P-n junction

# P-n junction

Overview
{{lowercase}} A p–n junction is formed at the boundary between a P-type
P-type semiconductor
A P-type semiconductor is obtained by carrying out a process of doping: that is, adding a certain type of atoms to the semiconductor in order to increase the number of free charge carriers ....

and N-type
N-type semiconductor
N-type semiconductors are a type of extrinsic semiconductor where the dopant atoms are capable of providing extra conduction electrons to the host material . This creates an excess of negative electron charge carriers....

semiconductor created in a single crystal of semiconductor by doping
Doping (semiconductor)
In semiconductor production, doping intentionally introduces impurities into an extremely pure semiconductor for the purpose of modulating its electrical properties. The impurities are dependent upon the type of semiconductor. Lightly and moderately doped semiconductors are referred to as extrinsic...

, for example by ion implantation
Ion implantation
Ion implantation is a materials engineering process by which ions of a material are accelerated in an electrical field and impacted into another solid. This process is used to change the physical, chemical, or electrical properties of the solid...

, diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...

of dopant
Dopant
A dopant, also called a doping agent, is a trace impurity element that is inserted into a substance in order to alter the electrical properties or the optical properties of the substance. In the case of crystalline substances, the atoms of the dopant very commonly take the place of elements that...

s, or by epitaxy
Epitaxy
Epitaxy refers to the deposition of a crystalline overlayer on a crystalline substrate, where the overlayer is in registry with the substrate. In other words, there must be one or more preferred orientations of the overlayer with respect to the substrate for this to be termed epitaxial growth. The...

(growing a layer of crystal doped with one type of dopant on top of a layer of crystal doped with another type of dopant). If two separate pieces of material were used, this would introduce a grain boundary
Grain boundary
A grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material...

between the semiconductors that severely inhibits its utility by scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

the electrons and holes.{{Citation needed|date=April 2010}}. P–N junctions are elementary "building blocks" of most semiconductor electronic devices
Semiconductor device
Semiconductor devices are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductors. Semiconductor devices have replaced thermionic devices in most applications...

such as diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

s, transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

s, solar cell
Solar cell
A solar cell is a solid state electrical device that converts the energy of light directly into electricity by the photovoltaic effect....

s, LEDs
LEDS
LEDS can be initials for:* Law Enforcement Data System* Link Eleven Display System* Low Energy Dislocation Structure* Land Electronic Defence System * LEDs * Life-Events and Difficulties Schedule...

, and integrated circuit
Integrated circuit
An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

s; they are the active sites where the electronic action of the device takes place.
Discussion
 Ask a question about 'P-n junction' Start a new discussion about 'P-n junction' Answer questions from other users Full Discussion Forum

Unanswered Questions
Recent Discussions
Encyclopedia
{{lowercase}}
A p–n junction is formed at the boundary between a P-type
P-type semiconductor
A P-type semiconductor is obtained by carrying out a process of doping: that is, adding a certain type of atoms to the semiconductor in order to increase the number of free charge carriers ....

and N-type
N-type semiconductor
N-type semiconductors are a type of extrinsic semiconductor where the dopant atoms are capable of providing extra conduction electrons to the host material . This creates an excess of negative electron charge carriers....

semiconductor created in a single crystal of semiconductor by doping
Doping (semiconductor)
In semiconductor production, doping intentionally introduces impurities into an extremely pure semiconductor for the purpose of modulating its electrical properties. The impurities are dependent upon the type of semiconductor. Lightly and moderately doped semiconductors are referred to as extrinsic...

, for example by ion implantation
Ion implantation
Ion implantation is a materials engineering process by which ions of a material are accelerated in an electrical field and impacted into another solid. This process is used to change the physical, chemical, or electrical properties of the solid...

, diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...

of dopant
Dopant
A dopant, also called a doping agent, is a trace impurity element that is inserted into a substance in order to alter the electrical properties or the optical properties of the substance. In the case of crystalline substances, the atoms of the dopant very commonly take the place of elements that...

s, or by epitaxy
Epitaxy
Epitaxy refers to the deposition of a crystalline overlayer on a crystalline substrate, where the overlayer is in registry with the substrate. In other words, there must be one or more preferred orientations of the overlayer with respect to the substrate for this to be termed epitaxial growth. The...

