Junction Capacitance

A PN junction diode does not behave purely as a resistive element. Depending on the bias condition, it stores charge in ways that resemble a capacitor. This charge-storage behavior introduces junction capacitance, which limits the switching speed of diodes and is a critical parameter in high-frequency circuit design and GATE problems.

Core Concept Explanation

Two distinct types of capacitance arise in a PN junction depending on the bias condition. Under reverse bias, the dominant effect is transition capacitance. Under forward bias, diffusion capacitance dominates. Understanding which one applies and why requires thinking about how charge is distributed near the junction.

When a PN junction is reverse biased, free carriers are pushed away from the junction, leaving behind a region of fixed ionized donors and acceptors. This depletion region is almost devoid of mobile charges and behaves electrically like the dielectric between two parallel metal plates. The two sides of the depletion boundary carry equal and opposite fixed charges, forming a natural capacitor. This is called transition capacitance (CT), also called junction capacitance or depletion capacitance.

As reverse bias increases, the depletion width W grows because more fixed charges are uncovered. Since capacitance is inversely proportional to separation, CT decreases with increasing reverse voltage. This voltage-dependent behavior is exploited in varactor diodes, which are used in voltage-controlled oscillators in communication systems.

Under forward bias, the depletion region shrinks and minority carriers are injected across the junction. These injected minority carriers accumulate near the junction boundaries before recombining. This stored minority charge constitutes diffusion capacitance (CD). Since the injected charge increases exponentially with forward voltage, CD increases steeply with forward bias. Diffusion capacitance is typically much larger than transition capacitance in forward bias.

Mathematical Expression

The transition capacitance for an abrupt PN junction is modeled as a parallel plate capacitor formed by the depletion region. The standard expression is:

CT = εA / W, where ε is the permittivity of the semiconductor, A is the junction cross-section area, and W is the total depletion width. Since W depends on reverse voltage VR as W proportional to (Vbi + VR)^(1/2) for an abrupt junction, it follows that CT proportional to (Vbi + VR)^(-1/2). The built-in potential Vbi is typically 0.6–0.7 V for silicon.

For diffusion capacitance, the expression is CD = tau * gm, where tau is the mean minority carrier lifetime and gm = IC / VT is the small signal transconductance of the diode at the operating point. Here VT is the thermal voltage (approximately 26 mV at room temperature). Since gm increases with forward current, CD increases rapidly with bias current.

Practical Understanding

In switching applications, a diode transitioning from forward to reverse bias must remove the stored minority charge before it can block current. The time taken for this is the reverse recovery time (trr), which is directly related to diffusion capacitance and minority carrier lifetime. Diodes with shorter carrier lifetime switch faster.

In RF and microwave circuits, transition capacitance limits the usable frequency range of a junction. A varactor diode uses the reverse-bias tunable transition capacitance to create electronically adjustable resonant circuits. GATE problems frequently test whether students apply the correct capacitance formula for the given bias condition.

Given:
Junction area A = 1e-4 cm², relative permittivity εr = 11.7 (silicon), ε0 = 8.85e-14 F/cm
Depletion width W = 0.5 μm = 0.5e-4 cm at reverse bias VR = 5 V

Why this formula applies:
Reverse bias means transition capacitance dominates; depletion region behaves as parallel plate capacitor.

Formula:
CT = ε * A / W = (εr * ε0 * A) / W

Substitution:
CT = (11.7 × 8.85e-14 × 1e-4) / (0.5e-4)

Calculation:
Numerator = 11.7 × 8.85e-14 × 1e-4 = 1.036e-16
Denominator = 0.5e-4 = 5e-5
CT = 1.036e-16 / 5e-5

Final Answer:
CT ≈ 2.07 pF

Exam Tip: CT decreases with increasing reverse voltage (CT proportional to VR^(-1/2) for abrupt junction). CD increases with forward current. GATE often asks which capacitance dominates under a given bias: always check bias direction first.

• Transition capacitance arises from the fixed charge stored in the depletion region under reverse bias.
• Diffusion capacitance arises from minority carriers stored near the junction under forward bias.
• CT decreases as reverse voltage increases because depletion width W grows with reverse bias.
• CD increases with forward current because injected minority charge increases exponentially.
• Reverse recovery time trr in switching diodes is directly linked to minority carrier lifetime and diffusion capacitance.

Quick Revision

• Two types: Transition capacitance CT (reverse bias) and Diffusion capacitance CD (forward bias).
• CT = εA/W; increases as W decreases (i.e., less reverse bias).
• CD = τ × gm = τ × IC/VT; increases with forward current.
• For abrupt junction: CT proportional to (Vbi + VR)^(-1/2).
• Varactor diodes exploit CT voltage dependence for tunable circuits.
• GATE trap: Do not apply CT formula in forward bias; CD dominates there.
• Larger minority carrier lifetime means larger CD and slower switching speed.