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Amorphous/crystalline silicon heterojunction solar cells, TCO/a-Si:H(n)/c-Si(p), are investigated by means of numerical computer simulation. The influence of (1) the a-Si:H(n) emitter thickness, (2) the defect density of the emitter/wafer interface and (3) the TCO/emitter front contact system on the solar cell-performance is studied and compared with experimental results. The use of an intrinsic a-Si:H(i) buffer layer and of a p-doped a-Si:H(p) back surface field layer is addressed, modelling TCO/a-Si:H(n)/a-Si:H(i)/c-Si(p)/a-Si:H(p) solar cell structures. Some general design criteria for a-Si:H/c-Si heterojunction solar cells are derived, suggesting an optimum emitter thickness for a given (measured) front contact TCO/emitter built-in potential.