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Those other space-charge layers
A313 Surface Science 98 (1980) 571488 0 North-Holland Publishing Company and Yamada Science Foundation THOSE OTHER SPACE-CHARGE
LAYERS
F. KOCH Physik-Department,
Technische
Universitiit Mtinchen, D-8064
Garching, Fed. Rep. of Germany
Received 23 July 1979; accepted for publication 15 December 1979 Although dominated by work on silicon, the study of transport in semiconductor surface charge layers is not an “all silicon” science. The large range of relevant material parameters available in other semiconductors provides for a rich field of activities. We review here the work on other than silicon surfaces.
Surface Science 98 (1980) 589-596 0 North-Holland Publishing Company and Yamada Science Foundation EFFECT OF THE ELECTRON-PHONON INTERACTION ON THE SUBBAND STRUCTURE OF INVERSION LAYERS IN COMPOUND SEMICONDUCTORS * Galen KAWAMOTO, Rajiv KALIA and J.J. QUINN Brown Ulrilversity, Providence,
Rhode Island 02912,
USA
Received 20 July 1979 Recently electron inversion layers have been fabricated on a number of compound (principally III-V) semiconductors. Because of the polar nature of these materials, the effect of the electron-optical phonon interaction is expected to be significant. This has certainly been true in recent calculations of the ground state energy and equilibrium density of electron-hole liquids in a number of compound semiconductors [ 11. We have calculated the subband structure of inversion layers in polar semiconductors. The starting point of our many-body calculation is the Hartree subband structure determined using a variational method described in ref. [ 21. Using the Hartree wavefunctions as basis functions we have calculated the self-energy of the ground and fist excited subbands to lowest order in the effective interaction. This interaction is the sum of Coulomb (direct and image) and electron-phonon terms which are screened by a dielectric function that includes both e-e and erph effects. The screening by inversion layer. electrons has been treated in the plasmon:pole gpproximation. We have obtained the electron self-energy, the quasi-particle energy, and the subband separations as a function of inversion layer concentration for parameters corresponding to GaAs. The coupling of electrons to bulk phonons is considered. Our results are compared to those obtained using the simpler e(; approximation [ 11. Here, explicit phonon terms are neglected, but the bare band mass is replaced by the polaron mass, and the high frequency dielectric constant (coo) is replaced by the static dielectric constant (eo). This approximation has been applied to the electron-hole liquid for situations in which the optical phonon frequency is larger than the electron plasma frequency. The idea behind the E: approximation is to account in a very rough way for vertex corrections to the electron-phonon interaction. A principal criticism of our dynamic RPA calculations is the neglect of vertex corrections in the effective interaction. In three-dimensional metallic systems (high density), Migdal’s theorem applies and vertex corrections are small. However, it is not clear that we may neglect such corrections in inversion layers. This point will be discussed further.
LAYERS
F. KOCH Physik-Department,
Technische
Universitiit Mtinchen, D-8064
Garching, Fed. Rep. of Germany
Received 23 July 1979; accepted for publication 15 December 1979 Although dominated by work on silicon, the study of transport in semiconductor surface charge layers is not an “all silicon” science. The large range of relevant material parameters available in other semiconductors provides for a rich field of activities. We review here the work on other than silicon surfaces.
Surface Science 98 (1980) 589-596 0 North-Holland Publishing Company and Yamada Science Foundation EFFECT OF THE ELECTRON-PHONON INTERACTION ON THE SUBBAND STRUCTURE OF INVERSION LAYERS IN COMPOUND SEMICONDUCTORS * Galen KAWAMOTO, Rajiv KALIA and J.J. QUINN Brown Ulrilversity, Providence,
Rhode Island 02912,
USA
Received 20 July 1979 Recently electron inversion layers have been fabricated on a number of compound (principally III-V) semiconductors. Because of the polar nature of these materials, the effect of the electron-optical phonon interaction is expected to be significant. This has certainly been true in recent calculations of the ground state energy and equilibrium density of electron-hole liquids in a number of compound semiconductors [ 11. We have calculated the subband structure of inversion layers in polar semiconductors. The starting point of our many-body calculation is the Hartree subband structure determined using a variational method described in ref. [ 21. Using the Hartree wavefunctions as basis functions we have calculated the self-energy of the ground and fist excited subbands to lowest order in the effective interaction. This interaction is the sum of Coulomb (direct and image) and electron-phonon terms which are screened by a dielectric function that includes both e-e and erph effects. The screening by inversion layer. electrons has been treated in the plasmon:pole gpproximation. We have obtained the electron self-energy, the quasi-particle energy, and the subband separations as a function of inversion layer concentration for parameters corresponding to GaAs. The coupling of electrons to bulk phonons is considered. Our results are compared to those obtained using the simpler e(; approximation [ 11. Here, explicit phonon terms are neglected, but the bare band mass is replaced by the polaron mass, and the high frequency dielectric constant (coo) is replaced by the static dielectric constant (eo). This approximation has been applied to the electron-hole liquid for situations in which the optical phonon frequency is larger than the electron plasma frequency. The idea behind the E: approximation is to account in a very rough way for vertex corrections to the electron-phonon interaction. A principal criticism of our dynamic RPA calculations is the neglect of vertex corrections in the effective interaction. In three-dimensional metallic systems (high density), Migdal’s theorem applies and vertex corrections are small. However, it is not clear that we may neglect such corrections in inversion layers. This point will be discussed further.