We present quantum-mechanical theory of impact ionization in semiconductorswith the direct band gap in \$\Gamma\$-point. It is shown that energydependence 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 stronglyanisotropic and quadratic in \$E-E_{th}\$, while another one is isotropic andcubic in \$E-E_{th}\$. Explicit form of the coefficients in such representationis derived in the framework of the 14-band \${\bf k\cdot p}\$ model, and weclaim the room temperature domination of the cubic contribution for most of thedirect-gap materials with \$E_g\$ up to 1.5 eV.
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