Study of the high pressure and temperature response of silicon, germanium and gallium arsenide electronic energy bands

Abstract

In this study we investigate the different temperature electronic energy band structure responses of silicon, germanium and gallium arsenide at various applied hydrostatic pressures within a range that does not exceed their structural phase transition pressure. The pressure coefficients for each material have been determined. An atomistic insight was presented into the question of how much of the electronic band structure deformation, due to hydrostatic pressure, originates from the valence or the conduction bands. It was observed that the rate of increase in energy of the conduction band minimum with an increase in pressure is greater than that of the valence band maximum for Ge and GaAs, while it is less than that of the valence band maximum for silicon. The origin of this negative value of the first order pressure coefficient of silicon was explained in terms of p and d conduction band orbitals coupling at the Xc high symmetry point of the Brillouin zone, hence exhibiting quantum level repulsion between them, thus forcing the conduction band edge downwards in energy relative to the maximum of the valence band at Tc. The hydrostatic volume deformation potential, ag is found to be constant for Ge and GaAs. Our results agree with the “empirical rules of pressure coefficients” for inter-band electronic transitions of types Tv →  Tc in gallium arsenide, Tv → Lc in germanium and Tv → Xc in silicon.  Key words: Hydrostatic deformation potential; pressure coefficients; inter-band electronic transitions; orbital coupling; quantum level repulsion.