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Encyclopedia of Nanoscience and Nanotechnology

Phonons in GaN-AlN Nanostructures

J. Frandon, J. Gleize, M. A. RenucciUniversit Paul Sabatier, Toulouse, France

CONTENTS

1. Introduction2. Raman Scattering in Hexagonal Crystals

and Nanostructures3. Phonons in Quantum Wells and Superlattices4. Phonons in Quantum Dots Structures5. Summary

GlossaryReferences

1. INTRODUCTIONThe scope of this chapter is the review of recent experi-mental studies of phonons in nanostructures made of nitridesemiconductors with an hexagonal structure. First let usrecall some basic denitions. A quantum well (QW) isdescribed as a thin layer exhibiting semiconducting proper-

ties, located between a couple of layers made of anothersemiconductor and playing the role of barriers. Indeed, theelectronic bandgap energy in the latter is higher than itscounterpart in the former, thus favoring carrier connementand electrical transport inside the well. Single or multipleQW 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 inanother semiconductor acting as barrier. It is usually char-acterized by a pyramidal shape and a small height (typically5 nm). The samples are periodic stackings of planes contain-ing 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 develop-ment of new devices, particularly laser diodes emitting inthe ultraviolet range. Their light emission is expected to bemuch stronger than from heterostructures made of GaN and AlN (or AlGaN) thick layers grown in the nineties, due tothe low-dimensional geometry of nanostructures. In addi-tion, the crystallographic structure of nitride semiconductorsis responsible for their piezoelectric properties, generating very strong electric elds in strained nanostructures; as a

result, the emission is signicantly red-shifted with respect tothe absorption edge by the so-called conned quantum Starkeffect, and the luminescence can be tuned within a wideinterval from the visible range up to the near ultraviolet.

Such high-performance devices, grown using techniquesrecently developed, are currently fabricated and are alreadyon the market. However, the knowledge of the structuraland optical properties involved in the light emission pro-cess must be improved. So numerous experimental studieshave been recently devoted to such nanostructures. Amongthe various techniques used for this purpose, Raman spec-troscopy is known to be a powerful probe of vibrationalmodes (or phonons) in semiconductor materials. Measure-ments of phonon frequencies in nanostructures give theopportunity of determining the strain state inside their con-stituent layers; these results are key data, directly related tothe light emission of the device. This kind of experiment israther simple, nondestructive, and usually needs no specialsample preparation. The size of the optical probe can be very small (as low as 1 m). In addition, this technique isaccurate 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 con-cerning phonons in bulk nitride semiconductors and GaN-based nanostructures, as well as Raman scattering, are givenin Section 1. Section 2 is devoted to the Raman studies onGaN-AlN (or GaN-GaAlN) QW structures and SLs, in non-resonant and resonant conditions. Section 3 of this chapterdeals mostly with phonons in QDs stackings.

2. RAMAN SCATTERINGIN HEXAGONAL CRYSTALSAND NANOSTRUCTURES

2.1. Phonons in BulkGaN-Like Semiconductors

Only GaN, AlN, or AlGaN semiconductors with wurtzitestructure will be considered in the present article. Beforedealing with nanostructures, we must recall briey the vibrational properties of bulk crystals, which were recently

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514 Phonons in GaN-AlN Nanostructures

reviewed by Frandon et al. [1]. In fact, almost all the samplesstudied up until now are layers grown on a substrate andon a buffer layer, but they behave usually as bulk mate-rials due to their large thickness. Hexagonal nitride crys-tals belong to the space group C 46v. The unit cell containstwo nitrogen atoms and two Ga or Al atoms [2]. The lat-tice constants a and c of GaN [3] and AlN [4] are given in

Table 1. In the following, the c axis of the hexagonal struc-ture will be chosen as the z axis. Let us recall briey howthe symmetry of Raman active modes are derived in thisstructure. Here we are only interested in the zone centerphonons, that is, characterized by a vanishing q wavevector.The 12-dimensional representation of the atomic motionsin the unit cell can be reduced into irreducible representa-tions of the C 6v group. Besides the acoustic modes and thesilent (inactive) B 1 optic phonons, one obtains four opti-cal modes, two nonpolar (infrared inactive), and two polar(both Raman and infrared active) phonons [5]. The non-polar phonons exhibit the E 2 symmetry, corresponding toatomic motions perpendicular to the z axis. One of themmay be observed at low frequency. The other, denoted by E 2(high), shows up at a higher frequency with a high intensityin Raman spectra recorded far from resonant conditions. Inaddition, it cannot couple to plasmons and does not displayany angular dispersion, on account of its nonpolar charac-ter. Therefore, it is frequently used as a probe of structuralproperties in the Raman characterization of nitride semi-conductors.

Polar optic phonons are characterized by their A1 or E 1symmetries, related to atomic motions, parallel or normalto the z axis, respectively. They may be either longitudinalor transverse (LO or TO). In these ionic crystals, the long-range forces associated with the strong macroscopic electriceld of longitudinal phonons are responsible for an impor-tant LO-TO splitting (202 cm 1 for GaN). Moreover, due

to the uniaxial properties of these crystals, the LO and oneof the TO phonons are extraordinary modes, thus exhibit-ing an angular dispersion; their frequency varies with theangle between the phonon wavevector q and the z axis [6].This variation range corresponds to the A 1-E 1 splitting gov-erned by short-range interatomic forces. However, it shouldbe noted that this variation (27 cm 1 for TO phonons of GaN) is much lower than the LO-TO splitting. The symme-try of the q = 0 extraordinary modes depends on the valueof ; for a vanishing angle, the LO and TO phonons exhibitthe A1 and E 1 symmetry, respectively, and the reverse isfound for = 90 . For intermediate q values, the extraor-dinary modes called quasi-LO and TO (QLO and QTO),have a mixed symmetry. Finally, the ordinary TO phonon is

nondispersive and keeps the E 1 symmetry when varying theangle . Table 2 gives the frequencies of the q = 0 phononsfor relaxed bulk GaN and AlN [7, 8].

