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Consider the following scenario. A material has the E-k band scheme as shown in the figure (extended scheme of zones). Could anyone give me a suggestion regarding the following :

  1. Electrical character of the material with the temperature.
  2. Sign of the Hall coefficient.
  3. Sign of the effective mass.

enter image description here

For the first case (Fermi level is the dotted line that appears for $E_{1}$), I have reasoned as follows:

  • As the conduction band is half-full for the Fermi level, we are dealing with a conductive material.
  • The effective mass is a tensor that describes the influence of internal forces on an electron that is subjected to an external force (usually an electric field). The effective mass is inversely proportional to the curvature of the electronic band, so the effective mass is negative.
  • As the effective mass is negative, the Hall's coefficient is positive.

Would it be so?

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  • $\begingroup$ The Fermi level is the dotted line that appears for $E_{1}$ @ProfM $\endgroup$ Dec 17 '20 at 15:58
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    $\begingroup$ Thanks for the clarification, but you should add this clarification to the question too. In the figure you have 5 different energies, so you must clarify that you are interested in $E_1$. $\endgroup$
    – ProfM
    Dec 17 '20 at 16:03
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As you say, the effective mass is inversely proportional to the curvature. However, it seems to me that $E_1$ corresponds to an inflection point in the band diagram. It means that the curvature and the effective mass change their signs around this point, with an divergent effective mass.

It's quite debatable as it relies on graph reading, but I guess that the point wasn't chosen randomly if this picture comes from some teaching material with the goal of making you think about the concepts at hand.

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  • $\begingroup$ This question was taken from an examination a few years ago. On the other hand, now that you mention it, it is true that $E_{1}$ corresponds to a turning point. What effect does this have on the sign of the effective mass? $\endgroup$ Dec 19 '20 at 19:03

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