(growing a layer of crystal doped with one type of dopant on top of a layer of crystal doped with another type of dopant). If two separate pieces of material were used, this would introduce a grain boundary
Grain boundary
A grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material...

between the semiconductors that severely inhibits its utility by scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

the electrons and holes.{{Citation needed|date=April 2010}}. P–N junctions are elementary "building blocks" of most semiconductor electronic devices
Semiconductor device
Semiconductor devices are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductors. Semiconductor devices have replaced thermionic devices in most applications...

such as diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

s, transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

s, solar cell
Solar cell
A solar cell is a solid state electrical device that converts the energy of light directly into electricity by the photovoltaic effect....

s, LEDs
LEDS
LEDS can be initials for:* Law Enforcement Data System* Link Eleven Display System* Low Energy Dislocation Structure* Land Electronic Defence System * LEDs * Life-Events and Difficulties Schedule...

, and integrated circuit
Integrated circuit
An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

s; they are the active sites where the electronic action of the device takes place. For example, a common type of transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

, the bipolar junction transistor
Bipolar junction transistor
|- align = "center"| || PNP|- align = "center"| || NPNA bipolar transistor is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons...

, consists of two p–n junctions in series, in the form n–p–n or p–n–p. The discovery of the p–n junction is usually attributed to American physicist Russell Ohl
Russell Ohl
Russell Shoemaker Ohl was an American engineer who is generally recognized for patenting the modern solar cell ....

of Bell Laboratories. A Schottky junction is a special case of a p–n junction, where metal serves the role of the n-type semiconductor.

## Properties of a p–n junction

The p–n junction possesses some interesting properties that have useful applications in modern electronics. A p-doped semiconductor is relatively conductive. The same is true of an n-doped semiconductor, but the junction between them can become depleted
Depletion region
In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region or the space charge region, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers have diffused away, or have been forced away by an...

of charge carriers, and hence non-conductive, depending on the relative voltages of the two semiconductor regions. By manipulating this non-conductive layer, p–n junctions are commonly used as diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

s: circuit elements that allow a flow of electricity
Electricity
Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire...

in one direction but not in the other (opposite) direction. This property is explained in terms of forward bias and reverse bias, where the term bias refers to an application of electric voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

to the p–n junction.

## Equilibrium (zero bias)

In a p–n junction, without an external applied voltage, an equilibrium condition is reached in which a potential difference is formed across the junction. This potential difference is called built-in potential $V_\left\{\rm bi\right\}$. After joining p-type and n-type semiconductors, electrons near the p–n interface tend to diffuse into the p region. As electrons diffuse, they leave positively charged ions (donors
Donor (semiconductors)
In semiconductor physics, a donor is a dopant atom that, when added to a semiconductor, can form n-type regions.For example, when silicon , having four valence electrons, needs to be doped as an n-type semiconductor, elements from group V like phosphorus or arsenic can be used because they have...

) in the n region. Likewise, holes near the p–n interface begin to diffuse into the n-type region, leaving fixed ions (acceptors
Acceptor (semiconductors)
In semiconductor physics, an acceptor is a dopant atom that when added to a semiconductor can form p-type regions.For example, when silicon , having four valence electrons, needs to be doped as a p-type semiconductor, elements from group III like boron or aluminium , having three valence...

) with negative charge. The regions nearby the p–n interfaces lose their neutrality and become charged, forming the space charge region or depletion layer (see figure A).
The electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

created by the space charge region opposes the diffusion process for both electrons and holes. There are two concurrent phenomena: the diffusion process that tends to generate more space charge, and the electric field generated by the space charge that tends to counteract the diffusion. The carrier concentration profile at equilibrium is shown in figure A with blue and red lines. Also shown are the two counterbalancing phenomena that establish equilibrium.
The space charge region is a zone with a net charge provided by the fixed ions (donors
Donor (semiconductors)
In semiconductor physics, a donor is a dopant atom that, when added to a semiconductor, can form n-type regions.For example, when silicon , having four valence electrons, needs to be doped as an n-type semiconductor, elements from group V like phosphorus or arsenic can be used because they have...

or acceptors
Acceptor (semiconductors)
In semiconductor physics, an acceptor is a dopant atom that when added to a semiconductor can form p-type regions.For example, when silicon , having four valence electrons, needs to be doped as a p-type semiconductor, elements from group III like boron or aluminium , having three valence...

