In this paper, an analytical model accounting for the quantum effects in MOSFETs has been developed to study the behaviour of $high-{kappa}$ dielectrics and to calculate the threshold voltage of the device considering two dielectrics gate stack. The effect of variation in gate stack thickness and permittivity on surface potential, inversion layer charge density, threshold voltage, and $I_D-V_D$ characteristics have also been studied. This work aims at presenting a relation between the physical gate dielectric thickness, dielectric constant and substrate doping concentration to achieve targeted threshold voltage, together with minimizing the effect of gate tunneling current. The results so obtained are compared with the available simulated data and the other models available in the literature and show good agreement.