Electronic Circuits 1: Lecture 3 - Carrier Transport and PN Junction

Review from Last Lecture

• Pure silicon has low conductivity; improve conductivity by adding impurities (doping).
• N-type Semiconductors: Doped with donor atoms like phosphorus (provides extra electron).
  • High doping level increases free electrons.
• P-type Semiconductors: Doped with acceptor atoms like boron (creates a hole by lacking an electron).
  • High doping level increases holes; free electron density decreases.
• Majority Carrier Creation: By doping - more electrons in n-type, more holes in p-type.

Carrier Transport

• Drift: Current due to applied voltage creating an electric field.

  • Velocity: Terminal velocity equal to mobility (μ) times electric field (E).
  • Total current: Velocity × Cross section area (W*H) × Carrier density (n or p) × Charge (q).
  • Current Density: Expressed per unit area (e.g., amperes per square centimeter).

• Diffusion: Current due to carrier concentration gradients (without electric field).

  • High to low concentration movement across a semiconductor.
  • Example: Ink dispersing in water demonstrates diffusion process.
  • Diffusion Current: J (current density) ∝ dn/dx (slope of concentration) for electrons, dp/dx for holes.
  • Equation: J = q * Dn * (dn/dx) for electrons, q * Dp * (dp/dx) for holes.
  • Diffusivity: Dn (electrons) and Dp (holes).
  • Units: Dn = 34 cm²/s, Dp = 12 cm²/s (Diffusivity values).

• Einstein's Relation: Connects mobility (μ) and diffusivity (D).

  • D/μ = kT/q = 26 mV at room temperature (constant).

PN Junction

• Formation and Structure:

  • P-type and N-type semiconductors connected forming a junction.
  • Applications in chargers, voltage multipliers, etc.
  • Essential for understanding diodes.

• Diffusion and Equilibrium:

  • Holes from p-region and electrons from n-region diffuse across junction, leaving behind ions.
  • Leads to formation of space charge region, creating an electric field opposing diffusion.
  • Depletion Region: Region around the junction depleted of free carriers, only ions.

Characteristics and Behavior

• Experiment: Current-Voltage (I-V) characteristics of resistors and PN junctions.

  • Resistor: Linear relationship (Ohm's Law).
  • PN Junction: Non-linear, exponential in forward bias, minimal current in reverse bias.
  • Different behaviors for positive and negative voltages.

• Important Questions:

  • How do charge carriers redistribute themselves at the P-N interface?
  • How does the junction behave under equilibrium, reverse bias, and forward bias?

Summary

• Two main effects for current transport: Drift (voltage-driven) and Diffusion (concentration gradient-driven).
• Understanding of both effects essential for building and analyzing devices like PN junctions (diodes).
• PN junctions present unique properties and behaviors, forming the basis for more complex semiconductor devices like transistors.