In this paper, we have studied and developed an analytical model for the inversion layer quantization in nano-metal oxide semiconductor field effect oxide (MOSFET) using the variation approach. Explicit surface potential solutions have been used in the model to accurately model the inversion layer quantization. Capacitance/voltage and Drain voltage/current models in ultra thin oxide MOSFETs have been using charge sheet approximation. Drain induced barrier lowering (DIBL) and mobility reduction effects are included in the model developed and hence extended to nanometer scale. Results predict that the inversion layer quantization results in a reduction in drain current and degradation of gate capacitance. The results match closely with the BSIM 5 models proving the accuracy of the model.
