Wannier-Slater theorem for solids with nonuniform band structure

C. M. van Vliet; A. H. Marshak

doi:10.1103/PhysRevB.26.6734

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Wannier-Slater theorem for solids with nonuniform band structure

C. M. van Vliet^*

A. H. Marshak

Department of Electrical Engineering, University of Florida, Gainesville, Florida 32611

Department of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, Louisiana 70803

^*On leave from Centre de Recherches des Mathématiques Appliquées, Université de Montréal, Montréal, Québec H3C 3J7, Canada.

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Phys. Rev. B 26, 6734 – Published 15 December, 1982

DOI: https://doi.org/10.1103/PhysRevB.26.6734

Abstract

The Wannier-Slater theorem for the Hamiltonian of a solid in an external field of force is generalized for solids with a nonuniform band structure, such as graded-gap mixed semiconductors. Our formulation is related to that of Gora and Williams, and their effectivemass equation is obtained if a $\vec{k}$ -space Taylor expansion is permissible. This paper extends a too-restricted, earlier discussion by us in connection with transport in position-dependent band structures. The concept of a graded effective mass $\overset{\leftrightarrow}{M}$ and position-dependent band bottom $E_{c}$ is derived from this treatment. It is pointed out, however, that the concept of a position-dependent effective mass has no strict quantum-mechanical validity. In the correspondence limit, Hamilton's equations lead to an acceleration which contains the effect of an external field ${\overset{\leftrightarrow}{M}}^{- 1} \cdot \vec{F}$ , plus a dissipative term which stems from the deviation in periodicity of the crystal potential.

Comments & Replies

Comment on "Position-dependent effective masses in semiconductor theory"

Carolyn M. Van Vliet and Alan H. Marshak

Phys. Rev. B 29, 5960 (1984)

References (11)

T. Gora and F. Williams, in II-VI Semiconducting Compounds, edited by D. G. Thomas (Benjamin, New York, 1967), p. 639
T. Gora and F. Williams, Phys. Rev. 177, 1179 (1969)
L. Leibler, Phys. Rev. B 12, 4443 (1975)
J. C. Slater, Phys. Rev. 76, 1592 (1949)
G. H. Wannier, Phys. Rev. 52, 191 (1937)
A. H. Marshak and K. M. van Vliet, Solid State Electron. 21, 417 (1978)
L. Leibler, J. Mycielski, and J. K. Furdyna, Phys. Rev. B 11, 3037 (1975)
J. Mycielski, G. Bastard, and C. Rigaud, Phys. Rev. B 16, 1675 (1977)
C. M. van Vliet and A. H. Marshak, in Proceedings of the International Workshop on Solid State Devices, Delhi, India, November, 1981
J. Bardeen and W. Shockley, Phys. Rev. 80, 72 (1950)
W. Jones and N. H. March, Theoretical Solid State Physics (Wiley, New York, 1973), Vol. 2, App. A8.1

[c1] T. Gora and F. Williams, in II-VI Semiconducting Compounds, edited by D. G. Thomas (Benjamin, New York, 1967), p. 639

[c2] T. Gora and F. Williams, Phys. Rev. 177, 1179 (1969)

[c3] L. Leibler, Phys. Rev. B 12, 4443 (1975)

[c4] J. C. Slater, Phys. Rev. 76, 1592 (1949)

[c5] G. H. Wannier, Phys. Rev. 52, 191 (1937)

[c6] A. H. Marshak and K. M. van Vliet, Solid State Electron. 21, 417 (1978)

[c7] L. Leibler, J. Mycielski, and J. K. Furdyna, Phys. Rev. B 11, 3037 (1975)

[c8] J. Mycielski, G. Bastard, and C. Rigaud, Phys. Rev. B 16, 1675 (1977)

[c9] C. M. van Vliet and A. H. Marshak, in Proceedings of the International Workshop on Solid State Devices, Delhi, India, November, 1981

[c10] J. Bardeen and W. Shockley, Phys. Rev. 80, 72 (1950)

[c11] W. Jones and N. H. March, Theoretical Solid State Physics (Wiley, New York, 1973), Vol. 2, App. A8.1

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Wannier-Slater theorem for solids with nonuniform band structure

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Comment on "Position-dependent effective masses in semiconductor theory"

References (11)

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