On the theory of the thermal capture of electrons in semi-conductors

The influence of the acoustic vibrations of the lattice on the capture of free carriers by impurities is investigated theoretically. The bound states considered are those whose energies are near the middle of the energy gap. For these states it is assumed that the interaction between the electron and the lattice is adequately described in the adiabatic approximation. It is also assumed that the bound electron displaces the equilibrium positions of the atoms of the lattice, but that it does not alter the velocity of sound in the solid. If this is the case, the ratio of the probability that the impurity will be ionized to the probability that the free carrier will be captured is exp ( —E1/kT), where E1 is the ionization energy. The principal new result of this paper is a formula for the capture rate which is valid when E1/k is very much greater than the Debye temperature. The formal theory is applied to the model of an impurity in a continuum. The capture rate is strongly dependent on the radius of the bound orbit, on the strength of the coupling between the electron and the lattice and on the temperature when the ionization energy is sufficiently large. The limitations of the model are discussed and the results are compared with experiment. The qualitative features of the model are, for certain values of the unknown parameters, in agreement with experiment although the absolute magnitudes of the capture rates may be too small to account for the observed lifetimes.