A computer simulation model of amorphous silicon thin film solar cells has been developed. Shockley-Read-Hall occupancy statistics are used for the band tail states, and multilevel statistics for the dangling bonds, taking into account their amphoteric character. Model parameters have been defined and checked by modeling a standard a-Si:H pin solar cell (with an a-SiC:H p-layer), both before and after light-induced degradation. The latter is assumed to raise the defect density of the i-layer. The results are in good agreement with experimental data. In order to find the potential of solar cells incorporating high quality SiGe layers with 1.55 eV band gap, we modeled three different types of such devices, a standard pin-solar cell with low band gap, a tandem cell with an a-Si:H-front cell and an a-SiGe:H back cell, and a solar cell with graded material composition, having a band gap profile of the form of a bottle-neck.