Intrinsic and Extrinsic Semiconductors

Why it matters

Intrinsic and extrinsic semiconductors form the backbone of modern electronic devices. Understanding these materials is essential for designing and optimizing components like diodes, transistors, and integrated circuits, which are pivotal in telecommunications, computing, and consumer electronics.

Key ideas

• Intrinsic Semiconductors: Pure semiconductor materials, typically silicon or germanium, with no impurities. They have equal numbers of electrons and holes as charge carriers.

  • At absolute zero, intrinsic semiconductors behave like insulators.
  • As temperature increases, thermal energy excites electrons, creating electron-hole pairs.

• Extrinsic Semiconductors: Doped semiconductors where impurities are added to modify electrical properties.

  • N-type: Doping with pentavalent atoms (e.g., phosphorus) adds extra electrons, increasing electron concentration.
  • P-type: Doping with trivalent atoms (e.g., boron) creates holes, increasing hole concentration.

• Doping: The process of adding impurities to intrinsic semiconductors to enhance conductivity.

  • Donor impurities: Provide extra electrons (N-type).
  • Acceptor impurities: Create holes (P-type).

• Charge Carriers: Electrons and holes that move through the semiconductor material, enabling current flow.

At thermal equilibrium in a nondegenerate semiconductor, np = n_i². Charge neutrality requires p + N_D⁺ = n + N_A⁻. For fully ionized uncompensated n-type material with N_D >> n_i, n ≈ N_D and p ≈ n_i²/N_D.

Formulas

• n_i = sqrt(N_c * N_v) * exp(-E_g / (2 * k * T))

  • n_i: Intrinsic carrier concentration (m^-3)
  • N_c: Effective density of states in the conduction band (m^-3)
  • N_v: Effective density of states in the valence band (m^-3)
  • E_g: Energy band gap (eV)
  • k: Boltzmann constant (8.617 x 10^-5 eV/K)
  • T: Temperature (K)

• σ = q * (n * μ_n + p * μ_p)

  • σ: Electrical conductivity (S/m)
  • q: Positive elementary-charge magnitude (1.6 x 10^-19 C)
  • n: Electron concentration (m^-3)
  • μ_n: Electron mobility (m^2/V·s)
  • p: Hole concentration (m^-3)
  • μ_p: Hole mobility (m^2/V·s)

Worked example

Given: An intrinsic silicon semiconductor at 300 K with N_c = 2.8 x 10^25 m^-3, N_v = 1.04 x 10^25 m^-3, and E_g = 1.12 eV.

1. Calculate intrinsic carrier concentration n_i.

   Formula: n_i = sqrt(N_c * N_v) * exp(-E_g / (2 * k * T))

   Substitute values:

   n_i = sqrt(2.8 x 10^25 * 1.04 x 10^25) * exp(-1.12 / (2 * 8.617 x 10^-5 * 300))

   n_i ≈ 6.67 x 10^15 m^-3

   Answer: n_i ≈ 6.67 x 10^15 m^-3

Common mistakes

• Confusing intrinsic and extrinsic semiconductors.
• Miscalculating the effect of temperature on carrier concentration.
• Incorrectly identifying donor and acceptor impurities.

For GATE EC

• Questions often involve calculating carrier concentrations and understanding the effects of doping.
• Practice problems on the temperature dependence of intrinsic carrier concentration and conductivity calculations.

Quick check

1. What is the primary difference between intrinsic and extrinsic semiconductors?
2. How does doping affect the conductivity of a semiconductor?
3. What type of impurity is added to create a P-type semiconductor?

Answers: 1. Intrinsic are pure, extrinsic are doped. 2. Doping increases conductivity. 3. Trivalent impurity.