Phonons in GaN-AlN Nanostructures

Encyclopedia of Nanoscience and Nanotechnology

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Phonons in GaN-AlN Nanostructures J. Frandon, J. Gleize, M. A. Renucci Université Paul Sabatier, Toulouse, France

CONTENTS 1. Introduction 2. Raman Scattering in Hexagonal Crystals and Nanostructures 3. Phonons in Quantum Wells and Superlattices 4. Phonons in Quantum Dots Structures 5. Summary Glossary References

1. INTRODUCTION The scope of this chapter is the review of recent experimental studies of phonons in nanostructures made of nitride semiconductors with an hexagonal structure. First let us recall some basic definitions. A quantum well (QW) is described as a thin layer exhibiting semiconducting properties, located between a couple of layers made of another semiconductor and playing the role of barriers. Indeed, the electronic bandgap energy in the latter is higher than its counterpart in the former, thus favoring carrier confinement and electrical transport inside the well. Single or multiple QW structures can be fabricated as well as superlattices (SL) which are periodic arrays of QWs. A quantum dot (QD) is an island made of a given semiconductor embedded in another semiconductor acting as barrier. It is usually characterized by a pyramidal shape and a small height (typically 5 nm). The samples are periodic stackings of planes containing the QDs, which can be self-assembled by the effect of vertical correlation. The purpose of the extensive work recently devoted to GaN-AlN or GaN-AlGaN nanostructures is the development of new devices, particularly laser diodes emitting in the ultraviolet range. Their light emission is expected to be much stronger than from heterostructures made of GaN and AlN (or AlGaN) thick layers grown in the nineties, due to the low-dimensional geometry of nanostructures. In addition, the crystallographic structure of nitride semiconductors is responsible for their piezoelectric properties, generating very strong electric fields in strained nanostructures; as a ISBN: 1-58883-064-0/$35.00 Copyright © 2004 by American Scientific Publishers All rights of reproduction in any form reserved.

result, the emission is significantly red-shifted with respect to the absorption edge by the so-called confined quantum Stark effect, and the luminescence can be tuned within a wide interval from the visible range up to the near ultraviolet. Such high-performance devices, grown using techniques recently developed, are currently fabricated and are already on the market. However, the knowledge of the structural and optical properties involved in the light emission process must be improved. So numerous experimental studies have been recently devoted to such nanostructures. Among the various techniques used for this purpose, Raman spectroscopy is known to be a powerful probe of vibrational modes (or phonons) in semiconductor materials. Measurements of phonon frequencies in nanostructures give the opportunity of determining the strain state inside their constituent layers; these results are key data, directly related to the light emission of the device. This kind of experiment is rather simple, nondestructive, and usually needs no special sample preparation. The size of the optical probe can be very small (as low as 1
m). In addition, this technique is accurate and very reproducible, allowing measurements of the phonon energy within an uncertainty lower than 1 cm−1 (about 0.1 meV). This chapter is organized as follows: basic concepts concerning phonons in bulk nitride semiconductors and GaNbased nanostructures, as well as Raman scattering, are given in Section 1. Section 2 is devoted to the Raman studies on GaN-AlN (or GaN-GaAlN) QW structures and SLs, in nonresonant and resonant conditions. Section 3 of this chapter deals mostly with phonons in QDs stackings.

2. RAMAN SCATTERING IN HEXAGONAL CRYSTALS AND NANOSTRUCTURES 2.1. Phonons in “Bulk” GaN-Like Semiconductors Only GaN, AlN, or AlGaN semiconductors with wurtzite structure will be considered in the present article. Before dealing with nanostructures, we must recall briefly the vibrational properties of bulk crystals, which were recently Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 8: Pages (513–526)

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reviewed by Frandon et al. [1]. In fact, almost all the samples studied up until now are layers grown on a substrate and on a buffer layer, but they behave usually as “bulk” materials due to their large thickness. Hexagonal nitride crys4 . The unit cell contains tals belong to the space group C6v two nitrogen atoms and two Ga or Al atoms [2]. The lattice constants a and c of GaN [3] and AlN [4] are given in Table 1. In the following, the c axis of the hexagonal structure will be chosen as the z axis. Let us recall briefly how the symmetry of Raman active modes are derived in this structure. Here we are only interested in the zone center phonons, that is, characterized by a vanishing q wavevector. The 12-dimensional representation of the atomic motions in the unit cell can be reduced into irreducible representations of the C6v group. Besides the acoustic modes and the “silent” (inactive) B1 optic phonons, one obtains four optical modes, two nonpolar (infrared inactive), and two polar (both Raman and infrared active) phonons [5]. The nonpolar phonons exhibit the E2 symmetry, corresponding to atomic motions perpendicular to the z axis. One of them may be observed at low frequency. The other, denoted by E2 (high), shows up at a higher frequency with a high intensity in Raman spectra recorded far from resonant conditions. In addition, it cannot couple to plasmons and does not display any angular dispersion, on account of its nonpolar character. Therefore, it is frequently used as a probe of structural properties in the Raman characterization of nitride semiconductors. Polar optic phonons are characterized by their A1 or E1 symmetries, related to atomic motions, parallel or normal to the z axis, respectively. They may be either longitudinal or transverse (LO or TO). In these ionic crystals, the longrange forces associated with the strong macroscopic electric field of longitudinal phonons are responsible for an important LO-TO splitting (202 cm−1 for GaN). Moreover, due to the uniaxial properties of these crystals, the LO and one of the TO phonons are extraordinary modes, thus exhibiting an angular dispersion; their frequency varies with the angle  between the phonon wavevector q and the z axis [6]. This variation range corresponds to the A1 -E1 splitting governed by short-range interatomic forces. However, it should be noted that this variation (27 cm−1 for TO phonons of GaN) is much lower than the LO-TO splitting. The symmetry of the q = 0 extraordinary modes depends on the value of ; for a vanishing angle, the LO and TO phonons exhibit the A1 and E1 symmetry, respectively, and the reverse is found for  = 90 . For intermediate q values, the extraordinary modes called quasi-LO and TO (QLO and QTO), have a mixed symmetry. Finally, the ordinary TO phonon is nondispersive and keeps the E1 symmetry when varying the angle . Table 2 gives the frequencies of the q = 0 phonons for relaxed “bulk” GaN and AlN [7, 8]. Table 1. Lattice constants a and c (nm) for wurtzite GaN and AlN.

