How it works
When a covalent bond in the silicon lattice breaks due to thermal energy, one free electron and one hole are created simultaneously — this is electron-hole pair generation. The reverse process, recombination, happens when a free electron drops back into a vacant bond. At thermal equilibrium these two rates balance, keeping carrier concentration steady. The mass action law states that n × p = ni², so in intrinsic silicon n = p = ni. Since both electrons and holes carry current, total conductivity is σ = q(nμe + pμh), where μe ≈ 1350 cm²/V·s and μh ≈ 480 cm²/V·s for silicon at 300 K.
Key points to remember
In intrinsic silicon, electron and hole concentrations are equal: n = p = ni ≈ 1.5 × 10¹⁰ /cm³ at 300 K. Electron mobility is always higher than hole mobility — in silicon, μe ≈ 1350 cm²/V·s versus μh ≈ 480 cm²/V·s — so electrons contribute more to conductivity even when concentrations are equal. The Fermi level sits exactly at mid-gap for a perfectly intrinsic semiconductor. Carrier concentration increases exponentially with temperature, which is why silicon devices de-rate above 150°C. The mass action law ni² = np holds even after doping is added.
Exam tip
Every Anna University analog electronics paper has a numerical asking you to calculate conductivity of intrinsic silicon using σ = q(nμe + pμh) — substitute ni = 1.5 × 10¹⁰, q = 1.6 × 10⁻¹⁹ C, and the mobility values and you'll get full marks.