S E M I C O N D U C T O R S A N D S E M I M E T A L S Edited by R. K. WILLARDSON BELL AND HOWELL RESEARCH CENTER PASADENA, CALIFORNIA ALBERT C. BEER BATTELLE MEMORIAL INSTITUTE COLUMBUS, OHIO VOLUME 2 Physics of 111-V Compounds 1966 ACADEMIC PRESS New York and London COPYRIGHT 0 1966, BY ACADEMIPCR ESSIN C. ALL RIGHTS RESWVED. NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS, WITHOUT WRITEN PERMISSION THE PUBLISHERS. FROM ACADEMIC PRESS INC. 1 f 1 Fifth Avenue, New York. New York 10003 United Kingdom Edition publhhed by ACADEMIC PRESS INC. (LONDON) LTD. Berkeley Square House, London, W. 1 LIBRAROYF CONG~CAST AJJX CARDN UMBER65:- 26048 IN THE STA'ZES OF AMERICA PRINTED UNITED List of Contributors in parentheses indicate the pages on which the authors’ contributions begin. Numbers F. G. ALLENB, ell Telephone Laboratories, Inc., Murray Hill, New Jersey (263) E. ANToNCiK, Institute of Solid State Physics, Czechoslovak Academy of Sciences, Prague, Czechoslovakia (245) J. R. DRABBLED, epartment of Physics, University of Exeter, Exeter, England (75) M. GERSHENZOBNe, ll Telephone Laboratories, Inc., Murray Hill, New Jersey (289) G. GIESECKREe,s earch Laboratory, Siemens Schuckertwerke AG, Erlangen, Germany (63) G. W.G OBELBI,e ll Telephone Laboratories, Inc., Murray HiN, New Jersey (115, 263) BERNARDG OLDSTEINRC, A, David Sarnofl Research Center, Princeton, New Jersey (1 89) M. G. HOLLANDR, aytheon Company, Research Division, Waltham, Massachusetts (3) A. U. MAC Bell Telephone Laboratories, Inc., Murray Hill, New RAE, Jersey (1 15) ROBERTL EEM JEHERD, epartment of Physics, Purdue University, Lafayette, Indiana (141) S. Moss, Royal Aircraft Establishment, Farnborough, Hants, England T. (205) S. I. NOVIKOVAA.A, . Baikov Metallurgical Institute, Moscow, U.S.S.R. (33) P. S. PERSHANH,a rvard University, Cambridge, Massachusetts (283) V vi LIST OF CONTRIBUTORS U. PIESBERGENP,h' ysikalisch-Chemisches Institut, Universitiit Zurich, Zurich, Switzerland (49) FRANKS TERN,I BM Watson Research Center, Yorktown Heights, New York (371) J. TAUCI,n stitute of Solid State Physics, Czechoslovak Academy of Sciences, Prague, Czechoslovakia (245) 'Present address : Emhart Zurich S.A., Zurich, Switzerland. Preface The extensive research devoted to the physics of compound semicon- ductors and semimetals during the past decade has led to a more complete understanding of the physics of solids in general. This progress was made possible by significant advances in material preparation techniques. The availability of a large number of compounds with a wide variety of different and often unique properties enabled the investigators not only to dis- cover new phenomena but to select optimum materials for definitive experimental and theoretical work. In a field growing at such a rapid rate, a sequence of books which will provide an integrated treatment of the experimental techniques and theoretical developments is a necessity. An important requirement is that the books contain not only the essence of the published literature, but also a considerable amount of new material. The highly specialized nature of each topic makes it imperative that each chapter be written by an authority. For this reason the editors have obtained contributions from ten to fifteen scientists to provide each volume with the required detail and complete- ness. Much of the information presented relates to basic contributions in the solid state field which will be of permanent value. While this sequence of volumes is primarily a reference work covering related major topics, the volumes will also be useful in graduate courses. Because of the important contributions which have resulted from studies of the 111-V compounds, the first few volumes of this series are devoted to the physics of these materials. Volume 1 reviews key features of the 111-V compounds, with special emphasis on band structure, magnetic field phenomena, and plasma effects. In Volume 2, the emphasis is on physical properties, thermal phenomena, magnetic resonances, and photoelectric effects, well as radiative recombination and stimulated as emission. Volume 3 is concerned with optical properties, including lattice effects, intrinsic absorption, free carrier phenomena, and photoelectronic effects. The editors are indebted to the many contributors and their employers who made this series possible. They wish to express their appreciation to the Bell & Howell Company and the Battelle Memorial Institute for providing the facilities and the environment necessary for such an endeavor. vii viii PREFACE Thanks are also due to the US. Air Force Offices of Scientific Research and Aerospace Research, whose support has enabled the editors to study many features of compound semiconductors. The assistance of Rosalind Drum, Jo Ann Gibel, Eleanor Quinan, and Inez Wheldon in handling the numerous details concerning the manuscripts and proofs is gratefully acknowledged. Finally, the editors wish to thank their wives for their patience and understanding. December, 1965 R. K. WILLARDSON ALBERTC . BEER CHAPTER 1 Thermal Conductivity M . . Holland G I . INTRODUCTION . . . . . . . . . . . . . . . . 