Table 1. Lattice constants a and c (nm) for wurtzite GaN and AlN.

a c

GaN a 0.31890 0.51864 AlNb 0.31106 0.49795

a From [3].b From [4].

Table 2. Long wavelength phonon frequencies (cm 1 for wurtzite GaNand AlN.

E 2 (low) A1 (TO) E 1 (TO) E 2 (high) A1 (LO) E 1 (LO)

GaN a 144 533 561 569 735 743 AlNb 249 610 669 656 889 912

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

Note that q = 0 phonons, usually not involved in rst-order Raman scattering, must be invoked in some cases,for example, when the translational symmetry is lost inthe sample under study. For hexagonal GaN, the phonondispersion q , which is quite distinct from the angulardispersion previously discussed, has been calculated in thehigh-symmetry directions of the Brillouin zone [9, 10] andhave 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 E 2 (high) phonon than for its LO coun-terpart, for example. We must keep in mind this difference when effects of phonon connement in the nanostructures will be considered later.

For bulk-disordered AlGaN solid solutions, the evolu-tion of phonon frequencies versus their aluminum cont-ent is characterized either by a two-mode or a one-modebehavior, depending on the symmetry of the vibrationalmode. In the rst case, corresponding to the E 2 (high)optic phonon for example, the GaN- and AlN-like oscillatorsexhibit strengths of comparable orders of magnitude in mostparts of the composition range. In the second case, observedfor A1 (LO) and E 1 (LO) phonons, the oscillator strengthis strongly transferred from one to the other type of oscil-

lators, thus allowing the observation of one mode only inthe whole composition range of the alloy [1216]. Evidencefor two-mode behavior of the E 1 (TO) mode has been givenfrom infrared measurements [17]. In contrast, the case of the A 1 (TO) phonon seems to be more complicated [16].

As previously mentioned, most samples are thick layersgrown on a substrate (sapphire, SiC, or Si) and on a bufferlayer (GaN or AlN). Due to the lattice mismatch and to thedifferent expansion coefcients of materials constituting thenanostructure, the layers are usually submitted to a strongbiaxial stress acting in the plane normal to the z axis of thehexagonal crystal. The induced strains zz and xx , respec-tively parallel and perpendicular to the z axis, modify thephonon frequencies in the layers. For the mode , the cor-

responding frequency shift with respect to its value in therelaxed material is given by the following linear equation

= 2 a xx + b zz (1)

where a and b are the deformation potentials of thephonon . The knowledge of these parameters is of crucialimportance for evaluating the strains in the thick layers as well as in the nanostructures. For GaN, the phonon defor-mation potentials were measured [1819] and calculated[2021], but they are more controversial for AlN [2225].Some of the calculated and experimental values of phonon


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Phonons in GaN-AlN Nanostructures 515

deformation potentials are given for wurtzite GaN and AlNin Table 3.

When the material is under biaxial stress B ( B > 0 forcompressive stress), one can also use the Raman stress coef-cient, dened by

K B = d

d B (2)

If Hookes law is obeyed, K B can be expressed using thedeformation potentials and the elastic constants only. Asa 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 NanostructuresLet us consider nanostructures made of alternate layersexhibiting the wurtzite structure, grown along the z axis.Their structural and optical properties have been extensivelystudied during recent years. Under adequate growth con-ditions, the StranskiKrastanov mechanism of strain relax-ation of GaN on AlN leads to the growth of strained GaNislands on very thin (two monolayers thick) GaN wettinglayers, embedded in the AlN barriers, leading to QD struc-tures [26]. Different experimental conditions allow a two-dimensional growth, thus leading to strained QW structuresor to SLs; the internal strain of the layers depends onnumerous factors, including the nature of the underlyingbuffer layer and the thicknesses of the layers in the struc-ture. Obviously, as a result of internal strains, the phononsfrom the wells and barriers will be shifted in the Ramanspectra according to Eq. (1). The same equation may also betentatively applied to QDs, assuming a nearly biaxial stress,in consideration of their pyramidal shape and their lateralsize usually about 10 times larger than their height.

But new vibration modes must be considered in nano-structures. Some phonons can be conned inside one typeof layer. Their properties have been extensively studied inthe SLs made of IIIV cubic semiconductors, such as GaAs

Table 3. Phonon deformation potentials in Wurtzite GaN and AlN.

a (cm 1)


GaN, calculated a + 75 640 717 742 664 775GaN, measured + 115b 630b 820b 850b, 818c 685c AlN, calculated a + 149 776 835 881 739 867 AlN, measured 930d 982d 1092d , 1083e 643d

b (cm 1)


GaN, calculated a 4 695 591 715 881 703GaN, measured 80b 1290b 680b 920b, 797c 997c AlN, calculated a 223 394 744 906 737 808 AlN, measured 904d 901d 965d , 1187e 1157d

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

and AlAs [27]. Conned vibrational modes are oscillationslocated in one type of layer and characterized by an effec-tive wavevector q z . The latter is quantized, due to boundaryconditions at the interfaces with the adjacent layers

q z = n d1

(3)

where n is an integer and d1 is the layer thickness. The fre-quencies of conned modes can be deduced from the LOphonon dispersion q of the bulk material along the zdirection; they correspond to the discrete q z values calcu-lated using Eq. (3). If the top of the branch of the LO branchis at the zone center , as for the LO phonon of GaN, fre-quency shifts towards lower frequencies are expected andcan be measured, specially for very thin (a few nanometersthick) layers. On the other hand, connement effects shouldbe negligible for the E 2 (high) phonon, due to the weak dis-persion of the corresponding branch in the Brillouin zone.

