Extrinsic Semiconductors 🚀

Adding just a few parts per million of the right impurity can make a sluggish intrinsic semiconductor spring to life! The boosted material is called an extrinsic (or doped) semiconductor. 🏃‍♂️ Its lattice stays almost unchanged because dopant and host atoms are nearly the same size. :contentReference[oaicite:0]{index=0}

Why Improve Conductivity? ⚡

  • At room temperature, intrinsic Si or Ge carries very little current, so it’s unusable for most devices. We fix that by doping.
  • Doping multiplies conductivity many-fold, enabling diodes, transistors, and integrated circuits. :contentReference[oaicite:1]{index=1}

Doping 101 🧑‍🔬

  • Dopant = the impurity atom we deliberately add.
  • Two main dopant families for tetravalent Si/Ge:
    • Pentavalent (valency 5) → As, Sb, P
    • Trivalent (valency 3) → B, Al, In
  • Dopant atoms slip into a few lattice sites without distorting the crystal. :contentReference[oaicite:2]{index=2}

n-Type (Donor) Material 🛠️

Insert a pentavalent atom. Four of its electrons bond; the fifth is almost free (needs only ≈ 0.01 eV in Ge or 0.05 eV in Si to break loose). That electron roams the lattice, so electrons dominate conduction. :contentReference[oaicite:3]{index=3}

The carrier count obeys \( n_e \gg n_h \)  (14.3). Electrons are the majority carriers; holes are minority. :contentReference[oaicite:4]{index=4}

p-Type (Acceptor) Material 💖

Swap in a trivalent atom. It can bond to only three neighbors, leaving one hole (an empty covalent spot). Nearby electrons hop in to fill the vacancy, but each hop just shifts the hole. Holes now carry the current, so \( n_h \gg n_e \)  (14.4). :contentReference[oaicite:5]{index=5}

Energy-Band Tweaks 🔋

  • Donor level \(E_D\) sits just below the conduction band \(E_C\); electrons need tiny energy to jump up and conduct. :contentReference[oaicite:6]{index=6}
  • Acceptor level \(E_A\) lies just above the valence band \(E_V\); a valence electron can hop into \(E_A\), leaving a mobile hole behind. :contentReference[oaicite:7]{index=7}
  • Overall carrier balance at thermal equilibrium follows the golden rule
    \( n_e\,n_h = n_i^{2} \)  (14.5). :contentReference[oaicite:8]{index=8}

Key Equations 📝

  • \( n_e \gg n_h \) (majority electrons in n-type)
  • \( n_h \gg n_e \) (majority holes in p-type)
  • \( n_e\,n_h = n_i^{2} \) (carrier product rule)

High-Yield NEET Nuggets 🎯

  1. Small-ppm doping rockets conductivity—essential for modern electronics.
  2. n-Type vs p-Type: know the dopant valency, majority carrier, and the inequalities \( n_e \gg n_h \) / \( n_h \gg n_e \).
  3. Donor and acceptor energy levels \(E_D\) and \(E_A\) sit close to the band edges, making carrier generation almost effortless.
  4. The equilibrium relation \( n_e\,n_h = n_i^{2} \) links majority and minority carriers and is a favorite conceptual question.
  5. Typical donor ionization energies (≈ 0.01 eV for Ge, 0.05 eV for Si) are orders of magnitude smaller than the band gap, explaining easy carrier release.

Happy learning! 😊