Transport equations in heavily doped silicon, and the current gain of a bipolar transistor

Abstract The Fermi level and effective density of states are calculated for heavily doped silicon, using methods similar to those of Kleppinger and Lindholm and Van Overstraeten et al. For the case in which Boltzmann statistics can be applied to both types of carriers, modified transport equations are obtained in terms of two “heavy doping parameters,” which measure the magnitude and skewness of the effective forbidden band. These results are applied to the calculation of the d.c. current gain of a diffused bipolar transistor. We obtain reasonable current gain values without employing short carrier lifetimes, and our numerically calculated dependence of the current gain on injection level is reasonable. However, the quantitative accuracy of our calculations is limited by several factors.

[1]  W. D. Ryan,et al.  Two-dimensional analysis of lateral-base transistors , 1971 .

[2]  D. P. Kennedy,et al.  Calculations of impurity atom diffusion through a narrow diffusion mask opening , 1966 .

[3]  D. P. Kennedy,et al.  Minority carrier injection characteristics of the diffused emitter junction , 1962, IRE Transactions on Electron Devices.

[4]  F. Stern.  Effect of Band Tails on Stimulated Emission of Light in Semiconductors , 1966 .

[5]  P. Dubock,et al.  D.C. numerical model for arbitrarily biased bipolar transistors in two dimensions , 1970 .

[6]  E. Kane,et al.  Thomas-Fermi Approach to Impure Semiconductor Band Structure , 1963 .

[7]  D. E. Thomas,et al.  Diffused emitter and base silicon transistors , 1956 .

[8]  F. Stern.  Optical Absorption Edge of Compensated Germanium , 1971 .

[9]  J. Slotboom.  Iterative scheme for 1- and 2- dimensional d.c.-transistor simulation , 1969 .

[10]  H. D. Man,et al.  The influence of heavy doping on the emitter efficiency of a bipolar transistor , 1971 .

[11]  T. N. Morgan.  Broadening of Impurity Bands in Heavily Doped Semiconductors , 1965 .

[12]  W. Kauffman,et al.  The temperature dependence of ideal gain in double diffused silicon transistors , 1968 .

[13]  Raya Mertens,et al.  Transport equations in heavy doped silicon , 1973 .

[14]  R. Dingle.  XCIV. Scattering of electrons and holes by charged donors and acceptors in semiconductors , 1955 .

[15]  Dale Buhanan.  Investigation of current-gain temperature dependence in silicon transistors , 1969 .

[16]  F. Lindholm,et al.  Impurity concentration dependent density of states and resulting fermi level for silicon , 1971 .

[17]  Mathematical Simulation of the Effects of Ionizing Radiation on Semiconductors , 1972 .