Other phonons specic to the SLs are the folded acous-tic phonons. Indeed, if the dispersion of acoustic branchesis similar in both materials, that is, when their sound veloc-ities are not too different, acoustic waves can propagatethrough the whole nanostructure. Folding of the acousticphonon branches of the constituent layers into the reducedBrillouin zone of the SL generate new vibrational modes, which are characteristic of the periodicity d = d1 + d2 of theSL (d1 and d2 stand for the thicknesses of wells and barri-ers, respectively). They may show up as doublets located inthe low-frequency range of the Raman spectra. The averagefrequencies of these doublets are given by [27]

n = n

2 v

d (4)

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


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

v = v1 v2

1 v 2 + v 1(5)

where = d2/ d 1 + d2 . The frequency difference betweenthe components of each doublet depends on the phonon wavevector q z

= 2 q z v (6)

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

2.3. ExperimentsIn the following, the incident (resp., scattered) light isdened by its wavevector k i , its frequency i , and its lin-ear polarization ei (resp., k S , S and eS ). The experimentalconguration will be indicated by the usual Portos notationk i ei eS k S . For bulk crystals, conservation law between theinitial and nal states is obeyed both by the wavevector and

the energy. In rst-order Raman scattering, the wavevectorq and the frequency of the phonon involved in the scat-tering process are given by

q = k i k S (7)

and

= i S (8)

According to Eqs. (7) and (8), q is completely dened by theexperimental geometry and the laser energy. In the particu-lar case of backscattering k S = k i , Eq. (7) can be writtenas

q = 2 k i = 4 ni

(9)

where n is the refractive index of the material at the fre-quency i , and i is the wavelength of the incident light.

Most Raman spectra of GaN-AlN or GaN-AlGaN nano-structures reported in the literature have been recorded atroom temperature. The simplest experiment is performedin a backscattering geometry along the growth axis z of thenanostructure, with polarizations of incident and scatteredlight either perpendicular or parallel, corresponding to thecongurations z xy z or z xx z , respectively. In the lattercase, both E 2 and A1 (LO) phonons are allowed. More-over, a micro-Raman spectrometer, using a small laser spot

whose diameter is lower than 1 m, allows the achievementof other scattering conditions, particularly backscattering onthe edge of the sample under study. In this conguration,the phonon wavevector q is perpendicular to the z axis andadditional phonons can be evidenced. The selection rulesfor all the Raman active phonons in wurtzite materials arerecalled in Table 4.

The excitation of Raman scattering is usually made usingthe monochromatic lines of an argon or krypton laser, eitherin the visible or ultraviolet range (from 3.41 eV to 3.80 eV).The experimental results strongly depend on the excitationenergy. If the latter corresponds to the visible range, that is,

Table 4. Selection rules for phonons in wurtzite crystals.

Conguration Allowed phonons

z xx z E 2, A 1 (LO)z xy z E 2x zz x A 1 (TO)x yy x E 2, A 1 (TO)

y zy x E 1 (LO) Note: The notation of phonons is that used in [5].

far from any electronic resonance, the dominant electron-phonon interaction is the deformation potential processand the nonpolar E 2 (high) optic phonon exhibits a scat-tering cross section much stronger than the other phonons,specially the A 1 (LO) mode also allowed in the z xx z con-guration. Note that the Raman spectra usually contain fea-tures from the GaN QDs or QWs and from the barriers of the nanostructure, but also from the underlying thick bufferlayer (usually GaN or AlN), due to the negligible opticalabsorption of the constituent layers in the visible range; thus

an unambiguous assignment of phonons may prove difcult.However, the signature of the nanostructure itself can beobtained using a confocal set-up with a low depth of focus,as illustrated later.

On the other hand, a strong enhancement of Raman scat-tering by the polar LO phonon is observed under near res-onant conditions, that is, if the energy of incident or/andscattered photons is close to an electronic transition energy, when the forbidden scattering process associated withthe intraband Frhlich electron-phonon interaction becomesdominant [28]. With the present materials, resonant condi-tions can be achieved in the ultraviolet range only; indeedthe room temperature bandgap energy is about 3.4 eV and6.1 eV for bulk GaN and AlN, respectively. The scatteringcross section of the A1 (LO) phonon can be enhanced byseveral orders of magnitude [29], thus allowing the signatureof very small volumes inside the sample. However, it shouldbe noted that the penetration depth of the incident light inthe sample is strongly reduced under ultraviolet excitation,due to high optical absorption. In addition, an intense pho-toluminescence (PL) band may show up in the spectra, mak-ing an observation of faint Raman features superimposedon the PL signal very difcult.

3. PHONONS IN QUANTUM WELLSAND SUPERLATTICES

3.1. Nonresonant Raman Scattering:Signature of Wells and Barriersin Superlattices

When Raman experiments are performed far from resonantconditions, the signal coming from the nanostructure itself is rather weak; it can be easily measured only if the sampleis thick enough (about 0.5 m), due to the low-scatteringcross section of GaN, and specially of AlN. Actually, thiskind of research study is still scarce; the main motivation isto determine the nature of the vibrational modes in the SLsand to derive the built-in strain of the constituent layers.


