Estimation of Volume Lifetimes in Small Square Pillars of Silicon using Empirical Formulae^*

Effective lifetimes measured by the frequency-dependent surface photovoltage method, become, more or less, shorter than volume lifetimes in a square pillar because of the carrier recombination at the lateral surfaces of the pillar. The volume lifetime in the pillar can be estimated using empirical equations based on the position-dependent effective lifetimes on the pillar surface. Thus, the maximum effective lifetime of 18.1 ms in an n-type silicon pillar of 20 x 20 x 80 mm(3) corresponds to a volume lifetime of 22.7 ms. The estimated lifetime is, however, longer than that of 18.0 ms obtained by the photoconductive decay method. The reason for this is discussed.