Mandelstamm-Brillouin studies of light scattered by (110) faces of GaAs, InSb and PbS crystals

PhysicsLettersAl70(1992) 165—170 North-Holland

PHYSICS LETTERS A

Mandelstamm—Brillouin studies of light scattered by (110) faces of GaAs, InSb and PbS crystals V.V. Aleksandrov, T.S. Velichkina, Ju.B. Potapova and l.A. Yakovlev Chairfor Crystallophysics, PhysicsDepartment ofshe Moscow State University, Moscow 117234, Russian Federation Received 20 July 1992; accepted for publication 5 August 1992

Communicated by V.M. Agranovich

Mandelstamm—Brillouin (MB) surface light-scattering spectra of (110)-cut GaAs, InSb, and PbS crystals were studied and surface wavevelocities were determined forvarious 0(110) values; 9(110) is the angle between the [0011direction and the plane of the incident light. Both GaAs and InSb crystals demonstrated aconsiderable GSW high-frequencyone-sided line broadening for 0(110) = 40°—45°. Observations made for a PbS crystal revealed a GSW—pseudo surface mode (PSM) transition at 9(110) = 70°— 80°.

1. Introduction Pioneering works of Dii and Brody [1] and Sandercock [2] started the wide application of the Mandelstamm—Brillouin (MB) high-resolution lightscattering technique for experimental studies of condensed matter surface excitations at thermal equilibrium conditions. Investigations of MB light scattered by the surface of an opaque medium revealed that besides Rayleigh-type generalized surface waves (GSW), leading to the observation of the principal MB satellites, spectral lines corresponding to so-called leaky surface waves may be detected [2—4]. Contrary to the GSW, which have three partial true surface waves elliptically polarized in the vertical plane not coinciding with the sagittal plane, one of the leaky surface waves, i.e. the pseudo surface mode (PSM), also elliptically polarized, has two of the partial waves with in-plane wave vectors, while the latter one is a slow quasi-transverse bulk wave with a wave vector deviating from the surface into the medium [5]. The velocity of the PSM, VPSM, lies between V~and V12, where V~is the velocity ofthe fast transverse bulk wave with the same propagation direction at the surface and V~2is that of the slow transverse one, MB experiments performed on GaAs crystals

[2,6,7], where both ripple and elasto-optic contributions are rather strong [2—4],make evident the existence ofanother leaky surface wave, the high-frequency pseudo surface mode (HFPSM). Unlike the PSM, it has a longitudinal character, and only one of three HFPSM partial waves is confined to the surface [6]. The HFPSM velocity VHFPSM satisfies V~< ~ VL, where VL is the velocity of the quasi-longitudinal bulk wave with the same propagation direction. The theoretical approach developed by Loudon [8], Subbaswamy and Maradudin [9], Rowell and Stegeman [10], Bortolani et al. [11], Marvin et al. [12], Velasco and Garcia-Moliner [4,131 and Camley and Nizzoli [3] successfully described the spectral content of light scattered by the surface of opaque media observed experimentally, especially those of elastically isotropic substances and for cubic crystals with high-symmetry planes. In the case of cubic crystals ofSi [21, Ge [14,15], GaAs [7], InSb [161 and Ni [17] z-cut in the region 9(001) oo_20 only the principal MB satellites caused by the GSW are experimentally detected, whereas for 0(001) strong solitary MB satellites corresponding to the PSM are observed. Here ~ is the angle between the (010) crystallographic plane and the sagittal one. The theoretical description of the GSW—PSM transition, made for

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the ripple scattering materials, also predicted the simultaneous existence of both the MB spectral lines relating to the GSW and the PSM in the intermediate 0(~1) region (0(001) 20°—35°),which was later detected in Ge [15], GaAs [7]and InSb [16]. In the case of cubic crystals of GaAs (111)-cut, as described in refs. [3,6,71, the principal MB satellite and the spectral line relating to the HFPSM were detected in the whole region 0(111)=0°—30°, while the satellite corresponding to the PSM was detected at 0(II1)~00_l80 [6,7]. Here 0(111) is the angle between the [110] crystallographic direction and the sagittal plane. On the other hand, observations described in ref. [2] on a GaAs crystal (110)-cut demonstrated the possibility to register the principal MB as well as the HFPSM ones. Nevertheless, systematic investigations of the MB light scattered by this plane, except for Ni [17], have not yet been made. Besides the possibility of studying the MB surface light-scattering spectra for materials with another surface light-scattering mechanism, i.e. ripples and elasto-optic, a sufficient enrichment of the MB spectral content should be expected for (110)-cut cubic !s= 2C44/ (C11 C12) < 1, with C11, C12 and C44 the corresponding elastic constants [5]. Contrary to Ni, InSb, GaAs, Ge, Si, where ~> 1, materials with jt < i are characterized by the presence of the (110) plane PSM branch, whereas in case ofthe (ill) and (001) planes the PSM branch is absent [5]. The aim of the present work was a systematic study of the MB light scattered by the (110) plane of the GaAs, InSb (~s=1.80, 1.99, respectively) and PbS (~u= 0.508) crystals. Light scattered by the studied specimens was obsurved backwards. The experimental setup for the registration of the MB light-scattering spectra was described earlier [18]. All the measurements were performed at room temperature. —

