HEMT modelling using semi-physical expressions for the equilibrium space-charge parameters of the modulation-doped heterojunction

Simple expressions are derived for the 2-DEG concentration in the lightly doped side and the partially depleted space-charge width on the heavily doped side of a modulation-doped heterojunction under equilibrium. The derivation employs physical reasoning to determine the mathematical form of the expressions and fixes the constants in the form empirically so that the results of the expressions agree with those of numerical calculations. It is shown that the expressions derived enable an easy estimation of the maximum gate voltage swing, and can be used to construct a mathematical representation of the nonlinear gradual saturation segment of the 2-DEG concentration against gate voltage characteristics, for circuit simulation purposes.