Quasi-three dimensional modeling of functionally-integrated elements of large-scale integrated circuits

Functional integration allows a substantial reduction in the number of metallized connections and contact areas to the individual regions of a semiconductor structure, and realization of the basic connections between the elements within the semiconductor volume. Planning of a functionally integrated structure (FIS), which assures device parameters optimum for circuit engineering applications, is unthinkable without consideration of sufficient precise machine models. A series of models concerned with the special features of construction of FIS of various types was developed. A quasi-three dimensional model is presented of the functionally integrated elements of a bipolar BIS, which are multilayer semiconductor structures with an arbitrarily arranged diffused region and metallized contacts, controlled by a current or voltage. The model is described by a system of differential equations in partial derivatives of the elliptical type with integral limitations. A numerical algorithm uses a Newtonian procedure of quasilinearization in conjunction with a block method of upper relaxation. The model is realized in FORTRAN IV for a unified system of computers, intended to solve a wide range of problems which originate during planning of BIS, in particular choice of the optimum versions of topology, routes, and the electrical regime of the elements.