Extrinsic Semiconductors

One may also dope the semiconductor material. Semi-conductor materials are doped with impurities chosen to give the material special characteristics. One may want to add extra electrons or remove electrons.

Figure 6: N-type silicon, doped with phosphorous

Figure 7: P-type silicon, doped with boron

Doping atoms are chosen from elements in group III or V of the periodic table[1] which are similar in size to silicon atoms. Thus individual intrinsic semiconductor atoms may be replaced with dopant atoms to form an extrinsic semi-conductor.

The binding energy of the outer electron added by the impurity is weak. This is represented by placing the excess electrons just below the conduction band. Thus very little energy is required to move these electrons into the conduction band. Thus an extrinsic semi-conductor operating at room temperature will have most of these "extra" electrons existing in the conduction band. Thus at normal operating temperature,

,

Where n_c is the number of conduction electrons and N_d is the number of dopant atoms.

Fermi Level

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

where m_e is the effective mass of an electron.

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

where m_h 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 n_c = n_v where n_c is the number electrons in the conduction band and n_v is the number of conduction holes in the valence band, given by:

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

n_c = n_v + n_d

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 τ_c.

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

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

The current density J_n 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:

J_n = 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 D_n is defined along with electron density gradient .

where

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

Date: 2016-01-03; view: 816