Multi-valley effective-mass approximation of group-V and group-VI donor states in silicon

Ning, Tak Hung

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https://hdl.handle.net/2142/55614 Copy

Description

Title

Multi-valley effective-mass approximation of group-V and group-VI donor states in silicon

Author(s)

Ning, Tak Hung

Issue Date

1971

Director of Research (if dissertation) or Advisor (if thesis)

Sah, Chih-Tang

Doctoral Committee Chair(s)

Sah, Chih-Tang

Committee Member(s)

• Bardeen, John
• Williams, Wendell

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D. (doctoral)

Degree Level

Dissertation

Keyword(s)

Silicon

Language

en

Abstract

The pseudopotential theory of a substitutional impurity in a semiconductor is formulated using the orthogonalized-Bloch-wave method. A pseudo wave equation is obtained which is the same as the starting equation of the Kohn-Luttinger effective-mass approximation (EMA), except that the true impurity potential is replaced by the pseudo impurity potential. By following the procedures of Kohn-Luttinger's one-valley EMA, but without neglecting the intervalley overlap terms, a multi-valley effective-mass approximation is developed for shallow-level donors in silicon. With a phenomenological two-parameter pseudo impurity potential, the levels of the group-V donor impurities in silicon are calculated using the variation method and plane-wave approximation of the Bloch waves. The potential parameters are adjusted to fit the observed 1s(A1) to 2p+- and 1s(T2) to 2p+- transition energies. It is shown that the proposed potential describes well the central-cell correction and the dielectric screening. For the p states it is found that the usual one-valley approximation is adequate. Also, in the multi-valley EMA, the valley-orbit interaction shifts the 1s(A1) level downward and the 1s(T2) and 1s(E) levels upward relative to the one-valley-EMA ls level. The effects of the uncertainty in the position of the delta1 conduction-band valleys and of the coupling between the ls and 2s states on the ground-state energy are shown to be negligible. Also, contribution from wave-function components of a L1 valley of the conduction band to the ground-state energy is computed to be about 1% of that from wave-function components of a delta1 valley. It indicates that the higher-energy subsidiary conduction-band valleys may be neglected. The ground-state trial wave functions are used to calculate the photo-ionization cross-section and the Fermi contact hyperfine constants. They are compared with reported experimental and theoretical results. It is suggested that the pseudo impurity potentials of the shallow-level group-V donors may be scaled to give the pseudo impurity potentials of the deep-level group-VI donors of the same row in the periodic table. By extending the multi-valley EMA to singly ionized sulfur donor centers in silicon, it is found that indeed the potential parameters of sulfur are essentially identical to those of phosphorus. A helium-like model in the multi-valley EMA is also developed and applied to the two-electron neutral group-VI donor centers in silicon. The calculated energies of neutral sulfur agree well with the experimental thermal activation energies obtained by Rosier and Sah. Using the scaled impurity potentials of As, Sb, and Bi, the energies of substitutional Se, Te, and Po in Si are predicted. A two-step thermal ionization process is proposed for sulfur centers in silicon. The rate equation governing the concentration of trapped electrons is derived. By comparing with experimental results of Rosier and Sah, it is found that the limiting step is the thermal excitation of electrons from the ground state to the n=2 excited states, while the thermal excitation from the excited states into the conduction band may be considered instantaneous. The rate equation for a two -step photothermal ionization process is also derived and related to the optical absorption cross-section.

Type of Resource

text

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Copyright 1971 Tak Hung Ning

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