I am not sure if I understand the question, but let me analyse Fermi-Dirac statistical distribution function with you. The Fermi-Dirac distribution function describes, as you probably know, the most probable way n-electrons can be distributed among N energy levels, constrained by a fixed energy for the ensemble. The contribution of the impurities is included by making some basic assumptions about the impurity behavior. This assumptions are mainly empirical in nature. You may postulate that the impurity atoms divide into two populations, one with n electrons and the other with n + 1 electrons for example. The electrons on any one atom in the first population may fall into any of g' possible equivalent levels, while for those in the second population there are g'' possible levels. Then the degeneracy factor in the Fermi occupancy function is found to be g'/g''. Acceptors provide an energy level realated to the structure of valence band of the material. You may distinguish two valence bands: a "heavy" hole valence band and a "light" hole valence band, either of which may populate the acceptor. Therefore, the degeneracy factor of 4 results from the possibility of either a spin-up or a spin-down electron occupying the level E(Acceptor), and the existence of two sources for holes of energy E(Acceptor), one from the "heavy" hole band and one from the "light" hole band. In contrast to acceptors, donors become positively charged and tend to give up an electron. So the degeneracy factor is 2 (because of the spin-up or spin-down possibilities for occupancy) and there is typically only one conduction band associated with the energy level E(Donor).

More information:

1. David C. Look (1983). “Chapter 2: Properties of semi-insulating GaAs: Appendix B”, Robert K. Willardson, Albert C. Beer: Deep levels, GaAs, alloys, photochemistry; volume 19 of Semiconductors and Semimetals. Academic Press, pp. 149 ff. ISBN 0127521194.

2. K Seeger (2004). “§3.2 Occupation probabilities of impurity levels”, Semiconductor physics: An introduction, 9th ed. Springer, pp. 41 ff. ISBN 3540219579.

3. Michael Reisch (2003). “§2.2.2 Ionization”, High-frequency bipolar transistors: physics, modelling, applications. Springer. ISBN 354067702X.

I am not sure if I understand the question, but let me analyse Fermi-Dirac statistical distribution function with you. The Fermi-Dirac distribution function describes, as you probably know, the most probable way n-electrons can be distributed among N energy levels, constrained by a fixed energy for the ensemble. The contribution of the impurities is included by making some basic assumptions about the impurity behavior. This assumptions are mainly empirical in nature. You may postulate that the impurity atoms divide into two populations, one with n electrons and the other with n + 1 electrons for example. The electrons on any one atom in the first population may fall into any of g' possible equivalent levels, while for those in the second population there are g'' possible levels. Then the degeneracy factor in the Fermi occupancy function is found to be g'/g''. Acceptors provide an energy level realated to the structure of valence band of the material. You may distinguish two valence bands: a "heavy" hole valence band and a "light" hole valence band, either of which may populate the acceptor. Therefore, the degeneracy factor of 4 results from the possibility of either a spin-up or a spin-down electron occupying the level E(Acceptor), and the existence of two sources for holes of energy E(Acceptor), one from the "heavy" hole band and one from the "light" hole band. In contrast to acceptors, donors become positively charged and tend to give up an electron. So the degeneracy factor is 2 (because of the spin-up or spin-down possibilities for occupancy) and there is typically only one conduction band associated with the energy level E(Donor).

More information:

1. David C. Look (1983). “Chapter 2: Properties of semi-insulating GaAs: Appendix B”, Robert K. Willardson, Albert C. Beer: Deep levels, GaAs, alloys, photochemistry; volume 19 of Semiconductors and Semimetals. Academic Press, pp. 149 ff. ISBN 0127521194.

2. K Seeger (2004). “§3.2 Occupation probabilities of impurity levels”, Semiconductor physics: An introduction, 9th ed. Springer, pp. 41 ff. ISBN 3540219579.

3. Michael Reisch (2003). “§2.2.2 Ionization”, High-frequency bipolar transistors: physics, modelling, applications. Springer. ISBN 354067702X.

Thank you for the best answer. Specifically, it's the answer I have needed. Although you said that the degeneracy factors for donor lever and acceptor is 2 and 4 respectively, being written in 1/2 and 2 in my text book. It's hard to understand where the difference come from.

I'm glad that I helped :)

very nice explanation. I also learned sth.

Thank it is good explanation