Δ₁ Conduction-band minimum of Ge from high-pressure studies on p-n junctions

Abstract

The effect of hydrostatic pressure on p-n junctions of germanium has been investigated with a view to determining the energy of the Δ₁ conduction-band minimum relative to that of the L₁ minimum. The pressure-induced shift in the forward bias voltage at a constant current level, which is a measure of the energy-gap change with pressure, passes through a maximum near the pressure at which the lowest conduction band shifts from the L₁ to the Δ₁ minimum. Because of the two-band conduction in Ge at pressures above 15 kbar, the observed shift in the forward bias voltage not only represent an effective-energy-gap change determined by the density-of-state average over the two bands and their pressure coefficients, but is also modified by the change in carrier mobility with pressure. Since the junction current in the present case was dominated by electrons, the observed shifts were corrected for the electronic-mobility change with pressure, using the pressure variation of the resistivity of n-type Ge. From the effective-energy-gap change with pressure given by ΔE_Geff=Δ(E_L-E_v)-kTln[1+(N_Δ/N_L)exp(-ΔE/kT)], and using dE_G/dV=3.7 eV (dE_G/dP=5.0×10^-3 eV/kbar), N_Δ/N_L=2.7, and d(ΔE)/dV=-4.6 eV [d(ΔE)/dP=-6.2× 10^-3 eV/kbar], the best fit to the experimental data yields 0.18±0.01 eV for the zero-pressure energy separation ΔE between the L₁ and Δ₁ minima. The observed shifts give initial pressure coefficients of 5.0±0.1× 10^-3 and -1.3±0.3×10^-3 eV/kbar for the L₁ and Δ₁ minima, respectively.