Forbidden gap in semiconductors.

[savi]

in books we have read that there lies a forbidden gap between conduction band and valence band. and electrons can not exist in this gap i.e. probability of electron being found in this region should be zero.
BUT the fermi level,which has 50% prabality to contain an electron is found in forbidden gap for a semi conductor generally. how can this be possible if no electron can exist in forbidden gap?

 

[ZapperZ]

Please read this thread:

https://www.physicsforums.com/showthread.php?t=133914

Zz.

 

[avinashikhar]

in books we have read that there lies a forbidden gap between conduction band and valence band. and electrons can not exist in this gap i.e. probability of electron being found in this region should be zero.
BUT the fermi level,which has 50% prabality to contain an electron is found in forbidden gap for a semi conductor generally. how can this be possible if no electron can exist in forbidden gap?

When atoms are brought close together, as in a solid, the electrons come under the influence of forces from other atoms, where the energy level merges into bands of energy levels. There are two distinct energy bands in which electrons could exist: the valence band and the conduction band . Separating these two bands is an energy gap , termed the forbidden gap, in which electrons cannot normally exist.

The central task of basic semiconductor physics is to establish formulas for the position of the Fermi level EF relative to the energy levels EC and EV (the level of the bottom of the conduction band and the top of the valence band), taking into account the effects of "doping". Doping introduces additional electron energy levels into the band gap, that may or may not be populated by electrons, dependent on circumstances and temperature, and causes the Fermi level EF to shift from the energy level (relative to the band structure) that it would have had in the absence of doping. This energy level that the Fermi level has in the absence of doping is called the intrinsic Fermi level (or "intrinsic level") and is usually denoted by the symbol Ei.

The theory of semiconductor physics is constructed in such a fashion that – in a situation of complete thermodynamic equilibrium – the position of the Fermi level, relative to the band structure, determines both the density of electrons and the density of holes.
Avinash Singh
Jr. YSR (ISCA)
Mech. Eng.
KIIT Univesity
BBSR