A. F. (1973). Proc. Infrared Informat. Symp. Detector Specialty Group. Rittner, E. S . (1956). In Photoconduct. Conf. (R. Breckenridge, B. Russell, and E. Hautz, eds.), p. 215ff. Wiley, New York. Shacham-Diamand, Y. J., and Kidron, I. (1981). Infrared Phys. 21, 105. Schmit, J. L. (1970). J . Appl. Phyc. 41, 2867. Schmit, J. L., and Stelzer, E. L . (1969). J . Appl. Phys. 40, 4865. Smith, D. (1981). Submitted for publication. Van der Ziel, A. (1959). “Fluctuation Phenomena in Semiconductors.” Butterworth, London. Van Vliet, K. M. (1958). Proc. IRE 46, 1004. Van Vliet, K. M. (1967). Appl. Opt. 6 , 1145. Van Vliet, K. M., and Fassett, J. R. (1965). Fluctuations due to electronic transistions and transport in solids, in “Fluctuation Phenomena in Solids” (R. E. Burgess, ed). Academic Press, New York. Williams, R. L. (1968). Infrared Phys. 8, 337.

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SEMICONDUCTORS AND SEMIMETALS, VOL. 18

CHAPTER 6

Photovoltaic Infrared Detectors M. B. Reine, A . K . Sood, und T . J . Tredwell I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . I . Applications jbr Hg,-,Cd,Te Photodiodes . . . . . . 2. Scope of This Chapter . . . . . . . . . . . . . . . 3. Summary (if Hg,-,Cd,Te Properties , . . . . . . . . 11. THEORY OF p-n JUNCTION PHOTODIODES . . . . . . . . 4. Current- Voltuge Characteristics . . . . . . . . . . 5. Photocurrent in p -n Junctions . . . . . . . . . . . 6. Noise Mechanisms . . . . . . . . . . , . . . . . 1. Responsivity, Noise Equivalent Power, and Detectivity 8 . Lateral Collection in Small-Area Junctions. . . . . . 9. Response Time . . . . . . . . . . . . . . . . . , 10. Auger Lifetime in p-Type H g , - , C d , T e . .. . . . . . 111. Hg,-,Cd,Te JUNCTIONPHOTODIODE TECHNOLOGY. .. . 1 1 . Ion Implantation . . . . . . . . . . . . . . . . . 12. Diffused Photodiodes . . . . . . . . . . . . . . . 13. Type Conversion in Hg,-,Cd,Te by Other Techniques. 14. Minority-Carrier Properties of p-Type Hg,-,Cd,Te . . 15. I/f Noise in Hg,-,Cd,Te Photodiodes. . . . . . . . 16. Schoitky Barrier Photodiodes . . . . . . . . . . . . 1V. SUMMARY A N D CONCLUSIONS . . . . . . . . . . . . . REFERENCES. . . . . . . . . . . . . . . . . . . , .

. .. .. .

. . . .

. . . . . . . .

.. .. .. . . . . . . . .

. . . . . . . . . .

20 1 202 204 205 201 201 221 232 235 238 240 243 246 247 272 283 286 291 301 303 305

1. Introduction

The semiconductor alloy Hg, -,Cd,Te is a remarkably versatile infrared detector material. Photoconductors, junction photodiodes, and several types of infrared-sensitive metal-insulator-semiconductor (MIS) devices, including charge coupled devices (CCDs), charge injection devices (CIDs), and recently metal-oxide-semiconductor field effect transistors (MOSFETs), have been realized in this material. Each of these quite different types of devices has certain advantages for infrared detection, depending on the particular application. In this chapter we review the status of Hg,,Cd,Te photovoltaic infrared detector technology. We concentrate almost exclusively on p - n junc20 1

Copyright 0 1981 by Academic Press. tnc. All rights of reproduction in any form reserved. ISBN 0-12-752118-6

202

M . 0. REINE, A . K . SOOD, AND T. J . T R E D W E L L

tion photodiodes, but will review also recent work on Hg,-,Cd,Te Schottky barrier photodiodes. Although there have been several interesting papers on photovoltaic effects in graded-bandgap Hg,-,Cd,Te structures (Marfaing and Chevallier, 1971a,b; Cohen-Solal and Marfaing, 1968), these effects are not included in this review. Photovoltaic effects were mentioned briefly in the first paper on Hg,-,Cd,Te by Lawson rt ul. (1959), and were attributed to an unintentional p-n junction at or near a contact to a photoconductive sample. In a later study of Hg, ,Cd,Te detectors, Kruse (1965) reported photovoltaic signals in n-type photoconductive samples at 77 K and attributed these to the bulk photovoltaic effect as described by Tauc (1962). The first intentional p-n junctions in Hg,-,Cd,Te appear to be those of Vdrid and Granger (1965) who observed injection luminescence at about 3.7 pm from these junctions at 77 K (see also Rodot rt ul., 1966). Since this first report of p - n junctions in Hg,-,Cd,Te by Verit and Granger (1965), over 100 papers, reports, and other publications dealing with Hg,-,Cd,Te photodiodes have appeared in the open literature. Cutoff wavelengths have ranged from 1.0 to beyond 48 pm. Junctions have been formed by ion implantation, impurity diffusion, and both outdiffusion and in-diffusion of mercury. Avalanche gains of about 20 have been reported in Hg,,Cd,Te photodiodes with 2-pm cutoff wavelengths. Hg, -,Cd,Te photodiodes have been reviewed previously by Long and Schmit (1970), Melngailis (1973), by Harman and Melngailis (1974), and by Reine and Broudy (1977). I . APPIKATIONSFOR Hg,-,Cd,Te

JUNCTION PHOTODIODES

Initially the Hg,-,Cd,Te junction photodiode attracted interest for use as a high-speed detector for COz laser radiation around 10.6 pm. Operating at 77 K in the heterodyne mode, this type of photodiode has recently achieved a noise equivalent power which is only a factor of 1.4 above the theoretical quantum limit at a frequency of 2 GHz. Operation at these high frequencies is possible because of the low junction capacitance achievable in Hg,-,Cd,Te, which in turn is a result of its relatively low static dielectric constant. As pointed out by Melngailis (1973), Hg,-,Cd,Te is superior to Pb,-,Sn,Te for wide-bandwidth applications because of the much larger static dielectric constant of Pb,-,Sn,Te. Hg, -,Cd,Te junction photodiodks continue to be developed for advanced 10.6-pm direct detection and heterodyne applications. At present, efforts are being directed toward a 10.6-pm heterodyne detector that operates at a temperature of around 200 K so that it can be conveniently cooled by a thermoelectric cooler. More recently, interest has focused on Hg, junction photo- -,Cd,Te .

6.

PHOTOVOLTAIC INFRARED DETECTORS

203

diodes for use with silicon CCDs in hybrid mosaic focal plane arrays for direct detection, principally in the 3-5 and 8- 12 pm spectral regions. Hybrid mosaic focal planes utilizing Hg,-,Cd,Te photodiodes have been reviewed by Broudy and Reine (1977) and by Broudy el al. (1978, 1980). A hybrid mosaic focal plane array consists of a two-dimensional array of large numbers of Hg,-,Cd,Te junction photodiodes in contact with a silicon CCD chip. Each photodiode is connected electrically to one CCD stage. Charge that is photogenerated in and separated by each photodiode is injected into each CCD stage. Once it is within the silicon CCD chip, this charge is transferred laterally to the edge of the chip and is available for further processing. In this application, the photovoltaic (PV) mode is preferred over the photoconductive (PC) mode. These mosaic focal plane arrays will contain tens of thousands of detector elements or more and will operate at cryogenic temperatures, so that minimizing power dissipation is important. Unlike the photoconductor, the photodiode requires no dc bias power. Because of its relatively high impedance, the photodiode matches directly into the input stage of a silicon CCD, whereas the photoconductor would require a buffer preamplifier, which itself would dissipate power and occupy valuable real estate on the silicon CCD chip. Hybrid mosaic focal plane arrays utilizing Hg,,Cd,Te junction photodiodes and silicon CCD chips are being developed in two different configurations: the so-called planar processed configuration shown in Fig. la and the backside-illuminated configuration shown in Fig. lb. In the planar hC Insulator

Layer

Interconnect Metallization

Silicon CCD Chip

Input Node

CCD

Silicon CCD Chip

._

\"put Nodes

FIG. 1. Schematic illustrations of the (a) planar processed and (b) backside-illuminated hybrid mosaic focal plane schemes utilizing a silicon CCD processing chip together with Hg, -,Cd,Te junction photodiodes.

204

M.

€3.

REINE,

A. K. SOOD, A N D T. J . TREDWELL

processed configuration, the silicon CCD chip is actually used as a substrate. A Hg,-,Cd,Te wafer is epoxied to the silicon chip, is lapped and etched to an appropriate thickness, usually on the order of 10-15 p m , junctions are formed and metal films are evaporated to connect each junction to the CCD stage immediately below it. In the backside-illuminated configuration, a mosaic of Hg, -,Cd,Te junctions is processed separately on an optically transparent substrate. Contact bumps of indium are plated on each junction and on each CCD input stage. Finally, the Hg,-,Cd,Te mosaic is flipped over and connected to the silicon chip by means of the contact bumps. In the backside-illuminated configuration, the Hg,-,Cd,Te active layer could be grown by liquid phase epitaxy onto a CdTe substrate. In both the planar-processed and backside-illuminated configurations, the Hg,,Cd,Te active layer must be fairly thin, on the order of 10- 15 pm, which in turn is on the order of or less than a minority-carrier diffusion length. This requirement of thinness has important consequences on photodiode performance. The choice of the PV mode over the PC mode for hybrid mosaic focal planes is not because of any inherent superiority of the PV mode in terms of sensitivity or operating temperature. Long (1977) in fact has pointed out that the theoretical limits to signal-to-noise ratio and operating temperature are the same for all intrinsic quantum detectors, no matter whether they are photovoltaic or photoconductive. His arguments can be shown to hold true also for the MIS detector described by Kinch in this volume. 2. SCOPEOF THISCHAPTER This chapter is organized into four parts. Part 11 reviews the theory of operation and the fundamental and practical limits to the performance of p-n junction infrared photodiodes. In the thirty years since Hg,,Cd,Te Shockley’s classic paper (Shockley, 1949) there have been many excellent textbooks on p-n junctions, among the most notable being those by Grove (1967) and Sze (1969), to which we make frequent reference. The purpose of Part I1 is not to repeat what is already well written, but rather to summarize the information needed to understand the operation and predict the performance of Hg,-,Cd,Te infrared photodiodes. Part I1 borrows liberally from the excellent discussions of Hg,-,Cd,Te photodiodes by Long (1977) and of photodiodes in general by Kingston (1978). Part I11 summarizes the state of the art in Hg,-,Cd,Te p - n junction technology. There have been impressive advances recently with the use of ion implantation; the review of these is followed by a review of photodiodes formed by diffusion of both impurities and mercury. Recent results

6.

PHOTOVOLTAIC INFRARED DETECTORS

205

on Schottky barrier photodiodes and Ilfnoise in reverse-biased p - n junction photodiodes are reviewed. Part I11 also contains a summary of what information various measurements on p - n junctions have yielded about the minority-carrier properties of p-type Hg,-,Cd,Te. Nearly all research and development on Hg,-,Cd,Te has been funded by various Department of Defense and National Aeronautics and Space Administration contracts. We have tried to reference all unclassified contract reports relevant to Hg,-,Cd,Te junction photodiode technology, and have added to each such reference either the "AD" number for ease of obtaining copies from the Defense Documentation Center or the appropriate NASA reference number.

3. SUMMARY OF Hg,-,Cd,Te

PROPERTIES

A summary of the most important electrical and optical properties of Hg,,Cd,Te with alloy compositions between 0.19 and 0.55 is contained in Table I. The values shown should be regarded as highly approximate. We include it to give the reader a general idea of how these properties vary with alloy composition and temperature over those ranges which will be encountered in this chapter. The energy gap Eg(x,T)was taken from the empirical expression of Schmit and Stelzer (1969). The cutoff wavelength A,, is that wavelength at which the photodiode response has dropped to 50% of its peak value. The values in Table I were approximated by the simple relationship

A,,

= hC/&

>

(1)

where h is Planck's constant and c is the speed of light. If A,, is in pm and Eg in eV, then A,, (pm) = 1.24/Eg (eV).

(2)

The values for the peak wavelength A, were assumed to be about 10% less than those for Ac,. Values for the intrinsic carrier concentration ni(x,T) were calculated from the semiempirical expression of Schmit (1970). The values for the electron mobility pe were taken from the data of Scott (1972) for n-type samples with carrier concentrations less than 2 X lOI5 cmP3. Similarly, the values for the hole mobility p h were taken from data for p-type samples. The values for x = 0.2 are from data (see Fig. 44) for gold-doped samples with net acceptor concentrations of 0.4-2 X 10"j cmP3. The values for x = 0.3 were taken from the data of Riley et al. (1978b) with net acceptor concentrations of 0.8-2 x IOl5 ~ m - The ~ . data for x = 0.40 and 0.55 were taken from the data of Scott et al. (1976) for samples with net acceptor concentrations around 1 X 10'' cmP3. Values for the band-edge effective mass ratios m, ,mlh, and m h h for the conduction

TABLE I

SUMMARY OF Hg,-,Cd,Te ELECTRICAL A N D OFTKAL PROPERTIES (ALL VALUESSHOWN ARE HIGHLY APPROXIMATE) Hg,-,Cd,Te alloy composition Temperature

x

-

T

(K)

Energy gapo Cutoff wavelength Peak wavelength

E.

(eV)

Electron mobility in n-type Hole mobility in p-type

I4

I

77

~~

170

0.079

0.107 11.6 10.5

14.4

A,

c(h

-

0.19

0.094 13.2 12.0

0.080 15.4 14.0

(cmz/V sec) 2 x 10s (cmz/V sec) 1,4W

2 x 105 8006

-

0.006

Conduction and light-hole massg m, ,mlh Heavy-hole mas9 hh Kane's matrix elements EL'

(eV)

19

19

Static dielectric constanta High-frequency dielectric constant!

G

-

17

17

c.,

-

12.5

12.5

From Schmit and Stelzer (1969). * From Schmit (1970). From Scott (1972). See Fig. 44b. From Riley ef nl. (1978b). From Scott cr al. (1976). a From Weiler (1981). From Domhaus and Nimtz (1976).

'

0.008

0.006

0.5

0.251 4.9 4.4

0.260 4.8 4.3

0.275 4.5 4.1

0.425 2.9 2.6

0.433 2.9 2.6

I x 108 3 x 1W2 3 x lo1* 6 x I@*

6

5x104 500"

3 x IW 1w

2x104

3w

1x104 200"

4x109

1w

X

10"

0.656 1.9 1.7

I

0.007

11

IOl3

2 x Iff 2w

0.5

12

X

110

6.

PHOTOVOLTAIC INFRARED DETECTORS

207

band and the light- and heavy-hole valence bands and the value for Kane's matrix element Ep were obtained from the review of Hg,,Cd,Te magnetooptical data by Weiler (1981). The dielectric constants were taken properties by Dornhaus and Nimtz from the review of Hg,-,Cd,Te (1976). 11. Theory of p - n Junction Photodiodes 4. CURRENT-VOLTAGE CHARACTERISTICS

The current-voltage (or I-V) characteristics of a p - n junction photodiode determine its dynamic impedance and its thermally generated noise. In this section we consider those mechanisms which produce dark current in a nonilluminated photodiode, in which the only departure from thermal equilibrium is due to a voltage externally applied to the device. Photocurrent will be discussed in Section 5. In many direct detection applications the photodiode is operated at zero-bias voltage. The photodiode dynamic resistance at zero-bias voltage is denoted by R, and is related to the current-voltage characteristic W )by

A frequently encountered figure of merit for a photodiode is its RJ product, which is simply R, given by Eq. (3) multiplied by the junction area A . If J = Z/A is the current density, then the R,A product is given by (&A)-' =

1

v=o

.

(4)

Equation (4) shows that the R,A product is independent of junction area, which is one of the reasons for the widespread use of R,,A as a figure of merit. This will not be the case when the dimensions of the junction area are comparable to a minority-carrier diffusion length, and considerable care will be needed in using the R,A product as a figure of merit because of the effects of lateral diffusion. These effects will be discussed in Section 8. a.

Diffusion Current

Diffusion current is the fundamental current mechanism in a p - n junction photodiode. It arises from the random thermal generation and recombination of electron-hole pairs within a minority-carrier diffusion length on either side of the space-charge region. Calculations of diffusion current are relatively straightforward since, unlike space-charge region g-r cur-

208

M . B . R E I N E , A . K . SOOD, A N D T. J . TREDWELI.

rent or interband tunneling current, it is largely insensitive to the actual details of the space-charge region. Diffusion current is the dominant junction current in Hg,-,Cd,Te photodiodes at higher temperatures. For example, diffusion current is usually dominant in 12-pm Hg,,,Cd,,,Te photodiodes at temperatures of roughly 77 K and above,. and for 4-5 pm H&.,Cdo.,Te photodiodes at temperatures of roughly 190 K and above. In this section we treat the p-n junction as simply as possible in what is generally referred to as the depletion approximation. Figure 2 shows a cross section of a simple n-on-p junction photodiode. We assume it can be divided into three regions: an electrically neutral n-type region of thickness a, a space-charge region of width W, and an electrically neutral p-type region of thickness d. We assume that the transition layers between adjacent regions are negligibly thin, that the n and p regions are uniformly doped, and that all of the applied voltage V is dropped across the space-charge region. We also restrict ourselves to the so-called low injection case in which departures of the carrier concentrations from their thermal equilibrium values in the n and p regions are small compared to the majority-carrier concentrations. Finally, we assume that the carrier distributions are nondegenerate so that the thermal equilibrium carrier concentrations n,(z) and p o ( zj in each region obey n,(z)po(zj = nf -

1 I

=

z=o

(5)

z=d

-a-W

FIG.2. Cross section of the simple n-on-pjunctions photodiode, showing the quasineutral n region ( - a - W < z < - W ) , the space-charge region (- W < z < 0). and the quasineutral p region (0 < x < d ) .

6.

PHOTOVOLTAIC INFRARED DETECTORS

209

With these assumptions, the minority-carrier concentrations in the regions satisfy the following familiar boundary conditions at the edges of the space-charge region (Hauser, 1971):

where pno and npo are the thermal equilibrium values of the minoritycarrier concentrations in the n and p regions, and where e is the electron charge, k is Boltzmann’s constant, and T i s the diode temperature. Within the space-charge region, these assumptions lead to the following relation for the nonequilibrium carrier concentrations (Moll, 1958):

which of course reduces to Eq. ( 5 ) for thermal equilibrium (V = 0). Consider first the p region. When thermal equilibrium is disturbed, the carrier concentrations in the p region are given by

We have assumed space-charge neutrality in the p region, so we have An(z,t)

=

Ap(z,t).

(10)

The minority-carrier concentration n(z,t) obeys the following continuity equation in the p region:

where the electron current density J , is an

J , = eD,--, az where D, is the electron diffusion coefficient. In Eq. (1 l), g(n,p) and r ( n , p ) are the electron generation and recombination rates per unit volume due to internal mechanisms such as radiative, Auger, o r Shockley-Read generation and recombination processes, whereas G,, represents external mechanisms such as photogeneration of electron-hole pairs due to incident nonequilibrium radiation.

210

M. B . REINE, A . K . SOOD, A N D T. J . TREDWELL

Consider steady-state solutions to Eq. (1 1). In general g ( n , p )and r ( n , p ) are functions of both n(z) and p ( z ) . For An(z) small compared to both ppo and nnc, we can expand (r - g ) in a Taylor series about npo and ppo; the first two terms in such an expansion are r - g = [ r h o ,ppo)- g(npor ~ p o ) l

The first term is zero since r = g in thermal equilibrium. If we define the minority-carrier lifetime T~ as

--

7

(14)

then the steady-state excess minority-carrier concentration is a solution to An 0 = D c -d 2 A n - -. dz2

7,

In order to solve Eq. (15) for An(z), we need another boundary condition in addition to the one at z = 0 given in Eq. (6b). For the moment let us assume that the boundary of the p region at z = d is far away. Then the other boundary condition is An (z

+. 00) +.

0,

(16)

and the solution for An(z) is

where the minority-carrier diffusion length L, is L,

=

G.

(18)

The boundary condition in Eq. (16) is equivalent to assuming that the p-region thickness d is large compared to L ,, in which case the nature of the interface at z = d does not affect the p-side diffusion current. The p-side diffusion current density J , is obtained from Eq. (12) evaluated at z = 0:

which is the familiar relationship of Shockley (1949). Here the subscript ~0 denotes that d >> L,.

6.

PHOTOVOLTAIC I N F R A R E D DETECTORS

211

The R,,A product due to p-side diffusion current is

(RJ)P m

kT 1 T ez n p o Le

=-->,

Using Eq. ( 5 ) with ppo = NA where NA is the net acceptor concentration on the p side, and using the Einstein relation

4= ( k T / e ) p e ,

(21)

one can rewrite Eq. (20) as

The dominant temperature dependence of (RoA),, is due to nf, and a versus 1/T would be nearly a straight line with semilog plot of (&A), a slope given approximately by E,/kT. Now consider diffusion current from the n side. Using the boundary condition in Eq. (6a) and assuming that the n-region thickness a is much larger than a minority-carrier diffusion length Lh given by L

h

=

G

,

(23)

where D h and T h are the minority-carrier diffusion coefficient and lifetime in the n region, one obtains an expression analogous to Eq. (20) for the RJ product due to n-side diffusion current:

This can also be written as nm

where we have set n,, = N,,, with N Dbeing the net donor concentration on the n side, and where we have used the Einstein relation Dh

=

(kT/e)ph.

(26)

The interfaces at z = - a - Wand z = d in Fig. 2 will have an effect on the diffusion current from the n side and the p side when they are within a diffusion length from the edges of the space-charge region. Consider the p region. The excess steady-state minority-carrier concentration An(z) is a solution to the continuity equation in Eq. (15), and the boundary condition at z = 0 is given by Eq. (6b). The boundary condition at z = d can be

212

M . B . REINE, A . K . SOOD, A N D T. J . TREDWELL

expressed conveniently in terms of the surface recombination velocity

s,: J,

(Z =

d ) = eD,-a

I

dz

z=d

= -eS, An(d).

The solution for Ahn(z) is

, (28) where p is defined as

P

=

S,Le/D,

($)I

(29)

= Sp/(Le/Te)r

and is just the ratio of the surface recombination velocity to the diffusion velocity LJT,. The resulting R,,A product is

[

1 + p tanh

(R0A)P = (ROA),,

p

e

+ tanh ($) ’

(30)

where &A), is given in Eq. (20). Equation (30) is plotted in Fig. 3 for various values of p. What it shows is that having an interface within a diffusion length of the depletion region can either enhance or degrade the R,,A product, depending on magnitude of S, relative to the diffusion velocity D e / L e .The effect of the n-side surface at z = - u - w in Fig. 2 can be treated in exactly the same way, with (&A), given by an expression like Eq. (30) with S, (the surface recombination velocity at z = - a - W), Lh and the n-region thickness u substituted appropriately. Minority-carrier diffusion lengths as long as 45 pm in p-type Hg,.,Cd,.,Te and 100 p n in p-type H&.,Cdo,,Te have been measured for moderately low carrier concentrations. These lengths are well in excess of the p-region thicknesses required for most mosaic focal plane array applications. Figure 3 shows the importance of having the thin (i.e., d << L,) p region terminate in an electrically reflecting or blocking boundary, Le., one in which the surface recombination velocity is negligible compared to the diffusion velocity. The boundary condition for such a boundary is, from Eq. (27),

Je(d) = 0;

(3 1)

that is, there is no net minority-carrier flow to or from the boundary at z =

6.

0.1

213

PHOTOVOLTAIC INFRARED DETECTORS

u. 1

1

10

FIG.3. The effect on R d of having various types of boundaries within a diffusion length of the space-charge region, as calculated from Eq. (30) for various values of p defined in Eq. (29).

p = 0, and L, >> d, the R A product for p-side diffusion current in Eq. (30) becomes

d. With

(&A),

kT

N A

re

= --- ,

e2 n: d

which shows that reducing the volume in which diffusion current is generated increases the corresponding R,A product by a factor ( L , / d ) . There are three ways to approach the ideal boundary condition of Eq. (31). As suggested by Long (1977), one can implant or diffuse acceptors into p-type Hg,-,Cd,Te to form a p + region of higher carrier concentration, resulting in a p+-p hi-lo junction which is relatively impermeable to minority-carrier flow but which is ohmic to majority-carrier flow and can be used as a backside contact to the p region. This n+-p-p+junction configuration has been discussed by Tredwell and Long (1977), Long (1977), Longer al. (1978), and Sood er al. (1979a,b,c). Second, through an appropriate surface treatment, one can adjust the surface potential to reduce

214

M . B . REINE, A. K. SOOD, A N D

T. J . TREDWELL

the surface recombination velocity S, . Third, the p-region Hg, -,Cd,Te layer can be grown via LPE onto a substrate, such as CdTe, with a wider bandgap. In the graded transition region the electric fields will be such as to repel both minority and majority carriers away from the interface and back into the p region. This type of boundary has been discussed by Lanir P t a / . (1979a,b) and by Lanir and Shin (1980). Progress in reducing the p-region diffusion volume will be reviewed in Section 11,e of this chapter. Diffusion current contributions from the n and p regions add to give the total diffusion current, and the resulting R,,A product due to diffusion current from both sides is 1

1

R,,A - (R,,AIn

1 +-(RoA),'

(33)

It is important to know the relative magnitudes of the n- and p-side contributions. For the ideal case of perfectly electrically reflecting boundaries at z = - ( a + W)and at z = d and L, >> d and Lh >> a , we have

If this ratio is much larger than unity, then p-side diffusion current will essentially determine the RoA product. The relatively small conduction-band effective mass in Hg,-,Cd,Te causes the electron distributions to be appreciably degenerate for the doping levels encountered in photodiodes, particularly in the ion implanted n-on-p configuration which has been almost universally adopted for direct detection applications. Equations (24), (25), and (34) are not entirely valid for n-side diffusion current when the n side is statistically degenerate. The effect of strong degeneracy in the n region is to make the nope product considerably less than n:. The boundary condition in Eq. (6a) at z = - W needs to be modified for degeneracy in the manner discussed by Marshak and Shrivastava (1979). Furthermore, the rapidly varying implanted donor profile should also be taken into account; this would have the effect of producing an electric field in the n region which might appreciably affect carrier transport through this region. This effect and its possible consequences were recently discussed by Redfield (1979) for the case of a strongly asymmetric silicon n+-on-pjunction. This effect should be much more pronounced in asymmetric n+-on-p Hg,-,Cd,Te junctions due to the much smaller conduction-band density of states. An additional complication in analyzing heavily doped n regions in Hg,-,Cd,Te is the uncertain behavior of the minority-carrier lifetime due to the Auger electron-electron collision mechanism in strongly degenerate n-type Hg,,Cd,Te.

6.

215

PHOTOVOLTAIC INFRARED DETECTORS

Because of these uncertainties, there have been no reported theoretical calculations of the n-side diffusion current for implanted n+-on-p Hg,,Cd,Te photodiodes. The implanted n regions are about 0.3-0.4 pm thick, whereas the p region is usually greater than 10 pm thick, so that geometry favors p-side diffusion current. Furthermore, in their study of 8- 14 pm photodiodes for high-temperature operation, Tredwell and Long (1977) argue qualitatively that n-side diffusion current should be small compared to p-side diffusion current in n+-on-p Hg, -,Cd,Te photodiodes. They point out that the Auger electron-electron collision generation rate, which determines the minority-carrier lifetime in n-type Hg,-,Cd,Te for x = 0.2, is greatly reduced when states at the bottom of the conduction band become filled. Long (1977) has calculated the upper theoretical limit for the R,A product due to diffusion current for a Hg,-,Cd,Te photodiode, subject to two assumptions: first, that n-side diffusion current can be neglected compared to p-side diffusion current; second, that the dominant recombination mechanism in technologically perfected p-type Hg,-,Cd,Te crystals (i.e., those entirely free of Shockley-Read recombination centers) is radiative recombination. This second assumption is subject to question in light of the recent theoretical work of Casselman and Petersen (1979a,b), who have shown that there is a hole-hole Auger collision mechanism which may be an important recombination mechanism in p-type Hg,,Cd,Te. The strength of this mechanism is still uncertain and there has been no clear experimental observation of it yet. Section 10 of this chapter discusses this mechanism in more detail, as does Petersen in Chapter 4. With these two assumptions, the upper theoretical limit to the RJ product due to diffusion current in a Hg,-,Cd,Te photodiode is (R,A), given by Eq. (32), which in turn assumes that L, >> d and that there is a perfectly electrically reflecting p-side boundary at z = d in Fig. 2. For re we take the radiative lifetime ?-,ad which, for small departures from thermal equilibrium, is given by (Blakemore, 1962)

where the approximation is for ppo = N A >> npo. The coefficient B has been evaluated by Hall (1960) for radiative recombination in simple parabolic bands: 1 3/2 1 1 300 3/2 B = 5.8 x dC m,> (1 + F,, (36) mc + -)(y) m, +

where Eg is in eV, B is in cm3/sec, T is in K, and where

cm is

the high-

216

M . B. REINE, A. K . SOOD, A N D T. J . T R E D W E L I

10) N

1-77 K

c: a 4

1 T 3OOK

150 K I0 ;

r

l

o

:

'

I ,LLLLL11.18

6

4

7

10

I2

14

16

c u i o n WAVELENGTH iMmi

FIG.4. The theoretical upper limit to the R,A product for a Hg,-,Cd,Te photodiode due to p-side diffusion current with radiative recombination, as calculated from Eq. (32) for a p region thickness d of 10 p m and for a perfectly electrically reflecting boundary.

frequency dielectric constant and m, and m , are the conduction- and valence-band effective mass ratios. For m, we take the heavy-hole mass ratio value of 0.5. We calculate m, from the following expression (Weiler, 1981)

(37)

m,

with F = 1.6, Ep = 19 eV, and A Sorger, 1972) E&)

=

9.5

=

1 eV. For e,(x) we use (Baars and

+ 3.5 [(0.6

-

~)/0.43].

(38)

We take &(x,T) from Schmit and Stelzer (1969) and nl(x,T) from an improved version of the expression of Schmit (1970). Note that the upper theoretical limit to (&A), is independent of acceptor concentration N,, . The upper theoretical limit to the RJ product so calculated is shown in Fig. 4 plotted versus cutoff wavelength [obtained from E,(x,T) via Eq. (I)] for various temperatures, and by the solid lines in Fig. 5 plotted versus reciprocal temperature. A p-region thickness d of 10 p n was chosen. b. Generlition -Recombinuiion Current from the Space-Charge Region

Impurities or defects located within the space-charge region can act as generation and recombination (g-r) centers of the Shockley-Read type

6.

PHOTOVOLTAIC INFRARED DETECTORS

217

r-

u 3 L3

0

a

LL

a PI

100DIT l K ~ ’ l

FIG.5. R A products due top-side diffusion current (solid lines), calculated from Eq. (32) for the same conditions as in Fig. 4, and due to space-charge region g-r current (dashed = 0.1 psec and eVbl = E,. lines), as calculated from Eq. (48) for W = 0.1 p m ,

(Shockley and Read, 1952) and thereby produce junction current. The importance of this current mechanism was first pointed out by Sah et a / . (1957), who showed that space-charge region g-r current could be more important than diffusion current at low temperatures, even though the width of the space-charge region is much less than a minority-carrier diffusion length. Space-charge region g-r current varies with temperature roughly as ni, whereas diffusion current varies as 4 . Diffusion current dominates at relatively high temperatures; diffusion current decreases as the temperature is lowered but space-charge region g-r current decreases less rapidly, so that a temperature is finally reached at which the two are

218

M . B . REINE, A. K . SOOD, A N D T. J . TREDWELL

comparable and below which space-charge region g-r current dominates. There are other junction current mechanisms which also decrease with decreasing temperature less rapidly than n:, such as surface generation-recombination and interband tunneling, which are discussed in the following sections, and so some care is needed in unambiguously determining which current mechanisms are important in a given photodiode at lower temperatures. For g-r centers located at an energy Et above the top of the valence band, the steady-state net recombination rate U(z)through these centers is

U(Z)= R ( z )- G(z) np

?po(n

+ nl) + ?no(p + P I )

nf

-

+ nl) + no(^ + PI)’

~po(n

(39)

where n = n ( z ) and p = p ( z ) are the nonequilibrium electron and hole concentrations within the space-charge region, and where

p1 = N , e x p ( s ) ,

where N , and N, are the conduction- and valence-band effective densities

of states, C , and C, are the capture coefficients for electrons and holes, and Nt is the number of g-r centers per unit volume. Under the simplifying assumptions discussed at the beginning of Section 4,a the product of the carrier densities n(z) and p ( z ) is roughly independent of position within the space-charge region and follows the approximate Shockley relation given in Eq. (7). Hence, the g-r centers provide net recombination for forward bias [i.e., U(z) > 01 and net generation for reverse bias [U(z) < 01* The junction current density Jg-rdue to these centers is obtained by integrating Eq. (39) over the space-charge region (see Fig. 2):

I, 0

J , - ~= e

~ ( z dz. )

(44)

In order to do this integral, n(z) and p ( z ) must be known within the space-

6.

PHOTOVOLTAIC INFRARED DETECTORS

219

charge region. Sah et al. (1957) assume that the potential varies linearly with distance over the space-charge region and obtain the following result:

where v b i is the built-in voltage of the p - n junction such that eVbi is the difference between the Fermi levels on the n side and the p side for zero-bias voltage applied to the junction. This equation is valid for reverse-bias voltage and for forward-bias voltage values that are less than vbi by several ( k T / e ) . The function f ( b ) is given approximately by

where

b

=

exp

(g)[y + (?)I, cosh

In

(47)

where Eiis the position of the intrinsic above the top of the valence band. When Et = Ei and T~,,= T~,,, V(z)in Eq. (39) has its maximum value for a given voltage V and the recombination center has its maximum effect. The RJ product due to g-r current originating in the depletion layer, as obtained from Eq. ( 4 9 , is

b is one for For the most effective g-r center (i.e., Et = Ei and 7n0= T~,,), V = 0 and f(0) = 1, so (RoA)g-r varies with temperature as n i l , as opposed to the R& product due to diffusion current which varies with temperature as n;* . Plots of (RJ)g-r calculated from Eq. (48) with f ( b ) = 1 for several Hg,,Cd,Te alloy compositions are shown by the dashed lines in Fig. 5 . For these curves we set T ~ , = , T~ = 0.1 psec and eV,, = E g . For W we use a value of 0.1 pm, which corresponds to an effective space~ . that both 7, and charge region doping Ns of around 1 x 10l6~ m - Note T ~ ,depend , on the concentration Nt of Shockley-Read centers, which will vary from crystal to crystal and may also depend on the junction formation method. The dashed curves in Fig. 5 are meant to illustrate the dependence on temperature of (RJ),-,as compared to (RJ), rather than predict the values of (RJ)g.-r likely to be encountered in Hg,-,Cd,Te photodiodes.

220

M . B. REINE, A . K . SOOD, A N D T. J . TREDWELL

Less effective g-r centers will have El # Ei. If IEl - EiI > kT, then the approximation for h > 2 of

f(b) = (In b ) / b

(49)

can be used to give

This results in (R,J)g-r increasing more rapidly than n;l with decreasing temperature. The ratio of the R,J products for depletion layer g-r current [Eq. (48)] and p-side diffusion current [Eq. (20)] is

where we have set f(b) = 1. Now ( L J W ) is on the order of 100 and (eVhi/k7')is also large, so a temperature for which tzi < N A x lop3or less will have to be reached for depletion layer g-r current to be dominant over diffusion current. Choo (1968) extended the theory of Sah et al. (1957) to the case of a strongly asymmetric p-n junction in which the doping levels on the n and p sides are quite different and also considered the case in which rn0and T~ may be quite different. Choo was able to show that significant differences from the simple Sah et al. treatment could occur for forward-bias voltage. However, near zero-bias voltage these differences are small and so Eq. (48) ought to give a reasonable estimate for even for strongly asymmetric junctions. Finally, it should be pointed out that generation and recombination processes which do not involve impurity or defect levels can also occur in the depletion region. Long (1977) considered both radiative and Auger electron-electron collision processes occurring in a depletion region free of Shockley-Read levels. In both cases, resulting R,A products had the same nc2 temperature dependence as conventional diffusion current (in the nondegenerate case) and were larger than the diffusion R A product by the ratio (L,/ W ) . c . Surfice Lecikrrge Current

Dark current in an ideal p-n junction is due to carrier generation and recombination in the quasineutral regions (diffusion current, which was discussed in Section 4,a) and in the space-charge region (g-r current, which was discussed in Section 4,b). Actual devices often have additional

6.

221

PHOTOVOLTAIC INFRARED DETECTORS

dark current, particularly at low temperatures, which is related to the surface. The semiconductor surface and its oxide and overlying insulator affect the junction current both through fast interface states, which act as g-r centers, and through fixed charge in the oxide and insulator, which modifies the surface potential on both sides of the junction. The combination of fast interface states and fixed charge result in a variety of surface-related dark current mechanisms. These surface-related currents frequently dominated diode characteristics in the initial development of germanium and silicon technology and have been widely studied (Sah, 1962; Grove and Fitzgerald, 1965, 1966) in these semiconductors. Figure 6 illustrates some of these surface-related dark current mechanisms. In the absence of oxide charge (Fig. 6a.) an annular area A, of the surface defined by the junction perimeter and the junction depletion layer width Wbwill lie within the depletion layer. Fast interface states in this depleted region of the surface will generate carriers. The magnitude of the surface generation current Z, is given by

where the surface recombination velocity so for a depleted surface is re-

f

kLC-!

OX IDE/INSULATOR

f

METALLURGICAL JUNCTION

F L c

i Id I

\ I 1 1 FIG. 6. Effect of fixed oxide/insulator charge on the effective junction space-charge region: (a) flat-band condition; (b) positive fixed charge causes inversion of the p side and formation of a n-type surface channel; (c) negative fixed charge causes accumulation of thep side and a narrow field induced junction at the surface; (d) larger amount of negative fixed charge causes inversion of the n side and formation of a p-type surface channel.

222

M . B. REINE, A . K . SOOD, A N D T. J . TREDWELL

lated to the number of fast interface states ZVss(E)per unit surface area per unit energy interval by

where C, and C , are defined in Eqs. (42) and (43). When sufficient positive fixed charge is present, the p side can become inverted and an n-type surface channel can form as shown in Fig. 6b. The space-charge region will become larger, and additional current can be collected by this field induced junction. The channel length L, will depend on the bias voltage applied to the junction, on the surface conductivity, and on the amount of current flowing across the field induced junction. The generation current due to Shockley-Read centers in the surface channel is given by an expression analogous to Eq. (45): where W, is the channel width and A, is the channel area. When negative fixed charge is present, the p side becomes accumulated and, as shown in Fig. 6c,a narrow field induced junction can occur at the surface, offering a region in which interband tunneling can occur. A larger amount of negative fixed charge can invert the n side (Fig. 6d) and form a p-type surface channel. In addition to thermal generation and recombination processes occurring at the surface and within surface channels, there is another class of surface-related current mechanisms which frequently limit junction performance. These currents are usually termed surface breakdown or surface leakage. They are characterized by ohmic or breakdownlike current -voltage characteristics and are nearly temperature independent. Surface breakdown occurs when a region of high electric field is created by a narrowing of the depletion layer where it intersects the surface. Figure 6c illustrates cases in which the depletion layer is narrowed by surface charge. The fixed charge strongly accumulates the lightly doped p side of the junction at the surface, pinching off the depletion layer. Since the electric field across the junction is given by ( V + VbJ/ W, where V,, is the built-in voltage and W the depletion layer width, surface breakdown can occur at low or even at zero applied voltage. In Fig. 6d the fixed charge inverts the heavily doped n side of the junction. Because of the high carrier concentration, the depletion layer between the inversion charge and the heavily doped region is very narrow and the electric field across the depletion layer correspondingly large. Again, breakdown would occur at comparatively low junction voltages. This latter form of surface channel

6.

