A gallium arsenide planar field-effect transistor (f.e.t.) structure is simulated using a particle-mesh computer model. The model incorporates two dimensions in configuration space and three dimensions in k-space; with a full description of the material scattering cross-section which is implemented using Monte-Carlo techniques. The f.e.t. static characteristic has been calculated together with the lumped equivalent-circuit paramters. A comparison is made between devices with and without substrate. Detailed information about electrostatic potential and valley population profiles is presented for the first time. Cole-Cole plots of complex output impedance are used in determining device frequency response.