On the Accuracy of the Depletion Layer Approximation for Charge Coupled Devices

1972 A m e r i c a n T e l e p h o n e a n d T e l e g r a p h T H E BELL SYSTEM TECHNICAL JOURNAL Vol. 51, No. 7, S e p t e m b e r , 1972 Printed in U.S.A. Company On the Accuracy of the Depletion Layer Approximation for Charge Coupled Devices By J. M c K E N N A and N. L. SCHRYER ( M a n u s c r i p t r e c e i v e d F e b r u a r y '28, 1972) In this paper we examine the accuracy of a variant of the depletion layer approximation as used in the analysis of the electrostatic potential, in the absence of mobile charge, in various charge coupled devices. The approximation is a linearization of the nonlinear potential equations and is important in the numerical solution of two-dimensional problems. A one-dimensional model is solved both exactly and by means of the depletion layer approximation and the two results are compared. We conclude that this variant of the depletion layer approximation is excellent for buried channel devices, and adequate though not as good for surface devices. Some criteria are given which indicate the excellence of the approximation and can be used to estimate errors in two-dimensional calculations. The purpose of this paper is to discuss the accuracy of a variant of the well known depletion layer approximation 1,2 used in the analysis of the electrostatic potential, in the absence of mobile charge, in various charge coupled devices (CCD's). 3,4 The approximation is a linearization of the nonlinear potential equations and is important in the numerical solution of two-dimensional problems.