Characterization and quantitative understanding of subthreshold swing of Si metal–oxide–semiconductor field effect transistors at cryogenic temperatures

The temperature and drain current (ID) dependencies of sub-threshold swing (SS) values of Si n- and p-channel metal–oxide–semiconductor field effect transistors (MOSFETs) with different substrate impurity concentrations ranging from the 1015 to 1018 cm−3 ranges are systematically and experimentally evaluated at cryogenic temperatures. It is found that SS of p-channel MOSFETs tends to increase with decreasing temperature, which contrasts with saturation of SS of n-MOSFETs at cryogenic temperatures, well reported by many previous works. To explain these SS behaviors quantitatively, we employ a density-of-state (DOS) model with tail states consisting of localized states in a deep energy range and mobile states in a shallow energy range, which are attributable to potential fluctuations caused by substrate impurities. It is shown that this model can quantitatively explain the temperature and ID dependencies of SS of both n-MOSFETs and p-MOSFETs. Then, we are assuming that the Si p-MOSFET has a higher density of localized states than the n-MOSFET. Thus, the increase in SS of the p-MOSFETs with decreasing temperature is explained by an increase in the density of localized states at the Fermi level with decreasing temperature, because the density of localized states increases with elevating the Fermi level position in the employed DOS model.