- Email: [email protected]
Low frequency Raman scattering in amorphous materials: a-Ge, a-InSb, and a-Ge0.5Sn0.5
Solid State Communications,
Vol. 11, pp. 1523—1527, 1972.
Pergamon Press.
Printed in Great Britain
LOW FREQUENCY RAMAN SCATTERING IN AMORPHOUS MATERIALS: a-Ge, a-InSb, AND a-Ge 05 Sn05 Jeffrey S. Lannin Max-Planck-Institut für Festkorperforschung, Stuttgart, Federal Republic of Germany
(Received 18 September 1972 by M. Cardona)
Low frequency Raman scattering measurements have been performed in the sputtered amorphous materials: a-Ge, a-InSb, and a-Ge0.5 Sn0.5. The experimental results in a-Ge indicate a frequency dependent coupling constant in the elastic continuum limit. The reduced Raman spectrum of a-InSb shows no wrong bond features suggested by earlier work. A comparison of the spectra indicates trends in the vibrational spectra of a-Ge1_~Sn~,alloys.
IN THE present work Raman scattering measurements are reported for the related series: a-Ge, a-Ge0,5 Sn0,5, and a-InSb. A third monochromator system has been employed here to appreciably reduce stray light,Previous allowing Raman measurements at lowerthe frequencies. scattering measurements 1.2 in opaque amorphous systems, such as group 4 and 3—5 compounds, have been confined to somewhat high frequencies ( ~ 50 cm”’) due to the relatively strong stray light contribution to the spectra. The lattice dynamics crystalline 3’4ofespecially InSb and grey Sn are rather similar, at low frequencies, so that the measurements presented here indicate trends in the vibrational spectrum in the a-Ge, -~Sn~ alloy series. In addition to information about low lying structure in the vibrational spectrum, low frequency measurements may assist in clarifying the theory of Raman scattering in disordered systems. The results presented here suggest a frequency dependent coupling constant in the scattering intensity,
composition on to a cooled substrate. This system is rather interesting since the equilibrium solid solubility of Ge in Sn is less than 1 per cent, while that of Sn in Ge is less than 10-2 per 6cent. and Shevchik’s X-ray radial distribution analysis that of Ternkin et al.7 suggest that a-Ge 05 Sn0,5 is a homogeneous mixture of Ge and Sn atoms in random tetrahedral coordination similar to that of a-Ge and a-Si. in a-InSb are of considerableRaman interestmeasurements since it has been suggested that ‘wrong bonds’ have been observed. The possible existence of an appreciable number of wrong bonds is of interest; recent work8 indicates that they may influence the optical spectra of stoichometric amorphous 3—5 semiconductors. The amorphous films studied in this work were prepared by sputtering in high purity argon at a rate of ‘~ 1 ii. /hr. Substrates of Cu were employed for a-InSb and a-Ge 0,5 Sn.0,5, the latter cooled to approximately — 100°C; a-Ge was deposited on glass. A polycrystalline InSb target and were a pressed powdered of 50% ofGe—50% Sn9 employed. The target composition the alloy rums were not determined, though sputtering 6 suggest that for targets properly conditioned studies by sputtering for several hours, the resulting
Amorphous Sri, in which the atoms are tetrahedrally coordinated as in a-Ge and a-Si, has not yet been prepared at the present It has in been 5 that the addition of Ge totime. Sn results a shown stabilization of the grey Sn form. Shevchik 6 has recently found that a-Ge 0,5 Sn0,5 canofbe by sputtering a compressed powder theformed same 1523
1524
LOW FREQUENCY RAMAN SCATTERING IN AMORPHOUS MATERIALS
Vol. 11, No. 11
U,
z a.InSb
>
~
0
50
100
150
~‘G~
200
Sr.,
~‘0e
250
300
350
WAVENUMBER (cm”) FIG. 1. Comparison of the reduced Raman intensity for a-InSb, a-Ge
0 5Sn0
~,
and a-Ge, normalized to the
high wavenurnber peak.
