TEMPERATURE INVERSION

TEMPERATURE INVERSION:

Traditionally MOSFET drive current (ID) reduced with increasing temperature. Hence for most cases worst case delay corner used to be high temperature (100C or higher, depending on target application). With transistor scaling, VDD and Vt have scaled but not as aggressively as the rest of the parameters (such as gate oxide thickness, channel length etc.). If you look at the MOSFET drive current equation,

So, ID varies linearly as u (mobility) and (V_GS-V_T)² or the overdrive voltage. Both mobility and Vt reduce with increasing temperature and vice versa. Interestingly, current is dependent on difference between Vg and Vt. So there is contention between mobility and the (Vg-Vt) term, and the one with more impact on the final current will determine if drive current increases or decreases with increasing temperature. For scaled nodes, i.e. at lower technologies VDD has scaled to values like 0.9V or lower, while Vt has not scaled as aggressively (0.3~0.4V), because of which even though mobility improves at low temperature, the increasing Vt and hence reducing (Vg-Vt) has a greater impact on the current, resulting in less drive current at lower temperature than at higher temperature. Hence, at scaled technology nodes, the low temperature becomes the SLOW corner, not HIGH temperature, especially for the HVT devices. This phenomenon is known has inverse temperature dependence in MOSFETs.