PHOTOVOLTAIC INFRARED DETECTORS

223

breakdown was observed by Grove and Fitzgerald (1965) in silicon p+-n junctions in which the oxide was heavily contaminated by sodium. The breakdown may proceed by avalanche, tunneling, or microplasma, with the latter two being more likely in narrow-gap semiconductors. Tunneling and microplasma are both nearly temperature independent. This is in contrast to the thermal generation currents, which decrease rapidly with temperature as the first or the second power of the intrinsic carrier concentration ni . Both thermal generation in surface channels and surface breakdown are observed in Hg,-,Cd,Te photodiodes, frequently in the same device. In such devices, thermal generation dominates at moderate temperatures with the dark current proportional to n i ; at lower temperatures the thermal generation in the channel decreases to a value less than the temperature-independent surface breakdown and the latter dominates device characteristics. In order to investigate surface-related current mechanisms, an insulated gate electrode is often fabricated around the junction perimeter in order to externally control the surface potential. Gate-controlled junctions are discussed in the textbook by Grove (1967). Experiments with Hg, -,Cd,Te gate-controlled photodiode structures are described in Section 11,d of this chapter. Figure 7 shows the qualitative behavior of the various surface-related current mechanisms as functions of applied gate voltage V , for a gate-controlled n-on-p junction. VG<0

VG

P

VG>>0

0

P

ACCUMULATION

I

I

P

I

lNVERSION Tunneling Across ieid Induced

J

c

5

5

Tunneling Across Field Induced Junction

1

I

0 3 VI VI

"

Y

X

Y

---FIG. 7. Qualitative behavior of the various excess (leakage) current mechanisms in a narrow-bandgap gate-controlled photodiode, shown as functions of gate voltage V,. The actual current versus gate voltage curve observed would be the sum of the currents from the various mechanisms.

224

M . B. REINE, A . K. SOOD, A N D 7’. J . TREDWELL.

d . Interband Tunneling Current

Interband tunneling is an important junction current mechanism to consider in the design of high impedance Hg, -,Cd,Te photodiodes, particularly for cutoff wavelengths in the 8- 12 pm range and beyond, and particularly for low temperatures where thermally generated junction currents are small. In this section we consider the effect of interband tunneling current on the junction resistance R, at zero-bias voltage. It is well known that tunneling can influence the reverse bias current-voltage characteristics of a junction even if another current mechanism is responsible for R, near zero-bias voltage. This is usually referred to as Zener breakdown or internal field emission. Interband tunneling can occur uniformly over the metallurgical junction area as well as across field induced junctions which are due to surface inversion or accumulation, as was discussed in the preceding section. There are two general types of tunneling transitions to be concerned with in Hg,-,Cd,Te. These are illustrated in Fig. 8: direct tunneling of an electron in an energy conserving transition from one side of the spacecharge region to the other (transition a), and trap-assisted tunneling in which impurities or defects within the space-charge region act as intermediate states (transitions b and c). Direct interband tunneling calculations for Hg,,Cd,Te MIS structures pulsed into deep depletion have been performed by Anderson (1977); these and their implications are discussed by Kinch in Chapter 7 of this volume. The importance of trap-assisted tunneling in Hg,_,Cd,Te MIS structures was suggested by Chapman ut (11. (1978), and is also discussed by Kinch in this volume. Calculations of the effect of trap-assisted tunneling on long-wavelength Hg, -,Cd,Te p - n junctions at low temperatures were recently reported by Wong (1980). n

P

FIG.8. Energy diagram for an n+-on-pjunction with a small reverse-bias applied, showing a direct energy-conserving tunneling transition (a) and two trap-assisted tunneling transitions (b) and (c). The trap level energy is Et. The n-side conduction band is degenerate, the p-side valence band is nondegenerate.

6.

PHOTOVOLTAIC INFRARED DETECTORS

225

Direct interband tunneling across p - n junctions has been extensively treated in the literature (Duke, 1969) for the case of tunnel diodes which generally consist of strongly degenerate n and p regions and which show a pronounced region of negative differential resistance at forward bias. This case is almost never encountered in Hg,,Cd,Te photodiodes. While the n region is usually degenerate even at relatively modest donor concentrations, the p region is almost always nondegenerate. However, even though the p region is nondegenerate, direct interband tunneling can still be an important mechanism, such as in the so-called backward diode (Sze, 1969, pp. 193-197), provided that the electric field in the spacecharge region is large enough. The junction current density Jt(V) due to direct interband transitions between the conduction band on the n side and the light-hole valence band on the p side, as calculated by Kane (1961), is of the form Jc = Be-AD(V),

(55)

where

@I2

e.

= eFh/21~

(57)

Here F is the electric field in the space-charge region, which Kane assumed was uniform, m* is the effective mass characterizing the edges of the conduction and light-hole bands, h is Planck's constant, and El is a kinetic energy associated with particle motion in the plane perpendicular to the tunneling direction:

El = e

m .

(58)

The factor D ( V ) in Eq. ( 5 5 ) represents the availability of initial and final states at the same energy on opposite sides of the space-charge region to participate in tunneling transitions. At zero-bias voltage, D(0) is zero and there is no net junction current. For the tunnel diode case in which both sides of the junction are strongly degenerate, the low-temperature approximation (Kane, 1961) for D ( V ) near zero-bias voltage is usually used: D(V) = eV,

(59)

and the R,A product due to tunneling current is, from Eqs. (4) and (55): --1

(&A),

- eB, exp(-A,)

226

M . B . REINE, A . K . SOOD, A N D T. J . TREDWELL

where the subscripts on A and B mean they should be evaluated at V = 0. The dominant dependence on temperature here is that of the energy gap Eg(T)through A,. Since Eg in Hg,-,Cd,Te decreases with decreasing temperature, this would say that ( R A ) ,should also decrease with decreasing temperature. For the more relevant case in which the n side is degenerate but the p side is nondegenerate, the simple approximation in Eq. (59) cannot be used. Small but finite acceptor activation energies are generally observed in p-type Hg,-,Cd,Te (see Section 14,a of this chapter), and so the freezeout of free holes in the p-side valence band at lower temperatures needs to be taken into account. If this is done, the approximate expression for D ( V ) near V = 0 is

where p , is the free hole concentration on the p side and valence-band effective density of states. (&A), then becomes

and one can see how the exponential dependence of p o on temperature, at low temperatures when freezeout is important, could cause (&A), to increase with decreasing temperature. This can be seen in Fig. 9, in which (R,A), is plotted as a function of reciprocal temperature for various acceptor activation energies Ea for direct interband tunneling transitions in a n+-on-p Hg0.,Cdo.,Te junction. Arbitrary units were chosen because of uncertainty in the space-charge region electric field F, which enters into the exponential via the term A in Eq. (56) and affects drastically the magnitude of (&A), . As temperature increases, ( R d ) ,increases sharply as the bands become "uncrossed" and direct energy-conserving tunneling transitions no longer occur. As temperature decreases, (&A), again increases for values of acceptor activation energy E A above about 0.003 eV due to hole freezeout in the p-side valence band. An acceptor activation energy of about 10 meV has been reported for p-type Hg.&d0.,Te (see Fig. 44). Behavior of R,,A qualitatively similar to that in Fig. 9 was obtained by Wong (1980) in his calculations of trap-assisted tunneling transitions in long-wavelength Hg,-,Cd,Te n-on-p junctions. It is not expected that interband tunneling, whether it be via energy conserving or trap-assisted transitions, will present a fundamental limitation to Hg,-,Cd,Te photodiode performance at low temperatures. The magnitude of the tunneling current depends strongly on the space-charge

6.

PHOTOVOLTAIC INFRARED DETECTORS

227

IOWiT I K - ' I

FIG.9. ( R J ) , versus reciprocal temperature for direct energy-conserving tunneling in an n+-on-p Hg,,.,C$,,Te junction, for several values of acceptor activation energy E A , and for N D = 1 x 10'' ~ r n - ~N;A = 4 x lot5 ~ r n - ~ .

region electric field, and suitable choices of doping concentrations and junction profile can lower this electric field throughout the bulk of the space-charge region to the point where tunneling currents will probably be small. More important is the surface where, as discussed in Section 3, field induced junctions can occur with much stronger electric fields. Careful control of surface potential will be necessary to minimize the occurrence of such field induced junctions.

5.

PHOTOCURRENT IN

p - n JUNCTIONS

Infrared radiation of wavelength A shorter than the cutoff wavelength A, is absorbed by the photodiode and produces electron-hole pairs. If the absorption occurs within the space-charge region, the electron-hole pairs are immediately separated by the strong electric field and contribute to photocurrent in the external circuit. If the absorption occurs within a

228

M . B . REINE, A . K . SOOD, A N D T . J . TREDWELL

diffusion length of the space-charge region in the n region or the p region, the photogenerated electron-hole pairs first must diffuse to the space charge region where they are then separated by the electric field and contribute to photocurrent in the external circuit. If no current can pass externally between the n and p terminals of the photodiode, then an open-circuit photovoltage (the photovoltaic effect) appears across the junction when it is illuminated. If the n and p terminals are connected to a very low impedance, the photodiode is short circuited and a short circuit photocurrent will flow when the photodiode is illuminated. If Q is the nonequilibrium steady-state photon flux in photons/cm2 sec incident on the photodiode, then the steady-state photocurrent density JdQ) is

where q is called the quantum efficiency of the photodiode. It is the number of electrons contributing to photocurrent per incident photon and has a maximum value of unity unless there is some. avalanche gain present. The quantum efficiency q is a function of the wavelength of the incident radiation and depends on the photodiode geometry and on the diffusion lengths for minority carriers within the quasineutral regions. Unless the photon flux Q is large enough to make the photogenerated excess minority carrier concentrations comparable to the majority-carrier concentrations (i.e., the so-called large injection case), the quantum efficiency q in Eq. (63) will be independent of photon flux and the photocurrent will be a linear function of Q . The current-voltage relation J(V,Q)for an illuminated photodiode with an applied bias voltage V is usually written as

where Jd(V)is the current-voltage relation for the unilluminated photodiode which was discussed in Section 4. Equation (64) says that the current through an illuminated photodiode is just the dark current (which depends only on V) minus the photocurrent (which depends only on Q ) . The applicability of this simple linear superposition of two independent currents has been recently examined in connection with Si and GaAs photovoltaic solar cells. Lindholm ef ul. (1979) considered ajunction in which the dark current was due to diffusion current and space-charge region g-r current and showed that Eq. (64)was valid so long as the low injection case obtained and the space-charge region did not contribute appreciably to both dark current and photocurrent. Subsequently, Tarr and Pulfrey (1979) showed that Eq. (64) could apply under certain circumstances even

6.

229

PHOTOVOLTAIC INFRARED DETECTORS

when space-charge region dark current and photocurrent were significant. So long as dark current and photocurrent are linearly independent, the quantum efficiency 7 can be calculated in a straightforward’manner as a function of wavelength for a specified photodiode geometry, optical absorption coefficient a@),and minority-carrier properties. This has been done by a number of authors including Melngailis and Harman (1970a) in and Pb,-,Sn,Se infrared photodiodes, their discussion of Pb,-,Sn,Te Van de Wiele (1976) in a more detailed treatment of photodiode quantum efficiency, and Hovel (1975) in his review of solar cells. We want to examine the effect of photodiode geometry and material properties on cutoff wavelength for the special case of ion implanted n-on-p Hg,-,Cd,Te photodiodes in which the n region and the spacecharge region are fairly thin. The geometry is shown in Fig. 10, where we assume that the p region is semiinfinitely thick. As shown by Van de Wiele (1976), the steady state photogenerated excess minority-carrier concentration An(z) in the p region is

(aLe = l), (65b)

0.2

r

E

1

2

l

I

I

3

4

5

ZIL,

FIG. 10. Normalized photogenerated excess minority-carrier concentration in the p region, plotted from Eq. (65) versus normalized distance for several values of cuL,.

230

M . B. REINE, A. K . SOOD, A N D T. J . TREDWELL

and the quantum efficiency, neglecting front surface reflections and any absorption in the n region and the space-charge region, is 7) =

a L e / ( a L e+ 1).

(66)

The quantum efficiency will depend on wavelength because the optical absorption coefficient a(A)does. Recent data for the optical absorption coefficient versus wavelength in Hg,-,Cd,Te for 0.205 < x < 0.220 and for temperatures between 80 and 300 K have been published by Finkman and Nemirovsky (1979). The cutoff wavelength A,, is defined as that wavelength at which the quantum efficiency has dropped to half its short-wavelength value. For values of a such that aLe >> 1, Eq. (66) says that 7) is essentially unity. From Eq. (66), the cutoff wavelength occurs when

(67)

a(A,,) = l/LI?-

In the semiinfinitely thick photodiode of Fig. 10, the cutoff wavelength depends not only on the alloy composition and the temperature, but also depends somewhat on the p-side minority-carrier diffusion length. But the dependence of A,, on L, is not large because the absorption coefficient varies so rapidly with wavelength near the absorption edge. For example, for an alloy composition of x = 0.210 at a temperature of 80 K, the data of Finkman and Nemirovsky (1979) would give a cutoff wavelength of 12.7 p m (a = 400 cm-') for a diffusion length of 25 p m according to Eq. (67), and would give a cutoff wavelength of 13.1 prn (a = 200 cm-l) for a diffusion length of 50 pm. This is roughly a difference of 0.4 pm for a factor of 2 change in diffusion length. The general behavior of An(z) as given by Eq. (65) is shown in Fig. 10. One can see from Eq. (65a) that the maximum value of An(z) occurs at zmax =

Le ln(aLe)/(aLe

= In(aLe)/a

-

1)

for aLe >> 1,

(68) (69)

and the maximum value of An is An(zmax) = [aQ~e/(aLe+ 111 exP(-azmaJ

(70)

So for a photon flux of 1 x loi7 ph/cm2 sec, a lifetime of 0.5 Fsec, an absorption coefficient of 5 x 103 cm-' and a diffusion length of 25 pm, Anmax is 1.6 X 10l2~ m - Here ~ . one can see that extremely large photon fluxes are needed to cause departures from the low injection region.

6.

PHOTOVOLTAIC INFRARED DETECTORS

231

For the case considered here, the p region will determine the cutoff wavelength. At wavelengths shorter than the cutoff wavelength, absorption within the n region and the space-charge region will become more important, even though those regions are quite thin compared to L, ,because the radiation will penetrate less as the absorption coefficient increases. If the n region is heavily doped, the Burnstein-Moss effect will tend to shift the absorption edge in this region to shorter wavelengths. Two other photodiode geometries are important to consider, the front-side-illuminated n-on-p photodiode with a p region of finite thickness (Fig. la) and the backside-illuminated n-on-p photodiode (Fig. Ib). In both cases, we usually want the p-region thickness d to be much less than a diffusion length in order to reduce p-side diffusion current as much as possible. In any event, the p region in. the backside-illuminated case needs to be at most a diffusion length thick so that nearly all photogenerated carriers reach the space-charge region before recombining. If d << L e , then the cutoff wavelength for both geometries is determined by the p-region thickness rather than the diffusion absorption in the n region and the space-charge region, and assuming a perfectly electrically reflecting surface at z = d (Fig. 2), one obtains the quantum efficiency (Van de Wiele, 1976) for the front-side-illuminated case

and for the backside-illuminated case

When d << L, and for wavelengths A < A,, so that aL, > 1, both equations reduce approximately to 7

1 - e-ad

(74) and the cutoff wavelength is now determined by the p-region thickness LI

a(&,) = 0.7fd.

(75) For example, if d is 10 pm, then a(A,,) is 700 cm-'; this corresponds to a cutoff wavelength of 12.4 pm for x = 0.210 at 80 K, which is somewhat shorter than the cutoffs of 12.7 and 13.1 pm for diffusion lengths of 25 and 50 pm for the semiinfinitely thick p-region case discussed earlier.

232

M . B . R E I N E , A . K . SOOD, A N D T. J . T R E D W E L L

In practice, it is generally easy to design a photodiode for high quantum efficiency. Reflection losses at Hg,-,Cd,Te amount to roughly 30% and these can be nearly eliminated over selected wavelength intervals by proper antireflection coating. High surface recombination velocities can reduce quantum efficiency and need to be taken care of, but one needs to do this anyway so that surfaces do not contribute appreciably to junction diffusion current. p-type Hg,-,Cd,Te is usually chosen as the material in which a large fraction of the radiation is absorbed, and diffusion lengths in p-type Hg,-,Cd,Te of low to moderate doping concentration are on the order of 20-50 pm, more than adequate for collection of photogenerated carriers.

6. NOISE MECHANISMS Noise in infrared photodiodes has been treated by a number of authors. Among the first were Pruett and Petritz (1959) who considered indium antimonide photodiodes. Long (1977) and Tredwell and Long (1977) showed that the fundamental noise mechanisms in Hg,,Cd,Te photodiodes and in Hg,-,Cd,Te photoconductors were the same and imposed the same limitations to the ultimately achievable sensitivities in both types of detectors. Noise in infrared photodiodes is treated in the books by Kruse P t a / . (1962) and by Kingston (1978), and in the reviews by van Vliet (1967) and van der Ziel and Chenette (1978). Noise induced in p-n junctions by high-energy radiation was treated by Fonger et a / . (1953). For a photodiode in thermal equilibrium (i.e., no applied bias voltage and no externally applied photon flux), the mean squared noise current 12, is just the Johnson-Nyquist noise of the photodiode zero-bias resistance R, :

I', = (4kT/R,) Af,

(76)

where Afis the noise bandwidth. Hence whatever junction current mechanism determines R, also determines the photodiode noise. In the following sections we discuss noise in a photodiode which is not in thermal equilibrium for the two special cases of diffusion current and space-charge region g-r current. Then we summarize l/f noise in p - n junctions. Photodiode I/f noise is of concern in low-frequency direct detection applications, particularly when the photodiode is coupled to a CCD and must operate at a reverse-bias voltage on the order of -20 to -50 mV. (1.

Noise with IXlfiision Current und Photocurrent Only

Noise in an infrared photodiode which is not in thermal equilibrium is conveniently treated in terms of shot noise. Consider first the ideal case of

6.

PHOTOVOLTAIC INFRARED DETECTORS

233

a photodiode in which the junction current Z(V) is due only to diffusion and a background photon flux Q B :

Iph

=

‘f?eQBAc,

(78)

where the A , is the optical collection area of the photodiode. The diffusion current is actually a sum of two currents, a forward current Zsa, exp(eV/kT), which depends on voltage, and a constant reverse current Isat. Since each of these two currents fluctuate independently, each will show full shot noise. The mean squared shot noise current 12, is then

where Af is the noise bandwidth. Photodiodes are frequently operated at zero-bias voltage, at which the resistance R, is

The noise current at zero-bias voltage is

I“, (V

: ; (-+ 2 q e Z Q d c )A f ,

= 0) =

where the first term is the Johnson noise of the zero-bias impedance and the second term is the shot noise on the background photocurrent. In order for the photodiode to be background limited, one wants R, to be large enough so that the second term is dominant, i.e., R, >> 2kT/vezQ&.

(82)

At reverse bias such that JeVl >> kT, the noise current from Eq. (79) and (80) is

and the photodiode shot noise is a factor of fi lower than the zero-bias case. Equation (79) is a special case of a somewhat more general expression given by Guggenbuehl and Strutt (1957) (see also van der Ziel and Chenette, 1978): I; ( V ) = [4kT Re( Y) - 2eZ(V)] Af,

(84)

234

M . B. REINE, A. K . SOOD, A N D T . J . TREDWELL

where Y is the photodiode admittance and Z(V) is the total dc current at the photodiode terminals, which is given by Eq. (77) for the ideal case considered here. It is sometimes important to take into account the dependence of the photodiode admittance Yon frequency. For an ideal photodiode in which only diffusion current from the p side is important, the ac admittance Y(V,w) is (see, for example, Sze, 1969, pp. 107- 109)

where a(w) and b(w) are dimensionless functions of COT,, where w is the angular frequency and T~ is the minority-carrier lifetime on the p side:

b(w) =

For low frequencies, a + 1 and b + 0 and Eq. (85) reduces to Eq. (80) for V = 0. For high frequencies, a ( w ) increases as ( W T , ) ~ / and ~, Re( Y) and the noise also increase. If the minority-carrier lifetime on the p side is 0.5 psec, these effects will begin to occur around 300 kHz. Hence, these effects are not important for most direct detection applications, but may be significant for high-frequency heterodyne applications. h. Noise with Space-Charge Region G - R Current

The noise in a p - n junction in which the dominant current mechanism is space-charge region g-r current has been treated by Lauritzen (1968), by van Vliet (1976) and by van Vliet and van der Ziel(1977), and has been summarized by van der Ziel and Chenette (1978). At zero-bias voltage, of course, the expression for (R&)g-r given in Eq. (48) can be substituted into Eq. (76) to give the noise current. As in the case of diffusion current, space-charge region g-r current is the sum of two currents:

zg-r = I , - I , ,

(88)

J -W

(90)

where

Zg

=

eA

G(z)d z ,

6.

PHOTOVOLTAIC INFRARED DETECTORS

235

where R(z) and G(z) are given in Eq. (39). For reverse biases such that eV >> kT, the recombination current component I,. is negligible. For a single trap level with Et = E, and 7,, = rpo= T , , the space-charge g-r current is

Van der Ziel and Chenette (1978) show that the mean squared noise current at low frequencies is

z

-

=

2eZg Af,

(92)

i.e., just the shot noise on the generation current Zg. At frequencies higher than the emission rates of the traps, the mean squared current is slightly lower:

I", = 3-(2eZg)Af.

(93)

c . l / f Noise

l/f noise has been most extensively investigated in silicon p-n junctions and MOS transistors. McWhorter (1957) measured l/f noise in semiconductor filaments and suggested that it originated in trapping of carriers by surface states. Later, Nobel and Thomas (1961) found experimentally that exposure of germanium filaments to various atmospheres resulted in variations in low-frequency noise and suggested that atmospheric exposure altered surface trapping by affecting the surface potential. Watkins (1954) found that surface treatment affected llfnoise in germanium junctions and Atalla et al. (1959) observed similar effects in silicon junctions. The first quantitative investigation of the correlation between surface state density and l/f noise was made by Sah and Hielscher (1966). A number of investigators (Terman, 1962; Nicollian and Goetzberger, 1967; Nicollian and Melchior, 1967; Prier, 1967; Christensson et al. 1968; Christenssen and Lundstrom, 1968) have since related l/f noise in MOS transistors to charge trapping in surface states. The first direct demonstration of the relationship between surface states and l/f noise in p-n junctions was reported by Hsu et al. (1968) and by Hsu (1970a,b). In those experiments a correlation between surface state density and l/f noise was observed in silicon gate-controlled diodes. Recent experiments on 1/ f noise in Hg,-,Cd,Te photodiodes are summarized in Section 15 of this chapter. 7. RESPONSIVITY, NOISEEQUIVALENT POWER, A N D DETECTIVITY The figures of merit usually used to characterize the sensitivity of infrared photodiodes in the direct detection mode are detectivity and noise

236

M . B. REINE, A. K . SOOD, A N D T. J . TREDWELL

equivalent power NEPA. These and other useful infrared detector figures of merit and their methods of measurement are reviewed by Eisenman c t ul. (1977). Suppose the photodiode is uniformly illuminated by a rms signal photon flux Qsof monochromatic radiation of wavelength A. From Eq. (63) the rms signal photocurrent I, is (94)

1s = ~ Q s - 4 ,

where A, is the photosensitive area. The rms signal radiation power P Areceived by the detector is

PA= (hc/A) Q A . The current responsivity A / W:

(95)

is just the ratio of I , to P Aand has units of =

(96)

(A/hc)q e .

The noise equivalent power NEPA is just that rms power of incident monochromatic radiation of wavelength A necessary to produce a signal-to-noise ratio of unity when the noise is normalized to unit bandwidth. The signal-to-noise ratio S I N for the detector described above is

where is the mean squared noise current in the bandwidth Af. The noise equivalent power obtained by setting ( S I N ) = 1 and normalizing the noise current to unit bandwidth is

The units of NEPA are W& The detectivity D f is related to the NEPA through a normalization to unit detector photosensitive area:

The units of D f are cm Hz’’*/W. At zero-bias voltage, the photodiode noise current is given by Eq. (81) and the detectivity from Eqs. (96) and (99) is =

A

1 rle [(4kT/R,A,)

+ 2qe2QB]1’2 ‘

6.

PHOTOVO LTA I c INFRARED DETECTORS

237

When the photodiode thermal noise is dominant, Eq. (100) reduces to

where the subscript th denotes the thermally limited case. In this equation one can see the direct relation between the R A c product and the thermally limited detectivity. Note that the area A, which appears is the optical collection area of photosensitive area of the photodiode. When the background photon flux noise is dominant, Eq. (100) reduces to

which is the well-known detectivity for a background limited infrared photodetector (BLIP). In the heterodyne mode of operation, different figures of merit are used to characterize the sensitivity of the photodiode. Consider the ideal case of a p - n junction photodiode in which only diffusion current is important. The diode is uniformly illuminated by two monochromatic coplanar radiation beams of constant amplitude: a local oscillator (LO) beam of photon flux Qm and a signal beam of photon flux Q,. The resulting photocurrent I p h ( t ) in the photodiode from these two ideally mixed beams is (Kingston, 1978, Chapter 3; Spears and Kingston, 1979) Zph(f)

= ZLO

+ 1s + 27)(wif) a

s

where Zm and Z, are the dc photocurrents due to

c

cos wifl,

QLO

and

Qs

(103) individually, ( 104a)

( 104b)

and where the ac term is due to the coherent mixing of the two beams. The modulation frequency wif is wif =

lwL0

-

4,

(105)

where hum and hw, are the photon energies of the LO and signal beams, and wif is assumed to lie below the upper-frequency response cutoff of the ) the dc phophotodiode. Note that the dc quantum efficiency ~ ( 0governs tocurrents ZLo and I s , but the ac quantum efficiency ?(wit) governs the obmodulated photocurrent. The rms heterodyne signal current Is,h(~if) tained from Eq. (103) is

238

M. B . REINE, A. K . SOOD, A N D T. J . TREDWELL

The noise current in the photodiode can be obtained from Eq. (79). Assume that Q,N >> Q s . Then the mean squared noise current is

where the first term represents photodiode thermal noise and the second term is the shot noise on the dc local oscillator photocurrent. The figure of merit which characterizes the photodiode hetrodyne sensitivity is the heterodyne noise equivalent power NEPh,A which is defined as that signal power necessary to produce a signal-to-noise power ratio of unity: From Eqs. ( 9 9 , (106), and (107) this gives

The units of NEPh,A are W/Hz. The theoretical quantum limit for the heterodyne noise equivalent power results from Eq. (109) by setting both q(0) and q(qf)equal to unity and assuming ZLo >> Isat:

NEPh,A = hc/A.

(1 10)

For A = 10.6 pm, this has the value of 2 x W/Hz.Equation (109) shows that one wants to design a heterodyne photodiode such that the dc local oscillator photocurrent ZLo can be made to dominate the dark current and, as pointed out by Spears and Kingston (1979), such that q ( O ) / q 2 ( w ) is as close to unity as possible.

8. LATERALCOLLECTION

IN

SMALL-AREA JUNCTIONS

When the dimensions of the junction are so small that they are comparable to a minority-carrier diffusion length, then the lateral diffusion of both photogenerated and thermally generated current to the junction edges needs to be explicitly taken into account. This situation is frequently encountered in infrared system applications, particularly with two-dimensional mosaic arrays. Often lateral collection effects can be used advantageously to increase the photosensitive area of a junction and allow the actual junction area to be reduced. This in turn reduces junction capacitance, space-charge region g-r current and leakage currents originating at the junction perimeter. There are three different geometrical areas to consider when lateral collection is important. These are shown in Fig. 1 I for a planar n-on-p junction photodiode with a shallow n region, which is generally the case for

6.

PHOTOVOLTAIC INFRARED DETECTORS

la1

239

bl

FIG.11. Cross sections and top views of an n-on-p photodiode showing diffusion collection volumes for the cases of (a) no optical mask and (b) with an optical mask. Surface generation and recombination at the front p surface are assumed to be negligible.

implanted photodiodes. Surface generation and recombination at the front p surface are ignored. Thejunction area A , is just the area of the implanted n region. The volume of the space-charge region is just AjW, where W is the space-charge region width. The collection area A, is larger than A, by approximately the area of an annular region of width L, around the junction perimeter. This would be the photosensitive area determined in a high resolution spot scan of the photodiode in Fig. 1la. It is also the area to be used for diffusion current calculations. The diffusion volume is given approximately by A,L, . Sometimes there is an optical mask used to define the optically active area of the detector. This is shown in Fig. 1lb, in which the optical area A,, defined by the mask is smaller than the collection area A, ; in this case a high resolution spot scan would measure A,, as the photosensitive area. However, the area to be used for diffusion current calculations is still the collection area A,. One can see that the situation with A, > A,, in Fig. l l b is not optimum for signal-to-noise ratio. The effective volume contributing to diffusion current is larger than necessary. The background limited detectivity will be the same, but one will have to cool the photodiode to a lower than necessary temperature to achieve it. Because the junction area Aj is larger than necessary, there will be more space charge region g-r current and junction space-charge capacitance will be larger. Because the junction perimeter is larger, there will be more leakage current from mechanisms located at the junction edge. These effects have been considered analytically by Holloway (1978, 1979) and by Gurnee et al. (1979). If the surface recombination velocity at the front p-type surface is large

240

M . 3. REINE, A. K . SOOD, A N D T. J . TREDWELL

enough, lateral collection of photogenerated electron-hole pairs will not be important. The effects of lateral collection on the photocurrent of small area, uriiformly illuminated photodiodes, including a finite surface recombination velocity s at the front p surface, were treated by Shappir and Kolodny (1977). For aL, > 1, which is usually the case for A < A,,, they show that maximum lateral collection occurs when s is small enough so that s < vD, where vl, is the diffusion velocity L e / 7 , . The amount of lateral collection decreases for s > vD; there is essentially no lateral collection for values of s about equal to or larger than the quantity D,a. If the p-surface recombination velocity is large, then the area of the p-side surface immediately adjacent to the junction edge could be a source of dark current, since it is within a diffusion length of the junction. An optical spot scan of the photodiode would indicate no appreciable lateral collection because photogenerated pairs would recombine at the surface. But when the photodiode is biased, the p surface would be a source of minority-carrier current. 9. RESPONSETIME In this section we consider those mechanisms which limit the ability of the photocurrent in Hg,,Cd,Te photodiodes to remain in phase with modulated infrared signal radiation when the modulation frequency becomes large. High-frequency limitations of photodiodes are discussed in general by Sze (1969, Chapter 12), and have been considered specifically for Hg,-,Cd,Te photodiodes by Cohen (1972), by Koehler and McNally (1974) and by Kingston (1978). The considerable interest in the behavior of the signal response of Hg,-,Cd,Te photodiodes at high frequencies has been mostly due to applications at 10.6 pm involving CO, laser heterodyne detection for laser radar or optical communications. There are basically three effects which determine the upper-frequency response of a photodiode to modulated signal radiation: (a) the time required for electron-hole pairs photogenerated in the quasineutral n or p regions to diffuse to the space-charge region; (b) the transit time required for photogenerated carriers to drift across the space-charge region; (c) the RC time constant associated with the junction capacitance and resistance combined with the impedance of the external circuit. In practice, it is generally found that either the first or the third of these determine the upper frequency response of Hg, -,Cd,Te photodiodes. u . Diffusion Effects in the Quasineutral Regions

Consider the case of the n-on-p photodiode shown in Fig. 10 and again assume that essentially all the incident signal radiation is absorbed in the quasineutral p region. The instantaneous generation rate per unit volume

6.

PHOTOVOLTAIC INFRARED DETECTORS

24 1

due to signal radiation modulated at an angular frequency o is G(z,t) = cuQ exp(-az

+ iot).

(111)

The photogenerated excess minority-carrier concentration An(z,t) is a solution to Eq. (1 l ) and is subject to the boundary condition

An(0,t) = 0,

(112)

and that An(z,t) vanish for large z. The solution for An(z,t) leads to a photocurrent density .Ip&) given by Jph(f)

= e q ( o > QexpCibt -

where the phase angle C#I is given by

413,

( 1 13)

.

and where the ac quantum efficiency is given by

Here a ( w ) and b(w) are the dimensionless functions of frequency given in Eqs. (86) and (87). In the limit of low frequency, a -+ 1 and b + 0, and q ( w ) reduces to the dc quantum efficiency given in Eq. (66). For high frequencies such that 07, >> I , q ( w ) reduces to q(w) + C Y L e / G .

(1 16)

An estimate of the frequencyf, above which the quantum efficiency decreases substantially below its dc value is obtained by equating Eqs. (66) and (116):

f, = ((~L,)~/27r7, = cu2D,/27r.

(1 17)

Let us estimate f, for p-type Hgo,,Cdo.,Te at 77 K. If the minority-carrier mobility can be taken as the electron mobility in low carrier concentration n-type Hg,,,Cd,.,Te (Table I), which is about 3 x lo5 cm2/V sec, then Eq. (21) gives a value for D, of 2 x lo4 cm2/sec. The frequency& will depend strongly on wavelength through a(X). For wavelengths not too much shorter than the cutoff wavelength, we can let a be about 500 cm-’, andf, turns out to be about 800 MHz. By analogy, one can see that the upper frequency response limit due to diffusion effects in n-type (HgCd)Te will be significantly less than that in p-type because of the much smaller hole mobility. A two order of magnitude smaller hole mobility will lead to a correspondingly smaller cutoff frequency & . The problem of the frequency response of a p region of finite thickness,

242

M . B . REINE, A. K . SOOD, A N D T. J . TREDWELL

including effects of surface recombination, has been treated by Sawyer and Rediker (1958). 6. Drift Ejjects in the Space-Charge Region

The effect of the finite transit time of photogenerated carriers on photodiode frequency response was considered by Gartner (1959) and is discussed in Sze (1969, Chapter 12). The transit time t, for carriers of drift velocity v d across a space-charge region of width W is t, =

w/v,.

(1 18)

If W is 1 pm and V d is limited by lattice scattering to a value of about 1 X lo7cm/sec, then the transit time is about 1 x lo-" sec. One would expect to see transit time effects in the frequency response at a frequency around (27rQ-l or at 16 GHz.

c . Junction Capacitance Effects The effects of junction capacitance, dynamic resistance, and series resistance, together with external circuit impedance, on the high-frequency response of 10.6-pm Hg,,,Cd,.,Te photodiodes have been analyzed by Peyton el al. (1972), by Koehler and McNally (1974), by Shanley et al. (1977) and by Shanley and Perry (1978a,b). Here we give a simplified discussion in which we assume that the only significant capacitance is the junction space-charge region capacitance Cj and the only significant resistance is the external load resistance RL. In this case, the upper-frequency limit f, is =

I/'LrRLCj.

(119)

For Cj we assume CJ = ~SEdZJIW,

where 8, is the static dielectric constant, E, is the permittivity of free space, Aj is the junction area, and W is the space-charge region width. For W we assume the usual abrupt junction expression W

=

d2&&,(VW- V ) / e N B ,

(121)

where NR[= NAND/(NA + N,)] is the effective doping concentration in the space charge region, and where Vbl is the built-in junction voltage given by

For a Hg0.206Cdo.,g4Te photodiode, the cutoff wavelength will be about

6.

PHOTOVOLTAIC INFRARED DETECTORS

243

12 km at 77 K, ni is about 5 x 1013cm-3 and E, is about 17 (Dornhaus and and N A = 1 X lo'' ~ m - Eq. ~ , (122) Nimtz, 1976). For ND = 2 x 1014 gives eVbi as 0.059 eV. Figure 12 contains plots of the cutoff frequency& versus applied reverse-bias voltage for a Hg,,to6Cdo.,aaTephotodiode. The cutoff frequencyf, was calculated from Eqs. (1 19)-(122) for a load resistance of 50 SZ, for ajunction area of Aj of 1 X lop4cm2,for N A = 1 X 10'' and for various values of ND.Also shown are the space-charge region width W and the capacitance per unit area Cj/Aj. In Fig. 12, the curves are not extended beyond what are reasonable values of reversebias voltage for 12-pm Hg,-,Cd,Te photodiodes. Still, one can see that cutoff frequencies of 2 GHz can be realized with the lowest n-side doping concentrations at reasonable reverse-bias voltages. It should be noted that any junction series resistance and stray capacitance will tend to lower & from these values (Shanley and Perry, 1978a,b). lo. AUGERLIFETIMEI N p-TYPE Hg,,Cd,Te It has been known for some time now (Peterson, 1970; Kinch et af., 1973) that an Auger electron-electron collision process involving two conduction band electrons has been an important recombination mechanism in n-type Hg,-,Cd,Te, particularly for x around 0.2 and at higher

0.Wl

0.01

0.1

1

10

REVERSE BIAS VOLTAGE (Vl

FIG.12. Calculated cutoff frequencyf, [from Eq. (1 19)] for a Hgo,,,C&,,,,Te photodiode at 77 K (&,, = 12 pm) with an aread, of 2 x cm2. The right-hand scales correspond to the depletion width W from Eq. (121) and to the junction capacitance per unit area C,/A, from Eq. (120).

244

M . B. REINE, A . K . SOOD, A N D T . J . TREDWELL

temperatures. Tredwell and Long (1977) showed that this electronelectron Auger process, which we denote as “Auger process 1,” was generally not expected to be significant in p-type Hg,,Cd,Te. Recently, Casselman and Petersen (1979, 1980) surveyed those Auger processes which could occur in p-type Hg,-,Cd,Te and found that there was one Auger hole-hole collision process involving a transition from the light-hole valence band to the heavy-hole band which might, on theoretical grounds, be expected to be important in p-type Hg,-,Cd,Te. Following Casselman and Petersen (1979, 1980), we call this process “Auger process 7.” In this section we derive the dependence of the Auger process 7 lifetime on excess carrier concentration. Using detailed balance arguments and assuming nondegenerate electron and hole distributions, Blakemore (1962, Chapter 6) shows that the recombination and generation rates rl and g , per unit volume for the electron-electron Auger process 1 in Fig. 13 are TI

= (1/27,)(n2p/n:),

gi = n/271,

(123)

where T~ is the Auger process 1 lifetime for an intrinsic semiconductor at thermal equilibrium. Let the electron and hole concentrations n ( t ) and p ( t ) undergo small departures from their steady-state values 7i and is: n(t) = F +

An(&

p(t)

= p + A&).

( 1 24)

Further assume that An(t) = A&). Then the incremental lifetime qnc which characterizes the exponential decay of An@) to zero is obtained from ( r - g ) as follows:

E

L

FIG. 13. Recombination transitions for the electron-electron collision (Auger process 1) and hole-hole collision (Auger process 7) mechanisms. The arrows indicate electron transitions, and i and f denote initial and final states for recombination. [From Casselman and Petersen (1979, 1980).]

Heavy-

Auger 1

Auger 7

6.

PHOTOVOLTAIC INFRARED DETECTORS

245

The incremental lifetime for Auger process 1 is then

Similar arguments can be applied to the hole-hole Auger process 7 (Casselman and Petersen, (1979, 1980) to give

l @ r, = 2~~ nT '

g7

=

e277

7

and the incremental lifetime for Auger process 7 is

The total incremental lifetime for both Auger processes is obtained by adding Eqs. (126) and (128):

where

T~ is

defined as

_1 -- _1 +-.1 7i 71

77

Consider now small departures from thermal equilibrium;

n = no and p

=

po can be substituted into Eq. (129), with the result

For an intrinsic semiconductor, one can see that Eq. (131) reduces to Eq. (130). The symmetry between Auger 1 and 7 is clear from Eq. (131). For heavily n-type material, Auger process 1 becomes more important, and Auger process 7 becomes more important for heavily p-type material. This behavior can be seen in Fig. 14, which is a qualitative representation of Eq. (13 1). The longest lifetime occurs when and Fig. 14 was drawn with the assumption that T~ < r7 so that the longest Auger lifetime would occur for p-type material. The problem of determining how important Auger process 7 is in p-type . though the necessary Hg,,Cd,Te lies in obtaining a value for T ~ Even regions of the Hg,-,Cd,Te band structure are probably known well enough, there are overlap integrals involved in any calculation of 77 (just

246

M . B. REINE, A . K . SOOD, AND T. J . TREDWELL

FIG.14. Qualitative behavior of the incremental Auger lifetime for processes 1 and 7 for small departures from thermal equilibrium, from Eq. (131).

as in T J which are difficult to evaluate with sufficient confidence to enable an a priori assessment of the magnitude of 77 (Casselman, 1981). The symmetry of the two mechanisms, as evident from Eqs. (129)-( 1301) will make it particularly difficult for experiments to determine independent values for T , and 77. For example, consider the photoconductive lifetime data of Kinch et al. (1973) on n-type Hgo.,Cd,.,Te samples. Their conclusion that Auger process 1 was operative in their samples was based in large part on the temperature dependence of the photoconductive lifetime between 125 and 200 K, where the samples were intrinsic. Both T~ and r7 have nearly the same temperature dependence. The intrinsic Auger lifetime is given in Eq. (130), so that the data of Kinch et al. (1973) in the intrinsic range can only provide an experimental value for [ 7 1 7 7 / ( 7 1 + T T ) ] rather than for either T~ or 71 separately. 111.