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The rst Raman study of an SL with a wurtzite structure was published by Gleize et al. [30]. This structure was madeof a hundred periods of undoped GaN wells and AlN barri-ers, with nominal thicknesses of 6.3 nm and 5.1 nm respec-tively, deposited by MBE on a thick AlN buffer layer and asapphire substrate. The layer thicknesses were large enoughfor neglecting the frequency shift of phonons induced by

connement, specially for the E 2 mode. Micro-Raman spec-tra were recorded in backscattering geometry under variouspolarization congurations, under a 2.54 eV excitation, farfrom resonant conditions. Thanks to selection rules, mostobserved features could be unambiguously assigned to alloptical phonons but the E 1 (LO), either from the underly-ing AlN buffer layer or from each type of SLs layers. Dueto internal strains, phonons from wells and barriers werefound signicantly shifted with respect to their frequency inrelaxed materials. Using the phonon deformation potentialsof 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 fromthe measured shift of the E 2 (high) phonon. This strain isclose to the value expected for a free-standing state of the

present nanostructure. On the other hand, the measured fre-quency shifts of AlN phonons, actually larger than those of GaN phonons, could not be used to determine the internalstrain in the barriers of the SL, because the correspondingdeformation potentials were not known at this time. Notethat a feature observed at 560 cm 1 in x yy x Raman spec-tra could not be associated to an A1 (TO) phonon fromstrained GaN layers, although it obeyed the regular selectionrules; it was thus tentatively assigned to an interface mode.Finally, micro-Raman spectra were also recorded from placeto place on a bevel made by mechanical polishing of thenanostructure; the angle between the beveled surface andthe (0001) plane was about 1 . The strain-induced shift of the E 2 (GaN) phonon was found higher in the deeper part

of the SL than near the surface, giving evidence for a partialstrain relaxation in the rst layers of the structure.Schubert et al. [3132] performed other investigations

combining Raman scattering and infrared ellipsometryexperiments. The latter is an indirect technique for inves-tigating the polar phonons, specially the E 1 (TO) phonon when a near normal incidence is used for the measurements. A standard calculation allows the reproduction of the exper-imental infrared spectrum; this model needs several ttingparameters, including the TO and LO phonon frequenciesof the constituent materials, together with the concentra-tion and mobilities (parallel and perpendicular to the z axisof the SL) of free carriers. The latter data must be intro-duced when the sample under study is doped, intention-

ally or not. Indeed, the free-carrier plasmon and the LOphonon, which are both longitudinal excitations, can cou-ple together if their energies are close to each other, thusshifting in frequency the high frequency component of thecoupled mode with respect to the uncoupled phonon [33].In [32], eight GaN-AlGaN SLs, grown by MOVPE or byMBE on thick GaN layer and on sapphire, exhibiting typi-cal layer thicknesses of 25 nm and various aluminum con-tents in the barriers (0 08 < x < 1), were compared. Asexpected, the strain-induced frequency shifts of the nonpolarE 2 phonon for each constituent layer, derived from Ramanmeasurements, proved that GaN (resp., AlGaN) layers were

submitted to an internal compressive (resp., tensile) stress. A detailed discussion of the Raman data suggested thatthese SLs were in a free-standing state: both kinds of lay-ers adopted a common in-plane lattice parameter, differentfrom the one of the underlying thick GaN layer. The analysisof infrared ellipsometry measurements led to the determi-nation of an electron concentration higher than 10 18 cm 3

in the GaN layers of the SLs; these free carriers could orig-inate from dislocation-activated donors or from the AlGaNlayers. Moreover, the in-plane mobility introduced for ttingthe infrared spectra was found higher than its out-of-planecounterpart: this result indicated a connement of free car-riers 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-raydiffraction 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 thereciprocal lattice, which was deduced from X-ray diffractionexperiments, gave the average value of both lattice constants

a and c of the whole SL. Figure 1 shows three micro-Ramanspectra recorded in the z xx z conguration, when the laserspot was focused slightly higher and higher upon the surfaceof the sample. The variation of relative intensities of theexperimental features made their assignment easy either tothe SLs layers or to the underlying buffer layer, allowing themeasurement of the strain-induced frequency shift of the E 2(high) phonons from the SL. Combining all these data andtaking into account the measured in-plane strain of GaNlayers ( xx = 2 35%) derived from in-situ RHEED exper-iments, both components of the biaxial strain of AlN andGaN 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 ( 2C 13/C 33 = 0 51). This difference is likely due to the large spontaneousand piezo-electric polarization effects which can signicantlydecrease this strain ratio in the hexagonal SL, as demon-strated in a calculation by Gleize et al. [35].

3.2. Resonant Raman Scattering: Signatureof Single or Multiple QWs

The rst resonant Raman study of single GaN QWs waspublished by Behr et al. [36]. In these samples grown byMOCVD directly on a sapphire substrate without any bufferlayer, the wells lying between thick Ga0 85 Al0 15N layers were2 nm, 3 nm, or 4 nm thick. As expected, only the phononsfrom the alloy were evidenced when the excitation wasachieved in the visible range, due to the negligible volumeof the QW. However, when the 3.54 eV laser line was usedfor the excitation, that is, for an energy close to the esti-mated fundamental electronic transitions in the wider QWs,the resonance conditions were nearly fullled and Frhlich-induced scattering by the GaN A 1 (LO) mode was favored. As can be shown in Figure 2, a Raman feature was observedat 732 cm 1 for the structures containing the 3nm- and 4nm- wide QWs. The origin of this feature could be unambigu-ously assigned to the single well; its measured frequencyshift was negligible, because both connement and strain


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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 anda 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 permissionfrom [34], J. Frandon et al., Physica E (2003). 2003, Elsevier Science.

effects were probably weak in the well. In contrast, the LOfeature was broadened and shifted towards higher frequen-cies for the 2 nm thick QW. This observation was explainedby cation intermixing at the GaN-AlGaN interface, whichcould not be neglected in that case. Smoothing of interfaceslikely due to poor growth conditions prevents the signatureof connement effects, which would induce an opposite fre-quency shift.

