Extrinsic Semiconductors

The process of adding impurities to an intrinsic semiconductor is called doping and the resultant semiconductor is called an extrinsic semiconductor.

External semiconductors are classified as N-type semiconductors and P-type semiconductors.

An N-type semiconductor material is formed by adding approximately 1 part in 10⁸ parts of pentavalent impurities to the intrinsic semiconductor material. Pentavalent atoms have five valence electrons and are referred to as donor atoms. Some examples of pentavalent atoms are Phosphorus, Antimony and Arsenic.

A P-type semiconductor is created by adding approximately 1 part in 10⁵ parts of trivalent impurity to the intrinsic semiconductor. Trivalent atoms have three electrons in their valence shell and are called acceptor atoms. Examples of trivalent impurities include Boron (B), Indium (In) and Gallium (Ga).

Figure below shows the crystal structure of an N-type semiconductor material. As we can see from the figure, four of the five electrons of the pentavalent impurity atom (Antimony) form covalent bonds with four intrinsic semiconductor atoms. The fifth electron loosely bound to the pentavalent atom, is relatively free to move within the crystal. It is referred to as the free electron. The energy required to detach this free electron from the atom is very small, of the order of 0.01 eV for Germanium and 0.05 eV for Silicon.

Crystal structure of an N-type semiconductor

In case of P-type semiconductor, since there are three electrons in the valence shell of these trivalent impurity atoms, only three covalent bonds are formed with the neighboring intrinsic semiconductor atoms. A vacancy exists in the fourth bond. This is highlighted in the figure given below.

This vacancy is referred to as the hole and is represented by a small hollow circle. The hole is ready to accept an electron from the neighboring atom, resulting in a hole in the neighboring atom. This hole in turn is ready to accept an electron, thereby creating another hole. In this way, the hole travels through the crystal.

Crystal structure of a P-type semiconductor

Refer to figure below. The effect of doping creates a discrete energy level called donor energy level in the forbidden band gap with energy level (E_D) slightly less than the conduction band. The difference between the energy levels of the conduction band (E_C) and the donor energy level (E_D) is the energy required to free the electron (0.01 eV for Germanium and 0.05 eV for Silicon).

Energy band diagram of an N-type semiconductor

Refer to figure below. The effect of doping creates a discrete energy level in the forbidden energy band gap with energy level (E_A) just above the valence band. This level is referred to as the acceptor energy level. The difference between the energy levels of the acceptor band (E_A) and the valence band (E_V) is the energy required by an electron to leave the valence band and occupy the acceptor band, thereby leaving a hole in the valence band. This difference is of the order of 0.08 eV for Silicon and 0.01 eV for Germanium.

Energy band diagram of a P-type semiconductor

In an N-type semiconductor, electrons are the majority carriers and the holes are the minority carriers. In an N-type semiconductor, the number of electrons increases and the number of holes decreases compared to those available in an intrinsic semiconductor. The decrease in the number of holes is attributed to the increase in the rate of recombination of electrons with holes.

In a P-type semiconductor, holes are the majority carriers and electrons are the minority carriers. In a P-type semiconductor, the number of electrons decreases and the number of holes increases compared to those available in an intrinsic semiconductor. The decrease in the number of electrons is attributed to the increase in the rate of recombination of electrons with holes.

The current in the N-type semiconductor is dominated by electrons, the majority carriers. The figure below shows the current flow in an N-type semiconductor. Here, I is total conventional current flow, I_e the current flow due to electrons and I_h the current flow due to holes.

Current flow in an N-type semiconductor

The current in the P-type semiconductor is dominated by holes, the majority carriers. Electrons are the minority carriers in a P-type semiconductor material. The current flow in a P-type semiconductor is shown in figure below. Here, I is the total conventional current flow, I_e the current flow due to electrons and I_h the current flow due to holes.

Current flow in a P-type semiconductor

Conductivity of an N-type semiconductor is higher than that of a P-type semiconductor because the mobility of electrons is greater than that of holes. For the same level of doping in the N-type and the P-type semiconductors, the conductivity of an N-type semiconductor is around twice that of a P-type semiconductor.

For an N-type semiconductor, the free electron concentration is approximately equal to donor atom concentration.

Free hole concentration in a P-type semiconductor is approximately equal to the acceptor atom concentration.

Drift current density in an N-type semiconductor is given by

Where,
μ_n is the mobility of free electrons in the semiconductor (cm²/Vs)
ε the applied electric field (V/cm)

Conductivity in an N-type semiconductor is given by

Drift current density in a P-type semiconductor is given by

Where,
μ_p is the mobility of holes in the semiconductor (cm²/Vs)
ε the applied electric field (V/cm)

The expression for conductivity for a P-type semiconductor is

Refer to figure below. The Fermi level in an N-type semiconductor is raised and is closer to the conduction band as there is a significant increase in the number of electrons in the conduction band and there are fewer holes in the valence band.

Fermi level in an N-type semiconductor

The Fermi level is given by

Where,
E_C is the energy at the bottom of the conduction band
k the Boltzmann constant in eV/°K (8.642 X 10^-5 eV/°K)
T the temperature in Kelvin
N_C the density of states in the conduction band (constant for a material at a given temperature)
N_D the donor atom concentration (number of atoms/cm³)

The value of N_C is given by

Where,
m_n is the effective mass of an electron
T the temperature in Kelvin
h the Plank’s constant
q the electronic charge (1.6 X 10^-19 C)

Figure below shows the Fermi level in a P-type semiconductor. The Fermi level in a P-type semiconductor is closer to the valence band and is lower than that of an intrinsic semiconductor. This is due to the fact that in a P-type semiconductor, there is a significant increase in the number of holes in the valence band and decrease in the number of electrons in the conduction band.

The expression for Fermi level (E_F) in a P-type semiconductor is

Where,
E_V is the energy at the top of the valence band
N_V the density of states in the valence band (constant for a material at a given temperature)
T the temperature in Kelvin.

The value of N_V is can be calculated using

Where,
m_p is the effective mass of a hole
h the Plank’s constant
T the temperature in Kelvin
q the electronic charge (1.6 X 10^-19 C)
k the Boltzmann constant in eV/°K (= 8.642X10^-5 eV/°K)
N_A the donor atom concentration (number of atoms/cm³)

Fermi level in a P-type semiconductor

As the temperature increases, more electron–hole pairs are generated in an extrinsic semiconductor. Therefore, the Fermi level shifts towards the center of the forbidden energy band gap with increase in temperature of an extrinsic semiconductor.

Law of mass action defines the concentration of holes and electrons in a semiconductor. According to the law of mass action, the product of free electron concentration and hole concentration in any semiconductor is constant and is given by

Where,
n is the free electron concentration (negatively charged carriers)
p the hole concentration (positively charged carriers)
n_i the intrinsic concentration.

From the law of mass action, it can be interpreted that the product of concentration of negative and positive charge carriers in a semiconductor is independent of the type and amount of doping and is equal to the square of the intrinsic concentration.

For an N-type semiconductor, number of free electrons (n) is equal to the donor atom concentration (N_D).

From law of mass action, the concentration of free holes (p) is given by

For a P-type semiconductor, number of free holes (p) is equal to the acceptor atom concentration (N_A).

From law of mass action, the concentration of free electrons (n) is given by

Mobility of a charge carrier is expressed as

Where,
μ is the mobility (cm²/Vs)
q is the electric charge (1.6 x 10^-19 C)
τ_s is the mean scattering time
m* is the effective carrier mass