Effect of Pressure on the Infrared Absorption of Semiconductors

Abstract

Measurements have been made of the effect of hydrostatic pressure upon the intrinsic infrared absorption of germanium, silicon, and tellurium in the pressure range 1-2000 atmospheres. In germanium the variation with pressure of the lowest lying conduction band minimum, (111), is found to be (7.3\ifmmode\pm\else\textpm\fi{}1.5)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ ev/atmos. It is suggested that the variation with pressure of the next highest conduction band edge, (000), has a value of (11\ifmmode\pm\else\textpm\fi{}3)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ ev/atmos. The shift of the infrared absorption edge with pressure in silicon is small and is toward smaller energy, amounting to about -2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ ev/atmos between 1 and 2020 atmospheres. The sign and magnitude of the pressure coefficient in this material are in agreement with the results of Warschauer, Paul, and Brooks. For tellurium both ${E}_{g\ensuremath{\perp}}$, the energy gap corresponding to light polarized perpendicular to the $c$-axis of the crystal, and ${E}_{g\mathrm{II}}$, the energy gap for polarization parallel to the $c$-axis, decrease as the pressure is increased. It appears that ${E}_{g\ensuremath{\perp}}$ decreases more rapidly with pressure than ${E}_{g\mathrm{II}}$. The mean pressure coefficient of ${E}_{g\ensuremath{\perp}}$ is - (2.2\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ ev/atmos. For ${E}_{g\mathrm{II}}$ the mean pressure coefficient is - (1.8\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ ev/atmos. The measured pressure coefficients are used to calculate the thermal dilation term in the equation for the change of the energy gap with temperature for each material. The electron-lattice interaction term appearing in this equation is then deduced. In silicon these two terms are of opposite sign with the electron-lattice term dominant. In germanium the electron-lattice interaction effect accounts for 75% of the effect of temperature on the energy gap. For tellurium the two effects are almost equal in magnitude but of opposite sign.