Why is the mobility of electrons greater than the mobility of holes?

Answer 1

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.

When an electric field is applied, both the valence electrons and the free electrons move in the same direction. The hole direction is opposite to that of valence electron but the mobility is the same, as explained earlier.

Even for the same electric field, valence electrons cannot move as freely as the free electrons because its movement is restricted. Therefore, the velocity of valence electrons is less compared to free electrons. In other words, the velocity of holes is less compared to free electrons. This means mobility is also less for a hole compared to free electron.

Thus, mobility of a free-electron (often abbreviated as 'electron') is greater than that of a hole (indirectly referring to valence electron).

Answer 2

Electrons can jump from valence shell to valence shell, or from hole to hole. Holes, which are actually atoms missing an electron in their valence shell, are locked in the lattice structure of the material that they are contained within. Holes are, in reality, a theoretical concept used to explain current flow - it is generally accepted by most main stream physicists today that current flow is electron flow - but the concept of hole flow allows some of the mathematics to be easier to deal with, i.e. without those nagging minus signs.