Impact ionisation probability in InSb

Abstract

An exact analytical expression for the impact ionisation probability for the main ionisation process in a semiconductor with a Kane-type bandstructure is derived. In a parabolic approximation the integrals involved can be evaluated and the result reduces to the simple relationv _i (E)=C(E−E _i )²Θ(E−E _i ) whereC is a material constant related to the transition matrix elements. From experimental results on the photo-quantum efficiency we can estimate the value ofC for InSb near 77 K, i.e.ħC ≈ 0.012 eV⁻¹. It is concluded that the impact ionisation probability cannot be described with a unit step function at the threshold energy as was done in many theories on the avalanche effect. The (effective) threshold is smooth and a more detailed description, as derived here, is necessary.