3 I1 . THEORY. . . . . . . . . . . . . . . . . . 5 1 . Phonons . . . . . . . . . . . . . . . . 6 2 . Electrons and Holes . . . . . . . . . . . . 10 3 . Other Heal Carriers . . . . . . . . . . . . . 10 111 . MEASUREMENTTE CHNIQUES. . . . . . . . . . . . 11 Iv. THERMACLO NDUCTION IN VARIOUS 1II-V COMPOUNDS . . . . 13 4 . InSb . . . . . . . . . . . . . . . . 13 5 . InAs . . . . . . . . . . . . . . . . . . 14 6.InP . . . . . . . . . . . . . . . . . . 11 1.GaAs . . . . . . . . . . . . . . . . . 11 8.GaSb . . . . . . . . . . . . . . . . . 18 9 . Other III-V Compounds . . . . . . . . . . . . . 20 V . SPECIAELF FECTS . . . . . . . . . . . . . . . 20 10 . Ternary Alloys . . . . . . . . . . . . . . . 20 11 . Magnetic Field Effects . . . . . . . . . . . . 21 12 . Electron Irradiation Effects . . . . . . . . . . . 22 VI . SUMMARY. . . . . . . . . . . . . . . . . 24 13. Boundary Scattering . . . . . . . . . . . . . 25 14 . Impurity Scattering . . . . . . . . . . . . . 26 IS . Resonance Scattering . . . . . . . . . . . . . 26 I6 . Electron-Phonon Scattering . . . . . . . . . . . 27 11 . Three-Phonon Processes . . . . . . . . . . . . 21 18 . Electronic Thermal Conductivity . . . . . . . . . 30 VII . CONCLUSIONS. . . . . . . . . . . . . . . . 30 . I Introduction The thermal conductivity of materials has been studied and understood qualitatively for many years. The early theoretical work of Debye’ and Peierls’ on materials which the heat is carried predominantly by phonons in P. Debye. in “Vortrage uber die kinetische Theorie der Materie und Elektrizitat.” Teubner. Berlin. 1914. R . Peierls. Ann . Physik 3. 1055 (1929). 3 4 G. HOLLAND M. indicated that the following behavior is to be expected: The thermal con- ductivity K at the lowest temperatures depends on the size and shape of the crystal (or crystallites). It increases with temperature with approximately the same temperature dependence as the specific heat and reaches a max- imum. At temperatures above this maximum, K is limited by the scattering of phonons by phonons and is characteristic of the material. Near the maximum, K is sensitive to the imperfections and impurities in the material. Electrons, when available in sufficient quantities, can also carry heat. This electronic contribution is usually significant only at very high temperatures in semiconductors. There has been a renewed interest in thermal conductivity in the last few years because of the availability of new and more accurate data3 on a large number of pure elements and compounds. Better data on a wider range of materials have led to an increased understanding of some of the phenomena involved in heat conduction in Many unsolved problems remain however ;m ost of these involve the scattering phenomena4 The 111-V compounds are attractive for thermal conductivity studies. These materials offer a wide range of lattice and electronic properties. They can, for the most part, be obtained in highly pure form,6 so that impurity effects are minimized and the intrinsic properties can be inves- tigated and compared. These materials can also usually be doped with known amounts of electrically active impurities, and the electronic effects can be compared. For these compounds information exists on properties such as sound velocity, Debye temperature, energy gap, electron and hole mobilities, and impurity ionization energy. But thermal conductivity measurements also assist in understanding the 111-V compounds. For example, information on impurities, both electrically inactive and active, can be obtained from the low temperature thermal conductivity.’ A comparison of the strength of the phonon-phonon inter- ’,* actions can be obtained from the data near the Debye temperature. Values for the energy gap and mobilities near the melting point can, in principle, be deduced from the electronic thermal conductivity. These are all properties of importance. Thermal conductivity is clearly also of technological importance. The thermal conductivity value is necessary in calculating the figure of merit See, for example, P. G. Klemens, Solid State Phys. 7, 1 (1958). P. Carruthers, Rev. Mod. Phys. 33, 92 (1961). ’ H. Bross, Phys. Star. Sol. 2, 481 (1961). See, for example, “Compound Semiconductors” (R. K. Willardson and H. L. Goering, eds.), Vol. 1 : “Preparation of 111-V Compounds,” Reinhold, New York, 1962. ’ M. G. Holland, Phys. Rev. 134, A471 (1964). E. F. Steigmeier and J. Kudman, Phys. Rev. 132, 508 (1963). 