9.3 P-N junctions

P-N Junction Fundamentals

A P-N junction forms where p-type and n-type semiconductor materials meet. This junction is the foundation of nearly every semiconductor device you'll encounter: diodes, transistors, solar cells, and LEDs all rely on P-N junction behavior. Understanding how charge carriers move (and don't move) across this junction is essential for the rest of this course.

Formation and Structure

When p-type and n-type materials are joined, electrons from the n-side and holes from the p-side diffuse across the boundary toward each other. As they cross over and recombine, they leave behind fixed ions that can no longer move. This creates the depletion region, a thin zone at the junction that's been swept clean of free charge carriers.

The fixed ions in the depletion region set up an electric field, which in turn creates a built-in potential (also called contact potential) across the junction. For silicon, this built-in potential is typically around 0.6–0.7 V. This voltage opposes further diffusion, so the system reaches equilibrium on its own with no external voltage applied.

The depletion region also stores charge, which means it behaves like a capacitor. This junction capacitance changes with applied voltage and becomes especially important in high-frequency circuit design.

Charge Distribution and Electric Field

Here's what's happening inside the depletion region at equilibrium:

• The p-side of the depletion region has a net negative charge (from fixed acceptor ions left behind after holes diffused away)
• The n-side of the depletion region has a net positive charge (from fixed donor ions left behind after electrons diffused away)
• The resulting electric field points from the n-side toward the p-side
• This field opposes further diffusion of majority carriers, balancing the system at equilibrium

Depletion Region Width and Junction Capacitance

The width of the depletion region depends on two things: the doping concentrations on each side and the applied voltage.

• Reverse bias widens the depletion region (more fixed ions are exposed)
• Forward bias narrows the depletion region (carriers are pushed back into the depleted zone)
• Higher doping on one side means the depletion region extends less into that side and more into the lightly doped side

Since junction capacitance is inversely proportional to depletion width, reverse bias decreases capacitance and forward bias increases it. This voltage-dependent capacitance is why P-N junctions can be used as variable capacitors (varactors) in tuning circuits.

Biasing and Current Flow

Forward Bias Condition

Forward bias means connecting the positive terminal to the p-side and the negative terminal to the n-side. Here's what happens step by step:

1. The external voltage opposes the built-in potential, lowering the barrier
2. The depletion region narrows
3. Majority carriers now have enough energy to cross the junction: electrons flow from n to p, holes flow from p to n
4. Diffusion current dominates, and current increases exponentially with voltage

This exponential relationship is captured by the Shockley diode equation:

$I = I_s\left(e^{qV/kT} - 1\right)$

Where:

• $I_s$ = reverse saturation current (a small constant, typically in the nanoamp range for silicon)
• $q$ = electron charge ($1.6 \times 10^{-19}$ C)
• $V$ = applied voltage
• $k$ = Boltzmann's constant ($1.38 \times 10^{-23}$ J/K)
• $T$ = absolute temperature in Kelvin

At room temperature (about 300 K), the quantity $kT/q$ is approximately 26 mV. This is called the thermal voltage and shows up constantly in semiconductor analysis.

Reverse Bias Condition

Reverse bias means connecting the positive terminal to the n-side and the negative terminal to the p-side. This increases the potential barrier and widens the depletion region.

• Majority carriers are pulled away from the junction, so almost no diffusion current flows
• A very small drift current (called leakage current) flows due to minority carriers being swept across by the electric field
• This reverse current is roughly constant and tiny (nanoamps in silicon) regardless of how much reverse voltage you apply

This holds until you reach the breakdown voltage, at which point current increases dramatically.

Current Components and Carrier Transport

Total current through a P-N junction has two components:

• Diffusion current: driven by the concentration gradient of carriers across the junction. Dominates under forward bias.
• Drift current: driven by the electric field in the depletion region. Dominates under reverse bias.

Within the depletion region, carriers can also recombine (an electron fills a hole, both disappear) or be generated (thermal energy creates a new electron-hole pair). These processes affect the actual current you measure, especially at low forward voltages where recombination current can be significant.

P-N Junction Characteristics

Current-Voltage (I-V) Characteristics

The I-V curve of a P-N junction has three distinct regions:

• Forward bias region: Current rises exponentially once the applied voltage exceeds roughly 0.6–0.7 V for silicon (about 0.3 V for germanium). Below this threshold, current is negligible.
• Reverse bias region: A small, nearly constant leakage current flows. The curve is almost flat.
• Breakdown region: Beyond the breakdown voltage, current shoots up rapidly.

The ideal diode approximation simplifies this: zero current in reverse bias, zero resistance in forward bias (turning on abruptly at the built-in potential). This is useful for quick circuit analysis, but real diodes have a gradual turn-on and nonzero reverse leakage.

Breakdown Mechanisms

When reverse voltage gets large enough, the junction "breaks down" and allows large reverse current. There are two distinct mechanisms:

• Avalanche breakdown: The strong electric field accelerates carriers to high speeds. When these fast carriers collide with atoms in the lattice, they knock loose new electron-hole pairs, which get accelerated and create even more pairs. This chain reaction causes current to multiply rapidly. Avalanche breakdown is typical in lightly doped junctions with wider depletion regions.
• Zener breakdown: In heavily doped junctions, the depletion region is very narrow. The electric field becomes strong enough that electrons can quantum-mechanically tunnel directly through the barrier without needing extra energy. This typically occurs at lower voltages (below about 5 V).

The breakdown voltage depends on doping concentrations and the semiconductor material's properties (bandgap, dielectric constant). Breakdown isn't necessarily destructive if current is limited; Zener diodes are specifically designed to operate in breakdown.

Applications and Device Considerations

P-N junctions are the basis for a wide range of devices:

• Rectifier diodes: Use forward bias to convert AC to DC by allowing current in only one direction
• Zener diodes: Operate in reverse breakdown to provide a stable reference voltage
• Solar cells: Absorb photons that generate electron-hole pairs near the junction; the built-in field separates them, producing current
• LEDs: Forward-biased junctions in certain materials emit photons when electrons and holes recombine
• Photodetectors: Reverse-biased junctions where incoming light generates carriers that produce a measurable current

When selecting or designing with P-N junction devices, junction capacitance matters for high-frequency applications (lower capacitance allows faster switching), and breakdown voltage sets the limit for how much reverse voltage the device can handle safely.