Effect of Pressure on the Energy Levels of Impurities in Semiconductors. I. Arsenic, Indium, and Aluminum in Silicon

Abstract

The changes in resistivity of silicon samples containing group III and group V impurities have been measured at hydrostatic pressures up to 6000 kg ${\mathrm{cm}}^{\ensuremath{-}2}$ at 50\ifmmode^\circ\else\textdegree\fi{}K. The changes are explained by a dependence on pressure of the ionization energy of the majority impurity center. The results indicate that the arsenic energy level moves toward the conduction-band edge at a rate of approximately 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ eV ${\mathrm{kg}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{2}$. The energy levels for indium and aluminum move away from the valence-band edge at rates of about 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ eV ${\mathrm{kg}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{2}$ and 1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ eV ${\mathrm{kg}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{2}$, respectively. Corrections for the changes in mobility with pressure have been applied for the $n$-type sample. The motion of the arsenic energy level is explained by a change in dielectric constant and effective mass with pressure, and indicates a change in the average effective mass of less than 1% in 5000 kg ${\mathrm{cm}}^{\ensuremath{-}2}$. The very small changes in ionization energy, while expected, are to be contrasted with the much larger changes found for the deep-lying levels produced by elements such as gold.