Raman scattering by surface polaritons in cubic GaN epitaxial layers

Solid

State Communications, Printed

Vol.

104, No. 7, pp. 397-400, 1997 0 1997 Elsevier Science Ltd in Grzat Britain. All rights reserved 0038-lOYX/Y7 $I7.Gfl+.oo

PII: SOO38-1098(97)00346-3

RAMAN SCATTERING V.Yu. Davydov,“,*

BY SURFACE

A.V. Subashiev,b

POLARITONS

IN CUBIC GaN EPITAXIAL

T.S. Cheng,” C.T. Foxon,” I.N. Goncharuk,” and R.V. Zolotarevaa

LAYERS

A.N. Smirnovn

“Ioffe Physical Technical Institute, St Petersburg 194021, Russia ‘Department of Experimental Physics, State Technical University, St Petersburg 19525 I, Russia ‘Physics Department, Nottingham University, Nottingham, NG7 2RD, U.K. (Received 7 July 1997; accepted

14 July 1997 by E. L. Ivchenko)

We present the results of Raman experiments on cubic GaN epitaxial layers grown on (0 0 1) GaAs substrates. A distinct line observed at the iowfrequency edge of the LO phonon in the backscattering spectra is shown to be due to the upper surface polariton mode. We show that the high transparency of the layer results in a weak efficiency of scattering by the lower polariton mode and strong increase of the scattering in backward configuration. The research reveals a high sensitivity of the surface polariton mode to the film thickness, doping level and quality of the GaN/GaAs interface. 0 1997 Elsevier Science Ltd Keywords: A. thin films, D. phonons, light scattering.

GaN is the most promising semiconductor for various optoelectronic, high temperature and high-frequency device applications [l]. Recently, cubic GaN layers grown on GaAs substrates have been reported, but their characterization methods are still being developed. In this paper we report the experimental results of the Raman scattering from cubic GaN layers. We demonstrate that the additional scattering line observed, but not identified, in the earlier studies [2] originates from surface polariton scattering. The samples investigated here were undoped and Sior Be-doped epitaxial layers MBE-grown on (1 0 0) GaAs substrates. The crystalline structure was deduced from X-ray measurements. The layer thicknesses of 0.4-0.6 pm were determined from oscillations of the Fabry-Perot type in the reflectivity spectra. Raman scattering was excited by the 457 nm, 488 nm and 514 nm lines of an Ar laser and the 647 nm line of aKr laser. Both back-scattering and forward scattering configurations were used. For cubic GaN, two lines associated with LO and TO optical phonons are expected in the first-order Raman

*To whom correspondence should be Electronic mail: [email protected]

addressed.

D. optical properties,

E. inelastic

spectra. The scattering geometries in which only LO- (or TO-) Raman scattering is allowed are strictly determined by the orientation of the crystallographic axes and polarization vectors of the incident and scattered light. Figure 1 shows the Raman spectra obtained for an undoped GaN-on-GaAs layer in the near back-scattering geometry. We use the following definitions: x, y and z correspond to the directions [I 0 01, [O 1 01 and [O 0 I] and x’, y’ are along [I 1 0] and [l f 0] respectively. The symmetry analysis of the spectra reveals the epitaxial mode growth with the cubic axis coinciding with the [O 0 I] direction of the substrate. No traces of the hexagonal phase were seen. The forbidden TO phonon line seen in Fig. 1 in the z(x, y)z geometry is apparently associated with the scattering in the heterointerface region with a high concentration of the structural defects and with the light reflection from the back surface of the layer. One can see from Fig. 1 that, in addition to LO and TO phonon lines, a new feature is observed at the low frequency edge of the LO phonon (see also the inset in Fig. 1). Below we present the results of the analysis of this feature. The samples were prepared with the GaAs substrate removed from a region ~400 pm by etching. (This type of sample will be referred to as a membrane.) The Raman 397

398

SURFACE

z(xx)Z !500

I

I

.

700

600

POLARITONS

IN CUBIC GaN

Vol. 104, No. 7

I

800

Raman shift , cm-’ Fig. 1. Polarized Raman spectra obtained from the layer plane and from the lateral side of the GaN epilayers grown on a (1 0 0) GaAs substrate. The inset shows growth of the additional line intensity on a membrane (m). spectra of both GaN-on-GaAs and GaN membrane are presented in the inset of Fig. 1. In the geometry chosen, the position of the additional line in both spectra is the same, but an enhancement of the line in the membrane spectrum is clearly seen. To obtain the dispersion curve, the angle of incidence was varied, while the direction of scattered light was kept strictly normal to the surface. In Fig. 2, Raman spectra from a membrane for several angles of incidence are shown. The shift of the additional line toward the LO-line with decrease of the angle of incidence can be interpreted as a manifestation of a strong spatial dispersion of the mode in the small wave-vector region. Between the frequencies w, and ol of the TO- and LO-phonons, the dielectric constant E(W) of the GaN layer is negative. Therefore the observed line can be related only to the surface lattice vibrations [3]. In the layer of finite thickness, two surface polariton modes (w+ and w_) are expected originating from the vibrations localized on the front and back surfaces of the layer. In the region of the polariton wave vectors kil> wale, where the retardation effects can be ignored, the surface polariton frequencies are given by (see, e.g. [4]): w_c=o,

(

1+

l/2

Eg- er. eL + $1 + ez) coth (k/a) + +&’

)

. (1)

Here, Z = (1 + e-2,)2coth*(kila) - 4e2, e2 is the substrate dielectric constant, and a is the layer thickness.

