Modeling of Silicon Bipolar Transistor's Current Gain at Cryogenic Temperatures Down to 40 K

This paper presents a modeling approach for predicting the DC current gain of Silicon Bipolar Junction Transistors (Si BJT) at temperatures between 40 K and 300 K using a TCAD environment. The study demonstrates that accurate modeling cannot be achieved solely by adjusting the technological parameters but requires modifications to physical models, particularly bandgap narrowing (BGN) and Shockley-Read-Hall (SRH) recombination. A reduced emitter doping concentration, which decreases BGN effects, is associated with higher DC current gain. Also, a lower base doping is shown to enhance DC current gain below 100 K due to reduced dopant ionization. However, these modifications must be carefully optimized to prevent base punchthrough. Standard Bennett-Wilson BGN model was modified to align with the experimentally determined temperature dependence of DC current gain below room temperature. Carrier lifetime adjustments in the SRH recombination model improved the agreement between simulations and measurements at 300 K. The model was validated by comparing simulated DC current gain values from 300 K to 40 K with measurements of the Horizontal Current Bipolar Transistor (HCBT), which recently demonstrated DC current gain recovery at cryogenic temperatures. The proposed modeling approach significantly improves the accuracy of HCBT DC current gain predictions compared to previous reports.