GaNa AlNb a b

From [3]. From [4].

a

c

0.31890 0.31106

0.51864 0.49795

Table 2. Long wavelength phonon frequencies (cm−1 for wurtzite GaN and AlN. E2 (low) A1 (TO) E1 (TO) E2 (high) A1 (LO) GaNa AlNb

144 249

533 610

561 669

569 656

735 889

E1 (LO) 743 912

a

From [7]. From [8]. Note: The notation of phonons is that used in [5].

b

Note that q = 0 phonons, usually not involved in firstorder Raman scattering, must be invoked in some cases, for example, when the translational symmetry is lost in the sample under study. For hexagonal GaN, the phonon dispersion q , which is quite distinct from the angular dispersion previously discussed, has been calculated in the high-symmetry directions of the Brillouin zone [9, 10] and have been recently determined by X-ray inelastic scattering [11]. A scatter of results is observed, but the dispersion of published data is always found much lower for the branch starting from the E2 (high) phonon than for its LO counterpart, for example. We must keep in mind this difference when effects of phonon confinement in the nanostructures will be considered later. For bulk-disordered AlGaN solid solutions, the evolution of phonon frequencies versus their aluminum content is characterized either by a “two-mode” or a “one-mode” behavior, depending on the symmetry of the vibrational mode. In the first case, corresponding to the E2 (high) optic phonon for example, the GaN- and AlN-like oscillators exhibit strengths of comparable orders of magnitude in most parts of the composition range. In the second case, observed for A1 (LO) and E1 (LO) phonons, the oscillator strength is strongly transferred from one to the other type of oscillators, thus allowing the observation of one mode only in the whole composition range of the alloy [12–16]. Evidence for two-mode behavior of the E1 (TO) mode has been given from infrared measurements [17]. In contrast, the case of the A1 (TO) phonon seems to be more complicated [16]. As previously mentioned, most samples are thick layers grown on a substrate (sapphire, SiC, or Si) and on a buffer layer (GaN or AlN). Due to the lattice mismatch and to the different expansion coefficients of materials constituting the nanostructure, the layers are usually submitted to a strong biaxial stress acting in the plane normal to the z axis of the hexagonal crystal. The induced strains zz and xx , respectively parallel and perpendicular to the z axis, modify the phonon frequencies in the layers. For the mode , the corresponding frequency shift with respect to its value in the relaxed material is given by the following linear equation   = 2 a xx + b zz

(1)

where a and b are the deformation potentials of the phonon . The knowledge of these parameters is of crucial importance for evaluating the strains in the thick layers as well as in the nanostructures. For GaN, the phonon deformation potentials were measured [18–19] and calculated [20–21], but they are more controversial for AlN [22–25]. Some of the calculated and experimental values of phonon

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deformation potentials are given for wurtzite GaN and AlN in Table 3. When the material is under biaxial stress  B ( B > 0 for compressive stress), one can also use the Raman stress coefficient, defined by d

d B

KB =

and AlAs [27]. Confined vibrational modes are oscillations located in one type of layer and characterized by an effective wavevector qz . The latter is quantized, due to boundary conditions at the interfaces with the adjacent layers qz = n ·

(2)

If Hooke’s law is obeyed, K B can be expressed using the deformation potentials and the elastic constants only. As a rule, the observed frequency shift of phonons is positive (resp., negative) if the material is under compressive (resp., tensile) biaxial stress.

2.2. Phonons in GaN-Based Nanostructures Let us consider nanostructures made of alternate layers exhibiting the wurtzite structure, grown along the z axis. Their structural and optical properties have been extensively studied during recent years. Under adequate growth conditions, the Stranski–Krastanov mechanism of strain relaxation of GaN on AlN leads to the growth of strained GaN islands on very thin (two monolayers thick) GaN wetting layers, embedded in the AlN barriers, leading to QD structures [26]. Different experimental conditions allow a twodimensional growth, thus leading to strained QW structures or to SLs; the internal strain of the layers depends on numerous factors, including the nature of the underlying buffer layer and the thicknesses of the layers in the structure. Obviously, as a result of internal strains, the phonons from the wells and barriers will be shifted in the Raman spectra according to Eq. (1). The same equation may also be tentatively applied to QDs, assuming a nearly biaxial stress, in consideration of their pyramidal shape and their lateral size usually about 10 times larger than their height. But new vibration modes must be considered in nanostructures. Some phonons can be confined inside one type of layer. Their properties have been extensively studied in the SLs made of III–V cubic semiconductors, such as GaAs

 d1

(3)

where n is an integer and d1 is the layer thickness. The frequencies of confined modes can be deduced from the LO phonon dispersion q of the bulk material along the z direction; they correspond to the discrete qz values calculated using Eq. (3). If the top of the branch of the LO branch is at the zone center  , as for the LO phonon of GaN, frequency shifts towards lower frequencies are expected and can be measured, specially for very thin (a few nanometers thick) layers. On the other hand, confinement effects should be negligible for the E2 (high) phonon, due to the weak dispersion of the corresponding branch in the Brillouin zone. Other phonons specific to the SLs are the “folded” acoustic phonons. Indeed, if the dispersion of acoustic branches is similar in both materials, that is, when their sound velocities are not too different, acoustic waves can propagate through the whole nanostructure. Folding of the acoustic phonon branches of the constituent layers into the reduced Brillouin zone of the SL generate new vibrational modes, which are characteristic of the periodicity d = d1 + d2 of the SL (d1 and d2 stand for the thicknesses of wells and barriers, respectively). They may show up as doublets located in the low-frequency range of the Raman spectra. The average frequencies of these doublets are given by [27]

n = n ·

2 · v d

(4)

where n is an integer and v is an average sound velocity in the nanostructure calculated from the sound velocities v1

Table 3. Phonon deformation potentials in Wurtzite GaN and AlN. a (cm−1 )

a

GaN, calculated GaN, measured AlN, calculateda AlN, measured

E2 (low)

A1 (TO)

E1 (TO)

E2 (high)

A1 (LO)

E1 (LO)

+75 +115b +149

−640 −630b −776 −930d

−717 −820b −835 −982d

−742 −850b , −818c −881 −1092d , −1083e

−664 −685c −739 −643d

−775 −867

b (cm−1 )

GaN, calculateda GaN, measured AlN, calculateda AlN, measured a

From [21]. From [19]. From [18]. d From [25]. e From [23]. b c

E2 (low)

A1 (TO)

E1 (TO)

E2 (high)

A1 (LO)

E1 (LO)

4 −80b −223

−695 −1290b −394 −904d

−591 −680b −744 −901d

−715 −920b , −797c −906 −965d , −1187e

−881 −997c −737 −1157d

−703 −808

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and v2 in the wells and barriers of the SL according to v=

v 1 · v2 1 −  v2 + v1

Table 4. Selection rules for phonons in wurtzite crystals.

(5)

where  = d2 /d1 + d2 . The frequency difference between the components of each doublet depends on the phonon wavevector qz  = 2 qz · v

(6)

The value of qz is determined by the experimental geometry of Raman scattering, as it will shown in the following section.

