Collector Transport in SiGe HBTs Operating at Cryogenic Temperatures

Quasiballistic electron transport in cryogenic SiGe HBTs studied using an exact, semi-analytic solution to the Boltzmann equation

“…Lastly, the asymptotic solution is restricted to values of average Knudsen number such that 2 c 1 < 1, which limits our analysis to a minimum base width of 40 nm for the chosen scattering rates. However, DC non-idealities were reported in devices with base widths on this order, [25][26][27] and again our analysis applies. Given these considerations, we conclude that quasiballistic transport is not responsible for non-ideal cryogenic DC characteristics of SiGe HBTs.…”

“…[50], the only effect of a field term is to modify M and thus change the value of c 1 , and our conclusions are robust to such changes. Second, modern devices may have base doping levels exceeding 10 19 cm −3 [25,27,51] to minimize base resistance and prevent carrier freeze-out. This high level of doping leads to degenerate carrier statistics, while we have assumed non-degenerate statistics.…”

“…Prior works have suggested that direct tunneling from the emitter to the collector is a possible origin of non-idealities in devices with narrow base widths ∼ 10 nm [25,26]. However, non-ideal cryogenic transconductance has been observed in first-generation SiGe HBTs with base widths on the order of 100 nm [24,27] for which the direct tunneling current is expected to be negligible. Further, non-idealities observed in the hole current cannot be explained by direct tunneling as the hole potential barrier terminates at the poly-Si emitter contact, which is hundreds of nanometers away from the base-emitter junction.…”

“…The latter effect has been phenomenologically described using an elevated electron temperature that is taken as the effective temperature for thermionic emission at the base-emitter junction [10,11,24]. As base widths were scaled further down to ∼ 20 nm in recent years, direct tunneling of electrons was reported to contribute to the collector current at biases approaching the built-in potential [25][26][27].…”

“…First, both base and collector currents exhibit non-idealities at cryogenic temperatures [11,25], and holes are unlikely to transport ballistically or tunnel across the emitter region. Further, at base doping levels above ∼ 3 × 10 18 cm −3 common in modern devices, [25,27] ionized impurity scattering is expected to dominate. Therefore, quasiballistic transport is not expected to be markedly more pronounced at cryogenic temperatures relative to room temperature as evidenced by the weak temperature dependence of the minority carrier mobility [11,[28][29][30].…”