An investigation is carried out into the relation between impact ionization threshold positions and the detailed band structure of a number of semiconductors. The band structures of the semiconductors investigated are reproduced, from the data published by previous workers, by the Empirical Pseudopotential Method (EPM). From these detailed band structures, the impact ionization threshold positions are calculated by a method developed in the present work, referred to as the Envelope Method, and are compared with the values calculated by using two different approximate band structure models. From the EPM, the plane-wave expansions of the wavefunctions of the electron states involved in each impact ionization threshold are then calculated. These wavefunctions are then used to evaluate the sizes of the matrix element (overlap integral) of the coulomb interaction corresponding to each threshold position determined. The relative significance of the threshold positions, particularly the lowest threshold positions, are compared with each other to determine the lowest significant threshold position. It is shown that it is dangerous to rely on impact ionization threshold values determined by approximate band structure models, and that realistic band structures should be used which are in substantial agreement with experimental data. It is also shown that it is necessary to consider the sizes of the matrix element of the coulomb interaction, since many impact ionization threshold positions have corresponding matrix element sizes which are insignificant.
|Date of Award||1975|