潘振林--A.doc

CHAPTER 3 The Semiconductor in Equilibrium
Figure energy-band diagram showing (a) the discrete acceptor energy state (T=0k) and (b) the effect of some acceptor states being ionized creating free holes (T>0k).
Ionization Energy
We can calculate the approximate distance of the donor electron the donor impurity ion, and also the approximate energy required to elevate the donor electron into the conduction band .This energy is referred to as the ionization energy. We will use the Bohr model of the atom for these calculations .The justification for using this model is that the most probable distance of an electron from the nucleus in a hydrogen atom, determined from quantum mechanics, is the same as the Bohr radius .The energy levels in the hydrogen atom determined from quantum mechanics are also the same as obtained from the Bohr theory.
In the case of the donor impurity atom, we can visualize the donor electron orbiting the donor ion, which is embedded in the semiconductor material .We will need to use the permittivity of the semiconductor material in the calculations rather than the permittivity of free space as is used in the case of the hydrogen atom .We will also use the effective mass of the electron in the calculations.
The analysis begins by setting the coulomb force of attraction between the electron and ion equal to the centripetal force of the orbiti