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Semiconductors: Types, Band Structures, and Temperature Dependence, Study notes of Physics

Koneru Lakshmaiah Education FoundationPhysics

The different types of semiconductors, intrinsic and extrinsic, and their band structures. It also compares the temperature dependence of conductivity in metals and semiconductors. diagrams and equations to illustrate the concepts.

Typology: Study notes

2021/2022

Available from 02/18/2023

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Semiconductors
1. Explain different types of semiconductors in detail with necessary bond diagrams.
There are two types of semi conductors.
1. Intrinsic semiconductors
2. Extrinsic semiconductors
Intrinsic semiconductors:
1. Highly pure semiconductors with no impurities are called intrinsic semiconductors.
2. In such a material there are no charge carriers at 0K because all electrons are bounded
in covalent bonds.
3. Since the valence band is filled and the conduction band is empty.
4. At higher temperatures, the electrons reaching the conduction band due to thermal
excitation leave equal number of holes in valence band i.e electron becomes free and
leaves a vacancy in the covalent bond which is called a hole.
5. In intrinsic semiconductor, the number of free electrons is equal to the number of
holes.
6. The bond structure of intrinsic semiconductors are shown in below figure.
7. In an electric field, electrons and holes move in opposite direction and participate in
conduction.Since both electrons and holes are charge carriers in an intrinsic
semiconductor, the conductivity is
8.
where p is the hole concentration and μh the hole mobility.
n is the electron concentration and is th electron mobility
9. Since n=p,
Extrinsic semiconductors: these are impure semiconductors. To increase the conductivity, the
pure semiconductors are doped with impurities.
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Semiconductors

1. Explain different types of semiconductors in detail with necessary bond diagrams. There are two types of semi conductors. 1. Intrinsic semiconductors 2. Extrinsic semiconductors

Intrinsic semiconductors:

  1. Highly pure semiconductors with no impurities are called intrinsic semiconductors.
  2. In such a material there are no charge carriers at 0K because all electrons are bounded in covalent bonds.
  3. Since the valence band is filled and the conduction band is empty.
  4. At higher temperatures, the electrons reaching the conduction band due to thermal excitation leave equal number of holes in valence band i.e electron becomes free and leaves a vacancy in the covalent bond which is called a hole.
  5. In intrinsic semiconductor, the number of free electrons is equal to the number of holes.
  6. The bond structure of intrinsic semiconductors are shown in below figure.
  7. In an electric field, electrons and holes move in opposite direction and participate in conduction.Since both electrons and holes are charge carriers in an intrinsic semiconductor, the conductivity is
  8. where p is the hole concentration and μh the hole mobility. n is the electron concentration and is th electron mobility
  9. Since n=p,

Extrinsic semiconductors : these are impure semiconductors. To increase the conductivity, the pure semiconductors are doped with impurities.

N-Type Semiconductor:

  1. When a pure si is doped with penta valent impurity it gives excess of electrons. Hence it is known as N-type semiconductors.
  2. Example: phosphorus (or As, Sb) with 5 valence electrons, is an electron donor in Si since only 4 electrons are used to bond to the Si lattice when it substitutes for a Si atom.
  3. Fifth outer electron of P atom is weakly bound in a donor state(~ 0.01 eV) and can be easily promoted to the conduction band.
  4. Impurities which produce extra conduction electrons are called donors.
  5. Here majority charge carriers are electrons and minority charge carriers are holes.
  6. Conductivity is

P-type extrinsic semiconductors:

  1. Excess holes are produced by substituting trivalent impurities.
  2. A bond with the neighbors is incomplete and can be viewed as a hole weakly bound to the impurity atom.
  3. Elements in columns III of the periodic table (B, Al, Ga) are donors for semiconductors in the IV column, Si and Ge.
  4. Impurities of this type are called acceptors.
  5. Here majority charge carriers are holes and minority charge carriers are electrons.
  6. Conductivity is

Valance Band

Conduction Band

E f

E g

T = 0 KT > 0 K

Donor State

σ = neμe^ n^ -^ type Semiconductors

(a) This process happens in P-type. This can be understand from energy band scheme.

