Hi,
I’m having trouble determining when the effective mass and group velocity of electrons and holes are positive or negative. In some exercises (1.1, 1.2, 2.2, and 3.1), the velocity for both holes and electrons is the same, but the effective mass is opposite. In other exercises, the velocities have opposite signs, while the effective masses are the same. I don’t understand the rationale behind this. My approach is to substitute the given dispersion relation into the formulas and calculate them for electrons, then make their signs opposite for holes, but this doesn’t always give me the right signs.
When you use the formula for the velocity you have to take into account that you’re not just substituting the energy E with Eh but also the momentum (expressed in k).
Since this momentum factor also carries a negative sign, because the k vector of the missing electron should be the opposite of the k of an electron. So they cancel out. For effective mass the k vector is squared you don’t that negative sign.
I got it now, thank you very much!