A flux-based study of carrier transport in thin-base diodes and transistors

Carrier transport in pn-junction is re-examined using McKelvey\´s flux method. A simple but physically based treatment of carrier transport leads to new expressions for the "law of the junction," quasi-Fermi level, I-V characteristics, base transit time, and probability of carrier backscattering from the space charge region, which are valid from the ballistic through the diffusive regimes. Comparison with Monte Carlo simulation shows that the deduced backscattering rate well describes the bias dependence. For silicon pn-junctions, the backscattering rate under reverse bias conditions is less than 5%, satisfying the Bethe condition of thermionic emission, while it rapidly increases with forward bias until drift-diffusion governs the transport. The effect of thin-base transport and backscattering on the current, carrier velocity, and distribution function is also investigated. It is found that for a base thickness less than 50 nm even silicon transistors enter the quasi-ballistic transport regime. These results should prove useful not only for fundamental understanding of the pn-junction transport, but also for careful design of advanced transistors.