The response function of an Si(Li) detector was calculated by using a Monte Carlo method for photon energies below 10 keV. In the simulation, electron elastic-scattering cross sections calculated using the partial-wave expansion method were used instead of the Born approximation to simulate the electron scattering more accurately. The carrier collection probability near the gold-silicon interface was derived by solving the carrier continuity equation with drift, diffusion and surface recombination by a finite recombination velocity. For two detectors, good agreement was found for low-energy tailing between measured and simulated response functions. The integrated detection efficiency is almost identical with the transmittance in the front gold electrode showing a maximum difference of 2% at the Au M(4)-absorption edge.