Analytical Studies on Effects of Surface Recombination on the Current Amplification Factor of Alloy Junction and Surface Barrier Transistors

The survival factor of minority carriers is one of the important factors which determine the current amplification factor of a junction transistor, and is generally known to be much more affected by the surface recombination of the minority carriers than by the volume recombination in the base region. It is therefore quite necessary in the design of transistors to get an expression of the survival factor ß in terms of the surface recombination velocity, the dimensions of the emitter and the collector electrodes, and the thickness of the base region. Because of the complexity of their geometries, however, analytical expressions of ß have not yet been obtained for alloy junction and other similar types of transistors. In this paper, analytical formulas for various idealized geometries are derived by means of approximating methods. From these results, many useful design data such as the optimum radius ratio of the emitter electrode and the collector are obtained and the effect of curvature of the electrode surfaces is made clear. It is also pointed out that the survival factor can be expressed by four dimensionless quantities, thus establishing the principle of similitude among transistors having different surface recombination velocities and difflerent geometrical dimensions of electrodes. The values of ß calculated from these formulas are in good agreement with the experimental values previously obtained by Stripp and Moore from an analogy of three-dimensional electrolytic conductance.