Computation of electron and hole quasi-Fermi levels in polycrystalline silicon films under uniform illumination and zero bias

Numerical computation of quasi-Fermi levels (QFL) is carried out in a polycrystalline silicon film under uniform illumination and zero bias. This analysis is based on a single trap level at the grain boundary (GB) and Shockley-Read-Hall recombination kinetics. Mobility values, approximately one tenth those of the bulk values, are used, and they are assumed to be constant throughout the entire grain-GB region. Results show that considerable bending of the QFL occurs in the vicinity of the GB, and this bending δ is dependent both upon illumination levels as well as on grain size. The maximum bending, δ
p
∼ 2.5 kT/q for majority-carrier QFL and δ
n
∼ - 10 kT/q for minority-carrier QFL, is found for a grain size of ∼-0.33 µm and a doping of 2.9 × 10
¹⁶
cm
^-3
. The GB diffusion potential V
b
decreases by as much as 14 kT/q with illumination for large grains; but, for grains smaller than ∼0.2 µm, v
b
is insensitive to illumination up to 5 suns.