A physically based, quantum mechanical (QM) model is presented for simulating low frequency gate C– V characteristics of MOS devices on arbitrary substrates including interface trap ( D it) effects. MOS electrostatics is determined from the self-consistent solution of one-dimensional Schrödinger’s and Poisson’s equations considering wave function penetration into the gate dielectric. The effects of strain and/or the variation of material composition in each layer of MOS structures on non-conventional substrates are also included in the model. The proposed model can support arbitrary D it distributions (both donor and acceptor types) within the entire bandgap as well as within the conduction and the valence bands. Comparisons with two other existing C– V models are also made. Numerical results show that for accurate simulation of the low frequency C– V characteristics, the energy distributions of the D it over the entire bias range and a model that considers QM effects with wave function penetration are necessary. Excellent agreement with published experimental data for MOS structures on Si, Ge and III–V substrates is achieved through appropriate selection of the D it distributions. The proposed model can be used to extract D it profiles of MOS structures on alternative substrates by comparing with measured low frequency C– V characteristics and to verify the accuracy of D it profiles extracted using other techniques.