2. Study of light scattered by a GaAs crystal (110)-cut Figure la represents the recorded spectra of MB light scattered by a (110)-cut GaAs crystal at 0(110)=0;hereO(IIo)istheanglebetweenthe [001] crystallographic direction and the plane of the in166

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cident light. The presence of the MB satellite pedestal in figs. 1 a and the following is due to the data accumulation conditions. Figures lb— 1 d represent the recorded spectra of light scattered by a GaAs specimen for O(IIo)=17.5°, 42.50 and 90°,respectively. The frequency shifts related to Ti, T2, and L are marked by the arrows. At 0(110) =0° the HFPSM line was not observed, whereas for 0(110)= lO°—90°the MB spectra in addition to the principal satellite contain the HFPSM line. The intensity of the HFPSM line rises cornparably with an increase of 0(110) from 10°to 90°, the GSW satellite intensity being decreased at O(IIØ) = 90°.The broadening ofthe principal MB satellite to the high-frequency region of 0(110) = 42.5° (fig. 1 c) should also be noted. The results ofthe determination of the (110) plane surface acoustic wave velocity versus 0(110) are shown in fig. 2. The proper GSW, Ti, T2 and L theoretical curves are also introduced here. Note that fig. 1 c (0(110) = 42.5°)with the broadened principal satellite corresponds to the region of 0(110) where the GSW curve approaches Ti and where the VGSW values were found to be systematically 1—3% higher than those introduced by the GSW ultrasonic data-based theoretical curve. The experimental GSW velocity values agree with the corresponding theoretical curves and in the case of the HFPSM they correlate with the VL-curve estimation [3], the experimental error of the HFPSM velocity determination being 2—3 times higher than for VGSW because of the considerable line width and the weakness of the HFPSM lines. 3. Study of light scattered by an lnSb crystal (110>cut The results ofthe determination of the (110) plane InSb crystal surface acoustic wave velocity versus 0(110) are represented in fig. 3. The behavior of the experimental V0~Wvalues is found to be similar to those for GaAs. Like in the case of GaAs a dramatic high-frequency broadening of the principal MB satellite is observed at a “bending-point” neighboring region, 0(110) = 40°.See fig. 4, where the Ti and the GSW curves come closer to each other. The GSW satellite at 0(jIo)=0° (fig. 4b) is also reproduced here, with line width and line shape scaling.

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Fig. 1. Spectra oflight scattered by the (110) plane ofa GaAs crystal. O(lIo)=0° (a), 17.5°(b), 42.5°(c), 90°(d). The electric vector E of the incident light was parallel to the plane ofincidence in all experiments. xis the normal to the crystal surface; k~,k and ~ are the wave vectors of the incident light beam, the scattered light beam and the GSW, respectively; a=53.5°is the angle of incidence, 1=488.0 nm is the wave length ofthe incident light. The intensity scale (y-axis) for (a)—(c) is the same.

The one-sided high-frequency broadening of the GSW satellites at 0(11o)=42.5°for the GaAs crystal (fig. lc) and at O(110)=40°for the InSb crystal (fig. 4a) demonstrate the strong surface excitations specific for these 0(1 lO) values.

4. Study of light scattered by a PbS crystal (110)-cut

Thç results of the experimental studies on the relation between the surface wave velocity and 0(110) in a (110)-cut PbS crystal are shown in fig. 5. The behavior of the V~1,V12 and V05~curves as a 167

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Fig. 2. Surface and bulk acoustic waves velocities of the (110)

plane GaAs crystal as a function of 9(110) ((<>) experimental GSWvelocity, (x) HFPSMvelocity).Thecurvefor V0~.,(solid line) is reproduced according to ref. [5]; curves corresponding to V~1,V12 and VL (dotted lines) were calculated using the material parameters of ref. [19].The normalized velocity ordinate scale, V/ V~is also shown; here V~= crystal mass density.

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Fig. 3. Surface and Tl, T2 transverse bulk acoustic wave velocities of the (110) plane InSb crystal versus 9(110) (((>) experimental V05w). The curve for V0~(solid line) is reproduced accordingtoref. [5];thetheoreticalcurvesfor ~ V~(douedlines) were calculated using the material parameters of ref. [19]. The normalized velocity ordinate scale, VI V~,is also shown.

function of 0(110) introduced here, significantly differ from those in the case ofthe GaAs and InSb crystais. In contrast to crystals with ti> 1 in PbS (js=0.508) at 0(11o)=90°the GSW degenerate into 168

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Frequency Shift, GHz Fig. 4. Spectrum of light scattered by an InSb crystal (110)-cut at °(O0I) =40° (a), 0°(b). a=60°, 1=488.0 nm.

the bulk transverse wave linearly polarized in the surface and the Rayleigh-type wave velocity belongs to the PSM branch [5]. Our experiments have shown that the position of the MB surface wave satellite correlates well with the GSW branch in the region 9(t1o~=O0_700, whereas for 0(IIo)~80°—90° it corresponds to the PSM one.