Hg,-,Cd,Te Junction Photodiode Technology

A wide variety of techniques has been used to form p-n junctions in Hg,,Cd,Te. Both n-on-p and p-on-n junctions have been formed, and type conversion has involved introduction of foreign atom impurities, controlled deviations from stoichiometry, and occasionally combinations of both. Junction formation techniques have included ion implantation of donors and acceptors, high energy proton bombardment, diffusion of donors and acceptors, in-diffusion and out-diffusion of mercury, creation of p-type surface layers on n-type material by intense pulsed laser radiation, and in situ cosputtering of donors and acceptors in sputtered Hg, ,Cd,Te layers.

6.

PHOTOVOLTAIC INFRARED DETECTORS

247

The most technologically significant of these techniques for high performance infrared detectors appear to be ion implantation and Hg indiffusion. For direct detection applications, the highest R A products for Hg,-,Cd,Te photodiodes to date have been reported for boron-implanted n-on-p photodiodes. For high-frequency 10.6-pm heterodyne applications, n-on-p planar photodiodes, formed by Hg in-diffusion into p-type Hgo,,Cdo.,Te containing a low concentration of donors, have given the widest bandwidths so far. 11. ION IMPLANTATION

Ion implantation has been used to form a variety of junction configurations in Hg,,Cd,Te during the past 10 years. Most of the implant work has been focused on forming n-on-p junction photodiodes for direct detection applications. This work and the work on forming p+-p and n+-n hi-lo junctions are reviewed in this section. Ion implantation has also been used to form n+-p-p--p+ avalanche photodiodes in Hgo.,Cdo.,Te (Koehler and Chiang, 1975) and, recently, n-channel MOS transistors in Hgo.71Cdo.zsTe (Kolodny et al., 1980) and n-channel insulated-gate field effect transistors in Hgo.,ssCdo.zlsTe(Nemirovsky et al., 1980). a. Summary of Ion-Implantation Work in Hg,-,Cd,Te Table I1 summarizes implantation work reported in Hg,-,Cd,Te to date. The proton bombardment results of Foyt et al. (1971) are included for comparison. Type conversion via high-energy electron irradiation is considered later in Section 13,a. The electrical behavior of the various implanted species shown in Table I1 is based on the conclusions of Johnson and Schmit (1977), who studied the doping properties of selected impurities in Hg,,Cd,Te. In their work, impurities were introduced either by diffusion or by melt doping during crystal growth. Their conclusions can be summarized as follows: (1) Ag, Cu, Au, and Li are fast diffusing acceptors; (2) Ga and In are fast diffusing donors; (3) A1 and Si are donors requiring high temperatures for diffusion; (4) Sn is inactive when diffused at or below 300°C; ( 5 ) P and As are slowly diffusing acceptors; and (6) Br is a slowly diffusing donor. has been devoted to the forMost of the implant work in Hg,,Cd,Te mation of n-on-p junction photodiodes. The first use of high-energy particle bombardment for type conversion in Hg, -,Cd,Te was reported by Foyt et al. (1971) who used proton bombardment to form n+-on-pjunction photodiodes. Type conversion in this work was most probably due to cre-

TABLE I1

SUMMA RY OF IOK IMPLANTATION WORKI N Hg,-,Cd,Te Implant species

Doping behavior in Hg,-,Cd,Te"

Protons

-

Hg

Unimportant as a donof

Implant energy (keV) Implant dose 200 200 100 30

5 x 10'4

Damage anneal

)

None

2 x 1014 1.6 x 1014 1012-

1013

Hg,-,Cd,Te alloy composition

0.25

Device configuration n+-on-p

0.31

0.5

NoG

Reference Foyt er al. (1971) [see also Elliott er al. (1972)l

0.2-0.5

n-on-p

Fiorito et a / ., 1973, 1975, 1978 [see also Fiorito el a!. (1976, 1977)]

0.20, 0.23

n-on-p

Marine and Motte (1973)

2wc

0.29

n-on-p

McNally (1974)

250"C, 5-10 min

0.2

p-on-n

Koehler (1977) Shanley et al. (1977)

0.2-1

n-on-p

Igras (1977)

~

Al

Donor

250

5 x 10'5

In

Donor

500

1013- 1014

Au

Acceptor

200

1014

In, A1 Hg

Donor Unimportant as a donof ? Acceptor AcceptoP

300"C, 1 h

~

Zn P, Au N

30- 140

10'"lO'j

None

No type conversion in n-type

(Continued.)

B

Dono?

110

3 x 1013-3 x 10l5

Al

Donor

3

Ne

Neutral

300 -

Si

Donor

-

CI B B

Donor' Dono? Donor'

60- 100 40 and l W

1014

B

Donold

110

3.7 x loLo-3.7 x

B

DonoP

100

P

Acceptor

P As

Acceptor Acceptor

B

DonoP

P

Acceptor

B

DonoP

20-250

B

Donor'

100-150

X

1013-3 -

X

lOI5

Some samples at 200°C

-

-

0.3

n+-on-p

Bratt (1978)

n +-on-p n+-on-p Sood and Tredwell (1978a)

0.2

N o type conversion in p-type n+-on-p n+-on-p n + / n-on-p

Yes; no conditions given

0.28

n-on-p

Riley et al. (1978b) (see Figs. 15 and 16)

I x 1013

None

0.33

n+-on-p

Lanir et al. (1978, 1979)

100

1 x 1013

300"C, 22 h

0.3

p-on-n

Chapman et a / . (1978)

150 200

1 x 10'5

150-200"C, 2 h

0.2

P+-P PI-P

Sood ef a / . (1979a) [see also Sood er a / . (1979b,c)]

I x

150"C, 2 h

0.39

n+/n-on-p

Tobin (1979); Schmit ef al. (1979)

250"C, 3 days in Hg vapor

0.2

p-on-n

See footnote e

n-on-p

Riley et a / . (1979) (see Fig. 17)

n-on-p

Wang et a l . , 1979

40 and l W 280

- 1015 I x 1015

1015

1.1014-3 x

lOI5

I x 1015

- 10'3

I

0.2

125-175"C, 1-3 h 150-2WC, 0.5-3 h

25O-45O0C, 4 h

-

0.2

TABLE XI (continued.)

B Be

Dono?

B

DonoP

-100

-5 x

1012

None

0.2

n-on-p

Chu er al. (1979); Bubulac er al. (1979)

20-150°C. 24 h in

0.21

n+-on-n

Margalit et al. (1979)

0.29

n-on-p

Kolodny and Kidron

?

150

1 x 10L1-lx lOI5

vacuum

Ar

Inert

In

Donor

P Au

Acceptor Acceptor

B A1 Ar P

Donold Donor Inert Acceptor

Hg

Unimportant as a donof

a

100 -

1 x IOL3-3 X

300 300

1 x 10'4 I x 1014

300

1 x lOI3-2 x lOI4

IOI5

65"C, 12 h

-

(1980)

25OoC, 30 min

Based on the conclusions of Johnson and Schmit (1977). Extrapolated from the conclusions of Johnson and Schmit (1977). Schmit and Stelzer (1978); Vydyanatb ef al., (1979). Double Implant. Private communication from P. R. Bratt, K. I. Riley, and A. H.Lockwood.

0.2

-

Bahir et al. (1980)

6.

PHOTOVOLTAIC INFRARED DETECTORS

25 1

ation of damage which was intentionally not annealed out after bombardment. Ion implantation of mercury to form n-on-p Hg,-,Cd,Te junction photodiodes was reported by Fiorito et af. (1973) and has been discussed by them in a series of subsequent papers (Fiorito et a/., 1975, 1976, 1977, 1978). No work damage anneals were performed, and damage is probably responsible for type conversion here also, particularly in view of the lack of evidence for interstitial mercury being a significant native donor in Hg,-,Cd,Te (Schmit and Stelzer, 1978; Vydyanath and Nelson, 1981). Implantation of the donors aluminum (Marine and Mott, 1973) and indium (McNally, 1974) with post-implant work damage anneals formed n-on-p Hg, ,Cd,Te junction photodiodes, but the roles of damage versus activated impurity donors were not delineated. Igras et a / . (1977) reported type conversion in p-type Hg,-,Cd,Te with implanted In, Al, Hg, and with Zn, but did not obtain type conversion of n-type Hg, -,Cd,Te via implantation of phosphorus, nitrogen, and gold. No post-implant damage anneals were performed, which probably accounts for the failure to achieve type conversion in n-type Hg,-,Cd,Te. Similar results were obtained by Kolodny and Kidron (1980), who formed n-on-p junctions in p-type H&.,,Cdo.2eTe by implantation of boron and aluminum as well as by implantation of phosphorus and argon, with damage anneals at 65°C for 12 h. They concluded that their implanted layers are n-type due to damage rather than to the implanted species. Margalit et al. (1979) studied the electrical and annealing properties of implanted n+ layers on low carrier concentration (about 5 x 1014 ~ m - ~ ) n-type Hgo.,,Cdo.,,Te wafers. They observed nf layer formation with implantation of boron, argon, indium, phosphorous, and gold. The boron implantations were performed through 2000-A insulating layers of either CdTe or ZnS. The implant energy was 150 keV and doses ranged from 1 x 10" - 1 x 1015cmP2.They found that the sheet electron concentration in the implanted (i.e., unannealed) n+layers, as determined from conductivity and Hall effect measurements on van der Pauw samples, was not very sensitive to either the implant species or the implant dose, for doses ranging between 5 x 10"-1 x 1015 cm-2. For example, sheet electron concentrations of around 1 X 1013cm-2 were obtained at an implant dose of 1 x 10l2cm-2, and sheet electron concentrations around 5 x lOI3ern+ were obtained at a dose of 1 x lOI5 cm-2. From these results, Margalit et af. conclude that the implanted n+ layers are due to implant damage rather than to substitutional doping. Margalit et a/. studied the effects of annealing samples after implant at temperatures ranging from 20-120°C for 24 h in vacuum. Samples implanted with gold at 5 X l O I 4 cmP2and with boron at 1 x 1015 cm-2 showed only a slight reduction in sheet electron concentrations at an annealing temperature of 120°C. Margalit et af. point

252

M . B. REINE, A. K . SOOD, A N D T. J . TREDWELL

out that implanted n+ layers, in addition to providing n+-on-pjunctions, could also prove useful for accumulating the surface of n-type Hg,,Cd,Te photoconductors to reduce surface recombination and to aid in forming ohmic contacts to n-type Hg,-,Cd,Te. There have been some reports of p-on-n junction photodiodes formed via acceptor ion implantation into n-type Hg,-,Cd,Te, although with work damage anneals at significantly higher temperatures than those of Margalit et ul. (1979) and Kolodny and Kidron (1980). Koehler (1977) and Shanley ef u / . (1977) reported the use of gold implantation to form p-on-n Hgo.,Cdo.2Tephotodiodes, with damage anneals at 250-300°C for 5 - 10 min being required for junction formation. Both Rileyt and Sood el a/. (1979a,b,c) have reported formation of p-on-n Hg,.,Cdo.2Te junctions via phosphorus implantation. In addition, formation of p+-p hi-lo junctions in p-type Hgo,,Cdo.2Tevia both phosphorous and arsenic implantation has been reported by Sood et c d . (1979a,b,c). Chapman et al. (1978) have formed p-on-n Hg,,Cdo,,Te junctions by phosphorous implantation. In all of this work, the implanted layers were n-type prior to annealing, and converted to p-type only after a work damage anneal. Implantation of boron into p-type Hg,-,Cd,Te has received considerable attention in the past several years and has become the most commonly used implant species for the formation of n+-on-p Hg,-,Cd,Te junction photodiodes. It is not known that boron is indeed a donor in Hg,-,Cd,Te, but boron is in the same column of the periodic table as aluminum, gallium, and indium which are known to be donors (Johnson and Schmit, 1977). Its small mass makes it a desirable choice from implant damage considerations. Riley et a / . (1978b) have reported SIMS analysis data (Fig. 15) for boron implanted at an energy of 110 keV into Hg0.,Cdo.,Te and Hgo.,Cdo.,Te. They show that their data for the concentration profile N ( x ) of implanted boron atoms follow generally the Gaussian behavior given by

W )= N,,, e W - i x

-

R,Y12(AR,)2),

(133)

and where cp is the boron ion dose, and where the mean projected range R, and the standard deviation AR, about the mean can be calculated from LSS theory (Mayer and Marsh, 1969; Pickar, 1975). For boron implanted into Hg,_,Cd,Te at 110 keV, R, is about 0.24 pm and AR, is about t Private communication from P. R. Bratt, K . J. Riley, and A . H. Lockwood.

6.

PHOTOVOLTAIC INFRARED DETECTORS

A I. 0

3 . 7 ~ 10l5 cmT2

110 k a v

0 0.4

3. 7 x 1014

110 keV

0 0.2

I . OX

.-

0.4

loL4 cm-2

253

110 keV

Calculated from U S Theory

Depth (rm)

FIG.15. SIMS analysis profiles of boron implants in Hg,,Cd,Te. of Eq. (135). [From Riley et al. (1978b).]

The solid lines are plots

0.15 pm. The solid curves in Fig. 15 were calculated from Eq. (135). Good agreement between Eq. (135) and SIMS data for boron implanted into H&,,Cdo.,Te at an energy of 100 keV and a dose of 4 x lOI4 cm-, has also been reported by Wang et a/. (1979). Riley et a / . (1978b) also reported data for the dependence of carrier concentration on implant dose in boron implanted n-type layers on p-type Hg,,7zCdo.zeTesamples. Their data, shown in Fig. 16, were obtained from both van der Pauw Hall samples and capacitance-voltage measurements on MIS samples. Evidence for additional donors due to implant damage is shown by the data for unannealed samples being about an order of magnitude above the straight line calculated from Eq. (136). The data for annealed samples are in good agreement with Eq. (136) for implant doses below about 1 x 1013 ~ m - ~ . as a Riley et a / . (1979) studied boron implantation into Hg,-,Cd,Te function of implant energy over the 20-250 keV range. Their data for the mean projected range Rp as determined by SIMS analyses of the implant profiles are shown in Fig. 17. After implantation, half of each sample was

254

M. B. REINE, A. K . SOOD, AND T . J . TREDWELL

DOSE

II+lCm2)

FIG.16. Donor concentration in n-type boron-implanted layers in H&.72C&.2aTeplotted versus implant dose. The straight line labeled nmaxwas calculated from Eq. (136). [From Riley et a / . (1978b).]

annealed for 4 h at the temperatures shown in Fig. 17. Except at the lowest implant energies, the data for both annealed and unannealed samples agree well with the values expected from LSS theory. Moreover, the data show that the boron profile is quite stable up to anneal temperatures of 450°C. Studies of implant damage in Hg-implanted H&&d,,Te via Rutherford back scattering (RBS) and proton-induced x-ray (PIXE) channeling experiments have been reported by Bahir et al. (1980). They used 300-keV Hg ions at implant doses ranging from 1 X 1013 cm-, to greater than 2 X 1014cm-*. From their RBS data, they observed a buildup of the damage until it reached a saturation level, beyond which no further changes in the RBS spectra were observed. The saturation dose was 2 X

6.

Irn

10

PHOTOVOLTAIC INFRARED DETECTORS

20

50

I00 ENERGY lkeVI

200

255

503

FIG.17. The mean projected range R, for boron implants into Hg,-,Cd,Te for various implant energies and for a dose of 1 x loL5cm-*. Data were determined via SIMS analysis. Data for both unannealed and annealed (for 4 h and at the temperatures indicated) samples are shown. 0, annealed; A, unannealed. [From Riley et a / . (1979).]

1014cm-2. From the position in energy of a “knee” in the RBS energy spectra obtained from implanted samples, they infer that the damage extends to a depth of about 1500 A into the sample. This is much deeper than the calculated range of about 500 A for 300-keV Hg ions in Hg,,Cd,Te. They found that the crystal structure could be nearly completely restored by annealing the implanted samples at 250°C for 30 min. The use of a double boron implant to tailor the boron profile within the implanted region of n+-on-p Hg,-,Cd,Te photodiodes was first reported by Sood and Tredwell(1978a). They specifically wanted to move the peak of the implanted profile towards the sample surface so that surface inversion would be less likely. They used sequential boron implants at 100 keV -~ a 1000-A thick ZnS layer, and 40 keV at doses of 1 x 1015 ~ r n through followed by annealing at temperatures between 150-200°C for times ranging between 0.5-3 h. SIMS analysis data reported by Sood et al. (1979~)for the n+/n boron atom profile introduced by such a double implant are shown in Fig. 18. These data are for a p-type Hg,,,,Cd,,.,Te sample with a native defect concentration of about 2-5 x lOI7

256

M . B. REINE, A. K . SOOD, A N D T. J . TREDWELL TIME (CYCLE NUMBER)

0

20

10

30

40

50

60

70

1

\

0 0 0

BACK -

GROUND \

P

, I000 8

\

+

- L I

10

0

\ \ \

I

I

I

I

0.75

0.5

0.75

1.0

DEPTH IN

Hyo

Te (urn)

FIG.18. SIMS analysis data for the boron atom profile introduced by adouble implant in a p-type Hgo,,Cdo,,Tesample with a 1000-A thick ZnS layer. 150°C anneal temperature ( 1 h). N A = 2.0-5.0 x I O l 7 cm-J. [From Sood P I trl. (1979c).]

which was annealed after implant at 150°C for 1 h. One can see that the boron atom distribution has roughly the double-Gaussian shape expected 1979~) were obfor the two sequential implants. Similar data (Sood rt d., tained for similarly implanted p-type Hg,.,Cd,.,Te samples with lower native defect acceptor concentrations (1 - 2 x 10l6 cm-3) which were post-implant annealed at 150°C for times ranging from 1-3 h ; no changes were observed in the boron atom profiles for the different anneal times. Double boron implants for n+/n-on-p photodiode configurations were also reported by Tobin (1979), Schmit ct 01. (1979) and Riley rf cil. (1979). b. Ion-Implanted Hg,-,Cd,Te

Photodiode Performance

There has been significant progress during the past three years in achieving high performance ion implanted Hg,-,Cd,Te photodiodes for direct detection applications. Space-charge region g-r and surface leak-

6.

PHOTOVOLTAIC INFRARED DETECTORS

257

age currents have been reduced to the point where diffusion current generally limits the R A products of 8-12 pm photodiodes at temperatures down to 77 K and of 3-5 pm photodiodes at temperatures around 170-200 K. In this section we summarize the state-of-the-art performance of implanted Hg,-,Cd,Te photodiodes with emphasis on these wavelengths and temperatures. The device configuration which has been almost universally adopted so far for 8-12 pm photodiodes for temperatures down to about 77 K and for 3-5 pm photodiodes for temperatures above 170 K is the n+-on-p or n-on-p configuration. There are both practical and theoretical reasons for this choice. As discussed in the preceding section, implanting n-type layers in p-type Hg,-,Cd,Te is more convenient than implanting p-type layers in n-type because damage anneals are less critical. Implant damage appears to consist of donorlike defects, and some workers (cf. Table 11) have entirely omitted the post-implant anneal, particularly at lower doses.

I o4

103/T

(K-I)

FIG.19. R A product versus 1000/Tfor a boron-implanted n+-on-p H&.,,5Cdo,3,5Tephotocmz. [From Tobin (1979).] diode. A, = 6.44 x

258

M. B. REINE, A. K . SOOD, A N D T. J . TREDWELL

In addition, one needs to be less concerned about the effects of the post-implant anneal on the stoichiometry of p-type substrates than of n-type substrates. Theoretical reasons for the choice of the n-on-p or the n+-on-p configuration include the significantly longer minority-carrier diffusion length in p-type Hg,-,Cd,Te and the possibility of achieving longer minority-carrier lifetimes in p-type Hg,-,Cd,Te than in n-type Hg,-,Cd,Te of comparable carrier concentration. Data for n+-on-p Hg,,6,Cdo.39Te photodiodes fabricated by a double boron implant in p-type material for a range of acceptor concentrations have been reported by Tobin (1979) (see also Schmit et af., 1979). The R,,A product for one of these elements is shown in Fig. 19. For temperatures above about 200 K the data vary with temperatures as $ , which is characteristic of diffusion current. The solid line in Fig. 19 was calculated from Eq. (22) for diffusion current from the p side. The fit between the data and this expression is excellent over three orders of magnitude. The dashed line is the R,,A product expected for space-charge region g-r current and is a plot of Eq. (48) forf(b) = l, and varies with temperature as n l l . Data for several arrays of these implanted d - 0 n - p Hgo.6,Cdo.,,Te photodiodes are shown in Fig. 20 plotted versus net acceptor concentra-

7

FIG.20. R,,A product data at 193 K for arrays of boron-implanted n+-on-p Hg,,.,,Cdo,asTe photodiodes plotted versus net acceptor concentration. [From Tobin, (1979).]

6.

259

PHOTOVOLTAIC INFRARED DETECTORS

tion (NA- ND).The data roughly follow the dashed line which has a slope of+. This would be expected from Eq. (22) if the lifetime T, varied with net acceptor concentration as ( N A - N J 1 . Minority-carrier lifetime data obtained on these photodiodes indeed confirmed this dependence of lifetime on ( N A - ND)at this temperature, as will be discussed in Section 14 of this chapter. Studies of boron-implanted n+-on-p Hgo.,Cdo.,Te photodiodes as a function of p-side acceptor concentration have been reported by Riley ef al. (1978b). Their results for R,A at 193 K versus the effective space-charge region doping NB[= N , N , / ( N , + ND)]are shown in Fig. 21. In their photodiodes, NB was determined by fits to the straight-line parts of junction capacitance versus voltage data plotted as C? versus V. The N Bvalues so determined were generally about eight times lower than the p-type base concentrations determined from Hall data. The relative insensitivity of R A at 193 K to N Bis attributed to the minority-carrier lifetime T, varying

-1

E

L

l

I

i

I

I

J

ctci

0.11014

Abrn - 5.7 urn

1015

1016

101'

NAND ,c,,-3,

N F D

FIG.21. &A product data at 195 K for boron-implanted H&,,Cdo,3Tephotodiodes plotted versus the space-charge region effective doping concentration N B . [From Riley er a / . 11978b).]

260

M . B . REINE, A . K . SOOD, A N D T. J . TREDWELL

FIG.22. Zero-bias capacitance per unit junction area C , / A , at 78 K for boron-implanted Hg,,,Ccb3Te photodiodes plotted versus space-charge region effective doping concentration Nn. A,x = -0.30. C , / A , a [ ( A J A N J / ( N k+ N,)JUaff. [From Riley et al. (1978b).]

as N i 2 , which behavior was observed in photoconductive decay measurements and is discussed in Section 14. Data for the zero-bias junction capacitance per unit area C,/Aj at 78 K versus N B are shown in Fig. 22 and vary as Wd2, as expected from Eqs. (120) and (121). Data for the reverse-bias breakdown voltage at 78 K versus NB are shown in Fig. 23. At this temperature, the reverse-bias characteristics are fairly soft and a breakdown voltage is not well defined. In Fig. 23 the breakdown voltage BV is defined as that reverse-bias voltage for which the reverse current is twice the sum of the short circuit photocurrent and the saturation current. What the data of Fig. 23 show is that the strength of the reverse current Reverse-bias leakage current mechamechanism varies roughly as are still not well understood, but the data of Fig. 23 nisms in Hg,,Cd,Te indicate that lower space-charge region doping concentrations NBare desirable, and this trend is consistent with tunneling through or avalanche multiplication within the space-charge region. Data for the R,A products at 193 K for near-infrared boron-implanted Hg, ,Cd,Te photodiodes are shown plotted versus cutoff wavelength in

6.

26 1

PHOTOVOLTAIC INFRARED DETECTORS

la 0

-

-> s >

0.1 1

17

NAND (cm-31 NA+ND

FIG.23. Reverse-bias breakdown voltage at 78 K for boron-implanted Hg,-,Cd,Te photodiodes plotted versus space-charge region effective doping concentration N s . BV = voltage where I = 2& + Zsat). BV = [ ( NAND) / ( NA + N,)]-0.56.[From Riley et al. (1978b).]

Fig. 24. These data are all for fairly small junction areas, on the order of 0.002 x 0.002 in2. to 0.003 X 0.005 in2. All are probably limited by diffusion current at this temperature. The solid curve is a plot of Eq. (32) for a p-region thickness of 10 pm and for the radiative lifetime given by Eqs. (35) and (36). The dashed curve is a plot of (R,A)pmgiven by Eq. (20) with N A = 1 x 10l6 cmP3,T~ = 2 psec and L, = 50 pm. Of course, other values could have been chosen, since it is the product (NA7,/L,) which enters into (R,A),, . Data for R,A versus reciprocal temperature for one of these elements are shown in Fig. 25. The cutoff wavelength is 4.08 pm at 193 K. The solid line is a plot of (R,A),, in Eq. (20) showing that diffusion current is dominant down to 170 K. Quite large R,,A products at 77 K for near-infrared implanted Hg,,Cd,Te photodiodes have been reported by Riley et af. (1978b) and by Gurnee et al. (1979). The I-V characteristics at 77 K and at 0" FOV for a boron-implanted Hg, ,Cd,Te photodiode with a cutoff wavelength of 4.2 pm at 77 K are shown in Fig. 26 (Gurnee et al., 1979). This element had an optical collection area A , of (25 pm)2 beneath a sputtered CdTe mask. At 77 K the zero-bias resistance R, was about 3.2 x 1013 Q, giving

-

1-

-

l

L

2pec

l

l

I

i

\

m

Le'W I

I

I

I

1

I

I

1

\ I

FIG.24. R,A products at 193 K for boron-implanted Hg,-,Cd,Te photodiodes versus cutoff wavelength. [From:0 , T . J . Tredwell (unpublished data): A, Riley er al. (1979);and 0 , Lanir ef a/. (1979b).] TEMPFRATURE

IOLWT

(K)

(K-')

FIG. 25. R d versus reciprocal temperature for a boron-implanted n+-p Hg,-,Cd,Te photodiode, x = 0.326; h,,(193 K) = 4.08 p m ; A, = 3 x 5 mil2. [From T. J . Tredwell, unpublished data.]

VOLTAGF f V I

FIG. 26. I-V characteristics at 77 K for a boron-implanted n+-on-p Hg,-,Cd,Te diode with a cutoff wavelength of 4.2 pm. [From Gurnee ei d.(1979).]

photo-

Theoretical Limit for Radiative Lifetime and d - 1 0 ~ m

10-41

1

1

a. o

I

I

I

I 10.0

1

I

I

1 I 12.0

I

I

CUTOFF WAVELENGTH (Hmi

FIG.27. R J , products at 145 K for 10 x 10 mil2 boron-implanted n+-on-p Hg,-,Cd,Te photodiodes versus cutoff wavelength. [Data from Sood et a / . (1979a).] The solid line is calculated from Eq. (32) for T~ = radiative lifetime and d = 10 pm. The dashed line is calculated from Eq. (20) for N , = 1 X 10l6 c m P , T~ = 0.3 psec, and L, = 50 p m .

264

M . B . REINE, A. K . SOOD, A N D T . J . TREDWELL

an R& product of about 2 x lo8 Q cmZ.The doping concentration of the p-type Hg,-,Cd,Te used was in the 1nid-10'~cmP3 range. Riley et d. (1978b) report a R,A product at 77 K of 1 x lo8 fk cm2 for a boronimplanted Hg,,Cd,Te photodiode with a cutoff wavelength at 77 K of 4.0 pm; they report the value of N B as being 8 x 1014c ~ n - ~ . Data for the R,A, products of long-wavelength, boron-implanted Hg,-,Cd,Te photodiodes with A j = 10 x 10 mil2 are shown in Fig. 27 for a temperature of 145 K (Sood rt ul., 1979a) and in Fig. 28 for a temperature of 77 K (Sood and Tredwell, 1978a; Longshore, 1979). As in Fig. 24, the solid lines are plots of the theoretical upper limit for p-side diffusion current with radiative recombination and a p-region thickness of 10 p m , and the dashed lines are plots of ( R d ) , , from Eq. (20) for the values of (NA7,/L,) shown. The data at 77 K show more spread and less agreement with Eq. (2O), probably due to the onset of leakage current mechanisms. I-V characteristics are shown in Figs. 29 and 30.

Fic;. 28. R,A, products at 77 K for photodiodes versus cutoff wavelength. line is calculated from Eq. (32) for 7 ,= calculated from Eq. (20) for N , = 1 x

10 x 10 mil' boron-implanted n+-on-p Hg,-,Cd,Te [Data from Sood and Tredwell (1978a,b).] The solid radiative lifetime and d = 10 p m . The dashed line is loL6C I - I - ~ , 7, = 0.15 p e c , and L, = SO p m ,

6.

PHOTOVOLTAIC INFRARED DETECTORS

265

FIG.29. I-V characteristics at 77 K (left) and 145 K (right) of a boron-implanted n'-on-p Hg,-,Cd,Te photodiode. This element had a junction area of 10 x 10 milz, a quantum efficiency of 60%, and a cutoff wavelength of 9.75 pm at 77 K and 8.7 pm at 145 K . The &Aj product at 77 K was 61 R cm-z and was 0.1 R cm2 at 145 K . [From Sood and Tredwell (1978a).]

Capacitance versus reverse-bias voltage data (Sood er af., 1978a) at 77 K for a boron-implanted n+-on-p Hg,,Cd,Te photodiode with a junccm2 are shown in Fig. 31. The str ;ght line is a tion area Aj of 6.25 x plot ofjunction capacitance as given by Eqs. (120) and (121) with the intercept giving Vbi = 130 mV and the slope giving NB= 3 X 1015~ m - The ~. intercept at C = 0 gives a value for C, of about 35 p F and a value for C , / A , of 0.056 pF/cm2. Hall data on thep-type Hg,,,Cdo.,Te samples gave ~, due to a hole concentration at 77 K of about 2 x 1 O I 6 ~ m - presumably native defect acceptors, which is appreciably larger than the value for NB obtained from the fit to the capacitance data in Fig. 31. Similar discrepancies between base acceptor concentration from Hall data and spacecharge effective doping NBfrom C2- V analysis have been reported for p-type Hgo.,Cdo,,Te by Bratt (1978) and by Riley el al. (1978b). Bratt

FIG. 30. I-V characteristics of a boron-implanted n+-on-p Hg,-,Cd,Te photodiode at 77 K. This element had ajunction area A , of 10 x 10 mil', a quantum efficiency of 62%. a cutoff wavelength of 9.0 p m and a R d , product of 410 cm2. [From Sood and Tredwell (1978b).]

266

M . B . REINE, A. K . SOOD, A N D T. J . T R E D W E L L

REVERSE B I A S VOLTAGE ( V I

FIG.31. Reciprocal of the capacitance squared versus reverse-bias voltage at 77 K for a 10 X 10 mil2 boron-implanted n+-on-p Hg,,,C$.,Te photodiode with a cutoff wavelength of 9.0 pm, a quantum efficiency of 66%, and a &A product of 910 R cm2. The intercept of the straight line through the data points gave V,, = 130 mV, and the slope gave N A N D / ( N A + ND) = 3 x loi5 cmF'. [From Sood and Tredwell (1978a).]

(1978) suggested that compensation of the base acceptors by the implanted donor atoms may occur within a narrow range near the spacecharge region. c. Large-ArPa Implanted Photodiodes Laser tracking and guidance applications frequently require relatively large area detectors, on the order of 2 x 2-5 x 5 mm2, usually in a quadrant array form. Boron-implanted n-on-p large area Hg, -,Cd,Te photodiodes have been reported for use at 2.06 F m (Bratt, 1978), at 3.85 pm (Bratt and Vanderwyck, 1977; Bratt, 1978) and at 10.6 p m (Riley et al., 1978a,b). A summary of the performance data for these detectors is contained in Table 111. AH data are for T = 77 K unless otherwise noted. Pulse response times were measured with a GaAs laser, with effective load resistances of 20-50 a. As expected, response times were limited by the RC products and usually decreased with reverse bias. Spot scan uniformities of 2% to -C 6% over the active areas were obtained.

*

d. Gate-Controlled Hg,-,Cd,Te

Photodiodes

The use of insulated field plates to externally vary the surface potential in the vicinity of a p-n junction is a standard diagnostic technique for localizing and identifying surface leakage current mechanisms. The effectiveness of this technique in silicon technology has been well documented

TABLE I11 LARGE-AREA BORON-IMPLANTED n-on-p Hg,-,Cd,Te

cutoff wavelength ( pm)

Peak wavelength ( Pm)

Junction area A j (cm')

Zero-bias capacitance per unit area (KFlcm')

2.2-2.5

2.1 -2.4

0.0645

0.04-0.08

3.8-4.3 11.0-11.5

3.6-4.1 10.2-10.6

0.284 0.0115

0.015-0.02 0.01'

~

200-400 (V = 0) 140 =

-1.6

R dJ

Series resistance

(0cm-Z)

'Q)

Detectivity cm Hzl@/W

Reference

~

~

~

~

(V

All data are for T = 77 K unless otherwise noted. Bratt (1978). Bratt and Vanderwyck (1977). Riley et nl. (1978a). Estimated from smaller-area devices. With load resistances of 20-50 Q. Data for T = 192 K.

Zero-bias resistancearea product

Pulse response time' sec)

