Fermi Level Concept: Probability & Forbidden Gap

[Ahmad Kishki]

I was wondering if the fermi level lies in the centre of the forbidden energy gap on pure semiconductors, then how does it (by definition) have a probability 1/2 of being filled? Shouldnt the fact that the fermi level lies in the forbidden, forbid the fermi level from having any probability of electrons?

I understand that its wrong to make sweeping remarks in the realm of quantum physics about probability being zero, but i can't find a mental picture for what's happening. Thanks :)

 

[kith]

In order to get the complete probability density, you have to mulitply the Fermi-Dirac distribution by the density of states which is zero in the forbidden region.

The mental picture would be that we are able to separate the complicated problem of finding the bound states of many electrons in the crystal lattice potential into two parts: a free electron gas where the electrons have an effective mass (this is described by the Fermi-Dirac distribution) and the influence of the lattice on the occupation of the free states (this is described by the density of states).

 

[Ahmad Kishki]

In order to get the complete probability density, you have to mulitply the Fermi-Dirac distribution by the density of states which is zero in the forbidden region.

The mental picture would be that we are able to separate the complicated problem of finding the bound states of many electrons in the crystal lattice potential into two parts: a free electron gas where the electrons have an effective mass (this is described by the Fermi-Dirac distribution) and the influence of the lattice on the occupation of the free states (this is described by the density of states).

Wow thanks :)

 

[kith]

You are welcome :-)