Figure 2. Resonant Raman spectra of GaN single QW with different widths embedded in Al 0 15Ga 0 85N barriers, recorded under the 3.54 eVexcitation. Reprinted with permission from [36], D. Behr et al., Appl. Phys. Lett. 70, 363 (1997). 1997, American Institute of Physics.

Further resonant scattering experiments on single or mul-tiple GaN-AlGaN QW structures will be reported in the fol-lowing. Later Ten GaN QWs of 1.5 nm width, embeddedin 5 nm wide Ga0 89 Al0 11N barriers and grown on a GaNbuffer 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, rst-order scatter-ing by the A1 (LO) phonons from GaN wells, favored bythe Frhlich interaction, was found strongly enhanced byelectronic resonance in the incoming channel when excita-tion is achieved using the 3.54 eV laser line. Indeed, theenergy of the incident photon was very close to the QWsfundamental transition, as estimated using the simple modelof independent square potential wells of nite height. Inthese experimental conditions, the second-order scatteringby the LO phonons from the thick buffer layer was domi-nant. Under a 3.70 eV excitation, LO phonons from GaN wells were clearly evidenced in the second-order scatteringsignal, due to electronic resonance in the outgoing channel; weak contributions from the barriers were also evidenced.Similar features were also observed in third-order scatteringunder 3.80 eV excitation.

Another study performed in resonant conditions has beendevoted to a collection of four different single GaN QWsseparated by 10 nm thick Ga 0 83 Al0 17N barriers and grownon a thick GaN buffer layer [38]; their thicknesses were1 nm, 2 nm, 3 nm, and 4 nm (corresponding, respectively, to4, 8, 12, 16 monolayers). The fundamental excitonic transi-tions in these wells were already determined from previousPL measurements performed at a low temperature. In this work, thick GaN and Ga 0 83 Al0 17N layers were also investi-gated in the same experimental conditions for comparison with the structure under study. The Raman spectra recordedat room temperature in backscattering geometry are shownin Figure 3. The PL signature of the various wells was clearlyobserved in the spectra, thus accurately giving the energy of the fundamental transitions in the wells at room tempera-ture. Under excitation at 3.53 eV, rst-order scattering byGaN A1 (LO) phonons conned in one of the wider QWs(3 nm) showed up in the spectra, enhanced by electronicresonance in the outgoing channel; no similar observationcould be achieved on the thick GaN layer used as reference,since the excitation was too far from resonance in the bulkmaterial. 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 eVexcitation was used, a rst-order Raman feature peakingat higher frequency (775 cm 1 and a weak contributionat lower frequency was observed. They are clearly relatedto phonons of the Ga 0 83 Al0 17N barriers and of the GaN wells, respectively. Scattering by vibrational modes of bothlayers requires an extended intermediate electronic stateof the QW with a signicant penetration into the barriers.This delocalization implies high-lying states whose energy isclose to the bandgap of the alloy. Resonance most likely


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Figure 3. Resonant Raman spectra of four single GaN QW in

Al0 17Ga 0 83N barriers, recorded using 3.53 eV and 3.70 eV excitations.The thicknesses of these QWs were 4, 8, 12, and 16 monolayers. Arrowsmark 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 photonenergy was almost tuned on the bandgap of the alloy. More-over, the Raman signal was found just superimposed on thePL signal from the thinner (1 nm) QW, centered at 3.60 eV;no similar Raman features could be observed with thickGaN or Ga 0 83 Al0 17N thick layers. The signal was thus likelyenhanced by a double resonance effect, as the second inter-mediate state involved in the Raman process was a boundelectronic state localized in the 1 nm-thick QW.

3.3. Calculations of Lattice-DynamicalProperties of Wurtzite Nanostructures

Komirenko et al. [39] rst investigated the extraordinarypolar phonons of wurtzite single QWs in the framework of a dielectric continuum model. The anisotropy of the materi-als was taken into account by introducing both components

and z ( ) of the frequency-dependant dielectric ten-sor of the constituent materials; the latter involve the fre-quencies of A1 and E 1 (LO and TO) phonons, polarizedalong the z axis and in the (xOy ) plane, respectively. Theelectrostatic boundary conditions on the interfaces, together with the assumption of a scalar potential vanishing far fromthe wells, were used. For a long wavelength phonon charac-terized by the in-plane q wavevector, the angular dispersioncan be deduced from the following equation:

q 2 + z q 2z = 0 (10)

where q z is the z component of an effective wavevector.Depending on the sign of the product z in eachmedium, q z is found either real or imaginary, leading to lin-ear superposition of oscillating or decaying solutions, respec-tively. Therefore, phonons could be classied according totheir localization. Conned modes are mainly located inside

the well but can penetrate signicantly into the surroundinglayers, interface modes decay exponentially from the inter-faces in both types of layers, and propagating modes oscillatein the whole structure. Their frequency variation versus theproduct q d was given for a GaN well of width d embed-ded in innite barriers made of AlN or of Ga 0 85 Al0 15N.Note that in another article, the same authors extended their

study to the calculation of scattering rates by the Frhlichelectron-phonon interaction in QW structures [40].Very few investigations of lattice dynamics in hexagonal