2.3. Experiments In the following, the incident (resp., scattered) light is defined by its wavevector ki , its frequency i , and its linear polarization ei (resp., kS , S and eS ). The experimental configuration will be indicated by the usual Porto’s notation ki ei eS kS . For bulk crystals, conservation law between the initial and final states is obeyed both by the wavevector and the energy. In first-order Raman scattering, the wavevector q and the frequency of the phonon involved in the scattering process are given by q = ki − kS

(7)

= i − S

(8)

and

According to Eqs. (7) and (8), q is completely defined by the experimental geometry and the laser energy. In the particular case of backscattering kS = −ki , Eq. (7) can be written as q = 2ki  =

4 · n i

(9)

where n is the refractive index of the material at the frequency i , and i is the wavelength of the incident light. Most Raman spectra of GaN-AlN or GaN-AlGaN nanostructures reported in the literature have been recorded at room temperature. The simplest experiment is performed in a backscattering geometry along the growth axis z of the nanostructure, with polarizations of incident and scattered light either perpendicular or parallel, corresponding to the configurations zxy z or zxx z, respectively. In the latter case, both E2 and A1 (LO) phonons are allowed. Moreover, a micro-Raman spectrometer, using a small laser spot whose diameter is lower than 1
m, allows the achievement of other scattering conditions, particularly backscattering on the edge of the sample under study. In this configuration, the phonon wavevector q is perpendicular to the z axis and additional phonons can be evidenced. The selection rules for all the Raman active phonons in wurtzite materials are recalled in Table 4. The excitation of Raman scattering is usually made using the monochromatic lines of an argon or krypton laser, either in the visible or ultraviolet range (from 3.41 eV to 3.80 eV). The experimental results strongly depend on the excitation energy. If the latter corresponds to the visible range, that is,

Configuration zxx z zxy z xzz x xyy x yzy x

Allowed phonons E2 , A1 (LO) E2 A1 (TO) E2 , A1 (TO) E1 (LO)

Note: The notation of phonons is that used in [5].

far from any electronic resonance, the dominant electronphonon interaction is the “deformation potential” process and the nonpolar E2 (high) optic phonon exhibits a scattering cross section much stronger than the other phonons, specially the A1 (LO) mode also allowed in the zxx z configuration. Note that the Raman spectra usually contain features from the GaN QDs or QWs and from the barriers of the nanostructure, but also from the underlying thick buffer layer (usually GaN or AlN), due to the negligible optical absorption of the constituent layers in the visible range; thus an unambiguous assignment of phonons may prove difficult. However, the signature of the nanostructure itself can be obtained using a confocal set-up with a low depth of focus, as illustrated later. On the other hand, a strong enhancement of Raman scattering by the polar LO phonon is observed under near resonant conditions, that is, if the energy of incident or/and scattered photons is close to an electronic transition energy, when the “forbidden” scattering process associated with the intraband Fröhlich electron-phonon interaction becomes dominant [28]. With the present materials, resonant conditions can be achieved in the ultraviolet range only; indeed the room temperature bandgap energy is about 3.4 eV and 6.1 eV for bulk GaN and AlN, respectively. The scattering cross section of the A1 (LO) phonon can be enhanced by several orders of magnitude [29], thus allowing the signature of very small volumes inside the sample. However, it should be noted that the penetration depth of the incident light in the sample is strongly reduced under ultraviolet excitation, due to high optical absorption. In addition, an intense photoluminescence (PL) band may show up in the spectra, making an observation of faint Raman features superimposed on the PL signal very difficult.

3. PHONONS IN QUANTUM WELLS AND SUPERLATTICES 3.1. Nonresonant Raman Scattering: Signature of Wells and Barriers in Superlattices When Raman experiments are performed far from resonant conditions, the signal coming from the nanostructure itself is rather weak; it can be easily measured only if the sample is thick enough (about 0.5
m), due to the low-scattering cross section of GaN, and specially of AlN. Actually, this kind of research study is still scarce; the main motivation is to determine the nature of the vibrational modes in the SLs and to derive the built-in strain of the constituent layers.

Phonons in GaN-AlN Nanostructures

The first Raman study of an SL with a wurtzite structure was published by Gleize et al. [30]. This structure was made of a hundred periods of undoped GaN wells and AlN barriers, with nominal thicknesses of 6.3 nm and 5.1 nm respectively, deposited by MBE on a thick AlN buffer layer and a sapphire substrate. The layer thicknesses were large enough for neglecting the frequency shift of phonons induced by confinement, specially for the E2 mode. Micro-Raman spectra were recorded in backscattering geometry under various polarization configurations, under a 2.54 eV excitation, far from resonant conditions. Thanks to selection rules, most observed features could be unambiguously assigned to all optical phonons but the E1 (LO), either from the underlying AlN buffer layer or from each type of SLs layers. Due to internal strains, phonons from wells and barriers were found significantly shifted with respect to their frequency in relaxed materials. Using the phonon deformation potentials of GaN, a biaxial stress of 6.3 GPa and an in-plane strain xx = −1 3% were derived for the GaN layers of the SL from the measured shift of the E2 (high) phonon. This strain is close to the value expected for a “free-standing” state of the present nanostructure. On the other hand, the measured frequency shifts of AlN phonons, actually larger than those of GaN phonons, could not be used to determine the internal strain in the barriers of the SL, because the corresponding deformation potentials were not known at this time. Note that a feature observed at 560 cm−1 in xyy x Raman spectra could not be associated to an A1 (TO) phonon from strained GaN layers, although it obeyed the regular selection rules; it was thus tentatively assigned to an interface mode. Finally, micro-Raman spectra were also recorded from place to place on a bevel made by mechanical polishing of the nanostructure; the angle between the beveled surface and the (0001) plane was about 1 . The strain-induced shift of the E2 (GaN) phonon was found higher in the deeper part of the SL than near the surface, giving evidence for a partial strain relaxation in the first layers of the structure. Schubert et al. [31–32] performed other investigations combining Raman scattering and infrared ellipsometry experiments. The latter is an indirect technique for investigating the polar phonons, specially the E1 (TO) phonon when a near normal incidence is used for the measurements. A standard calculation allows the reproduction of the experimental infrared spectrum; this model needs several fitting parameters, including the TO and LO phonon frequencies of the constituent materials, together with the concentration and mobilities (parallel and perpendicular to the z axis of the SL) of free carriers. The latter data must be introduced when the sample under study is doped, intentionally or not. Indeed, the free-carrier plasmon and the LO phonon, which are both longitudinal excitations, can couple together if their energies are close to each other, thus shifting in frequency the high frequency component of the coupled mode with respect to the uncoupled phonon [33]. In [32], eight GaN-AlGaN SLs, grown by MOVPE or by MBE on thick GaN layer and on sapphire, exhibiting typical layer thicknesses of 25 nm and various aluminum contents in the barriers (0 08 < x < 1), were compared. As expected, the strain-induced frequency shifts of the nonpolar E2 phonon for each constituent layer, derived from Raman measurements, proved that GaN (resp., AlGaN) layers were

