Contains report on one research project.Joint Services Electronics Program (Contract DA36-039-AMC-03200(E)

Geick, R.

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IV. OPTICAL AND INFRARED SPECTROSCOPY'Prof. C. H. Perry W. J. Hakel P. LubitzDr. R. Geick D. B. Hall E. C. Reifenstein IIID. P. Athans E. F. YoungA. TEMPERATURE DEPENDENCE OF THE FAR INFRARED REFLECTIVITY OFMAGNESIUM STANNIDEAmong the II-IV semiconducting compounds with the antiflourite structure, Magne-1-5sium Stannide has the smallest width of the forbidden gap with 0. 33-0. 36 ev.Consequently, at room temperature and above the intrinsic conduction dominates.1-7Measurements of the electrical properties cover the range 60 0 -1000 0 K. At hightemperatures Busch and Winkler l 2 found a T - 2 . 5 law for the mobility for which expla-nations have been given in terms of optical mode scattering 8 ' 9 and more phonon proc-esses.10 For the mixed conduction range, however, Lichter 7 reported a T-1. 5law inagreement with the theory concerning acoustical mode scattering.11 Similar resultshave been obtained for Mg 2 Ge and Mg 2 Si.8'With respect to lattice vibrations, Mg 2 Sn has for gz 0 an infrared active and a Ramanactive mode. The frequency of the infrared active mode at room temperature has beendetermined from the far infrared reflectivity. 1 13We have extended the study of the lattice vibrational properties to other temperaturesand investigated the electrical properties at infrared frequencies by measuring the-1 -ireflectivity of Mg 2 Sn in the region from 50 cm -370 cm at various temperatures inthe range 100 0-600°K. Two samples of different origin yielded the same reflectivitywithin experimental error. Both were pure material, and their reflectivities at 100 Kexhibited no indication of free-carrier effects (cf. Fig. IV-i). With increasing tempera-ture the influence of the free carriers becomes more and more important, and above400 'K this is dominant. The reflection spectrum of our samples at room temperatureis in good agreement with the data reported previously,13 except that the subsidiary bandin the Reststrahlenband has not been found with our samples.The reflection spectra were analyzed by means of a classical oscillator fit includingDrude terms for electrons, as well as for holes. Details of the dispersion formula and14the notation used have been previously published. In this analysis E = 16. 4 was used15according to the refractive index of Mg 2 Sn in the near infrared, and E. was assumedto be independent of temperature. Eo' 0 , and y in the lattice dispersion term weredetermined from the reflectivity and are shown as a function of temperature in Figs. IV-2and IV-3. At high temperatures y is nearly proportional to T 2 which means that pre-dominantly 3-phonon processes via quartic lattice potential terms determine the widthThis work was supported principally by the Joint Services Electronics program(Contract DA-36-039-AMC-03200(E).QPR No. 79WAVE LENGTH (microns)25 30 40 50 60 80 100 200 400625°K1 9070 520'K7050420"K-9060 360°K--207€ 330'K907050 295K30_-IO0100*K400 300 200 100 0WAVE NUMBER (cm- IFig. IV-1.Reflectivity of Mg 2 Sn at various temper-tures, experimental data (solid line) andcalculated by means of classical disper-sion formula (X).9.08wu 8.0190180200 400TEMPERATURE (OK)600Temperature dependence of the infrared eigenfrequency ° andthe oscillator strength (E -E ) of Mg Sn.QPR No. 79Fig. IV-2.(IV. OPTICAL AND INFRARED SPECTROSCOPY)30 -/iIIiII /I o/ ./200 300 400TEMPERATURE (OK)////1.5/T////, T600 800Fig. IV-3. Temperature dependence of the damping constant y inthe lattice dispersion term for MgzSn.of the fundamental lattice band. 16In the free-carrier part of the dispersion formula, too many parameters are involvedto determine them all from the reflection spectra. For T = 100°K the free-carriereffects could be neglected completely. At room temperature a reasonable fit wasobtained with the values reported from electrical measurements:3A. Intrinsic carrier concentration N. = 1. 5 • 10 cm1 * 3B. Conductivity effective masses of electrons and holes, respectively, me = 0.15m 0* 3and mh= 0. 10mo 9 3,7cmC. Mobilities of electrons and holes, respectively, = 370 VsecS3, 7cm300 cmV secand h =No attempt was made to vary the effective masses with temperature, and the room tem-perature values were used for all temperatures. The mobilities were assumed varyingproportional to T - 2 . 