# On the impact ionization rate in direct gap semiconductors

## TL;DR

This paper develops a quantum-mechanical model for impact ionization in direct gap semiconductors, revealing the energy dependence of the ionization rate near the threshold and identifying dominant anisotropic and isotropic contributions.

## Contribution

It provides an explicit form of the impact ionization rate near the threshold using a 14-band k·p model, highlighting the cubic term's dominance at room temperature for certain materials.

## Key findings

- Impact ionization rate near threshold is a superposition of anisotropic quadratic and isotropic cubic terms.
- The cubic term dominates at room temperature for direct-gap semiconductors with E_g up to 1.5 eV.
- Explicit coefficients for the impact ionization rate are derived within the 14-band k·p framework.

## Abstract

We present quantum-mechanical theory of impact ionization in semiconductors with the direct band gap in \$\Gamma\$-point. It is shown that energy dependence of the impact ionization rate \$\mathcal{W}(E)\$ near a threshold \$E_{th}\$ is given by superposition of the two terms, one of which is strongly anisotropic and quadratic in \$E-E_{th}\$, while another one is isotropic and cubic in \$E-E_{th}\$. Explicit form of the coefficients in such representation is derived in the framework of the 14-band \${\bf k\cdot p}\$ model, and we claim the room temperature domination of the cubic contribution for most of the direct-gap materials with \$E_g\$ up to 1.5 eV.