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P–n Junction: A Detailed Educational Resource

Semiconductor, Diode, Transistor, Integrated Circuit, Solar Cell, LED

Explore the fundamental properties and applications of the p–n junction, a key semiconductor structure in modern electronics.

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Introduction

A p–n junction is a fundamental building block in modern electronics, formed by joining two types of semiconductor materials: p-type and n-type within a single crystal structure. This junction exhibits unique electrical properties that are crucial for the operation of diodes, transistors, integrated circuits, and many other semiconductor devices.

p-type semiconductor: A semiconductor material that has been doped with impurities (like Boron) that create an excess of electron “holes,” which are locations where electrons are missing and can behave as positive charge carriers.

n-type semiconductor: A semiconductor material that has been doped with impurities (like Phosphorus) that contribute extra free electrons, which are negative charge carriers.

In an n-type semiconductor, there is a high concentration of free electrons, while a p-type semiconductor has a high concentration of electron holes. When these two materials are brought into contact to form a p–n junction, a fascinating phenomenon occurs at their interface, leading to the creation of a depletion region.

Depletion region: Also known as the depletion layer or space charge region, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers (electrons and holes) have been swept away by the electric field.

At the moment of junction formation, free electrons from the n-side diffuse across the boundary into the p-side, where they recombine with the abundant holes. Similarly, holes from the p-side diffuse into the n-side and recombine with electrons. This diffusion process doesn’t continue indefinitely because it creates an electric field across the junction. This electric field acts as a barrier, opposing further diffusion of charge carriers and leading to a state of equilibrium. The region near the junction becomes depleted of mobile charge carriers, hence the name “depletion region.”

A key characteristic of the p–n junction is its ability to conduct electric current predominantly in one direction. This unidirectional conductivity is the basis for the diode, the simplest semiconductor device.

Diode: A two-terminal electronic component that conducts current primarily in one direction (forward direction) and blocks current in the opposite direction (reverse direction). A p-n junction forms the core of most diodes.

Beyond diodes, p–n junctions are essential components in more complex semiconductor devices. For instance, the bipolar junction transistor (BJT) utilizes two p–n junctions in configurations like n–p–n or p–n–p to achieve amplification and switching functions.

Bipolar Junction Transistor (BJT): A three-terminal semiconductor device used for amplifying or switching electronic signals and power. It is composed of two p–n junctions.

Furthermore, by integrating numerous p–n junctions and other components on a single chip, engineers can create integrated circuits (ICs), which are the foundation of modern electronic systems.

Integrated Circuit (IC): Also known as a microchip or chip, is a set of electronic circuits on one small flat piece (or “chip”) of semiconductor material, usually silicon. Large numbers of tiny MOSFETs (metal-oxide-semiconductor field-effect transistors) integrate to form a complete electronic circuit.

Specialized p–n junctions are also at the heart of optoelectronic devices such as solar cells and light-emitting diodes (LEDs).

Solar cell: A photovoltaic device that converts light energy directly into electrical energy through the photovoltaic effect. It is essentially a specially designed p–n junction optimized for light absorption and electron-hole separation.

Light-emitting diode (LED): A semiconductor light source that emits light when current flows through it in the forward direction. The light emission occurs due to the recombination of electrons and holes near the p–n junction.

In a related structure called a Schottky junction, a metal is used in place of the n-type semiconductor to create a junction with a p-type semiconductor. Schottky junctions exhibit similar rectifying properties to p–n junctions and are used in various applications.

Schottky junction: A type of semiconductor junction formed between a metal and a semiconductor. It exhibits rectifying characteristics similar to a p–n junction diode.

History

The invention of the p–n junction is generally credited to American physicist Russell Ohl at Bell Laboratories in 1939. Ohl’s work during the early days of semiconductor research at Bell Labs was instrumental in recognizing the potential of p-n junctions.

