FDSOI MOS Thermal time constant

MOS devices in IC present process are getting smaller and smaller. The amount of silicon involved in a MOS channel is getting pretty low. So, a question can arise: How fast does a MOS body warm up when some power is suddenly dissipated ? This question is especially of importance for SOI devices since the power has to flow through an oxide layer that exhibits a thermal conductivity 100 times lower than that of silicon. For FDSOI, the MOS body is very thin, reducing further the amount of silicon and speeding up warming.

In order to get an answer to this question, EZMod3D solver was used in the first order complex mode.

A minimal device was used for that study. The process name, the device size and the layers thickness are not disclosed.

At low frequencies, thermal impedance is essentially real and reduces to the device thermal resistance. In this case, thermal resistance appears to be about 300000 K/W. This is quite a large value, but it has to be related to the very small amount of power the minimal device can dissipate.

Now, what happens at higher frequencies ?

Here is the thermal impedance magnitude vs. frequency:

This thermal impedance somewhat looks like a thermal resistance in parallel with a thermal capacitance. However, one can notice that transition from R to C regions takes over a decade. This is much softer than that of a first order R-C cell.

For comparison, here is the impedance of a parallel R-C cell fitted for R and C values together with above curve:

The other point to mention is that at 1 GHz, impedance has dropped only by 30%.

This means that for any signal below 1 GHz, the device temperature cannot be considered constant but changes with signal value !

What about phase lag ?

Here is a plot of phase lag versus frequency:

Again, transition is much smoother than that of a first order RC cell.

Such a frequency response, both in magnitude and phase, can be fitted properly by multiple poles and zeros for an accurate modeling.

In this case, 10 poles and zeros are required, with time constants range from 17.5 us to 37 ps.