GaAs lower conduction-band minima: Ordering and properties

D. E. Aspnes

doi:10.1103/PhysRevB.14.5331

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GaAs lower conduction-band minima: Ordering and properties

D. E. Aspnes

Bell Laboratories, Murray Hill, New Jersey 07974

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Phys. Rev. B 14, 5331 – Published 15 December, 1976

DOI: https://doi.org/10.1103/PhysRevB.14.5331

Abstract

Synchrotron-radiation Schottky-barrier electroreflectance spectra from the $Ga 3 d^{V}$ core levels to the lower $s p^{3}$ conduction band have shown that the $L_{6}^{C}$ lower conduction-band minima are located 170 ± 30 meV in energy below the $X_{6}^{C}$ minima in GaAs. Here, we investigate the implications of this ordering, which is opposite to that commonly accepted as correct. We find that, without exception, the results of previous experiments that apparently supported the opposite ordering can be reinterpreted within the $Γ_{6}^{C} - L_{6}^{C} - X_{6}^{C}$ model. By performing a line-shape analysis, we resolve an apparent discrepancy between intraconduction band absorption measurements of the $X_{6}^{C} - Γ_{6}^{C}$ energy separation. By comparing these optical results with other modulation spectroscopic ( $s p^{3}$ valence-conduction-band electroreflectance, high-precision reflectance) data, combining these with the results of photoemission, transport (high pressure and high temperature), semiconductor alloy, and luminescence measurements, nonlocal pseudopotential calculations $\vec{k} \cdot \vec{p}$ theory, the rigid-valence-band hypothesis, and using the systematics of other tetrahedrally bonded semiconductors with temperature and pressure, we obtain a set of consistent parameters describing the $Γ_{6}^{C}$ , $L_{6}^{C}$ , and $X_{6}^{C}$ lower conduction-band minima of GaAs. This model resolves the former contradictions in the apparent indirect threshold energy as determined previously by photoemission, transport, and optical measurements. Previous photoemission data for cesiated GaAs show clearly after structure reassignment that hot electrons thermalize in the $L_{6}^{C}$ minima. This implies that Gunn oscillator operation in GaAs involves the $L_{6}^{C}$ , and not $X_{6}^{C}$ , conduction-band minima. We obtain the variation of these minima with composition, $x$ , in the $Ga {As}_{1 - x} P_{x}$ alloy series, and show that the increase in binding energy of the N isoelectronic trap with increasing As fraction in this series is in qualitative agreement with the prediction of a two-level model wherein a Koster-Slater isoelectronic trap potential interacts with the densities of states of both $L_{6}^{C}$ and $X_{6}^{C}$ . These results have clear implications for the theory of operation of light-emitting diodes of GaAs and its alloys.

References (73)

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H. Ehrenreich, Phys. Rev. 120, 1951 (1960)
G. D. Pitt, J. Phys. C 6, 1586 (1973)
I. Balslev, Phys. Rev. 173, 762 (1968)
A. Onton, R. J. Chicotka, and Y. Yacoby, in Proceedings of the 11th International Conference on the Physics of Semiconductors, Warsaw (PWN-Polish Scientific, Warszawa, 1972), p. 1023
L. W. James, R. C. Eden, J. L. Moll, and W. E. Spicer, Phys. Rev. 174, 909 (1968)
L. W. James and J. L. Moll, Phys. Rev. 183, 740 (1969)
G. D. Pitt and J. Lees, Phys. Rev. B 2, 4144 (1970)
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M. G. Craford and N. Holonyak, Jr., in Optical Properties of Solids: New Developments, edited by B. O. Seraphin (North-Holland, Amsterdam, 1976), p. 187
D. E. Aspnes and A. A. Studna, Phys. Rev. B 7, 4605 (1973)
D. D. Sell, H. C. Casey, Jr., and K. W. Wecht, J. Appl. Phys. 45, 2650 (1974)
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(Onton, private communication)
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H. G. B. Hicks and D. F. Manley, Solid State Commun. 7, 1463 (1969)
A. Sagar, Phys. Rev. 117, 93 (1960)
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B. Welber, M. Cardona, C. K. Kim, and S. Rodriguez, Phys. Rev. B 12, 5729 (1975)
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J. S. Harris, J. L. Moll, and G. L. Pearson, Phys. Rev. B 1, 1660 (1970)
M. Cardona, Modulation Spectroscopy (Academic, New York, 1969)
A. R. Hutson, A Jayaraman, and A. S. Coriell, Phys. Rev. 155, 786 (1967)
H. B. Huntington, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic, New York, 1958), Vol. 7, p. 213
I. Balslev, Phys. Rev. 143, 636 (1966)
R. J. Nelson, N. Holonyak, Jr., and W. O. Groves, Phys. Rev. B 13, 5415 (1976)
D. E. Aspnes, C. G. Olson, and D. W. Lynch, Phys. Ref. B 14, 2534 (1976)
K. Y. Cheng, G. L. Pearson, R. S. Bauer, and D. J. Chadi, Bull. Am. Phys. Soc. 21, 365 (1976)
D. J. Wolford and B. G. Streetman (private communication and unpublished)
L. Ley, R. A. Pollak, F. R. McFeely, S. P. Kowalczyk, and D. A. Shirley, Phys. Rev. B 9, 600 (1974)
D. E. Aspnes, IEEE Trans. Electron Devices (in press)
P. J. Vinson, C. Pickering, A. R. Adams, W. Fawcett, and G. D. Pitt, in Proceedings of the 13th International Conference on the Physics of Semiconductors, Rome (to be published)
R. Dingle, R. A. Logan, and J. R. Arthur, Jr., in International Conference on GaAs and Related Materials (to be published)
R. Trommer and M. Cardona, Solid State Commun. (to be published)

