- Semiconductor Theory Definition: Semiconductor theory is the study of materials that have an energy gap of about 1 eV, making them neither conductors nor insulators.
- Energy Bands: The valence band contains electrons, and the conduction band is empty; conduction happens when electrons jump between these bands.
- Intrinsic Semiconductors: Pure semiconductors have equal numbers of electrons and holes, resulting in low conductivity.
- Extrinsic Semiconductors: Impure semiconductors, with added impurities, increase conductivity and are classified as N-type or P-type.
- Types of Semiconductors: N-type semiconductors have free electrons as majority carriers, while P-type semiconductors have holes as majority carriers.
Materials are classified by the energy gap between their valence band and conduction band. The valence band holds the valence electrons, while the conduction band is empty. Conduction occurs when electrons jump from the valence band to the conduction band, across the forbidden energy gap.
A wider gap between the valence and conduction bands means more energy is needed for electrons to move between them. Conductors have no energy gap because the bands overlap, making it easy for electrons to move. Examples of conductors include Silver, Copper, and Aluminium. Insulators have a large energy gap, making conduction difficult.
Insulators need a lot of energy to move electrons from the valence to the conduction band, making them poor conductors. Mica and Ceramic are common insulators. Semiconductors have an energy gap between that of conductors and insulators.
This gap is typically more or less 1 eV, and thus, one electron requires energy more than conductors but less than insulating materials for shifting valence band to conduction band.
At low temperatures, few electrons are in the conduction band of a semiconductor. As temperature rises, more electrons gain enough energy to move from the valence band to the conduction band. Thus, semiconductors don’t conduct electricity well at low temperatures, but conductivity increases with temperature. Silicon and Germanium are common semiconductors.
Definition of Semiconductor
Thus, the definition of semiconductor can be as follows.
Most common materials commercially used as semiconductors are germanium (Ge) and silicon (Si) because of their property to withstand high temperature. That means there will be no significant change in energy gap with changing temperature.
The relation between energy gap and absolute temperature for Si and Ge are given as,
Where, T = absolute temperature in oK
Assuming room temperature to be 300oK,
At room temperature resistivity of semiconductor is in between insulators and conductors. Semiconductors show negative temperature coefficient of resistivity that means its resistance decreases with increase in temperature. Both Si and Ge are elements of IV group, i.e. both elements have four valence electrons. Both form the covalent bond with the neighboring atom. At absolute zero temperature both behave like an insulator, i.e. the valence band is full while conduction band is empty but as the temperature is raised more and more covalent bonds break and electrons are set free and jump to the conduction band.
In the above energy band diagrams of a semiconductor. CB is the conduction band, and VB is the valence band. At 0oK, the VB is full with all the valence electrons.
Intrinsic Semiconductors
As per theory of semiconductor, semiconductor in its pure form is called as intrinsic semiconductor. In pure semiconductor number of electrons (n) is equal to number of holes (p) and thus conductivity is very low as valence electrons are covalent bonded. In this case we write n = p = ni, where ni is called the intrinsic concentration. It can be shown that ni can be written
Where, n0 is a constant, T is the absolute temperature, VG is the semiconductor band gap voltage, and VT is the thermal voltage.
The thermal voltage is related to the temperature by VT = kT/q
Where, k is the Boltzmann constant (k = 1.381 × 10 − 23 J/K).
In intrinsic semiconductors conductivity (σ) is determined by both electrons (σe) and holes (σh) and depends on the carrier density.
σe = neμe, σh = peμh
Conductivity, 
Where n, p = numbers of electrons and holes respectively.
μh, μe = mobility of free holes and electrons respectively
N = n = p
e = charge on carrier
Extrinsic Semiconductors
As per theory of semiconductor, impure semiconductors are called extrinsic semiconductors. Extrinsic semiconductor is formed by adding a small amount of impurity. Depending on the type of impurity added we have two types of semiconductors: N-type and P-type semiconductors. In 100 million parts of semiconductor one part of impurity is added.
N type Semiconductor
In this type of semiconductor majority carriers are electrons and minority carriers are holes. N – type semiconductor is formed by adding pentavalent (five valence electrons) impurity in pure semiconductor crystal, e.g. P. As, Sb.
Four of the five valence electron of pentavalent impurity forms covalent bond with Si atom and the remaining electron is free to move anywhere within the crystal. Pentavalent impurity donates electron to Si that’s why N-type impurity atoms are known as donor atoms. This enhances the conductivity of pure Si. Majority carriers are electrons therefore conductivitry is due to these electrons only and is given by,
σ = neμe
P type Semiconductors
In this type of semiconductor majority carriers are holes, and minority carriers are electrons. The p-type semiconductor is formed by adding trivalent ( three valence electrons) impurity in a pure semiconductor crystal, e.g. B, Al Ba.
Three of the four valence electron of tetravalent impurity forms covalent bonds with Si atoms. The phenomenon creates a space which we refer to a hole. When the temperature rises an electron from another covalent bond jumps to fill this space. Hence, a hole gets created behind. In this way conduction takes place. P-type impurity accepts electrons and is called acceptor atom. Majority carriers are holes, and therefore conductivity is due to these holes only and is given by,
σ = neμh
