Multiplication measurements on GaAs p+-i-n+s with i-region thicknesses, w, between 1 μm and 0.025 μm and Monte Carlo (MC) calculations of the avalanche process are used to investigate the applicability of the local ionization theory. The local expressions for multiplication are able to predict the measured values surprisingly well in p+-i-n+s with i-region thicknesses, w, as thin as 0.2 μm before the effect of dead-space, where carriers have insufficient energy to ionize, causes significant errors. Moreover, only a very simple correction to the local expressions is needed to predict the multiplication accurately where the field varies rapidly in abrupt one-sided p+-n junctions doped up to 1018 cm-3. However, MC modeling also shows that complex dead-space effects cause the local ionization coefficients to be increasingly unrepresentative of the position dependent values in the device as w is reduced below 1 μm. The success of the local model in predicting multiplication is therefore attributed to the dead-space information already being contained within the experimentally determined values of local coefficients. It is suggested that these should therefore be thought of as effective coefficients which, despite the presence of dead-space effects, can be still be used with the existing local theory for efficiently quantifying multiplication and breakdown voltages
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