517 submitted to an internal compressive (resp., tensile) stress. A detailed discussion of the Raman data suggested that these SLs were in a free-standing state: both kinds of layers adopted a common in-plane lattice parameter, different from the one of the underlying thick GaN layer. The analysis of infrared ellipsometry measurements led to the determination of an electron concentration higher than 1018 cm−3 in the GaN layers of the SLs; these free carriers could originate from dislocation-activated donors or from the AlGaN layers. Moreover, the in-plane mobility introduced for fitting the infrared spectra was found higher than its out-of-plane counterpart: this result indicated a confinement of free carriers inside the wells along the z axis, the AlGaN layers of the SL acting as barriers for the free electrons as expected. Another more recent article combining Raman and X-ray diffraction measurements [34] deals with a GaN-AlN SL grown on an AlN buffer layer and on a 6H-SiC substrate; the GaN wells were specially thin (1.5 nm) in this sample, compared to the AlN barriers (10 nm). The map of the reciprocal lattice, which was deduced from X-ray diffraction experiments, gave the average value of both lattice constants a and c of the whole SL. Figure 1 shows three micro-Raman spectra recorded in the zxx z configuration, when the laser spot was focused slightly higher and higher upon the surface of the sample. The variation of relative intensities of the experimental features made their assignment easy either to the SLs layers or to the underlying buffer layer, allowing the measurement of the strain-induced frequency shift of the E2 (high) phonons from the SL. Combining all these data and taking into account the measured in-plane strain of GaN layers ( xx = −2 35%) derived from in-situ RHEED experiments, both components of the biaxial strain of AlN and GaN layers could be determined. The out-of-plane strain zz was found almost negligible for both types of layers, giving for the ratio zz / xx a value quite different from that predicted from the simple elastic theory (−2C13 /C33 = −0 51). This difference is likely due to the large spontaneous and piezo-electric polarization effects which can significantly decrease this strain ratio in the hexagonal SL, as demonstrated in a calculation by Gleize et al. [35].

3.2. Resonant Raman Scattering: Signature of Single or Multiple QWs The first resonant Raman study of single GaN QWs was published by Behr et al. [36]. In these samples grown by MOCVD directly on a sapphire substrate without any buffer layer, the wells lying between thick Ga0 85 Al0 15 N layers were 2 nm, 3 nm, or 4 nm thick. As expected, only the phonons from the alloy were evidenced when the excitation was achieved in the visible range, due to the negligible volume of the QW. However, when the 3.54 eV laser line was used for the excitation, that is, for an energy close to the estimated fundamental electronic transitions in the wider QWs, the resonance conditions were nearly fulfilled and Fröhlichinduced scattering by the GaN A1 (LO) mode was favored. As can be shown in Figure 2, a Raman feature was observed at 732 cm−1 for the structures containing the 3nm- and 4nmwide QWs. The origin of this feature could be unambiguously assigned to the single well; its measured frequency shift was negligible, because both confinement and strain

518

Figure 1. Micro-Raman spectra recorded in backscattering along the z axis, on a GaN (1.5 nm)-AlN (10 nm) SL grown on an AlN BL and a SiC substrate. The excitation was made at 2.33 eV. Spectra 1 to 3 were obtained by focusing farther and farther away from the surface of the sample. Modes from the SL and the BL are indicated by arrows. Asterisks mark phonons from the substrate. Reprinted with permission from [34], J. Frandon et al., Physica E (2003). © 2003, Elsevier Science.

effects were probably weak in the well. In contrast, the LO feature was broadened and shifted towards higher frequencies for the 2 nm thick QW. This observation was explained by cation intermixing at the GaN-AlGaN interface, which could not be neglected in that case. Smoothing of interfaces likely due to poor growth conditions prevents the signature of confinement effects, which would induce an opposite frequency shift.

Figure 2. Resonant Raman spectra of GaN single QW with different widths embedded in Al0 15 Ga0 85 N barriers, recorded under the 3.54 eV excitation. Reprinted with permission from [36], D. Behr et al., Appl. Phys. Lett. 70, 363 (1997). © 1997, American Institute of Physics.

Phonons in GaN-AlN Nanostructures

Further resonant scattering experiments on single or multiple GaN-AlGaN QW structures will be reported in the following. Later Ten GaN QWs of 1.5 nm width, embedded in 5 nm wide Ga0 89 Al0 11 N barriers and grown on a GaN buffer layer, have been investigated under various ultraviolet excitations [37]. In the present structure, the QWs were nearly relaxed, whereas the barriers were submitted to an internal compressive stress, due to the presence of the underlying buffer layer. As expected, first-order scattering by the A1 (LO) phonons from GaN wells, favored by the Fröhlich interaction, was found strongly enhanced by electronic resonance in the incoming channel when excitation is achieved using the 3.54 eV laser line. Indeed, the energy of the incident photon was very close to the QWs’ fundamental transition, as estimated using the simple model of independent square potential wells of finite height. In these experimental conditions, the second-order scattering by the LO phonons from the thick buffer layer was dominant. Under a 3.70 eV excitation, LO phonons from GaN wells were clearly evidenced in the second-order scattering signal, due to electronic resonance in the outgoing channel; weak contributions from the barriers were also evidenced. Similar features were also observed in third-order scattering under 3.80 eV excitation. Another study performed in resonant conditions has been devoted to a collection of four different single GaN QWs separated by 10 nm thick Ga0 83 Al0 17 N barriers and grown on a thick GaN buffer layer [38]; their thicknesses were 1 nm, 2 nm, 3 nm, and 4 nm (corresponding, respectively, to 4, 8, 12, 16 monolayers). The fundamental excitonic transitions in these wells were already determined from previous PL measurements performed at a low temperature. In this work, thick GaN and Ga0 83 Al0 17 N layers were also investigated in the same experimental conditions for comparison with the structure under study. The Raman spectra recorded at room temperature in backscattering geometry are shown in Figure 3. The PL signature of the various wells was clearly observed in the spectra, thus accurately giving the energy of the fundamental transitions in the wells at room temperature. Under excitation at 3.53 eV, first-order scattering by GaN A1 (LO) phonons confined in one of the wider QWs (3 nm) showed up in the spectra, enhanced by electronic resonance in the outgoing channel; no similar observation could be achieved on the thick GaN layer used as reference, since the excitation was too far from resonance in the bulk material. The measured frequency was close to 734 cm−1 , corresponding to relaxed GaN, because the well involved was almost unstrained in the nanostructure. In this case, the Raman signature of the 3 nm-thick well, whose PL signal was located at 3.43 eV, close to the observed Raman feature, could be obtained. On the other hand, when the 3.70 eV excitation was used, a first-order Raman feature peaking at higher frequency (775 cm−1 and a weak contribution at lower frequency was observed. They are clearly related to phonons of the Ga0 83 Al0 17 N barriers and of the GaN wells, respectively. Scattering by vibrational modes of both layers requires an extended intermediate electronic state of the QW with a significant penetration into the barriers. This delocalization implies high-lying states whose energy is close to the bandgap of the alloy. Resonance most likely

