The discussion revolves around the concepts of holes and electrons in solid-state physics, specifically addressing the charge of holes, their mobility compared to electrons, and the effective mass of holes. The scope includes theoretical explanations and conceptual clarifications related to charge carriers in semiconductor physics.
Participants express differing views on the nature of holes and their charge, with some agreeing on the conceptual framework while others raise questions. The discussion on effective mass and mobility remains exploratory without a consensus.
Participants reference the Drude model and the concept of effective mass, but the discussion does not resolve the implications of these concepts or their mathematical underpinnings.
Defennder said:Consider this in 1D:
We all know that J=nev where n is the concentration of electrons, v is the drift velocity.
Suppose the valence band is completely full of N electrons, then it goes without saying there can be no current flow:
[tex]J_{x} = \sum_i^N -ev_{i} = 0[/tex]
But on the other hand suppose there is one missing electron, one vacancy in the valence band where an electron should be:
[tex]J_{x}=\sum_i^{N-1}-ev_{i} = \sum_i^N -ev_{i} -(-ev_{j}) = ev_{j}[/tex]
Notice that the final expression on the right can be thought of as current due to the drift of a single positive charge, since there is no minus sign. That is why we are justified in thinking that we can treat absence of negative charges as positively charged holes.