Two years later, in 1941, Vadim Lashkaryov reported the observation of p–n junctions in cuprous oxide (Cu2O) and silver sulfide photocells, as well as selenium rectifiers. Lashkaryov’s findings provided further evidence and validation of the p–n junction phenomenon in different materials.

The modern theoretical understanding of p–n junctions was significantly advanced by William Shockley in his seminal book, Electrons and Holes in Semiconductors (1950). Shockley’s work provided a comprehensive theoretical framework for describing the behavior of electrons and holes in semiconductors and the operation of p–n junctions, laying the foundation for the development of transistor technology and the semiconductor industry as we know it today.

Properties

Both p-doped and n-doped semiconductors are individually relatively conductive due to the presence of mobile charge carriers (holes in p-type, electrons in n-type). However, the junction between them, the interface where these two materials meet, becomes electrically unique. At this boundary, the depletion region forms, which, under certain conditions, can become devoid of mobile charge carriers. The electrical behavior of the p–n junction is highly dependent on the bias applied across it.

Bias: The application of a voltage across a p–n junction or other electronic component to control its operating point and electrical characteristics.

There are two primary biasing conditions for a p–n junction: forward bias and reverse bias.

Forward bias: A voltage applied across a p–n junction in a direction that reduces the depletion region width and allows current to flow easily. In forward bias, the p-side is connected to the positive terminal and the n-side to the negative terminal of a voltage source.

Reverse bias: A voltage applied across a p–n junction in a direction that widens the depletion region and restricts current flow. In reverse bias, the p-side is connected to the negative terminal and the n-side to the positive terminal of a voltage source.

In essence, a p–n junction acts like a one-way valve for electric current. It readily allows current to flow when forward-biased and significantly restricts current flow when reverse-biased. This rectifying property is what makes p–n junctions indispensable in modern semiconductor electronics.

When a p–n junction is forward-biased, the energy barrier for charge carriers to cross the junction is lowered. Consequently, electrons from the n-side can easily flow to the p-side, and holes from the p-side can easily flow to the n-side, resulting in a significant current.

Conversely, when the p–n junction is reverse-biased, the energy barrier is increased. This makes it difficult for charge carriers to cross the junction, leading to a very small current, ideally close to zero. The increased resistance in reverse bias mode is a crucial characteristic for diode operation.

Equilibrium (Zero Bias)

In the absence of an external applied voltage (zero bias), a p–n junction reaches a state of equilibrium. Even in equilibrium, there’s a potential difference that naturally arises across the junction, known as the built-in potential (Vbi).

Built-in potential: Also called the junction potential or diffusion potential, is the electric potential difference that exists across the depletion region of a p–n junction in equilibrium (zero bias). It arises from the diffusion of charge carriers across the junction.

This built-in potential is a direct consequence of the diffusion of charge carriers at the junction.

Diffusion: The movement of particles from a region of high concentration to a region of low concentration due to random thermal motion. In semiconductors, both electrons and holes undergo diffusion.

Initially, at the junction, free electrons from the n-type region, being in a region of high concentration, start to randomly migrate into the p-type region (lower electron concentration). Similarly, holes from the p-type region diffuse into the n-type region (lower hole concentration).

As electrons diffuse into the p-type region, they encounter and recombine with holes, effectively cancelling each other out in the vicinity of the junction. The same happens with holes diffusing into the n-type region and recombining with electrons.

Crucially, the dopant atoms themselves, which create the n-type (donor atoms, positively charged) and p-type (acceptor atoms, negatively charged) characteristics, are fixed in the crystal lattice and cannot move. As electrons leave the n-side near the junction, they leave behind positively charged donor ions. Conversely, as holes leave the p-side near the junction, they leave behind negatively charged acceptor ions.

This process leads to the formation of the depletion region, where:

These layers of fixed charges create an electric field that is oriented from the positive n-side to the negative p-side. This electric field opposes further diffusion of mobile charge carriers. Eventually, an equilibrium is established when the electric field is strong enough to exactly counteract the diffusion force, preventing any further net flow of electrons and holes across the junction. This equilibrium state is characterized by the built-in potential and the depletion region.