Fig. 2. Polarized Raman spectra of the GaN membrane in the backscattering configuration for several angles of incidence of the excitation light. The upper and lower polariton branches for GaN-onGaAs and GaN membrane as functions of kp are plotted in the inset of Fig. 3. The parameters of GaN and GaAs used areeo=9.4e,=5.3 ande*=ll.l [5].Askll--,m,the lower branch frequency w- approaches the frequency of the surface polariton mode on a single GaN/GaAs interface, w- -0, = wy (~0 + e2>/(ez + e2) = 614 cm-‘, whereas the upper branch frequency w+ approaches the frequency 00 = W, (~0 + l>/(ez + 1) = 708.9 cm-’ of a polar&on on a free surface of GaN. This frequency is very close to the frequency of the Raman line observed at large angles of incidence. For the membrane, the two polariton modes have different electric field distributions inside the layer. The normal component of the polar&on electric field is symmetric relative to the membrane’s center plane for the upper (w,) mode and antisymmetric for the lower (o-) polariton branch. At small wave vectors, kip < 1 (but still kli> w/c> the polariton modes approach the bulk phonon frequencies, w+ = wI and w _ = wy, while as kll - ~0, wt approach wo. In Fig. 3 we plotted the dispersion of the upper polariton branches for the GaN-on-GaAs and GaN membrane. According to equation (1) a shift of the polariton line towards lower frequencies is expected when changing from the membrane to the GaN-onGaAs layer and from a thin layer to a thicker one in a fixed scattering geometry, while an increase in the wavelength of the excitation line must lead to the polariton line shift towards the higher frequencies. All these features were experimentally observed. The

Vol. 104, No. 7

SURFACE

POLARITONS

IN CUBIC GaN

399

The problem of the relative scattering efficiencies for the upper and lower polariton branches in forwardscattering and backward-scattering configurations was extensively discussed in a number of theoretical papers (see [8]). The authors concluded that for GaAs layers the back-scattering efficiency of the surface modes is very low, whereas the forward scattering efficiency of the surface polariton modes can be sizable. However, we would like to point out that the Raman scattering in highly-transparent layers (such as GaN films) has specific features due to the contribution to the scattering efficiency from the light reflected by the back surface of the layers. In the near back-scattering configuration the crosssection of the Raman scattering (when reflected waves are taken into account) can be written as Wave Vector, k, , a Fig. 3. The dispersion of the upper polar&on branch w+&) for the GaN membrane (solid) and GaN-onGaAs layer (dashed), calculated using eqn (1). The points represent the experimental data: full squares and triangles, membranes of different thicknesses; open circles, a GaN-on-GaAs layer. The inset shows the dispersion curves for both (upper and lower) surface polariton modes. experimental polariton frequencies for a number of polariton wave vectors are shown in Fig. 3. When calculating the polariton wave vector, we took into account a finite aperture (13“) of the collecting experimental setup which shifted the values of the wave vector transferred to the polariton at small incidence angles and also contributed to the uncertainty of the wave vector. The agreement between the data and the theory is very good. Thus on the basis of the layer thickness, excitation energy and scattering angle dependence of the Ran-tan line, we conclude that the additional peak observed in cubic GaN layers is due to the upper branch of the surface polaritons. Still the polariton Raman spectra of cubic GaN layers differ considerably from those in the extensively studied GaAs layers [6,7]: (i) the scattering intensity in forwardand back-scattering configurations differ by less than 3.5 times, while in GaAs layers the polariton scattering intensity is negligible in back-scattering geometry, (ii) we have never observed scattering from the lower branch predicted by equation (1) in GaN membranes, while in GaN-on-GaAs structure the scattering line was quite weak, (iii) the intensity of the polariton line for membranes was at least 2.5 times larger than in GaN-on-GaAs structures, the ratio varying for different samples and being dependent on the GaN layer doping.

s, =S’O’+2R b

23 S’O’ f .

(2)

Here, Sip’ (Go)) is the backward-scattering (forwardscattering) cross-section in the absence of the layer back-surface reflection, Rz3 is the reflection coefficient for the back surface of the GaN layer (which is with high accuracy the same for the incident and scattered light). The reflection-originated corrections to the forward scattering efficiency are found to be of minor importance. (Here we do not consider a special case of the interference oscillations of Fabry-Perot type.) In the case of scattering in GaN-on-GaAs layers and membranes Akf = k;) - kf’ << I$, 1< Ak, = kp) + k,6) ,

(3)

where kr) and kr’ are the perpendicular components of the wave vectors of the incident and scattered radiation. Therefore while S’“‘/S’o’ b f = (Akf/Ak,)* < 1 (see, e.g. [S]), we eitimate the ratio of the backward-scattering to the forward-scattering cross-section in a transparent layer to be &,/sf = 2R23.

