Theory of Semiconductor:
The materials can be arranged on the premise of vitality crevice between their valence band and conduction band. The valence band is the band comprising of free valence electron and the conduction band is vacant band. Conduction happens when an electron hops from valence band to conduction band and the crevice between these two groups is vitality hole. More extensive the crevice between the groups, higher the vitality it requires to move the electron to conduction band.
If there should be an occurrence of directors, this vitality crevice is missing or at the end of the day conduction band and valence band cover one another. In this manner electron requires least vitality to hop from valence band, e.g. Silver, Copper and Aluminum. In covers, this hole is expansive. In this manner, it requires substantial measure of vitality to move an electron from valence to conduction band. In this manner protectors are poor conveyors of power, e.g. mica, precious stone.
Semiconductors have energy gap in between conductors and insulators (~1 eV) and thus require energy more than conductors but less than insulators. They don’t conduct electricity at low temperature but as temperature increases conductivity increases e.g. silicon and germanium. This is the most basic theory of 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 used as semiconductors are germanium (Ge) and silicon (Si) because of their property to withstand high temperature. For Si and Ge energy gap is given as,
Eg = 1.21 – 3.6 X 10-4T eV (for Si)
Eg = 1.21 – 3.6 X 10-4T eV (for Si)
Eg = 0.785 – 2.23 X 10-4T eV (for Ge)
Where, T = absolute temperature in oK
Assuming room temperature to be 300 oK, Eg = 0.72eV for Ge and 1.1eV for Si.
At room temperature resistivity of semiconductor is in between insulators and conductors.Semiconductors show negative temperature coefficient of resistivity i.e. 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 covalent bond with neighbouring atom. At absolute zero temperature both behave as insulator i.e. the valence band is full while
conduction band is empty but as temperature is raised more and more covalent bonds break and electrons are set free and jump to conduction band.
Assuming room temperature to be 300 oK, Eg = 0.72eV for Ge and 1.1eV for Si.
At room temperature resistivity of semiconductor is in between insulators and conductors.Semiconductors show negative temperature coefficient of resistivity i.e. 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 covalent bond with neighbouring atom. At absolute zero temperature both behave as insulator i.e. the valence band is full while
conduction band is empty but as temperature is raised more and more covalent bonds break and electrons are set free and jump to conduction band.
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
ni = n0T3/2 exp(-VG /2VT)
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 = peh
Conductivity, σ = σe + σh = neμe + peμh = Ne (μe + μh)
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
ni = n0T3/2 exp(-VG /2VT)
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 = peh
Conductivity, σ = σe + σh = neμe + peμh = Ne (μe + μh)
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
σ = neμe
P-type Semiconductors
In this kind of semiconductor dominant part transporters are openings and minority bearers are electrons. P-sort semiconductor is framed by including trivalent ( three valence electrons) debasement in immaculate semiconductor precious stone, e.g. B, Al Ba.
Three of the four valence electron of tetravalent contamination frames covalent bond with Si iota. This leaves an unfilled space which is alluded to as gap. At the point when temperature is raised electron from another covalent bond hops to fill this vacant space. This deserts a gap. Along these lines conduction happens. P-sort pollution acknowledges electron and is called acceptor iota. Lion’s share bearers are openings and subsequently conductivity is because of these gaps just and is given by,