Theory of Non‐Radiative Multiphonon Capture Processes. Solution of Old Controversies

The solution is given for long persisting controversial problems in the theory of non‐radiative multiphonon capture of free carriers. Taking the adiabatic wave functions as basic states for the perturbational treatment of the transition probability particular attention is focused on the correct determination of the transition matrix elements. In this framework it is shown that to first order in the non‐diagonal matrix element of the electron‐lattice interaction all approaches developed so far (Condon approximation, non‐Condon approximation, static approximation, etc.) lead to the same result, in contradiction to statements in the literature. In particular, the reason is found why earlier results for the transition rate within the adiabatic and Condon approximation are much too small. The static approximation is shown to be the lowest approximation to the adiabatic approach.