[c1] D E. Aspnes, C. G. Olson, and D. W. Lynch, Phys. Rev. Lett. 37, 766 (1976)

[c2] H. Ehrenreich, Phys. Rev. 120, 1951 (1960)

[c3] G. D. Pitt, J. Phys. C 6, 1586 (1973)

[c4] I. Balslev, Phys. Rev. 173, 762 (1968)

[c5] A. Onton, R. J. Chicotka, and Y. Yacoby, in Proceedings of the 11th International Conference on the Physics of Semiconductors, Warsaw (PWN-Polish Scientific, Warszawa, 1972), p. 1023

[c6] L. W. James, R. C. Eden, J. L. Moll, and W. E. Spicer, Phys. Rev. 174, 909 (1968)

[c7] L. W. James and J. L. Moll, Phys. Rev. 183, 740 (1969)

[c8] G. D. Pitt and J. Lees, Phys. Rev. B 2, 4144 (1970)

[c9] P. Blood, Phys. Rev. B 6, 2257 (1972)

[c10] J. A. Copeland and S. Knight, in Semiconductors and Semimetals, edited by R. K. Willardson and A. C. Beer (Academic, New York, 1971), Vol. 7, p. 3

[c11] M. G. Craford and N. Holonyak, Jr., in Optical Properties of Solids: New Developments, edited by B. O. Seraphin (North-Holland, Amsterdam, 1976), p. 187

[c12] D. E. Aspnes and A. A. Studna, Phys. Rev. B 7, 4605 (1973)

[c13] D. D. Sell, H. C. Casey, Jr., and K. W. Wecht, J. Appl. Phys. 45, 2650 (1974)

[c14] D. D. Sell, S. E. Stokowski, R. Dingle, and J. V. DiLorenzo, Phys. Rev. B 7, 4568 (1973)

[c15] M. B. Panish and H. C. Casey, Jr., J. Appl. Phys. 40, 163 (1969)

[c16] M. G. Craford, R. W. Shaw, A. H. Herzog, and W. O. Groves, J. Appl. Phys. 43, 4075 (1972)

[c17] W. O. Groves, A. H. Herzog, and M. G. Craford, Appl. Phys. Lett. 19, 184 (1971)

[c18] R. J. Nelson, N. Holonyak, Jr., J. J. Coleman, D. Lazarus, W. O. Groves, D. L. Keune, M. G. Craford, D. J. Wolford, and B. G. Streetmen, Phys. Rev. B 14, 685 (1976)

[c19] K. C. Pandey and J. C. Phillips, Phys. Rev. B 9, 1552 (1974)

[c20] J. R. Chelikowsky and M. L. Cohen, Phys. Rev. Lett. 32, 674 (1974) Phys. Rev. B 14, 556 (1976)

[c21] H. Ehrenreich, J. Appl. Phys. 32, 2155 (1961)

[c22] M. Cardona and D. L. Greenway, Phys. Rev. 125, 1291 (1962)

[c23] D. Auvergne, J. Camassel, H. Mathieu, and M. Cardona, Phys. Rev. B 9, 5168 (1974)

[c24] J. Camassel and D. Auvergne, Phys. Rev. B 12, 3258 (1975)

[c25] D. L. Camphausen, G. A. N. Connell, and W. Paul, Phys. Rev. Lett. 26, 184 (1971)

[c26] D. J. Wolford, B. G. Streetman, W. Y. Hsu, J. D. Dow, R. J. Nelson, and N. Holonyak, Jr., Phys. Rev. Lett. 36, 1400 (1976)

[c27] R. A. Faulkner, Phys. Rev. 175, 991 (1969)

[c28] J. C. Campbell, N. Holonyak, Jr., M. G. Craford, and D. L. Keune, J. Appl. Phys. 45, 4543 (1974)

[c29] S. F. Ross and M. Jaros, Solid State Commun. 13, 1751 (1973)

[c30] J. B. Gunn, IBM J. Res. Dev. 8, 141 (1964)

