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 s tudied in detail by comparing its results with corresponding Schrodinger-Po isson calculations, A key element of density-gradient theory is the equatio n of state used to model the response of the electron gas. A variety of suc h equations are considered including new approaches for modeling the liftin g of the conduction band valley degeneracy and for representing exchange-co rrelation effects. On the whole, the theory does remarkably well over a wid e range of biases, oxide thicknesses, and doping concentrations. For shallo w wells and for simulating the density deep inside the semiconductor densit y-gradient theory actually outperforms the quantum mechanical approach unle ss the latter includes large numbers of subbands, When comparing with exper iment, neither theory works that well in a predictive sense because of unce rtainties in the treatment of the oxide and of the gate.