The temperature dependence of the amplification factor of bipolar-junction transistors

It is widely known that the current gain of the bipolar transistor is degraded by low-temperature operation. However, the temperature dependence of another important parameter, the amplification factor, has not been reported. This brief presents theory and experimental results demonstrating the temperature independence of the Early voltage, and showing as a consequence that the amplification factor is inversely proportional to temperature. Using this information and the bandgap narrowing theory for current gain reduction, predictions and measurements are offered for simple bipolar amplifier circuits. Furthermore, the product of the current gain and amplification factor is proposed as a figure of merit for the transistor. The temperature that optimizes the gain product can be below 100 K for transistors with current gains that are weak functions of temperature.