The size of the depletion region is not uniform; it typically extends further into the less doped side of the junction to maintain charge neutrality. This is because the total charge on both sides of the depletion region must be equal in magnitude but opposite in sign.

Forward Bias

When a p–n junction is forward-biased, the p-type side is connected to the positive terminal of a voltage source, and the n-type side is connected to the negative terminal. This applied voltage opposes the built-in potential and alters the energy band diagram of the junction.

The applied forward bias effectively reduces the height of the potential barrier at the junction. This reduction in the potential barrier allows majority charge carriers to overcome the junction and flow across.

As these carriers reach the junction, the reduced depletion region width facilitates their movement across. Electrons are injected into the p-type material, and holes are injected into the n-type material.

Once injected into the opposite type material, these carriers become minority carriers. For example, electrons injected into the p-type region are minority carriers there. These minority carriers then undergo diffusion away from the junction into the neutral regions of the semiconductor.

The average distance a minority carrier travels before recombining with a majority carrier is known as the diffusion length.

Diffusion length: The average distance a minority carrier (electron in p-type or hole in n-type) travels before recombining with a majority carrier.

Although individual electrons may only travel a short diffusion length into the p-type material before recombining, the electric current through the diode is continuous. This is because holes (majority carriers in the p-type) simultaneously flow in the opposite direction towards the junction and into the n-type region.

According to Kirchhoff’s current law, the total current must be constant throughout the circuit.

Kirchhoff’s current law: States that the algebraic sum of currents entering a node (junction) in a circuit must equal the algebraic sum of currents leaving the node. In simpler terms, the total current in a circuit loop is constant.

Therefore, the current flow in a forward-biased p–n junction is a combination of electron flow from n to p and hole flow from p to n. Although they move in opposite directions, their conventional current direction is the same due to their opposite charges.

The relationship between the current through a p–n junction and the applied forward voltage is described by the Shockley diode equation (also known as the diode law).

Shockley diode equation: A mathematical equation that describes the current-voltage (I-V) characteristic of an ideal diode. It relates the diode current to the applied voltage, temperature, and diode parameters.

This equation models the exponential increase in current with increasing forward voltage, which is a key characteristic of diode behavior in forward bias.

Reverse Bias

In reverse bias, the connections are reversed: the p-type region is connected to the negative terminal, and the n-type region is connected to the positive terminal of the voltage supply. This configuration significantly alters the behavior of the p–n junction.

When reverse bias is applied:

This pulling away of charge carriers from the junction causes the depletion region to widen. As the depletion region widens, the potential barrier across the junction increases, making it even more difficult for charge carriers to cross. Consequently, the resistance of the p–n junction increases dramatically, and the current flow is reduced to a very small value, ideally close to zero (except for a small reverse saturation current due to minority carriers).

However, if the reverse bias voltage is increased beyond a certain critical point, a phenomenon called breakdown occurs, and the diode starts to conduct in the reverse direction. There are two primary mechanisms for breakdown: Zener breakdown and avalanche breakdown.

Zener breakdown: A breakdown mechanism in reverse-biased diodes that occurs at high doping concentrations and relatively low reverse voltages. It involves quantum mechanical tunneling of electrons through the narrow depletion region.

Avalanche breakdown: A breakdown mechanism in reverse-biased diodes that occurs at lower doping concentrations and higher reverse voltages. It involves impact ionization, where accelerated charge carriers collide with atoms in the depletion region, generating more electron-hole pairs and leading to a rapid increase in current.

Both Zener and avalanche breakdown are typically non-destructive processes, provided the current is limited to prevent overheating and thermal damage to the semiconductor material.

The breakdown phenomenon in reverse bias is utilized in Zener diodes, which are specifically designed to operate in the breakdown region for voltage regulation applications.

