Understanding and resolving the discrepancy between differential and actual minority carrier lifetime
Differential light-biased dynamic measurements of charge carrier recombination properties in semiconductors have long been known to yield only differential rather than actual recombination properties. Therefore, the determination of injection-dependent recombination properties from such measurements was previously found to require integration over the entire injection range. Recent investigations of the phase shift between a time-modulated irradiation of silicon samples and excess carrier density reveal a striking analogy to the above findings: the phase shift is greater than the actual effective carrier lifetime in the case of a positive derivative of lifetime with respect to excess carrier density, and vice versa. This work attempts to rearrange the mentioned previous findings in a quantitative theoretical description of light-biased dynamic measurements of effective carrier lifetime. Both light-biased differential lifetime measurements as well as harmonically time-modulated methods without additional bias light are shown to represent a limiting case in a general treatment of light-biased dynamic lifetime measurements derived here. Finally, we sketch a way to obtain actual recombination properties from differential measurements-referred to as a differential-to-actual (d2a) lifetime analysis, which does not require integration over the entire injection range.