films have compositions near to that of the starting material. Raman measurements were performed in the back scattering configuration with the 5145 A beam of a Coherent Radiation argon laser. A Spex third monochromator system and an RCA cooled photomultiplier tube (C31034) along with a multichannel analyzer were employed for photon counting. The third monochromator functions essentially as a spatial band pass filter to reduce the large stray light at low wavenumber differences. -
along L—KW) in the zone. Neutron diffraction measurements in these directions have not been performed in InSb, however, lattice dynamical calculations for grey Sn and InSb suggest an LA peak between 120 and 130 Cm”’. The low frequency peak observed near SOcm’ is shifted from the TA peak in the crystalline density of states, which is expected at an energy of “- 35cm’. 1,2 This shift to higher frequencies has similarly been observed in3’4and other group and 3—5understood. amorphous is not4 clearly semiconductors, This point will be discussed further below. The
Figure 1 presents the reduced Raman scattering intensity, PR, for amorphous InSb. This is obtained by dividing the intensity by c’Y’ (n + 1), where n is the Bose—Einstein factor. The peak at higher energies is shifted by approximately —‘10 cm ‘ from the crystalline density of states peak. This shift to lower energies is similar to that observed in other group 4 and 3—5 amorphous systems. The shoulder observed near 120—125 cm”’ is similar in form to that observed for example in a-Ge, a-GaAs, and a-Si1’2 and occurs at energies near to the peak in the LA branch in the crystal. Neutron diffraction measurements and a critical point analysis by Nelin and Nilsson ~ for Ge indicate that the peak associated with the LA branch is attributed to critical points at Q and
similarity of the lattice dynamics of crystalline InSb and grey Sn suggests that a-Sn, if found, would yield a reduced Raman spectrum similar to that of a-InSb with a high frequency peak centered near l8Ocm Previous measurements by Wihi et at.4 in a-InSb suggested the presence of an appreciable number of wrong Sb—Sb bonds. In addition to wrong bonds due to possible local compositional disorder, models for the amorphous state12 require wrong bonds due to topological disorder ( e.g. S membered rings,). The results of Wihl et at. appear, however, to show clear indications of sharp structure near that expected for crystalline InSb and Sb. It is quite possible that these films were
Vol. 11, No, 11 LOW FREQUENCY RAMAN SCATTERING IN AMORPHOUS MATERIALS
1525
partially crystallized as well as phase separated at the surface. In the present samples no sharp structure was observed; similarly, structure in the neighbourhood of 260 cm” was not observed, Recent measurements in a-Sb1 ~ indicate a peak in the reduced Raman intensity near 145—150cm”’. In addition, the low frequency peak for a-Sb is expected to occur above that of a-InSb.14 If an appreciable number of wrong Sb—Sb bonds exist, their contribution would be immersed in the continuim of states of InSb and might not be observable as distinct structure.
to attribute a precise meaning to the peak of such a broad structure. This structure is a 1 between broadened peak centered at ~ 70cm” that observed in a-Ge and a-InSb. In the following discussion it will be suggested that the peak in the density of vibrational states may not occur at the peak in the reduced Raman intensity due to a frequency dependent coupling constant.
Figure 1 illustrates the reduced Raman inten5’16 sitytheforvibrational a-Ge0,5 Sno,5 . Theoretical calculations’ of spectra of two component lattices have shown that for atom mass ratios greater than approximately 2 the density of states maintains in part features similar to those of the heavy mass component even at 50% concentration, A recent Raman study17 in a-Ge 0.5Si0,5 (mass ratio 2.6) indicates structure associated with high frequency modes of Ge—Ge and Ge—Si pairs. In a-Ge 0 5Sn05 the mass ratio is 1.6, so that it is perhaps not surprising that distinct structure associated with high frequency Sn—Sn modes expected between 180—190 cm is not observed, In a-Ge0,5Si0,5 modes associated with Ge—Si pairs occured at frequencies consistent with Raman scattering measurements18 and tunneling
a-Sn are reasonably similar, as is theancrystalline forms suggest, then this figure indication of the progression of the Raman intensity in the a-Ge ~ system. At low frequencies the modes of amorphous or crystalline materials are similar to those of an elastic continuim. At such frequencies the density of vibrational states, p(w) ~2, i.e. 20 A reasonable estithe modes Debye like. like behaviour can be mate of theare extent of Debye obtained for the amorphous system by comparison