) that have been left uncovered by majority carrier diffusion. When equilibrium is reached, the charge density is approximated by the displayed step function. In fact, the region is completely depleted of majority carriers (leaving a charge density equal to the net doping level), and the edge between the space charge region and the neutral region is quite sharp (see figure B, Q(x) graph). The space charge region has the same magnitude of charge on both sides of the p–n interfaces, thus it extends farther on the less doped side (the n side in figures A and B).

## Forward bias

In forward bias, the p-type is connected with the positive terminal and the n-type is connected with the negative terminal. With a battery connected this way, the holes
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...

in the P-type region and the electrons in the N-type region are pushed toward the junction. This reduces the width of the depletion zone. The positive charge applied to the P-type material repels the holes, while the negative charge applied to the N-type material repels the electrons. As electrons and holes are pushed toward the junction, the distance between them decreases. This lowers the barrier in potential. With increasing forward-bias voltage, the depletion zone eventually becomes thin enough that the zone's electric field cannot counteract charge carrier motion across the p–n junction, as a consequence reducing electrical resistance. The electrons that cross the p–n junction into the P-type material (or holes that cross into the N-type material) will diffuse in the near-neutral region. Therefore, the amount of minority diffusion in the near-neutral zones determines the amount of current that may flow through the diode. Only majority carriers (electrons in N-type material or holes in P-type) can flow through a semiconductor for a macroscopic length. With this in mind, consider the flow of electrons across the junction. The forward bias causes a force on the electrons pushing them from the N side toward the P side. With forward bias, the depletion region is narrow enough that electrons can cross the junction and inject into the P-type material. However, they do not continue to flow through the P-type material indefinitely, because it is energetically favorable for them to recombine with holes. The average length an electron travels through the P-type material before recombining is called the diffusion length, and it is typically on the order of microns
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...

. Although the electrons penetrate only a short distance into the P-type material, the electric current continues uninterrupted, because holes (the majority carriers) begin to flow in the opposite direction. The total current (the sum of the electron and hole currents) is constant in space, because any variation would cause charge buildup over time (this is Kirchhoff's current law). The flow of holes from the P-type region into the N-type region is exactly analogous to the flow of electrons from N to P (electrons and holes swap roles and the signs of all currents and voltages are reversed). Therefore, the macroscopic picture of the current flow through the diode involves electrons flowing through the N-type region toward the junction, holes flowing through the P-type region in the opposite direction toward the junction, and the two species of carriers constantly recombining in the vicinity of the junction. The electrons and holes travel in opposite directions, but they also have opposite charges, so the overall current is in the same direction on both sides of the diode, as required. The Shockley diode equation models the forward-bias operational characteristics of a p–n junction outside the avalanche (reverse-biased conducting) region.

## Reverse bias

Reverse-biased usually refers to how a diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

is used in a circuit
Electronic circuit
An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow...

. If a diode is reverse-biased, the voltage at the cathode is higher than that at the anode. Therefore, no current will flow until the diode breaks down. Connecting the P-type region to the negative terminal of the battery and the N-type region to the positive terminal corresponds to reverse bias. The connections are illustrated in the following diagram: Because the p-type material is now connected to the negative terminal of the power supply, the 'holes
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...

' in the P-type material are pulled away from the junction, causing the width of the depletion zone to increase. Likewise, because the N-type region is connected to the positive terminal, the electrons will also be pulled away from the junction. Therefore, the depletion region
Depletion region
In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region or the space charge region, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers have diffused away, or have been forced away by an...

widens, and does so increasingly with increasing reverse-bias voltage. This increases the voltage barrier causing a high resistance to the flow of charge carriers, thus allowing minimal electric current to cross the p–n junction. The increase in resistance of the p–n junction results in the junction behaving as an insulator. The strength of the depletion zone electric field increases as the reverse-bias voltage increases. Once the electric field intensity increases beyond a critical level, the p–n junction depletion zone breaks down and current begins to flow, usually by either the Zener or the avalanche breakdown
Avalanche breakdown
Avalanche breakdown is a phenomenon that can occur in both insulating and semiconducting materials. It is a form of electric current multiplication that can allow very large currents within materials which are otherwise good insulators. It is a type of electron avalanche...