GIA, ~

~~~~~~~~~~

PHOTODIODE PERFORMANCE SUMMARY"

0.17-5.7

V)

100 35-110 (V = 0) 8 (V = -1.5 V)

X

104

(0.2-1.9 X 103)' 200-600 1.2-2.8

50-70

7 4.3

2.4-8.5

X

10"

(0.4-3.1 X lo''), 3-4 x 10" 3.5-4.6 X 10'O

h

b, c

d

268

M . B . REINE, A. K. SOOD, A N D T . J . TREDWE1.L

by Grove (1967) and others. It was discussed briefly in Section 4,c of this chapter. The insulated field plate has also been used to provide external control of the surface potential in high-impedance InSb and InAsSb infrared junction photodiode arrays. Leonberger et al. (1971) and Hurwitz et al. (1972) found that insulated field plates on proton-bombarded planar n-on-p InSb photodiodes could reduce surface leakage current considerably at 77 K. More recently, insulated field plates were used in a backside-illuminated impurity-diffused mesa p-on-n InSb hybrid 32 X 32 mosaic array (Hoendervoogt ut nl., 1978) and in backside-illuminated InAs,.,Sb,., 32 x 32 mosaic arrays (Tennant et a / . , 1979). The first experiments with gate-controlled Hg,,Cd,Te photodiodes were reported by Sood and Tredwell (1978) (see also Sood and Tobin, 1980). Their results for the R,A product versus temperature of a boronimplanted gate-controlled n+-on-p planar Hg, ,Cd,Te photodiode are shown in Fig. 32; a cross section of the device is also shown. A thin layer of ZnS insulated the evaporated field plate from the p region. For zero gate voltage, R& saturates with decreasing temperature to a value of about 2 0 cm2 at 77 K. Applying a positive gate voltage between the gate and the common p-side contact increased R,A at 77 K by two orders of magnitude; more positive gate voltage again caused RJ to decrease. The best explanation for these data seems to be that the bands in the p region just below the field plate are at or close to flat-band conditions at + 4.5 V , are inverted for less positive gate voltages, and are accumulated for more positive gate voltages. When the p side is inverted, there is more junction current due to g-r centers within the field-induced junction and due to interband tunneling transitions across the field-induced junction. When the p side is accumulated, there is more current due to interband tunneling across the field-induced junction between the n* and p' regions at the surface. Effects similar to those were also seen in experiments with boron-implanted n+-on-p gate-controlled Hgo.66Cdo,3,Tephotodiodes at 77 K by Gurnee et crl. (1979). The effect of gate voltage on the R d product can be seen more clearly in Fig. 33, in which the R,Aj product'at 40 K of a gate-controlled boron-implanted H&.,Cdo.2Tephotodiode is plotted versus p-side surface potential. This photodiode had a cutoff wavelength of 14.2 pm at 40 K and the same configuration as shown in Fig. 32. Conversion from gate voltage V , to surface potential cps was made by assuming a flat-band voltage of + 5.4 V, a p-side acceptor concentration of 2 x 10l6 and an oxide/insulator thickness of 0.6 p m . A strong decrease in R,A, occurs for both accumulation and strong inversion of the p-side surface, with an optimum gate voltage which just depletes this surface. Experiments on gate-controlled implanted n+-on-p mesa Hgo.,2Cdo.2sTe

6.

269

PHOTOVOLTAIC INFRARED DETECTORS

-

V=I.OV

pn/=

0-0-0

v =o

oYo 9 0 - 0 -

/O-

,

0

Y

0

o/o

In-2

6

7

8

9

10

II

I2

13

IM)O/T (K)-I

Fic. 32. R A product versus reciprocal temperature for a 10 x 10 mil2 gate-controlled boron-implanted n+-on-p Hg,,,Cd,,,Te photodiode with a cutoff wavelength at 80 K of 9.5 Frn, a p-side acceptor concentration of about 2 x 1OI8 ~ m - and ~ , a n-side donor concen~ m - Data ~ . are shown for various values of positive voltage V, aptration of about 1 x plied to the gate electrode. [From Sood and Tredwell (1978a); see also Sood and Tobin (1980).]

photodiodes have been reported recently by Kolodny and Kidron (1980). They employed an evaporated indium field plate which overlapped the junction at the surface. The insulator was ZnS. The flat-band voltage, as determined by C-V measurements between the field plate and the p-side common contact, was +4.5 V, which corresponded to a negative fixed charge density of about 3 x 10" electrons/cm2. They observed excess junction current for gate voltages on either side of the flat-band voltage, which they also interpreted in terms of tunneling current across fieldinduced junctions. e . Phntodiodrs with Reduced Diffusion Volumes

As discussed in Section 4,a of this chapter, reducing the volume of the p-side region in which diffusion current is generated should reduce the

270

M . B. REINE, A . K . SOOD, A N D T. J . TREDWELL

SURFACF POTENTIAL

'p,

(eV)

FIG.33. R d , product at 40 K versus gate voltage for a gate-controlled boron-implanted n-on-p Hgo.,Cdo,,Te photodiode. Conversion from gate voltage to surface potential was made assuming a flat-band voltage of +5.4 V, a p-side acceptor concentration of 2 x 1OI8 cm-3, and an insulator thickness of 0.6 prn. [From S . P. Tobin, J. W. Marciniec, and A . K . Sood (private communication).]

amount of diffusion current and should increase the photodiode R,,A product due to diffusion current. This reduction of diffusion current will occur only if the p region terminates in an electrically reflecting boundary. There have been two experiments to achieve this boundary in so far, one using an acceptor-implanted p + - p hi-lo junction Hg,,Cd,Te (Sood er al., 1979a,b,c) and one using the graded bandgap transition LPE layer and its CdTe substrate region between a p-type Hg,,Cd,Te (Lanir et a)., 1979b; Lanir and Shin, 1980). Data for the zero bias resistances at 145 K for linear arrays of n+-p-p+ Hg,,Cd,Te photodiodes with a tapered variation in the p-region thickness along the length of the array are shown in Fig. 34. The n+ regions were 3 x 5 mil2 in area and were formed by boron implantation.

6.

PHOTOVOLTAIC INFRARED DETECTORS

271

P-REGION THICKNESS ( u r n )

FIG.34. Zero-bias resistance at 145 K versus p-region thickness for five linear arrays of n+-p-p+ Hg,-,Cd,Te photodiodes formed by boron and phosphorous implantation. [From Sood et a / . (1979c).]

The common p+-p hi-lo junction, which also acted as a common p-side contact, was formed by phosphorous implantation. The solid lines in Fig. 34 are plots of Eq. (30) for /3 = 0 (i.e., perfectly electrically reflecting boundary):

with L, set equal to 25 pm and with chosen for each array to give the best fit to the data. The data do show a trend consistent with Eq. (135). However, two of the arrays show additional features which probably reflect variations in base material properties along the length of the arrays. The (&A),, values chosen to fit Eq. (135) are all lower than the best val-

272 HgCdTeICdTe INTERFACE

M . B . REINE, A . K . SOOD, A N D T. J . TREDWELL

p-n JUNCTION

FIG.35. Electron-beam-induced current (EBIC) scan of a boron-implanted n+-on-p H&.,Cd,,Te photodiode formed on a LPE layer grown onto a CdTe substrate. [From Lanir and Shin (1980).]

U 10 urn

ues reported for n+-on-p Hg,,Cd,Te photodiodes with thick p regions (cf. Fig. 27). Boron-implanted n+-on-pjunction photodiodes formed on relatively thin (10-30 pm) Hgo.,Cdo.,Te LPE layers on CdTe substrates have been reported by Lanir et (11. (1979b) and Lanir and Shin (1980). Electronbeam-induced current (EBIC) data for one of these devices at 200 K are shown in Fig. 35. These data were obtained by scanning a 20-keV electron beam across a cleaved surface perpendicular to the junction plane and the Hgo,,Cdo.,Te/CdTe interface plane. The p-type Hgo,,Cd,.,Te layer was grown from a Te-rich solution at a temperature around 500°C. The graded-bandgap transition region at the film-substrate interface was estimated to be less than 3 pm thick. The EBIC data of Fig. 35 indicate a minority-carrier diffusion length of around 60 pm in the p region. Electron-hole pairs created in the CdTe substrate do not contribute to the EBIC scan due to their short diffusion length of about 3 pm. By fitting the normalized EBIC profiles away from the interface region to an expression similar to Eq. (30). Lanir and Shin (1980) deduce a value for p in Eq. (29) of about 0.05 at 80 and 210 K for the Hg,,,Cdo,,Te/CdTe interface.

12. DIFFUSED PHOTODIODES Junction photodiodes have been formed in Hg, ,Cd,Te by diffusion of acceptors into n-type material, by diffusion of donors into p-type matenal, and by converting thin layers of p-type material to n-type (or from n-type to p-type) by appropriate annealing in a Hg atmosphere. Such anneals are believed to proceed by diffusion of Hg either into the sample to fill and thereby reduce the concentration of metal vacancy acceptor sites, or out of the sample to create metal vacancy acceptor sites. A layer of the sample at the surface will convert from p-type to n-type during Hg in-

6.

PHOTOVOLTAIC INFRARED DETECTORS

273

diffusion if the impurity donor concentration in the sample exceeds the impurity acceptor concentration and if the in-diffusion temperature and time are chosen so as to reduce the metal vacancy acceptor concentration below this level. Analogous arguments apply for Hg out-diffusion. Contrary to much earlier speculation, it does not appear that native donor defects play an important role at the concentration levels normally encountered in infrared detectors (Schmit and Stelzer, 1978; Vydyanath et af., 1979; Vydyanath, 1980). were The first p-n junction photodiodes reported in Hg,,Cd,Te n-on-p junctions formed in p-type Hg0.35Cd0.65Te with a native defect acceptor concentration of 2 x 1017 cmP3 by Hg in-diffusion (VCriC and Granger, 1965). Subsequently the formation of n-on-p junctions via Hg in-diffusion was reported in Hg,-,Cd,Te with alloy compositions of 0.15 < x < 0.28 (VtriC and Ayas, 1967), of x = 0.45 (Figurovskii et al., 1979), and of x = 0.2 (Cohen-Solal and Riant, 1971). The longestwavelength Hg, -,Cd,Te photodiodes reported to date were Hg indiffused n-on-p devices which had cutoff wavelengths at 4.2 K of 35 pm (x = 0.179) and beyond 48 pm (x = 0.171) (Melngailis and Harman, 1970b). There is very little information in the literature on diffusion of Hg in Hg,,Cd,Te. Spears (1977) reports forming an n-type region about 5 pm deep in p-type Hgo.,Cdo.,Te wafers (with a hole concentration at 77 K of about 2 X 1017cm-3) by a Hg anneal at 240°C for 30 min. For similar diffusion conditions, Shanley and Perry (1978a) estimate a junction depth of about 2 pm for p-type Hgo.,Cdo.2Teof comparable acceptor concentration. a.

Diffusion of Indium and Gold in Hgl-,Cd,Te

The diffusion properties of several impurities in Hg,,Cd,Te have been discussed by Johnson and Schmit (1977) (see also Schmit and Johnson, 1977). In this section we summarize some recent data on indium diffusion in Hg,-,Cd,Te and review some data on gold diffusion which have not been widely reported. Diffusion of indium into n-type Hg,.,Cdo.,Te was reported recently by Beck and Sanborn (1979). Films of indium were evaporated onto the 111B surfaces of n-type samples with donor concentrations of 2-3 x lo1, ~ m - ~ . This was followed by anneals at 71°C and 95°C for 1 h in a dry nitrogen atmosphere. The increase in donor concentration was measured via C-V measurements on MIS samples on a beveled surface. Their data for the net indium donor concentration following a l-h anneal at 95°C are shown in Fig. 36. The data fit reasonably well the conventional complementary error function distribution. Beck and Sanborn fit these data and data at

214

M . B. REINE, A . K . SOOD, A N D T . J . TREDWELL

Dl PIH 111 LOW SlJRFACC IPm)

FIG.36. Data for indium diffusion into n-type H&,,Cd,..,Te at 95°C for 1 h. The data point of 1.5 X is an extrapolated value. [From Beck and Sanborn (1979).]

71°C to the usual expression for the diffusion coefficient D: (136) Do exp(- E,/kT), and obtained a value of 1.6 eV for the activation energy E, and an estimate for Do of about 10l2cm2/sec. Margalit and Nemirovsky (1980) report diffusion data for indium into ern+ at 77 K) Hg,-,Cd,Te with x = 0.215 and p-type (about I x x = 0.29 for the temperature range of 70- 160°C. Their results for Do and Ea for In are given in Table IV along with the results of Beck and Sanborn. Some data on gold diffusion have been reported by Soderman (1970b) for Hgo.,Cd,,Te and by Timberlake and Soderman (1972) for HgJdo.pTe. Radioactive gold (atomic weight 199 with a half-life of 3.15 days) was deposited onto the surfaces of n-type samples from a gold chloride (AuCI,) electroless plating solution. The gold was diffused at a temperature of 275°C. Radioactive tracer analysis measurements were performed as material was successively lapped away to determine the gold concentration profile. The resulting profile for the x = 0.4 sample is shown in Fig. 37. A similar profile was obtained for the x = 0.2 sample. D

=

6.

27s

PHOTOVOLTAIC INFRARED DETECTORS

TABLE IV DATAON THE DIFFUSION OF I N D I U M Hg,-,Cd,Te alloy composition

Sample type and doping concentration

0.4

n-type; 2-3 x 1014cm-3 p-type; 1 x lOI5 c m P

0.215-0.29

(I

INTO

D O

(cm*/sec) 1

X

5.25

lox2 X

E, (ev)

Hg,-,Cd,Te Diffusion temperature range ("C)

1.6

lOI4

0.37

?

0.01

Reference

71 -95

a

70-160

6

Beck and Sanborn (1979).

* Margalit and Nemirovsky (1980).

I

o

:

1015

2

O

l

3 DISTANCE FROM SURFACF (mils)

FIG. 37. Data for gold diffusion into n-type H&,.,C&,,Te at 275°C as determined from radioactive isotope tracer analysis. [From Soderman (1970b).]

276

M . B. REINE, A. K . SOOD, A N D T. J . TREDWELL

The data were interpreted in terms of two diffusion mechanisms, one much faster than the other. The fast component was described by an exponential profile and was attributed to diffusion along dislocations. The slow component was interpreted in terms of a complementary error function profile as expected from Fick's law. From the slow diffusion data, diffusion coefficients of about cm2/sec for x = 0.4 and about 5 x cmz/sec for x = 0.2 were deduced. The slow diffusion component was attributed to out diffusion of mercury atoms and the subsequent filling of mercury vacancies with gold atoms. Scott and Kloek (1973) reported a diffusion coefficient of about loa9 cm2/sec for gold diffused into Hg,.,Cd,.,Te at 300°C with no mercury overpressure. They also observed that the rate of gold diffusion decreased strongly with applied mercury overpressure, indicating that the gold diffusion mechanism involves mercury vacancies. Additional data on gold diffusion in Hg,,,Cd,.,Te as well as on copper diffusion in Hgo.,Cdo,Te were reported by Andrievskii et al. (1974). Their experiments on n-type samples with carrier concentrations at 77 K of 2-7 x 10l6 cm" gave a diffusion coefficient D for gold at 300°C of 5.2 x lop9 cm2/sec. From data on anneals between 200°C and 450"C, they deduced an activation energy E, of 0.4 e V and a diffusion coefficient Do of 5.6 x cm2/sec. Their diffusions were done in a Hg atmosphere and diffusion depths were estimated from the p - n junction depth as measured by thermoelectric probing.

b. Wide-Bandwidth 10.6-pm Photodiodes The most important application of Hg in-diffused n-on-p Hg, ,Cd,Te photodiodes so far has been as wide-bandwidth 10.6-pm COz laser detectors. Verit and Sirieix (1972) first pointed out that the Hg in-diffused n--on-p Hg,,,Cdo.2Te photodiode was useful for COz laser heterodyne detection out to frequencies beyond about 1 GHz. This type of detector has been the subject of considerable developmental effort since then, both in single-element form with useful bandwidths out to 2 GHz (Spears et ul., 1973, 1974; Spears and Freed, 1973; Koehler, 1976a,b; Shanley et al., 1977; Shanley and Perry, 1978a,b) as well as in quadrant array form (Spears, 1977; Shanley and Hanagan, 1980) and in 12-element array form (Spears and Hoyt, 1978). A cross section of this photodiode is shown in Fig. 38. Initially, a mesa configuration was used for this type of device. The planar version with its greater versatility for arrays is now generally used. An insulator, usually ZnS, is evaporated or sputtered over the surface of a p-type Hgo.,Cdo.,Te wafer. Openings in the ZnS film are opened photolithographically to define the active areas. The wafer is then annealed in a Hg atmosphere with

6.

PHOTOVOLTAIC INFRARED DETECTORS

277

\Charge Region

Common p-Side Contact

FIG. 38. Cross section of the Hg in-diffused planar n--on-p photodiode configuration usually used for wide-bandwidth 10.6-pm C02 laser detectors.

the ZnS film acting as a diffusion mask. n-type regions approximately 2 - 4 p m deep are formed where the ZnS film has openings. p-type Hg,.,Cd,,,Te of fairly high carrier concentration, on the order of 1 X 10'' cmP, is generally used. The n-type regions formed usually have low carrier concentrations, on the order of 1 x 1015 cmP3or less, so that nearly all of the space-charge region occurs on the n-side. Hence, the donor concentration in this region determines the space-charge region width and the junction capacitance. For wide bandwidth, one wants low capacitance and hence low donor concentration. Donor concentrations down to 2.5 X 1014 cmP3have been reported in photodiodes of this type (Shanley et al., 1977). However, low donor concentrations in the n region also cause an appreciable series resistance. Since for wide bandwidth one also wants low series resistance as well as low capacitance, the surface of the n region is usually accumulated or given a shallow n+doping. Spears (1977) reported the use of a thin layer of indium placed over the p-type Hg,.,Cdo.,Te surface prior to Hg in-diffusion, which produced a n+ surface layer on the n- region. An additional advantage of the n+ surface layer is to provide a donor concentration gradient which in turn sets up an electric field in the n region. This electric field can assist transport of photogenerated holes to the space-charge region. I-V curves at 77 K for a wide-bandwidth n--on-p Hg,&do.2Te photodiode are shown in Fig. 39. The R& product of about 0.1 n cm2 is quite low compared with those obtained in implanted n-on-p photodiodes of the same cutoff wavelength (Fig. 28) and is believed to be due to surface leakage current. Capacitance versus voltage data at 77 K for this photodiode are shown in Fig. 40 and indicate an n-side doping concentration of about 4 x 1014cmP3.In the heterodyne mode, this device had a noise equivalent W/Hz, at a frequency of 1.75 GHz, which is only a power of 6.2 x factor of 3 above the quantum limit of 2 x lo-*, W/Hz given in Eq. (1 10).

278

M . B . REINE, A . K. SOOD, A N D T. J . TREDWELL

FIG.39. I-V characteristics for a Hg in-diffused planar n--on-p Hg,,,Cdo.,Te photodiode at 77 K. The cutoff wavelength is 11.5 p m , the quantum efficiency at 10.6 p m is 34%. the the forward resistance is 16 R, the zero-bias resistance is junction area is 1.8 x lo-' or, 775 R, and the heterodyne bandwidth is 2.0 GHz. [From Shanley and Perry (1978a).]

c . Hgl-,Cd,Te 10.6-pm Photodindes at High Temperatures

Hg, -,Cd,Te photodiodes designed for 10.6-pm operation with a thermoelectric cooler at temperatures of 170 K and higher have been reported by Koehler and Chiang (1975) and by Koehler (1976a,b). These n-on-p photodiodes were formed by diffusion of indium into p-type Hg, -,Cd,Te For these temperawith acceptor concentrations of 0.6-2 x lo'' 08

1.8

0.6

--

1.41

g y1

1.58

0.4

%

2

2 4

-

Y

n

N

1.82

5 0.2

9

?, 23

3.01

0

REVERSE-BIAS VOLTAGE (Vl

FIG.40. Reciprocal of the capacitance squared versus reverse-bias voltage at 77 K for a wide-bandwidth Hg in-diffused n-on-p Hg,.,Cdo,,Te photodiode with A, = 1.8 X lo-' cm2. The straight-line fit to the data gave values for Vb, of 70 mV and for NBof 4 x lof4c ~ n - ~ . [From Shanley and Perry (1978a).]

6.

PHOTOVOLTAIC INFRARED DETECTORS

279

tures and bandgap, diffusion current is the dominant junction current mechanism. These photodiodes had an active area diameter of 150 pm (Aj = 1.8 x lop4cm,). The best device had a reverse saturation current of 8.8 mA (50 A/cm2) at 174 K and a quantum efficiency of 21% at 10.6 pm. Measurements on this device in the heterodyne mode at 174 K gave a noise equivalent power at 10.6 pm and 10 MHz of 8 X W/Hz for an applied local oscillator power of 0.5-1 mW, as compared to the quantum limit of 2 x W/Hz at this wavelength. The bandwidth was 23 MHz, less than that anticipated from junction capacitance considerations, and was attributed to minority-carrier diffusion in the p region. The junction saturation current density Jsatof 50 A/cm2 at 174 K reported by Koehler (1976a,b) corresponds to, according to Eq. (80), an RJ product of 3 x R cm2, whereas the ultimate theoretical limit (Tredwell and Long, 1977) is around I x R cm2 at this temperature. There is still interest in a thermoelectrically cooled 10.6-pm Hg, ,Cd,Te heterodyne photodiode. Further development could reduce the junction saturation current so that the photodiode noise can be dominated by local oscillator noise for lower local oscillator power levels, thus reducing the heat load on the thermoelectric cooler. The same approaches which are being developed to increase the photodiode RJ product for direct detection applications are useful here also. These include the use of p-type Hg,-,Cd,Te with long minority-carrier lifetime and photodiode configurations with reduced diffusion volume. Bandwidths limited by p-side diffusion times with values on the order of 100 MHz ought to be achievable. From Eq. (1 17) the p-region cutoff frequency fo is about 270 MHz at 170 K for CY = 2000 cm-' and for an electron mobility equal to the value of 3 x lo4 cm2/V sec measured by Scott (1972) for low carrier concentration n-type Hgo.8Cdo.zTeat 170 K. Shanley et al. (1980) have reported CO, laser heterodyne measurements on boron-implanted n+-on-p Hg,,,Cdo.,Te photodiodes at temperatures up to 145 K. Their data show that this type of device is capable of achieving bandwidths of approximately 475-725 MHz at 145 K. Noise equivalent powers of 3.2 X W/Hz at 77 K and 1.0 x W/Hz at 145 K were reported. d. Wide-Bandwidth 1-2 p m Hg,-,Cd,Te Room Temperature

Photodiodes at

Among the first applications considered for Hg,-,Cd,Te photodiodes was room temperature detection of pulsed laser radiation in the 1-2 pm spectral region. The feasibility of this type of detector was shown by Kohn and Schlickman (1969) who reported photovoltaic contact effects in Hg,-,Cd,Te samples with an alloy composition of x = 0.58 and a peak

280

M . B. REINE, A . K . SOOD, A N D T. J . TREDWELL

. 2 h

3

10.0

r

:: z E: m

75% QUANTUM E F F I C I E N C Y

8 1 .o

40% QUANTUM I

1.O

I

EFFICIENCY I

2. 0

I

.1

3.0

WAVELENGTH OF PEAK SPECTRAL RESPONSE (urn)

FIG.41. Detectivity (A) and current sensitivity (Le., current responsivity) ( x ) for n+-on-p Hg,-,Cd,Te photodiodes at 300 K, plotted versus the wavelength of peak response. The curve through the detectivity data points is a smooth fit to the data. The curves through the current sensitivity data points are plots of Eq. (96) for values of quantum efficiency of 0.40 and 0.75. [From Sodermdn and Pinkston (1972).]

response wavelength of 1.45 p m at room temperature. Scott (1970) reported response times around 40 nsec for reverse-biased diffused p-on-n Hg,-,Cd,Te photodiodes with alloy compositions ranging between x = 0.32-0.55. Soderman (1970a,b) fabricated gold-diffused p+-on-n cm2 and Hg,-,Cd,Te mesa photodiodes with junction areas of 3-5 x with peak response wavelengths of 1.8-2.3 p m at room temperature. and These devices had noise equivalent powers of 1-5 x lo-'* W/& response times of 30-60 nsec at room temperature. Soderman and Pinkston (1972) fabricated 1-3 pm n-on-p and p-on-n Hg, ,Cd,Te photodiodes by several different methods (impurity diffusion, alloying and proton bombardment); their data are shown in Figs. 41 and 42. The junction areas were about 5 X cm2. The response times

6.

PHOTOVOLTAIC INFRARED DETECTORS

281

t

'$

E

\Rd

I

E-

101

t-

I

I

1

I

2

Ap (,urn)

FIG.42. Junction resistance Rd (A) and junction capacitance C, ( X ) at zero-bias voltage for n+-on-p Hg,,Cd,Te photodiodes at 300 K , plotted versus the wavelength A, of peak response. The dashed curves are smooth fits to the data. [From Soderman and Pinkston ( 1972) .]

obtained for some of these devices at room temperature were approximately 20 nsec and were limited by the RC product and preamplifier bandwidth. With a very broadband preamplifier, the pulse response was limited to 0.5 nsec and a secondary time constant of about 5 nsec was attributed to carrier transit time. Probably the largest difficulty in developing Hg,-,Cd,Te photodiodes with peak spectral response wavelengths less than 2 pm has been the high mercury vapor pressures involved in conventional bulk growth of crystals from pseudobinary melts. [Crystal-growth techniques for Hg,-,Cd,Te have been reviewed recently by Nelson et al. (1980)l. For example, a cutoff wavelength of 1.5 pm corresponds to an alloy composition of x = 0.64. The liquidus temperature increases with alloy composition, being around 760°C for x = 0.2 and around 950°C for x = 0.6. Mercury vapor

282

M. B. REINE, A. K. SOOD, A N D T. J. TREDWELL

pressure increases exponentially with temperature to the point where conventional bulk crystal growth becomes quite difficult for material of wavelength less than about 2 p m . The use of liquid phase epitaxial (LPE) growth of Hg,-,Cd,Te from ternary melts (either Hg- or Te-rich solutions) overcomes these difficulties by allowing growth films at significantly lower temperatures (Mroczkowski and Vydyanath, 1980; Bowers et al., 1979, 1980; Schmit and Bowers, 1979). One would expect that LPE grown layers would be utilized in further development of 1-2 pm Hg,-,Cd,Te photodiodes. Piotrowski (1977) has reported data for Hgand acceptor-diffused Hg,-,Cd,Te photodiodes, fabricated on epitaxial graded-gap Hg,,Cd,Te layers grown on CdTe substrates, with peak response wavelengths down to 1.0 pm at room temperature. Fabrication TEMPERATURE IKI

300

lo8

I

250

170

200

I

I

I

150

125

I

110

-

I

/

5

N-

/

lo5k

/

I

in

I 2

10 I I 3

I 4

I

I

I

I

5 6 1WOiT IK-’I

I

I I 1

I

I 8

FIG. 43. RJ products versus reciprocal temperature for a 23-element planar Hg,,,C&.rrTe array. Element area was 4.5 X 4.5 mil2 (1.3 X lo-’ cm2), cutoff wavelength was 2.15 p m , and the zero-bias capacitance was 6 pF. [From Tredwell (1977).] The solid, nearly horizontal lines are calculated from Eq. (101) for A = 2 p m and 7) = 0.5.

6.

PHOTOVOLTAIC INFRARED DETECTORS

283

of p-n junctions in epitaxially grown Hg,-,Cd,Te has also been reported by Becla and Pawlikowski (1976) and by Pawlikowski and Becla (1975). Magnetic quantum oscillations in the photovoltaic response spectra of such n-on-p epitaxially grown Hg, -,Cd,Te junctions have been reported by Dudziak et al. (1978). Data for Hg-diffused n-on-p planar arrays of Hg,-,Cd,Te photodiodes with cutoff wavelengths between 2.0-2.3 pm have been reported by Tredwell (1977) for lower frequency applications. Data for a 23-element array with a cutoff wavelength of 2.15 pm are shown in Fig. 43. Junction zero-bias capacitances were about 6 pF, corresponding to a value for C,,/Aj of about 0.05 pF/cm2. In many of the devices, the reverse-bias breakdown mechanism involved an avalanche process; avalanche multiplications as large as 30 were observed in the photocurrent at large reverse bias. 13. TYPECONVERSION I N Hg,-,Cd,Te

BY

OTHERTECHNIQUES

a. Electron Irradiation of Hg,-,Cd,Te

High-energy electron irradiation is not a useful technique for p-n junction formation because the range of electrons is quite large. For example, the range of 2.5-MeV electrons in Hg,-,Cd,Te is about 1.2 mm. Electron irradiation studies are important, however, in that they give information devices and on the hardness (i.e., radiation resistance) of Hg,,Cd,Te they can be helpful in understanding the behavior of lattice defects in Hg, -,Cd,Te. Radiation hardness experiments on Hg, ,Cd,Te have recently been reported by Kalma and Cesena (1980). The effects of high-energy electron irradiation on the electrical and optical properties of Hg, -,Cd,Te have been studied by Melngailis er al. (1973) for initially p-type samples at about 8 K, by Mallon et al. (1973, 1975) for initially n-type samples at 10 and 80 K, and recently by Voitsehovski et al., (1979) for both initially n-type and initiallyp-type samples at 300 K. These experiments are summarized in Table V. In all cases, electron irradiation produced donor defects which were easily annealed out. Melngailis et al. (1973) found that the electrical properties of the irradiated samples could be restored to their initial values by annealing, and that most of the changes anneal out at temperatures around 55-75 K. They found a donor introduction rate at about 8 K of 28 cm-' for an initially p-type H&.,,Cdo.22Te sample. They found that electron irradiation broadened and shifted to longer wavelengths the photoluminescence spectrum at 8 K of an initially p-type Hg,,,,Cdo.31Te sample, and that most of these effects seem to anneal out at temperatures between 106-231 K. Similar behavior was reported by Mallon et al. (1973, 1975) in their

TABLE V

ELECTRON IRRADIATIONEXPERIMENTS IN Hg,-,Cd,Te Sample Maximum temperature Reirradiation Donor Electron electron during Preirradiation carrier Preirradiation introduction energy dose irradiation electrical Alloy concentration" mobility" rateb (cm-l) (MeV) (cm-2) type ( ~ r n - ~ ) (cm-*/v sec-I) composition (K) 2.5 5 5

5 2

4.7 x 1015

s

x

1014

4x

1014

8.5 x 1014 2 x 1018

25

P

2.5 x 10l6

780

P

4 x 10'6 2.6 x 1014 1.3 x 1015

300

80

n

10, 80

n

80

n

300

P P

n n n a

5.8 x 1014 1.5 x 1015

6 X IOl3 2.7 x 1OI6 9.6 x lOI6 1.7 x 10'5

117 2.5 x 104

1.2 x 1015 2.6 x 1015

2 x 104

Based on 80-K Hal! data. Measured at the temperature of sample irradiation.

322

1 x 105

0.22

0.3 I

0.188 0.20 0.20 0.26 0.26 0.24

0.26 0.28

28 -

5.7 16 (10K) 6 (80 K)

Reference Melngaiiis ef a / . (1973) Mallon et al. (1973) Mallon ef al. (1975) Leadon and Mallon (1975) Brudnyi er al. (1977)and Voitsehovski et al. (1979)

6.

PHOTOVOLTAIC INFRARED DETECTORS

285

experiments on low carrier concentration n-type Hg,,,Cd,.,Te samples at 10 K and 80 K. They reported donor introduction rates of about 16 cm-' at 10 K and 6 cm-l at 80 K. Anneals up to 340 K caused a nearly complete return of the irradiated sample electrical properties to their preirradiation values. They also found (Mallon et a f . , 1975) that gamma irradiation and high-energy neutron irradiation created donor defects which behaved the same as those produced by electron irradiation. The electron irradiation experiments of Voitsehovski et a f . (1979) were performed with the Hg,,Cd,Te samples at a temperature of 300 K during irradiation. For electron doses up to about 2 x lo1* cm-2, the initially n-type samples showed no significant change in carrier concentration. The initially p-type samples, however, converted to n-type at a dose of 5-8 x 10'' ~ m - These ~ . donor defects annealed out within the 360-430 K temperature range.

6. Sputtered H g , ,Cd,Te

Photodiodes

The growth of polycrystaline Hg,-,Cd,Te films onto either CdTe or Hg,-,Cd,Te substrates by means of triode sputtering in a mercury plasma has been reported by Cohen-Solal et al. (1974, 1976) (see also Zozime et target was cooled during sputtering. The a f . , 1975). The Hg,,Cd,Te CdTe or Hg,-,Cd,Te substrates were heated during sputtering in the 50-250°C range. The Hg,,Cd,Te films were doped either p or n during growth by cosputtering from either a gold or an aluminum target. Both p-on-n and n-on-p junction photodiodes were formed by sputtering the doped Hg, ,Cd,Te films onto substrates of the opposite conductivity type. Cohen-Solal et a f . (1974, 1976) report a value of 1.8 fl cm2 for the R d j product at 77 K of a sputtered p-on-n photodiode with a cutoff wavelength of 12.0 pm, which compares favorably with those obtained in implanted junctions (cf. Fig. 28). c. Junction Formation by Pulsed Laser Irradiation

The use of pulsed laser radiation to form p-on-n junctions in n-type Hg,,Cd,Te was reported by Lutsiv et al. (1978). Their starting material was n-type Hg,-,Cd,Te with x = 0.20-0.25 and with carrier concentrations at 77 K of 1-3 x IOl5 cmP3and mobilities of 1-2 x lo5 cm2/V sec. Samples were mounted on a heat sink in an evacuated ampoule during irradiation from either a ruby (0.694 pm) or neodymium (1.06 pm) laser. p-type surface layers about 10-30 pm deep were formed with laser intensities low enough to cause no visible surface damage. They postulate that the p-type surface layers result from metal vacancy acceptors which are formed when the laser pulse heats the sample surface to temperatures of about 500-600°C and which are subsequently quenched in during the

286

M. 9. REINE, A. K. SOOD, A N D T. J . TREDWELL

rapid sample cooling. Not enough information is given to assess the quality of the junctions formed, but the spectral response data show evidence of significant surface recombination effects. 14. MINORITY-CARRIER PROPERTIES OF

TYPE Hg,-,Cd,Te

The considerable interest in ion-implanted and diffused n-on-p Hg,-,Cd,Te photodiodes has focused both experimental and theoretical attention on the properties of p-type Hg,-,Cd,Te, particularly with respect to minority-carrier lifetime mechanisms. As discussed in Section 4,a of this chapter, the minority-carrier properties of the p region determine the diffusion current and the R,A product of 3-5 pm n-on-p photodiodes at temperatures above about 170 K and of 8-12 p m n-on-p photodiodes at temperatures above about 77 K. It is standard practice to characterize infrared photodiodes by measuring their I-V curves and R, versus temperature. But it is difficult to compare R,(T) to, say, Eq. (20) and then deduce values for the minority-carrier lifetime and mobility. One can at best get only the T e / p , ratio. But even this has considerable uncertainty, since the deduced value of 7,/pe depends on on It: and on N i , and usually ni and N , are not known accurately enough in a given photodiode to give appreciable confidence in the values of ~ ~ so /ob- p tained. In order to determine the minority-carrier properties of p-type Hg, -,Cd,Te, several techniques which have proven useful in widebandgap semiconductor technology have been applied. Measurements of the minority-carrier lifetime in p-type Hg, -,Cd,Te have been performed on implanted it+-on-p photodiodes by means of the reverse-bias step recovery technique. The electron-beam-induced current (EBIC) technique has been used with n+-on-p photodiodes to measure the minoritycarrier diffusion length in p-type Hg,-,Cd,Te. Recently the technique of deep-level transient spectroscopy (DLTS) has been used with implanted It+-on-p photodiodes to provide some information on trap energies, concentrations and emission rates in p-type Hg, -,Cd,Te. Nearly all minority-carrier lifetime data taken so far has been interpreted in terms of Shockley-Read recombination involving one or more deep levels within the forbidden energy bandgap. However, recent theoretical work by Casselman and Petersen (1979, 1980), which is discussed by Petersen in this volume and in Section 10 of this chapter, has shown that an Auger hole-hole collision process involving both the light- and heavy-hole valence bands may be an important recombination mechanism in p-type Hg, ,Cd,Te. There has been no reported experimental confirmation of this mechanism so far.

~

6.

PHOTOVOLTAIC I N F R A R E D DETECTORS

287

a . Electrical Properties The electrical properties of p-type Hg,-,Cd,Te with alloy compositions in the semiconductor range 0.21-0.60 have been studied by Elliott et al. (1972) and by Scott et al. (1976). Unlike n-type Hg,-,Cd,Te, for which no evidence of donor freezeout has been reported, p-type Hg,-,Cd,Te generally shows appreciable acceptor freezeout at low temperatures. From Hall data and photoluminescence data on p-type Hgo.,Cdo.3Tesamples with net acceptor concentrations around 3 X 10l6 cmP3, Elliott et a/. (1972) concluded that there existed a singly ionized acceptor level with an activation energy on the order of 20 mV. From Hall data together with far infrared photoconductivity and transmission data, Scott et al. (1976) report an acceptor activation energy for p-type Hgo.,Cdo.,Te samples of about 14 meV for net acceptor concentrations around 3 x 1015~ m - the ~; activation energy decreased with increasing net acceptor concentration and was about 3-4 meV for N A - N D = 1 x 10'' cmP3. Photoluminescence and cathodoluminescence data for both n-type and p-type HgO,,Cdo.,Tecrystals have been reported by Ivanov-Omskii et a/. (1978). Samples of both types showed an impurity luminescence band about 15 meV lower than the intrinsic (i.e., band-to-band) luminescence band. The impurity luminescence band was attributed to transitions from the conduction band to Hg vacancy acceptor levels located about 15 meV above the top of the valence band. It is interesting that evidence has been found for an acceptor level with similar properties in n-type H&.,Cdo,3Te. In experiments with n-type H&.,Cdo.,Te samp!es at 16 K with carrier concentrations of 2-5 x 1014 ~ m - Andrukhiv ~, et a/. (1979) report a photoluminescence peak which is shifted by about 18 meV below the band-to-band recombination peak. They interpret the peak as being due to transitions from the conduction band to an acceptor level lying about 18 meV above the top of the valence band. Data on the acceptor activation energies in p-type Hgo.,Cdo.,Te have only recently become available. In the past, difficulties were frequently encountered with n-type surface inversion layers on p-type Hg0.,Cdo,,Te samples of low to moderate acceptor concentrations which dominated the low-temperature Hall data (Scott and Hager, 1971; Wong, 1974). The recent data? in Fig. 44 on gold doped p-type H&.,Cdo.,Te samples show no evidence of such inversion layers, even for doping concentrations as low as 3.5 x lOI5~ m - From ~ . these data Bratt et al. deduced an acceptor actit Private communications from P. R. Bratt, K . J. Riley, and A . H. Lockwood.

288

M . B. REINE, A. K . SOOD, A N D T. J . TREDWELL

2w

102

I 104€-r t

50

40

30

20

I

I

I

I

1IT ( K - ' )

FIG.44. Hall coefficient (a) and mobility (b) versus reciprocal temperature for three gold-doped p-type Hgo.,Cdo.zTesamples of different net acceptor concentrations N A - N D : 0, 2 x 10l8 cmV3;A,6 x loLscmP; 0 , 3.5 x loL5~ m - The ~ . magnetic field was 1000 G. [From P. R . Bratt, K . J. Riley and A. H. Lockwood (private communication).]

6.

PHOTOVOLTAIC INFRARED DETECTORS

289

vation energy of about 10 meV. Tobin et a1.t obtained a value of 13 meV for the acceptor activation energy in p-type Hgo.,Cdo.,Te with N A - N D = 5 x 1015cm-3 from an analysis of the series resistance of boron-implanted photodiodes at temperatures below 30 K. b. Minority-Carrier Lifetime

Minority-carrier lifetime in implanted n+-on-p Hg, ,Cd,Te photodiodes has been measured for alloy compositions in the range 0.2-0.4 by the reverse-bias step recovery technique. The technique consists of abruptly switching a forward-biased n+-on-p junction into reverse bias and observing the transient current response. The technique is based on the analysis of p - n junction switching transients which was originally performed by Kingston (1954) and by Lax and Neustadter (1954) and later reformulated by Kuno (1964). The applicability of the technique for determination of minority-carrier lifetime has been recently discussed by Tobin (1979).$ In reverse-bias pulse recovery experiments on implanted n+-on-p photodiodes fabricated from p-type Hgo.,Cdo.,Te samples with net acceptor concentrations in the range 0.1-3 x 10l6 cmP3, Tobin (1979) found that the lifetime data could be explained by a single Shockley-Read recombination level at 140 meV above the top of the valence band. In p-type material, the net Shockley-Read recombination rate per unit volume from Eq. (39) is approximately

U

= h / T , =

An/Tno[l

+ pl/pO].

(137)

Setting

(138)

P o = N v exp(-EF/kT)

gives the following approximate expression for

T~ :

Data for 7, versus temperature are shown in Fig. 45 for a n+-on-p Hg0.61Cd0.39Te photodiode with a net acceptor concentration of 1.4 x lOI5 in the p region. The data agree well with Eq. (141) with E, = 140 meV and T,, = 90 nsec. Data for T , at 295 K determined via reverse-bias step recovery for n+-on-p Hg,.61Cdo.39Tephotodiodes are shown in Fig. 46 plotted versus t Private communication from S. P. Tobin, J. W. Marciniec, and A. K. Sood. t Tobin's work is also contained in Schmit et al. (1979) and is summarized in Tobin and Schmit (1979).

290

M . B . REINE, A. K . SOOD, A N D T . J . TREDWELL

FIG.45. Reverse-bias step recovery lifetime data versus reciprocal temperature for a boron-implanted n’-on-p Hgo,,,Cdo.3sTephotodiode with a net p-side acceptor concentration of 1.4 x lOl8 cm+. The maximum minority-carrier density An injected into the p region was about 2 x C I I - ~ . Lifetime was deduced from the measured data via the method of Kingston (1954). The upper curve is the calculated radiative lifetime and the curve through the data represents a Shockley-Read model. [From Tobin (1979).]

net acceptor concentration or, equivalently, hole concentration p o since po = N A - N Dat room temperature. Also, EF> Et at room temperature so that p1 >> p o . Hence the p ;I dependence shown by the data of Fig. 46 is to be expected from Eq. (139). At low temperatures, T~ = T,, which, according to Eq. (42) should vary as N ; ' . In fact the data for T, at low temperature did show roughly a N;l dependence on acceptor concentration, which led to the conclusion that the concentration N t of Shdckley Read centers was proportional to the acceptor concentration NA. As shown in Fig. 46 most of the Hgo.,,Cdo.39Te samples used in this study were p type due to native defect (metal vacancy) acceptors. Riley ~t a / . (1978a,b) have reported lifetime data for acceptor-doped p-type Hgo,,zCdo.zeTesamples measured via photoconductivity decay resulting from a GaAs laser pulse. They claim that the lifetime mechanism in their samples is due to Shockley-Read centers. They find that the lifetime T~ over the temperature range for which the material is extrinsic

6.

PHOTOVOLTAIC I N F R A R E D DETECTORS

291

An = o

