A physical theory of junction transistors in the collector-voltage-saturation region

A physical theory has been formulated for the operation of junction transistors in the "collector-voltage-saturation" region or "on" region. Transistor characteristics in this region are important for switching applications, Class A or Class B amplifiers, as well as other large signal applications. The formulation is based on the physical consideration that in the "collector-voltage-saturation" region the collector-base junction is forwardly biased, and that the injection level is high. Two-dimensional distributions of carrier densities, current densities, and electric field are obtained for separate portions of the base region. Using these distributions, theoretical expressions are derived for the characteristics of p-n-p and n-p-n transistors including saturation voltage, base input voltage, and dc current amplification factor. Good agreement between theoretical and experimental results indicates that the approximations used in the theory are valid. Numerical calculations have been carried out for the saturation voltage, base input voltage, and dc current amplification factor for different geometrics and material properties. The calculation illustrates the use of the theory for quantitative designs of transistor characteristics.