Quantum model for phonon-assisted tunnel ionization of deep levels in a semiconductor

We have developed a new quantum theory for phonon-assisted tunnel emission of electrons from deep semiconductor levels. Linear coupling of a deep level with lattice-phonon modes is assumed and a perturbation approach is used to calculate the tunnel ionization rate. For a single-phonon mode, the resulting phonon-assisted tunneling rate is first derived with the use of the Condon approximation and is found to be a function of the phonon linear coupling constant $S$ and of the phonon energy $\hslash \omega$. A non-Condon approach is then used and results in an expression almost identical to the "Condon" one, except that the coupling constant $S$ is replaced by a modified effective value. The limit of validity of the Condon treatment is then clearly deduced. The new quantum model readily lends itself to generalization such as coupling to multiple phonon modes. Experimental results are presented and confirm the validity of the model.