Electron hole theory in Semiconductors

[slaw]

Hi guys. Could someone please explain to me this electron hole theory that people use to describe the behavior of electrons inside semiconductors? How do these holes move, in and out of a potential difference?


Thanks guys.

 

[Azael]

The holes are just the abscence of a electron in a energy band. But its easier to describe the abscence of a electron as a single moving positive charge than it is to describe the motion of all the other electrons in the band.

Think of it like this. In a band you have N electrons. Remove one of those electrons(by for instance p-doping) and you have N-1 electrons left. Now you can either choose to describe this with the behavior of those N-1 electrons. Or you can choose to describe it as if there is one single hole moving around in the band.

So mathematicly the holes behave just like a positivly charged electron.

But the holes themself never move in or out of potential differences because the holes are just a mathematical trick. What moves in and out of those potential differences are the N-1 electrons.

I hope this explanation makes sense and answered your question :)

 

[Gokul43201]

Think of it like this. In a band you have N electrons. Remove one of those electrons(by for instance p-doping) and you have N-1 electrons left. Now you can either choose to describe this with the behavior of those N-1 electrons. Or you can choose to describe it as if there is one single hole moving around in the band.

Stricly speaking, you can treat this as a band with one single hole and N electrons. But since a filled band (with N electrons) can not produce currents, the electrons can be ignored (to a very good approximation), and the band treated as though it had just the one hole.

 

[slaw]

Hm...I sort of understand the whole idea of the electron leaving to the conductor band leaving behind a hole which can act as a positive charge electron. But I don't understand how the electrons and hole will move when that piece of semiconducting material is used in a circuit. (Its really annoying how I keep spelling hole as whole...)

 

[zebra.9]

In an intrinsic semiconductor, a few electrons get thermally excited and break from their valence bond to become a free electron. This leaves behind a vacancy in its place called 'hole'.
In a P-type semiconductor, B with 3 electrons replaces a Si atom with 4 electrons in the lattice. 3 covalent bonds are formed by B with 3 neighbouring Si. But there is a deficiency of one electron in B for bonding with the 4th Si. This deficiency/vacancy is called a hole.

When an electric potential difference is present, the electrons from adjacent valence bond moves into the vacancy near it while moving along the potential.
The following represents the movement of valence electron.

Terminology:
* represents valence electron
_ represents hole
A is -ve and B is +ve.


..I A * * * _ * * * B

.II A * * _ * * * * B

III A * _ * * * * * B

IV A _ * * * * * * B

I- Hole is at the 4th position.
II- At first, the 3rd electron from left shifts right to fill the vacancy and leaves behind a vacancy in its place. The vacancy is at the 3rd position.
III- Next, the 2nd electron from left has shifted to the 3rd place and filled up that vacancy but leaves a vacancy at its place. The vacancy is at 2nd position.
IV- Now, the 1st electron from left moves to occupy the vacancy at the 2nd position creating another vacancy in its own place. The vacancy is at 1st position.

As the electrons moved right, the vacancy moved left. The vacancy is called a hole (just a shorter name for convenience). The movement of holes is really the movement of electron in the valence band. Therefore, the mobility of a hole is indirectly the mobility of valence electrons.
Mobility is the velocity acquired per unit electric field.

In the intrinsic and N type semiconductors, many free electrons are present i.e. electrons in conduction band which are free to move in the crystal as against valence electrons which can only move in the lattice points.

The right end of the material is applied a positive potential which attracts electrons. The electron which is at position 3 moves into the adjacent atomic vacancy at 4 due to the attraction and availability of free space to do so, otherwise it would have remained in its place. It created a vacancy in its previous atom which is used by the valence electron from 6. The electrons move from 3 to 4, 2 to 3, 1 to 2 and so on. This pushed back the vacancy step by step and it now stands at 1. Call it the hole and you may say tht "hole moved from right to left" while the "bonded electron moved from left to right". Hole is just a shorter name used for convenience.

Notice that the bonded electron and free electron move towards positive potential alike, because they are both electrons.

Hole movement is opposite to that of bonded electron(as can be understood from the illustration). So it is also opposite to free electron movement, infact, opposite to any electron movement! Also note that the velocity with which the bonded electron moves can be associated with the hole too since hole is simply a physical complement of the bonded electron. This means that their physical parameter like rate of change holds the same value for them both.
The movement of holes is really the movement of electron in the valence band. Therefore, the mobility of a hole is indirectly the mobility of valence electrons.

 

[Dr Lots-o'watts]

It's like those sliding puzzles where you slide tiles to try to make the picture. You actually slide the tiles but in effect, it's as if it was the missing tile that was tracing a trajectory.

http://en.wikipedia.org/wiki/File:15-puzzle.svg