Semi-empirical equations for electron velocity in silicon: Part I—Bulk

A simple semi-empirical equation for the electron drift velocity in silicon as a function of electric field and temperature is derived from elementary physical assumptions. The parameters in this equation, namely the low field mobility, effective mass, and optical phonon energy, are well defined physical quantities, Excellent agreement with the empirical Scharfetter-Gummel equation is obtained. The temperature dependence of the saturation velocity and the warm electron coefficient β are also well described. A field dependent mobility scaling factor is derived to account for the steeper rise of the velocity-field profile in doped silicon which results from decreased coulombic scattering of hot carriers. The longitudinal electron diffusion is also crudely predicted.