The relationship between the thermal and electrical conductivities in semiconductors is quite lawful, the law of Wiedemann-Franz has only a few exceptions and deviations. But this law is about semiconductors as materials. So the question I needed answered is whether this law also persists when you start fiddling with the electrical conductivity of the semiconductors by making a junction, like a diode, bi-polar transistor or MOSFET. I would say yes, but (from my point of view) material science is sometimes dangerously unintuitive.
As for an example, consider the following case of the schematic in attachment. Is the thermal conductive path between the battery cell and the resistor in which heat is created dependent on whether the MOSFET is on/off or it's duty cycle?
I know electronics, but I am not a materials expert. I don't find any publications regarding the matter. Any answers, publications or ideas on how to set-up an experiment (you should take into account the heat losses when changing between on-and off) are welcome.
Dear Boudewijn,
your question contains some wrong assumptions which I must correct.
The Wiedemann Franz law is valid for metals. It applies definitely not for semiconductors.
The thermal path between battery and resistor is electrically insulating. If the mosfet is on, heat flows from resistance to the battery over the "substrate". The heat flow depends on the thermal conductivity of the substrate and the temperature difference (Fourier equation). The thermal conductivity of a material is proportional to the specific heat, the velocity of sound and the mean free path of phonons. Because the heat transport is phononic (by sound) and not electronic, the Wiedemann Franz law fails.
With Regard
R. Mitdank
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