The potential in a charge coupled device with no mobile minority carriers and zero plate separation

A two-dimensional analysis of the potential in charge coupled devices is presented. It is assumed that there are no mobile minority carriers, that the plate separation is zero, and that the plate voltage does not vary with time. The depletion layer approximation is used to linearize the equations, which are then solved exactly with the use of Fourier series. Both surface and buried channel devices are analyzed. These solutions can typically be evaluated on a computer in less than a tenth of the time it takes to obtain a solution by the method of finite differences. The solutions obtained here provide an important tool for the designer of charge coupled devices. In addition to describing the method of obtaining the solutions, we evaluate them to show the effects of a number of different design parameters, and compare the cost of these solutions with the cost of obtaining finite difference solutions.