[c31] B. K. Ridley and T. B. Watkins, Proc. Phys. Soc. Lond. 78, 293 (1961) B. K. Ridley, ibid. 82, 954 (1963)

[c32] C. Hilsum, Proc. IRE 50, 185 (1962)

[c33] C. D. Thurmond, J. Electrochem. Soc. 122, 1133 (1975)

[c34] Y. P. Varshni, Physica (Utr.) 39, 149 (1967)

[c35] (Onton, private communication)

[c36] R. A. Smith, Semiconductors (Cambridge U.P., Cambridge, England, 1961)

[c37] J. G. Gay, Phys. Rev. B 4, 2567 (1971)

[c38] G. Dolling and J. L. T. Waugh, in Proceedings of the International Conference on Lattice Dynamics, Copenhagen, edited by R. F. Wallis (Pergamon, London, 1965), p. 19

[c39] C. J. Hwang, J. Appl. Phys. 40, 3731 (1969)

[c40] C. D. Thurmond (private communication)

[c41] P. J. Dean, G. Kaminsky, and R. B. Zetterstrom, J. Appl. Phys. 38, 3551 (1967)

[c42] A. G. Thompson, J. C. Woolley, and M. Rubenstein, Can. J. Phys. 44, 2927 (1966)

[c43] L. W. Aukerman and R. K. Willardson, J. Appl. Phys. 31, 939 (1960)

[c44] G. D. Pitt, Solid State Commun. 8, 1119 (1970)

[c45] Q. H. F. Vrehen, J. Phys. Chem. Solids 29, 129 (1968)

[c46] G. Dresselhaus and M. S. Dresselhaus, Phys. Rev. 160, 649 (1967)

[c47] A. Onton, Phys. Rev. 186, 786 (1969)

[c48] C. Hilsum, in Semiconductors and Semimetals, edited by R. K. Willardson and A. C. Beer (Academic, New York, 1966), Vol. I, p. 3

[c49] D. L. Rode, Phys. Rev. B 2, 1012 (1970)

[c50] D. L. Rode and S. Knight, Phys. Rev. B 3, 2534 (1971)

[c51] C. Hilsum and J. Welborn, J. Phys. Soc. Jpn. Suppl. 21, 532 (1966)

[c52] W. Fawcett, A. D. Boardman, and S. Swain, J. Phys. Chem. Solids 31, 1963 (1970)

[c53] C. Herring, Bell. Syst. Tech. J. 34, 237 (1955)

[c54] M. G. Craford, W. O. Groves, A. H. Herzog, and D. E. Hill, J. Appl. Phys. 42, 2751 (1971)

[c55] H. G. B. Hicks and D. F. Manley, Solid State Commun. 7, 1463 (1969)

[c56] A. Sagar, Phys. Rev. 117, 93 (1960)

[c57] B. B. Kosicki, A. Jayaraman, and W. Paul, Phys. Rev. 172, 764 (1968)

[c58] B. Welber, M. Cardona, C. K. Kim, and S. Rodriguez, Phys. Rev. B 12, 5729 (1975)

[c59] M. Konczykowski, J. Chroboczek, and S. Porowski, in , p. 1050

[c60] J. S. Harris, J. L. Moll, and G. L. Pearson, Phys. Rev. B 1, 1660 (1970)

[c61] M. Cardona, Modulation Spectroscopy (Academic, New York, 1969)

[c62] A. R. Hutson, A Jayaraman, and A. S. Coriell, Phys. Rev. 155, 786 (1967)

[c63] H. B. Huntington, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic, New York, 1958), Vol. 7, p. 213

[c64] I. Balslev, Phys. Rev. 143, 636 (1966)

[c65] R. J. Nelson, N. Holonyak, Jr., and W. O. Groves, Phys. Rev. B 13, 5415 (1976)

[c66] D. E. Aspnes, C. G. Olson, and D. W. Lynch, Phys. Ref. B 14, 2534 (1976)

[c67] K. Y. Cheng, G. L. Pearson, R. S. Bauer, and D. J. Chadi, Bull. Am. Phys. Soc. 21, 365 (1976)

[c68] D. J. Wolford and B. G. Streetman (private communication and unpublished)

[c69] L. Ley, R. A. Pollak, F. R. McFeely, S. P. Kowalczyk, and D. A. Shirley, Phys. Rev. B 9, 600 (1974)

[c70] D. E. Aspnes, IEEE Trans. Electron Devices (in press)

[c71] P. J. Vinson, C. Pickering, A. R. Adams, W. Fawcett, and G. D. Pitt, in Proceedings of the 13th International Conference on the Physics of Semiconductors, Rome (to be published)

[c72] R. Dingle, R. A. Logan, and J. R. Arthur, Jr., in International Conference on GaAs and Related Materials (to be published)

[c73] R. Trommer and M. Cardona, Solid State Commun. (to be published)

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GaAs lower conduction-band minima: Ordering and properties

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