processes. Both of these breakdown processes are non-destructive and are reversible, as long as the amount of current flowing does not reach levels that cause the semiconductor material to overheat and cause thermal damage. This effect is used to one's advantage in Zener diode
Zener diode
A Zener diode is a special kind of diode which allows current to flow in the forward direction in the same manner as an ideal diode, but will also permit it to flow in the reverse direction when the voltage is above a certain value known as the breakdown voltage, "Zener knee voltage" or "Zener...

regulator circuits. Zener diodes have a certain - low - breakdown voltage. A standard value for breakdown voltage is for instance 5.6 V. This means that the voltage at the cathode can never be more than 5.6 V higher than the voltage at the anode, because the diode will break down - and therefore conduct - if the voltage gets any higher. This in effect regulates the voltage over the diode. Another application where reverse biased diodes are used is in Varicap
Varicap
In electronics, a varicap diode, varactor diode, variable capacitance diode, variable reactance diode or tuning diode is a type of diode which has a variable capacitance that is a function of the voltage impressed on its terminals....

diodes. The width of the depletion zone of any diode changes with voltage applied. This varies the capacitance of the diode. For more information, refer to the Varicap
Varicap
In electronics, a varicap diode, varactor diode, variable capacitance diode, variable reactance diode or tuning diode is a type of diode which has a variable capacitance that is a function of the voltage impressed on its terminals....

article.

## Electrostatics

For a p–n junction Poisson's equation
Poisson's equation
In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in electrostatics, mechanical engineering and theoretical physics...

becomes $\Delta \varphi =-\frac\left\{\rho \right\}\left\{\varepsilon \right\}=\frac\left\{q\right\}\left\{\varepsilon \right\}\left\left( \underbrace \left\{\left\{lowercase\right\}\right\}$
A p–n junction is formed at the boundary between a P-type
P-type semiconductor
A P-type semiconductor is obtained by carrying out a process of doping: that is, adding a certain type of atoms to the semiconductor in order to increase the number of free charge carriers ....

and N-type
N-type semiconductor
N-type semiconductors are a type of extrinsic semiconductor where the dopant atoms are capable of providing extra conduction electrons to the host material . This creates an excess of negative electron charge carriers....

semiconductor created in a single crystal of semiconductor by doping
Doping (semiconductor)
In semiconductor production, doping intentionally introduces impurities into an extremely pure semiconductor for the purpose of modulating its electrical properties. The impurities are dependent upon the type of semiconductor. Lightly and moderately doped semiconductors are referred to as extrinsic...

, for example by ion implantation
Ion implantation
Ion implantation is a materials engineering process by which ions of a material are accelerated in an electrical field and impacted into another solid. This process is used to change the physical, chemical, or electrical properties of the solid...

, diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...

of dopant
Dopant
A dopant, also called a doping agent, is a trace impurity element that is inserted into a substance in order to alter the electrical properties or the optical properties of the substance. In the case of crystalline substances, the atoms of the dopant very commonly take the place of elements that...

s, or by epitaxy
Epitaxy
Epitaxy refers to the deposition of a crystalline overlayer on a crystalline substrate, where the overlayer is in registry with the substrate. In other words, there must be one or more preferred orientations of the overlayer with respect to the substrate for this to be termed epitaxial growth. The...

(growing a layer of crystal doped with one type of dopant on top of a layer of crystal doped with another type of dopant). If two separate pieces of material were used, this would introduce a grain boundary
Grain boundary
A grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material...

between the semiconductors that severely inhibits its utility by scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

the electrons and holes.{{Citation needed|date=April 2010}}. P–N junctions are elementary "building blocks" of most semiconductor electronic devices
Semiconductor device
Semiconductor devices are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductors. Semiconductor devices have replaced thermionic devices in most applications...

such as diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

s, transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

s, solar cell
Solar cell
A solar cell is a solid state electrical device that converts the energy of light directly into electricity by the photovoltaic effect....

s, LEDs
LEDS
LEDS can be initials for:* Law Enforcement Data System* Link Eleven Display System* Low Energy Dislocation Structure* Land Electronic Defence System * LEDs * Life-Events and Difficulties Schedule...

, and integrated circuit
Integrated circuit
An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

s; they are the active sites where the electronic action of the device takes place. For example, a common type of transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

, the bipolar junction transistor
Bipolar junction transistor
|- align = "center"| || PNP|- align = "center"| || NPNA bipolar transistor is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons...