superlattices by ab initio calculations have been published upuntil now. Wagner et al. [41] computed the structural, dielec-tric, and lattice-dynamical properties of short-period hexag-onal GaN-AlN SLs, which were compared to their cubiccounterparts. In this calculation, the widths of barriers as well as of QWs were as low as two monolayers. Both typesof layers were assumed to be pseudomorphically strainedon the same in-plane lattice constant; the latter could beeither that of relaxed constituent materials (AlN or GaN)or an average value corresponding to an elastically relaxedSL. The goal of this work was to study the angular dis-persion 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 thez axis, within the framework of the density-functional pertur-bation theory. Most calculated modes were assigned eitherto conned phonons or to interface phonons. The atomsinvolved in each vibration mode, together with the strengthof the associated dynamical polarization, were also given.The angular dispersion of these modes is shown in Figure 4for a GaN-AlN wurtzite SL in several strain states. Actu-ally, only a few differences were evidenced in the angulardispersions of cubic and hexagonal SLs. In both cases, foran increasing in-plane lattice constant, all modes decreasein frequency, except the folded TA modes; the downwardshift was found more pronounced for LO phonons than forthe TO phonons. The only remarkable difference affects theTO modes conned in the GaN layers of the hexagonal SL,spreading in a narrower range than their counterparts in thecubic nanostructure.

However, the latter results cannot be easily checked.Indeed, experimental studies are usually performed onnanostructures with much larger periods. An alternativecalculation based on the dielectric continuum model, rstdeveloped in [39] for the GaN QWs, was applied to wurtziteSLs with more realistic periods [4244]. Within this framework, the vibrational modes were described by the dynami-cal polarization associated with the atomic motions in each

type of layer. The Maxwell equations, the electric bound-ary conditions at each interface, and the Blochs theorem,taking into account the SLs periodicity, were used together with the q = 0 phonon frequencies of the two types of lay-ers in the strain state actually achieved in the SL. Notethat the phonon dispersion q of the bulk constituents was ignored in this model. For GaN-AlN SLs, this calcula-tion predicted two types of polar phonons characterized byan angular dispersion . The rst ones were the inter-face modes which have been already found for SLs of cubicstructure; the corresponding amplitude of atomic motionsdecreases from the interface in both types of layers. Their


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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 strainsituations. From (l)(r), the results are given for SLs pseudomorphic on AlN, elastically relaxed on an average in-plane lattice constant, andpseudomorphic on GaN. Reprinted with permission from [41], J. M. Wagner et al., IPAP Conference Series 1, 669 (2000). 2000, Institute of Pureand Applied Physics.

dispersion is related to the anisotropy of the nanostruc-ture. In contrast, another type of phonon, the quasi-connedmodes, exhibit an angular dispersion originating from theanisotropy of the constituent materials. Indeed, the frequen-cies of the A 1 and E1 phonons of GaN and AlN, in theTO as well in the LO range, are the limits of their spectralregions; the corresponding intervals are nite for wurtzitecrystals, but vanish for isotropic materials. Quasi-connedmodes correspond to oscillations in one type of SLs layers

but, in contrast with conned modes in cubic SLs, the asso-ciated electric eld penetrates into the adjacent layer witha decay length much larger than the lattice constant: that is why they are called quasi-conned. Note that modes delo-calized throughout the whole nanostructure, characterizedby an oscillatory behavior in both types of layers, were foundonly in GaN-GaAlN SLs with barriers made of Ga-richalloys within this dielectric approach.

Very recently, Romanov et al. [4546] calculated the polarphonons of a single GaN QD, within the framework of amacroscopic continuum dielectric model. They obtained for-mal analytical solutions for the surface vibrations of a GaNQD exhibiting an oblate spheroidal form, embedded in AlN.These modes are not discrete, in contrast with their coun-terparts in cubic GaAs-AlAs QDs, and they are found insidea continuous, allowed frequency range, due to the crystalanisotropy. In addition, two other types of phonons werefound: runaway modes that freely leave the QD surface andquasi-stationary leaky modes.

The inuence of strong electric elds present in GaN- AlN nanostructures has been discussed by Coffey and Bock[47]. These authors calculated the wavefunctions associated with electron and holes conned in strained GaN-AlN QWs.The inuence of the electric elds (up to 1 MV/cm) inducedby internal strains on these states was shown in the par-ticular case of a 2.6 nm-thick QW: holes and electrons are

spatially separated in the QW by the conned quantumStark effect. Strong effects on the Raman cross section by A 1 (LO) phonons conned in the GaN layer were provento proceed from the breaking of symmetry with respect tothe center plane of the well. In the calculated cross sec-tion, both contributions to the electron-phonon interactionassociated with deformation potentials and Frhlich pro-cesses were taken into account. For vanishing electric elds,only conned phonons characterized by a quantum number

of even parity are allowed. In contrast, it was found thatconned phonons with an odd parity dominate the calcu-lated Raman spectrum when strong elds are present in theinvolved layer. Therefore, it was suggested that this break-down of parity selection rules could be used for measuringthe electric eld in wurtzite nanostructures. Unfortunately,the frequencies given for conned modes is questionable,considering the dispersion q calculated by the authors forthe LO phonon of bulk GaN, which is in agreement neither with measurements nor with calculations already published[911].