  1. In P-type semiconductor, when a pure si is doped with trivalent impurity it gives excess of holes in covalent bonds. Hence it is known as N-type semiconductors.
  2. Each impurity atom of this type introduces an energy level within the band gap, above yet very close to the top of the valence band.
  3. All holes present in this impurity level.
  4. If we give some energy corresponding to the gap between this impurity level and valence band. Then the excitation takes place from the valence band into this impurity electron state, as demonstrated in Figure.
  5. With such a transition, only one carrier is produced a hole in the valence band; a free electron is not created in either the impurity level or the conduction band.
  6. Hence maximum excitations are takes place from valence band to impurity level when compared with valence band to conduction band.
  7. An impurity of this type is called an acceptor, because it is capable of accepting an electron from the valence band, leaving behind a hole. It follows that the energy level within the band gap introduced by this type of impurity is called an acceptor state.

5. Compare the temperature dependence of the conductivity for metals and intrinsic semiconductors. Briefly explain the difference in behavior. In case of metals: As the temperature increases then the resistivity of metals increases because lattice thermal vibrations increases due to this the scattering of electrons takes place and mobility of the electrons decreases. Hence in metals the conductivity decreases with the increase of temperature. In case of semiconductors: As the temperature increases, the resistivity of semiconductors decreases because the excitation of electrons takes place from valence band to conduction band. Hence with the increase of temperature more number of electrons and holes produced. Hence conductivity increases in semiconductors with the increase of temperature. 6. Diagrammatically show Fermi energy level, in pure semiconductor and acceptor **and donor energy levels in impure semiconductors.

  1. Explain band structures of intrinsic and extrinsic semiconductors with neat** diagrams Intrinsic semiconductors Highly pure semiconductors with no impurities are called intrinsic semiconductors. In such a material there are no charge carriers at 0K. Since the valence band is filled and the conduction band is empty. At higher temperatures, the electrons reaching the conduction band due to thermal excitation leave equal number of holes in valence band. In intrinsic semiconductor, the number of free electrons is equal to the number of holes.
  1. If we give some energy corresponding to the gap between this impurity level and valence band. Then the excitation takes place from the valence band into this impurity electron state, as demonstrated in Figure.
  2. With such a transition, only one carrier is produced a hole in the valence band; a free electron is not created in either the impurity level or the conduction band.
  3. Hence maximum excitations are takes place from valence band to impurity level when compared with valence band to conduction band.
  4. An impurity of this type is called an acceptor, because it is capable of accepting an electron from the valence band, leaving behind a hole. It follows that the energy level within the band gap introduced by this type of impurity is called an acceptor state. 8. Distinguish between n-type and p-type semiconductors.

N-type semiconductor P-type semiconductor These are formed by adding pentavalent (V group elements) impurity in a pure semiconductor

These are formed by adding trivalent impurity (III group elements) in a pure semiconductor Ex: Si doped with Phosphorous Ex: Si doped with Boran These impurities are called donars These impurities are called acceptors Here majority charge carriers are electrons

Here majority charge carriers are holes

Conductivity is Conductivity is

9. Sketch the temperature dependence of carrier concentration in case of intrinsic and extrinsic semiconductors and write conclusions from them. Temperature dependence of carrier concentration in case of intrinsic semiconductors: Conclusions: 1. Figure drawn between logarithm of the intrinsic carrier concentration versus temperature for both silicon and germanium.

  1. The concentrations of electrons and holes increase with temperature because, with rising temperature, more thermal energy is available to excite electrons from the valence to the conduction band
  2. At all temperatures, carrier concentration in Ge is greater than for Si.This effect is due to germanium’s smaller band gap (Si - 0.67 versus Ge- 1.11 eV) 4. For Ge, at any given temperature more electrons will be excited across its band gap.

Temperature dependence of carrier concentration in case of extrinsic semiconductors:

Conclusions:

  1. Electron concentration versus temperature for silicon that has been doped with phosphorus atoms is plotted in Figure.
  2. This graph has three regions.
  3. First region is called as freeze-out region in which at low temperatures, below about 100 K, electron concentration drops with decreasing temperature, and approaches zero at 0 K. here temperature is insufficient to excite electrons from the P donor level into the conduction band.
  1. For dopant concentrations of 10^20 /m^3 and below both electrons and holes mobilities are independent of acceptor/donor concentration
  2. As the dopant concentrations increases both the plots are shifted to lower mobility values with increasing dopant.