studies 19 in polycrystalline alloys. In addition the peak position agreed with a calculated estimate obtained by using the average plasma frequency for the constituents obtained from an average reduced mass and atomic volume. A similar calculation for a-Geo, 5Sno,5 yields an expected peak near 250 cm”. In addition, the peak in the reduced Raman intensity in a-Ge occurs at 270cm” so that Ge—Ge modes might contribute to the high frequency peak. The appreciable width of the high frequency peak compared to that of a-Ge and a-InSb suggest contributions from Sn—Sn, Ge—Sn, and Ge—Ge modes in the ensemble of possible structural and compositional configurations. Structure observed near 140cm”’ is near to that observed in a-InSb, however, shifted by approximately 15—20 cm”. The low frequency peak in the reduced Raman intensity is considerably broader than that of a-Ge, (Fig. 1). It is difficult
Figure 2 presents a comparison of the low frequency measured intensities above background for a-InSb, a-Ge 0 5Sn~ ~, and a-Ge. If the low frequency vibrational spectrum of a-InSb and
with the crystal, if the short range order is similar. Recent neutron scattering measurements in Ge by Nelin and Nilsson’ 1 have shown that p(~.~) 2 —. up to approximately 3~ cm “1 2,the At oflow frequencies, such that 3 for “~cthe Raman model Shuker and Gamon2’ yields intensity =
~_C3 w’(n
1)
where Cg is the coupling constant for mode f3, often assumed to be frequency independent. Under this assumption 1(a) reduces to a constant for hw/kT <<1. Figure 2, however, clearly indicates a frequency dependence to I(a) below 35cm”’ for a-Ge. Walley and Bertie 22 have indicated that the coupling constant is aproportional at low 23 Such dependencetois~ suggested frequencies. by the fact that in the limit of infinite wavelength, corresponding to uniform translational motion, the coupling constant should tend to zero. Under the condition that ~(
1526
LOW FREQUENCY RAMAN SCATTERING IN AMORPHOUS MATERIALS
Vol. 11, No. 11
U,
o-~aSb >-
~-G.
sr.
s’G~
1a~
4
~ 4
2
a
sb
125
WAVENUMBER (cm”) FIG. 2. Comparison of the Raman intensity measured for a-InSb, a-Ge 0,5 Sn0 ~, and a-Ge at low frequencies. The maxima were normalised to the same height.
to higher frequencies corresponding to the entire acoustic branch of the crystal. Under these conditions the peak in the vibrational density of states will be shifted from that of the reduced Raman intensities of Fig. 1, in the direction of lower frequencies. It thus becomes difficult to interpret small shifts between the peak in the reduced Raman intensity and the peak in the density of states without a more complete theory for the coupling constants. Measurements are in progress to extend the results presented here to lower frequencies to check more accurately the w~dependence.
Acknowledgements
— I wish to thank Javier Tejeda for his invaluable help in preparing the films studied here. I would also like to thank Dr. Nigel Shevchik for extremely helpful discussions of structural questions about amorphous materials and their preparation. Helpful discussions with Drs. B. Gliss, M. Bell and M. Thorpe were most appreciated. The InSb target was made by Dr. E. Schänherr whom I would like to thank. I wish also to thank Prof. Manuel Cardona for a number of very helpful discussions during the preparation of this manuscript.
REFERENCES 1. 2.
SMITH J.E., BRADSKY M.H., CROWDER B.L. and NATHAN M.I., Proc. of the 2nd mt. Conf. on Light Scattering in Solids, (Edited by BALKANSKI M.), p. 330, Flaum,narion, Paris (1971). WIHL M., CARDONA M. and TAUC J., Proc. 4th mt. Conf. on Amorphous and Liquid Semicond., (Edited by COHEN M. and LUCOVSKY G.) J. Non Cryst. Solids 8—10, 172 (1972).
3.
PRICE DL. and ROWE J.M., Solid State Commun. 7, 1433 (1969).
4.
PRICE DL., ROWE J.M. and NICKLOW R.M., Phys. Rev. 3, 1263 (1971).
5.
EWALD A.W., J. appi. Phys. 25, 1436 (1954).
6. 7.
SHEVCHIK N.J., Techn. Report No. HP—29, Division of Engineering and Applied Physics, Harvard University, Cambridge, Mass. (1972); SHEVCHIK N.J. and PAUL W., to be published. TEMKIN R.J., CONNELL G.A.N. and PAUL W., to be published.
8.
CONNELL G.A.N., to be published.
9.
Target produced by Haselden Co., San Jose, Calif.
10.
TUBINO R., PISERI L. and ZERBI G., J. Chem. Phys. 56, 1022 (1972).
Vol. 11, No. 11 LOW FREQUENCY RAMAN SCATTERING ~T AMORPHOUS MATERIALS
1527
11.