, consists of two p–n junctions in series, in the form n–p–n or p–n–p. The discovery of the p–n junction is usually attributed to American physicist Russell Ohl
Russell Ohl
Russell Shoemaker Ohl was an American engineer who is generally recognized for patenting the modern solar cell ....

of Bell Laboratories. A Schottky junction is a special case of a p–n junction, where metal serves the role of the n-type semiconductor.

## Properties of a p–n junction

The p–n junction possesses some interesting properties that have useful applications in modern electronics. A p-doped semiconductor is relatively conductive. The same is true of an n-doped semiconductor, but the junction between them can become depleted
Depletion region
In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region or the space charge region, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers have diffused away, or have been forced away by an...

of charge carriers, and hence non-conductive, depending on the relative voltages of the two semiconductor regions. By manipulating this non-conductive layer, p–n junctions are commonly used as diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

s: circuit elements that allow a flow of electricity
Electricity
Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire...

in one direction but not in the other (opposite) direction. This property is explained in terms of forward bias and reverse bias, where the term bias refers to an application of electric voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

to the p–n junction.

## Equilibrium (zero bias)

In a p–n junction, without an external applied voltage, an equilibrium condition is reached in which a potential difference is formed across the junction. This potential difference is called built-in potential $V_\left\{\rm bi\right\}$. After joining p-type and n-type semiconductors, electrons near the p–n interface tend to diffuse into the p region. As electrons diffuse, they leave positively charged ions (donors
Donor (semiconductors)
In semiconductor physics, a donor is a dopant atom that, when added to a semiconductor, can form n-type regions.For example, when silicon , having four valence electrons, needs to be doped as an n-type semiconductor, elements from group V like phosphorus or arsenic can be used because they have...

) in the n region. Likewise, holes near the p–n interface begin to diffuse into the n-type region, leaving fixed ions (acceptors
Acceptor (semiconductors)
In semiconductor physics, an acceptor is a dopant atom that when added to a semiconductor can form p-type regions.For example, when silicon , having four valence electrons, needs to be doped as a p-type semiconductor, elements from group III like boron or aluminium , having three valence...

) with negative charge. The regions nearby the p–n interfaces lose their neutrality and become charged, forming the space charge region or depletion layer (see figure A).
The electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

created by the space charge region opposes the diffusion process for both electrons and holes. There are two concurrent phenomena: the diffusion process that tends to generate more space charge, and the electric field generated by the space charge that tends to counteract the diffusion. The carrier concentration profile at equilibrium is shown in figure A with blue and red lines. Also shown are the two counterbalancing phenomena that establish equilibrium.
The space charge region is a zone with a net charge provided by the fixed ions (donors
Donor (semiconductors)
In semiconductor physics, a donor is a dopant atom that, when added to a semiconductor, can form n-type regions.For example, when silicon , having four valence electrons, needs to be doped as an n-type semiconductor, elements from group V like phosphorus or arsenic can be used because they have...

or acceptors
Acceptor (semiconductors)
In semiconductor physics, an acceptor is a dopant atom that when added to a semiconductor can form p-type regions.For example, when silicon , having four valence electrons, needs to be doped as a p-type semiconductor, elements from group III like boron or aluminium , having three valence...

) that have been left uncovered by majority carrier diffusion. When equilibrium is reached, the charge density is approximated by the displayed step function. In fact, the region is completely depleted of majority carriers (leaving a charge density equal to the net doping level), and the edge between the space charge region and the neutral region is quite sharp (see figure B, Q(x) graph). The space charge region has the same magnitude of charge on both sides of the p–n interfaces, thus it extends farther on the less doped side (the n side in figures A and B).

## Forward bias

In forward bias, the p-type is connected with the positive terminal and the n-type is connected with the negative terminal. With a battery connected this way, the holes
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...

