Semiconductor Physics: Intrinsic and Extrinsic For students.

Semiconductor physics studies materials whose electrical conductivity sits between conductors (like copper) and insulators (like rubber) — and, crucially, can be controlled. Silicon and germanium are the classic examples. Adding tiny amounts of impurities (doping) tunes how many free charge carriers it has — the trick behind every transistor, diode and microchip.

It matters because the entire digital world rests on this one controllable property. A transistor is a semiconductor switch turned on and off billions of times per second; understanding intrinsic and extrinsic semiconductors means understanding the raw material of all electronics.

Key Concepts

• Energy bands — electrons live in the valence band (bound to atoms) or the conduction band (free to carry current). The band gap between them is about 1.12 eV for silicon at room temperature.
• Intrinsic semiconductor — pure silicon. Heat kicks a few electrons across the gap, creating equal free electrons (n) and holes (p) — holes are missing electrons behaving like positive charges. Here n = p = ni ≈ 1.5 × 10¹⁰ cm⁻³ for silicon at 300 K.
• Extrinsic semiconductor — doped silicon. n-type uses pentavalent atoms (phosphorus) donating extra electrons; p-type uses trivalent atoms (boron) creating extra holes.
• Majority/minority carriers — in n-type, electrons are the majority and holes the minority (reversed in p-type). The mass action law always holds: n × p = ni².
• Drift and diffusion — carriers move by drift (pushed by an electric field) and diffusion (spreading from high to low concentration); both currents flow inside every diode and transistor.

Formulas

• Mass action law: n × p = ni². With doping n ≈ Nd = 10¹⁶ cm⁻³ and ni = 1.5 × 10¹⁰ cm⁻³, p = ni²/n = 2.25 × 10²⁰/10¹⁶ = 2.25 × 10⁴ cm⁻³.
• Conductivity: σ = q(nμn + pμp), with q = 1.6 × 10⁻¹⁹ C and μn, μp the mobilities. Doping raises n by orders of magnitude, so conductivity follows.
• Thermal voltage: VT = kT/q ≈ 25.85 mV at 300 K — it appears in almost every diode and transistor equation.

Worked Example

Silicon is doped with phosphorus at Nd = 10¹⁶ cm⁻³ (n-type). At 300 K, ni = 1.5 × 10¹⁰ cm⁻³. Find the carrier concentrations and the increase over pure silicon.

1. Each phosphorus atom donates one electron: n ≈ 10¹⁶ cm⁻³.
2. p = ni²/n = (1.5 × 10¹⁰)²/10¹⁶ = 2.25 × 10²⁰/10¹⁶ = 2.25 × 10⁴ cm⁻³.
3. Pure silicon has n = 1.5 × 10¹⁰ cm⁻³. The doped wafer has 10¹⁶/(1.5 × 10¹⁰) ≈ 6.7 × 10⁵ times more electrons — nearly a million-fold increase from just 1 impurity atom per 5 million silicon atoms.
4. This enormous, precisely controlled change in conductivity is why doping is the foundation of all semiconductor devices.

Common Misconceptions

• "Doped silicon has a net electric charge." It does not — each donated electron is balanced by a fixed positive donor ion in the crystal, so the material stays neutral overall.
• "More doping is always better." Heavy doping shrinks the depletion region and can cause tunnelling or breakdown; designers choose doping levels carefully per application.

Real-World Applications

• Transistors: every CPU holds billions of MOSFETs built from precisely doped n-type and p-type regions.
• Solar cells: a large pn junction of doped silicon converts sunlight directly into electricity.
• Sensors: the strong temperature dependence of ni makes semiconductors excellent temperature sensors.

Semiconductor physics boils down to one controllable idea: pure silicon barely conducts, but a pinch of the right impurity adds nearly a million times more charge carriers. Intrinsic material gives the baseline; extrinsic doping gives engineers the knob.