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

The changes in resistivity of silicon samples containing group III and group V impurities have been measured at hydrostatic pressures up to 6000 kg ${\mathrm{cm}}^{-2\mathrm{}}$ at 50°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×${10}^{-8\mathrm{}}$ eV ${\mathrm{kg}}^{-1\mathrm{}}$ ${\mathrm{cm}}^2$. The energy levels for indium and aluminum move away from the valence-band edge at rates of about 5×${10}^{-8\mathrm{}}$ eV ${\mathrm{kg}}^{-1\mathrm{}}$ ${\mathrm{cm}}^2$ and 1×${10}^{-8\mathrm{}}$ eV ${\mathrm{kg}}^{-1\mathrm{}}$ ${\mathrm{cm}}^2$, 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 ${\mathrm{cm}}^{-2\mathrm{}}$. 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.