A Nonlinear Diffusion Analysis of Charge-Coupled-Device Transfer

Abstract

In those charge‐coupled devices (CCD's) which have regions under each electrode which are substantially free of externally applied tangential electric fields, charge motion takes place by space charge assisted diffusion, and this relatively slow process represents a limitation to the operating frequency of CCD's with large plates. In this paper, subject to certain approximations, the equations of motion for CCD charge transfer have been derived, yielding a nonlinear diffusion equation. The solution of this equation by a stable finite difference scheme is described, and the solutions are applied to predicting the operating characteristics of CCD's. The results in synopsis are: The n‐channel devices will have lower losses at a given frequency than the p‐channel devices, and a higher upper frequency limit. Higher amplitude signals (more charge) yield lower losses. Losses can be reduced an order of magnitude by using zero's which carry a substantial amount of charge. For example, with 2‐MHz clocking of a 25‐μm plate (pad), p‐channel 2‐phase device, a 2‐volt one is diminished by 4 percent per transfer with empty zero's, but with 1‐volt zero's, the diminution is 0.26 percent per transfer. Reasonably efficient CCD operation should be possible up to the 50‐MHz range using contemporary design tolerances. Diffusion is important for reaching high transfer efficiencies. The frequency limitations described in this paper can be overcome by using a structure in which the distance between the electrodes and transferring charge is comparable to the electrode width and spacing.

<title>CCD Image Simulation</title>

“…The average number of thermal noise carriers is n TNC = (N+l-i) N^NT (4) where N is the total number of CCD elements in the column, i is the CCD pixel position in the column, N is the number of clock phases and N is the number of thermally generated carriers during one integration time in one pixel.…”

Investigation of Charge Coupled Devices for Signal Processing.

“…For very high surface potential values, E also depends on the surface potential [14]. This dependence is not considered here.…”

Analysis of Field-Aided, Charge-Coupled Device Transfer

“…3, we assume that the charge can be described by a charge density q(x, t). Here, χ is the distance under the plates (see Fig.…”

“…A calcu lation of the motion of charge in a CCD, starting from the coupled, nonlinear Poisson and charge-conservation equations and taking into account the full geometry of the device, has so far proved impossible. However, Strain and Schryer 3 and, independently, Kim and Lenzlinger 4 developed and studied an approximate, one-dimensional model of charge transfer in a CCD. The original analysis considered motion owing only to diffusion and the mutual repulsion of the charge carriers.…”

“…1 Slower but similar results are obtained for surface devices. 3 solved, by the method of finite differences, a transport equation quite similar to the one we study here. However, their method of solution proved inadequate when applied to our equation.…”