Why does high temperature increase delay of CMOS inverter?

Question

I simulated a ring oscillator made of lots of inverters at different temperatures:

I got the following results

@ 25 C

@ 125 C

I think the increment of temperature caused a large propagation delay, thus longer period, but I don't know why the delay of the inverters increases as the temperature increases.

Doesn't the current increase when the temperature is high?

Answer 1

The delay increases at high temperature because carrier mobility decreases. The decrease in carrier mobility causes a larger effect on drain current than the decrease in threshold voltage, so the drain current decreases. As the drain current decreases, the time it takes to charge or discharge a capacitive load increases so we see increased rise/fall times for inverters.

Image from https://www.researchgate.net/figure/Effective-channel-mobility-versus-temperature-characteristics-for-n-and-p-channel-MOSFET_fig2_273393402

Answer 2

Propagation delay is caused by internal resistances and capacitances - simply T = R x C.

As the temperature increases the resistance of some parts of the die increases. The amount of increase depends on the structure.

Again, depending on the structure, the internal capacitance(s) may or may not change (for power MOSFETs they generally hardly change with temperature).