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I'm coming from a microelectronics background and I was always taught that mobility of electrons decreases as temperature increases as there are more collisions with lattice atoms that are vibrating.

I recently came across this figure: enter image description here

This seems to indicate mobility increases with temperature first before it decreases -> a parabolic relationship.

In some other places online I found this: enter image description here

For higher dopant concentrations, it appears that the mobility always decreasing with temperature.

Can anyone comment on this and perhaps give a simplified explanation of lattice and impurity scattering for a circuit designer to understand?

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  • $\begingroup$ At low doping level, the impurity density is low. The turning-over point will goes to a much lower temperature, when the mean-free-path of the conduction electron is comparable to the average separation between two adjacent impurities. $\endgroup$
    – ytlu
    Feb 1, 2022 at 19:48
  • $\begingroup$ You will find an excellent explanation here: en.m.wikipedia.org/wiki/Electron_mobility $\endgroup$
    – my2cts
    Jan 23 at 8:57

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I think you are confused about why carrier mobility could increases with temperature (T) rising since this phenomenon is opposite to what you've been always taught.

The fact is the main carrier scattering sources is different within different T. At low T range, the main source is charged impurities (such as ionized donors/acceptors, substitutional impurities, charged surface states) . At high T range, the main source is lattice.

Let's focus on low T range since the mobility behavior looks strange. Actually, there are two competing effects when talking about charged impurity scattering: the charge screening effect that enhance the mobility and charged impurity scattering that lower the mobility. The reason why charge screening effect could enhance the mobility is because the Coulomb potential is screened by the surrounding electrons, thus other electrons will be less influenced by the Coulomb potential which consequently move faster under more thermal energy (which means increased T). As you can see in the second figure, the parabolic relationship become significant under high carrier concentration. For now, you can explain why there is a parabolic relationship exists under high carrier concentration situation.

Additionally, when you compare all the curves in the second figure, it's apparently that the mobility decreases with increased carrier concentration during the whole T range. Thus, all in all, scattering always decreases the mobility, but you have to consider the charge scattering effect under high carrier concentration.

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When initially Temperature increases, oscillation of ions and si atom is so less that electron faces almost no obstacles to travel. Hence mobility increases initially. We should note that mobility is not increasing due to impurity scattering. (Scattering always decreases the mobility). But after T>300k atoms gets desired amount of energy to oscillate and lattice scattering role take place.

Impurity scattering is due to the creation of ions after doping. Whereas the the scattering faced by electron due to si atom's oscillation is lattice scattering.

When doping is done there are certain amount of imperfections appears(there are many kinds of imperfections). Hence impurity scattering increases due to increase in doping.

The second mobility vs T graph provided by you is not complete. People often gets confused in this mobility temp graph, they think before 300k there will be impurity scattering and after 300k there will be lattice scattering but it's not.

What actually happens is:
for T<300K: Dominant scattering mechanism is impurity scattering.

Whereas for T>300K: Dominant scattering mechanism is lattice scattering.

Apology for any mistake.

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