Equations of state for silicon inversion layers

The accuracy of a generalized diffusion-drift description known as density-gradient theory for modeling the quantized inversion layer on (100) Si is studied in detail by comparing its results with corresponding Schrodinger-Poisson calculations, A key element of density-gradient theory is the equation of state used to model the response of the electron gas. A variety of such equations are considered including new approaches for modeling the lifting of the conduction band valley degeneracy and for representing exchange-correlation effects. On the whole, the theory does remarkably well over a wide range of biases, oxide thicknesses, and doping concentrations. For shallow wells and for simulating the density deep inside the semiconductor density-gradient theory actually outperforms the quantum mechanical approach unless the latter includes large numbers of subbands, When comparing with experiment, neither theory works that well in a predictive sense because of uncertainties in the treatment of the oxide and of the gate.