519

Phonons in GaN-AlN Nanostructures

Figure 3. Resonant Raman spectra of four single GaN QW in Al0 17 Ga0 83 N barriers, recorded using 3.53 eV and 3.70 eV excitations. The thicknesses of these QWs were 4, 8, 12, and 16 monolayers. Arrows mark the PL signal from the QWs. Reprinted with permission from [38], F. Demangeot, Phys. Stat. Sol.(B) 216, 799 (1999). © 1999, Wiley-VCH.

occurred in the incoming channel, as the incident photon energy was almost tuned on the bandgap of the alloy. Moreover, the Raman signal was found just superimposed on the PL signal from the thinner (1 nm) QW, centered at 3.60 eV; no similar Raman features could be observed with thick GaN or Ga0 83 Al0 17 N thick layers. The signal was thus likely enhanced by a double resonance effect, as the second intermediate state involved in the Raman process was a bound electronic state localized in the 1 nm-thick QW.

3.3. Calculations of Lattice-Dynamical Properties of Wurtzite Nanostructures Komirenko et al. [39] first investigated the extraordinary polar phonons of wurtzite single QWs in the framework of a dielectric continuum model. The anisotropy of the materials was taken into account by introducing both components ⊥  and z ( ) of the frequency-dependant dielectric tensor of the constituent materials; the latter involve the frequencies of A1 and E1 (LO and TO) phonons, polarized along the z axis and in the (xOy) plane, respectively. The electrostatic boundary conditions on the interfaces, together with the assumption of a scalar potential vanishing far from the wells, were used. For a long wavelength phonon characterized by the in-plane q⊥ wavevector, the angular dispersion can be deduced from the following equation: ⊥  · q⊥2 + z  · qz2 = 0

(10)

where qz is the z component of an effective wavevector. Depending on the sign of the product ⊥ · z in each medium, qz is found either real or imaginary, leading to linear superposition of oscillating or decaying solutions, respectively. Therefore, phonons could be classified according to their localization. Confined modes are mainly located inside

the well but can penetrate significantly into the surrounding layers, interface modes decay exponentially from the interfaces in both types of layers, and propagating modes oscillate in the whole structure. Their frequency variation versus the product q⊥ · d was given for a GaN well of width d embedded in infinite barriers made of AlN or of Ga0 85 Al0 15 N. Note that in another article, the same authors extended their study to the calculation of scattering rates by the Fröhlich electron-phonon interaction in QW structures [40]. Very few investigations of lattice dynamics in hexagonal superlattices by ab initio calculations have been published up until now. Wagner et al. [41] computed the structural, dielectric, and lattice-dynamical properties of short-period hexagonal GaN-AlN SLs, which were compared to their cubic counterparts. In this calculation, the widths of barriers as well as of QWs were as low as two monolayers. Both types of layers were assumed to be pseudomorphically strained on the same in-plane lattice constant; the latter could be either that of relaxed constituent materials (AlN or GaN) or an average value corresponding to an elastically relaxed SL. The goal of this work was to study the angular dispersion of phonons in the structures. The frequency of the zone center phonons was calculated as a function of , the tilt angle of the phonon wavevector with respect to the z axis, within the framework of the density-functional perturbation theory. Most calculated modes were assigned either to confined phonons or to interface phonons. The atoms involved in each vibration mode, together with the strength of the associated dynamical polarization, were also given. The angular dispersion of these modes is shown in Figure 4 for a GaN-AlN wurtzite SL in several strain states. Actually, only a few differences were evidenced in the angular dispersions of cubic and hexagonal SLs. In both cases, for an increasing in-plane lattice constant, all modes decrease in frequency, except the folded TA modes; the downward shift was found more pronounced for LO phonons than for the TO phonons. The only remarkable difference affects the TO modes confined in the GaN layers of the hexagonal SL, spreading in a narrower range than their counterparts in the cubic nanostructure. However, the latter results cannot be easily checked. Indeed, experimental studies are usually performed on nanostructures with much larger periods. An alternative calculation based on the dielectric continuum model, first developed in [39] for the GaN QWs, was applied to wurtzite SLs with more realistic periods [42–44]. Within this framework, the vibrational modes were described by the dynamical polarization associated with the atomic motions in each type of layer. The Maxwell equations, the electric boundary conditions at each interface, and the Bloch’s theorem, taking into account the SLs periodicity, were used together with the q = 0 phonon frequencies of the two types of layers in the strain state actually achieved in the SL. Note that the phonon dispersion q of the bulk constituents was ignored in this model. For GaN-AlN SLs, this calculation predicted two types of polar phonons characterized by an angular dispersion  . The first ones were the interface modes which have been already found for SLs of cubic structure; the corresponding amplitude of atomic motions decreases from the interface in both types of layers. Their

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Phonons in GaN-AlN Nanostructures

Figure 4. Angular dispersion of zone-center phonons of an ultra-thin hexagonal GaN (0.5 nm)-AlN (0.5 nm) SL calculated in different strain situations. From (l)–(r), the results are given for SLs pseudomorphic on AlN, elastically relaxed on an average in-plane lattice constant, and pseudomorphic on GaN. Reprinted with permission from [41], J. M. Wagner et al., IPAP Conference Series 1, 669 (2000). © 2000, Institute of Pure and Applied Physics.

