IMPACT-IONIZATION THEORY CONSISTENT WITH A REALISTIC BAND-STRUCTURE OF SILICON

We investigate impact-ionization processes in Si with use of a realistic band structure. The band structure and the corresponding wave functions, obtained with an empirical pseudopotential method, are used to evaluate the matrix elements for the ionization transitions. The matrix element includes the direct and the exchange terms with the umklapp terms associated with the periodic part of the Bloch function. It is shown that these ionization processes are inherently anisotropic and that it is crucial to take account of this anisotropy in analyzing the ionization processes. The anistropy (wave-vector dependence) of the ionization probability is manifested through the strong restrictions imposed by energy and the momentum conservation during the transition under a realistic band structure.