Analytic solution of carrier concentration as an explicit function of gate voltage in AlGaN/GaN HEMTs using the Lambert W-function

Simple analytic expressions are presented for the two-dimensional electron gas density and the drain current in a high-electron mobility transistor. These compact expressions, which are based on the Lambert W-function, are continuous over the entire range of interest. The analytic differentiation or integration of the drain current can also be expressed in terms of the Lambert W-function. The expression for carrier density is in close agreement with rigorous numerical calculations while the expression for the drain current presents reasonable agreement with measurements.