This project is primarily concerned with the incorporation of quantum effects into physical models for heterojunction field effect transistors. Several simulations have been developed including a one-dimensional Schottky-gate model which self-consistently solves the effective mass Schrodinger equation with Poisson’s equation. This model employs a fast, accurate and robust solution algorithm based upon an expanded Newton scheme. This work is extended to two-dimensions, permitting charge transport and hence adding the current-continuity equation. All three equations are solved under non-equilibrium conditions. Finally a quasi-two-dimensional HFET model has been written, also including quantum mechanics which produces excellent agreement with measured characteristics. As a rigorous solution of the full two-dimensional Schrodinger equation and corresponding transport equation is very demanding and computationally expensive the problem has been simplified to by assuming the electron wavefunction to take the form of Bloch, or travelling wave solutions is the directions parallel to the heterojunction interface is then solved by taking multiple one-dimensional solutions sampled at various positions throughout the device. This new approach requires alternative solution algorithms to be developed since the conventional schemes are not applicable. This thesis reviews the physics behind semiconductor heterojunctions, discusses the solution schemes used in the models and presents results from the one-dimensional, two-dimensional and quasi-two-dimensional simulations.