FIG.46. Summary of reverse-bias step recovery lifetime data at room temperature versus net acceptor concentration for boron implanted n+-on-p Hg,,,Cd,,,,,Te photodiodes. The solid curves are the calculated radiative lifetimes for two values of injected minority-carrier density An. 0, quench/anneal material doped by stoichiornetry; A,quench/anneal material doped by copper: 0, zone-leveled material doped by stoichiometry. [From Tobin (1979).]

varies with acceptor concentration as re = 2 x 1024/Ni,

( 140)

for samples with N A between 6.5 x loi4 ~ r n and - ~ 3.1 x 1015~ m - Note ~. that this corresponds to measured lifetimes of about 2 psec at 77 K for N A = 6.5 x 1014 ~ r n -and ~ about 0.3 psec at 77 K for N A = 3.1 x 1015

~rn-~. Minority-carrier lifetime data obtained via the reverse-bias step recovery technique for boron-implanted Hg,,,Cd,,,Te photodiodes have been reported by Polla (1979) and by Sood et al. (1978a, 1979a,c; 1980). Data for an alloy composition x = 0.234 are shown in Fig. 47. The solid curve is a plot of Eq. (141) with Et = 56 meV. The reverse-bias step recovery technique has been used with both n-on-p Hg,-,Cd,Te photodiodes and with Schottky barrier photodiodes on p-type Hg,-,Cd,Te with alloy compositions in the range x = 0.2-0.4.

292

M. B. REINE,

A . K . SOOD, A N D T . J . TREDWELL

Shockley-Read Et = 56 meV

-

1

6

8

10 lWOlT ( K - l l

12

FIG.47. Reverse-bias step recovery lifetime data versus reciprocal temperature for a boron-implanted n+-on-p Hg,.77Cd,,.rsTephotodiode with a cutoff wavelength of 8.4 p m at 80 K and with an estimated p-side acceptor concentration of 1-4 X 1 O I g The upper curve is the calculated radiative lifetime and the lower curve through the data represents a Shockley-Read mechanism. [From Sood et a / . (1979a).]

In nearly all cases the data for lifetime versus temperature can be reasonably well fit by Eq. (141). The values of the Shockley-Read energy levels Et so obtained are summarized in Fig. 48. Also plotted is the energy gap E J x ) for different temperatures (Schmit and Stelzer, 1969). From studies of photoconductivity in n-type Hgo.8Cdo.zTe,Kinch et a f . (1973) reported a Shockley-Read recombination level at an energy of about 30 meV above the top of the valence band in certain samples. This value agrees quite well with the data shown in Fig. 48. The samples in Kinch's work generally had carrier concentrations less than 4 x 1014 and Hall mobilities at 77 K less than 1 x lo5 cm2/V sec which, for an alloy composition of x = 0.2, could mean that these samples were actually p type with inverted surfaces (Scott and Hager, 1971; Wong, 1974).

c . Minority-Carrier Dufusion Length Use of the electron-beam-induced current (EBIC) technique for directly measuring the minority-carrier diffusion length in implanted n+-on-p Hg,-,Cd,Te photodiodes has been reported by Lanir er al.

6.

PHOTOVOLTAIC INFRARED DETECTORS

293

FIG. 48. Summary of the Shockley-Read trap energies Et as determined for p-type Hg,-,Cd,Te by measurements of reverse-bias step recovery lifetime versus temperature for n+-on-p junctions 0, 0 , [from Tobin (1979); Sood and Tredwell (1978a); Sood et al. (1978a)l and Schottky barrier photodiodes A [from Polla and Sood (19SO)l. Also shown is the energy gap Eg for 77 and 300 K as calculated from Schmit and Stelzer (1969).

(1978a,b, 1979a,b), by Polla (1979), by Tobin (1979), and by Iverson (1979). In this technique, a scanning electron microscope is used to generate electron-hole pairs near the junction and the electron-beam-induced current in the junction is measured as a function of the distance between the electron-beam spot and the junction edge. Under appropriate conditions, the electron-beam-induced current varies exponentially with the separation between the beam spot and the junction edge, with the characteristic length being the minority-carrier diffusion length L, . An EBIC image of the photodiode can be obtained by operating the scanning electron microscope in the scanning mode and letting the electron-beam-induced junction current modulate the intensity of the CRT display. This is sometimes useful for junction diagnostics. An EBIC photodiode at about image of a boron-implanted d - o n - p Hg, ,Cd,Te 80 K is shown in Fig. 49. The implanted junction area is 0.025 x 0.025

294

M. B . REINE,

A.

K. SOOD, A N D T. J. TREDWELL

FIG.49. Electron-beam-induced current (EBIC) image of a boron-implanted n+-on-p H&.8Cdo.zTephotodiode at 80 K. The implanted junction area was 10 x 10 mil2. (Courtesy of R . P. Murosako and D. L. Polla.)

cm2.The lead bonded to the center of the n+ region is evident. The bright annular region around the n+ region is about a diffusion length L, wide and shows the largest EBIC response. The n+ region is less bright, possibly due to higher recombination rates. Minority carrier diffusion length data obtained by Tobin (1979) via the EBIC technique for a boron-implanted Hg,,,,Cdo.,,Te photodiode are shown in Fig. 50. The p-region net acceptor concentration was 1.4 x loi5

0 1 1 1 70 80

1

I

I

I

I

100

140

180

2T'

260

d

31111

TEMPERATURE IKt

FIG.50. EBIC p-side diffusion length data versus temperature for the boron-implanted [From Tobin d - 0 n - p Hgo,,Cd,,,,Te photodiode of Fig. 45. N , - N D = 1.4 x l O I 5 (1979).]

6. lo5

295

PHOTOVOLTAIC I N F R A R E D DETECTORS

-

-

-

-

-P

SCOTT'S DATA:

-

>

\

MAJORIW-CARRIER MOBILITY in n-type

-5 t_

=

0"z

6E

k! Y

CALCULATED AMBIPOLAR

lo4

-

-

MINORITY-CARRIER MOBlLlW, colculoted

from

m e o w e d L, and Te

I

lo3. 10

I

1

I

1

I l l 1 100

I

, lo00

TEMPERATME (K)

FIG.51. Electron mobility in p-type H&.,,Cd,,,,Te as deduced from measured values for L, (Fig. 50) and T, (Fig. 45) (light solid line). Data for the electron mobility in n-type Hg,-,Cd,Te are indicated by the heavy solid lines (Scott, 1972). The dashed line is the effective mobility calculated from Eq. (144). [From Tobin (1979).]

~ m - The ~ . minority-carrier lifetime data versus temperature for this photodiode were given in Fig. 45. From the data for L, and 7, Tobin (1979) was able to compute the minority-carrier mobility pefrom the relationship Le = d ( k T / e ) PeTe

7

(141)

and compare p,,(T) determined in this way with the data of Scott (1972) for the majority-carrier mobility in n-type Hg,-,Cd,Te. This comparison is shown in Fig. 51. The solid curves are taken from Scott's data for n-type Hgo.5,Cdo.41Teand Hgo.64Cdo.3aTe samples with electron carrier ~ . dashed line is the calculated concentrations less than 2 x 1015~ m - The effective mobility pa in p-type Hgo.61Cdo.39Te calculated from (Smith, 1978, p. 194)

( n + p ) / [ ( n / ~ J+ ( p / ~ e ) I , (142) where p,(T) was extrapolated from Scott's data, p h was taken as 200 cmZ/V sec, N A was taken as 1.4 x 1015 and where n(T) = n f / p ( T ) . Agreement between pa(T) as calculated from Eq. (144) and pe(T)as deduced from data for L,(T) and T J T )via Eq. (143) is quite good for temperp a

=

296

M. B. REINE,

A . K . SOOD, A N D T . J .

TREDWELL

atures above about 170 K. Below 170 K there is significant disagreement with p, at 77 K being about a factor of 4 too low. This could be due to surface recombination affecting the values of L, measured via EBIC at the lower temperatures. However, excellent agreement between Scott’s mobility data and the mobility deduced via Eq. (143) from measured values for L, and 7, was obtained over the 77-300 K range for a sample with a somewhat higher acceptor concentration of 4.3 x 1015 cm-3 (Schmit et d,, 1979). EBIC data for L, taken on boron-implanted n+-on-p Hg,.,,Cd,.,,Te photodiodes of various net p-side acceptor concentrations are shown in Fig. 52. Data for L, at 195 K follow generally a (NA-ND)pl’z dependence, which which would be expected from Eq. (143) if 7, varies as (ZVn-ZV,J1, it generally did at 195 K in these photodiodes. Diffusion length data obtained via EBIC for a boron-implanted n-on-p Hg,,.mCdo.,2Tephotodiode were reported by Lanir er al. (1978a,b). They scanned a cleaved surface that was perpendicular to the junction plane. For a base acceptor concentration of 1 x lo1‘~ m - they ~ , report values for L, of 65 pm at 210 K and of 106 p m at 90 K. EBIC measurement of L, in a boron-implanted n+-on-p Hg,-,Cd,Te photodiode with a cutoff wavelength of 9.5 pm at 77 K have been reported by Polla (1979). For a sample at 81 K, he reports a value for L, of 45 pm. The base acceptor concentration was estimated to be around 1 x 1OI6 cmp3,

,,

I

FIG.52. EBIC data for L, taken on boron-implanted n+-on-p Hgo.,,Cdo,,,Te photodiodes of various p-side acceptor concentrations. 0,T = 195 K; A, T = 77 K . [From Tobin (1979).]

6.

PHOTOVO LTAIC INFRARED DETECTORS

297

d. Deep-Level Transient Spectroscopy Studies The deep-level transient spectroscopy (DLTS) technique (Lang, 1974a,b) has been used extensively in recent years for studying the nature and behavior of various impurity centers in elemental and compound semiconductors. Its application to the study of impurity centers in GaAs and GaP has been discussed by Lang and Logan (1975). In a recent article, Miller et al. (1977) summarized recent advances in the technique itself and discussed briefly the results obtained on impurity centers in 111-V compound semiconductors. In 11-VI compounds, there has also been some recent work on the study of impurity centers in CdTe by Legros et al. (1978) using the thermally stimulated capacitance measurement technique. The first use of the DLTS technique in narrow-bandgap semiconductors has been on Hg,,Cd,Te and was reported recently by Polla and Jones (1980). They investigated impurity centers in p-type Hg,-,Cd,Te with ion implanted n+-p junctions and showed the presence of a deep recombination center in p-type H&.,,Cd,,,,Te. Their data suggest the presence of an electron trap approximately 0.049 eV above the valence band, which is in excellent agreement with the Shockley-Read level energies determined by reverse-bias pulse recovery lifetime measurements (cf. Fig. 48). The DLTS technique appears quite promising for measuring the position, nature and concentration of various hole and electron traps in the Hg, ,Cd,Te semiconductor alloy system. Understanding and identification of these impurity states will help in improvement of the electronic properties of Hg,,Cd,Te (such as lifetime and diffusion length) and hence will lead to improved device performance. 15.

NOISE

IN

Hg,,Cd,Te

PHOTODIODES

A study of llfnoise in implanted n+-on-p Hg,,Cd,Te photodiodes has recently been reported by Tobin et al. (1980) (see also Gurnee et al., 1979). By measuring l/f noise while varying background photon flux, temperature, reverse-bias voltage, and the potential applied to an insulated gate electrode, they showed that the llfnoise was independent of both photocurrent and diffusion current, but was linearly proportional to surface leakage current. Moreover, they showed that the rms llfnoise current I,,,, as a function of measurement frequency f,reverse-bias voltage V, applied gate voltage V, and temperature T was given by the following relationship: (143) ~ zn,ex(f,v,vg ,T) = [ ~ e x ~ s ( v ~ v g ~ ) / d ~ ~ W where Z, (V,V,,T) is the photodiode surface leakage current, which does

298

M. B. REINE,

A.

K. SOOD, A N D T. J . TREDWELL

depend strongly on reverse-bias voltage, gate voltage, and temperature, and where the dimensionless coefficient aeXhad a value of about 1 x lop3 for all photodiodes measured in their study. In Eq. (145) Af is the noise bandwidth which is assumed small compared to$ Their results on the effects of photocurrent and reverse-bias voltage can be understood with reference to Fig. 53 which shows schematically the I-V curves of a photodiode in the dark and with illumination. In thermal equilibrium (point A) no llfnoise was observed down to frequencies of 0.1 Hz. When the photodiodes were illuminated but kept at zero-bias voltage (point B), the total photodiode noise current increased by an amount 2eZphdue to the added shot noise in the photocurrent Zphbut no llfnoise was observed. When the photodiodes were reverse biased without illumination (point C) so that a reverse current comparable to Zph flowed, l/f noise was usually observed. However, when the reverse-biased photodiodes were illuminated (point D), no additional l/f noise was observed. These results showed that llfnoise was not simply related to the total current in the photodiode, but depended on the mechanism by which the current was generated. Thus they were able to rule out the metalsemiconductor contacts and current flow through the quasineutral regions and the space-charge region of the photodiode as mechanisms for l/f noise.

k-”o

Current

Illuminated

B

FIG. 53. I-V curves for a photodiode in the dark and with a net photocurrent -Iph flowing due to illumination. No llfnoise was observed when the photodiode was at points A (thermal equilibrium) and B. llfnoise was observed at points C and D, and its magnitude was independent of Iph.[After Tobin cr al. (198Q.l

6.

PHOTOVOLTAIC INFRARED DETECTORS

10-'0

IO-~

10-8

299

lo-'

DARK CLJRHFNT AT 50-mV REVERSE RlAS ( A )

FIG. 54. I/f noise current plotted against dark current for a reverse-biased n+-on-p H&.,C&,,Te array at temperatures between 83-160 K. In this temperature range, the dark current was due to a surface leakage mechanism. The straight line has a slope of unity. 0 , 83 K; 0, 100 K; A, 120 K ; 0,140 K ; 0,160 K. [From Tobin et a / . (1980).]

Figure 54 shows the Ilfnoise current plotted versus dark current, both measured at a reverse-bias voltage of - 50 mV, for an implanted n+-on-p Hg,.,Cdo,,Te photodiode array over the 83- 160 K temperature range. The junction areas ranged from 1.3 x 10-5-4.8 x lop4cmz. Over this temperature range, the dependence of dark current on junction area indicated that the dark current was due to a surface g-r mechanism. The solid line is a plot of Eq. (145) with aeXset equal to 1 x lop3.At temperatures above 180 K, the dark current in these photodiodes became dominated by diffusion current and the correlation between llfnoise and dark current was no longer observed. Figure 55 shows dark current and Ilfnoise current, both measured at a reverse bias of -50 mV, as functions of temperature for one of the Hg,.,Cdo,Te photodiodes. At temperatures between 110 and 180 K the dark current is dominated by surface leakage current and varies with temperature roughly as the intrinsic carrier concentration ni(T). Over this temperature range the l/f noise current displays the same temperature

300

M . B . REINE, A. K . SOOD, A N D T . J . TREDWELL

Io

-~

10-10

10-11

Io-I?

I000IT (K-I)

FIG. 55. Dark current (circles) and l/f noise current (squares) versus lOOO/T for two reverse-biased n+-on-p Hh,,Cd,,,Te photodiodes. 0,dark current; 0,l/f noise. [From Tobin er al. (1980).]

dependence as the dark current. Below 110 K the diode in Fig. 55 is limited by a temperature-independent surface current leakage; the l/f noise continues to follow the temperature dependence of the dark current. At temperatures above 180 K, the dark current of the diodes in Fig. 55 is limited by diffusion current. The I/fnoise current, however, continues to display the same temperature dependence as the surface generation current. These data indicate that it is only the surface generation component of the dark current which is related to llfnoise. The relationship in Eq. (145) obtained by Tobin et al. (1980) for implanted n+-on-p Hg,,Cd,Te photodiodes is similar to that observed by Hsu et (11. (1968; Hsu, 1970a,b) for gate-controlled silicon junctions. Hsu proposed a model in which the current fluctuations were a result of a modulation of the surface generation current by fluctuations in surface potential. The data on Hg,,Cd,Te photodiodes could be explained by such a model. However, a better understanding of the nature of the surface

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leakage current in Hg,,Cd,Te photodiodes is required to gain a deeper understanding of l/f noise in these devices. 16. SCHOTTKY BARRIERPHOTODIODES The previous sections of this chapter have been concerned exclusively with p-n junction photodiodes in Hg,-,Cd,Te. In this section we review some recent work in Schottky barrier diodes in Hg,,Cd,Te. Schottky barrier diodes have been studied quite extensively in several semiconductors (Henisch, 1957; Rhoderick, 1978) and can be quite suitable for use as visible and infrared detectors. The rectification properties of a Schottky barrier diode are determined by the work function of the metal and the height of the metal-semiconductor barrier. The electrical properties of the Schottky barrier diodes in most of the semiconductors studied so far are strongly influenced by surface preparation and by thin interface layers on the semiconductor prior to the deposition of the metal. Several papers have discussed these effects in silicon (Turner and Rhoderick, 1968) and in gallium arsenide (Childs et al., 1978). Barrier formation can be quite complex for several reasons. Chemical reactions at the metal-semiconductor interface can play a role in establishing a barrier. This could become especially important if there is a thin interfacial layer initially present on the semiconductor surface. Schottky barrier diodes have been formed on such ternary semiconductors as GaAs,P,, (Neamen and Grannemann, 1971) and In,Ga,,As (Kajiyama er al., 1973). Schottky barrier infrared photodiodes have been formed on the narrow-bandgap semiconductor Pb,,Sn,Te (Melngailis, 1973; Harman and Melngailis, 1974). The only reported work on Schottky barriers in Hg,,Cd,Te has been by Polla (1979) and by Polla and Sood (1978, 1980). They utilized Schottky barrier structures primarily to determine the minority-carrier properties of p-type Hg,-,Cd,Te for 0.2 Ix s 0.4. Polla (1979) fabricated Schottky barrier diodes on bulk-grown crystals of p-type Hg,-,Cd,Te with net acceptor concentrations of 0.5-2 x 10ls ~ m - ~Aluminum, . manganese and chromium were selected as barrier metals on the basis of the conclusions of Johnson and Schmit (1977), which are summarized in Section 1 1 ,a of this chapter. Polla (1979) showed that all three of these metals formed Schottky barriers on p-type Hg,-,Cd,Te. Aluminum is a known donor in Hg,,Cd,Te; however, Johnson and Schmit (1977) showed that it diffuses quite slowly. They found no signs of diffusion of aluminum from a sputtered layer about 1 p m thick on p-type Hg,.,Cdo.,Te samples after a heat treatment at 290°C for 2 h. Current-voltage characteristics at 77 K for an aluminum Schottky bar-

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M . B. REINE, A . K. SOOD, A N D T . J . TREDWELL

FIG. 56. Current-voltage characteristics at 77 K for an aluminum Schottky barrier on p-type Hg,.,,Cdo,,eTe. [From Polla and Sood (1980).]

ner on p-type Hq,7,Cd,,,2Te are shown in Fig. 56. The electrical properties at 77 K of this diode and of a chromium Schottky barrier on p-type Hg,,78Cd0.32Teare summarized in Table VI (Polla and Sood, 1980). The barrier metals were thermally evaporated in a circular geometry of area 1.14 x lop3 cm2. The barrier metal layers were not thin enough to be transparent, but cutoff wavelengths were able to be determined from the measured photoresponse due to carriers photogenerated near the edge of the barrier metal. The reverse bias characteristics in these devices TABLE VI ELECTRICAL PROPERTIES AT 77 K OF Two Hg,-,Cd,Te Hg,-,Cd,Te alloy composition x Energy gap E , Cutoff wavelength A,, Acceptor concentration N,, Barrier metal Zero-bias resistance R , R J , (A, = 1.14 x cmz) Barrier height (a) from I-V data (b) from C-V data

SCHOTTKY BARRIERDIODES

0.22 0.136 eV 9.1 p m 2 x 10'6 cm-ti

0.32 0.288 eV 4.3 p m 8 x cmP

Aluminum

Chromium 4.4 x 104 n 50.6 fi cmz

0.101-0.104 eV

Q.272-0.275 eV 0.220 eV

1.3 x 104 n 1.49 cmz

0.071 eV

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showed excess leakage currents which were perhaps due to edge breakdown. Attempts were made to determine values for the barrier height both from detailed current-voltage and from capacitance-voltage measurements. The barrier height values deduced from current -voltage measurements were consistently higher than those deduced from capacitancevoltage measurements. This discrepancy in barrier height has also been observed for Schottky barriers in silicon (Tongson el al., 1979) and in GaAs (Childs et al., 1978). The explanation for this behavior is that surface states block majority carriers traveling from the semiconductor to the metal under forward bias. The shielding effect is not present for capacitance - voltage measurements since the majority-carrier current is small and the barrier height is determined by modulating the depletion layer width. Hence, barrier height values deduced from capacitance-voltage data should be more reliable than those from current -voltage data. IV. Summary and Conclusions

As this chapter has indicated, there is considerable interest in Hg,-,Cd,Te junction photodiodes for a wide range of infrared detector applications. The performance levels achieved so far in these devices indicate that this interest will continue. For 3-5 pm applications at operating temperatures around 190 K, and for 8-12 pm applications at around 77 K , ion implanted n-on-p Hg, ,Cd,Te junction photodiodes have already demonstrated sufficiently high R,,A products.? For these combinations of cutoff wavelength and operating temperature, p-side diffusion current generally dominates the I-V characteristics near V = 0. Efforts are being directed toward further reduction of p-side diffusion current by reducing the p-side diffusion volume and by using p-type Hg,-,Cd,Te with long minority-carrier lifetime. Efforts are also being directed toward the further reduction of various other junction current mechanisms in order to reduce I/’noise at reverse bias and to increase the overall yield of diffusion-limited junctions photodiode arrays. Issues such as long-term device reliability are beginning to be addressed. Improved surface passivation techniques are being explored in order to achieve better control of surface potential and lower surface state densities. For applications at lower temperatures where conventional diffusion current is negligible, various leakage current mechanisms have generally t The applicability of photovoltaic Hg,-,Cd,Te detector mosaic arrays for advanced thermal imaging systems has been reviewed recently by Grant and Hutcheson (1979).

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kept junction impedances below their desired values so far. This is particularly so for junctions with longer cutoff wavelengths, and is presumably due to the ease with which interband tunneling can occur across the narrow bandgaps involved. Here efforts are being directed toward identifying the origins of leakage currents, with particular emphasis on control of surface potential and surface state density and on device designs which are less conducive to interband tunneling. Recently? there has been encouraging progress in this area with zero-bias impedances of 1 x lo9 0 being measured at 4.2 K in boron-implanted n-on-p Hg,-,Cd,Te junction photodiodes with cutoff wavelengths around 17 pm.The junction area for these laboratory device was I x cm2, which gives R,Aj products around 1 x 1W R cm2. Whereas photoconductive Hg,-,Cd,Te detector technology has exclusively been based on n-type material of low carrier concentration (usually ~ m - ~photovoltaic ), Hg,,Cd,Te detector technology less than 5 x has to date relied essentially on p-type material with carrier concentrations generally in the 5 x lOl5-I x 10'' cm-3 range. Improved understanding and control of p-type Hg,-,Cd,Te are critical to the continued development of Hg,-,Cd,Te junction photodiode technology. For example, the roles of various impurities, acceptor dopants, and native defects in determining the rninority-carrier lifetime in p-type Hg,-,Cd,Te need to be better understood. The DLTS and reverse bias step recovery techniques should prove useful in this regard. There needs to be an experimental determination of the strength of the theoretically proposed Auger 7 recombination process in p-type Hg,-,Cd,Te. In addition to being the basis for n-on-p Hg, ,Cd,Te junction photodiode technology for hybrid mosaic focal planes, p-type material will also be quite important to monolithic Hg,-,Cd,Te IR/CCDs (Kinch rt al., 1980) because of its large minority-carrier mobility. Finally, it is important that there be increased basic and applied research in the interrelated areas of Hg,-,Cd,Te crystal growth, defect chemistry, surface science, and junction formation, passivation, and contact technology. There remains much to be done in each of these areas besemiconductor alloy system can fore the full potential of the Hg,,Cd,Te be realized.

ACKNOWLEDGMENTS The preparation of this chapter was aided by many pleasurable, informative, and stimulating discussions which the authors had with their colleagues at the Honeywell Electro-Optics

t Data on Honeywell laboratory devices taken by W. L. Eisenman, D. Arrington and C. Sayre of the Naval Ocean Systems Center.

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Operations and the Honeywell Corporate Material Sciences Center. In particular, we thank Messrs. D. L . Polla and S. P. Tobin, and Drs. T. N. Casselman, P. LoVecchio, and J. F. Shanley for providing papers and other information prior to their publication for use in this chapter; and we acknowledge valuable discussions on space-charge region g-r current with Drs. P. H. Zimmermann and R. J. Briggs. We also thank the following individuals for providing preprints, unpublished information, and in some cases original figures which could be used in preparing this chapter: Professors R. Kalish and I. Kidron of Technion-Israel Institute of Technology, Dr. M. Lanir of Rockwell International Science Center, Dr. K. J. Riley of Santa Barbara Research Center, and Professor M. H. Weiler of the Massachusetts Institute of Technology.

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Nelson, D. A., Higgins, W. M., and Lancaster, R. A. (1980). Proc. Soc. Photo-Opt. Instrum. Eng. 225, 48. Nemirovsky, Y., Margalit, S., and Kidron, I. (1980). Appl. Phys. Lett 36, 466. Nicollian, E. H., and Goetzberger, A. (1967). Bell Syst. Tech. J . 46, 1055. Nicollian, E. H., and Melchior, H. (1967). Bell Syst. Tech. J . 46, 2019. Noble, V. E., and Thomas, Jr., J. E. (1961). J . Appl. Phys. 32, 1709. Pawlikowski, J. M., and Becla, P. (1975). infrared Phys. 15, 331. Petersen, P. E. (1970). J. Appl. Phys. 41, 3465. Peyton, B. J., DiNardo, A. J., Kanischak, G. M., Arams, F. R., Lange, R. A., and Sard, E. W. (1972). IEEE J . Quantum Electron. QE-8,252, Pickar, D. A. (1975). In “Applied Solid State Science” (R. Wolfe, ed.), Vol. 5 , pp. 151-249. Academic Press, New York. Piotrowski, J. (1977). Fiz. Tekn. Provodn. 11,1088 [English transl.: Sov. Phys.-Semicond. 11, 643 (1977)l. Polla, D. L. (1979). P-(Hg,Cd)Te Schottky Barrier Photodiodes. B. S. Thesis, M. I. T. Cambridge, Massachusetts. Polla, D. L., and Jones, C. E. (1980). Solid State Commun. 36, 809. Polla, D. L., and Sood, A. K. (1978). IEEE Int. Electron Device Meeting Tech. Digest 419. Polla, D. L., and Sood, A. K. (1980). J . Appl. Phys. 51,4908. Preier, H. (1967). Appl. Phys. Lett. 10, 361. Pruett, G. R., and Petritz, R. L. (1959). Proc. IRE 47, 1524. Redfield, D. (1979). Appl. Phys. Lett. 35, 182. Reine, M. B., and Broudy, R. M. (1977). Proc. Soc. Photo-Opt. Instrum. Eng. 124, 80. Rhoderick, E. H. (1978). “Metal-Semiconductor Contacts,” Oxford Univ. Press (Clarendon), London and New York. Riley, K. J., Bratt, P. R., and Lockwood, A. H. (1978a).Proc. Joint Meeting IRIS Specialty Groups Infrared Detectors and Imaging 1, 333 (DDC AD B033464). Riley, K. J., Lockwood, A. H., and Bratt, P. R. (1978b). Proc. Joint Meeting IRIS Specialty Groups Infrared Detectors and Imaging 1, 363 (DDC AD B033464). Riley, K. J., Myrosznyk, J. M., Bratt, P. R., and Lockwood, A. H. (1979). Proc. Meeting IRIS Specialty Group Infrared Detectors (U)1, 199. Rodot, M., VBrit, C., Marfaing, Y., Besson, J., and Lebloch, H. (1966). IEEE J . Quantum Electron. QE-2, 586. Sah, C. T. (1962), IRE Trans. Electron Devices ED-9, 94. Sah, C. T., and Hielscher, F. H. (1966). Phys. Rev. Lett. 17, 956. Sah, C. T., Noyce, R. N., and Shockley, W. (1957). Proc. IRE 45, 1228. Sawyer, D. E., and Rediker, R. H. (1958). Proc. IRE 46, 1122. Schmit, J . L. (1970). J . Appl. Phys. 41, 2876. Schmit, J . L., and Bowers, J. E. (1979). Appl. Phys. Lett. 35, 457. Schmit, J. L., and Johnson, E. S. (1977). Exploratory Development on Hg,-,Cd,Te Improvement, Phase 11. Final Technical Rep., Air Force Materials Laboratory Contract F33615-74-C-5041(DDC AD B020360L). Schmit, J. L., and Stelzer, E. L. (1969). J . Appf. Phys. 40, 4865. Schmit, J. L., and Stelzer, E. L. (1978). J . Electron. Muter. 7 , 65. Schmit, J. L., Tobin, S. P., and Tredwell, T. J. (1979). Minority Carrier Lifetime and Diffusion Length in P-Type Mercury Cadmium Telluride. Final Rep., Air Force Materials Laboratory Contract F33615-77-C-5142, Rep. No. AFML-TR-79-4036 (DDC AD A07 1094). Scott, W. (1970). Solid State Sensors Symp. Proc. (R. H. Dyck, ed.), IEEE Catalog No. 70C25-Sensor, pp. 75-78. Scott, W. (1972). J. Appl. Phys. 43, 1055.

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Scott, W., and Hager, R. J. (1971). J. Appl. fhys. 42, 803. Scott, M. W., and Kloek, A. E. (1973). PN Junctions in Mercury Cadmium Telluride, U.S. Patent 3,743,533. Scott, W., Stelzer, E . L., and Hager, R. J. (1976). J. Appl. f h y s . 47, 1408. Shanley, J. F., and Flanagan, C. T . (1980). f r o c . S o c . Photo-Opt. Instrum. Eng. 227, 123. Shanley, J. F., and Perry, L. C. (1978a). Infrared Heterodyne Photodiode Development and Characterization. Final Rep., Ballistic Missile Defense Advanced Technology Center Contract DASG60-77-C-0081 (DDC AD B033680L). Shanley, J. F., and Perry, L. C. (1978b). IEEEInt. Electron Device Meeting Tech. Digest 424. Shanley, J . F., Koehler, T., Lang, K., MacDonald, D., Peyton, B. J., and Wolczok, J. (1977). 10.6 Micrometer (Hg,Cd)Te Mixer/Detector Development: A Wideband Heterodyne Ladar Receiver. Final Rep., Ballistic Missile Defense Advanced Technology Center Contract (DASG60-75-C-0079) (DDC AD B020165L). Shanley, J . F., Flanagan, C. T., and Reine, M. B. (1980). f r o c . Soc. Photo-Opt. Instrum. Eng. 227, 117. Shappir, J., and Konodny A. (1977). lEEE Trans EIectrori Devices ED-24,1093. Shockley, W. (1949). Bell S y s t . T e c h . J . 28, 435. Shockley, W., and Read, Jr., W. T. (1952). f h y s . Rev. 87, 835. Smith, R. A. (1978). “Semiconductors,” 2nd ed. Cambridge Univ. Press, London and New York. Soderman, D. A. (1970a). f r o c . Nor. Electron. Conf. 26, 273. Soderman, D. A. (1970b). Mercury Cadmium Telluride Detector. Final Tech. Rep., U.S. Army Electronics Command Contract DAAB07-69-C-0328 (DDC AD 880272). Soderman, D. A,, and Pinkston, W . H. (1972). Appl. Opt. 11, 2162. Sood, A. K., and Tobin, S. P. (1980). Electron Device Lett. EDL-1, 12. Sood, A. K., and Tredwell, T. J . (1978a). 8-14 Micrometer Photovoltaic Detectors. Final Rep., U.S. Army Night Vision and Electro-Optics Laboratory Contract DAAK70-76-C-0237 (DDC AD B037083L). Sood, A. K., and Tredwell, T. J . (1978b). IEEE Int. Electron Device Meeting Tech. Dige.rt 434. Sood, A. K., Marciniec, J . W., and Reine, M. B. (1979a). Moderate Temperature Detector Development. Final Rep. for NASA Contract NAS9-15250. Sood, A. K., Marciniec, J. W., and Reine, M. B. (1979b). Proc. Meeting IRIS Speciulty Group Infrured Detectors ( U )Vol 1, 171 (DDC AD B053886). Sood, A. K., Marciniec, J. W., and Reine, M. B. (1979~).Final Rep., U.S. Naval Research Laboratory Contract N 00173-78-C-0145. Spears, D. L. (1977). Infrared f h y s . 17, 5 . Spears, D. L., and Freed, C. (1973). Appl. f h y s . L e t t . 23, 445. Spears, D. L.. and Hoyt, C. D. (1978). M. I. T. Lincoln Laboratory Solid State Research Rep., #1, pp. 1-5 (DDC AD A056715). Spears, D. L., and Kingston, R. H. (1979). Appl. f h y s . Lett. 34, 589. Spears, D. L . , Harman, T . C., Melngailis, I., and Freed, C. (1973). M. I. T . Lincoln Laboratory Solid State Research Rep., #2, pp. 2-6 (DDC AD 766233). Spears, D. L, Harman, T. C., and Melngailis, I. (1974). M. I. T. Lincoln Laboratory Solid State Research Rep., #4, pp. 5-7 (DDC AD A004763). Sze, S . M. (1969). “Physics of Semiconductor Devices.” Wiley, New York. Tarr, N. G., and Pulfrey, D. L. (1979). Solid Stute Electron. 22, 265. Tauc, J. (1962). “Photo and Thermoelectric Effects in Semiconductors.” Pergamon Press, New York.

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SEMICONDUCTORS A N D SEMIMETALS, VOL. I8

CHAPTER 7

Metal-Insulator-Semiconductor Infrared Detectors M . A . Kinch

. . .

. . . . . . I . General MIS Theory . . 2. (HgCd)Te MIS Theory .

. . . . . . .. . . . . (HgCd)Te MIS EXPERIMENTAL DATA . . 3. Thermal Equilibrium Mode . . . . . . 4 . Dynamic M o d e . . . . . . . . . . . .

. . . . . . . .. . . . . . . .. . . . . (HgCd)Te MIS PHOTODIODE TECHNOLOGY . . . 5.Theory . . . . . . . . . . . . . . . . . . 6. Performance Datu . . . . . . . . . , . . . 7. Surface-Controlled Photoconductor . . . . .

.. . . . . ... . . . . . . . . . .. . .. , . . . . . . . . . . . . . ... . . . . . . . . . . . . . ( H g C d ) T e CHARGE TRANSFER DEVICETECHNOLOGY .. . . 8. (HgCd)Te CTD Theory and Design. . . . . . . . . . . . 9. (HgCd)Te CCD Performance D a t a . . . . . . . . . . . . SUMMARY . . . . . . . . . . . . . . . . . . .. . . . . REFERENCES. . . . . . . . . . . . . . . . . . . . . . .

I. INTRODUCTION. . 11. MIS T H E O R Y . .

111.

IV.

V.

VI.

. . . .

. . . .

. . . . . . . .

.

. . . . . . . . . . .

,

313 315 315 322 339 339 346 349 349 354 360 364 364 371 376 377

I. Introduction The realm of discrete intrinsic infrared detectors has long been dominated by photoconductive devices, and to a lesser extent metallurgically formed photodiodes. This dominance has continued even into current generation focal planes, in which arrays of photoconductive elements are fabricated in (HgCd)Te utilizing conventional photolithographic techniques, with the number of elements, each with its own preamplifier, typically being less than 200. The characteristics of these devices have now advanced to the stage in which background limited operation (BLIP) is expected even for systems operating at greatly reduced bandwidths and background flux levels. However, the performance parameters that will be demanded of the next generation of infrared systems are such as to require a significant increase in the number of detectors employed in the 313 Copyright @ 1981 by Academic Press. Inc. All rights of reproduction in any form reserved. ISBN 0-12-752118-6

314

M.

A . KINCH

focal plane to values in excess of lo4, and photoconductive detectors will not be able to meet this need. Signal processing on the focal plane itself will be mandatory, with such signal processing functions envisioned as time delay and integration (TDI) for scanning systems, multiplexing, area array staring mode operation, antiblooming, and background subtraction, to name but a few. To this end both charge coupled (CCD) and charge injection (CID) device technology will be employed. Three different approaches have been proposed to meet these onfocal-plane signal processing requirements: ( I ) The hybrid (Long0 et ul., 1978), which represents a marriage of present-day technologies, utilizing conventional intrinsic infrared photodiode arrays and silicon signal processing electronics electrically and mechanically mated together. (2) Extrinsic silicon (Nummedal er nf., 1979, which utilizes the material in which signal processing is most advanced but whose infrared capabilities are severely limited. (3) The intrinsic monolithic (Chapman et al., 1978) approach, which utilizes the materials that are at the forefront of present-day infrared detector technology but whose signal processing capabilities are largely unproven. The intrinsic material approach, although perhaps technologically the most challenging, offers the distinct advantages of the highest temperature of operation consistent with the system spectral window, a high quantum efficiency and hence a low cross-talk capability, a minimal power dissipation on the focal plane, and a minimal number of focal plane interconnects. Although signal processing in (HgCd)Te is as yet in its infancy high-quality materials (Kinch er af.,1973) and single-level metalinsulator-semiconductor technologies (Tasch et uf., 1970; Kinch 1974) have been developed over the years in support of the present-day infrared systems effort utilizing photoconductive (HgCd)Te. The surface technology which is required to reduce surface recombination velocity and I/f noise effects in photoconductive detectors has also been utilized to fabricate MIS photodiode detector arrays in (HgCd)Te, and it is this technology which forms the foundation on which this chapter is based. The general theory of metal-insulator-semiconductor (MIS) devices as applied to (HgCd)Te is reviewed briefly in Part I1 and compared with experimental data in Part 111. The utilization of this predominantly single-level MIS technology to detect infrared radiation in the conventional discrete manner, in the form of an MIS photodiode, is discussed in Part IV together with a brief excursion into the realm of the surfacecontrolled photoconductor. The extension of this single-level (HgCd)Te MIS technology into the multilevel capability required for charge transfer

7.

METAL-INSULATOR-SEMICONDUCTOR

I N F R A R E D DETECTORS

315

device (CTD) operation is described in Part V from both a theoretical and experimental standpoint with specific regard to (HgCd)Te infrared sensitive CCD shift register performance. 11. MIS Theory

1 . GENERAL MIS THEORY

The simple metal-insulator-semiconductor device is shown in Fig. 1 and consists of a metal gate separated from a semiconductor surface by an insulator of thickness to, and dielectric constant E,, . The surface potential of the semiconductor is controlled by the bias voltage applied to the metal I

,-METAL

‘OX

INSULATOR

f

SEMICONDUCTOR

’r

FIG.1. Metal-insulator-semiconductor (MIS) structure.

gate with respect to the substrate, and the energy-band diagram for an n-type semiconductor biased to the threshold of strong inversion is shown in Fig. 2. A quantitative expression for the potential r#~as a function of distance from the surface x is given by a solution of the one-dimensional Poisson’s equation which for nondegenerate statistics and thermal equilibrium is given by

The electric field at any point is

where

nno and ppo represent the majority- and minority-carrier densities in the

316

M. A . KINCH

INSULATOR-’

FIG.2. Energy-band structure for n-type semiconductor MIS structure biased to threshold of strong inversion.

bulk of the semiconductor, and E is the semiconductor dielectric constant. The space charge per unit area at the semiconductor surface is given by Gauss’s law, namely

Qs= E E ~ =E 2 ~ (~EE,,~T)”~F(C#J).

(4)

A typical variation of the space-charge density as a function of surface potential c$~ for n-type 0.25-eV (HgCd)Te (cutoff wavelength, A, = 5 pm) with no = 2 x l O I 5 cm-3 is shown in Fig. 3 for a temperature of 77 K. For the surface is accumulated and the function F ( 4 ) depositive values of C& fined by Eq. (3) is dominated by the first term, and Qs exp(q4,/2kT). For values of bSbelow flat band the second term in Eq. (3) dominates and Qs l ~ $ ~ and l ~ / the ~ , semiconductor space charge is determined by the ionized impurities in the depletion region formed at the surface. At larger negative values of surface potential the minority-carrier density at the surface is much greater than the bulk majority-carrier concentration, and the space charge is dominated by the fourth term in Eq. (3), such that Qs exp(ql+,l/2kT). Strong inversion is seen to occur in Fig. 3 for values of surface potential I+,] > 1244, where 4Frepresents the bulk Fermi potential, as defined in Fig. 2. This condition for strong inversion is equivalent

-

-

-

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

-0 3

-0.I

-0.2

0

317

+0.05

0,( e v i

FIG.3. Variation of space-charge density Qsas a function of surface potential 0.25-eV n-type (HgCd)Te with no = 2 X 1015 c m P , T = 77 K.

QS,

for

to

or nno

= Pno exp(-q4PV/kT) = ~ s r

(5)

where ps represents the surface concentration of minority carriers. The differential capacitance associated with the semiconductor space-charge region is given by

M.

318

A . KINCH

Again for ds > 0, the surface is accumulated and Eq. (6) approximates to C,,, 0: exp(q+,/2kT), so that for values of +s in excess of a few ( k T / q )the space-charge capacitance is high. In the other extreme of strong inversion Eq. (6) becomes Cinva exp(ql&l/2k7‘), and again for +s > few ( k T / q ) the capacitance associated with the inversion layer is very large. For values of surface potential in the depletion-weak inversion range where the space charge is dominated by depletion, Eq. (6) reduces to c d = ( e ~ ~ q N / 2 + ~ ) ~ ’ * , the familiar depletion region capacitance (= EE,/ W, as shown in Fig. 2). In the idealized MIS device biased to strong inversion the inversion layer is assumed to be in the form of a sheet of charge Qinvimmediately at the surface and the associated depletion region is assumed devoid of charge carriers. The applied gate voltage VG is dropped partly across the insulator and partly across the space-charge region, such that by Gauss’s law =

EOXEO

to,

Qinv+ q N W ,

(7)

where N is the net impurity concentration in the depletion layer W. The surface potential +s associated with the applied gate voltage V , is given by (Macdonald, 1964) =

v;:+ v, - (2VAV0 + v“,)”’,

(8)

with Vo = q N E E o / C , x Vh = (VG - VFB) + Qinv/Cox C o x = &oxEo/fox where VFBrepresents the device flat-band voltage. The total capacitance of the idealized MIS device is the series combination of the insulator capacitance Coxand the space-charge capacitance Cd, namely 9

c = coxcd/(cox + c d ) *

9

9

(9)