3.4. Experimental Investigations of Phononsin Nitride-Based Superlattices

As previously shown for superlattices made of cubic IIIVsemiconductors, the Raman signatures of disordered solidsolutions and ordered nanostructures with the same meancomposition are quite different, except for SLs containingultra-thin (thinner than three monolayers) layers. Evidencefor SL ordering can thus be achieved by Raman spec-troscopy, which is a nondestructive technique in contrast totransmission electron microscopy (TEM) needing cross sec-tions of the samples. However, Raman spectra of GaN-AlNSLs and AlGaN alloys can at rst sight exhibit some sim-ilarities, specially concerning the frequencies of E 2 (high)


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phonons, due to the two-mode behavior of the lattermodes in the alloy (see Section 2.2). Gleize et al. [30] haveobserved that the ambiguity could be lifted by consideringthe A 1 (LO) phonon which is, on the contrary, characterizedin alloys by its one-mode behavior. Indeed, the phonon fre-quency expected for the A1 (LO) mode of the Ga 1 x AlxNalloy with the mean Al content of the SL under study ( x =

0 45) would be 821 cm 1

[13]. Actually, the only feature obey-ing the appropriate selection rules, found at a much lowerfrequency (738 cm 1 in Raman spectra, was assigned to A 1(LO) phonons conned in the wells, slightly shifted fromthe corresponding frequency in relaxed GaN by the oppo-site effects of connement and strain. It should be notedthat the A 1 (LO) phonon conned in the barriers could notbe observed, likely due to the low-scattering cross section of AlN. Finally, it was concluded that the SLs modes could beunambiguously probed by nonresonant Raman scattering.

At this point of the discussion, one can wonder if Ramanexperiments can determine the nature of the SL phonons,delocalized or conned in one type of layer. A simple crite-rion has been suggested by Davydov et al. in several articles

[4850]; if two distinct phonons of the same symmetry canbe evidenced in Raman spectra from short period SLs, thecorresponding modes are claimed to be conned in one typeof layer. In the opposite case, the modes can be consideredas delocalized. However, it should be noted that the weak-ness of the Raman signal coming from one type of layer canmake a convenient use of this criterion difcult. The sameapproach has been used by Gleize et al. [30], who implicitlyconsidered phonons conned in each type of layer, with theexception of a phonon exhibiting the A1 (TO) symmetry,assigned to an interface mode.

Chen et al. [51] claimed to obtain the rst evidence fora connement effect of the A1 (LO) phonon in GaN lay-ers of an hexagonal superlattice. In this study, three GaN-

Ga 0 8 Al0 2N SLs were investigated; the thickness of the GaNlayers was 1.2 nm, 2.4 nm, and 3.6 nm, respectively. Theauthors concentrated on the A1 (LO) mode observed inz xx z micro-Raman spectra. The corresponding broad fea-ture was slightly red shifted in frequency, compared tothe relaxed material; this shift was found increasing forshrinking GaN wells. An approximate t of the measuredfrequencies was obtained, using q z sin

2 q z c/ 4 forthe dispersion of the LO branch of GaN. However, it shouldbe noted that the SLs contained only 30 periods and that thetotal thickness of GaN in the SL was as low as 36 nm for thethinner layers; one can thus wonder if a clear signature of the wells could be really obtained in nonresonant scatteringconditions, considering the presence of an underlying thick

GaN buffer layer.Davydov et al. [4850] investigated by nonresonant

Raman scattering a set of GaN-Ga 1 x AlxN superlattices,grown by MOCVD on buffer layers and sapphire substrates.The SL period was varied between 2.5 nm and 320 nm. Forthe sake of simplicity, the thicknesses of wells and barri-ers in the various nanostructures were the same in all thenanostructures investigated. The aluminum content x in thealloy of the barriers was lower than 50%. The total thicknessof the SLs under study was sufcient for achieving Ramanexperiments in nonresonant scattering, with an excitation at2.54 eV. In the recorded spectra, E 2 (high) and E 1 (TO)

phonons from GaN were observed and assigned to connedmodes in the wells, whereas their counterparts could not beevidenced for the AlGaN layers of the SL. The lack of signalfrom the barriers has been tentatively attributed to the low-scattering cross section by phonons of the AlGaN alloy. Onthe other hand, the E 2 (low) phonon conned in the barri-ers of the SL was also found in the low-frequency range of

the spectra, together with that from GaN layers [50]. Due toits high sensitivity to the Al content (but not to the built-instrain), the E 2 (low) phonon from the alloy could be usedas a probe of the composition in the barriers of the SL. Thesame authors also gave evidence for connement of the A 1(LO) phonon either in GaN or in GaAlN layers. In Figure 5,two modes are clearly observed in z yy z spectra from var-ious SLs where the alloy content of the barriers was keptconstant (28%). Note that the range of investigated periods was very wide, between 5 nm and 3 m.

In contrast, the behavior of E 1 (LO) and A1 (TO)phonons was found quite different. Actually, each of them isalways observed as a single line; its location in Raman spec-tra is similar to that in a Ga 1 x AlxN disordered alloy, whose

composition corresponds to the mean Al content in the SL

x = x d2

d1 + d2(11)

where d1 and d2 are the width of wells and barriers, respec-tively. Accordingly, these modes are considered as delocal-ized 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 28Ga 0 72N 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.


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A1 (TO) phonons from the SLs under study and from thecorresponding ternary alloy were found rather similar. Thesame observation was made on the E 1 (LO) phonons. Thiskind of evolution seems to be consistent with results of acalculation performed in the framework of a dielectric con-tinuum model, where the nanostructure was treated as anhomogeneous 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 angulardispersion experimentally, if the latter is signicantlydifferent from that of the bulk material. This has beendone by Gleize et al. [44] for polar phonons through anexperimental study of a GaN-AlN SL, performed for check-ing the validity of the continuum dielectric model previ-ously developed [42]. Micro-Raman spectra were recordedunder 2.54 eV excitation, in backscattering geometry on thetop surface ( = 0), on the edge ( = 90 ), and also on abevel at 45 fabricated on the edge of the nanostructureby ion etching. The variation of the angle around theabove values was achieved by tilting the sample with respect

to the incident light beam; in this experiment, the uncer-tainty on was lower than 5 . The measured frequencies of various polar modes from the SL could be compared withthe predicted ones. As observed in Figure 6, the agreement was found rather satisfactory, particularly for the TO modesquasi-conned in GaN and AlN layers, which could not beconfused with the dispersive extraordinary TO modes fromthe underlying thick AlN buffer layer.