Zener diode: A special type of diode designed to reliably operate in the reverse breakdown region. It exhibits a sharp breakdown voltage and is used for voltage regulation and voltage reference applications.

For example, a Zener diode with a breakdown voltage of 5.6V will maintain a nearly constant voltage of 5.6V across it in reverse bias, even if the current through it varies within a certain range. This makes them useful for creating stable voltage references in circuits.

Another application of reverse biasing is in Varactor diodes (also known as varicap diodes or tuning diodes).

Varactor diode: A type of diode whose capacitance varies with the reverse voltage applied across it. The depletion region width changes with reverse voltage, altering the diode’s capacitance.

In Varactor diodes, the width of the depletion region, and hence the capacitance of the diode, is controlled by the reverse bias voltage. This voltage-variable capacitance property makes Varactor diodes useful in electronic tuning circuits, voltage-controlled oscillators, and frequency multipliers.

Governing Equations

Size of Depletion Region

To understand the quantitative behavior of the depletion region size, we can use Poisson’s equation, which relates the electric potential to the charge density.

Let:

Poisson’s Equation:

Poisson’s equation: A fundamental equation in electrostatics that relates the Laplacian of the electric potential to the charge density. In semiconductor physics, it is used to analyze the electric field and potential distribution within devices like p–n junctions.

The one-dimensional Poisson’s equation in this context is:

-{\frac {\mathrm {d} ^{2}V}{\mathrm {d} x^{2}}}={\frac {\rho }{\varepsilon }}={\frac {q}{\varepsilon }}\left[(P_{0}-N_{0})+(C_{D}-C_{A})\right]

Where:

Permittivity: A measure of how easily an electric field can propagate through a medium. It represents the ability of a material to store electrical energy in an electric field.

For an abrupt p–n junction (where doping changes sharply at the junction interface), and assuming complete depletion within the depletion region (i.e., P0 = N0 = 0 within the depletion region), we can simplify the analysis.

Let dp and dn be the widths of the depletion region in the p-side and n-side, respectively. Due to charge neutrality, the total charge on both sides of the depletion region must be equal in magnitude:

d_{p}C_{A}=d_{n}C_{D}

The potential difference (ΔV) across the depletion region can be derived by integrating Poisson’s equation and is related to the depletion widths and doping concentrations:

\Delta V={\frac {C_{A}C_{D}}{C_{A}+C_{D}}}{\frac {q}{2\varepsilon }}(d_{p}+d_{n})^{2}

If d is the total depletion region width (d = dp + dn), then:

d={\sqrt {{\frac {2\varepsilon }{q}}{\frac {C_{A}+C_{D}}{C_{A}C_{D}}}\Delta V}}

The potential difference ΔV can be further broken down into the built-in potential (ΔV0) and any externally applied voltage (ΔVext): ΔV = ΔV0 + ΔVext.

The built-in potential (ΔV0) can be calculated using the Einstein relation and assuming a non-degenerate semiconductor:

Einstein relation: In semiconductor physics, the Einstein relation connects the diffusion coefficient and the mobility of charge carriers. It is important for understanding transport phenomena in semiconductors.

\Delta V_{0}={\frac {kT}{q}}\ln \left({\frac {C_{A}C_{D}}{P_{0}N_{0}}}\right)={\frac {kT}{q}}\ln \left({\frac {C_{A}C_{D}}{n_{i}^{2}}}\right)

Where:

Boltzmann constant: A physical constant relating energy at the individual particle level with temperature at the bulk level. It is fundamental in thermodynamics and statistical mechanics.

Current across Depletion Region

The current-voltage characteristics of a p–n junction are described by the Shockley ideal diode equation. The total current is a result of different current components:

The Shockley diode equation, based on these current components, provides a comprehensive model for the electrical behavior of p–n junctions, particularly in forward bias and reverse bias (excluding breakdown).

See also

References

Further reading