The dopant density and temperature dependence of hole mobility and resistivity in boron doped silicon

Abstract

Theoretical expressions for computing resistivity and conductivity mobility of holes as functions of dopant density and temperature have been derived for boron-doped silicon. The model is applicable for dopant densities from 10 13 to 3 × 10 18 cm −3 and temperatures between 100 and 400 K. Using a 3-band [i.e. heavy-hole, light-hole and the spin-orbit splitting (SO) band] model, the hole mobility was calculated by properly combining the contributions from scattering by lattice phonons, ionized impurities and neutral impurities. In addition, the effects of hole-hole (h-h) scattering and nonparabolicity of valence bands were taken into account in the mobility formulation. To verify our theoretical calculations, resistivity measurements on nine boron-doped silicon slices with dopant densities from 4.5 × 10 14 to 3.2 × 10 18 cm −3 were performed for 100 ≤ T ≤ 400 K, using planar square-array test structure. Agreement between our calculated and measured resistivity values was within 6 percent over the entire range of dopant density and temperature studied here. Excellent agreement (within ±5%) between our calculated hole mobility values and those of Wagner [9] was obtained for N A ≤ 10 17 cm −3 for boron-doped silicon, while discrepancies were found for boron densities greater than 10 17 cm −3. This discrepancy is attributed to neglecting the effect of deionization of boron impurities at higher dopant densities by Wagner (i.e. assuming hole density is equal to the total boron density).