The merits and limitations of local impact ionization theory

Multiplication measurements on GaAs p(+)-i-n(+)s with i-region thicknesses, w, between 1 mu m and 0.025 mu m and Monte Carlo (MC) calculations of the avalanche process are used to investigate the applicability of the local io nization theory. The total expressions for multiplication are able to predi ct the measured values surprisingly well in p(+)-i-n(+)s with i-region thic knesses, w, as thin as 0.2 mu m before the effect of dead-space, where carr iers have insufficient energy to ionize, causes significant errors, Moreove r, only a very simple correction to the local expressions is needed to pred ict the multiplication accurately where the field varies rapidly in abrupt one-sided p(+)-n junctions doped up to 10(18) cm(-3). However, MC modeling also shows that complex dead-space effects cause the local ionization coeff icients to be increasingly unrepresentative of the position dependent value s in the device as w is reduced below 1 mu m. The success of the local mode l in predicting multiplication is therefore attributed to the dead-space in formation already being contained within the experimentally determined valu es of local coefficients. It is suggested that these should therefore be th ought of as effective coefficients which, despite the presence of dead-spac e effects, can be still be used with the existing local theory for efficien tly quantifying multiplication and breakdown voltages.