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,m _t the carrier transverse effective mass, and δ_t a correction factor for the anisotropy. δ_t is calculated as a function of the ratio of transverse to longitudinal effective mass. For an isotropic system δ_t is unity. For the conduction bands in Si and Ge, δ_t is 0.85 and 0.82, respectively.