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Fig. 5. Surface and TI, T2 transverse bulk acoustic wave velocities of the (110) plane PbS crystal versus °(IIo) ((<>) expenmental surface acoustic wave velocity). The curve for VQSW (solid line) is reproduced according to ref. [5]; the theoretical curves for V, 1, V~2(dotted lines) were calculated using the material parameters of ref. [19]. The cross-surface acoustic wave velocity corresponding to the PSM branch is taken from ref. [51.The normalized velocity ordinate scale, V/ V~,is also shown.

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At 0(I1o)=74°,i.e. the intermediate 0(110) region, we simultaneously detect the satellite caused by the GSW and that ofthe PSM (see fig. 6). The GSW and PSM line intensities are found to be approximately 2 times lower than for the GSW satellite at 0(110) = 0° (fig. 6b). The GSW—PSM transition observed here as the simultaneous registration of both the GSW and the PSM spectral lines, qualitatively similar to those of (001) Ge, and GaAs [15,7] results, where for 0(110) near 0° the main MB peak was due to the GSW branch and to the PSM branch for 0(110) near 45°, and where in the intermediate 0(110) region both branches contribute significantly to the spectral content of the scattered light [13]. Meanwhile the theoretical treatment GSW—PSM light-scattering transition forof ~
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Frequency Shift, GHz Fig. 6. Spectrum of light a=70°,/=488.0 scattered by a PbSnm. crystal (110)-cut at 74° (a), 0°(b). Ooou=

tected at 0(110) = 10°—90 The InSb crystal as well as the GaAs crystal demonstrated a considerable GSW high-frequency line broadening at 0(110) = 40°— The GSW—PSM transition at 0(110) = 700_800 °.

450•

responding surface and pseudosurface acoustic wave

was observed in the case of PbS. Satellites caused by

velocities were determined. In the case of a GaAs crystal, in addition to the MB satellite caused by the GSW, the line corresponding to the HFPSM was de-

both the GSW and the PSM were simultaneously registered at 0(110) = 700. 169

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Acknowledgement The authors are thankful to Professor A.M. Dyakonov and to Dr. V.M. Avdiuhina, for the perfect GaAs, InSB and PbS crystals, to Dr. V.M. Avdiuhina, for the X-ray measurements, to Dr. V.M. Mozhaev and Professor K.N. Baransky, for fruitful discussions, and to Professor V.R. Velasco for his interest in our work. References [1]J.G. Dii and E.M. Brody, Phys. Rev. B 14 (1976) 5218.

[2] J.R. Sandercock, Solid State Commun. 26 (1978) 547. [31R.E. Camley and F. Nizzoli, J. Phys. C 18 (1985) 4795.

[4] V.R. Velasco and F. Garcia-Moliner, Solid State Commun. 33(1980)1. [5] G.W. Faniell, in: Physical acoustics, Vol.6, ed. W.P. Mason and R.N. Thurston (Academic Press, New York, 1970) ~. 109—166. [6] 6. Cariotti, D. Fioretto, L. Giovannini, F. Nizzoli, G. socino and L. Verdini, J. Phys. Condens. Matter 4 (1992) 257. [7] V.V. Aleksandrov, T.S. Velichkina, Ju.B. Potapova and l.A.

Yakovlev, JETP (1992), accepted for publication.

[8] R. Loudon, J. Phys. C 11(1978) 2623. [91K.R. Subbaswamy and A.A. Maradudin, Phys. Rev. B 18 (1978) 4181. [10] N.L. Rowell and 6.1. Stegeman, Phys. Rev. B 18 (1978) 2598. [11] V. Bortolani, (1978) 39. F. Nizzoli and G. Santoro, Phys. Rev. Lett. 41

[121A.M. Marvin, V. Bortolani and F. Nizzoli, J. Phys. C 13 (1980) 299.

[131V.R. Velasco and F. Garcia-Moliner, J. Phys. 2237.

C 13 (1980)

[14] M.W. Elmiger, J. Henz, H. von Klinel, M. Ospelt and P. Wachter, Surf. Interface Anal. 14 (1989) 18. [15]V.V. Aleksandrov, T.S. Velichkina, V.G. Mozhaev and L.A. Yakovlev, Solid State Commun. 77 (1991) 559. [16]V.V. Aleksandrov, T.S. Velichkina, Ju.B. Potapova and l.A. Yakovlev, to be published. [171 M. Mendlik and P. Wachter, Helv. Phys. Acta 63 (1989) 479. [18] V.V. Aleksandrov, T.S. Velichkina, V.1. Voronkova, A.M. Dyakonov, P.P. Syrnikov, L.A. Yakovlev and V.K. Yanovskii, preprint Fizicheskogo Fakulteta MGU no. 10/1989 [in Russian]; Phys. Lett. A 142 (1989) 307. [19] Landolt-BOnistein, Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie, Bd. 1.

Elastische, piezooptische Konstanten von Kristallen (Springer, Berlin, 1971).

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