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 s_eff 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.