Analysis of the photo voltage decay (PVD) method for measuring minority carrier lifetimes in P-N junction solar cells

Abstract

When the diffusion length of minority carriers becomes comparable or even larger than the thickness of a P-N junction solar cell, the characteristic decay of the photogenerated voltage becomes a mixture of contributions with different time constants. The minority carrier recombination lifetime τ and the time constant l2/D, where l is essentially the thickness of the cell and D the minority carrier diffusion length, determine the signal as a function of time. It is shown that for ordinary solar cells (N+-P junctions), particularly when the diffusion length L of the minority carriers is larger than the cell thickness l, the excess carrier density decays according to exp(−t/τ−π2Dt/4l2), τ being the lifetime. Therefore, τ can be readily determined by the photo voltage decay (PVD) method once D and l are known. For ideal back-surface-field (BSF) cells (N+-P-P+ junctions) under the same circumstances the excess number density of carriers decays purely exponentially as exp(−t/τ). However most BSF solar cells are not ideal, possessing an effective surface recombination velocity seff of 100 to 1000 cm/sec at the high-low junction. Therefore, PVD measurements for BSF cells must be treated with caution and must be supplemented with other nonstationary methods recently developed. These facts are important for a determination of diffusion lengths since steady-state methods are notoriously unreliable when the cell thickness is smaller than the diffusion length. Finally a connection will be made with older work on the same subject.