A model, adapted from the Shockley-Queisser detailed balance model to tandem solar cells with a monolithically grown GaAsxP1-x top junction on a Si bottom junction, has been developed. Updated data have been used for the absorption spectrums. Two surface geometries, flat and ideally textured, have been investigated. As an important improvement over existing models, the effects of threading-dislocations-related Shockley-Read-Hall recombinations in the GaAsxP1-x, cell, due to the lattice mismatch between the GaAsxP1-x epilayers and the Si substrate, have been taken into consideration. Auger recombinations in the Si bottom cell and luminescent coupling between the cells have also been considered. For a dislocation-free 2-mu m-thick top cell, maximal theoretical efficiencies of 41.6% and 39.1% have been calculated for a textured and a flat surface, respectively. For threading dislocation (TD) densities below 10(4) cm(-2), the impact of TDs in the GaAsxP1-x layers on the solar cell performances is very limited. With TD densities over 10(5) cm(-2), the top cell open-circuit voltage is reduced, hence the overall efficiency. For TD densities over 4 x 10(6) cm(-2), as the diffusion length of minority carriers in the base gets smaller than the base thickness, the short-circuit current in the top GaAsxP1-x is also reduced, resulting in a decrease in the optimal top cell bandgap. Using non-ideal EQEs and surface recombination rates from published experimental data, the long-term efficiency potential of the investigated technology has been estimated to be similar to 35.1% for an ideally textured GaAsxP1-x/Si tandem cell with a TD density of 10(5) cm(-2) (similar to 33.0% with a flat surface). (C) 2015 Elsevier B.V. All rights reserved.