dispersion is related to the anisotropy of the nanostructure. In contrast, another type of phonon, the quasi-confined modes, exhibit an angular dispersion originating from the anisotropy of the constituent materials. Indeed, the frequencies of the A1 and E1 phonons of GaN and AlN, in the TO as well in the LO range, are the limits of their spectral regions; the corresponding intervals are finite for wurtzite crystals, but vanish for isotropic materials. Quasi-confined modes correspond to oscillations in one type of SLs layers but, in contrast with confined modes in cubic SLs, the associated electric field penetrates into the adjacent layer with a decay length much larger than the lattice constant: that is why they are called “quasi-confined.” Note that modes delocalized throughout the whole nanostructure, characterized by an oscillatory behavior in both types of layers, were found only in GaN-GaAlN SLs with barriers made of Ga-rich alloys within this dielectric approach. Very recently, Romanov et al. [45–46] calculated the polar phonons of a single GaN QD, within the framework of a macroscopic continuum dielectric model. They obtained formal analytical solutions for the surface vibrations of a GaN QD exhibiting an oblate spheroidal form, embedded in AlN. These modes are not discrete, in contrast with their counterparts in cubic GaAs-AlAs QDs, and they are found inside a continuous, allowed frequency range, due to the crystal anisotropy. In addition, two other types of phonons were found: runaway modes that freely leave the QD surface and quasi-stationary leaky modes. The influence of strong electric fields present in GaNAlN nanostructures has been discussed by Coffey and Bock [47]. These authors calculated the wavefunctions associated with electron and holes confined in strained GaN-AlN QWs. The influence of the electric fields (up to 1 MV/cm) induced by internal strains on these states was shown in the particular case of a 2.6 nm-thick QW: holes and electrons are

spatially separated in the QW by the confined quantum Stark effect. Strong effects on the Raman cross section by A1 (LO) phonons confined in the GaN layer were proven to proceed from the breaking of symmetry with respect to the center plane of the well. In the calculated cross section, both contributions to the electron-phonon interaction associated with deformation potentials and Fröhlich processes were taken into account. For vanishing electric fields, only confined phonons characterized by a quantum number of even parity are allowed. In contrast, it was found that confined phonons with an odd parity dominate the calculated Raman spectrum when strong fields are present in the involved layer. Therefore, it was suggested that this breakdown of parity selection rules could be used for measuring the electric field in wurtzite nanostructures. Unfortunately, the frequencies given for confined modes is questionable, considering the dispersion q calculated by the authors for the LO phonon of bulk GaN, which is in agreement neither with measurements nor with calculations already published [9–11].

3.4. Experimental Investigations of Phonons in Nitride-Based Superlattices As previously shown for superlattices made of cubic III–V semiconductors, the Raman signatures of disordered solid solutions and ordered nanostructures with the same mean composition are quite different, except for SLs containing ultra-thin (thinner than three monolayers) layers. Evidence for SL ordering can thus be achieved by Raman spectroscopy, which is a nondestructive technique in contrast to transmission electron microscopy (TEM) needing cross sections of the samples. However, Raman spectra of GaN-AlN SLs and AlGaN alloys can at first sight exhibit some similarities, specially concerning the frequencies of E2 (high)

521

Phonons in GaN-AlN Nanostructures

phonons, due to the “two-mode behavior” of the latter modes in the alloy (see Section 2.2). Gleize et al. [30] have observed that the ambiguity could be lifted by considering the A1 (LO) phonon which is, on the contrary, characterized in alloys by its “one-mode behavior.” Indeed, the phonon frequency expected for the A1 (LO) mode of the Ga1−x Alx N alloy with the mean Al content of the SL under study (x = 0 45) would be 821 cm−1 [13]. Actually, the only feature obeying the appropriate selection rules, found at a much lower frequency (738 cm−1 in Raman spectra, was assigned to A1 (LO) phonons confined in the wells, slightly shifted from the corresponding frequency in relaxed GaN by the opposite effects of confinement and strain. It should be noted that the A1 (LO) phonon confined in the barriers could not be observed, likely due to the low-scattering cross section of AlN. Finally, it was concluded that the SLs modes could be unambiguously probed by nonresonant Raman scattering. At this point of the discussion, one can wonder if Raman experiments can determine the nature of the SL phonons, delocalized or confined in one type of layer. A simple criterion has been suggested by Davydov et al. in several articles [48–50]; if two distinct phonons of the same symmetry can be evidenced in Raman spectra from short period SLs, the corresponding modes are claimed to be confined in one type of layer. In the opposite case, the modes can be considered as delocalized. However, it should be noted that the weakness of the Raman signal coming from one type of layer can make a convenient use of this criterion difficult. The same approach has been used by Gleize et al. [30], who implicitly considered phonons confined in each type of layer, with the exception of a phonon exhibiting the A1 (TO) symmetry, assigned to an interface mode. Chen et al. [51] claimed to obtain the first evidence for a confinement effect of the A1 (LO) phonon in GaN layers of an hexagonal superlattice. In this study, three GaNGa0 8 Al0 2 N SLs were investigated; the thickness of the GaN layers was 1.2 nm, 2.4 nm, and 3.6 nm, respectively. The authors concentrated on the A1 (LO) mode observed in zxx z micro-Raman spectra. The corresponding broad feature was slightly red shifted in frequency, compared to the relaxed material; this shift was found increasing for shrinking GaN wells. An approximate fit of the measured frequencies was obtained, using qz ≈ sin2 qz · c/4 for the dispersion of the LO branch of GaN. However, it should be noted that the SLs contained only 30 periods and that the total thickness of GaN in the SL was as low as 36 nm for the thinner layers; one can thus wonder if a clear signature of the wells could be really obtained in nonresonant scattering conditions, considering the presence of an underlying thick GaN buffer layer. Davydov et al. [48–50] investigated by nonresonant Raman scattering a set of GaN-Ga1−x Alx N superlattices, grown by MOCVD on buffer layers and sapphire substrates. The SL period was varied between 2.5 nm and 320 nm. For the sake of simplicity, the thicknesses of wells and barriers in the various nanostructures were the same in all the nanostructures investigated. The aluminum content x in the alloy of the barriers was lower than 50%. The total thickness of the SLs under study was sufficient for achieving Raman experiments in nonresonant scattering, with an excitation at 2.54 eV. In the recorded spectra, E2 (high) and E1 (TO)

phonons from GaN were observed and assigned to confined modes in the wells, whereas their counterparts could not be evidenced for the AlGaN layers of the SL. The lack of signal from the barriers has been tentatively attributed to the lowscattering cross section by phonons of the AlGaN alloy. On the other hand, the E2 (low) phonon confined in the barriers of the SL was also found in the low-frequency range of the spectra, together with that from GaN layers [50]. Due to its high sensitivity to the Al content (but not to the built-in strain), the E2 (low) phonon from the alloy could be used as a probe of the composition in the barriers of the SL. The same authors also gave evidence for confinement of the A1 (LO) phonon either in GaN or in GaAlN layers. In Figure 5, two modes are clearly observed in zyy z spectra from various SLs where the alloy content of the barriers was kept constant (28%). Note that the range of investigated periods was very wide, between 5 nm and 3
m. In contrast, the behavior of E1 (LO) and A1 (TO) phonons was found quite different. Actually, each of them is always observed as a single line; its location in Raman spectra is similar to that in a Ga1−x Alx N disordered alloy, whose composition corresponds to the mean Al content in the SL

x = x

d2 d1 + d 2

(11)

where d1 and d2 are the width of wells and barriers, respectively. Accordingly, these modes are considered as delocalized in the whole structure. The frequency variations of the

Figure 5. Raman spectra in the region of the A1 (LO) phonons, recorded in backscattering along the z axis, on a set of GaN– Al0 28 Ga0 72 N SL with different periods: (1) 3
m, (2) 640 nm, (3) 320 nm, (4) 160 nm, (5) 80 nm, (6) 40 nm, (7) 20 nm, (8) 10 nm, (9) 5 nm. The thicknesses of wells and barriers in the SLs were the same (unpublished results). Reprinted with permission from V. Yu. Davydov.

