Intrinsic semiconductors are semiconductors with very low level of impurity concentration. They have purity levels are of the order of 1 part in 10 billion. Examples of intrinsic semiconductors include Silicon, Germanium, Gallium Arsenide and Indium Antimonide.
Conduction in intrinsic semiconductors is either due to thermal excitation or due to crystal defects.
Silicon has four valence electrons and is therefore referred to as a tetravalent atom. These four electrons are shared by four neighboring atoms in the crystal. Due to this sharing of four electrons of an atom with their respective neighboring atoms, this constitutes a total of eight electrons in its valence shell. This bonding of atoms due to sharing of electrons is called covalent bonding. Owing to the covalent bonding, the valence electrons are tightly bound to the nucleus resulting in poor conductivity of Silicon crystal at absolute zero temperature (0K) and low temperatures. Figure below shows the crystal structure of Silicon at absolute zero temperature (0K)
Crystal structure of Silicon (Si) at absolute zero temperature (0K) and low temperatures
At room temperature (300K), the thermal energy of the atom is sufficient enough to break some of the covalent bonds. These electrons are raised to the conduction band and are referred to as free electrons. The free electrons are available for conduction. Figure below shows the crystal structure of Silicon at 300K.
Crystal structure of Silicon (Si) at room temperature
Intrinsic semiconductors can be classified as
- Direct band gap semiconductors
- Indirect band gap semiconductors
Direct band gap semiconductors have the maximum energy of the valence band at the same momentum value as the minimum energy of the conduction band. Figure below shows the energy-momentum diagram of a direct band gap semiconductor.
Energy-momentum diagram of direct band gap intrinsic semiconductor
Examples of direct band gap semiconductors include Gallium Arsenide and Mercury Cadmium Telluride.
In a direct band gap semiconductor, when electrons present at the minimum of conduction band combine with holes present at the maximum of valence band, the momentum is conserved. The energy released due this recombination is emitted in the form of photon of light. Hence, direct band gap semiconductors are used in making light-emitting diodes (LED) and laser diodes.
In an indirect band gap semiconductor, the maximum energy of the valence band occurs at a different momentum value than the minimum energy of the conduction band as shown in Figure below
Energy-momentum diagram of indirect band gap intrinsic semiconductor
Silicon and Germanium are examples of indirect band gap semiconductors.
In indirect band gap semiconductors, direct transition of electrons and holes across the band gap does not conserve momentum and does not emit photons of light. Instead, the energy in this case is released in the form of heat.
In an intrinsic semiconductor, the number of holes is equal to the number of electrons. Therefore,
n=p=ni
Where,
n is the electron concentration (number of electrons/cm3)
p is the hole concentration (number of holes/cm3)
ni is the intrinsic concentration.
The value of ni is given by
Where,
T is the temperature in Kelvin
EG0 is the energy gap at 0K
k is the Boltzmann constant in eV/K
A is a constant
The value of ni is given by
From the above equation, we can infer that the intrinsic concentration ni increases with increase in temperature.
Drift Current density in any material is given by
Where,
J is the current density in Amp/cm2
n is the electron concentration (number of electrons/cm3)
p is the hole concentration (number of holes/cm3)
μ is the mobility of an electron in the material in cm2/Vs
μ is the mobility of a hole in the material in cm2/Vs
q is the charge of an electron (1.6 × 10–19 C)
ε is the applied electric field in V/cm
Since in an intrinsic semiconductor, n = p = ni, therefore the drift current density in an intrinsic semiconductor is given by
The expression for conductivity (&sigma) is given by
Therefore, for an intrinsic semiconductor, the expression for conductivity is
The energy band gap [EG(T)] for Silicon at temperature T (K) is given by
The energy band gap [EG(T)] for Germanium temperature T (K) is given by
Where,
T is the temperature in Kelvin
The values of band gap energies for Silicon and Germanium at room temperature (300K) are 1.1 and 0.72 eV, respectively.
The value of band gap energy decreases with increase in temperature.
The probability that an energy level (E) in a semiconductor is occupied by an electron is given by Fermi–Dirac probability function [f(E)]. The expression for this function is
Where,
k is the Boltzmann constant (8.642 × 10–5eV/℃K)
T is the temperature in Kelvin
EF is the Fermi level in eV
It may be mentioned here that the expression for Fermi–Dirac probability function for an extrinsic semiconductor is same as that for the intrinsic semiconductor.
In an intrinsic semiconductor at 0K, the probability of finding an electron in the valence band is 100% and the probability of finding the electron in the conduction band is 0%. Therefore, the Fermi level in an intrinsic semiconductor at 0K lies at the center of the forbidden band gap as shown in the figure below.
Fermi–Dirac probability function of an intrinsic semiconductor at 0K
As the temperature increases, some of the electrons are excited to higher energy levels and they leave the valence band and jump to the conduction band. Thus, the probability of finding an electron in the valence band decreases and the probability of finding an electron in the conduction band increases. The Fermi level still remains at the center of the forbidden band gap as shown in the Figure below.
Fermi–Dirac probability function of an intrinsic semiconductor at 300K
Intrinsic semiconductors have very limited applications as they conduct a very small amount of current.
The electrical characteristics of an intrinsic semiconductor are changed significantly by adding impurity atoms to the pure semiconductor material. The impurities added are of the order of 1 part in 105 parts to 1 part in 108 parts.