Junction Capacitance, Switching & Breakdown

Why a diode is not an ideal switch. Learn depletion (junction) capacitance C_j = εA/W and its reverse-bias dependence, the C–V method for doping profiling, diffusion (storage) capacitance from injected charge, the charge-control model, forward and reverse recovery (storage time t_s, t_rr, Q_rr, soft vs snappy recovery), and breakdown mechanisms — avalanche (impact ionisation) and Zener (band-to-band tunnelling) — their doping and temperature dependence, dynamic resistance, pulse/energy ratings and safe operation — with Python computing C_j(V), C_d, storage time and breakdown voltage vs doping.

A diode stores charge: the fixed charge of the depletion region (like a capacitor whose plate spacing changes with voltage) and the injected minority carriers under forward bias. Removing that charge takes time and current, limiting switching speed and causing losses in power converters.

At high reverse voltage the junction breaks down. Used deliberately (Zener and TVS diodes) or avoided (rectifiers, transistors), breakdown sets the voltage rating of every semiconductor device.

An analogy

A forward-biased diode is like a sponge soaked with water (stored minority carriers): when you suddenly reverse it, water keeps flowing out the wrong way until the sponge is squeezed dry — that's reverse recovery.

Two capacitances

Junction capacitance comes from depletion charge changing with voltage; it dominates in reverse bias and is small (pF). Diffusion capacitance comes from stored minority charge Q = τI; it dominates in forward bias and can be nF–µF. Both appear in small-signal models and determine high-frequency behaviour: above ~1/(2πr_dC) the diode stops rectifying efficiently.

Switching behaviour

Key effects:

Breakdown mechanisms

Avalanche: carriers accelerated by high fields gain enough energy to create new electron–hole pairs (impact ionisation), multiplying current. It dominates above ~6–8 V (lightly doped junctions) with a positive temperature coefficient (more phonon scattering → higher BV at higher T). Zener: in heavily doped junctions (BV < ~5 V) the depletion layer is so thin that electrons tunnel directly from valence to conduction band; negative temperature coefficient. Near 5–6 V the two mechanisms mix, giving near-zero TC.

Practical breakdown and ratings

Planar junction curvature, surface charge and edges reduce BV below the parallel-plane value — terminations (guard rings, field plates, JTE, bevels) recover it. Devices are rated for repetitive peak reverse voltage (V_RRM), non-repetitive surge, avalanche energy (E_AS for MOSFETs), and pulse power (TVS). Breakdown itself is not destructive; excess energy (heating, current crowding, second breakdown) is.

Formulas

Worked example: C_j at bias

Given: C_j0 20 pF, V_bi 0.8 V, abrupt, V_R 7.2 V

Find: C_j.

Answer: 6.3 pF

Worked example: Diffusion capacitance

Given: τ 100 ns, I 5 mA

Find: C_d.

Answer: 19.3 nF

Worked example: Recovery loss

Given: Q_rr 200 nC, V_R 400 V, 50 kHz

Find: P.

Answer: 4 W

Reverse recovery waveform

  i_D
  I_F ──────┐
            │ di/dt set by circuit
   0 ───────┼─────────────────────────── t
            │     storage (t_s)  │ recovery
       −I_RM ─────────────────────╲___╱── (soft) or sharp snap (ringing, EMI)
            ├──────── t_rr ────────────┤   Q_rr = area of negative current

After the current reverses, the junction stays forward-biased while stored minority carriers are removed (storage phase), then the depletion region forms and current returns to zero. Q_rr and the snappiness of the tail set switching loss and EMI in converters.

Capacitances, storage time and breakdown voltage

import math
# Junction and diffusion capacitance, reverse-recovery storage time and avalanche breakdown voltage
Cj0, Vbi, m = 10e-12, 0.75, 0.5
for Vr in (0, 1, 5, 20):
    print(f"Cj at Vr = {Vr:2d} V: {Cj0/(1+Vr/Vbi)**m*1e12:.2f} pF")
tau, VT = 1e-6, 0.02585
for I in (1e-3, 10e-3):
    print(f"diffusion capacitance at {I*1e3:.0f} mA (tau 1 us): {tau*I/VT*1e9:.1f} nF")
IF, IR = 1.0, 0.5
ts = tau * math.log(1 + IF / IR)
print(f"storage time for IF 1 A switched to IR 0.5 A: ts = tau*ln(1 + IF/IR) = {ts*1e6:.2f} us")
q, eps = 1.602e-19, 11.7 * 8.854e-14
for N, Ecrit in ((1e14, 2.0e5), (1e15, 3.0e5), (1e16, 4.0e5), (1e17, 6.0e5)):
    BV = eps * Ecrit**2 / (2 * q * N)
    print(f"one-sided junction, N = {N:.0e}: Ecrit ~ {Ecrit:.1e} V/cm -> BV ~ {BV:.0f} V")
# Cj at Vr =  0 V: 10.00 pF
# Cj at Vr =  1 V: 6.55 pF
# Cj at Vr =  5 V: 3.61 pF
# Cj at Vr = 20 V: 1.90 pF
# diffusion capacitance at 1 mA (tau 1 us): 38.7 nF
# diffusion capacitance at 10 mA (tau 1 us): 386.8 nF
# storage time for IF 1 A switched to IR 0.5 A: ts = tau*ln(1 + IF/IR) = 1.10 us
# one-sided junction, N = 1e+14: Ecrit ~ 2.0e+05 V/cm -> BV ~ 1293 V
# one-sided junction, N = 1e+15: Ecrit ~ 3.0e+05 V/cm -> BV ~ 291 V
# one-sided junction, N = 1e+16: Ecrit ~ 4.0e+05 V/cm -> BV ~ 52 V
# one-sided junction, N = 1e+17: Ecrit ~ 6.0e+05 V/cm -> BV ~ 12 V

Reverse bias halves the junction capacitance within a few volts (C ∝ 1/√V) — the basis of varactors. Diffusion capacitance is huge (tens of nF) under forward current and dominates switching. A 1 µs lifetime gives ~1.1 µs storage time. Breakdown voltage scales inversely with doping: kilovolt devices need ~10¹⁴ cm⁻³ drift layers, while 10¹⁷ doping breaks down near 12 V.

Common mistakes

Applications

Key takeaways

Going further