PN Junction Forward Bias

Connecting the positive terminal of a battery to the p-side of a silicon diode pushes the diode into forward bias. This is the only condition under which a diode conducts significantly, and it is what makes the 1N4007 rectifier work in every AC-to-DC power supply on your desk.

Core Concept

In forward bias, the external voltage opposes the built-in electric field of the depletion region. The positive terminal connects to the p-side, pushing holes towards the junction. The negative terminal connects to the n-side, pushing electrons towards the junction. The depletion region narrows and the barrier potential falls.

Once the applied voltage exceeds the threshold voltage (about 0.6V for silicon), the barrier is low enough for majority carriers to cross in large numbers. Current rises exponentially with voltage, following the Shockley equation. At 0.7V across a 1N4007, you might have 10 to 100 mA flowing.

Minority carrier injection also occurs. Electrons are injected from n-side into p-side and diffuse away from the junction. Holes are injected from p-side into n-side. These minority carriers recombine within a diffusion length of the junction, releasing energy. In a light-emitting diode (LED) like the HLMP-D150, this recombination produces light.

Key Equations

Diode current (Shockley): I = IS × (e^(V / nVT) - 1) IS = reverse saturation current (≈ 10⁻¹⁰ A for 1N4007), n = ideality factor (1 for ideal), VT = 26 mV.

Threshold voltage for silicon: Vth ≈ 0.6 to 0.7V; for germanium: Vth ≈ 0.2 to 0.3V.

Dynamic resistance at operating point: rd = nVT / ID where ID is the quiescent forward current.

Diffusion length of minority carriers: Lp = sqrt(Dp × τp) where Dp = hole diffusion coefficient and τp = minority carrier lifetime.

Given:
  IS = 10⁻¹⁰ A (1N4007 reverse saturation current)
  n = 1 (ideal diode)
  VT = 26 mV = 0.026 V
  Applied forward voltage V = 0.65 V

Why this formula:
  The Shockley equation gives the exact forward current
  at any applied voltage in the exponential region.

Formula:
  I = IS × (e^(V / nVT) - 1)

Substitution:
  I = 10⁻¹⁰ × (e^(0.65 / 0.026) - 1)

Calculation:
  Exponent = 0.65 / 0.026 = 25
  e^25 = 7.20 × 10¹⁰
  e^25 - 1 ≈ 7.20 × 10¹⁰
  I = 10⁻¹⁰ × 7.20 × 10¹⁰
  I = 7.20 A

  Note: At V = 0.65V this current is unrealistically high
  for a real circuit. A series resistor limits it.
  With a 100Ω series resistor and 5V supply:
  IF = (5 - 0.65) / 100 = 43.5 mA (practical answer)

Final Answer:
  Intrinsic diode current at 0.65V ≈ 7.2 A
  With 100Ω series resistor: IF = 43.5 mA

Exam Tip: When GATE asks for forward diode current, decide whether to use the Shockley equation or the approximate circuit model (Vd = 0.7V, ideal). For circuit analysis problems, always use the 0.7V drop model. For physics questions, use I = IS×(e^(V/VT)-1). A common trap: forgetting that the diode voltage is fixed at 0.7V in a resistor-diode circuit, so increasing the supply only increases the resistor voltage. The voltage across the diode stays approximately 0.7V regardless of current (over a reasonable range).

Key Properties

• Forward voltage drop ≈ 0.7V for silicon, 0.3V for germanium, 1.8–3.5V for LEDs depending on colour.
• Current rises exponentially with voltage. A 60 mV increase at room temperature approximately multiplies current by 10.
• Dynamic resistance rd = VT/ID ≈ 26 mV / ID. At 26 mA, rd = 1Ω. At 1 mA, rd = 26Ω.
• Minority carrier injection occurs across the junction. In LEDs, this recombination is radiative (produces light).
• Forward voltage decreases with temperature at approximately -2 mV/°C. A diode at 100°C conducts at a lower voltage than at 25°C.
• The 1N4007 is rated at 1A average forward current, 1.1V maximum forward voltage at 1A, and can handle 30A peak surge for 1 cycle.

Quick Revision

• Forward bias: positive to p-side, negative to n-side.
• Depletion width narrows; barrier potential reduces.
• Current flows when V > 0.6V (Si). Model in circuits as VD = 0.7V.
• Shockley equation: I = IS × (e^(V/VT) - 1).
• Dynamic resistance: rd = VT / ID = 26 mV / ID.
• VD decreases by ≈ 2 mV per °C temperature rise.
• 60 mV additional forward voltage multiplies current by about 10 at 300K.
• Exam trap: using Shockley equation directly without a series resistor gives unrealistically large currents. In circuit problems, fix VD = 0.7V and solve for current using Ohm's law on the rest of the circuit.