1. THERMAL CONDUCTIVITY 5 for thermoelectric devices9 Of greater importance would be the ability to control the processes which limit conduction so that the thermal conduc- tivity could be altered. For example, decreasing the thermal conductivity while the electrical conductivity remained the same (or increased) would increase the efficiency of thermoelectric devices. For power dissipating devices such as diodes, transistors, or lasers it is useful to know the value of the thermal conductivity to assist in device and circuit design.” For example, for a GaAs injection laser operating at 4.2”K it is clearly better to remove the heat through the n-type material which has at least two orders of magnitude higher thermal conductivity than the p-type layer. There are other areas in which the thermal conductivity can be of importance. For phonon amplifiers’ or problems of microwave phonon attenuation,I2 thermal conductivity can provide information on the relaxa- tion times for the high frequency (thermal) phonons. This is necessary to understand the interactions affecting the low frequency (5l o1’ cps)phonons which are being propagated and studied. The high thermal conductivity coupled with the low electrical conductivity of some of the purer 111-V compounds would make these materials excellent heat shields at low temperatures. Some of the properties of GaAs in a magnetic fieldI3 might lead to a useful heat switch at low temperatures. The same might be true of InSbI4 at high temperatures. In this chapter we first review the theory of thermal conductivity (Part 11) and give a short resume of the methods of measurement (Part 111). Part IV presents the data available for the 111-V compounds, with emphasis on the most up-to-date material, while Part V contains information on ternary alloys, magnetic field effects, and radiation damage effects. Part VI is a summary, followed by some general conclusions in Part VII. 11. Theory There are several excellent reviews of the general theory of thermal A. F. Joffe, “Semiconductor Thermoelements and Thermoelectric Cooling” Infosearch, London, 1957. lo W. W. Gartner, “Transistors, Principles, Design, and Applications.” Van Nostrand, Prince- ton, New Jersey, 1960; W. N. Carr and G. E. Pittman, Appl. Phys. Letters 3, 173 (1963). D. L. White, J. Appl. Phys. 33, 2547 (1962). ”See, for example, A. H. Nethercot, Jr., and H. H. Nickle, Proc. 8th Intern. ConJ Low Temp. Phys., London, 1962, p. 300. Butterworth, London and Washington, D.C., 1963. l3 M. G. Holland, in “Physics of Semi-Conductors” (Proc. Intern. Con€ Phys Semicond., Paris, 1964), p. 713. Dunod, Paris and Academic Press, New York, 1964. D. Kh. Amirkhanova and R. I. Bashirov, Fir. Tverd. Teia 2, 1597 (1960) [English Transt.. l4 Soviet Phys.-Solid State 2, 1447 (1961)]. 6 M. G. HOLLAND cond~ction,~~so~ o~n'ly~ ~a 's~h ort summary is presented here. In an elementary way we can describe the heat conducted by any excitation (phonon, electron, photon) by the equation K = fCul, (1) where is the heat capacity, u the propagation velocity, and 1 the mean C free path of the excitation. If there are several types of excitations, is the IC sum of a contribution from each. If the mean free path is limited by several scattering processes, the effective mean free path is given by where lj is the free path determined by the jth scattering process alone. 1. PHONONS Equation (1) must be generalized in order to account for the heat carried by all the phonons. The specific heat per normal phonon mode is given by' where x = hw/kT and w is the phonon frequency. If we now add up the contributions due to each mode we obtain the total specific heat where q is the wave vector and A the polarization of the phonons. Now, if we generalize the mean free path to 1 = (v,,a)z(q, 4, (5) where u is the phonon velocity and t(q,A) is the relaxation time for the phonon (9, A), then The frequency and wave vector have been related in the Debye approxima- tion (for low wave vectors) by o = uq, and we have assumed an isotropic phonon spectrum. Equation (6) can also be obtained from a Boltzmann equation appr~ach.I~n 'p~la ce of Eq. (2) we write K. Mendelssohn and H. M. Rosenberg, Solid State Phys. 12, 223 (1961). J. M. Ziman, "Electrons and Phonons." Oxford Univ. Press (Clarendon), London and New l6 York, 1960.