Discretization problem for multidimensional current flow

An examination is made of discretization methods for the two-dimensional current continuity equation used in device simulation. The authors have introduced the Baliga-Patankar discretization scheme to a device simulator for the first time and compared this scheme with the popular Scharfetter-Gummel scheme by using silicon n⁺-p diode current-voltage characteristics. Test computation reveals that the two schemes result in a 16% difference in the current values for 1.5 V of forward bias and a two-dimensional n⁺-p diode structure. The Baliga-Patankar scheme is rather insensitive to mesh, compared with the Scharfetter-Gummel scheme. On the other hand, the two schemes result in the same current-voltage characteristics for a one-dimensional diode structure. These results originate from the one-dimensional nature of the Scharfetter-Gummel scheme for drift dominant flow. The Baliga-Patankar scheme is robust for the two-dimensional current flow case, since this scheme defines a current density vector within each element