The Conduction-Diffusion Theory of Semiconductor Junctions

This is a mathematical analysis of the conduction-diffusion equation, which governs the carrier motions in semiconductor materials. The model used for the junction devices is based on the Fletcher—Harrick injection relations at junctions and on the vanRoosbroeck conduction—diffusion equation in bulk regions. The exact solution of this analysis is obtained by numerical computation using the Automatic Taylor Series (ATS) method. Besides the numerical solution, there is a closed-form exact solution for zero recombination; this is the Gunn solution. The limitations of this analysis are those imposed on the Fletcher—Harrick and vanRoosbroeck developments. They are the abrupt-junction condition, and the quasineutrality condition. Satisfaction of the first condition depends on device fabrication. This analysis does not include the effects found in diffused junctions. Satisfaction of the quasineutrality condition depends on the internal electric fields in the devices. This analysis examines these electric fields and keeps watch over its own validity. The characteristics of semiconductor junction devices are analyzed by the conduction—diffusion theory with mathematical uniformity and exactitude. Application of this theory to the p—n and n—n+ junctions yields these results. The characteristics of p—n junctions analyzed here basically agree with the results of previous researchers. The n—n+ junction exhibits a current-saturation effect in the forward bias direction. This is due to a limitation on the injected carrier concentration in this device. The p—n—n+ and n+—n—n+ junctions are analyzed to eliminate metal contacts to the base region, because the quasineutrality condition is violated near these contacts. The three-layer devices have basically the same characteristics as the two-layer diodes. In p—i—n junction devices with long base regions, the quasineutrality condition is violated in the middle of the base region. In such cases, the solutions of Lampert and Rose and of Baron are more appropriate.