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Intrinsic & Extrinsic Semiconductors

Semiconductor Devices · 10 min read

Pure Si is an insulator: every valence electron is locked in a covalent bond. Doping — replacing ~1 in 10⁷ atoms with an impurity — turns it into a controllable conductor.

  • Intrinsic: pure Si, n=p=nin = p = n_i.
  • Extrinsic: doped Si, majority carrier set by the dopant.

1. Carriers in intrinsic silicon

At 300 K thermal energy occasionally breaks a covalent bond, freeing one electron and leaving a hole. Both carriers drift under an applied field.

bond 0-0bond 0-1bond 0-2bond 1-0bond 1-1bond 1-2bond 2-0bond 2-1bond 2-2SiSiSiSiSiSiSiSiSiSiSiSie⁻h⁺
Figure 1. Intrinsic Si at 300 K: a broken bond releases an electron (green) and leaves a hole (red). Generation and recombination balance, so n = p.
ni=pi≈1010  cm−3  (Si, 300 K)n_i = p_i \approx 10^{10}\;\text{cm}^{-3}\;\text{(Si, 300 K)}
  • Si atom density: ∼5×1022  cm−3\sim 5\times 10^{22}\;\text{cm}^{-3}.
  • Only 1 bond in 5 × 10¹² is broken at any instant.
  • Hence intrinsic Si has very high resistivity (~2 × 10⁵ Ω·cm).

2. n-type doping (donors)

Replace one Si with a Group-V atom (P, As, Sb). Four of its five valence electrons bond; the fifth ionises easily and becomes a free conduction electron.

bond 0-0bond 0-1bond 0-2bond 1-0bond 1-1bond 1-2bond 2-0bond 2-1bond 2-2SiSiSiSiSiP⁺SiSiSiSiSiSie⁻
Figure 2. n-type Si: a phosphorus donor (blue) sits in the lattice. Four electrons bond; the fifth (green) ionises into the conduction band, leaving a fixed P⁺ ion.
ED≈0.045  eV≪kBT≈0.026  eV at 300 KE_D \approx 0.045\;\text{eV} \ll k_B T \approx 0.026\;\text{eV at 300 K}
  • Majority carriers: electrons (negative).
  • Donor concentration: NDN_D.
  • At room temperature n≈NDn \approx N_D (full ionisation).

3. p-type doping (acceptors)

Replace one Si with a Group-III atom (B, Al, Ga). Three valence electrons bond normally; the fourth bond is missing an electron — a hole that propagates as a positive carrier.

bond 0-0bond 0-1bond 0-2bond 1-0bond 1-1bond 1-2bond 2-0bond 2-1bond 2-2SiSiSiSiSiB⁻SiSiSiSiSiSih⁺
Figure 3. p-type Si: a boron acceptor (orange) takes a Si electron to complete its bond, becoming a fixed B⁻ ion. The vacated bond (red) drifts as a mobile hole.
  • Majority carriers: holes (positive).
  • Acceptor concentration: NAN_A.
  • p≈NAp \approx N_A at room temperature.

4. Mass-action law

Doping changes which carrier is dominant, not whether generation–recombination balance holds. At equilibrium the product np\,n p is fixed.

n⋅p=ni2n \cdot p = n_i^2
n ↑p ↓n · p = n_i² (constant)
Figure 4. Mass-action seesaw: in n-type, n ↑ and p ↓ such that the product stays at n_i². Fixing one carrier with the dopant locks the other.

Example: ND=1015  cm−3N_D = 10^{15}\;\text{cm}^{-3} in Si gives n≈1015n \approx 10^{15} and p≈ni2/ND=105  cm−3p \approx n_i^2 / N_D = 10^{5}\;\text{cm}^{-3}.

5. Charge neutrality

Each free electron pairs with a fixed donor ion; each free hole pairs with a fixed acceptor ion. Net charge of the bulk crystal is zero — doping rearranges charge, it does not add it.

p+ND+=n+NA−p + N_D^+ = n + N_A^-

6. Conductivity gain

n_i ≈ 10¹⁰10^1010^1410^1810^1010^1410^18N_D (cm⁻³)n (cm⁻³)
Figure 5. Carrier density vs. doping (Si, 300 K, log scale). Going from intrinsic to N_D = 10¹⁵ cm⁻³ raises n by five decades; resistivity drops by the same factor.
σ=q (n μn+p μp)\sigma = q\,(n\,\mu_n + p\,\mu_p)
  • Si mobilities: μn≈1350  cm2 V−1s−1\mu_n \approx 1350\;\text{cm}^2\,\text{V}^{-1}\text{s}^{-1}, μp≈480  cm2 V−1s−1\mu_p \approx 480\;\text{cm}^2\,\text{V}^{-1}\text{s}^{-1}.
  • Doping range used in ICs: 101410^{14} to 1020  cm−310^{20}\;\text{cm}^{-3}.
  • Resistivity tuneable over ~9 decades.
Group V → n-type, majority electrons, fixed +ions. Group III → p-type, majority holes, fixed −ions. Minority concentration is locked by np=ni2np = n_i^2; bulk stays neutral.