Concept of Holes

Now consider the 1st band where N states are filled by N electrons at room temperature. With external voltage, electrons will move with velocity But the band is symmetric about . For every electron with a given direction, there will be another electron with the same in -x direction.

Thus first band no current,

So totally filled energy band do not contribute to the charge transport process.

Thus first band on current,

So totally filled energy band do not contribute to the charge transport process.

Asymmetry applied electric field.

For nearly empty third band current

where L length of 1D crystal and

For the nearly filled second band current

This summation is more difficult to evaluate as we have very large number of states filled.

Now if the band was completely filled,

Therefore, we can write

This current is the same as if a positively charge particle is placed on the empty states and the remaining states are unoccupied.

Overall motion of electrons in nearly filled energy band can be described by the empty electronic states provided that the effective mass of the empty states is taken to be negative of , i.e.

Now in this example empty energy states are at the top of the bands effective mass there. Therefore, Empty energy states at the top of a band +ve charge with +ve

Normally the electron or holes stay mostly at the edge of a band (holes in top of Valence band and electrons in the bottom of conduction band) where parabolic band approximation can be applied. So in semiconductors electrons and holes generally have constant effective mass and the classical treatment/behaviour is a good approximation.

Valence Band

1. Maxima occurs at zone center at k = 0
2. Valence band = three sub bands

Two bands are degenerate (have same allowed energy) at k = 0. Third band max

at reduced energy k =0.

1. At k = 0, the shape and curvature are orientation independent.

Conduction Band

1. Somewhat similar, but minimum where electrons will gather varies from material to material.
2. Ge C Band minima at zone boundary (8 such min)
3. Si C Band minima at from the zone center.
4. GaAs C Band min at k = 0. Direct bandgap good for light emission conservation of momentum transition from V Band to C Band.
5. 3D structure is tensor.

Band gap Energy

It is the range from Valence Band maximum to Conduction Band minimum.

At

A decrease in T results in a contraction of crystal lattice

stronger atomic bonds

increase in Band gap energy

is a good model