(4)

Thus, the reflection from the back surface makes it possible to observe the reflected light of the fimturdscattering process and forward-scattering process of the reflected light. For a GaN membrane R23 = R, where R is the reflection coefficient for a free GaN surface, R = 0.155 [5], so that we have s&f = 0.31. Thus, the theoretical estimates of the ratio of the backward- to forwardscattering efficiencies are in line with the experimental data. Then, we infer from the fact that only forwardscattering processes with a very small wave vector z-component Akf transferred to the surface polariton are observed that onZy the upper polariton mode (with a symmetrical field distribution) must be observed in the

400

SURFACE

POLARITONS

Raman scattering spectra of membranes, while the forward scattering by antisymmetrical lower polariton mode is strongly suppressed. This conclusion is also in a good agreement with our experimental findings. For excitation energies used in [6, 71 in the GaAs layers studies (when (YU> 1, (Y being the absorption coefficient) the transferred z-component of the wave vector A$ was of the order of (Y. Therefore the effect of asymmetry-originated quenching for the lower mode was negligible and the contributions of the upper and lower polariton modes to the scattering cross section were of the same order of magnitude. For some of the GaN-on-GaAs samples we observed a considerable weakening of the polariton line, accompanied in some cases by the weakening of the modulation in the layer reflection spectra, the polariton line intensity being also dependent on the type and concentration of the doping impurity. A possible explanation would involve the effects of the compensation of the polariton electric field in the GaN layer and the substrate ]3]. Besides, quenching of the surface polariton can be due to the surface conductivity originating in doped GaN samples from the surface band bending and space charge layer formation resulting from large band offsets on the GaNlGaAs interface [9]. Note that the effect is of major importance for the lower polariton mode, while the upper polariton mode in the GaN/GaAs structure is localized near the free GaN surface and therefore is less sensitive to the effects of the interface. A more detailed account of the results will be published in a separate paper. To summarize, we observed a strongly dispersive mode in a GaN cubic layer on GaAs substrate and GaN layer with an etched substrate by means of Raman scattering. We identified this mode as the upper surface polariton branch of the structures. The scattering by the lower polariton mode is shown to be suppressed because of its symmetry. In GaN layers, the scattering efficiencies

Vol. 104, No. 7

IN CUBIC GaN

for backward and forward configurations are found to be comparable. This fact is attributed to the reflection of the incident and scattered light from the back surface of the layers. Acknowledgements-We wish to thank D.N. Mirlin for useful discussion and N. Zinov’ev for critical reading of the paper. VYuD, ING, ANS and RVZ appreciate the support of the Ministry of Sciences of Russia, Program “Physics of Solid State Nanostructures” (grant No. 97-1035). ABC’s activity was partly supported by the Russian Program “Surface and Atomic Structures”, Grant No. 95-1.23. TSC, CTF gratefully acknowledge the support of this work from INTAS grant 94-2608. REFERENCES 1.

2.

3.

4. 5.

6. 7. 8. 9.

Morkoq, H., Strite, S., Gao, G.B., Lin, M.E., Sverdlov, B. and Bums, M., J. Appl. Phys., 76, 1994, 1363. Giehler, M., Ramsteiner, M., Brandt, O., Yang, H. and Ploog, K., Appl. Phys. Lett., 67, 1995, 733; Tabata, A., Enderlein, R., Leite, J.R., da Silva, S.W., Galzerani, J.C., Schikora, D., Kloidt, M. and Lischka, K., J. Appl. Phys., 79, 1996,4137. Agranovich, V.M. and Ginzburg, V.L. Spatial Dispersion in Crystal Optics and the Theory of Excitons. Springer Verlag, 1982. Mills, D.L. and Maradudin, A.A., Phys. Rev. Lett., 31, 1973, 372. Data in Science and Technology, Semiconductors, Group IV Elements and II-V Compounds (Edited by 0. Madelung). Springer-Verlag, Berlin, 1991. Evans, D.J., Ushioda, S. and McMullen, J.D., Phys. Rev. Z-&t., 31, 1973, 369. Prieur, J.-Y. and Ushioda, S., Phys. Rev. Len., 34, 1975, 1012. Surface Polaritons (Edited by V.M. Agranovich and D.L. Mills). North-Holland, 1982. Vinogradov, E.A., Zhizhin, G.N., Mal’shukov, A.G. and Yudson, V.I., Solid State Commun., 23, 1977,915.