The theoretical variation of C versus V , for such an idealized MIS device (with VFB = 0) is shown in Fig. 4, for a particular set of device parameters on n-type 0.25-eV (HgCd)Te, with no = 1015 cmP3. The general features follow from a consideration of Eqs. (6) and (9). At positive gate voltages the surface is accumulated and Cd (= C,,,) is large; thus the total capacitance is essentially that of the insulator Cox.As the gate voltage is reduced to values such that +s < 0, a depletion layer is formed with capacitance , ) ”the ~ , total capacitance decreases. Upon given by Cd = ( E E , ~ N / ~ +and further decreasing V G the surface is biased into strong inversion and the space-charge capacitance is now Cinv,which is very large, and the total capacitance increases until it again approximates Cox.Thus, the measured

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

319

m L

standard

A

I

-

high frequency

-*. I -0.8

pulsed

1

I

-0.6

-0.4

1

0 -0.2 Gate Vollaqe (VI

1 t0.2

I t0.4

I 10.6

FIG.4. Capacitance versus gate voltage for Eg 0.25-eV n-type (HgCd)Te at 77 K . no = lot5~ m - r~# ;~=~ 0.092 eV; Cox= 2.1 x lo-’ F/cm2. Vectors are indicated by overarrows in figures and by bold letters in text. [Chapman (1978).]

device capacitance exhibits a minimum and this curve is designated low frequency in nature. This terminology is used because throughout the above theory it has been tacitly assumed that the carriers can follow the applied voltages. This is certainly true for the accumulation and depletion regimes but is not necessarily correct for the minority carriers in the inversion layer. These carriers have a finite response time to an applied ac signal that is dependent on the availability of minority carriers to the surface region, i.e., the inversion layer response time is inversely related to the minority-carrier dark current in the device. At sufficiently high ac signal frequencies the inversion layer cannot follow the applied ac voltage even though it is in equilibrium with the dc gate bias and the capacitance-voltage curve exhibits a high-frequency response, as shown in Fig. 4, with a limiting capacitance given by CoxCd/(CoX + Cd). This variable frequency response is typically represented by a finite resistance connecting the majority- and minority-carrier bands in a device equivalent circuit. Also shown in Fig. 4 is a curve labeled “pulsed” response. This curve represents the measured capacitance of the MIS device when biased into deep depletion by a voltage pulse which is sufficiently fast that minority carriers cannot appear at the surface of the semiconductor in the time available. The measured capacitance is then given by Coxin series with Cd, where Cd is determined by the depletion layer associated with the surface potential +s obtained by solving Eq. (8) with Qinv = 0. Figure 4 also includes the effects of degeneracy and nonparabolicity on the total capacitance in the accumulation region ( V , large and positive), and these

320

M . A. KINCH FIXED OXIDE CHARGE

+

1

]+

I I I

t

I I

SLOW (INTERFACE)

-

I -

-

-

I

HgCdTe

I I le- -100 OXIDE

A

FIG.5 . Surface states of (HgCd)Te.

result in a reduction in the value of C,,, as compared to the theory of Eq. (6). designated by the standard curve in Fig. 4. Surface states have been ignored thus far in the above theory. The oxide-semiconductor interface is shown in Fig. 5 , and the three main types of state of importance in (HgCd)Te are indicated, namely fixed oxide charge, and slow and fast surface states. The magnitude of the fixed oxide charge is important in determining the device flat-band voltage. The slow surface states, typically within a tunneling distance of the interface, manifest themselves as hysteresis effects in capacitance-voltage curves due to minority-carrier trapping. The fast interface states cause deviations of measured C-V characteristics from those values predicted above, depending upon the applied frequency, temperature, and surface potential, and can also cause excessive dark currents. The kinetics of generationrecombination through fast surface states is identical to that through bulk Shockley-Read centers (Shockley and Read, 1952), and is depicted in Fig. 6 for an n-type substrate biased into depletion. The thermal generation rate out of Nfscan be represented by associated resistances R,,# and Rp2 to the respective band edges, and these impedances vary exponentially with energy from the appropriate band. Also included in Fig. 6 are the minority-carrier dark current contributions due to diffusion from the neutral bulk region and generation-recombination in the depletion region. When biased to depletion-inversion the MIS device can be accurately represented (Lehovec and Slobodskoy , 1964) by the equivalent circuit shown in Fig. 7a, which includes the aforementioned effects due to finite inversion layer response time and surface states. The equivalent circuit is greatly simplified for the MIS device biased into strong inversion. In this

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

321

n - TYPE

Jdif

FIG.6 . Surface of an n-type semiconductor biased into depletion, including fast surface states.

case R,,g + m, RP,*+ 0 , and ( w C , ~ ~<< ) -(wCJ', ~ and R d , at all reasonable frequencies, and the circuit of Fig. 7a reduces to that of Fig. 7b. A simple analysis of the circuit of Fig. 7b gives for the measured admittance across the MIS device

=

G,,, + jwC,.

Thus, in the low-frequency regime, oRd(Cox+

(10) cd)

< 1, Eq. (10) gives

FIG. 7. Equivalent circuit of an n-type

MIS device for (a) depletion-inversion, and (b) strong inversion.

(a)

322

M. A . KINCH

In the high-frequency regime, wRd(Cox + + c d ) , and G , = RdlC&/(Cox + C#. Measurements of the MIS device in strong inversion can thus be utilized to provide information regarding the doping level of the substrate (from the measured C,) and the minority-carrier dark current (from the measured Rd). Estimates of the fast interface state parameters C, and R, necessitate measurements in the depletion-weak inversion regime and as such require analysis by the full equivalent circuit of Fig. 7a. A variety of measurement techniques has been proposed for this purpose, the most notable of which are those of conductance (Nicollian and Goetzberger, 1967), quasistatic capacitance (Kuhn, 1970), and capacitance derivative (Amelio, 1972).

Cm

cd)

= Coxand G , =

dG&.

> 1 , however, Cm =

coxcd/(c,,x

2. (HgCd)Te MIS THEORY a . Relevant (HgCd)Te Parameters The variation of energy gap with composition and temperature has been determined by (Schmit and Stelzer, 1969) for the Hg,-,Cd,Te alloy system, and the corresponding intrinsic carrier concentration values by (Schmit, 1970) utilizing a k p calculation to account for nonparabolic effects. The Kane model (Kane, 1957) for the conduction band in (HgCd)Te has been verified directly by cyclotron resonance measurements (Kinch and Buss, 1971) on various compositions, and the band-edge effective mass in the range 0.19 < x < 0.40 is estimated to be (m*/m,) = 7.5 X 10+ E g , where Eg is the bandgap in eV. The heavy-hole valence-band mass is assumed to be 0.55m0 (Galazka and Zakrzewski, 1967). Measurements (Carter et al., 1971) of the dielectric properties indicate that the static and high-frequency dielectric constants of composition x = 0.204 are E, = 19.5, and em = 14.0, which are essentially those of HgTe. The mobility of carriers in (HgCd)Te (Scott, 1972; Reynolds et al., 1971) is limited primarily by polar mode scattering for temperatures above 100 K, with varying degrees of ionized impurity scattering dominating below 100 K depending upon the degree of impurity doping and compensation. Unpublished data of mobility of electrons and holes versus temperature are shown in Fig. 8 for three representative compositions x 0.2, 0.3, and 0.4, which correspond to cutoff wavelengths at 77 K of 13, 5 , and 3 pm, respectively. The magnitude of the mobility due to polar scattering at 77 K is in good agreement with theory (Stratton, 1958), which includes carrier-carrier interactions, for both electrons and holes. The varying degrees of ionized impurity scattering (Brooks, 1955) exhibited in Fig. 8 are indicative of sizable impurity compensation effects for this material with typically 1014 < N D - N A < 1015cm-s, and ND+ NA 1015 cm+.

-

-

-

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

323

FIG. 8. Mobility versus temperature for electrons and holes in Hg,-,Cd,Te with x 0.2, 0.3, 0.4.

-

1 ;q\,, , , ,

102

10

'+.

100

1000

T IK)

The remaining parameter of importance for Hg,-,Cd,Te MIS performance is the minority-carrier lifetime. This has been investigated fairly extensively (Kinch et ai., 1973) in n-type photoconductor quality material, but little has been reported onp-type Hg,-,Cd,Te. In the best quality n-type material, at temperatures not too far removed from the intrinsic range, the minority-carrier lifetime is limited by band-to-band Auger recombination. A comparison of experimental (Kinch et al., 1973; Simmons, 1973) and theoretical values for minority-carrier lifetime in n-type material for x = 0.195 and 0.275 is shown in Figs. 9 and 10. The theoretical intrinsic Auger curves labeled TAi are calculated using the analysis of Petersen (1970) and the intrinsic radiative curves T~~ are by Hall (1959). The dominant effect is Auger and little evidence is observed of radiative lifetimes, although for compositions x > 0.3 T~~ must become important because of the relative dependence of these two mechanisms on bandgap E g . Indeed, the lifetime data for x = 0.275 shown in Fig. 10 cannot be fitted by rAalone and indicates a possible contribution due to rR which is a factor of 5 weaker than the theoretical values. The measured value of rAis a factor of 1.5 larger than the indicated theoretical values in Figs. 9 and 10. Evidence of Shockley -Read recombination is observed in some n-type Hg,-,Cd,Te devices, particularly in the more compensated material with

-

M. A. KINCH

324

FIG. 9. Experimental and theoretical dependence of minority-carrier lifetime 7 versus 1B/T for n-type Hg,,Cd,Te with x = 0.195.

to-’,

;

I

I

I

I

I

5

6

7

8

9

10

103/T (KdJ

FIG. 10. Experimental and theoretical dependence of minority-camer lifetime 7 versus = 0.275.

1V/Tfor n-type Hg,-,Cd,Te with x

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

325

N D - N A < 3 x l O I 4 ~ m - The ~ . temperature variation of 7 indicates in some cases levels in the range of 20-30 mV from the valence band. In others the lifetime is temperature invariant which can indicate a Shockley-Read center at the intrinsic level or a very high density of recombination centers at an arbitrary level in the energy gap. Auger recombination will not be important in p-type material and the limiting band-to-band recombination mechanism will be radiative. No direct measurements of T~ have been reported for bulk p-type material, although various authors have attempted to fit measured photodiode dark current (Polla and Sood, 1978; Lanir et al., 1978; Sood and Tredwell, 1978) data with lifetimes predicted by radiative limitations, with values approaching T~ to within a factor of 2 for po concentrations in the range 2-5 x 10l6 ~ m - The ~ . calculated radiative lifetime should be identical to that for n-type material. b . ( H gCd)Te MIS Cha ract eris t ics The above band structure parameters for (HgCd)Te give a density of states in the conduction band, N , = 6.5 x 1OI6 (Eg)3’2~ m - where ~ , Eg is in eV, and a density of states in the valence band N , = 2 X 10l8 cm-3 at a temperature of 77 K. The gross dissimilarity in conduction-band and heavy-hole valence-band effective masses results in an intrinsic level considerably above mid-gap for all reasonable temperatures which must be taken into account when calculating #IF. Degeneracy and nonparabolic effects have already been mentioned in describing the theoretical capacitance-voltage curve of an idealized MIS device on 0.25-eV n-type (HgCd)Te at 77 K shown in Fig. 4.The capacitance in accumulation is seen to rise less steeply toward the asymptotic value of C,, than predicted from classical theory for the conduction band. In experimental (HgCd)Te MIS devices there can occur three basic deviations from the theoretical C-V curve shown by the curve designated “thermal” in Fig. 11. Firstly, a finite background flux aBcan increase the minority-carrier density in the vicinity of the semiconductor surface above its thermal equilibrium value and the pnoappearing in the expression for Q s , namely Eq. (4), must be replaced by pa. The effect of the background flux is to essentially forward bias the depletion region induced under the field plate, thus increasing its associated capacitance, and is illustrated by the low-frequency curve labeled QB. The highfrequency capacitance is also increased over and above the thermally limited case, because the maximum potential dropped across the depletion region is now (2#IF- V,), where V , is the forward bias induced by the finite background flux. The second phenomenon that can affect the measured C-V characteristic is the presence of fast surface states, and this is

326

M. I

A. KINCH

I

I

I

!

I

___-- ---oulsed I

i

-0.4

I -0.3

I

-0. 2

I

-0.I

I

I

0

0. I

2

V G IVI

Fic. 11. Capacitance versus gate voltage for 0.25-eV n-type (HgCd)Te MIS device including effects due to background flux QB and fast surface states N f 3 .T = 77 K ; C,, = F/cm*; no = 7.5 x lo" ~ r n - ~[Chapman . (1978).] 2.1 x

also shown in Fig. 11 for a uniform density of surface states across the bandgap of Nf,= 1, and 2 x 10" ern+ V-l. The effect of these fast interface states is twofold; the charge trapped in the states as the dc gate voltage is increased modifies the surface potential corresponding to that gate bias and results in a horizontal shift of the C-V curve in the direction of increasing fixed oxide charge, and also if the states are capable of following the applied signal they will result in an increase in the space-charge capacitance, i.e., a vertical shift in the C-V curve. The states included in Fig. 11 are assumed to follow the applied signal. The frequency response of these surface states is described phenomenologically by the RC time constant of the state to the majority-carrier band, as indicated by the device equivalent circuit of Fig. 7a. For an n-type substrate, assuming that Rd >> Rnc, we thus have (Nicollian and Goetzberger, 1967) T , , , ~ = RnaC8,and at the Fermi level Rn,*C8= ( y , p ~ ~ )where - ~ , yn is the capture coefficient of the surface state for electrons, and n, is the surface concentration of electrons. The surface state capacitance is q N f , . It is of interest to estimate the frequency response of surface states located at the intrinsic level at 77 K for particular Hg,-,Cd,Te compositions. For A, = 5 pm, measurements of Shockley-Read lifetime in bulk material indicate

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

327

values of recombination center capture coefficients in the range , R,,C, = (.ynni)-l = 1-10 10-1°-10-9 cm3/sec, and ni lo9 ~ r n - ~hence sec. Thus, fast surface states located at the intrinsic level will not, follow applied ac signals. For A, = 12.5 pm, however, ni 3 X 1013 at 77 K, and R,,C, = 33-330 psec. Intrinsic level surface states can thus follow applied signals in the 5-500 KHz frequency range, and some dispersion in capacitance -voltage characteristics will become apparent for any significant density of surface states in this material. The third factor that can affect experimental capacitance-voltage characteristics is that of a finite distribution in fixed oxide charge (McNutt and Sah, 1974; Chang and Johnson, 1978). This effect is due to the fact that the density of fixed charge at the surface is not strictly uniform and is typically represented by a Gaussian with a finite width. The effect of this distribution is similar to that of fast surface states, and a width of a few kT can result in significant smearing out of the capacitance-voltage characteristics. The impact of surface states (Nicollian and Goetzberger, 1967) and distribution of fixed oxide charge (Brews, 1972) on conductance-voltage characteristics in the depletion-weak inversion regime is well documented; however, for typical (HgCd)Te MIS devices at 77 K little evidence is found of these effects. For the strong inversion regime their importance is also minimal. The equivalent circuit for the MIS device in strong inversion is shown in Fig. 7b and our discussions of conductance will be limited mainly to this mode of operation. The conductance of the MIS device in strong inversion, following the simple theory of Eq. (lo), gives a direct indication of the minority-carrier dark current associated with the depletion region under the gate, for both the low- and highfrequency signal regimes. The minority-carrier dark current perhaps represents the single most vital parameter with regard to the successful operation of MIS devices as detectors of infrared radiation. This applies to operation in the thermal equilibrium mode as discussed at length above, in which the dark current determines the MIS diode impedance, and to operation in the dynamic, or integrating mode, in which the minority-carrier dark current determines the storage time of the device. In the dynamic mode of operation the MIS gate is pulsed into deep depletion and the surface potential approximates the gate voltage for reasonable values of insulator capacitance. The capacitance of the device is given by the “pulsed” C-V characteristic shown in Fig. 11, and the band bending at the surface of an n-type substrate is shown in Fig. 12a, with the depletion region reaching far into the semiconductor. Thereafter, the potential well begins to fill with minority-carrier holes, generated either thermally or photoelectrically via background or signal photons incident on the device. As the potential well fills the sur-

-

-

328

M.

A . KlNCH

Metal

Insulator

I

n-type semiconductor

la1

-w+ n-type semiconductor (bl

FIG. 12. MIS device (a) immediately after voltage pulse V, and (b) after reaching thermal equilibrium.

face potential, given by Eq. (€9, collapses until eventually it reaches thermal equilibrium with a greatly reduced depletion region width, the greater part of the applied gate bias now being dropped across the insulator. The suitability of such a device for reading optical information obviously depends upon the time taken to relax back to thermal equilibrium; this is defined as the storage time of the MIS device given by Tst

= COXV/Jd

7

(1 1)

where CoxVessentially represents the well capacity of the device per unit area, and Jd is the total minority-carrier dark current density. c'.

Minority-Carrier Dark Current

The dark current density in an n-type (HgCd)Te MIS device biased into deep depletion is given by

where the first term represents the current due to minority carriers generated in the neutral bulk and diffusing to the depletion region; the second is due to minority carriers generated in the depletion region of width W; the third is due to generation out of fast surface states represented by a surface recombination velocity s; the fourth is due to the incident background photon flux; the fifth is due to tunneling of carriers from the valence band to the conductance band across the bandgap. These same currents are important for MIS equilibrium mode device operation but the expressions appropriate for zero bias are necessary, as opposed to those above which are equivalent to reverse-bias operation. For this reason the

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

329

performance of MIS equilibrium diodes is often defined by reference to device &A product, where R, is the diode impedance at zero bias, and A the device area. A theoretical consideration of these various dark current contributions appropriate for (HgCd)Te is as follows. (i) Diffusion Current. Minority-carrier diffusion current for an n-type substrate is given by Jdif

=

qnfLp/noT~ 3

(13)

where Lp is the minority-carrier diffusion length and T~ the bulk minority-carrier lifetime. For high-quality material the lifetime is limited by an Auger band-to-band recombination mechanism, and is given by 7 A

= 2nf7A~/no(no + pol,

(14)

where T A is ~ the Auger lifetime for intrinsic material. Thus from Eqs. (13) and (14), for no >> p o t Jdif

=~ n l [ ~ ~ k ~ / ~ q ~ A i I ~ ” ~

(15)

and p p is the hole mobility. The Auger-limited diffusion current thus has no adjustable parameters; all of the quantities in Eq. (15) are well defined and Jdlfis calculable for all temperatures and compositions of n-type (HgCd)Te. Such a calculation is shown in Fig. 13 for a range of compositions 0.20 < x < 0.35, whose

T(K)

FIG. 13. Auger-limited diffusion current versus temperature for various compositions of n-type Hg,-,Cd,Te.

M.

330

A. K I N C H

bandgaps cover the cutoff wavelength range 13.5 < A, < 4 pm. This calculated value of dark current for n-type material represents a lower limit at any specific temperature unless geometrical artifacts such as the use of substrates with thicknesses << Lp are employed. However, such techniques are extremely limited on n-type material due to the values of Lp which typically fall in the range 25-75 pm. For p-type material, as discussed earlier, the limiting band-to-band recombination process is radiative, and TR = 27Rini/po

9

(16)

where T R is ~ the radiative lifetime for intrinsic material. The diffusion limited dark current is then

and where p n is the electron mobility. Thus in this instance J d i f 0~ some advantage can be gained by employing higher doping levels to minimize the dark current. However, care must be exercised in increasing po too much as this will result in higher depletion layer capacitances, decreased diffusion lengths, and lower breakdown voltages in the reversewith temperature bias mode of operation. The predicted variation of .Idlr for p-type (HgCd)Te of a constant cutoff wavelength A, = 5 p m and a value of po = loi5 cmP3is shown in Fig. 14, utilizing the value of TRi estimated earlier in the discussion of minority-carrier lifetime measurements of (HgCd)Te. For comparison purposes the Auger-limited diffusion current for an n-type substrate is included. It is apparent that for the chosen value of po = 1015 cmP3the diffusion current in p-type material exceeds the that in n-type material by a factor of 3. For a value of p o = lois two values would be comparable. The reason for the excessive diffusion currents in p-type material is the high value of minority-carrier (electron) mobility shown earlier in Fig. 8. However, this high value of mobility also leads to large diffusion lengths and in this case, unlike n-type material, thin substrates can be used to great advantage to reduce the full diffusion current component given by Eq. (17). This can be accomplished either by mechanically thinning the substrate, or by employing a p - p + epitaxially grown substrate, where the p layer is just thick enough to support the required depletion layer. (ii) Depletion Current. Generation current from Shockley -Read centers located in the depletion region of a strongly reverse-biased diode is given by (Sah et al., 1957) Jdepi

= 4Wnf/(~poni + ~ n o ~ i ) ,

(18)

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

331

1 IKI

FIG. 14. Jdlrversus temperature for p-type radiative (HgCd)Te of constant cutoff wavelength. kc = 5 pm; p o = loB5cm3. [Kinch ef d.(1980).]

where W is the depletion width, n, = N , exp[-q/kT], p 1 = N , exp[(-E, + e t ) / k T ] , T~~ = ('ypNd-', T~~ = ( Y ~ N ~ N ) -, ~and , N , are the densities of states for the conduction and valence bands, respectively, and 'yp and 'yn represent the capture coefficents of the Shockley-Read centers for holes and electrons, respectively. N R is the density of centers located at a level a distance .st from the conduction band. A slightly different expression (Sah et al., 1957) than Eq. (18) is appropriate for diode operation close to V = 0. If the trap level is located at the intrinsic level, n, = p 1 = n i , and if yn = 'yp, then we have Jdepl

= 4Wni/270

3

(19)

where 7, = ( Y ~ N ~ )and - ~ this , is the expression used in Eq. (12). For this depletion current case it is obvious that the current is not constant but varies directly as the depletion width. Thus the generation current in a dynamic mode device will be greater for large MIS gate voltages (and hence well capacities) and will also vary as n;1'2, as given by the ex-

332

M . A . KINCH

pression for the depletion width

w = (2EE,4,/qn,)"2,

(20)

where #s is the surface potential corresponding to the applied gate voltage. Figure 15 shows the dependence of depletion current on temperature for three constant cutoff wavelengths assuming a lifetime T~ = sec, no = 5 x lo1*cmP3, and c$~ = 3.5 V. These calculated curves represent the current for #s = 3.5 V, and for an MIS device pulsed into deep depletion they are only indicative of the initial dark current. The depletion current will in fact decrease as the well fills (and hence the depletion region collapses). (iii) Surface Current. The generation current out of fast surface states is analogous to the depletion current out of bulk Shockley-Read centers and is given by Js = Bqnts

(21)

where s is the maximum surface recombination velocity associated with the fast surface states at the intrinsic level. At 77 K for A, = 10 pm, ni = 6 x loi2 ~ m - and ~ , Eq. (21) gives J , = 5 x lO-'s A/cm2. For well-fabricated devices the value of s will be low enough (<<1W cm/sec) that J, will be unimportant at 77 K. (iv) Buckground Current. The current generated by the incident background photon flux is

Id

10'

7 (K)

FIG.15. Depletion current versus temperature for three cutoff wavelengths o f (HgCd)Te. sec; $ I = 3.5 V . cm-"; T,,= n, = 5 x

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

333

where r) is the quantum efficiency of the device and +* is the background photon flux density. Equation (22) represents the limiting current for an infrared device operating in a particular environment and obviously for BLIP performance this current must dominate all other dark current contributions. (v) Tunnel Current. Although categorized as tunnel current this component should perhaps be described as due to high field breakdown, which can occur at relatively low values of electric field for the narrower bandgaps of the (HgCd)Te composition range. High field breakdown can be caused by avalanche multiplication or by interband tunneling. Avalanche breakdown calculations on a variety of materials (Baraff, 1962; Hauser, 1978) indicate that this may be important in (HgCd)Te at low doping concentrations (- 1014 ~ m - ~ however, ), tunneling is expected to constitute the most significant problem for realistic doping levels. The tunnel current through a simple triangular barrier is (Sze, 1969)

where E is the electric field associated with the barrier. The electric field at the semiconductor surface of an MIS diode is

Es = (2qno4s/~~o)1’2, (24) where dS represents the empty well surface potential, hence from Eqs. (23) and (24), and assuming (Kinch and Buss, 1971) (rn*/m,) = 7 x Eg, we have

where n, is in ~ r n - E, ~ , and C#Js in volts. The tunnel current is seen to have an extremely strong dependence on semiconductor bandgap, and a somewhat weaker dependence on doping concentration and surface potential. The dependence of tunnel current on empty well surface potential for various values of doping concentration n, given by Eq. (25) is shown in Figs. 16 and 17 for two selected bandgaps, Eg = 0.25 eV and 0.1 eV, respectively. Also included in Figs. 16 and 17 are the two values of background flux generated current appropriate for the cutoff wavelength under consideration assuming a quantum efficiency r) = 0.5, and a typical infrared system field of view off/2.5. It is apparent that for the Eg = 0.25 eV (A, = 5 pm) case fairly substantial values of C#Js (and hence well capacity, QFw Cox+,)can be achieved before the tunnel current exceeds that due to the background flux even for doping concentrations in the 1015 cmP3 range. The maximum electric field at the surface corresponding to the values of dSgiving .Itunnel = Jmas given by Eq. (24) is relatively insensitive to

-

+ (V) FIG.16. Tunnel current dependence on empty well surface potential for various carrier concentrations of E. = 0.25 eV.

+s ( V ) FIG.17. Tunnel current dependence on empty well surface potential for various carrier concentrations for E, = 0.1 eV.

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

335

the value of no and is approximately 3 x 104 V/cm. For the Eg = 0.1 eV case, however, even though Jmis larger by almost two orders of magnitude, because of the strong dependence of tunnel current on bandgap given by Eq. (25) the condition that Jtunnel IJmcan only be achieved for empty well surface potential values I1 V, even for the stringent materials requirement of no = 1014 ~ m - It ~ .is thus much more difficult to achieve meaningful well capacities at this cutoff wavelength (A, = 12.5 pm) than at A, = 5 pm. The maximum electric field achievable in Eg = 0.1 eV material is 7 x 103 V/cm. The above calculation is somewhat oversimplified in that the expression given by Eq. (25) is based on a uniform field model for the potential barrier which is not strictly correct for an MIS diode. A more physically realistic tunnel calculation has been developed by Anderson (1977) that assumes a uniform charge model for the potential barrier and also accounts for nonparabolicity of the band structure, and this not surprisingly results in values of tunnel current somewhat smaller than those shown here because of the associated decrease of electric field away from the semiconductor surface. Furthermore, the tunnel current given by Eq. (25) is strictly valid only for the approximately empty well condition. As the well fills, the tunnel current tends to decrease due to the collapse of the well. Numerical calculations which include the above refinements indicate that the tunnel currents given by Eq. (25) represent an overestimate by approximately a factor of 5- 10 of the average current present during the collapse of the well to thermal equilibrium. The theory considered thus far concerns direct interband tunneling; however, tunneling between the valence band and conduction band of a semiconductor is possible by means other than a direct transition. Direct interband tunneling is indicated in Fig. 18a by transition (1). Transition (2)

(a)

(bi

FIG. 18. (a) Various tunneling mechanisms in (HgCd)Te, and (b) tunneling via bulk Shockley - Read centers.

M. A . KINCH

336

takes place by thermal excitation from the valence band to a ShockleyRead recombination center NR,and then via tunneling from NRto the conduction band. Transition (3) takes place by thermal excitation from the valence band to a surface state Nfs,and then via tunneling from Nfsto the conduction band. The excess tunnel current via these intermediate bandgap states is similar in nature to that found in tunnel diodes (Sah, 1961). The effect of tunneling via bandgap states can be visualized with reference to the normal generation of minority carriers out of Shockley-Read centers in the depletion region of an MIS diode pulsed to deep depletion by a consideration of transition (2) of Fig. 18a. This transition is detailed in Fig. 18b for a Shockley-Read center of density N R , a distance et from E,, with capture coefficients for electrons and holes given by ynr yp, respectively. N c and N , represent the density of states in the conduction and valence bands, respectively, and the tunneling probability from the NR center to the conduction band is o. The net capture rate of electrons into NRcenters is

ue == 3/n(NR- nr)n - ')'nnlnr

- n#(Nc

-

nc) + (NR-

nr)Wnc,

(26)

and for holes u h =

ypnrp

-

yppl(NR - nr),

(27)

where n, is the density of N R centers occupied by electrons, nc is the density of electrons in the conduction band at the tunneling energy, nl = Nc exp[ - ( E , - &,)/kT],and pi = Nv exp[ - q / k T ] . At equilibrium We = Uh, giving

and

If tunneling is negligible then Eq. (29) provides the normal generation rate out of NRgiven by (for yn = yn) the denominator having its minimum value, namely, n1 = p1 = n i ; for deep depletion we have n = 0, p = 0, and = Uh = - t N R y p n i = -(ni/270),

(30)

hence, the dark current is Jded =

niqW/270

A/cm2,

(19)

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

337

the familiar expression for thermal generation current from the depletion region. However, if tunneling is important, then we can neglect the ynnl thermal transitions-and

Here ypynnfis negligible, and N , >> n c , hence

ue =

uh

=

- NRypPl~Nc/(~OPl + ON,),

(32)

and again the rate will optimize when the denominator is a minimum, occurring for yppl = ON,, giving

ue = u h = - ~ N R Y ~ P I 9

(33)

which can be significantly larger than the thermally limited case, as p 1 >> n l , depending on where the Shockley-Read level is relative to the valence band. Similar arguments apply to surface states, and NR is replaced by Nfs(kT/q).The magnitude of the tunneling rate ON, is obviously critical in determining the importance of this effect. The tunnel diode theory of (Sah, 1961) indicates that the tunneling rate out of the NR centers is given by

where all quantities have been previously defined except for M, which represents the matrix element of the trap potential energy between the unnormalized trap-state wave function and the band-edge Bloch wave function, normalized in unit volume. The experimentally determined value of V cm3. Assuming a the quantity W ( m * / m , )for silicon is found to be similar value for (HgCd)Te, Eq. (34) gives

) in volts, and E in V/cm. For h, = 12.5 km, for where E, and (E, - E ~ are instance, Eg = 0.1 eV and the critical field for significant direct tunneling is approximately 7 x lo3 V/cm. The generation rate of Eq. (32) will maximize at the value of ct given by the solution of yppl = O N , , where y p for (HgCd)Te lies in the range 10-lo-lO-g cm3/sec. Utilizing Eq. (35) and a value for yp = 5 x 10-lo cm3/sec the optimum level is given by .zt = 42.5 mV, for E = 7 X 101 V/cm and T = 77 K. The value of ON, = yppl = 2 x lo6 sec-l, and p1 = 4 x 1015 ~ m - The ~ . generation rate given and (ypNR)-' again represents the bulk by Eq. ( 3 3 ) is Ue = - (NRypp1)/2

M.

338

A . KINCH

Shockley-Read lifetime associated with minority-carrier holes in (HgCd)Te. High-quality material will have values of (ypNR)-l in excess of 5 psec, in which case the tunnel current associated with the generation rate of Eq. (33) is given by Jtunnel

= tqNRypp1W = 6.4 X 10 W A/cmZ.

(36)

The value of W will be given by that part of the depletion region over which (i) the combined thermal-tunnel transition is allowed, and (ii) the electric field is a maximum. For MIS devices pulsed into deep depletion W may be a significant fraction of the total depletion region, but for devices in thermal equilibrium the relevant W will be a much smaller fraction of the space-charge region. However, if the reasonable value for W = 10-5-10-4 cm is assumed, then the current due to the above mechanism will be Jtunnel= 6.4 X 10-*-6.4 x lop3 A/cm2. To achieve tunnel currents smaller than this will require the use of material with ShockleyRead lifetimes in excess of 5 psec, or operation at temperatures below 77 K, assuming that the above calculation from N R centers is the right order of magnitude. The validity of the calculation rests mainly on the assumed value for M ,the matrix element of the trap potential between the trap-state wave function and the band-edge Bloch function. Similar reasoning will apply to fast surface states and band-tail states. For instance, the current generated from tunneling via a uniform density of fast surface states across the bandgap will be given by Jtunnei

= -!iqypP~[N&T/q] = 1.75

X

l0-''Nfs A/cm2.

(37)

A/cmZ for Ni,= 10l2 cm-2/V, so surface Thus, .Itunnel = 1.75 x states must also be kept to minimum. d. Storage Time

The dark currents discussed at length above can be utilized to predict upper limits for R,,A products of thermal equilibrium diodes or for storage times of dynamic mode devices. Infrared detector operation is typically required at the highest possible temperature compatible with system performance, and this temperature will not be too far removed from the intrinsic range for any cutoff wavelength. Under these circumstances the dominant dark current mechanism, particularly for n-type substrates, is via diffusion from the bulk of the semiconductor, with some possible contribution from the various tunneling mechanisms at cutoff wavelengths beyond 10 pm, depending on the desired well capacity. Utilizing the earlier diffusion current theory Fig. 19 shows the calculated dependence of storage time on temperature for n-type (HgCd)Te of two specific cutoff wavelengths, namely A, = 5 pm and A, = 10 pm. These calculations are for a constant cutoff wavelength as opposed to a constant composition

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

339

TlKl

FIG.19. Auger-limited storage time versus temperature for constant cutoff wavelengths A, = 5 pm, 10 pm. n-type (HgCd)Te: C A V = 2 x lo-' C/cm2.

and utilize the Auger-limited diffusion current data contained in Fig. 13 together with the mobility data of Fig. 8. The assumed value for well capacity is 2 x coulomb/cm2. Included in Fig. 19 on the right-hand axis is the equivalent background flux for any specific storage time, assuming a quantum efficiency q = 0.5. In other words, the current generated by the indicated background flux levels, namely qqaB,will limit storage time values to T , ~= 2 x 10-7/(qq@B).As a specific example consider a 5-pm device operating in a background flux environment of 5 X 1014photons/cm2 sec (anf/2.5 system); the storage time limit will be 5 X lop3sec. For the MIS device to be background limited the thermally generated dark currents must be less than qq@* which according to the A, = 5 pm curve will necessitate operation at temperatures below 155 K. Similar arguments apply to other cutoff wavelengths. III. (HgCd)Te MIS Experimental Data

3. THERMAL EQUILIBRIUM MODE A simple single-level MIS device on (HgCd)Te typically incorporates a layer of thermally evaporated zinc sulfide, with thicknesses between

M.

340

A. KlNCH

1000 A and 10,000 A, on top of a layer of native oxide (Catagnus and Baker, 1976) to form the overall insulator, although the native oxide alone can be employed with a layer of 700- 1300 A. Zinc sulfide is used because of its excellent infrared properties and dielectric strength, and the native oxide for its high-quality interface properties. A variety of metals have been employed as gate material, and for infrared response measurements transparent electrodes consisting of thin layers of metal (-100 A) are utilized. Photoconductive-quality (HgCd)Te is grown by the solid-state recrystallization technique which is based on quenching a high-purity melt of the proper composition followed by recrystallizing the resulting polycrystalline ingot at a temperature just below the solidus temperature. The result is a homogeneous, high-purity (determined by the purity of the starting constituents) boule consisting of a few large crystallites of the desired alloy. The majority of ingots prepared in this manner contain to a greater or lesser degree some substructure, or low angle grain boundaries, although some are entirely free of this defect and are single crystal. No direct evidence has yet been found that the degree of substructure, unless extremely bad, has any deleterious effect on MIS performance. Bearing this in mind, no attempt will be made throughout these experimental sections to correlate device performance with known crystal orientation. The measured capacitance-gate voltage characteristic at 77 K and f = 1 KHz for a typical 5-pm n-type (HgCd)Te device fabricated on 700 8, of native oxide is shown in Fig. 20. The device is 12 x 12 mil in area and the oxide capacitance is -2.3 x lo-' F/cmZwhich indicates an oxide dielectric constant of 18.3. The flat-band voltage occurs at negative gate volt-

/+I

200

-

150

-

G w E

s Y

w

U

-

100-

50

-

I

I

FIG. 20. Capacitance (C) and dC/dV versus gate voltage for 0.25-eV n-type (HgCd)Te at 77 K , f = 103 Hz.

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

341

ages which, if work function differences are ignored, implies a fixed positive charge density in the oxide -10l2 cm+. This value of fixed positive charge is typical of the (HgCd)Te-oxide interface and has been verified for a variety of oxide-ZnS thickness combinations. Hysteresis effects are observed at 77 K and indicate a slow surface state density for hole trapping -1 to 5 x 1Olo cm-2. No evidence of mobile charge hysteresis is observed. The measured dC/dV curve shown in Fig. 20 can be utilized together with Amelio's theory to provide a value for the fast surface state density capable of responding to the applied signal frequency of 3 x 10" cm-2/V, assuming that the distribution in fixed oxide charge is negligible. Typical values obtained for Nfs by this technique on both n-type and p-type material lie in the range 5 X lolo-5 x 10" cm-2/V, and for the most part are frequency independent exhibiting no strong features across the accessible part of the bandgap. The measured conductance for the device in Fig. 20 is essentially zero, indicating that under these conditions (77 K, thermal background) the dark current associated with the depletion region under the gate is zero. This is substantiated by the fact that the highfrequency behavior of Fig. 20 is followed even at a frequency of 10 Hz. No frequency dispersion of capacitance is normally observed over the range 10- lo6 Hz, indicating that fast surface states are not contributing to the device capacitance even in the depletion range of surface potential. This is somewhat surprising in view of the predicted magnitude of the equivalent circuit R,,C, discussed earlier, and suggests that the value of 3 x 10" cm+/V for Nfsobtained by the Amelio technique is not correct, as a fast surface state density of this magnitude should be readily apparent in the C-V characteristics in the depletion range. Conductance measurements at higher device temperatures also typically show an absence of the conductance dispersion effects normally associated with surface states densities Nfs> 1Olo cm+/V. This is not always the case and a measured C-V characteristic for an n-type 0.25-eV (HgCd)Te device at 146 K is shown in Fig. 21 which indicates the presence of surface state dispersion in the frequency range 103-104 Hz, even though no effects due to these states were obvious at 77 K. The use of the higher temperature for 0.25-eV material enables one to probe levels deeper into the bandgap at the applied signal frequency simply because of the increased thermal transition rates from Nfsto the majority-carrier band. A somewhat different approach can be utilized to investigate transitions from Nfs to the minority-carrier band which involves the use of background photon flux. The incident photon flux effectively lowers the resistance Rd connecting the minority- and majority-carrier bands in the equivalent circuit Fig. 7a to a negligible value. Thus, in the gate bias region corresponding to weak inversion Rpa << R,, and the fast surface states in this region of the gap