NELIN G. and NILSSON G., Phys. Rev. B5, 3151 (1972).
12.
POLK D.E., J. Non Cryst. Solids 5, 365 (~971).
13.
WIHL M., STILES P.J. and TAUC published.
14.
SHARP R.I. and WARM(NGS E., J. Phys. F. Metal Phys. 1, 570 (1971).
15.
DEAN P., Rev. Mod. Phys. 44, 127 (1972).
16.
PAYTON ON. and VISCHER W.M., Phys. Rev. 175, 1201 (1968).
17.
SHEVCHIK N.J., LANNIN
18.
RENUCCI M.A., RENUCCI J.B. and CART)ONA M., Proc. of the 2nd mt. Conf. on Light Scattering in Solids, (Edited by BALKANSKI M.), p. 326, Flaummarion, Paris (1972). LOGAN R.A., ROWELL J.M. and TRUMBORE F.A., Phys. Rev. 136, A1751 (1964).
19.
J.
J. Proc. 11th mt. Conf. Phys. Semicorzd., Warsaw, 1972,
and TAJEDA
J.
to be
to be published.
20.
‘Special’ low frequency modes, such as those suggested to explain the anomalous specific heat of 1 and are not considered here, FULDE P., Private certain glasses, probably occur below 1cm communication.
21.
SHUKER R. and GAMON R.W., Phys. Rev. Lett. 25, 222 (1970).
22.
WHALLEY E. and BERTIE J.E., J. Chem. Phys. 46, 1264 (1966).
23.
These authors have omitted the statistical factor c~f’(n mode coordinates.
+
1) due to the matrix element of the normal
Es wurde die niederfrequente Raman-Streuung an folgenden kathodenzerstäubten Materialien gemessert: a-Ge, a-InSb und a-Ge 0.5 Sn05. Die experimentellen Resultate in a-Ge deuten auf eine frequenzabhängige Kopplungskonstante im elastischen Kontinuum. Das reduzierte Ramanspektrum von a-InSb zeigt keine Eigenschaften, die auf falsche Bindungen hinweisen, im Gegensatz zu Vermutungen friiherer Arbeiten. Em Vergleich der Spektren zeigt Trends in den Gitterschwingungsspektren von a-Ge1 ~Sn~ Legierungen.
Vol. 11, pp. 1523—1527, 1972.
Pergamon Press.
Printed in Great Britain
LOW FREQUENCY RAMAN SCATTERING IN AMORPHOUS MATERIALS: a-Ge, a-InSb, AND a-Ge 05 Sn05 Jeffrey S. Lannin Max-Planck-Institut für Festkorperforschung, Stuttgart, Federal Republic of Germany
(Received 18 September 1972 by M. Cardona)
Low frequency Raman scattering measurements have been performed in the sputtered amorphous materials: a-Ge, a-InSb, and a-Ge0.5 Sn0.5. The experimental results in a-Ge indicate a frequency dependent coupling constant in the elastic continuum limit. The reduced Raman spectrum of a-InSb shows no wrong bond features suggested by earlier work. A comparison of the spectra indicates trends in the vibrational spectra of a-Ge1_~Sn~,alloys.
