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Lesson 9.1 • Competency 9.1Complete Lesson
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Semiconductors & Doping

Explore energy band theory, intrinsic silicon and germanium lattices, trivalent (p-type, holes) and pentavalent (n-type, electrons) doping, majority/minority carriers, and the mass action law.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • Distinguish conductors, semiconductors, and insulators using energy band gaps (valence, forbidden, conduction bands).
  • Explain intrinsic conduction via thermally generated electron-hole pairs and the effect of temperature.
  • Explain extrinsic semiconductor formation through trivalent (acceptor) and pentavalent (donor) doping and apply the mass action law n_e · n_h = n_i².

Core Theory & Concepts

Modern solid-state electronics relies fundamentally on controlling the electrical conductivity of tetravalent group 14 elements—primarily Silicon and Germanium. By selectively introducing microscopic concentrations of group 13 or group 15 impurity atoms (doping), charge carrier concentrations can be engineered across eight orders of magnitude.

Energy Band Gaps

Insulators possess wide forbidden gaps (Eg > 5 eV), conductors have overlapping bands (Eg = 0), and semiconductors have moderate gaps: Silicon Eg ≈ 1.1 eV, Germanium Eg ≈ 0.67 eV at 300 K.

E_g(\text{Si}) \approx 1.1\text{ eV}, \quad E_g(\text{Ge}) \approx 0.67\text{ eV}

Mass Action Law

In thermal equilibrium, the product of electron concentration n_e and hole concentration n_h is independent of doping level and depends only on temperature.

n_e \cdot n_h = n_i^2

Overall Neutrality

Despite doping, extrinsic semiconductors remain macroscopic electrically neutral because donor and acceptor ions retain equal and opposite charges to the added mobile carriers.

q(N_D^+ + p) = q(N_A^- + n)

Common Misconceptions

Misconception

An n-type semiconductor carries a net negative electric charge.

Physical Clarification:An n-type crystal is electrically neutral. For every extra free electron donated, an immobile positive donor ion (e.g., P⁺) remains bound in the crystal lattice.

Syllabus Topic Outline

Competency 9.1
  • 1Energy bands: valence band, forbidden gap (Eg), conduction band
  • 2Intrinsic semiconductors (Si: Eg ≈ 1.1 eV, Ge: Eg ≈ 0.67 eV)
  • 3Extrinsic n-type (donor doping, Group 15, majority electrons)
  • 4Extrinsic p-type (acceptor doping, Group 13, majority holes)
  • 5Mass action law: n_e · n_h = n_i² and overall electrical neutrality

Practice Problems

1
Competency 9.1 • foundation

Which impurity element produces a p-type semiconductor when added to pure Silicon?