M. A. KINCH

342

-14

I

I

-12

-10

I

I

1

-8

-6

-4

V G (VI

FIG.21. Capacitance-gate voltage characteristic at 146 K indicating surface state disperF/cmZ. sion for 0.25-eV n-type (HgCd)Te. Cox= 2 x

will contribute to capacitance and conductance dispersion. This phenomenon has been observed in 0.25-eV n-type (HgCd)Te at 77 K. The effect of background photon flux on inversion layer response time (Le., R d ) is shown in Fig. 22. The signal frequency for this C-V characteristic is 10 Hz and the 0.25-eV n-type MIS device exhibits a high-frequency behavior at 77 K. The introduction of a small amount background photon flux (2.8" FOV = 5 x 1OI2 photons/cm2 sec) produces low-frequency behavior due to the reduction in the value of Rd in the device equivalent circuit Fig. 7a. Increasing amounts of background flux cause the C-V characteristics to behave in a predictable manner, namely the capacitance minimum moves to higher capacitance values due to the reduction in depletion layer width and the conductance becomes finite and follows the simple theory given in Eq. (10). Low-frequency conductance measurements as a function of temperature on 5-pm (& = 0.25 eV) n-type (HgCd)Te devices biased to strong inversion indicate that the dominant dark current in the temperature range 130-200 K is diffusion limited, with the impedance Rd [obtained with Eq. (lo)] varying as n i z . A weaker dependence on temperature is observed at lower temperatures which is probably indicative of depletion currents. This will be discussed further in Section 4. Similar effects are observed in p-type material except for the problem associated with the positive fixed oxide charge which in this case drives the surface to inversion. The shunting effect of this inversion layer requires the use of overlapping guard rings for MIS device isolation; an example of the effect of this guard ring on a capacitance-voltage character-

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

-

343

J 3'FOV

1

-I. 5

-I. 0 V G IVI

FIG.22.

-0. 5

-1

-6

-4

-5 VG

-3

IVI

FIG.23.

FIG.22. Capacitance-gate voltage characteristic at 77 K as a function of background photon flux for 0.25-eV n-type (HgCd)Te.f = 10 Hz. [Kinch er al. (1980).] FIG.23. Effect of guard ring on 0.25-eV p-type (HgCd)Te MIS device at 77 K, f = 200

Hz.

istic atf = 200 Hz is shown in Fig. 23. Again, for these devices typically no capacitance dispersion is observed over the frequency range 10-10s Hz. The dependence of capacitance (C), conductance (G), and dC/dV on gate voltage, measured at 77 K and f = lo4 Hz, for a typical 0.1-eV n-type (HgCd)Te (A, = 12.5 pm) MIS device fabricated on native oxide is shown in Fig, 24. Values of MIS device parameters are similar to those found for 0.25-eV (HgCd)Te; the fixed oxide charge is positive and -10l2 cm-2, the fast surface density indicated by the Amelio dC/dV technique is in the range 5 x lolo-5 X 10" cm+ V-' and the slow surface state den' ern+-. The capacitance characteristic exhibits lowsity is -1-5 x 1OO frequency behavior at the 104-Hz signal frequency and as such G, = 0 2 c x R d thus, ; the measured conductance is a direct indication of the impedance associated with the depletion region beneath the MIS gate, i.e., it varies inversely with device dark current. The magnitude of the measured conductance for 0.1-eV devices at 77 K and zero background flux is consistent with dark current contributions from an Auger-limited diffusion process modified by tunneling currents. The peak conductance

344

M . A. KINCH

-2. 0

-1. 0 Field Plate Bias I V I

0

1.0

FIG.24. Capacitance (0,conductance ( G ) ,and dC/dV versus gate voltage for 0.1-eV n-type (HgCd)Te at 77 K , f = 104 Hz,x - 0.2. [Kinch et a / . (1980).]

of these devices correspond to RJ products in the range 1-7 0 cm-2, which are considerably below the upper limit predicted by Auger-limited diffusion (Kinch and Borrelo, 1975) for this material. An RJ product of 7 0 cm2 is equivalent to a dark current Jd = lop3A/cmP. At the thermal backgrounds involved the background flux current is negligible. A current of this magnitude caused by carrier generation-recombination in the depletion region would require a lifetime T~ = ( T ~ T ~ ~of) ~ ’ * sec, where rm and T,, represent the lifetimes of holes and electrons associated with the dominant centers in the bandgap. Lifetimes of this magnitude are unlikely in view of the large values found in n-type bulk material; also this type of current will effectively saturate for gate biases for which +s > 2&, as the depletion width is thereafter constant. Surface recombination currents of this magnitude are also unlikely, requiring surface recombination velocities > 103 cm/sec, a value totally out of context with measured recombination velocities on n-type (HgCd)Te photoconductive detectors fabricated using similar surface processing techniques. It is thought that the dominant current contribution is due to tunneling, although it cannot be of the direct interband variety, because at the indicated gate bias voltages the conduction and valence bands do not overlap. Tunneling via

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

345

bandgap states is possible, however, in the manner discussed earlier in Section 2. Following that theory, even for high-quality material with T~ = 5 psec, tunnel currents A/cm2 will be generated for average electric fields of 7 x 103 V/cm effective over a distance cm. A thermal transition is involved in this process which indicates that this tunnel component should be strongly temperature dependent, however, attempts to measure this effect are masked somewhat by the fairly strong decrease of the (HgCd)Te bandgap (and hence increased tunneling probability) with temperature. The peak conductance, however, does show a very marked increase as the temperature is reduced even to as little as 55 K, indicating that the above mechanism is indeed the dominant one. Again in this material, as in the 0.25-eV (HgCd)Te, little evidence is found of dispersion in either capacitance or conductance measurements that could be attributed to fast interface states. This would again indicate that the observed slope dC/dV is mainly due to a distribution in fixed oxide charge, and that the surface state density of the typical (HgCd)Te-native oxide interface is in the low 1O'O cm-2/V range. At intermediate compositions of (HgCd)Te between the 0.1- and 0.25-eV bandgap values the general trends reported above hold. A specific example of x = 0.22 is shown in Fig. 25, which has a measured cutoff wavelength of A, = 9.8 pm at 77 K. Tunneling effects are again in evidence but are not as severe as the A, = 12.5 pm case. The indicated RJ product at the conductance peak is -1.2 X 102 SZ cm2.

FIG. 25. Capacitance (0 and conductance (G) versus gate voltage for x = 0.22 n-type (HgCd)Te at 77 K . no = 7 x 10"

~rn-~.

ih, I c l

U 0

-7

-6

-5

-

-3 VG IVI

-2

-I

346

M. A. KINCH

4. DYNAMIC MODE

Operation of MIS devices in a pulsed or dynamic mode provides a direct measurement of the storage time of the well formed under the gate, and hence the magnitude of the device dark current under these operating conditions. The discussion of dark current and storage time in Section 2 indicated that (HgCd)Te MIS devices should be limited by diffusion currents over a wide temperature range. For n-type substrates the upper limit on storage time, T , ~ ,is given by an Auger band-to-band recombination mechanism and the theoretical predictions were summarized in Fig. 19. The absence of adjustable parameters in the theory of Auger-limited diffusion currents at any specific temperature suggests that a high confidence factor can be placed in these calculations. This has been verified by measurements of storage time versus temperature on a variety of compositions, one of which is shown in Fig. 26. The composition is x = 0.30, which corresponds to a cutoff wavelength at 77 K of A, = 4.9 prn, and at 200 K of A, = 4.5 pm. The measured storage time closely tracks the theoretical prediction over the range 130-200 K. Below 130 K a weaker dependence on temperature is observed which could be attributed to generation currents associated with the depletion region. It is interesting to note that significant storage times are available in the thermoelectric cooler range of temperatures, namely 170-200 K, with measured values in the 100-psec range for this composition. The magnitude of the various dark current components at 77 K can be

ID

FIG.26. Experimental and theoretical storage time versus temperature for x n-type Hg,-,Cd,Te. A, = 4.9 km at 77 K; C A V = 6 x lo-* C/crnWa.

- 0.295

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

347

estimated from the theory summarized in Section 2, and as a specific example let us consider the composition x = 0.285 (A, = 5.4 p m at 77 K, which is identical to InSb). For reasonably low gate voltages, tunnel currents can be ignored and at zero background the dark current is given by Ea.- (12): . . J~ = qni

[%+ 270" + I

For (HgCd)Te, ni = 7 x lo9 ~ m - T~~ ~ ; = 105 sec; p p = 450 cm2/V sec. Assuming a voltage swing of 0.5 V, and material parameters no = 3 X 1015 ~ m - T~, ,= 2 x sec, then the depletion region width is W = cm. The thermal terms become [2~~~V/q= n ~6.1 ] ~x/ ~

gnW , = 2.0 x lo-* A/cm2, 270

7

= 5.6 X 10-lo s A/cmZ.

Thus, the dominant dark current, for reasonable surface recombinatim velocities (s < 102 cm/sec), is due to generation in the depletion region, and for a native oxide device with Cox 2 X lo-' F/cm2, and a gate voltage pulse of 0.5 V the predicted storage time will be rSt= C,,AV/Jd = 5 sec. The accuracy of the above calculation has been verified by storage time measurements on an MIS device fabricated from just such material. The measured storage time is illustrated in Fig. 27 and is - 5 sec.

-

HORIZONTAL ( I 5 ~ c / c i i i ]

FIG.27. Measured storage time at 77 K for x = 0.285 (Ac with n, = 3 x lOl5 ~ m - ~ .

- 5.4 Fm) n-type Hg,-,Cd,Te

M.

348

A. KINCH

Storage time measurements on narrow-gap (HgCd)Te indicate, as expected, that tunneling plays a significant role in this material. The theoretical prediction for a cutoff wavelength A, = 10 prn given in Fig. 19 for Auger-limited diffusion currents indicates that Tst values in excess of 100 psec should be possible at temperatures in the liquid nitrogen range. The measured dependence of T,$ versus temperature for a composition x = 0.23 (A, = 9.3 pm at 50 K) is shown in Fig. 28, for a fixed gate voltage pulse -0.75 V. For temperatures above 100 K the values of rStare in approximate agreement with diffusion current theory for a ShockleyRead limited minority-carrier lifetime. This Shockley -Read limited diffusion current can be estimated at temperatures above 110 K from thermal equilibrium MIS conductance measurements. The calculated storage time based on this estimate is indicated at 112 K in Fig. 28, and agrees very well with the measured value of TSt. At temperatures below 100 K the measured 7,t exhibits a strong departure from the diffusion-limited curve. This is attributed to tunnel current contributions to the device dark current. In devices pulsed into depletion both direct interband tunneling and tunneling via bandgap states is possible, however, the observed plateau in TSt versus temperature indicates that the dominant mechanism is via bandgap states. If direct tunneling dominates then due to the decrease of the (HgCd)Te bandgap with temperature one would expect the measured

50

60

70

an

90

Tprriperarure

ion

iio

120

(K)

FIG.28. Storage time versus temperature for x = 0.23 (A, = 9.3 p m at 50 K) n-type F/crn. Hg,-,Cd,Te. V,,,, = 0.75 V; no = 5 x 10" ern-? Cox= 4 X

7.

METAL-INSULATOR-SEMICONDUCTOR I N F R A R E D DETECTORS

349

storage time at constant gate bias (or well capacity) to show a marked decrease at lower temperatures. However, the bandgap state tunneling involves a thermal transition and the two effects might be expected to cancel each other out depending upon the position in the energy gap of the relevant Shockley-Read center. At lower values of gate bias voltage than 0.75 V the measured storage time increases as the temperature is decreased, and values -100 psec are observed at 55 K for this material. This lends further credence to the importance of the tunneling mechanism involving bandgap states. IV. (HgCd)Te MIS Photodiode Technology 5 . THEORY

The MIS photodiode (Phelan and Dimmock, 1967; Kinch, 1974) is merely a photon detector that utilizes the equilibrium depletion region induced under the transparent gate of an MIS structure biased into strong inversion to collect minority carriers generated by incident photons from less than a diffusion length away. It will become apparent that for all practical purposes the MIS photodiode behaves as an open-circuit photodiode that is capacitively coupled to the outside world. The potential diagram for an n-type MIS device biased to strong inversion is shown in Fig. 29 for the two cases of (a) thermal equilibrium and

FIG.29. Potential diagram for n-type MIS device biased to inversion (a) at thermal equilibrium, and (b) with incident back-

I

ground photon flux.

I

(a1

M.

350

A . KINCH

(b) an incident photon flux OBsufficient to give a hole quasi-Fermi level From the general MIS theory discussed in Section 1 we have from Eq. ( 5 ) that strong inversion begins when

@. significantly different from the electron Fermi level

a.

p S = P , exp( - q+PVlkT) 2 no ,

i.e., when the surface concentration of holes becomes greater than the bulk majority-carrier concentration. For the case of an incident photon flux, surface inversion occurs for lower values of +s than the thermal equilibrium case because the valence band crosses the hole quasi-Fermi level Ef for smaller values of surface potential, i.e., +f(inv) < &"(invj. The associated depletion width W will also be narrower for the incident photon flux case. The relationship betweenp, and +,(inv) is given by Eq. (5) to be A+,(inv) = ( k T / q ) Apolpo;

(38)

thus a change of Ap, due to a change in photon flux results in a corresponding change in A&(inv), given by Eq. (38), and a change AW in maximum depletion layer width. This effect can be utilized to detect infrared radiation in the following manner. Consider the expression for space-charge density at the surface given by Eqs. (3) and (4), namely,

+

(e-q@8/kT

+& kT -

y2. (39)

The dependence of Qs on +s is shown in Fig. 30 with p , as a variable parameter (due to incident photon flux, say). Let us assume that the MIS gate is biased to a voltage V corresponding to a surface potential appropriate for strong inversion and then the gate is floated. Any change in incident photon flux after this point in time will result in a change in surface potential given by Eq. (39). In strong inversion Qs = ( 2 ~ ~ , k T p , e - ~ @ J ~ ~ ) ~ ~ ~ ,

(40)

and for the floating gate we have, differentiating Eq. (40) and assuming Qs is constant, A+s =

(kT/q)A~olpo,

(41)

which is equivalent to Eq. (38). The charge on the gate is constant, hence the voltage drop across the insulator must be constant and therefore A+s = AV, the change in voltage on the floating gate. Thus a change in photon flux has been translated into a change in voltage on the MIS gate

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

351

$s (ev)

FIG.30. Variation of space-change density in 0.25-eV n-type (HgCd)Te as a function of surface potential for no = 2 x loxscm-3, T = 77 K, for various minority-camer concentrations.

given by Eq. (41). This expression can be recast into more familiar terms. Consider the case of the MIS device limited by diffusion currents, in which case the impedance of the diode region is given by RdAd = kT/qJdif,

which from Eq. (13) = kTTp/q2poLp,

(42)

where L, is the minority-carrier diffusion length, T, the minority-carrier lifetime, and Ad the device area. Assuming that Apo is due to an incident signal photon flux A
(43)

Thus, the change in surface potential due to an incident photon flux A@B is exactly that expected for an open-circuit photodiode of impedance Rd . The MIS photodiode as a circuit element is shown in Fig. 31a and its equivalent circuit based on the above arguments is shown in Fig. 31b. The surface directly under the field plate is biased to inversion by the application of a dc negative bias (for an n-type substrate); hence, we essentially have a diode in series with the insulator capacitor Cox.The incoming signal photons are incident through the transparent field plate and gener-

M. A. KINCH

352

(b)

FIG,31. MIS photodiode (a) in circuit (b) equivalent circuit.

ate a charge flow in the open-circuit diode portion of the circuit. The signal appearing at the XX terminals can be envisioned by considering a sudden turning on of signal photons A@g. The voltage across R , changes by an amount qq A a g R d d in a time - R d C d . This voltage instantaneously appears across RL if R,C,, >> RdCd and is passed through to the preamplifier. This voltage will decay with a characteristic time RLCoxuntil the insulator capacitor charges up to the point where no further current flows. A large value of RLC,, essentially constitutes the floating gate of our earlier discussion. In ac terminology, if the incident photon flux is modulated at a frequency o m ,then the ac signal appearing at XX is given by

For WmRdCd -K 1, and omRLco,>> 1 , Eq. (44) reduces to L\v = qq A@B R,,Ad, which again is simply the signal voltage across the open circuit diode. The theoretical frequency dependence of the MIS photodiode given by Eq. (44) is shown in Fig. 32. With an incident background flux OBon the MIS detector, the impedance at sufficiently low temperatures will be determined by aB.For a diffusion-dominated depletion region the current flowing is given by I

=

Z,(exp(qV/kT) - 1) -

7)@&d

=0

for the open-circuit case. Hence, for V > k T / q , we have

(45)

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

353

log f

FIG.32. Dependence of MIS photodiode signal on frequency.

Thus, from Eqs. (43) and (46),

AV = (kT/q) A@B/@B

(47)

and the signal voltage is independent of quantum efficiency. Therefore, although the device responsivity is less than for a photodiode operating at zero-bias voltage (in that mode of operation the diode impedance is determined by the thermal dark currents flowing in the depletion region), it is independent of quantum efficiency. Equations (46) and (47) can be combined to give the familiar expression for the BLIP specific detectivity, namely,

D* = (1/2h~)[7/@B]~”.

(48)

Arguments similar to those above can be made for nonideal depletion regions (e.g., dominated by generation-recombination currents in the depletion region) with essentially similar results. Theoretical D* values will only be achieved provided the detector noise dominates all other noise sources, and this will be true provided the value used for RL is sufficiently large. In fact the noise voltage output across the XX terminals is approximately given by VN

%

4kTdRd Af

+ l/joCox12Af + 4kTRLIRd IRL + Rd + ~/jWCoxl~

4kTdRd Af

4kT Af + RLO~C~,, ’

(49)

if wCOxRL> 1 ; T in Eq. (49) refers to the temperature of the load resistor

354

M.

A.

KINCH

7

"TR2

FIG.33. MIS photodiode coupled to Si CCD via gate of input MOSFET.

R, ,and Td to that of the detector. Thus the noise from Rd will be observed across XX provided RL

'( T / T d ) ( l / R d ~ 2 ~ x ) *

(50)

The equivalent circuit of Fig. 31b includes the input impedance RA and input capacitance C A associated with the following preamplifier. For optimum device performance it will also be required that RA > RL and CA < cox.

Thus far we have limited our discussion to preamplification of the detector voltages prior to any form of signal processing. Various schemes have also been proposed (e.g., Bate et ai., 1973) to utilize the compatibility of the MIS photodiode with silicon CCD signal processors for signal multiplexing prior to preamplification. Just one such scheme is illustrated in Fig. 33 in which the output from the MIS photodiode is coupled to the gate of the MOSFET input to a silicon CCD shift register, and thus modulates the charge input to the CCD wells. The bias voltage of the MIS device is periodically reset via the MOSFET switch V,, to the value required for surface inversion. The limitation on the usefulness of this signal multiplexing scheme will be determined by a consideration of the thermal noise of the CCD input compared to the noise of the MIS photodiode. 6. PERFORMANCE DATA A typical M I S photodiode is illustrated in Fig. 34. The insulator in this instance is 600 A thick. The thick insulator underneath the bonding pad is shown as photoresist, but obviously other insulating materials may be used. Ohmic contact to the n-type substrate is made via a large-area indium bonding pad. It is meaningful to calculate the magnitude of the MIS photodiode

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

355

Photons

htilk contact Au h a l l h o n d I

n d i uiii bond

t nad

\

6 0 0 - i oxide

depletion reqion n - t y p e (HqCd)Te

FIG.34. MIS photodiode structure

parameters for thermal background operation in the temperature range in which diffusion dominates the device dark current, say for T > 130 K for a 0.25-eV (A, = 5 pm) n-type (HgCd)Te substrate. The impedance associated with the diode region is given by Eq. (42) Rd

=

kT7p/q2PoLpAd

(42)

3

and in the best available material T~ is limited by an Auger band-to-band recombination process, and is given by Eq. (14) TP

where

T A represents ~

(14)

= 2TAin?/no(no -k P o ) ,

the Auger lifetime for intrinsic material. Thus,

where all the parameters are well defined at any specific temperature. As an example consider operation at 190 K, when ni = 2 x lOI4 ~ m - p~p,= 200 cm2/V sec-l, and rAi= 4 X sec; thus R d d = 8 fl cm2, and for a 1.5 X cm2 device Rd = 5.3 X 104 a. The dependence of R d d on temperature as given by Eq. (51) is shown in Fig. 35, assuming a constant cutoff wavelength A, = 5 pm. The capacitance per unit area associated with the depletion region is given by Cd/& = EEo/ W, where the depletion width W is given by

W 2= 4 ~ ~ , + d n , q , +F

being the bulk Fermi potential. For n-type 0.25-eV material

(52)

E

- 19.5,

M.

356

A. KINCH

-

-

-

-

- in' - -

--

3 \

r. , -

r .

-

I

" *o

10'2

-

- 10

a.

r D

I DO

i 70

1'10

I60

I A0

200

220

(K)

r)

FIG.35. L)' and Rg, versus temperature for Auger-limited 0.2s-eV n-type (HgCd)Te. = 1 .O; A, = 5.0 Nm,

-

and for no = lOI5 cm", & 25 mV and W = 3.4 x lo+ cm, giving CdAd = 5.3 X lop8F/cm2. Thus the capacitance of a 1.5 x cm2 device is C, = 8 pF, and the response time under these conditions is RdCd = 4.25 X lO-'sec. The value of the insulator capacitance is determined by the thickness of the insulator, which is typically 700 8, of native 18.3. Hence, &/Ad = oxide, with a static dielectric constant E,, 2.3 x 10'' F/cm2. The value of the device components in the equivalent circuit of Fig. 31b for this 0.25-eV n-type (HgCd)Te MIS device of area 1.5 X 10" cm2 operating at 190 K will thus be Rd = 5.3 X lW 0;Cd = 8.0 pF; and Cox= 34.5 pF. The signal voltage appearing across RL is that given by Eq. (44),and provided RL is large enough, the noise voltage V, across RL will be determined by Rd. The condition on RL is given by Eq. (50) to be RL >> 6.1 x lOI4f2 a, wherefis in Hz,assuming that T = 300 K Thus V , will be determined by Rd at f = 1V Hz if RL >> 6.1 X 108 R. The magnitude of V, under these circumstances will be given by Eq. (49), namely (4kTd& Af)1'2 = 2.4 X V/Hz112.The detectivity is thus given by Eqs. (44) and (49):

-

D*

=

AV(Ad

Af)"2/v,. h @hVAd ~

= (174/2hV)[RdAd/kTl1'*,

(53)

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

357

hence D* = 10” cm I - I P / W for the above set of parameters, assuming the quantum efficiency q = 1.0. The dependence of D* on temperature given by Eqs. (51) and (53) is included in Fig. 35. The only reported data on (HgCd)Te MIS photodiodes (Kinch, 1974) dealt with n-type substrates of photoconductive quality material. The dependence of MIS photosignal magnitude on applied gate bias for a typical 0.25-eV device at 77 K is shown in Fig. 36, for a background photon flux level of 4 x I O l 4 photons/cm2 sec. Also included is the measured dependence of capacitance and conductance at 5 x lo4 Hz, and the inversion layer exhibits a high-frequency response at this frequency. The photosignal, however, is measured at 700 Hz where umRdCd< 1, and it is readily apparent that the photosignal appears as the surface is driven into inversion and thereafter remains at a constant magnitude, as does the measured device conductance at both high and low frequencies. Figure 37 shows the measured dependence of photosignal on inverse temperature for the same device. The indicated temperature dependence follows closely the theory of Eq. (51) for the composition x = 0.285 although the magnitude is low by a factor -2.5 for the measured quantum efficiency 7 = 0.7. The photosignal reaches a background limited value for T < 130 K with an indicated peak responsivity Rh = 1.2 x lo6 V/W, which is

VG

(v)

FIG.36. Capacitance ( C ) ,conductance ( G ) ,and photosignal (V.1 versus gate voltage for 0.25-eV n-type MIS photodiode at 77 K.

358

M . A. KINCH


b

x

=

0.285

FIG.37. Detectivity, responsivity, and noise voltage versus temperature for x p-type (HgCd)Te MIS photodiode.

- 0.285

-

again lower than theory would predict by 2.5. The measured noise voltage per unit bandwidth at a frequency of 103 Hz is shown in Fig. 37 and is primarily device limited for T < 130 K. However, at higher temperatures the noise is determined by the RL load resistor, as Eq. (50) is not satisfied for the bias circuit. The indicated D* below 130 K approaches BLIP for T,I = 0.7; however, at higher temperature the D* values decrease approximately as R Adue to the excess noise, and the predictions of Eq. (53) are not followed. The discrepancy observed in the measured responsivity is undoubtedly due to preamplifier loading in that CA =K C,, and K A RL 1080 for the preamplifier bias circuit used in the reported measurement. Refinements in this circuitry have yielded responsivity values fully consistent with Eq. (51). The spectral response of a typical MIS photodiode with x - 0.285 is shown in Fig. 38, at temperatures of 80 and 150 K. The measured response is quantum in nature except for the modification due to an antireflection coating of zinc sulfide evaporated over the transparent electrode. MIS photodiodes have been investigated on a number of other

-

359

7. METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

. a’

FIG. 38. Spectral response of X,

- 5 prn

MIS photodiode with antireflectioncoating.

* c

0 CI

--

,$ m

LL

-0

3

4 Wavelenqth &m)

5

I

(HgCd)Te compositions ranging from 0.20 < x < 0.40, and it is perhaps pertinent to discuss some of the results for A, = 12.5 pm. The measured capacitance-voltage characteristics for an array of 300 x 300-pm MIS photodiodes is shown in Fig. 39 for a measuring frequency of los Hz, at a temperature of 77 K. The measured response is tending towards high frequency and the indicated device uniformity is excellent. At lower frequencies the capacitance and conductance characteristics for typical 0.1-eV n-type devices are as shown in Fig. 24. The conductance at low frequencies ( mRd) exhibits a fairly broad maximum and the measured photosignal closely follows this behavior, thus for these devices there exists an optimum inversion bias voltage, unlike the 0.25-eV material. The measured conductance values indicate thermally limited RdAdproducts in the range 1-7 R cm2, thus for a quantum efficiency 7 = 0.5, a 125 X 125-pm device will have maximum impedance in the range of 6.6 x 103-4.6 x lo4 R with peak responsivity values of 3.3 x 104-2.3 x 105 V/W, when thermally limited at 77 K. The value of c d will be slightly higher than for 0.25-eV material for the same doping level because of the narrow bandgap and hence smaller values of c#J~,the bulk Ferrni potential. Coxvalues will of course be essentially the same. The major problem associated with the operation of small 0.1-eV MIS photodiodes is the requirement on RL given by Eq. (50), namely RL > T/(T&02G,). For a typical value of Rd = 2 x lo4 R, at 77 K with Cox= 30 pF, the noise associated with Rd will only dominate at lo3 Hz for RL > 5 x log R, with an equally stringent limitation on R A . The best value reported for a 0.1-eV device is D* = 3 x 10’O cm H Z ” ~ / Wmeasured at

360

M . A. KINCH

b

C u Y

'F Y 0

-I

5

-1 0

-0 5

0

0 5

1.0

I.5

vc ( \ I ) FIG.39. Capacitance versus gate voltage for a 14-element 0.1-eV n-type (HgCd)Te MIS photodiode array at 77 K , f = lo8 Hz.

lo4 Hz with a 22" FOV (+B = 4 x lois photons/cm2 sec) and a quantum efficiency 7 = 0.2. The associated peak responsivity was R A = 3 x 104 V/W with Ad = 1.5 X cm2. 7. SURFACE-CONTROLLED PHOTOCONDUCTOR It has long been realized that the effective photoconductive lifetime of a material is strongly dependent on surface conditions, or more precisely on fast surface state density N,, and surface potential &. Consider the energy level diagram in Fig. 40. If the density of fast surface states is suffi-

E:

E"

Ftc. 40. Simplified band model for sur. face of (HgCd)Te photoconductor.

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

361

ciently high then electron-hole recombination will proceed through these states at a more rapid rate than through the dominant recombination process in the bulk (which is determined by an Auger, radiative, or Shockley-Read mechanism). This recombination rate is defined in terms of the surface recombination velocity s given by

where yn and yp represent the familiar recombination coefficients of the surface states for electrons and holes, respectively. Ersis the surface state Equation (54) defines the surface recombinenergy, and uo = ln(-yp/yn)1’2. ation velocity for a monoenergetic surface state at Efs. If the surface states form a continuum, as indicated in Fig. 40, then it is obvious from Eq. (54) that the most effective states for surface recombination will be those at the intrinsic level E i , as this minimizes the denominator, provided that yp = yn. In the equivalent circuit of Fig. 7a representing the surface depletion region this condition is equivalent to R,,8 = Rp,8.The surface recombination velocity will be symmetrical with surface potential about this position. However, it must be pointed out that the surface potential can have a drastic influence on bulk photoconductive lifetime even if no surface states are present. This becomes obvious if one considers the dark currents flowing in the surface region of Fig. 40, which is depicted at strong inversion. Electron-hole pairs photogenerated within the depletion region or within a diffusion length of it will be physically separated as shown, and they will recombine at a rate determined by the RdCdof the depletion region w. At thermal equilibrium this time constant will be controlled by the dominant current source as discussed at length in Section 2, namely due to (a) diffusion, (b) depletion region, (c) surface, or (d) tunnel currents. (c) is the contribution described by the surface recombination velocity expression Eq. (54).The effect of these current contributions can be qualitatively estimated in the following manner. The incident photon flux density A@B changes the voltage drop across the depletion region, and hence its width, by essentially forward biasing the region in the manner described in Eqs. (38) and (43). This voltage change is given by

A v = 7)q A@B R&j.

(43)

The change in depletion width A W corresponding to this change in barrier height is given by

362

M.

A . KINCH

This change AW in the width of the depletion layer releases noAW electrons per unit area in the n-type bulk region of the photoconductor. This is equivalent to an effective change in majority-carrier concentration in the photoconductor of thickness t of

Ano =

no AW t

'

which by Eqs. (43) and ( 5 5 ) is Ano = -R~ 7 A@B = RdCd W t TP

(57)

where Apo represents the concentration of minority carriers generated by the signal flux A@* if the bands at the surface are flat, and rP is the bulk minority-carrier lifetime. Therefore, from Eq. (57), if the depletion layer response time T = RdCd> then the sensitivity of the photoconductive element is increased over and above the bulk value. If RdCd C T~ then a decrease in photoconductive sensitivity will result. To this end the quantity RdCd/rpmay be considered a trapping gain (Kinch and Boyd, 1973). The variation of photoconductive signal with inverse temperature for the surface-controlled photoconductor will depend on the nature of the dominant current contribution. For a diffusion current dominated surface region RdCd0~ nF2, and the photosignal will exhibit an activation energy of E,; for depletion currents on the other hand RdCda nrl, and the thermal activation energy will be E,/2. The contributions due to surface and tunnel currents should be relatively temperature independent. An example of surface-controlled photoconductivity is shown in Fig. 41 I

I

Capacitance

-45

-40

-j5

-?O

-20

-75

vc,

-15

-10

-5

0

(V)

FIG.41. Photoconductive signal and capacitance versus gate voltage for 0. I-eV n-type (HgCd)Te photoconductor at 77 K .

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

363

for 0.1-eV n-type (HgCd)Te at 77 K. The photosignal is measured on a photoconductive element 20 pm thick fabricated with the upper surface completely controlled by a transparent field plate on a 1-pm layer of ZnS + native oxide. The flat-band voltage for this MIS structure is - 27 V, and the measured bulk lifetime in accumulation ( V , more positive than - 27 V) is 3 psec. The measured photosignal is relatively flat in the region of surface accumulation. However, as VG is increased to larger negative values the photosignal decreases dramatically and is reduced by more than an order of magnitude for a strongly inverted surface condition. This is because a typical RdCd time constant for 0.1-eV material is 5 2 x lo-' sec at 77 K. There is also an indication in Fig. 41 of the classical surface recombination velocity effect of Eq. (54), given by the slight minimum in photosignal observed in the region of field plate bias at which the surface is approximately intrinsic (VG - 29 V). The wider-gap composition of (HgCd)Te at 77 K, on the other hand, will exhibit a photosignal enhancement upon surface inversion, relative to the accumulated condition, because the values of RdCd associated with the depletion region are considerably in excess of 7p(which is typically in < 7p < 4 x the range sec). An example of this photosignal enhancement is shown in Fig. 42 for a composition x 0.30 at 77 K with an indicated minority-carrier trapping gain -70. The measured dependance of the inverted surface photosignal on inverse temperature for this x 0.30 composition is shown in Fig. 43, and the measured thermal acti-

-

-

-

-

-

-

IO?/T IK-')

FIG.42.

FIG.43.

FIG.42. Photoconductive signal versus gate voltage for x toconductor at 77 K . FIG.43. Photoconductive signal versus lff/Tfor x verted, and (b) accumulated surfaces.

- 0.30 n-type Hg,-,Cd,Te

- 0.30 n-type Hg,-,Cd,Te

pho-

for (a) in-

364

M. A. K l N C H

vation energy is approximately E g / 2 indicating that the dominant current associated with the depletion region is due to generation-recombination currents. The saturation of photosignal at lower temperatures is due to incident background flux. For comparison purposes the measured dependance of photosignal with inverse temperature for an accumulated surface condition is shown in Fig. 43 (Borrello et a / . , 1973).

V. (HgCd)Te Charge Transfer Device Technology 8. (HgCd)Te CTD THEORY A N D DESIGN

The (HgCd)Te MIS photodiode can be utilized in the dynamic, or integrating, mode to detect infrared radiation and it is perhaps this mode of operation which holds the greatest promise for this device. The performance improvements demanded of the next generation of infrared systems require a significant increase in the typical number of detectors employed in the focal plane to values in excess of lo4, thus ruling out conventional arrays of photoconductors of photodiodes with individual preamplifiers as used in current infrared systems. This detector requirement will necessitate that a considerable amount of signal processing be performed on the focal plane; possible signal processing functions envisioned are time delay and integration (TDI) for scanning systems, multiplexing outputs, area array staring mode operation, antiblooming, and background subtraction. To this end both charge coupled (CCD) (Boyle and Smith, 1970) and charge injection (CID) (Burke and Michon, 1976) device technology on the infrared sensing material itself can be employed, and both have been developed at Texas Instruments Incorporated. The charge-coupled device is somewhat the more challenging of the two in that a considerable number of charge transfers are involved in signal readout which necessitates a high quality of both material and semiconductor-oxide interface technology, and it is this structure that will be described at length here to demonstrate the feasibility of (HgCd)Te charge transfer devices. A simplistic example of focal plane architecture appropriate for a scanned infrared system is shown in Fig. 44. The current generation linear array of photodetectors is essentially replaced by a linear array of “superdetectors,” or columns containing N individual detectors. These columns are in fact CCD shift registers fabricated on infrared sensitive material and are aligned with the direction of image scan such that the potential wells collecting charge from the various pixel elements of the scene can be clocked down the shift register in synchronization with the mechanical rate of scan. In this manner each pixel is integrated over a considerably longer period of time than the conventional linear array, in fact, for

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

365

I iiiaqr

Scan D i rec t i o n

FIG.44. Second generation scanning focal plane.

where T~~~~is a horizontal line time. The columns are then fed in parallel into a multiplexer again fabricated on (HgCd)Te, and the signal is fed out serial fashion. In the ideal case all of the columns of the focal plane are multiplexed with a single CCD shift register and fed out through a single preamplifier. However, in reality the number of columns that can be handled by a single parallel- serial multiplexer will be determined by such considerations as charge transfer efficiency, CCD noise, and data rates, and compromises will have to be made for large focal planes. Thus, the concept of the (HgCd)Te CCD shift register combines the functions of photon detection, time delay and integration (in the case of the scanned system), and signal multiplexing into the same advice. The integration of signal and noise in the charge domain not only results in a significant increase in system sensitivity but also occurs prior to preamplification with a considerable relaxation of preamplifier area and power requirements. The single-level (HgCd)Te MIS technology discussed throughout this chapter has recently (Chapman et al., 1978; Kinch et al., 1980) been extended into the multilevel capability required for the fabrication of CCD shift registers. The reported designs have incorporated both 8- and 16-bit four-phase stepped insulator geometries with overlapping gates and an electrostatically controlled channel stop. Figure 45 shows the longitudinal and transverse sections of the CCD design, together with the thicknesses of the various layers of insulator (ZnS) employed. The high quality of semiconductor-insulator interface required for successful CCD operation was achieved with a native oxide -700 A thick. The gate lengths employed were 10 p m with various channel widths between 50-125 pm. The above design is dominated by two basic features of CCD operation in intrinsic infrared sensitive materials, namely, the high field breakdown associated with the narrow bandgaps in question, and the well capacity

366

M.

A . KINCH

Potential Profile

(bl

FIG.45. (HgCd)Te CCD (a) longitudinal section and (b) cross section. [Kinch ef al. (1980).]

required for the photon fluxes involved. An upper limit is placed on the clock voltages that can be employed, depending on the doping level of the substrate, consistent with the predicted breakdown field for the composition in question. The tunneling calculations earlier indicate that this field is 3 V/pm for A, = 5 pm, and 1 V/pm for A, = 10 pm. These values of surface electric field are sufficient to generate a tunneling current equal to approximately 10% of the background flux generated current for a typical system with f/2.5. This limit on clock voltages is determined by both normal and tangential field considerations, and as such makes the choice of a stepped insulator virtually mandatory for maximum well capacity CCD operation at these wavelengths. Channel stops can be formed in one of three ways, namely by the use of a heavily doped region (typically an ion implant), or a stepped insulator, or an electrostatic shield. The heavily doped region is ruled out by high field breakdown considerations at the channel edge, and the stepped insulator design requires the use of thick gate metals for edge coverage with inherent yield problems. The electrostatic shield (field plate) channel stop does not suffer from these disadvantages and provides the added benefit of a field stop for infrared radiation when opaque. A variety of metals have been employed for gate fabrication, with aluminum the most common for opaque, and nickel for transparent metallizations. Contact to the various levels is made by via etching and evaporated indium bonding pads. A photograph of the 16-bit, 2-mil wide