522 A1 (TO) phonons from the SLs under study and from the corresponding ternary alloy were found rather similar. The same observation was made on the E1 (LO) phonons. This kind of evolution seems to be consistent with results of a calculation performed in the framework of a dielectric continuum model, where the nanostructure was treated as an homogeneous and anisotropic crystal, characterized by an average dielectric constant z  . Another possible evidence for the nature, localized or not, of SLs phonons could be found by measuring their angular dispersion  experimentally, if the latter is significantly different from that of the “bulk” material. This has been done by Gleize et al. [44] for polar phonons through an experimental study of a GaN-AlN SL, performed for checking the validity of the continuum dielectric model previously developed [42]. Micro-Raman spectra were recorded under 2.54 eV excitation, in backscattering geometry on the top surface ( = 0), on the edge ( = 90 ), and also on a bevel at 45˚ fabricated on the edge of the nanostructure by ion etching. The variation of the angle  around the above values was achieved by tilting the sample with respect to the incident light beam; in this experiment, the uncertainty on  was lower than 5 . The measured frequencies of various polar modes from the SL could be compared with the predicted ones. As observed in Figure 6, the agreement was found rather satisfactory, particularly for the TO modes quasi-confined in GaN and AlN layers, which could not be confused with the dispersive extraordinary TO modes from the underlying thick AlN buffer layer.

3.5. Folded Acoustic Phonons in Hexagonal Superlattices The work published by Davydov et al. [49] on GaN-AlGaN superlattices has evidenced for the first time zone-centerfolded acoustic phonons in hexagonal SLs, characteristic of

Figure 6. Angular dispersion of polar phonons of a GaN (5 nm)- AlN (5 nm) superlattice. Full circles and full lines correspond to the experimental values and to the calculated variation, respectively. The angular dispersion of the relaxed thick buffer layer is indicated by dashed lines. Reprinted with permission from [44], J. Gleize et al., Phys. Stat. Sol. (A) 195 (2003). © 2003, Wiley-VCH.

Phonons in GaN-AlN Nanostructures

their periodicity. As shown in Figure 7, remarkable sharp Raman features were detected in the low-frequency range of the spectra recorded in the zyy z scattering configuration, from a few nanostructures made of GaN and Al0 28 Ga0 72 N layers of same thicknesses, with SLs periods ranging between 6.1 nm and 23.8 nm. Actually, only the doublet expected from the first folding of acoustic branches was clearly observed in each case. As expected, the mean frequency of the doublet increases for decreasing SLs periods. The measured frequencies of both components of the doublet obeyed fairly well Eqs. (4) and (6) appearing in Section 1.2. An average sound velocity v = 8140 m/s in the nanostructure was derived from these measurements. Finally, different scattering configurations were achieved for changing the z component qz of the wavevector of the phonon involved in Raman scattering. This experiment allows the probing of the frequency dispersion of the folded acoustic modes [27]. Indeed, the authors found that the spectral spacing of both lines in the doublet was decreasing with qz .

4. PHONONS IN QUANTUM DOTS STRUCTURES 4.1. Nonresonant Raman Scattering The first Raman signature of QD structures has been published by Gleize et al. [52]. The samples were stackings of GaN-AlN QDs grown along the (0001) direction on an AlN buffer layer and a sapphire substrate. As demonstrated by TEM studies [53], GaN islands exhibited a pyramidal shape with a broad basis (about 30 nm) and a typical height of 4 nm, as shown in Figure 8. Micro-Raman spectra were recorded under 2.54 eV excitation, in a backscattering geometry along the z axis. However, the whole sample was probed

Figure 7. Raman spectra of GaN–Al0 28 Ga0 72 N superlattices with different periods (23.8 nm, 12.8 nm, and 6.1 nm), recorded under a 2.54 eV excitation. Only the low frequency part of the spectra, exhibiting the folded acoustic phonons, is shown. Reprinted with permission from [49], Phys. Stat. Sol. (A), 188, 863 (2001). © 2001, Wiley-VCH.

Phonons in GaN-AlN Nanostructures

Figure 8. Cross section of a GaN-AlN QD stacking, observed by transmission electron microscopy. The typical height of GaN QDs was 4 nm. Reprinted with permission from [53], C. Adelmann, Compte-Rendus Academ. Sci. (Paris) 1, Serie IV, 61 (2000). © 2000, Bruno Daudin.

under visible excitation and the distinction between signals originating from the stacking and the buffer layer was not straightforward. In order to overcome this difficulty, the confocal configuration was used and the laser spot was focused higher and higher above the surface, inducing a relative intensity variation of the E2 phonons from the buffer layer and from the QDs, as already illustrated for SLs. It allowed the unambiguous signature of the GaN islands. A slight (tensile) strain of the AlN spacers was deduced from the measured (negative) frequency shift of the E2 phonon. The effect of vertical correlation of QDs in these structures can be evidenced from small changes of the strain measured for the spacers. Another study has been devoted to a set of GaN-AlN QD stackings characterized by various heights and densities of dots, deposited either on sapphire or on silicon [54]. Using various backscattering geometries, most Raman-active optic phonons from the structure could be observed. Except for the A1 (LO) mode, the measured phonon frequencies were rather close to those found in the similar disordered AlGaN alloy. The observed frequency shifts were assigned to strain effects, as in the case of SLs. An in-plane strain in GaN dots of −2 4% or −2 6% was estimated from the frequency shift (as high as +35 cm−1 or +38 cm−1 of the corresponding E2 phonon, using the corresponding deformation potentials. The QDs were found completely strained on AlN in all the structures under study, as expected. Obviously, the mean strain in the AlN spacers, tentatively derived from the experimental data, was found much lower.

