Intrinsic Semiconductor

Intrinsic Semiconductor

A natural semiconductor is an undoped semiconductor. This implies holes in the valence band are vacancies made by electrons that have been thermally excited to the conduction band, rather than doped semiconductors where gaps(holes) or electrons are provided by an “outside” or (foreign) particle/atom going about as an impurity.

They are so called (semiconductor) because their conductivity (ability to conduct electricity) lies between a conductor and an insulator. Semiconductors which are chemically pure, meaning free of impurities, are called Intrinsic Semiconductors or Undoped Semiconductor or i-type Semiconductor. The most common intrinsic semiconductors are Silicon (Si) and Germanium (Ge), which belong to Group IV of the periodic table. The atomic numbers of Si and Ge are 14 and 32, which yields their electronic configuration as 1s2 2s2 2p6, 3s2 3p2 and 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p2, respectively. This indicates that both Si and Ge have four electrons each in their outer-most i.e. valence shell (indicated by red colour). These electrons are called valence electrons and are responsible for the conduction-properties of the semiconductors.Crystal lattice of Silicon (it is the same even for Germanium) in two-dimension is as shown in Figure 1. Here it is seen that each valence electron of a Si atom pairs with the valence electron of the adjacent Si atom to form covalent bond.

Upon pairing, the intrinsic semi-conductor will be deprived of free charge carriers which are nothing but the valence electrons. Hence, at 0K the valence band will be full of electrons while the conduction band will be empty (Figure 2a). At this stage, no electron in the valence band would gain enough energy to cross the forbidden energy gap of the semiconductor material. Thus the intrinsic semiconductors act as insulators at 0K (-273oC).

However at room temperature, the thermal energy may cause a few of the covalent bonds to break, thus generating the free electrons as shown by Figure 3a. The electrons thus generated get excited and move into the conduction band from the valence band, overcoming the energy barrier (Figure 2b). During this process, each electron leaves behind a hole in the valence band. The electrons and holes created in this way are called intrinsic charge carriers and are responsible for the conductive properties exhibited by the intrinsic semiconductor material. Although the intrinsic semiconductors are capable of conducting at room temperature, it is to be noted that the conductivity so exhibited is low as there are only a few charge carriers. But as the temperature increases, more and more covalent bonds break which results in more and more number of free electrons. This in turn results in the movement of greater number of electrons into the conduction band from the valence band. As the population of the electrons in the conduction band increases, the conductivity of the intrinsic semiconductor also increases. However, the number of electrons (ni) in the intrinsic semiconductor remains always equal to the number of holes in it (pi).

On applying an electric field to such an intrinsic semiconductor, the electron-hole pairs can be made to drift under its influence. In this case, the electrons move in the direction opposite to that of the applied field while the holes move in the direction of the electric field as shown by Figure 3b. This means that the direction along which the electrons and the holes move are mutually opposite. This is because, as an electron of a particular  atom  moves towards say, left, by leaving a hole in its place, the electron from the neighbouring atom occupies its place by recombining with that hole. However while doing so, it would have left one more hole in its place. This can be viewed as the movement of the holes (towards right side in this case) in the semiconductor material. These two movements, although opposite in direction, result in the total flow of  current  through the semiconductor.

Mathematically the charge carrier densities in intrinsic semiconductors are given by Here, Nc is the effective densities of states in the conduction band. Nv is the effective densities of states in the valence band. k = 1.38 × 10-23 JK-1 is the Boltzmann constant. T is the temperature. EF is the Fermi energy. Ev indicates the level of valence band. Ec indicates the level of conduction band. h = 6.624×10-34 Js is the Planck constant. mh is the effective mass of a hole. me is the effective mass of an electron.

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Semiconductors Theory

Semiconductors  Theory

Semiconductors are usually classified by the energy gap between their valence band and the conduction band. The valence band is the band consisting of the valence electron, and the conduction band remains empty. Electrical Conduction takes place when an electron jumps from valence band to conduction band and the gap between these two bands is forbidden energy gap. Wider the gap between the valence and conduction bands, higher the energy it requires for shifting an electron from valence band to the conduction band. In the case of  conductors , this energy gap is absent or in other words conduction band, and valence band overlaps each other. Thus, electron requires minimum energy to jump from valence band. The typical examples of conductors are Silver, Copper, and Aluminium. In  insulators , this gap is vast. Therefore, it requires a significant amount of energy to shift an electron from valence to conduction band. Thus, insulators are poor conductors of electricity. Mica and Ceramic are the well-known examples of insulation material.

Semiconductors, on the other hand, have an energy gap which is in 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 insulators for shifting valence band to conduction band. At low temperature there are very less number of electrons in conduction band in a semiconductor crystal but when the temperature is increased more and more electrons get sufficient energy to migrate from valence band to conduction band. Because of that, they don’t conduct electricity at low temperature but as the temperature increases the conductivity increases. The most typical examples of the semiconductors are silicon and germanium.

What is a Semiconductor?

The materials that are neither conductor nor insulator with energy gap of about 1 eV (

 electron volt 

) are called semiconductors.

Most common type of materials that are 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 4 valence electrons. Both form the covalent bond with the neighbouring atom. At absolute zero temperature both behave as 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.

From the energy band diagrams of a semiconductor above, CB is the conduction band and VB is the valence band. At 0oK, the VB is full with all the valence electrons.

Intrinsic Semiconductors

Reference to the semiconductor theory, 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 conductivity is due to these electrons only and is given by, σ = neμe.

P-type Semiconductors

In  p- type of semiconductor majority carriers are holes and minority carriers are electrons.  P- type semiconductor  is formed by adding trivalent ( three valence electrons) impurity in pure semiconductor crystal, e.g. B, Al, Ba.

Three of the four valence electron of tetravalent impurity forms covalent bond with Si atom. This leaves an empty space which is referred to as hole. When temperature is raised electron from another covalent bond jumps to fill this empty space. This leaves a hole behind. In this way conduction takes place. P- type impurity accepts electron and is called acceptor atom. Majority carriers are holes and therefore conductivity is due to these holes only and is given by, σ = neμh