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

367

FIG.46. Micrograph of lbbit, 2-mil wide shift register. [Kinch et al. (1980).]

channel shift register is shown in Fig. 46, and a cross-section schematic in Fig. 47 together with the silicon output buffer circuit. Input to the register is made by biasing the input gate to high field breakdown, and the output signal is sensed by the floating gate circuit shown in Fig. 47. Operation of the floating gate output is as follows. The output transfer gate is operated “on” so that when 44 is turned off the signal charge transfers over this output gate onto the floating gate. Imme-

Reset

Staye 16

I

I

-

&

FIG. 47. Schematic of 16-bit shift register with floating gate output circuit. Substrate bias = V,. [Kinch et al. (1980).]

368

M . A . KINCH

diately prior to this the floating gate is preset to reference voltage Vrervia a voltage pulse applied to the gate of the reset MOSFET, and then floated. The input of charge under the floating gate from #4 changes the voltage there, which is then sensed by the source follower circuit. After sensing, the floating gate is discharged prior to the arrival of the next signal pulse. This is accomplished in Fig. 47 by the application of a positive injection pulse (for ap-channel device) to the floating gate, which dumps the charge into the substrate where it recombines within a minority-carrier lifetime (0.1 - 10 psec). The floating gate is then preset again to Vretand the cycle repeats. The signal on the floating gate is detected after an ac-coupled correlated double sampling circuit (White er d.,1974) which clamps immediately before injection and samples the voltage on the floating gate immediately after the injection pulse. A typical timing sequence for this mode of operation is shown in Fig. 48. The performance parameters associated with (HgCd)Te CCD operation can be predicted utilizing any of the standard texts (e.g., Sequin and Tompsett, 1975) and will not be treated here, with the exception of the expected value of the charge transfer efficiency. The primary source of charge transfer loss at low frequencies in CCDs operating with a fat-zero charge is trapping in fast interface states at the edge of the CCD well. Simple theory (Kosonocky and Carnes, 1973) for the loss at the edges pre-

clamp preset

inject

t

T I 1-1 k

FIG.48. Typical clock sequence for (HgCd)Te CCD operation. [Kinch et a / . (1980).]

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

369

dicts a fractional loss per transfer, for p-channel (HgCd)Te, given by

edge linear dimension; density of fast surface states; signal charge per unit area; emission coefficient for holes from surface states; clock frequency; gate voltage in escess of threshold; surface potential; semiconductor dielectric constant.

For 0.25-eV (A, = 5 pm) (HgCd)Te at 77 K, assuming that Cox= 2.3 x F/cm2, then we have Et

=

1.58 x 10-4

w

10'0

(59)

( J - ) ( ~ ) ( ~ ) l i 2 ,

where Wc is the channel width in mils, and Nfs is in units of cm-2/V. The signal charge is assumed 0.8 of full well capacity, and k4 = upvthNvr where upis the surface state capture cross section for holes, Vth 5 X lo6 cm/sec, N, 2x ~ m - and ~ , we have assumed up lo-'' cm2, giving k4 lo* sec-'. Equation (59) assumes four-phase operation at a frequency f = 5 X 104 Hz, with a clock voltage of V = 5 V riding on a substrate bias 0.5 V in excess of threshold. At higher frequencies with optimum design the transit time across a CCD gate is determined by fringing field drift. Drift theory (Carnes et af., 1971) applied to (HgCd)Te with a combination oxide-ZnS insulator for a four-phase structure gives for the transit time of a carrier across a gate:

-

-

-

-

where for 0.25-eV n-type (HgCd)Te at 77 K the appropriate parameters are

L. = gate length = 0.4 mil; p = surface mobility for holes = 250 cm2/V sec; fox = insulator thickness = 3400 A; V = clock voltage on electrodes = 5 V; W = depletion layer thickness = [ 2 ~ ~ ~ + ~ / l t ~ q ] ' ~ ~ . +s

is the surface potential under the transferring electrode, which is as-

370

M. A . KINCH

4

2

1

VG - VFB (VI

FIG.49. Empty well surface potential versus gate voltage for typical (HgCd)Te CCD level ~. r f a / . (1980).] geometries. no = 1OIs ~ r n - [Kinch

sumed to carry a gate voltage equal to half the clock voltage (relative to flat band). The expression for empty well surface potential is given by Eq. (8):

4s =

vo

+ (VG

-

VFd

- [c + 2v01,(vG-

vFB)]”*,

(8)

where v o

= q~notf/E’x%.

The variation of #Bs with (V, - VFB)is shown in Fig. 49 for typical firstand second-level insulator thicknesses employed. For a substrate bias 0.5 V in excess of flat band and 5-V clocks, the value of #Bs under the transfer electrode will be approximately 2.0 V, providing W = 2.15 X cm. For no = lOI5 cmP3, Eq. (61) gives rtr= 6.7 X sec. The charge transfer loss is related to the fringing field drift time by (Carnes et al., 1971) .sc =

7.4 exp(-t,,/0.33~~~) = 7.4 exp[-l/(l.33fc~,,)].

(61)

The loss per transfer based on Eqs. (59), (60), and (61) is shown in Fig. 50 for the particular set of CCD parameters listed. The sharp increase in transfer loss at higher frequencies can be greatly reduced by (1) reducing the gate length, (2) decreasing the doping level, and hence increasing the maximum employable gate voltage V and depletion depth W, or (3) using

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

lo-4

371

-

lo-[ I

o4

I o4

I

I

I l l

I

I

l i t Io6

I0 5

I

I

I I , 10'

Frequency ( H I )

FIG.50. Theoretical charge transfer inefficiency versus frequency for 0.25-eV p-channel (HgCd)Te CCD at 77 K, with typical operating parameters. Nf, = 5 x 10'O cm-* V-I; Cox= 2.3 x IO-'F cmP; no = lOI5 cmP; V = 5 V; I* = 250 cm2/V sec. [Kinch er al. (1980).

n-channel devices, for which the surface mobility is expected to be in excess of 2 X lo4 cm2/V sec for 0.25 eV material. The effect of reducing the gate length is shown in Fig. 50 for a realistic value of L = 0.25 mil, together with a calculation for different channel widths. It is apparent from Fig. 50 that good transfer efficiencies in n-type substrates can be achieved up to frequencies of los Hz provided that the fast surface state density can be held at reasonably low values (NfsI5 x 1010 crn-z/V). 9. (HgCd)Te CCD PERFORMANCE DATA

The CCD shift register performance data reported thus far has been concerned entirely with n-type (HgCd)Te substrates of composition x 0.30 (A, 5 pm at 77 K), with typical doping levels of no = IOl5 ~ m - No ~. diodes have been incorporated into the shift registers. Input is by high field breakdown of the signal gate, and output sensing is by the floating gate technique described earlier, followed by substrate injection of the signal charge.

-

-

M.

372

A.

KINCH

I

L , 1 s t Level

7nd LPvrl

15

10

~5

0

-8

-6

-4

-2

0

FiPld Plate Bias I V I

FK. 51. Capacitance-voltage characteristics for the gates of a 16-bit. 0.25-eV (HgCd)Te CCD measured at 77 K , f = 103 Hz.[Kinch er a / . (1980).]

n-type

A typical set of capacitance-voltage curves at 77 K for a 16-bit shift register with a 2-mil wide channel is shown in Fig. 51, measured at a frequency of lo3 Hz and a thermal background environment. The characteristics exhibit all of the properties described earlier for 0.25-eV n-type material and the device uniformity is seen to be very good. The absence of dark current results in a considerable degree of charge storage even for the slowest ramp speeds employed, as evidenced by the vertical displacement of the forward and reverse C-V curves on all gates. The capacitance curve in the direction of increasing negative bias voltage is reminiscent of a deep depletion characteristic. The output observed from the correlated double sampler (CDS) of a 16-bit, 5-mil wide shift register with 0.4-mil opaque gates operated in a four-phase mode is shown in Fig. 52, together with the high field breakdown pulses applied to the signal gate. Charge transfer is clearly demonstrated by the delay of the CDS output relative to the input signal by the required number of bits. The fat-zero necessary for optimum transfer efficiency is introduced into this device by biasing the clock voltages to val-

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

373

FIG.52. ( 1 ) Signal input and (2) signal output from the correlated double sampling (CDS) unit of a 16-bit, four-phase, 5-mil wide (HgCd)Te CCD (0.25-eV n-type) at 77 K , clock frequency = 50 kHz.[Kinch ef a / . (19801.1

ues sufficiently close to high field breakdown to generate the desired charge. This fat-zero can also be introduced by pulse biasing the input signal gate. The CCD clock frequency employed in Fig. 52 is 5 X lo4 Hz, and an expanded photograph of this pulse train is shown in Fig. 53. This signal represents approximately 0.8 of full well as indicated by signal saturation, and the charge transfer efficiency as measured from the leading and trailing edge losses is 0.9994 for this particular four-phase device. There is no evidence of fixed charge loss at the leading edge; both the leading and trailing edges are essentially symmetrical. The highest transfer efficiency report thus far (Kinch et al., 1980) is 0.9995 for a 16-bit, 2-mil wide channel, with 0.4-mil gates, operating in a four-phase mode, with device parameters approximating those used in Eq. (60). If the measured transfer loss is due to fast surface states then N,,= 6.3 x 1O'O cm-'/V. This value is somewhat below the norm obtained for this material by dC/dV techniques, as discussed in Section 3, and tends to confirm the hypothesis that a finite distribution of fixed oxide charge is responsible for the apparent density of surface states calculated by this method. As discussed earlier, this observation is in line with the absence of capacitance and conductance dispersion effects in typical MIS devices fabricated on (HgCd)Te. The magnitude of the signal voltage is given by an analysis of the equiv-

M. A . KINCH

374

FIG.53. CDS output from 16-bit, four-phase (HgCd)Te CCD with 0.4-mil gates, showing CTE = 0.9994. [Kinch et UI. (1980).]

alent circuit of the floating gate output shown in Fig. 54. The floating gate signal voltage AVs is related to the input signal charge AQs (from 44gate) injected onto the node between the oxide capacitance Coxand the depletion layer capacitance Cd by

AVs =

+

[AQsCox/(Cox

cp)l/[cd

+ CoxCp/(Cox

-I- Cp>I3

(62)

where C , represents the parasitic capacitance of the circuit including the input capacitance of the source follower, the overlap capacitances between the floating gate and its adjacent electrodes, the capacitance associated with the injection circuit, and the capacitance of the interconnect between the (HgCd)Te IRCCD and the silicon IC. For the present multilevel technology status Cox Cd << C,, and Eq. (63) reduces to AVs AQs/2C,, and for a typical signal charge, i.e., the charge in the well over and above fat-zero, of lo-' coulomb/cm2 the ac coupled signal output will be -6 x 10+ V, assuming a gate area of 1 mil2 and Cp = 5 pF. Improve-

-

FIG. 54. Equivalent circuit for floating gate output. [Kinch et ul. (1980).]

-

7.

METAL-INSULATOR-SEMICONDUCTOR INFRARED DETECTORS

375

ments in this technology will result in increases in Coxsuch that Cox>> c d , in which case the output signal will become AVs AQs/C,. Preliminary infrared measurements have been reported (Kinch et al., 1980) on (HgCd)Te CCD shift registers employing 130-A thick semitransparent nickel gates. The response of a 16-bit CCD to a GaAs emitter pulsed at a much slower rate than the clock frequency of 5 X lo4 Hz is shown in Fig. 55. The 16 bits of increasing and decreasing infrared signal at emitter turn-on and turn-off are evident, with an excellent degree of signal linearity. Quantitative blackbody measurements of signal and noise on these devices indicate that the theoretical enhancement factor due to time delay and integration is achieved. Consider a linear shift register with transparent gates of quantum efficiency 7 with a signal flux A@B incident uniformly on the structure. The number of signal generated minority carriers in a potential well that has traversed the full length of the register is q A a B Adq where Ad is the area of one bit of the CCD (i.e., four gates) and T~ is the total integration time down the shift register. The variance in the number of carriers in the well is determined by the background flux density @B(>>A@B) and is given by (q@’gAdq)1/2. The bandwidth of the sampled system is f , / 2 , where f , is the clock frequency, and hence the noise/Hz1/2for carriers in the well is (27)@’gAdT1/fc)~/~. Thus, the theoretical D* for the shift register is given by

-

-

D* = ( ~ / h V ) [ ~ / 2 @ ~ ] 1 ’ 2 ( f c T r ) 1 / 2 ,

(63)

FIG.55. Response of ]&bit, 5-mil wide (HgCd)Te CCD to a GaAs emitter pulse (upper trace) at 77 K. [Kinch et a / . (1980).]

376

M. A . KINCH

and for a CCD shift register with N bits the total integration time T~ is N clock periods = N / f , , giving D$o, = (l/hv)"77/2@,]'/2 = MI2x

D$ngle,

(64) (65)

where D&,glerepresents the D* of a single CCD bit. Equation (66) represents the expression for D* enhancement obtained because of time delay and integration. Measurements have been reported for a background flux environment of QB = 5 x 1014 photons/cm2 sec, which for a 16-bit shift register, with q = 0.16 should give a theoretical D&,I = 1.1 x 10l2 cm HZ'/~/W.The measured value for such a 5-mil wide channel device was D&,I = 1.02 x 1012cm HZ"~/W.The advantage of integrating and multiplexing in the charge domain prior to preamplification is illustrated by the measured noise voltage which was -50 nV/Hz1/2,a noise value that is readily achievable with today's MOSFET technology even in relatively narrow bandwidth systems with their possible l/f noise contributions. Recent measurements (Borrello, 1978) on shift registers with thinner gate metals have yielded significantly higher values of quantum efficiency (q 0.5) with an equally good TDI enhancement factor to that quoted above.

-

VI. Summary

In this chapter we have attempted to review the current status of (HgCd)Te metal-insulator-semiconductor technology with particular regard to its application in the field of detection of infrared radiation. The performance of the MIS thermal equilibrium mode detector is seen to be equivalent to that of an open-circuit photodiode. BLIP operation can be achieved although with smaller peak responsivity values than for a photodiode operated at V = 0, in that the MIS diode impedance is determined by the background photon flux and not by thermally generated currents. The detector signal under these BLIP conditions is, however, independent of device quantum efficiency. The dominant redeeming feature of the MIS photodiode as compared to the metallurgically formed photodiode is the relative ease of device fabrication, the absence of processing extremes such as ion implantation, high-temperature annealing, and high-temperature diffusion to form the photosensitive junction, and the degree of control over surface leakage. In effect, the quality of the MIS photodiode is determined almost completely by the properties of the substrate material. Operation of (HgCd)Te MIS photodiodes in the dynamic, or integrating mode has been analyzed both from an experimental and a theoretical

7.

METAL-INSULATOR-SEMICONDUCTOR I N F R A R E D DETECTORS

377

standpoint, and infrared generated charge transfer action with minimal loss demonstrated. CCDs and CIDs can be considered a present-day technology in (HgCd)Te, and the development of monolithic infraredsensitive integrated circuits, with all of the ramifications with regard to advanced signal processing on the focal plane, is clearly a very viable alternative for future generation infrared focal planes. Ending on a somewhat philosophical note, it can be said that the (HgCd)Te MIS device has come a long way in a relatively short period of time, from its early role as an investigative tool for understanding the subtleties of photoconductive detecting elements, to its present-day position as a detector in its own right, with a very real large-scale integrated circuit capability. The indicated high quality of both the (HgCd)Te-oxide interface and the (HgCd)Te material itself promise much for this technology. Although a great deal of work remains to be done with regard to totally understanding all the facets of (HgCd)Te MIS device fabrication and operation, the potential reward is great-and the prospect exciting!

ACKNOWLEDGMENTS The author would like to acknowledge the assistance given by all of his colleagues at Texas Instrqpents Incorporated. A major portion of this chapter can be considered a testimonial to their efforts over recent years. The support of various government agencies is also gratefully acknowledged, in particular the U. S. Air Force Avionics Laboratory, the Naval Research Laboratory, and the Defense Advanced Research Projects Agency.

REFERENCES Amelio, G. F. (1972).Surface Sci. 29, 125-143. Anderson, W. W.(1977).Infrared Phys. 17, 147-164. Baraff, G. A. (1962).Phys. Rev. 128, 2507-2517. Bate, R. T.,Kinch, M. A , , and Buss, D. D. (1974).U. S. Patent No. 3,808,435. Borrello, S. R. (1978).Unpublished work, Texas Instruments. Borrello, S. R., Kinch, M. A., and Blouke, M. (1973).Proc. IRIS Det. Spec. Grp. (unpublished). Boyle, W. S., and Smith, G. E. (1970).BSTJ 49, 587-593. Brews, J. R. (1972).J. Appl. Phys. 43, 2306-2316. Brooks, H.(1955).Adv. Electron. 7, 85-182. Burke, H. K.,and Michon, G. J. (1976).IEEE Trans. Electron Devices ED-23, 189-195. Carnes, J. E.,Kosonocky, W. F., and Ramberg, E. G. (1971).IEEE J . Solid State Circuits SC-6, 322-326. Carter, D. L., Kinch, M. A , , and Buss, D. D. (1971).J. Phys. Chem. Solids Suppl. I 32, 273-277. Catagnus, P. C., and Baker, C. T. (1976).U. S. Patent No. 3,977,018. Chang, C. C.,and Johnson, W. C. (1978)'IEEETrans. Electron Devices ED-25,1368-1374. Chapman, R. A. (1978).Unpublished work, Texas Instruments.

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Chapman, R. A. et ul. (1978). Appl. f h y s . Lett. 32, 434-436. Galazka, R. R., and Zakrzewski, T. (1967). f h y s . Status. Solidi. 23, K39-K43. Hall, R. N . (1959). P r o r . Inst. Elec. Eng. B Suppl. 106, 923-931. Hauser, J. R. (1978). Appl. Phys. Lett. 33, 351-353. Kane, E. 0. (1957). J. f h y s . Chern. Solids 1, 249-261. Kinch, M. A. , (1974). f r o c . IRIS D e t . Spec. Grp. (unpublished). Kinch, M. A., and Borrello, S . R. (1975). Infrared Phys. 15, 111-124. Kinch, M.A., and Boyd, D. R. (1973). f r o c . IRIS D e f . Spec. Crp. (unpublished). Kinch, M. A., and Buss, D. D. (1971). J . f h y s . Chem. Solids Suppl. I 32, 461-469. Kinch, M. A,, Brau, M.J., and Simmons, A. (1973). J . Appl. fhys. 44, 1649-1663. Kinch, M.A., Chapman, R. A., Simmons, A., Buss, D. D., and Borrello, S. R. (1980). Infrored Phys. 20, 1-20. Kosonocky, W. F., and Carnes, J. E. (1973). NASA Final Rep. No. NASA Cr-132304, 12. Kuhn, M. (1970). Solid Stute Electron. 13, 873-886. Lanir, M., Wang, C. C., and Vandenvyck, A. H. B. (1978). Proc. IEDM, Wushington pp. 421-423. Lehovec, K., and Slobodskoy, A. (1964). Solid State Electron. I, 59-80. Longo, J. T., Cheung, D. T., Andrews, A. M., Wang, C. C., and Tracy, J. M.(1978). IEEE Trans. Electron Devices ED-25, 213-231. Macdonald, J. R. (1964). J . Chem. Phys. 40, 3735-3737. McNutt, M. J., and Sah, C. T. (1974). J . Appl. Phys. 45, 3916-3921. Nicollian, E. H., and Goetzberger, A. (1967). BSTJ 46, 1055-1133. Nummedal, K., Fraser, J. C., Su, S. C., Baron, R.,and Finnila, R. M. (1975). Proc. CCD Appl. Conf., San Diego, California pp. 19-30. Petersen, P. E. (1970). J . Appl. f h y s . 41, 3465-3467. Phelan, R. J., Jr.. and Dimmock, J. 0. (1967). Appl. Phys. Lett. 10, 55-58. Polla, D. L., and Sood, A. K. (1978). Proc. IEDM. Wushfngfonpp. 419-421. Reynolds, R. A., Brau, M. J., Kraus, H., and Bate, R. T. (1971). J. f h y s . Chem. Solids S ~ p p l 1. . 32, 511-521. Sah, C. T. (1961). Phys. Rev. 123, 1594-1612. Sah, C. T., Noyce, R. N., Shockley, W. (1957). f r o c . I R E 45, 1228-1243. Schmit, J. L. (1970). J . Appl. fhy.s. 41, 2876-2879. Schmit, J. L., and Stelzer, E. L. (1969). J. Appl. f h y s . 40,4865-4869. Scott, W. (1972). J . Appl. f h y s . 43, 1055-1062. Sequin, C. H., and Tompsett, M. F. (1975). In “Charge Transfer Devices,” Suppl. 8 for Adv. Electron. El. Phys., Chapter 4. Academic Press, New York. Shockley, W., and Read, W. T., Jr. (1952). Phys. Rev. 87, 835-842. Simmons, A. (1973). Unpublished work, Texas Instruments. Sood, A. K., and Tredwell, T. J. (1978). f r o c . IEDM, Washington pp. 434-437. Stratton, R. A. (1958). f r o c . R. Soc. London Ser. A 246, 406-422. Sze, S. M.(1969). I n “Physics of Semiconductor Devices,” p. I 11. Wiley, New York. Tasch, A. F., Jr., Chapman, R. A., and Breazeale, B. H. (1970). J. Appl. Phys. 41, 4202 -4204. White, M. H., Lampe, D. R., Claha, F. C., and Mack, I. A. (1974). IEEE J . Solid Stute Circuits sc-9, 1-13.

Index

A

lead distribution, 3 1 tin distribution, 31 zinc distribution, 31 Crystal growth, 47- 115, see also (HgCd)Te Bridgman method, 66, 71 -76 composition variation, 73-76 furnace, 66, 71 Czochralski method, 80 direct deposition, 102- 105 composition dependence on substrate temperature, 104 evaporation/condensation, 102- 104 sputtering, 105 sublimation, 102- 104 epitaxial, 85- 106 composition profile, 86, 90,95, 97, 98, 101, 107-110 growth rate, 94, 99 liquid phase, 86-92 vapor phase, 92- 106 furnace considerations, 62 liquid phase epitaxy, 86-92 composition profile, 86, 90 solvent systems, 88-92 liquid/solid growth, 70-85 Bridgman method, 66, 71-76 composition variations, 73-76, 79, 83 Czochralski method, 80 replenished solution growth, 84 slush growth, 80-84 traveling solvent zone melting, 78-80 zone melting, 76, 77 quenching, 65-68

Auger recombination, 121- 154, 243-246 degenerate material, 143- 148 lifetime, 125-151 carrier dependence, 132, I50 degenerate material, 143-148, 245 experimental values, 147-150 magnetic field dependence, 151 nondegenerate material, 126- 143 p-type material, 243-246 temperature dependence, 133, 138, 147, 149 light-hole transition, 139-143 nondegenerate material, 126- 143 nonparabolic bands, 135- 138 parabolic band approximation, 126135 threshold energy, 138- 140 tabulation, 140 transitions, 123, 124 C

Cd commercial grade, analysis, 25 purification, 24-32,41-44 distillation, 25-29 vapor pressures, 26 electrolysis, 25 vacuum distillation, 29 zone refining, 29-32 copper distribution, 30

379

380

INDEX

Crystal growth (continued) quench/recrystallization method, 63-70 low-angle grain boundary, 69 preparation, 63-65 quenching, 65-68 recrystallization, 68-70 recrystallization, 68-70 replenished solution growth, 84 slush growth, 80-84 composition profile, 83 special considerations, 106- 115 dislocations, 110-1 12 etch pits, 110- 112 homogeneity, 107- 110 optical imaging, 114 ordering, 114, 115 x-ray topography, I 12- 114 theory, 62, 63 traveling solvent zone melting, 78-80 composition variation, 79 vapor phase epitaxy, 92-106 composition profile, 95, 97, 98 direct deposition methods, 102- 105 growth rates, 94, 99 interdiffusion coefficient variation, 101 zone melting, 76, 77 D

Detector array, 4, 196-198, 202-204, 271, 282, 283, 299, 364-377

F FLIR (Forward looking infrared system), 5 G Ge :Au, infrared-sensitive material, 2 Ge: Hg, infrared-sensitive material, 2, 4

H Hg activity coefficient over (HgCd)Te, 54 partial pressure over (HgCd)Te, 54

purification, 32-34, 39-41 chemical methods, 33, 34 distillation, 34, 39-41 vacuum distilltion, 34, 41 solubility of (HgCd)Te, 57 (HgCd)Te Au diffusion data, 273-276 Auger lifetime in p-type material, 243246 Auger-limited diffusion current vs. temperature, 329 Auger recombination, 121- 154, see also Auger recombination carrier density dependence on temperature, effective mass, I45 CCD, performance data, 371-376 charge transfer device technology, 364376 crystal growth, 47-1 15 CTD, theory and design, 364-371 density, 18 disorder, 114 electrical properties, 5- 18, 205-207 electron effective mass, 9, 10 temperature dependence, 10 electron mobility, 11- IS, 323 composition dependence, 11-15, 323 temperature dependence, 11- 15, 323 energy-band structure, 6-9 energy gap, 7-9 composition dependence, 7, 8, 169, 170 temperature dependence, 8, 169, 170 Fermi energy, 10, 11 temperature dependence, 10, 11 hole mobility, 13, 14, 16, 323 temperature dependence, 13, 16, 323 indium diffusion data, 273-275 infrared-sensitive material, I - 18 historical overview, 1-5 lattice constant, 18, 89 mercury activity coefficient, 54 mercury vapor pressure, 53, 54 microhardness, 114, 115 minority-carrier lifetime dependence on temperature, 324 minority-carrier properties in p-type material, 286-297 deep-level transient spectroscopy studies, 297

38 1

INDEX

electrical properties, 287, 288 minority-carrier diffusion length 292296 minority-carrier lifetime, 289-292 MIS characteristics, 325-328 MIS experimental data, 339-349 MIS photodiode technology, 349-364 MIS theory, 322-339 mobility vs. temperature, 11-16, 323 optical absorption coefficient, 16, 17 composition dependence, 16, 17 optical absorption edge, 17 optical properties, 5-18, 205-207 phase diagrams, 48-59 phonon frequencies, 17 photoconductive detectors, 157- 197, see also Photoconductive detector photovoltaic infrared detectors, 201304, see atso Photovoltaic IR detector preparation of high-purity elements, 21 45 production technology, 38 properties vs. composition, 205,206 purity, 60, 61 requirements of elements Cd, 41-43 Hg.39-41 Te, 41-43 recombination mechanisms, 121-154, 215-222, 329-332 lifetime, 125, 126, 132, 133, 138, 141151, 215, 329-332 solubility in Hg, 57 special requirements for raw materials, 38-44 structural properties, 5- 18 surface states, 320 trace impurities, 61 influence of crystal growth methods, 61 type conversion by various techniques electron irradiation, 283, 284 pulsed laser irradiation, 285-286 sputtering in Hg plasma, 285 High-purity elements, preparation of, 21 45, see also specific elements Cd, 24-32, 41-44 general discussion, 21 -24 Hg, 32-34, 39-41 Te, 34-38, 41-44

I Infrared detector, see specific type infrared-sensitive material, I- 18 Ge : Au, 2 Ge: Hg, 2 , 4 (HgCd)Te, 1-18 InSb, I , 2, 4 measurement, 4 PbS, I PbSe, 1 (PbSn)Te, 5 PbTe, 1 InSb, infrared-sensitive material, I , 2, 4 Ion-implanted photodiode, 247-272 arrays, 271, 282, 299 breakdown voltage, 261 capacitance, 260, 266 dark current, 300 gate-controlled (HgCd)Te photodiodes, 266-269 (HgCd)Te ion implantation work, 247256 (HgCd)Te performance, 256-266 I-V characteristics, 263, 265 large-area, 266 Ilf noise, 297-301 performance summary, 267 profiles, 253, 254 range of implant, 255, 256 R,A products, 257-259, 262-264, 269, 270 reduced diffusion volumes, 269-272

J Junction photodiode energy diagram for n+-on-p junction, 224 fabrication technology, 246-303 junction current density, 225 photocurrent in p-n junction, 227-232 theory, 207-246, see also p-n junction current-voltage characteristics

M Metal-insulator-semiconductor IR detector, 313-377

382

INDEX

Metal-insulator-semiconductor IR detector (continued ) capacitance vs. gate voltage, 319, 326, 340-345, 357, 360, 362 dark current, 346, 347 depletion current, 330-332 detectivity, 353, 358 diffusion current, 329, 330 energy-band structure, 316 general MIS theory, 315-322 (HgCd)Te charge transfer device technology, 364-376 CCD performance data, 371-376 CTD theory and design, 364-371 (HgCd)Te MIS experimental data, 339349 dynamic mode, 345-349 thermal equilibrium mode, 339-345 (HgCd)Te MIS photodiode technology, 349-364 performance data, 354-360 surface controlled photoconductor, 360-364 theory, 349-354 (HgCd)Te MIS theory, 322-339 characteristics, 325- 328 minority-carrier dark current, 328-338 relevant parameters, 322-325 storage time, 338, 339 minority-carrier dark current, 328-338 noise, 358 performance data, 354-371 photodiode signal dependence on frequency, 353 relevant material parameters, 322-325 responsivity, 358 storage time vs. temperature, 338-349 surface current, 332, 333 tunnel current, 333-338 variation of space-charge density with surface potential, 317

P PbS, infrared-sensitive material, 1 PbSe, infrared-sensitive material, 1 (PbSn)Te, infrared-sensitive material, 5 PbTe, infrared-sensitive material, 1 Phase diagram, 48-60

consequences, 59, 60 (HgCdfTe, 48-59 pseudobinary, 48-55 ternary, 55-59 Photoconductive detector, 157- 197 ambipolar quantities, 177 amplifier noise, 166, 167, 187 array fabrication, 197 BLIP (background limited infrared photodetector), 162, 167, 168 camer lifetime augmentation, 191- 194 charge separation, 192- 196 analysis, 192- 194 JFET analysis, 194 complex device configurations, 189, 190 detectivity, 159-162, 167, 168, 181, 198 background dependence, 168- 170 D*,167, 183, 187, see ulso Photoconductive detector, detectivity field dependence, 181 temperature-dependent, 168- 170, 183 device analyses, 170- 187 one-dimensional approximation equations, 187 Ilfnoise, 166, 173-176, 187 power dissipation, 170, 171 surface recombination, 171- 173, 190, 191 transport effects, drift and diffusion, 175- 186 device design, 187- 1% charge separation effects, 192- 194 extended contacts, 188, 189 transverse field effects, accumulation layers, 190, 191 trapping photoconductivity, 1911% drift and diffusion, 175-186 ambipolar coefficient, 176, 177 transient decay, 186 fabrication technology, 196- 198 fundamental limit of performance, 161, 162 general discussion, 157- 159 generation-recombination noise, 165, 166, 179, 187 bias-dependent, 183 temperature and background dependence, 168-170 Johnson noise, 165, 166, 187

INDEX

maximum performance requirements, 185 noise, 164-167, 173-176, 179, 180, 183, 187 amplifier noise, 166, 167 characteristic spectrum, 167 generation-recombination noise, 165, 166 in (HgCd)Te photoconductor, 173-176 l/f, 166, 173-176, 187 total, 167 nonuniformity effects, 184, 185 parameters of typical (HgCd)Te device, 172, 195 performance expressions, 187 performance parameters, 159- 170, 187, 194-196 background effects, 168-170 detectivity, 167, 168, 181, 183, 187, 198 figures of merit, 159-161 fundamental performance limit, 161, 162 noise, 164- 167, 173- 176, 179, 180, 183, 187 responsivity, 163, 164, 178, 180, 182, 187, 189, 194, 195 temperature effects, 168- 170 photoconductive gain, 195 power dissipation, 170, 171 quantum efficiency, 160 responsivity, 159, 160, 163, 164, 178, 187, 194 bias dependent, 182 field dependence, 180 temperature and background dependence, 168-170 surface recombination, 171, 172 reduction, 190, 191 sweepout factor, 187 time constant, 186 transient decay of photoconductivity, 186 transport effects, drift and diffusion, 175-186 fundamentals, 175- 177 one-dimensional formulation with ohmic contacts, 177-187 transverse field devices, 192- 196 transverse field effects

383

accumulation layers, 190, 191 trapping photoconductivity, background and older theories, 191, 192 Photovoltaic IR detector, 162, 201-304, see also Junction photodiode applications for (HgCd)Te photodiodes, 202-204 arrays, 202-204, 282, 283, 299 background limited infrared photodetector (BLIP), 237 cutoff wavelength, 230, 231 dark current, 220, 221 detectivity, 236, 237 diffusion coefficient, 21 1 dynamic resistance at zero-bias (&), 207, see also Photovoltaic IR detector, R,A product Einstein relation, 21 1 general discussion, 201-207 generation-recombination current, 2 16220, 222, 223 heterodyne operation, 237 (HgCd)Te properties, 205, 206 interband tunneling current, 224-227 ion-implanted arrays, zero-bias resistance, 271 ion-implanted photodiode, 247-272, see also Ion-implanted photodiode junction photodiode fabrication technology, 246-303 diffused photodiodes, 272-283 ion implantation, 247-272, see also Ion-implanted photodiode minority-carrier properties of p-type (HgCd)Te, 286-297 llfnoise in (HgCd)Te photodiodes, 297-301 Schottky barrier photodiodes, 301-303 type conversion in (HgCd)Te by various techniques, 283-286 minority-carrier diffusion length, 2 10 minority-carrier lifetime, 2 10 mosaic focal plane arrays, 203, 204 noise diffusion current and photocurrent only, 233, 234 Ilf, 235 space-charge region g-r current, 234, 235

384

INDEX

Photovoltaic 1R detector (continued) noise equivalent power, 236, 238 p-n junction photodiodes, theory, 207246 Auger lifetime in p-type (HgCd)Te, 243-246 current-voltage characteristics, 207227, see also Current-voltage characteristics detectivity, 235-237 lateral collection in small-area junctions, 238-240 noise equivalent power, 235, 236, 238 noise mechanisms, 232-235 photocurrent in junctions, 227-232 quantum efficiency 230-233, 236-238, 24 1 response time, 240-243 responsivity, 235, 236 quantum efficiency, 228-233 ac, 237, 241 dc, 237 radiative lifetime, 215 R,A product, 207, 211-214, 216, 217, 219, 220, 225, 257-259, 262-264, 269, 270, 282 as figure of merit, 207 ion-implanted diodes, 257-259, 262264, 269, 270 response time, 240-243 diffusion effects in quasineutral regions, 240-242 drift effects in space-charge region, 242 junction capacitance effects, 242, 243 responsivity, 236 Schottky barrier photodiode, 301-303 current - voltage characteristics, 302 electrical properties, 302 surface leakage current, 220-224 surface recambination velocity, 212, 221, 222 wide bandwidth 1-2 pm (HgCd)Te photodiodes, 279-283 detectivity, 280 junctions resistance, 28 I

wide bandwidth 10.6-pm photodiode, 276-283 Hg in-diffused photodiode configuration, 277, 278 high-temperature operation, 278, 279 P-N junction current-voltage characteristics, 207-227, 263-265 dark current, 220, 221 diffusion current, 207-217 energy diagram for n+-on-pjunction, 224 generation-recombination current, 2 16220, 222, 223 interband tunneling current, 224-227 photocurrent in junction, 227-232 surface leakage current, 220-224 Preparation of high-purity elements, see High-purity elements, specific elements Purification procedures, see specific element

R Recombination, 121-154, 216-222, 329332, see also Auger recombination Auger lifetime, see Auger recombination, lifetime lifetime, definition, 125, 126 surface, 171-173, 190, 191, 212, 221, 222, 332

T Te, purification, 34-38, 41-44 chloride refining, 36 commercial grade, analysis, 35 crystallization and precipitation, 36 distillation, 37 electrolytic, 37 hydride process, 36 solvent extraction, 36 zone refining, 37, 38, 41-44 impurity distribution coefficient, 37 trailing ends, 44

Contents of Previous Volumes Volume 1 Physics of 111-V Compounds C. Hilsum, Some Key Features of 111-V Compounds Franco Bassani, Methods of Band Calculations Applicable to 111-V Compounds E. 0. Kane, The k . p Method V. L. Bonch-Bruevich, Effect of Heavy Doping on the Semiconductor Band Structure Donald Long, Energy Band Structures of Mixed Crystals of 111-V Compounds Laura M. Roth and Petros N . Argyres, Magnetic Quantum Effects S. M. Puri and T. H. Geballe, Thermomagnetic Effects in the Quantum Region W. M. Becker, Band Characteristics near Principal Minima from Magnetoresistance E. H. Putley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity in InSb H . Weiss, Magnetoresistance Betsy Ancker-Johnson, Plasmas in Semiconductors and Semimetals

Volume 2 Physics of 111-V Compounds M. G. Holland, Thermal Conductivity S . I. Novkova, Thermal Expansion U.Piesbergen, Heat Capacity and Debye Temperatures G. Giesecke, Lattice Constants J . R . DrabbL, Elastic Properties A. U.Mac Rae and G. W . Gobeli, Low Energy Electron Diffraction Studies Robert Lee Mieher, Nuclear Magnetic Resonance Bernard Goldstein, Electron Paramagnetic Resonance T. S. Moss, Photoconduction in 111-V Compounds E. AntonEik and J . Tauc, Quantum Efficiency o f the Internal Photoelectric Effect in InSb G . W. Gobeli and F. G . Allen, Photoelectric Threshold and Work Function P. S. Pershan, Nonlinear Optics in 111-V Compounds M. Gershenzon, Radiative Recombination in the HI-V Compounds Frank Stern, Stimulated Emission in Semiconductors

Volume 3 Optical of Properties 111-V Compounds Marvin Hass, Lattice Reflection William G . Spitzer, Multiphonon Lattice Absorption D. L. Sfierwalf and R . F . Potter, Emittance Studies H . R. Philipp and H . Ehrenreich, Ultraviolet Optical Properties Manuel Cardona, Optical Absorption above the Fundamental Edge Earnest J . Johnson, Absorption near the Fundamental Edge John 0. Dimmock, Introduction to the Theory of Exciton States in Semiconductors B. Lax and J . G. Mavroides, Interband Magnetooptical Effects

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386

CONTENTS OF PREVIOUS VOLUMES

H. Y. Fan, Effects of Free Carriers on Optical Properties Edward D. Palik and George B. Wright, Free-Carrier Magnetooptical Effects Richard H. Bube, Photoelectronic Analysis B. 0.Seraphin and H. E. Bennett, Optical Constants

Volume 4 Physics of III-V Compounds N . A . Coryunova, A. S. Borschevskii. and D. N . Tretiakov, Hardness N . N . Sirotu, Heats of Formation and Temperatures and Heats of Fusion of Compounds AIIIBV Don L. Kendall, Diffusion A . G . Chynowerh, Charge Multiplication Phenomena Robert W . Keyes, The Effects of Hydrostatic Pressure on the Properties of 111-V Semiconductors L. W . Aukerman, Radiation Effects N . A . Goryunova, F. P. Kesamanlyp und D. N.Nasledov, Phenomena in Solid Solutions R. T. Bate, Electrical Properties of Nonuniform Crystals

Volume 5 Infrared Detectors Henry Levinstein, Characterization of Infrared Detectors Paul W . Kruse, Indium Antimonide Photoconductive and Photoelectromagnetic Detectors M. B. Prince, Narrowband Self-Filtering Detectors Ivars Melngailis and T. C . Harman, Single-Crystal Lead-Tin Chalcogenides Donald Long and Joseph L. Schmit, Mercury-Cadmium Telluride and Closely Related Alloys E . H. Purley, The Pyroelectric Detector Norman B. Stevens, Radiation Thermopiles R . J . Keyes and T. M.Quisr. L o w Level Coherent and Incoherent Detection in the Infrared M. C. Teich, Coherent Detection in the Infrared F. R . Arams, E. W . Surd, B. J . Peyton, and F. P.Pace, Infrared Heterodyne Detection with Gigahertz IF Response H. S. Sommers, Jr., Microwave-Based Photoconductive Detector Robert Sehr and Rainer Zuleeg, Imaging and Display

Volume 6 Injection Phenomena Murray A . Lampert and Ronald B. Schilling. Current Injection in Solids: The Regional Approximation Method Richard Williams, Injection by Internal Photoemission Allen M. Barnett, Current Filament Formation R. Baron and J . W . Mayer, Double Injection in Semiconductors W . Ruppel, The Photoconductor-Metal Contact

Volume 7 Application and Devices: Part A John A. Copeland and Stephen Knight, Applications Uiilizing Bulk Negative Resistance F. A . Padovani. The Voltage-Current Characteristics of Metal-Semiconductor Contacts P.L. Hower, W . W . Hooper, B. R. Cairns, R . D. Fairman, and D.A. Tremere, The GaAs Field-Effect Transistor

CONTENTS OF PREVIOUS VOLUMES

387

Marvin H. White. MOS Transistors G. R . Antell, Gallium Arsenide Transistors T. L. Tansley, Heterojunction Properties

Volume 7 Application and Devices: Part B T. Misawa, IMPATT Diodes H. C. Okean, Tunnel Diodes Robert B. Campbell and Hung-Chi Chang, Silicon Carbide Junction Devices R. E. Ensrrom, H . Kressel, and L. Krassner, High-Temperature Power Rectifiers of GaAs,-,P,

Volume 8 Transport and Optical Phenomena Richard J. Stirn, Band Structure and Galvanomagnetic Effects in 111-V Compounds with Indirect Band Gaps Roland W .Ure, Jr., Thermoelectric Effects in 111-V Compounds Herber? Piller, Faraday Rotation H. Barry Bebb and E. W . Williams, Photoluminescence I: Theory E. W . Williams and H . Barry Eebb, Photoluminescence 11: Gallium Arsenide

Volume 9 Modulation Techniques B. 0.Seraphin, Electroreflectance R. L. Agganval, Modulated Interband Magnetooptics Dank! F. Blossey and Paul Handler, Electroabsorption Bruno Batz, Thermal and Wavelength Modulation Spectroscopy Ivar Balslev, Piezooptical Effects D. E. Aspnes and N . Bortka, Electric-Field Effects on the Dielectric Function of Semiconductors and Insulators

Volume 10 Transport Phenomena R . L. Rode, Low-Field Electron Transport 1. D. Wifey, Mobility of Holes in 111-V Compounds C. M. Wove and G. E. Stillman, Apparent Mobility Enhancement in Inhomogeneous Crystals Roberr L. Peterson, The Magnetophonon Effect

Volume 1 1 Solar Cells Harold J . Hovel, Introduction; Carrier Collection, Spectral Response, and Photocurrent; Solar Cell Electrical Characteristics; Efficiency; Thickness; Other Solar Cell Devices; Radiation Effects; Temperature and Intensity; Solar Cell Technology

Volume 12 Infrared Detectors (11) W. L. Eiseman, J . D. Merriam, and R. F. Potter, Operational Characteristics of Infrared Photodetectors Peter R . Erart. Impurity Germanium and Silicon Infrared Detectors

388

CONTENTS OF PREVIOUS VOLUMES

E . H. Putley, InSb Submillimeter Photoconductive Detectors G . E . Stillman, C . M . Wove, and J . 0.Dimmock, Far-Infrared Photoconductivity in High Purity GaAs G . E. Stillman and C . M . Wove, Avalanche Photodiodes P . L. Richards, The Josephson Junction as a Detector of Microwave and Far-Infrared Radiation E. H. Purley, The Pyroelectric Detector-An Update

Volume 13 Cadmium Telluride Ketincrh Zanio, Materials Preparation; Physics; Defects; Applications

Volume 14 Lasers, Junctions, Transport N . Holonyak, Jr. and M. H . Lee, Photopumped Ill-V Semiconductor Lasers Henry Kressel and Jerome K . Butler. Heterojunction Laser Diodes A. Van der Ziel, Space-Charge-Limited Solid-state Diodes P e r u J . Price, Monte Carlo Calculation of Electron Transport in Solids

Volume 15 Contacts, Junctions, Emitters B . L. Sharma, Ohmic Contacts to 111-V Compound Semiconductors Allen Nussbaum, The Theory of Semiconducting Junctions John S. Escher, NEA Semiconductor Photoemitters

Volume 16 Defects, (HgCd)Se, (HgCd)Te Henry Kressel, The Effect of Crystal Defects on Optoelectronic Devices C. R . Whitsefr, J . G . Broerman, and C . J . Summers, Crystal Growth and Properties of Hg,-,Cd,Se Alloys M . H . Weiler, Magnetooptical Properties of Hg,-,Cd,Te Alloys Paul W . Kruse and John G. Ready, Nonlinear Optical Effects in Hg,-,Cd,Te