Basic principles: Sign of the hole mass

Physics Q&A
1

I’m not sure if this was asked before, but I couldn’t find it anywhere.
In the lecture notes for Semiconductors: Basic principles, we look at the holes as particles. In the section “Properties of holes” you write that m_h<0 from the equation of motion. In the section on “Materials with two bands”, however, you write that m_h > 0 since they are particles in the valence band.

I don’t really get why there are these two different signs for m_h. Is it because one is valid in the conduction band, and one in the valence band? But in that case summing over the masses in the valence band would give a wrong result.

Could you explain why there is this change of sign?

2

I don’t see where it is stated that m_h<0. Instead, we have m_h=-m_e

Note that the sign of the mass is given by the sign of the curvature of the dispersion. So you are correct: the sign of the mass at the bottom of the conduction band is opposite to that at the top of the valence band (because of the opposite signs of the curvatures)

3

Right, so m_h and m_e are actually the effective mass of holes and electrons?
That makes sense, thank you!