We present a one-dimensional simulation study of the capacitance-voltage (C-V) and current-voltage (I-V) characteristics in MOS devices with high mobility semiconductors (Ge and III-V materials) and non-conventional gate stack with high-κ dielectrics. The C-V quantum simulation code self-consistently solves the Schrödinger and Poisson equations and the electron transport through the gate stack is computed using the non-equilibrium Green's function formalism (NEGF). Simulated C-V characteristics are successfully confronted to experimental data for various MOS structures with different semiconductors and dielectric stacks. Simulation of I-V characteristics reveals that gate leakage current strongly depends on gate stacks and substrate materials and predicts low leakage current for future CMOS devices with high mobility materials and high-κ dielectrics.