# Does the temperature of a processor influence its energy consumption?

I don't have a very strong background in physics and electrical engineering but just from knowing that the major or basically all energy consumption of a processor comes from switching its transistors and from the the electrical resistance, which is very high I would say as a processor is basically a very thigh cable at very low voltages and very high currents, and that the resistance and hence the wasted heat is lower at lower temperatures, I would conclude, that a processor in a cooler environment also consumes less energy.

This also leads to another other question: assuming that a CPU has a specific power consumption at a specific level of utilisation, would the power consumption be much more than twice as high at "double" utilisation (although this is hard to define in practice) as the overall temperature would increase and the same "work" would lead to more energy loss due to more resistance?

To give a short background on the question: I was wondering if my notebook battery life lasts longer if I'm using it outside in the winter for example. Of course this is hard to answer as there are many other factors like the behaviour of the battery itself at different temperatures and the display, but this has lead to the basic question described above.

• Yes. Higher temperature results in higher resistance. That's why superconductors are so popular. – zx485 Nov 20 '16 at 19:17
• Heat is a form of energy and its not free when being released from a hot CPU. – soosai steven Nov 20 '16 at 22:18
• Temperature almost always effects everything. Or, said another way, everything has a temperature coefficient. But I don't know whether dissipation increases or decreases with temperature. The dynamic power dissipation is proportional to V^2 * C * f, where C is the gate capacitance and f is the switching frequency. So the real question is, does the gate capacitance go up or down with temperature? I don't know. Static dissipation definitely goes up with temperature. – mkeith Nov 21 '16 at 9:18

## 2 Answers

A CMOS chip ideally acts as you suggest with the dynamic power consumption proportional to the switching speed and the square of the power supply voltage (and the static power consumption with clock halted zero).

However, as you try to lower the supply voltage (for reasons obvious from the above) the transistors no longer quite turn off all the way, and an ever larger static consumption appears. This is called subthreshold power leakage and increases with temperature. There is also gate oxide leakage.

There are mitigation techniques, including circuit design and using exotic materials such as high-K dielectrics that can reduce the effect. At one time it was predicted that static power consumption could approach dynamic power consumption but I don't think that has happened.

• The dynamic consumption is proportional to V^2Cf. Does C go up or down with temperature? I am asking because I don't know off hand. – mkeith Nov 21 '16 at 9:06
• @mkeith I don't think it changes much. Silicon dioxide capacitors have a low tempco. – Spehro Pefhany Nov 21 '16 at 15:30

Back in the days I cooled down a 500MHz Celeron-Processor down to -18°C with a self-made water-based-cooling-system connected to a fridge. I could tune its speed up to 650MHz.

Above that, the L2-Cache stopped working which made further cooling irrelevant, because the speed dropped significantly if I disabled it.

So yes, the temperature matters!

How was that possible?

Higher temperature results in higher resistance. That's why superconductors are so popular. So by reducing the temperature I could reduce the resistance of the paths' in the CPU and therefore increasing the speed of the CPU. The basic principle of Overclocking.

If I'd run the CPU at the same speed as before, the power consumption would have dropped accordingly.

Higher temperature -> higher resistance = higher power consumption -> lower possible speed


or the inverse:

Lower temperature -> lower resistance = lower power consumption -> higher possible speed

• The OP asks specifically if temperature matters for energy consumption, not for overclocking. – marcelm Nov 20 '16 at 19:44
• @marcelm: Thank you for your constructive criticism. My answer has not been thorough enough. I improved that aspect. – zx485 Nov 20 '16 at 20:08
• So the appended formulae at the end looks more or less logical, but nevertheless I think that the answer is a bit weird. Although I'm not an expert in these areas as mentioned, I would say that in practice there are mostly other factors than the temperature that are responsible that a CPU works at a given frequency or not. If your assumption is right, it should be theoretically possible to clock a processor at 100 GHz for example if the workload is just low enough, it doesn't produce that much heat respectively wich is obviously not possible. – critop Nov 21 '16 at 16:21
• @critop: You could operate a processor at 100 GHz if you could decrease its operating temperature to a certain level. That's right. Unfortunately this temperature would be below 0 Kelvin, so it's only theoretically possible. AFAIK quantum effects would set a far higher limit, i.e 4Ghz at ~20°C or so(whatever). But my main point stays valid: the lower the temperature -> the lower the resistance -> the higher the speed (of the electrons). – zx485 Nov 21 '16 at 20:31
• In silicon, higher temperatures generally lead to lower resistance (negative temperature coefficient). – mkeith Nov 23 '16 at 8:32