We did a classical Hall Effect experiment where we measured Hall Coef. given by $R_H=\frac{E_H}{J\cdot B}$. The setup was a rectangular Germanium semiconductor placed perpendicular to a magnetic field generated by a large coil.

We did several measurements: First, we applied a current of 2mA and measured the Hall voltage ($E_H \cdot width$) as a function of the magnetic field strength, from which we derived $R_H$. Then we did the same thing, only setting the field constant and changing the current.

We expected to get roughly the same values for $R_H$, but we got totally wild results. We can't figure out or even suggest an hypothesis to explain the data. The figures are attached below, $R_H$ is given in arbitrary units.

Three main features trouble me: a) the big difference in Hall coef. that was observed in the different experiments; b) the fact that it seems to diverge at small magnitudes of the magnetic field; and c) it changes signs passing from negative to positive values of the magnetic field! This as I understand really should not happen unless the conditions are quite exotic.

Any help would be appreciated! Thanks

enter image description here

  • $\begingroup$ The Hall effect, which seems so simple in semi-classical models of metals, is actually quite complicated. The fact that it is complicated basically means that the band structure (Fermi surface, intervalley scattering, etc.) is complicated. As an example, the Hall coefficient in aluminum changes sign as the field increases, indicating that at high fields conduction is dominated by holes (see R. Luck, phys. stat. sol 18, 49 (1966)). $\endgroup$ – Jon Custer Feb 23 '17 at 14:03
  • $\begingroup$ This is just a lab course experiment though, and the same setup has been run over and over again I suppose, so from looking at the results of others it seems that in the examined parameter space the Hall coef. should be pretty much constant. One possibility is that the measurements were not done properly, and then the question is what can result in these drastic differences? Perhaps the orientation of the semiconductor? It was kept constant though. Otherwise, maybe I shouldn't expect it to be constant as you mentioned. Are these abberations relevant in these scales of fields and currents? $\endgroup$ – Yoni Feb 23 '17 at 14:15
  • $\begingroup$ I addressed the big question - is it constant. What happened in your particular lab experiment is up to you to figure out! Half the fun of lab experiments is figuring out what went 'wrong' - if it all just worked there wouldn't be much learning... $\endgroup$ – Jon Custer Feb 23 '17 at 14:27
  • $\begingroup$ I spent the past few days trying deparately to find an adequate explanation for these data. I really did. If you have any useful references or anything I would very much appreciate it. This is not my first lab course, and I know part of the business is trying to figure things out on your own, and I really am trying. But here I am just about willing to give up. I really don't know what to make of it. $\endgroup$ – Yoni Feb 25 '17 at 23:01

I just got the same results for an experiment I did :). I believe that what is going on is that for low magnetic fields the Lorentz force is not strong enough to produce any Hall voltage. This is reflected in an apparent increase in the Hall resistance. This reasoning seems to suggest that as the magnetic field grows the Hall resistance should decrease. However, due to the thermal interactions involved, after the concentration gradient due to the Lorentz force is countered by the concentration gradient due to the collisions between the carriers one reaches a hold. This explains the constant behavior of the Hall coefficient at big magnetic fields.

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