Relationship between capture coefficient and capture cross-section: Average velocity of a maxwellian distribution of carriers in a medium with an anisotropic effective mass tensor

Abstract

The capture cross section of a trapping or recombination center for a charge carrier has been defined as the quotient of the capture coefficient and the average thermal velocity of the carrier distribution. For a Maxwellian distribution in a semiconductor band with an ellipsoidal effective mass tensor, this average velocity can be expressed as $$\left\langle v \right\rangle _{th} = \left[ {\frac{{8KT}}{{\pi m_t }}} \right]^{\frac{1}{2}} \delta _t $$ whereK is the Boltzmann constant,T the absolute temperature,mt the carrier transverse effective mass, and δt a correction factor for the anisotropy. δt is calculated as a function of the ratio of transverse to longitudinal effective mass. For an isotropic system δt is unity. For the conduction bands in Si and Ge, δt is 0.85 and 0.82, respectively.