IN THE present work Raman scattering measurements are reported for the related series: a-Ge, a-Ge0,5 Sn0,5, and a-InSb. A third monochromator system has been employed here to appreciably reduce stray light,Previous allowing Raman measurements at lowerthe frequencies. scattering measurements 1.2 in opaque amorphous systems, such as group 4 and 3—5 compounds, have been confined to somewhat high frequencies ( ~ 50 cm”’) due to the relatively strong stray light contribution to the spectra. The lattice dynamics crystalline 3’4ofespecially InSb and grey Sn are rather similar, at low frequencies, so that the measurements presented here indicate trends in the vibrational spectrum in the a-Ge, -~Sn~ alloy series. In addition to information about low lying structure in the vibrational spectrum, low frequency measurements may assist in clarifying the theory of Raman scattering in disordered systems. The results presented here suggest a frequency dependent coupling constant in the scattering intensity,
composition on to a cooled substrate. This system is rather interesting since the equilibrium solid solubility of Ge in Sn is less than 1 per cent, while that of Sn in Ge is less than 10-2 per 6cent. and Shevchik’s X-ray radial distribution analysis that of Ternkin et al.7 suggest that a-Ge 05 Sn0,5 is a homogeneous mixture of Ge and Sn atoms in random tetrahedral coordination similar to that of a-Ge and a-Si. in a-InSb are of considerableRaman interestmeasurements since it has been suggested that ‘wrong bonds’ have been observed. The possible existence of an appreciable number of wrong bonds is of interest; recent work8 indicates that they may influence the optical spectra of stoichometric amorphous 3—5 semiconductors. The amorphous films studied in this work were prepared by sputtering in high purity argon at a rate of ‘~ 1 ii. /hr. Substrates of Cu were employed for a-InSb and a-Ge 0,5 Sn.0,5, the latter cooled to approximately — 100°C; a-Ge was deposited on glass. A polycrystalline InSb target and were a pressed powdered of 50% ofGe—50% Sn9 employed. The target composition the alloy rums were not determined, though sputtering 6 suggest that for targets properly conditioned studies by sputtering for several hours, the resulting
Amorphous Sri, in which the atoms are tetrahedrally coordinated as in a-Ge and a-Si, has not yet been prepared at the present It has in been 5 that the addition of Ge totime. Sn results a shown stabilization of the grey Sn form. Shevchik 6 has recently found that a-Ge 0,5 Sn0,5 canofbe by sputtering a compressed powder theformed same 1523
1524
LOW FREQUENCY RAMAN SCATTERING IN AMORPHOUS MATERIALS
Vol. 11, No. 11
U,
z a.InSb
>
~
0
50
100
150
~‘G~
200
Sr.,
~‘0e
250
300
350
WAVENUMBER (cm”) FIG. 1. Comparison of the reduced Raman intensity for a-InSb, a-Ge
0 5Sn0
~,
and a-Ge, normalized to the
high wavenurnber peak.
films have compositions near to that of the starting material. Raman measurements were performed in the back scattering configuration with the 5145 A beam of a Coherent Radiation argon laser. A Spex third monochromator system and an RCA cooled photomultiplier tube (C31034) along with a multichannel analyzer were employed for photon counting. The third monochromator functions essentially as a spatial band pass filter to reduce the large stray light at low wavenumber differences. -
along L—KW) in the zone. Neutron diffraction measurements in these directions have not been performed in InSb, however, lattice dynamical calculations for grey Sn and InSb suggest an LA peak between 120 and 130 Cm”’. The low frequency peak observed near SOcm’ is shifted from the TA peak in the crystalline density of states, which is expected at an energy of “- 35cm’. 1,2 This shift to higher frequencies has similarly been observed in3’4and other group and 3—5understood. amorphous is not4 clearly semiconductors, This point will be discussed further below. The
Figure 1 presents the reduced Raman scattering intensity, PR, for amorphous InSb. This is obtained by dividing the intensity by c’Y’ (n + 1), where n is the Bose—Einstein factor. The peak at higher energies is shifted by approximately —‘10 cm ‘ from the crystalline density of states peak. This shift to lower energies is similar to that observed in other group 4 and 3—5 amorphous systems. The shoulder observed near 120—125 cm”’ is similar in form to that observed for example in a-Ge, a-GaAs, and a-Si1’2 and occurs at energies near to the peak in the LA branch in the crystal. Neutron diffraction measurements and a critical point analysis by Nelin and Nilsson ~ for Ge indicate that the peak associated with the LA branch is attributed to critical points at Q and
similarity of the lattice dynamics of crystalline InSb and grey Sn suggests that a-Sn, if found, would yield a reduced Raman spectrum similar to that of a-InSb with a high frequency peak centered near l8Ocm Previous measurements by Wihi et at.4 in a-InSb suggested the presence of an appreciable number of wrong Sb—Sb bonds. In addition to wrong bonds due to possible local compositional disorder, models for the amorphous state12 require wrong bonds due to topological disorder ( e.g. S membered rings,). The results of Wihl et at. appear, however, to show clear indications of sharp structure near that expected for crystalline InSb and Sb. It is quite possible that these films were
Vol. 11, No, 11 LOW FREQUENCY RAMAN SCATTERING IN AMORPHOUS MATERIALS
1525
partially crystallized as well as phase separated at the surface. In the present samples no sharp structure was observed; similarly, structure in the neighbourhood of 260 cm” was not observed, Recent measurements in a-Sb1 ~ indicate a peak in the reduced Raman intensity near 145—150cm”’. In addition, the low frequency peak for a-Sb is expected to occur above that of a-InSb.14 If an appreciable number of wrong Sb—Sb bonds exist, their contribution would be immersed in the continuim of states of InSb and might not be observable as distinct structure.
to attribute a precise meaning to the peak of such a broad structure. This structure is a 1 between broadened peak centered at ~ 70cm” that observed in a-Ge and a-InSb. In the following discussion it will be suggested that the peak in the density of vibrational states may not occur at the peak in the reduced Raman intensity due to a frequency dependent coupling constant.
