A new quasi-two-dimensional HEMT model has been developed that solves the physical device equations in a more rigorous fashion than previously reported, The model incorporates a quantum mechanical description of the free electron concentration, self-consistently solving the Schrodinger and Poisson equations, The influence of traps and incomplete donor ionization are also included, The conventional one-dimensional charge-control approach is shown to be inadequate for HEMT's and is replaced by a two-dimensional version that more accurately describes the channel dynamics under normal bias conditions. This allows the simulation to accurately model pinch-off characteristics, which are essential for digital, power and low-noise device characterization. The scheme also includes a detailed energy transport model, avalanche breakdown and gate conduction terms, The highly efficient model is applied to the de and microwave characterization of AlGaAs/GaAs and pseudomorphic HEMT's.