Diodes and Rectification

Introduction

A diode passes substantial current more readily in one voltage direction than the other. That asymmetry, or rectification, follows from how an applied voltage changes a p–n junction's depletion barrier and the injection of minority carriers. The familiar exponential equation captures a useful regime, but real diodes also have recombination, series resistance, surface leakage and breakdown. Knowing both the model and its limits is more useful than memorising a single forward voltage.

Core explanation

Connect the p side to the positive terminal and n side to the negative terminal for forward bias . The applied field opposes the built-in field, reducing the barrier and allowing majority carriers to cross the junction. Electrons injected into the p side become minority carriers there; holes injected into the n side become minority carriers there. They diffuse and eventually recombine. With reverse bias , the external field reinforces the built-in field, the depletion region widens and majority-carrier injection is suppressed. A small reverse current can still flow from thermally generated minority carriers and leakage mechanisms. MIT's junction lecture treats bias and rectification alongside junction electrostatics.

An ideal relation is I = I₀[exp(eV/(ηk BT)) − 1] , where I₀ is a current scale, V is junction voltage positive in forward bias, and η is an ideality factor used to represent the dominant process. In a simple diffusion-limited ideal diode, η ≈ 1. Recombination within the depletion region can produce a different slope, often described by η nearer 2 over some range. I₀ is not “zero current”; it depends strongly on temperature, materials, geometry and carrier lifetimes. The thermal voltage k BT/e is about 25.9 mV near 300 K, but that is not the forward voltage of a complete practical diode at an arbitrary specified current.

At moderately positive V, the exponential dominates and small voltage changes can cause large current changes. At sufficiently high current, bulk and contact series resistance reduce the observed slope. Under reverse bias, the ideal expression tends toward −I₀, but actual leakage may vary with voltage, surface condition and temperature. Beyond a material- and structure-dependent reverse voltage, avalanche or Zener-type breakdown can produce large current. Breakdown is not automatically damage if current is limited in a device designed for it; uncontrolled heating can still destroy the junction.

Rectification is an electrical response , not one-way movement of all particles. Minority carriers still move under reverse bias, and a forward-biased diode stores charge. The diode equation assumes appropriate injection conditions and quasi-neutral regions; an LED, photodiode or heavily doped tunnel diode may require additional processes. MIT's device-course junction notes cover the transition from junction electrostatics to current–voltage models.

Step-by-step reasoning

1. Label p and n sides and the external terminal polarity. 2. Decide whether applied voltage lowers or raises the depletion barrier. 3. Identify majority-carrier injection and subsequent minority-carrier diffusion in forward bias. 4. If conditions fit, apply the diode equation with kelvin and consistent voltage units. 5. Check whether high current, leakage, light or breakdown invalidates a simple fit.

Visual explanation

Draw two band diagrams: forward bias shows a reduced barrier and reverse bias a larger one. Under them plot current versus voltage, with an exponential rise on the positive side and small negative current before breakdown. Label voltage across the junction , not necessarily the entire external circuit when series resistance is present.

Real-world analogy

A hill between two reservoirs can be made lower or higher by changing an external control. Lowering the hill allows many particles to cross; raising it leaves only rare crossings. The analogy explains barrier modulation but not the full minority-carrier diffusion, recombination or quantum transport in a real diode.

Real-world example

A rectifier circuit converts an alternating voltage into a current that mainly passes during one polarity. Real power diodes heat because they have a finite forward voltage at operating current and may suffer switching losses. A protective diode intentionally operated in reverse breakdown needs current-limiting circuitry. Both devices exploit a polarity-dependent response, but their required material properties and operating regimes differ.

Why?

Why does forward bias inject carriers rather than merely moving existing carriers faster? Reducing the junction barrier changes the number of carriers that can cross from their majority side. Once across, they are minorities in the receiving region and create a concentration gradient that drives diffusion. The exponential response arises from barrier-dependent carrier populations, not from a sudden increase in the speed of every electron.

Common misconception

“A silicon diode always drops exactly 0.7 V” is a rough circuit approximation, not a universal physical constant. Forward voltage varies with current, temperature, device area and construction. “Reverse current is exactly zero” is also false. Keep the p-positive convention clear so forward and reverse are not accidentally swapped.

Worked example

For an illustrative diode at 300 K, let η = 1, I₀ = 1.0 nA and V = 0.120 V. Since eV/k BT ≈ 0.120/0.0259 = 4.63, I ≈ (1.0 nA)(e^4.63 − 1) ≈ 101 nA . At V = −0.120 V, the same ideal model gives I ≈ (1.0 nA)(e^−4.63 − 1) ≈ −0.990 nA . The example shows rectification in the ideal regime; it does not account for series resistance or breakdown.

Quick check

1. Which terminal polarity forward-biases an ordinary p–n junction diode? Answer: Positive on the p side and negative on the n side.

Exam focus

Connect polarity to barrier change before writing the equation. Define V as the junction voltage and use T in kelvin. Explain the origin of minority-carrier injection. Mention series resistance, recombination and leakage when a measured curve departs from a single ideal exponential.

Advanced insight

The ideality factor is often extracted from a semilog I–V slope, but a fitted value by itself does not uniquely prove one microscopic pathway. Real junctions can have spatially nonuniform barriers and multiple parallel currents. At high switching speeds, charge stored in forward-injected minorities affects reverse recovery, an important property of power electronics.

Summary

Forward bias reduces a p–n junction's barrier and increases carrier injection; reverse bias raises it and usually leaves a much smaller current. An exponential equation describes a useful ideal regime, while actual diode behaviour also depends on recombination, resistance, leakage and breakdown.

Practice questions

1. What happens to depletion width under moderate reverse bias? Answer: It generally widens because the applied field reinforces the built-in field. 2. At V = 0, what current does the ideal diode equation predict? Answer: Zero, because exp(0) − 1 = 0 in equilibrium. 3. Why is I₀ not a universal constant for all diodes? Answer: It depends on material, temperature, geometry, minority-carrier properties and device construction. 4. What can make a measured high-current forward curve less steep than the ideal exponential? Answer: Series resistance in the bulk, contacts or wiring can consume part of the applied voltage.