A Physics-Based Analytical Formulation for the Tunneling Current Through the Base of Bipolar Transistors Operating at Cryogenic Temperatures

A physics-based analytical solution for the direct tunneling current through the base region of bipolar transistors operating at cryogenic temperatures (CTs) is derived. The obtained formulation is continuously differentiable over the entire bias region and contains only few experimentally determinable model parameters, which makes it well-suited for compact circuit modeling. Very good agreement of the new formulation with both a numerical evaluation of the tunneling current integral and experimental data of two silicon-germanium (SiGe) heterojunction bipolar transistor (HBT) process generations is demonstrated.