Electron Distribution in Degenerate Semiconductors

As we’ve discussed, to get the right density of states we should replace m by me . In addition, the energy that appears in the square root in the density of states really came from changing variables from momentum to energy. At the bottom of the conduction band, the electrons presumably have very little momentum. That is, the first state to be filled corresponds to an electron wave which is a standing wave made up of the smallest possible momentum components. The energy ǫc is negative and is mostly due the interactions with the atoms (remember, before the atoms formed a crystal, the atomic state that gave rise to the conduction band was a bound electronic state). The upshot of all this is that we should replace the energy in the density of states expression by ǫ − ǫc and the integral should start at ǫc. We have