5 according to the results of Busch and Winkler. 1 ' 2 The mobilityratio used was e/ph = 1. 23 independent of temperature.3' 7 The carrier concentrationwas determined from the reflectivity (cf. Fig. IV-4). For comparison Ni was calculated* 3 * 3 1using the values m = 1. 20m 3 and mh = 1. 30m 3 for the density of states effectivemasses and the value of the band gap energy Eg (0.36-2.8 -4 1 - 3masses and the value of the band gap energy Eg = (0.36-2.8 10 T) ev (cf. Fig. IV-4).QPR No. 79100I I I i I . . . .I00 I I 1 I I i I / j--(IV. OPTICAL AND INFRARED SPECTROSCOPY)The agreement of the experimental data with the calculated values is reasonable.An attempt was also made to fit the reflectivity with mobilities proportional to T-1. 5according to the results of Lichter 7 in the mixed conduction range. The calculatedT (OK)800 500 3005 502 -20109 -- 10EFig. IV-4.0 5 -5SIntrinsic carrier concentration N. versus 1/Tz i -as determined from reflection spectra withS-2 5 -1. 52 2 5 ~ T (0) and with ~ T (X), calcu-H lated values of N. ( ) and total static1< conductivity (-- ).5210172 3 4I/TxlO3reflectivity is the same as in the former case within 2-3%0 for all temperatures and con-sequently, only one calculated value is shown in Fig. IV-1. The carrier concentrationdeviates systematically from the calculated values, and the ratio of the calculated to theexperimental values is proportional to T. The resulting total static conductivity a- isothe same in both cases and thus the reflectivity is sensitive to the conductivity only.Furthermore, the plot log -o versus 1/T is not a straight line, which indicates once-2 5more a T law for the mobilities (cf. Fig. IV-4). This means that already in thetemperature range covered by our measurements the temperature dependence of themobility cannot be explained by acoustical mode scattering only, 1 1 and that optical modescattering or more phonon processes have to be considered.8- 1 0Because of the relatively low mobility in Mg 2 Sn, the free-carrier effects produce nosharp plasma edge in the reflectivity which would have provided additional information.QPR No. 79(IV. OPTICAL AND INFRARED SPECTROSCOPY)Such a minimum and a steep vise of the reflectivity always occur when the real part ofthe dielectric constant changes from positive to negative values with increasing wave-length and the imaginary part is sufficiently small. The corresponding condition is fora lattice dispersion termo o(1)>> 1, ( )and for a Drude term* 2Nm iE -> . (2)Lattice*2For MgZSn, condition 1 is fulfilled, but Nm Z < 1 for electrons, as well as for holes.ELatticeTherefore no plasma edge has been found in the spectra.We wish to thank Professor D. W. Lynch, of Iowa State University, for providing oneof the Mg 2 Sn samples. All computations were performed on the IBM 7094 computer atthe Computation Center, M. I. T.R. GeickReferences1. G. Busch and U. Winkler, Physica 20, 1067 (1954).2. U. Winkler, Helv. Phys. Acta 28, 633 (1955).3. H. G. Lipson and A. Kahan, Phys. Rev. 133, A800 (1964).4. R. F. Blunt, H. P. R. Frederikse, and W. R. Hosler, Phys. Rev. 100, 663 (1955).5. W. D. Lawson, S. Neilson, E. H. Putley, and W. Roberts, J. Electronics 1, 203(1955).6. H. P. R. Frederikse, W. R. Hosler, and D. E. Roberts, Phys. Rev. 103, 67(1955).7. B. D. Lichter, J. Electrochem. Soc. 109, 819 (1962).8. R. D. Redin, R. G. Morris, and G. C. Danielson, Phys. Rev. 109, 1916 (1958).9. R. G. Morris, R. D. Redin, and G. C. Danielson, Phys. Rev. 109, 1909 (1958).10. Ch. Entz, Physica 20, 983 (1954); Helvetia Phys. Acta 27, 199 (1954).11. F. Seitz, Phys. Rev. 73, 549 (1948).12. D. McWilliams and D. W. Lynch, Phys. Rev. 130, 2248 (1963).13. A. Kahan, H. G. Lipson, and E. V. Loewenstein, Physics of Semiconductors, Pro-ceedings of the 7t h International Conference, Paris, 1964, p. 1067.14. R. Geick and C. H. Perry, Quarterly Progress Report No. 77, Research Labora-tory of Electronics, M. I. T. , April 15, 1965, pp. 41-48.15. D. McWilliams and D. W. Lynch, J. Opt. Soc. Am. 53, 298 (1963).16. D. W. Jepsen and R. F. Wallis, Phys. Rev. 125, 1496 (1962).QPR No. 79

Optical and Infrared Spectroscopy

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Optical and Infrared Spectroscopy

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