Intrinsic Semiconductor
Pure Si lattice — thermal breaking of covalent bonds creates e⁻/hole pairs (n=p=n_i).
Key Notes
An INTRINSIC semiconductor is pure — no dopants. Examples: ultra-pure Si and Ge.
At T = 0 K: VB fully filled, CB empty ⇒ behaves as insulator.
At room T: a few electrons thermally excited to CB, leaving an equal number of HOLES in VB ⇒ n = p = n_i.
Carrier density depends exponentially on temperature: n_i ∝ T^(3/2) · exp(−E_g/2k_BT).
For intrinsic Si at 300 K: n_i ≈ 1.5 × 10¹⁰/cm³. For Ge: ~2.4 × 10¹³/cm³.
Holes drift in the OPPOSITE direction to electrons in an applied field ⇒ both contribute to current in the SAME direction.
Intrinsic conductivity at room T is too small for practical devices ⇒ doping is essential.
Formulas
Carrier density
Strongly T-dependent.
Mass-action law
Valid in any semiconductor at equilibrium (also for doped).
Intrinsic conductivity
Both electrons and holes contribute.
n_i values (room T)
Reference numbers.
Important Points
n = p in intrinsic semiconductors — equal numbers of electrons and holes.
Conductivity is highly sensitive to temperature — intrinsic Si conductivity doubles roughly every 10°C.
Holes are NOT real particles — they are vacancies in the VB that behave as effective + charges.
Electron and hole mobilities differ: μ_e > μ_h typically (~1350 vs 480 cm²/V·s in Si).
Practical use of intrinsic semiconductors: thermistors (R drops fast with T), photoresistors (light creates carriers).
Doping increases conductivity ENORMOUSLY at the cost of breaking n = p.
Intrinsic Semiconductor notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.