Understanding PN Junction Diodes

Jan 4, 2025

Notes on PN Junction Diode Lecture

Introduction to PN Junction Diode

  • PN Junction Diode: Discussed under no applied bias.
  • Built-in Potential: Also known as barrier potential.

Depletion Layer Formation

  • Depletion Layer: Created due to charge carrier diffusion.
  • Diffusion: Process of free charge carriers recombining.
    • Example:
      • Hole combines with electron → immobile negative ion.
      • Electron combines with hole → immobile positive ion.
  • Charge Neutrality: Maintained when immobile ions and holes/electrons are present.
  • Immobile Ions:
    • P-side: Layer of negative immobile ions (from hole combining with electrons).
    • N-side: Layer of positive immobile ions (from electron combining with holes).
  • Barrier Potential:
    • Acts as a barrier, preventing further charge movement.
    • Positive layer repels holes; negative layer repels electrons.

Expression for Barrier Potential

  • Formula:
    • Barrier potential (V_B) = [ V_B = \frac{kT}{e} \ln \left( \frac{n_a n_d}{n_i^2} \right) ]
  • Components:
    • (k): Boltzmann constant, (1.38066 \times 10^{-23}) J/K.
    • (T): Absolute temperature in Kelvin.
    • (e): Charge of an electron, (1.6 \times 10^{-19}) C.
    • (n_a): Acceptor concentration.
    • (n_d): Donor concentration.
    • (n_i): Intrinsic carrier density.

Thermal Voltage (V_T)

  • Definition: Equivalent voltage of temperature.
  • Formula: ( V_T = \frac{kT}{e} )
  • Example Calculation: For room temperature (27°C):
    • Absolute temperature: 273 + 27 = 300 K.
    • ( V_T = 0.026 ) V (valid for room temperature).

Generalization of Thermal Voltage

  • For any temperature (T') in °C:
    • Absolute temperature: (T = 273 + T') K.
    • Generalized form of (V_T): ( V_T = \frac{(273 + T')}{11600} )

Numerical Problem Example

  • Given:
    • Acceptor concentration (n_a): (10^{16}) cm⁻³
    • Donor concentration (n_d): (10^{17}) cm⁻³
    • Intrinsic carrier density (n_i): (1.5 \times 10^{10}) cm⁻³
  • Calculation of Barrier Potential:
    • Use formula: ( V_B = V_T \ln \left( \frac{n_a n_d}{n_i^2} \right) )
    • Result: ( V_B = 0.757 ) V (for silicon PN junction at room temperature).

Important Values

  • Barrier potential for silicon: 0.7 V.
  • Barrier potential for germanium: 0.3 V.

Next Lecture Preview

  • Discussion on width of depletion region and related numerical problems.