Semiconductor devices are generally analyzed with relatively simple equations or with detailed computer simulations. Most text-books use these simple equations and show device diagrams that are frequently very simplified and occasionally incorrect. For example, the carrier densities near the pinch-off point in MOSFETs and JFETs and the minority carrier density in the base near the reverse-biased base-collector junction are frequently assumed to be zero or near zero. Also the channel thickness at the pinch-off point is often shown to approach zero. None of these assumptions can be correct. The research in thesis addresses these points. I simulated the carrier densities, potentials, electric fields etc. of MOSFETs, BJTs and JFETs at and near the pinch-off regions to determine exactly what happens there. I also simulated the behavior of the quasi-Fermi levels. For MOSFETs, the channel thickness expands slightly before the pinch-off point and then spreads out quickly in a triangular shape and the space-charge region under the channel actually shrinks as the potential increases from source to drain. For BJTs, with collector-base junction reverse biased, most minority carriers diffuse through the base from emitter to collector very fast, but the minority carrier concentration at the collector-base space-charge region is not zero. For JFETs, the boundaries of the space-charge region are difficult to determine, the channel does not disappear after pinch off, the shape of channel is always tapered, and the carrier concentration in the channel decreases progressively. After simulating traditional sized devices, I also simulated typical nano-scaled devices and show that they behave similarly to large devices. These simulation results provide a more complete understanding of device physics and device operation in those regions usually not addressed in semiconductor device physics books.