Lecture 3: Electronic Circuits I - Carrier Transport and PN Junctions

Introduction

• Topic: Carrier transport in semiconductors and introduction to PN Junction.
• Instructor: Business Savvy.

Review of Previous Lecture

• Pure silicon: Low conductivity (~10^10 free electrons/cm³).
• Doping to increase conductivity:
  • N-type semiconductors: Doped with donor atoms (e.g., phosphorus) which provide extra electrons.
  • P-type semiconductors: Doped with acceptor atoms (e.g., boron) that create holes.

Carrier Dynamics in Doping

• N-type:
  • High doping level (e.g., 10^15 or 16) leads to free electrons approximately equal to dopant atoms.
• P-type:
  • High hole density equals the number of acceptor atoms, reducing the number of electrons.

Carrier Transport Mechanisms

Drift

• Caused by voltage across semiconductor creates an electric field.
• Carrier velocity reaches terminal velocity, given by:
  • Velocity = Mobility (μ) x Electric Field (E)
• Current expression derived:
  • I = Velocity x Area x Carrier Density x Charge on Electron
• Current expressed as current density (J) for unit area (A/cm²):
  • J = q(nμE + pμE)

Diffusion

• Movement of charge carriers from high to low concentration without electric field.
• Example: Ink molecules diffusing in water.
• Current due to diffusion (J):
  • J = -D(dn/dx) imes q (for electrons)
  • J = D(dP/dx) imes q (for holes)
• Diffusion current results from gradients in concentration.
• Recombination leads to disparities in carrier concentration.

Current Behavior in N-type Semiconductors

• Injecting electrons results in initial high concentration.
• Current decreases due to recombination with holes, implying fewer electrons remain.
• No recombination scenario leads to constant current.

Diffusivity Values

• D_n (electron diffusivity): 34 cm²/s
• D_p (hole diffusivity): 12 cm²/s

Relationship Between Mobility and Diffusivity

• Einstein's Relation:
  • D/μ = kT/q (where k is Boltzmann's constant, T is absolute temperature, q is electron charge).
  • At room temperature, this quantity is approximately 26 mV.

Transition to PN Junctions

• The simplest electronic device: two terminals (P-type and N-type).
• Applications: Diodes, voltage multipliers, chargers, etc.
• Unique characteristics compared to resistors (non-linear response to voltage).

Questions to Explore About PN Junctions

1. What happens to charge carriers at the junction?
2. Behavior of the junction under equilibrium, reverse bias, and forward bias conditions.

Equilibrium Condition of PN Junction

• P-type material has many holes, N-type has many electrons.
• Upon contact:
  • Holes diffuse to N-side, electrons diffuse to P-side.
  • Positive ions left in N-side, negative ions in P-side create an electric field.
• Depletion region forms where no free carriers exist, only ions.
• The electric field opposes further diffusion, leading to equilibrium.

Summary

• Mechanisms of drift and diffusion are essential for understanding charge transport in semiconductors.
• PN Junction formed through contact between P and N-type materials has unique behaviors driven by diffusion and electric fields.