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Semiconductor Electronics - Classification of Metals, Conductors and Semiconductors

Grade 12CBSEPhysics

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Electrical Conductivity (σ\sigma) and Resistivity (ρ\rho): Materials are classified based on their ability to conduct electricity. They are related by the formula ρ=1σ\rho = \frac{1}{\sigma}.

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Metals: These possess very low resistivity and high conductivity. The resistivity ranges from 10−210^{-2} to 10−8 Ωm10^{-8} \, \Omega m and conductivity ranges from 10210^{2} to 108 Sm−110^{8} \, S m^{-1}.

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Semiconductors: These have resistivity and conductivity values intermediate between metals and insulators. Resistivity ranges from 10−510^{-5} to 106 Ωm10^{6} \, \Omega m and conductivity ranges from 10510^{5} to 10−6 Sm−110^{-6} \, S m^{-1}.

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Insulators: These have very high resistivity and very low conductivity. Resistivity ranges from 101110^{11} to 1019 Ωm10^{19} \, \Omega m.

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Energy Bands: In solids, energy levels of electrons form continuous bands. The highest occupied energy band is the Valence Band (VB), and the next higher unoccupied band is the Conduction Band (CB).

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Energy Gap (EgE_g): The separation between the top of the Valence Band and the bottom of the Conduction Band is called the energy band gap (Eg=EC−EVE_g = E_C - E_V).

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Classification by Energy Gap: In metals, Eg≈0E_g \approx 0 (bands overlap). In semiconductors, 0<Eg<3 eV0 < E_g < 3 \, eV. In insulators, Eg>3 eVE_g > 3 \, eV.

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Elemental Semiconductors: These are composed of single atoms like Silicon (SiSi) and Germanium (GeGe).

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Compound Semiconductors: These are made of two or more elements, such as Gallium Arsenide (GaAsGaAs), Cadmium Sulfide (CdSCdS), or Anthracene (organic).

📐Formulae

ρ=1σ\rho = \frac{1}{\sigma}

Eg=EC−EVE_g = E_C - E_V

Eg(Si)≈1.1 eVE_g(\text{Si}) \approx 1.1 \, eV

Eg(Ge)≈0.72 eVE_g(\text{Ge}) \approx 0.72 \, eV

💡Examples

Problem 1:

A material has a band gap of Eg=5.5 eVE_g = 5.5 \, eV. Classify the material as a conductor, semiconductor, or insulator.

Solution:

Since the energy gap Eg=5.5 eVE_g = 5.5 \, eV is greater than 3 eV3 \, eV, electrons in the valence band do not have enough energy to jump to the conduction band even at room temperature.

Explanation:

According to the energy band theory, materials with Eg>3 eVE_g > 3 \, eV are classified as insulators.

Problem 2:

Calculate the conductivity (σ\sigma) of a sample if its resistivity (ρ\rho) is measured to be 2.5×10−4 Ωm2.5 \times 10^{-4} \, \Omega m.

Solution:

σ=1ρ\sigma = \frac{1}{\rho} σ=12.5×10−4\sigma = \frac{1}{2.5 \times 10^{-4}} σ=0.4×104 Sm−1\sigma = 0.4 \times 10^{4} \, S m^{-1} σ=4000 Sm−1\sigma = 4000 \, S m^{-1}

Explanation:

Conductivity is the reciprocal of resistivity. The unit is Sm−1S m^{-1} or Ω−1m−1\Omega^{-1} m^{-1}.

Problem 3:

If the energy of the conduction band minimum is EC=−4.5 eVE_C = -4.5 \, eV and the valence band maximum is EV=−5.6 eVE_V = -5.6 \, eV, find the energy gap and identify the material type.

Solution:

The energy gap is given by: Eg=EC−EVE_g = E_C - E_V −4.5−(−5.6)1.1\begin{array}{r} -4.5 \\ - (-5.6) \\ \hline 1.1 \end{array} Eg=1.1 eVE_g = 1.1 \, eV

Explanation:

Since the energy gap is 1.1 eV1.1 \, eV, which is less than 3 eV3 \, eV, the material is a semiconductor (specifically, this matches the value for Silicon).