3.5. Folded Acoustic Phonons inHexagonal Superlattices

The work published by Davydov et al. [49] on GaN-AlGaNsuperlattices has evidenced for the rst time zone-center-folded 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 experi-mental values and to the calculated variation, respectively. The angulardispersion 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.

their periodicity. As shown in Figure 7, remarkable sharpRaman features were detected in the low-frequency range of the spectra recorded in the z yy z scattering conguration,from a few nanostructures made of GaN and Al 0 28Ga 0 72Nlayers of same thicknesses, with SLs periods ranging between6.1 nm and 23.8 nm. Actually, only the doublet expectedfrom the rst folding of acoustic branches was clearly

observed in each case. As expected, the mean frequency of the doublet increases for decreasing SLs periods. The mea-sured frequencies of both components of the doublet obeyedfairly well Eqs. (4) and (6) appearing in Section 1.2. An aver-age sound velocity v = 8140 m/s in the nanostructure wasderived from these measurements. Finally, different scatter-ing congurations were achieved for changing the z compo-nent q z of the wavevector of the phonon involved in Ramanscattering. This experiment allows the probing of the fre-quency dispersion of the folded acoustic modes [27]. Indeed,the authors found that the spectral spacing of both lines inthe doublet was decreasing with q z .

4. PHONONS IN QUANTUMDOTS STRUCTURES4.1. Nonresonant Raman ScatteringThe rst Raman signature of QD structures has been pub-lished by Gleize et al. [52]. The samples were stackings of GaN-AlN QDs grown along the (0001) direction on an AlNbuffer layer and a sapphire substrate. As demonstrated byTEM 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 wererecorded under 2.54 eV excitation, in a backscattering geom-etry along the z axis. However, the whole sample was probed

Figure 7. Raman spectra of GaNAl 0 28Ga 0 72N superlattices with dif-ferent periods (23.8 nm, 12.8 nm, and 6.1 nm), recorded under a 2.54 eVexcitation. Only the low frequency part of the spectra, exhibiting thefolded acoustic phonons, is shown. Reprinted with permission from [49], Phys. Stat. Sol. ( A), 188, 863 (2001). 2001, Wiley-VCH.


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Figure 8. Cross section of a GaN-AlN QD stacking, observed by trans-mission electron microscopy. The typical height of GaN QDs was 4nm. 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 notstraightforward. In order to overcome this difculty, the con-focal conguration was used and the laser spot was focusedhigher and higher above the surface, inducing a relativeintensity variation of the E 2 phonons from the buffer layerand from the QDs, as already illustrated for SLs. It allowedthe unambiguous signature of the GaN islands. A slight(tensile) strain of the AlN spacers was deduced from themeasured (negative) frequency shift of the E 2 phonon. Theeffect of vertical correlation of QDs in these structures canbe evidenced from small changes of the strain measured forthe spacers.

Another study has been devoted to a set of GaN-AlN QDstackings characterized by various heights and densities of

dots, deposited either on sapphire or on silicon [54]. Using various backscattering geometries, most Raman-active opticphonons from the structure could be observed. Except forthe A 1 (LO) mode, the measured phonon frequencies wererather close to those found in the similar disordered AlGaNalloy. The observed frequency shifts were assigned to straineffects, as in the case of SLs. An in-plane strain in GaNdots of 2 4% or 2 6% was estimated from the frequencyshift (as high as + 35 cm 1 or + 38 cm 1 of the correspond-ing E 2 phonon, using the corresponding deformation poten-tials. The QDs were found completely strained on AlN inall the structures under study, as expected. Obviously, themean strain in the AlN spacers, tentatively derived from theexperimental data, was found much lower.

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

were used. In fact, large internal electric elds take placein this kind of nanostructure, thus lowering the fundamen-tal bandgap energies signicantly. In the present structure,this quantum conned Stark effect was specially strong. Theroom temperature PL originating from GaN QDs was cen-tered around 2.35 eV, much lower than the excitation energy,and thus did not merge the Raman signal. The more inter-

esting result was obtained using the 3.80 eV laser line. A fea-ture clearly showed up in the rst-order scattering rangeat 744 cm 1 in Raman spectra from the nanostructure, incontrast to those recorded on the GaN layer used as a refer-ence (see Fig. 9). The observed peak, which could not orig-inate 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 associ-ated with the nonpolar E 2 phonon from the strained dots.It should be noted that the latter mode could be observedunder the 2.33 eV excitation, that is, at an energy closeto the PL maximum, in contrast to the A1 (LO) phononfrom QDs. These results gave evidence for a strong reso-nant enhancement of the scattering by polar phonons in the

incoming channel at 3.80 eV, implying probably an excitedstate of the dots. Another original study was carried out by Kuball et al.

[56] on a single plane of self-assembled GaN QDs grownon a Al0 15Ga 0 85N layer, using silicon as anti-surfactant.Two clearly distinct distributions of QD sizes were revealedby means of atomic force microscopy. The Raman spectrafrom the nanostructures are shown on the top of Figure 10.Under a 3.53 eV excitation, rst-order scattering located at736 cm 1, superimposed onto a broad PL band, was assignedto the A 1 (LO) phonon from the large (about 40 nm high)dots, where connement effects on the LO phonon fre-quency are almost negligible. In the same experimental con-ditions, a phonon was observed at the same frequency but

with a lower intensity, on another sample grown in similar

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


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