Figure 1 illustrates the reduced Raman inten5’16 sitytheforvibrational a-Ge0,5 Sno,5 . Theoretical calculations’ of spectra of two component lattices have shown that for atom mass ratios greater than approximately 2 the density of states maintains in part features similar to those of the heavy mass component even at 50% concentration, A recent Raman study17 in a-Ge 0.5Si0,5 (mass ratio 2.6) indicates structure associated with high frequency modes of Ge—Ge and Ge—Si pairs. In a-Ge 0 5Sn05 the mass ratio is 1.6, so that it is perhaps not surprising that distinct structure associated with high frequency Sn—Sn modes expected between 180—190 cm is not observed, In a-Ge0,5Si0,5 modes associated with Ge—Si pairs occured at frequencies consistent with Raman scattering measurements18 and tunneling
a-Sn are reasonably similar, as is theancrystalline forms suggest, then this figure indication of the progression of the Raman intensity in the a-Ge ~ system. At low frequencies the modes of amorphous or crystalline materials are similar to those of an elastic continuim. At such frequencies the density of vibrational states, p(w) ~2, i.e. 20 A reasonable estithe modes Debye like. like behaviour can be mate of theare extent of Debye obtained for the amorphous system by comparison
studies 19 in polycrystalline alloys. In addition the peak position agreed with a calculated estimate obtained by using the average plasma frequency for the constituents obtained from an average reduced mass and atomic volume. A similar calculation for a-Geo, 5Sno,5 yields an expected peak near 250 cm”. In addition, the peak in the reduced Raman intensity in a-Ge occurs at 270cm” so that Ge—Ge modes might contribute to the high frequency peak. The appreciable width of the high frequency peak compared to that of a-Ge and a-InSb suggest contributions from Sn—Sn, Ge—Sn, and Ge—Ge modes in the ensemble of possible structural and compositional configurations. Structure observed near 140cm”’ is near to that observed in a-InSb, however, shifted by approximately 15—20 cm”. The low frequency peak in the reduced Raman intensity is considerably broader than that of a-Ge, (Fig. 1). It is difficult
Figure 2 presents a comparison of the low frequency measured intensities above background for a-InSb, a-Ge 0 5Sn~ ~, and a-Ge. If the low frequency vibrational spectrum of a-InSb and
with the crystal, if the short range order is similar. Recent neutron scattering measurements in Ge by Nelin and Nilsson’ 1 have shown that p(~.~) 2 —. up to approximately 3~ cm “1 2,the At oflow frequencies, such that 3 for “~cthe Raman model Shuker and Gamon2’ yields intensity =
~_C3 w’(n
1)
where Cg is the coupling constant for mode f3, often assumed to be frequency independent. Under this assumption 1(a) reduces to a constant for hw/kT <<1. Figure 2, however, clearly indicates a frequency dependence to I(a) below 35cm”’ for a-Ge. Walley and Bertie 22 have indicated that the coupling constant is aproportional at low 23 Such dependencetois~ suggested frequencies. by the fact that in the limit of infinite wavelength, corresponding to uniform translational motion, the coupling constant should tend to zero. Under the condition that ~(
1526
LOW FREQUENCY RAMAN SCATTERING IN AMORPHOUS MATERIALS
Vol. 11, No. 11
U,
o-~aSb >-
~-G.
sr.
s’G~
1a~
4
~ 4
2
a
sb
125
WAVENUMBER (cm”) FIG. 2. Comparison of the Raman intensity measured for a-InSb, a-Ge 0,5 Sn0 ~, and a-Ge at low frequencies. The maxima were normalised to the same height.
to higher frequencies corresponding to the entire acoustic branch of the crystal. Under these conditions the peak in the vibrational density of states will be shifted from that of the reduced Raman intensities of Fig. 1, in the direction of lower frequencies. It thus becomes difficult to interpret small shifts between the peak in the reduced Raman intensity and the peak in the density of states without a more complete theory for the coupling constants. Measurements are in progress to extend the results presented here to lower frequencies to check more accurately the w~dependence.
