An Improved Analytical Model for Carrier Multiplication Near Breakdown in Diodes

The charge carrier contributions to impact ionization and avalanche multiplication are analyzed in detail. A closed-form analytical model is derived for the ionization current before the onset of breakdown induced by both injection current components. This model shows that the ratio of both injection current components affects the multiplication factor at relatively low fields before breakdown, but does not affect the reverse breakdown voltage. Furthermore, the model indicates that in case the ionization coefficients of electrons and holes are quite different in value, which depends upon the semiconductor material, the ionization coefficient of the charge carrier with the highest value can be extracted at those low fields. The one with the lowest value can be obtained by fitting the current close to breakdown. The model is compared and verified with TCAD simulations, and to some extent with experimental data, for silicon p-i-n diodes.