Is it possible to label the Debye temperature on a graph of

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The discussion centers on the relevance of Debye temperature in relation to resistivity graphs of semiconductors. Participants question whether the Debye temperature indicates a transition point where semiconductors behave more like metals, particularly where the resistivity curve shifts from minimum to linear. There is confusion regarding the relationship between Debye temperature and resistivity, with references made to various derivations related to heat capacity and electron-phonon interactions. The conversation highlights the complexities in connecting theoretical models to practical observations in materials. Ultimately, the significance of Debye temperature in resistivity analysis remains a point of contention.
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Resistivity. Take this graph for example, is the Debye temperature relavant here? Would the Debye temperature be the point where the semiconductor starts to become like a metal? i.e. where the curve goes from minimum to linear?

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I understand the heat capacity relation i.e. from T^3 to 3nNk but struggling with the resistivity relation.
 
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This temperature is related to the excitation energy of the donors.Why do you think it will be related to Debye temperature?
 
nasu said:
This temperature is related to the excitation energy of the donors.Why do you think it will be related to Debye temperature?

We have done several derivations that have different results for temperatures below and above the debye temperature. But I'm struggling to relate it to the resistivity of a material. Are you saying it would not represent anything significant on the above graph?

thanks for the reply!
 
Derivations of what?
 
nasu said:
Derivations of what?

Einstein’s approximation for the lattice contribution to the heat capacity
Phonon contribution to the thermal conductivity with the temperature
Electron-Phonon scattering: contribution to thermal electronic transport relaxation
Electron-Phonon scattering: contribution to charge electronic transport relaxation
Debye’s model for the lattice contribution to the heat capacity

All these for high and low debye temperatures
 
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