523 were used. In fact, large internal electric fields take place in this kind of nanostructure, thus lowering the fundamental bandgap energies significantly. In the present structure, this quantum confined Stark effect was specially strong. The room temperature PL originating from GaN QDs was centered around 2.35 eV, much lower than the excitation energy, and thus did not merge the Raman signal. The more interesting result was obtained using the 3.80 eV laser line. A feature clearly showed up in the first-order scattering range at 744 cm−1 in Raman spectra from the nanostructure, in contrast to those recorded on the GaN layer used as a reference (see Fig. 9). The observed peak, which could not originate from the underlying GaN buffer layer of the sample, was assigned to the polar A1 (LO) phonon from the QDs. A weaker Raman feature located at 602 cm−1 was associated with the nonpolar E2 phonon from the strained dots. It should be noted that the latter mode could be observed under the 2.33 eV excitation, that is, at an energy close to the PL maximum, in contrast to the A1 (LO) phonon from QDs. These results gave evidence for a strong resonant enhancement of the scattering by polar phonons in the incoming channel at 3.80 eV, implying probably an excited state of the dots. Another original study was carried out by Kuball et al. [56] on a single plane of self-assembled GaN QDs grown on a Al0 15 Ga0 85 N layer, using silicon as anti-surfactant. Two clearly distinct distributions of QD sizes were revealed by means of atomic force microscopy. The Raman spectra from the nanostructures are shown on the top of Figure 10. Under a 3.53 eV excitation, first-order scattering located at 736 cm−1 , superimposed onto a broad PL band, was assigned to the A1 (LO) phonon from the “large” (about 40 nm high) dots, where confinement effects on the LO phonon frequency are almost negligible. In the same experimental conditions, a phonon was observed at the same frequency but with a lower intensity, on another sample grown in similar

4.2. Resonant Raman Scattering Room temperature micro-Raman experiments have been also performed on QD structures using ultraviolet laser lines, in order to enhance the scattering intensity by means of electronic resonance. In the paper by Gleize et al. [55] the sample under study was a stacking of 39 periods of GaN QDs embedded in 18 nm thick AlN spacers, grown on both GaN and AlN buffer layers and on a Si (111) substrate. A thick GaN unstrained layer was also available for comparison. Three laser lines at 3.41 eV, 3.70 eV, and 3.80 eV

Figure 9. Raman spectra of a thick GaN layer (a) and of a GaN–AlN quantum dot structure (b) grown on GaN and AlN buffer layers and on a Si substrate, recorded in backscattering along the z axis under 3.41 eV and 3.80 eV excitations. Reprinted with permission from [44], J. Gleize et al., Phys. Stat. Sol. (A), 95 (2003). © 2003, Wiley-VCH.

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Phonons in GaN-AlN Nanostructures

diffraction. The shift towards lower frequencies observed in the Raman spectra for the E2 (high), E1 (TO), and A1 (TO) phonons of GaN was associated with nanosize effects. Demangeot et al. [58–59] studied structures made of nanometer-size GaN pillars designed for photonic crystals. The samples were obtained by reactive ion-etching using a mask technique on 300 nm thick GaN layers grown on a thick AlN buffer layer and on a sapphire substrate. Individual pillars of 300 nm in height, with diameters ranging between 5
m and 100 nm, were fabricated in this way. The samples were investigated by micro-Raman spectroscopy under a 2.54 eV excitation. No one-dimensional effects were observed as expected, considering the pillar size. Spectra recorded in the zxx z configuration showed the allowed phonons from each pillar. Due to the compressive strain of the larger pillars, the E2 (high) mode was slightly shifted from the frequency of relaxed material; in contrast, strain relaxation was evidenced in smaller pillars. Moreover, the upward shift of the LO phonon in the smaller pillars could be explained by angular dispersion (see Section 2.1). Indeed, the wavevector transferred to the phonon by the incident and scattered light entering and coming out, respectively, through the facets of the pillars was tilted with respect to the z axis, leading to the observation of a shifted quasiLO mode. The measured frequency shift was found in good agreement with the value of the facet angle (25 ).

Figure 10. Raman spectra of self-assembled GaN QDs grown on Al0 15 Ga0 85 N using Si as antisurfactant A , and of a continuous GaN layer grown on Al0 15 Ga0 85 N B . The spectra have been recorded at 3.53 eV (top) and at 5.08 eV (bottom). In the latter case, a reference spectrum of an Al mirror shows the system response function. Asterisks and circles mark laser plasma lines and the Raman signal from the SiC substrate, respectively. Reprinted with permission from [56], M. Kuball et al., Appl. Phys. Lett. 78, 987 (2001). © 2001, American Institute of Physics.

conditions but without Si, made of a continuous 0.3
m thick GaN layer on the alloy layer. The spectra recorded at 3.70 eV and 3.81 eV did not give any signature of the QDs. But under excitation in the far ultraviolet (5.08 eV), a significant shift (9 cm−1 towards lower frequencies was observed for the A1 (LO) phonon from the GaN dots, as shown on the bottom of Figure 9. In the same experimental conditions, no frequency shift could be evidenced with the continuous GaN layer. The feature found at 727 cm−1 was thus assigned to the A1 (LO) phonon in “small” QDs; the shift should be due to confinement effects in dots exhibiting smaller heights of about 2–3 nm. The electronic transition favoring the resonant effect under the 5.08 eV excitation was not yet identified.

4.3. GaN Nanowires and Pillars Several investigations of samples containing GaN nanowires have been recently published. For example, Jun-Zhang and Lide-Zhang [57] studied by Raman spectroscopy such as nanostructures, made of nanowires embedded in the nanochannels of an anodic alumina membrane. The hexagonal structure of the nanowires was checked by X-ray

5. SUMMARY Hexagonal GaN-AlN or GaN-GaAlN QW and QD structures have been extensively studied in the last few years, on account of their important applications in opto-electronics. The lattice-dynamical properties of two-dimensional systems have been reviewed in this article. Only a few calculations of phonons in such nanostructures have been performed yet. Most articles published are actually devoted to experimental studies by Raman spectroscopy, or less often by infrared measurements. The signature of QW and QD structures has been obtained from nonpolar or polar phonons, by means of nonresonant or resonant Raman scattering, respectively. The results allowed the probing of internal strains and confinement effects in the constituent materials. Up until now, specific modes of GaN-AlN or GaN-GaAlN SLs have been the subject of a few investigations. However, phonon confinement in layers of the structures has been evidenced for SLs in a wide range of periods. Moreover, the angular dispersion of quasi-confined and interface modes has been predicted and checked experimentally for the former. Finally, GaN pillars recently investigated by Raman spectroscopy did not exhibit lattice dynamical properties characteristic of onedimensional systems.

GLOSSARY Quantum dot (QD) A small island made of a given semiconductor embedded in another semiconductor. Quantum well (QW) A thin layer made of a given semiconductor located between two other semiconductors called barriers. Superlattice (SL) A periodic array of wells and barriers.

Phonons in GaN-AlN Nanostructures

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