PN Junction Reverse Bias

Flip the battery terminals so the negative terminal connects to the p-side of a silicon diode and you have reverse bias. The 1N4007 blocks up to 1000V in this condition, which is exactly why bridge rectifiers can handle mains voltage without blowing up.

Core Concept

In reverse bias, the applied voltage adds to the built-in barrier. The negative terminal on the p-side pulls holes away from the junction. The positive terminal on the n-side pulls electrons away from the junction. The depletion region widens and the electric field across it grows stronger.

No majority carriers can cross the widened barrier. A tiny reverse saturation current IS flows because thermally generated minority carriers (electrons on the p-side, holes on the n-side) are swept across by the field. For a 1N4007, IS is in the range of 5 to 10 µA at room temperature. This current is nearly independent of the reverse voltage.

If the reverse voltage exceeds the breakdown voltage VBR, the current rises sharply. In the 1N4007, VBR = 1000V. Zener diodes are designed to operate in breakdown at controlled voltages (2.4V to 200V) and are used as voltage references. The BZX55C5V1 is a common 5.1V Zener in the 500mW package.

Key Equations

Reverse current (Shockley, V negative): I ≈ -IS for V << -VT Since e^(V/VT) → 0 for large negative V, I approaches -IS.

Depletion width under reverse bias: W(VR) = sqrt(2ε(V0 + VR)/q × (1/NA + 1/ND)) where VR is the magnitude of reverse voltage.

Junction capacitance (varactor effect): Cj = Cj0 / sqrt(1 + VR/V0) where Cj0 is the zero-bias junction capacitance.

Avalanche breakdown field for silicon: E_crit ≈ 3 × 10⁵ V/cm

Given:
  NA = 10¹⁶ cm⁻³
  ND = 10¹⁵ cm⁻³
  V0 = 0.64 V (calculated earlier)
  VR = 10 V (reverse bias applied)
  ε_Si = 11.7 × 8.85 × 10⁻¹² = 1.036 × 10⁻¹⁰ F/m
  q = 1.6 × 10⁻¹⁹ C

Why this formula:
  Reverse bias adds to V0, widening the depletion region.

Formula:
  W = sqrt(2ε(V0 + VR)/q × (1/NA + 1/ND))

Substitution (using SI: NA=10²² m⁻³, ND=10²¹ m⁻³):
  V_total = 0.64 + 10 = 10.64 V
  1/NA + 1/ND = 10⁻²² + 10⁻²¹ = 1.1 × 10⁻²¹ m³

Calculation:
  Numerator = 2 × 1.036×10⁻¹⁰ × 10.64 = 2.204 × 10⁻⁹
  Denom factor = 1.6×10⁻¹⁹ / 1.1×10⁻²¹ = 145.5
  W² = 2.204×10⁻⁹ × 1.1×10⁻²¹ / 1.6×10⁻¹⁹
     = 2.204×10⁻⁹ × 6.875×10⁻³
     = 1.515×10⁻¹¹
  W = sqrt(1.515×10⁻¹¹) ≈ 3.89 × 10⁻⁶ m = 3.89 µm

Final Answer:
  Depletion width at VR = 10V is approximately 3.89 µm
  Compare with W ≈ 1.06 µm at zero bias (VR = 0)

Exam Tip: GATE tests the junction capacitance formula Cj = Cj0 / sqrt(1 + VR/V0) and asks you to find how capacitance changes with reverse voltage. Cj decreases as VR increases. This is the principle of the varactor (variable capacitance diode) used in VCOs. Students often write that IS increases with reverse voltage; it does not. IS is essentially constant until breakdown. Also, IS doubles approximately every 10°C rise in temperature for silicon.

Key Properties

• Reverse current ≈ IS (saturation), nearly independent of reverse voltage until breakdown.
• Depletion width grows as sqrt(V0 + VR). At 10V reverse bias, W is about 3–4 µm for typical doping.
• Junction capacitance Cj = Cj0 / sqrt(1 + VR/V0) decreases with increasing reverse bias.
• IS approximately doubles for every 10°C temperature increase in silicon.
• Avalanche breakdown (1N4007 VBR = 1000V) occurs when the electric field reaches ~3×10⁵ V/cm and carrier multiplication by impact ionisation starts.
• Zener breakdown occurs at lower voltages (< 5V) due to quantum tunnelling. Both effects are used in Zener diodes depending on the doping profile.
• Varactor diodes (BB910 for FM tuners, SMV1235 for RF) exploit the voltage-controlled capacitance of reverse-biased junctions.

Quick Revision

• Reverse bias widens the depletion region and increases the barrier.
• Reverse current ≈ -IS (nA to µA range), constant with voltage.
• IS doubles every ~10°C for silicon.
• Junction capacitance: Cj = Cj0 / sqrt(1 + VR/V0).
• W grows as sqrt(V0 + VR); heavier doping → narrower W.
• 1N4007: VBR = 1000V (avalanche). BZX55C5V1: VZ = 5.1V (Zener/avalanche mix).
• Varactor: uses voltage-dependent Cj to tune oscillator frequency.
• Exam trap: writing that reverse current IS increases linearly with reverse voltage. IS is saturated and nearly constant. Only at breakdown does reverse current rise sharply.