In this paper by using an L[sup ∞] estimate for elliptic equations, we study the well-posedness of the stationary semiconductor equations arising from modeling a nondestructive testing technique LBIC. It is shown that when the extra source term is small, the system has a unique weak solution, and the solution is continuously dependent on this source term. The validity of an approximate model derived for the study of the inverse problem is established. The existence result is then extended to the case of constant mobilities without the assumption on the size of the source term.