Continuous advances in silicon processing technology have enabled devices to be more miniaturised and sophisticated. Most scientific Charge-Coupled Devices (CCDs), for example those used in astronomy, are following this trend; they are being scaled down and their doping profiles are becoming more complicated. Such trends increasingly require the use of three-dimensional (3-D) numerical simulations to provide improved designs. This thesis covers work focused on the three-dimensional simulation of buried-channel (BC) MOSFETs and CCDs. For BC MOSFETs a 1-D analytic model is developed to study their electrical characteristics and this is followed by 3-D numerical simulation work. Geometric-induced physical effects are thoroughly investigated using the 3-D simulation to optimise the scaling factor for the device. This simulation shows that 2-D simulation cannot estimate accurately the electrical characterisations of the narrow-channel and small geometry devices. For BC CCDs two X-ray astronomy CCDs are introduced: EPIC CCD as an open- electrode CCD imager and JET-X CCD. The optical properties of the EPIC CCD, used for ultra-low signal applications, were shown to be critically dependent on the dead layers and optical filter. It was clearly shown, for both devices, that 3-D simulations are useful for analysing charge storage and handling despite the complicated doping profile and sophisticated design structure. The charge handling capability of the JET-X CCD was found to be 9900 (electrons/?.m) using a 1-D analytical model. A 3-D static simulation of the JET-X CCD enabled estimations of the full-well capacity (60040 electrons), different depletion edge positions (<5 % errors) and an optimised output gate voltage (between 3 and 4 V) for a higher charge transfer efficiency and demonstrated routes for optimisation and improvement. A 3-D transient simulation of the same device enabled estimations of the dynamic full- well capacity (61110 electrons), a dark current contribution (<1 electron for a pixel clock cycle of 1.85 ?s) and a charge transfer inefficiency (<0.001 % for a pixel clock cycle of 4.2 ns with a fall time of 0.4 ns). The 3-D simulation work suggests that a higher charge detection efficiency and charge transfer efficiency can be achieved with a higher-resistivity epi-material and a pixel clock cycle with a longer fall time (i.e. >0.4 ns).