Acknowledgements
— I wish to thank Javier Tejeda for his invaluable help in preparing the films studied here. I would also like to thank Dr. Nigel Shevchik for extremely helpful discussions of structural questions about amorphous materials and their preparation. Helpful discussions with Drs. B. Gliss, M. Bell and M. Thorpe were most appreciated. The InSb target was made by Dr. E. Schänherr whom I would like to thank. I wish also to thank Prof. Manuel Cardona for a number of very helpful discussions during the preparation of this manuscript.
REFERENCES 1. 2.
SMITH J.E., BRADSKY M.H., CROWDER B.L. and NATHAN M.I., Proc. of the 2nd mt. Conf. on Light Scattering in Solids, (Edited by BALKANSKI M.), p. 330, Flaum,narion, Paris (1971). WIHL M., CARDONA M. and TAUC J., Proc. 4th mt. Conf. on Amorphous and Liquid Semicond., (Edited by COHEN M. and LUCOVSKY G.) J. Non Cryst. Solids 8—10, 172 (1972).
3.
PRICE DL. and ROWE J.M., Solid State Commun. 7, 1433 (1969).
4.
PRICE DL., ROWE J.M. and NICKLOW R.M., Phys. Rev. 3, 1263 (1971).
5.
EWALD A.W., J. appi. Phys. 25, 1436 (1954).
6. 7.
SHEVCHIK N.J., Techn. Report No. HP—29, Division of Engineering and Applied Physics, Harvard University, Cambridge, Mass. (1972); SHEVCHIK N.J. and PAUL W., to be published. TEMKIN R.J., CONNELL G.A.N. and PAUL W., to be published.
8.
CONNELL G.A.N., to be published.
9.
Target produced by Haselden Co., San Jose, Calif.
10.
TUBINO R., PISERI L. and ZERBI G., J. Chem. Phys. 56, 1022 (1972).
Vol. 11, No. 11 LOW FREQUENCY RAMAN SCATTERING ~T AMORPHOUS MATERIALS
1527
11.
NELIN G. and NILSSON G., Phys. Rev. B5, 3151 (1972).
12.
POLK D.E., J. Non Cryst. Solids 5, 365 (~971).
13.
WIHL M., STILES P.J. and TAUC published.
14.
SHARP R.I. and WARM(NGS E., J. Phys. F. Metal Phys. 1, 570 (1971).
15.
DEAN P., Rev. Mod. Phys. 44, 127 (1972).
16.
PAYTON ON. and VISCHER W.M., Phys. Rev. 175, 1201 (1968).
17.
SHEVCHIK N.J., LANNIN
18.
RENUCCI M.A., RENUCCI J.B. and CART)ONA M., Proc. of the 2nd mt. Conf. on Light Scattering in Solids, (Edited by BALKANSKI M.), p. 326, Flaummarion, Paris (1972). LOGAN R.A., ROWELL J.M. and TRUMBORE F.A., Phys. Rev. 136, A1751 (1964).
19.
J.
J. Proc. 11th mt. Conf. Phys. Semicorzd., Warsaw, 1972,
and TAJEDA
J.
to be
to be published.
20.
‘Special’ low frequency modes, such as those suggested to explain the anomalous specific heat of 1 and are not considered here, FULDE P., Private certain glasses, probably occur below 1cm communication.
21.
SHUKER R. and GAMON R.W., Phys. Rev. Lett. 25, 222 (1970).
22.
WHALLEY E. and BERTIE J.E., J. Chem. Phys. 46, 1264 (1966).
23.
These authors have omitted the statistical factor c~f’(n mode coordinates.
+
1) due to the matrix element of the normal
Es wurde die niederfrequente Raman-Streuung an folgenden kathodenzerstäubten Materialien gemessert: a-Ge, a-InSb und a-Ge 0.5 Sn05. Die experimentellen Resultate in a-Ge deuten auf eine frequenzabhängige Kopplungskonstante im elastischen Kontinuum. Das reduzierte Ramanspektrum von a-InSb zeigt keine Eigenschaften, die auf falsche Bindungen hinweisen, im Gegensatz zu Vermutungen friiherer Arbeiten. Em Vergleich der Spektren zeigt Trends in den Gitterschwingungsspektren von a-Ge1 ~Sn~ Legierungen.