The validity of the depletion approximation applied to a bulk channel charge-coupled device

The solution of the equations which determine the potential profile in bulk channel charge-coupled devices (BCCD´s) in the presence of a nonuniform fixed impurity concentration and mobile charge in the channel is quite complex. A major simplification results from the assumption that the mobile charge completely neutralizes the fixed impurity charge over a region of space surrounding the potential minimum. It is shown in this paper that, based upon physical argumentS, this assumption must give results accurate to within 0.1 V for the value of the potential minimum. Further, it is possible to accurately predict the region in the channel within which virtually all of the free charge must reside. Thus these two important design parameters can be deduced from the simple depletion approximation with an accuracy good enough for most practical applications. The validity of the physical argument is demonstrated by the close agreement of results based upon this approximation with results obtained on the same structures by numerical integration, Comparison is also made with results previously published by other authors. Agreement is generally satisfactory but in some cases the discrepancies are greater than can be readily explained.