Search

Statistical models [F91], [L00], [MRS90], [To93] are used to describe electron transport in semiconductors at a mesoscopic level. The basic model is given by the Boltzmann transport equation (BTE) for semiconductors in the semiclassical approximation: 7.1.1$$ \frac{{\partial f}} {{\partial t}} + \frac{1} {\hbar }\nabla _k \varepsilon \cdot \nabla _x f - \frac{\mathfrak{e}} {\hbar }E \cdot \nabla _k f = Q(f), $$ where f represents the electron probability density function (pdf) in phase space k at the physical location x and time t. ħ and $$ \mathfrak{e} $$ are physical constants; the Planck constant divided by 2π and the positive electric charge, respectively. The energy-band function ε is given by the Kane non-parabolic band model, which is a non-negative continuous function of the form 7.1.2$$ \varepsilon (k) = \frac{1} {{1 + \sqrt {1 + 2\frac{\alpha } {{m^* }}\hbar ^2 \left k \right^2 } }}\frac{{\hbar ^2 }} {{m^* }}\left k \right^2 , $$ where m* is the effective mass and α is the non-parabolicity factor. In this way we observe that setting α = 0 in Equation (7.1.2) the model is reduced to the widely used parabolic approximation. [ABSTRACT FROM AUTHOR]