Analysis of the early voltage in bipolar transistors

The Early voltage of the bipolar transistor is calculated considering the current gain of the device due to the emitter injection efficiency as well as the volumetric recombination in the base. The impurity profile in the base is assumed to be exponential. The calculated values and the measured values of the Early voltage VAare seen to be in good agreement. Seven high-voltage transistors having a wide range of physical and device parameters were taken for the experimental verification. The Early voltage is seen to increase with the increase in the diffusion length of minority carriers in the base where as it decreases when the emitter Gummel number rises. Curves are also plotted showing the effect of other parameters on VA. The values of VAare also calculated when the minority-carrier lifetime in the base is infinite and these values are compared with the corresponding measured values. As a check on the analysis, comparison is made between the calculated and the measured values of the Early voltage of the devices in the inverse mode of operation. The agreement is good.