An accurate numerical steady-state one-dimensional solution of the P-N junction

Abstract A numerical method of solution of the fundamental semiconductor steady-state one-dimensional transport equations, already available in the literature, is improved and extended, and is applied to a single-junction device. A reduced set of ‘exact’ relations is derived directly from the fundamental set with none of the conventional assumptions or approximations, and is solved numerically by a simple iterative procedure. Freedom is available in the choice of the doping profile, recombination law, mobility dependencies, injection level, and boundary conditions applied solely at the external contacts. In spite of the generality of the original method, its analytical formulation is shown to be unsuitable for generating a sound numerical algorithm sufficiently acccurate and valid for high reverse-bias conditions. Difficulties and limitations are exposed, and overcomeby an improved formulation extended to any bias condition. Emphasis is on the selection of a numerical algorithm sufficiently sound and efficient to cope with the several fundamental difficulties present in the numerical analysis, and on achieving a high degree of accuracy in the final results (the most delicate problem). As a simple application of the improved formulation, ‘exact’ and first-order theory results for an idealized structure are presented and compared. The poorness of some of the basic assumptions of the conventional first-order theory is exposed, in spite of a satisfactory agreement between the exact and first-order results of the terminal properties for particular bias conditions. The computation time for the achievement of one set of very accurate solutions for a specified applied voltage amounts to approx 1 min on an IBM 7094/7040 shared-file system.

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