Fermi Level

The number of energy levels in the conduction band is given by[2] Nc:

where me is the effective mass of an electron.

The number of energy levels in the valence band is given by Nv

where mh is the effective mass of a hole.

For an intrinsic semi-conductor, the number of conduction electrons must equal the number of conduction holes. Such that

nc = nv

where nc is the number electrons in the conduction band and nv is the number of conduction holes in the valence band, given by:

for an n-type extrinsic semiconductor, the number of conduction electrons nc must equal the number of conduction holes plus the number of ionized donor atoms, nd.

nc = nv + nd

where:

Figure 8: Carrier density for doped semiconductor

Figure 8 shows this relationship against temperature. At the operating temperature, the electrons available for conduction is relatively constant, as most donor electrons exist in the conduction band. For high temperatures electrons from the valance band begin to populate the conduction band, significantly increasing the carrier density. The electrons in the conduction band are now dominated by electrons from the intrinsic semiconductor and it is said to be intrinsic. For very low temperatures, the donor electrons no longer populate the conduction band and the semi-conductor is said to freeze out.

Conduction

electron mobility: When an electric field is applied to a semiconductor, the electrons experience a force and are accelerated in the opposite direction of the electric field. This acceleration is inhibited by what we term 'collisions' [1].

When a collision occurs, the velocity of the electron drops to zero and it accelerates again. The average time between collisions is given by τc.

The effect is a constant drift velocity for an n-type semiconductor Vn given by:

where μ is the mobility. Its derivation is complicated as the velocities have a Maxwellian distribution.

The current density Jn is given by:

where n is the number of electrons per unit volume A and q their charge. One may also express the current density in terms of the conductivity σ:

Jn = σξ

σ = qnμ

where σ is the conductivity in siemens per meter and ξ the electric field.

Conduction is further complicated by additional diffusion of carriers. The voltage drop across the semiconductor is gradual and therefore sets up an electron density gradient. Electrons which exist at higher densities experience a force towards less dense region. Thus a Diffusion co-efficient Dn is defined along with electron density gradient .

where

The same equations also apply for a p-type semicondcutor with a few minor differences.

Kevin M Contreras H
Electrónica del Estado Sólido
http://en.wikibooks.org/wiki/Semiconductors/What_is_a_Semiconductor