The dopant density and temperature dependence of electron mobility and resistivity in n-type silicon

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Traditional analysis of electron mobility in n-type silicon neglects the effect of electron-electron scattering in the mobility calculations. As a result, theory fails to conform with experiment when dopant density exceeds 2 × 1016 cm−3. In this work, an improved theoretical model for computing mobility and resistivity as functions of dopant density and temperature has been developed for n-type silicon. The model has been applied to phosphorus-doped silicon for dopant densities from 1013 to 1019 cm−3, and temperatures between 100 and 500 K. The mobility was calculated analytically by appropriately combining lattice, ionized impurity and neutral impurity scattering contributions. The effect of electron-electron scattering was incorporated empirically for dopant densities greater than 2 × 1016 cm−3. Additionally, the anisotropic scattering effect was included in the mobility formulations. Resistivity measurements on seven phosphorus-doped silicon wafers with dopant densities from 1.2 × 1014 to 2.5 × 1018 cm−3 were carried out for temperatures from 100 to 500 K. Electron mobility at 300 K was deduced from resistivity and junction C-V measurements for dopant densities from 1014 to 1018 cm−3. Agreement between theoretical calculations and experimental data for both electron mobility and resistivity of phosphorus-doped silicon was within ±7% in the range of dopant densities and temperatures studied.