Semiconductor statistics

The number of distinguishable ways to distribute all of the conduction electrons in their various energy cells is then simply the product 

The same analysis can be carried out for the valence band, giving 

Now the inclusion of impurities is relatively simple if we assume that each impurity has only one bound state within the band gap. (This condition will be relaxed later.) That is, suppose that if a particular impurity atom contains just na electrons, it takes more than band-gap energy (E0) to excite any one of them to the conduction band, whereas if this same atom contains na + 1 electrons, it takes an energy of only Elk to excite one of them, where EXk Ea. To complete this picture, we must further suppose that any atoms having a larger number of electrons (i.e., na + 2, na + 3, etc.) are resonant in energy with the conduction 

if there are several donor or acceptor impurities (or defects), designated by = 1, 2. then 

There are two constraints that must be obeyed while maximizing In W conservation of the number of electrons Ne and conservation of total energy e,. 

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Noise. So fat, as indicated at the beginning of this section on semiconductor statistics, equihbtium statistics have been considered. Actually, there ate fluctuations about equihbtium values, AN = N— < N >. For electrons, the mean-square fluctuation is given by < ANf >=< N > 1- ) where (Ai(D)) is the Fermi-Dirac distribution. This mean-square fluctuation has a maximum of one-fourth when E = E-. These statistical fluctuations act as electrical noise and limit minimum signal levels. 

Blakemore JS (1987) Semiconductor statistics. Dover Publications, Inc., Mineola, NY... 

Bell, R.J. (1972). Introductory Fourier Transform Spectroscopy. Academic Press, New York. Blakemore, J.S. (1987). Semiconductor Statistics. Dover Publ. Inc., New York. 

Statistical Physics, Gregory H. Wannicr. (65401-X) 10.95 Electron Paramagnetic Resonance of Transition Ions, A. Abragam and B. Bleaney. (65106-1) 17.95 Ultrasonic Absorption, A. B. Bhatia. (64917-2) S8.95 Semiconductor Statistics, J. S. Blakcmore. (65362-5) 9.95 Ellipsoidal Figures of Equilibrium, S. Chandrasekhar. (65258-0) 7.95 Magnetism and Metallurgy of Soft Materials, Chih-Wen Chen. (64997-0) 14.95... 

Refs. [i] Blakemore JS (1987) Semiconductor statistics. Dover, New York [ii] Ashcroft W, Mermin ND (1976) Solid state physics. Saunders College, Philadelphia... 

Refs. [i] Shockley W (1950) Electrons and holes in semiconductors. Van Nostrand, New York [ii] Blakemore JS (1987) Semiconductor statistics. Dover, New York [Hi] Rhoderick EH (1978) Metal-semiconductor contacts. Clarendon Press, Oxford [iv] Ashcroft W, Mermin ND (1976) Solid state physics. Saunders College, Philadelphia [v] SeegerK (1991) Semiconductor physics - an introduction. Springer, Berlin... 

We have seen in the previous section that the bulk semiconductor is characterised by a filled valence band and an empty conduction band with a distribution of acceptor and donor levels. Provided that there is no nett charge on the semiconductor, the position of the Fermi level in the semiconductor is then determined solely by the semiconductor statistics as shown above. However, once immersed in an electrolyte, the interfacial potential change, and therefore the charge on the semiconductor, can be externally controlled and the distribution of energy levels becomes more complex [7-15]. The general theory will be developed below, but some important... 

Blakemore, J.S. "Semiconductor Statistics" Pergamon Press New York, 1962 p. 122. 

J.S. Blakemore, Semiconductor Statistics (Dover Publications, Mineola, New York, 2002)... 

JS Blakemore. Semiconductor Statistics. Oxford Pergamon Press, 1962. 

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