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Currently, I'm taking a course in modern physics experiments and last week I was asked to study the hall effect in a semiconductor. One of the experiments was with a germanium chip where a steady current of $20\,mA$ was flowing and with a uniform magnetic field going through it, standard hall effect setup. The variable that we controlled was the temperature of the chip, we started at room temperature (300 K) and heated it up to 420 K, meanwhile reading off the hall potential $V_{hall}$. Here is the result:

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$V_{hall}$ initially increased with the temperature increase but suddenly, somewhere between 380-400 K, it started to drop. We learned that $V_{hall}$ should obey this equation:

$V_{Hall} = \frac{IH}{enw}$

Where I is the current, H is the magnetic field, e is the elementary charge, n is the density of the charge carriers and w is the width of the chip. So I did some research and found this:

As you know hall coefficient depends on the carrier density and type of carriers,So in metals electrons scattering increases with phonons with increase in temperature so the free electron density changes.

Raising the temperature should raise the number of phonons that will scatter the charge carriers and thus $n$ will drop, raising the value of $V_{hall}$. OK, my data supports this between 300-400K. My question is: why it started to drop at higher temperatures? I researched for it and couldn't find the answer.

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  • $\begingroup$ In a semiconductor, carrier concentrations are strong functions of temperature. $\endgroup$ – Jon Custer Jun 20 at 20:17
  • $\begingroup$ Jon, do you have an equation that correlates carrier concentration to temperature? $\endgroup$ – Tandeitnik Jun 20 at 20:58

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