in the P-type region and the electrons in the N-type region are pushed toward the junction. This reduces the width of the depletion zone. The positive charge applied to the P-type material repels the holes, while the negative charge applied to the N-type material repels the electrons. As electrons and holes are pushed toward the junction, the distance between them decreases. This lowers the barrier in potential. With increasing forward-bias voltage, the depletion zone eventually becomes thin enough that the zone's electric field cannot counteract charge carrier motion across the p–n junction, as a consequence reducing electrical resistance. The electrons that cross the p–n junction into the P-type material (or holes that cross into the N-type material) will diffuse in the near-neutral region. Therefore, the amount of minority diffusion in the near-neutral zones determines the amount of current that may flow through the diode. Only majority carriers (electrons in N-type material or holes in P-type) can flow through a semiconductor for a macroscopic length. With this in mind, consider the flow of electrons across the junction. The forward bias causes a force on the electrons pushing them from the N side toward the P side. With forward bias, the depletion region is narrow enough that electrons can cross the junction and inject into the P-type material. However, they do not continue to flow through the P-type material indefinitely, because it is energetically favorable for them to recombine with holes. The average length an electron travels through the P-type material before recombining is called the diffusion length, and it is typically on the order of microns
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...

. Although the electrons penetrate only a short distance into the P-type material, the electric current continues uninterrupted, because holes (the majority carriers) begin to flow in the opposite direction. The total current (the sum of the electron and hole currents) is constant in space, because any variation would cause charge buildup over time (this is Kirchhoff's current law). The flow of holes from the P-type region into the N-type region is exactly analogous to the flow of electrons from N to P (electrons and holes swap roles and the signs of all currents and voltages are reversed). Therefore, the macroscopic picture of the current flow through the diode involves electrons flowing through the N-type region toward the junction, holes flowing through the P-type region in the opposite direction toward the junction, and the two species of carriers constantly recombining in the vicinity of the junction. The electrons and holes travel in opposite directions, but they also have opposite charges, so the overall current is in the same direction on both sides of the diode, as required. The Shockley diode equation models the forward-bias operational characteristics of a p–n junction outside the avalanche (reverse-biased conducting) region.

## Reverse bias

Reverse-biased usually refers to how a diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

is used in a circuit
Electronic circuit
An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow...

. If a diode is reverse-biased, the voltage at the cathode is higher than that at the anode. Therefore, no current will flow until the diode breaks down. Connecting the P-type region to the negative terminal of the battery and the N-type region to the positive terminal corresponds to reverse bias. The connections are illustrated in the following diagram: Because the p-type material is now connected to the negative terminal of the power supply, the 'holes
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...

' in the P-type material are pulled away from the junction, causing the width of the depletion zone to increase. Likewise, because the N-type region is connected to the positive terminal, the electrons will also be pulled away from the junction. Therefore, the depletion region
Depletion region
In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region or the space charge region, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers have diffused away, or have been forced away by an...

widens, and does so increasingly with increasing reverse-bias voltage. This increases the voltage barrier causing a high resistance to the flow of charge carriers, thus allowing minimal electric current to cross the p–n junction. The increase in resistance of the p–n junction results in the junction behaving as an insulator. The strength of the depletion zone electric field increases as the reverse-bias voltage increases. Once the electric field intensity increases beyond a critical level, the p–n junction depletion zone breaks down and current begins to flow, usually by either the Zener or the avalanche breakdown
Avalanche breakdown
Avalanche breakdown is a phenomenon that can occur in both insulating and semiconducting materials. It is a form of electric current multiplication that can allow very large currents within materials which are otherwise good insulators. It is a type of electron avalanche...

processes. Both of these breakdown processes are non-destructive and are reversible, as long as the amount of current flowing does not reach levels that cause the semiconductor material to overheat and cause thermal damage. This effect is used to one's advantage in Zener diode
Zener diode
A Zener diode is a special kind of diode which allows current to flow in the forward direction in the same manner as an ideal diode, but will also permit it to flow in the reverse direction when the voltage is above a certain value known as the breakdown voltage, "Zener knee voltage" or "Zener...

regulator circuits. Zener diodes have a certain - low - breakdown voltage. A standard value for breakdown voltage is for instance 5.6 V. This means that the voltage at the cathode can never be more than 5.6 V higher than the voltage at the anode, because the diode will break down - and therefore conduct - if the voltage gets any higher. This in effect regulates the voltage over the diode. Another application where reverse biased diodes are used is in Varicap
Varicap
In electronics, a varicap diode, varactor diode, variable capacitance diode, variable reactance diode or tuning diode is a type of diode which has a variable capacitance that is a function of the voltage impressed on its terminals....

diodes. The width of the depletion zone of any diode changes with voltage applied. This varies the capacitance of the diode. For more information, refer to the Varicap
Varicap
In electronics, a varicap diode, varactor diode, variable capacitance diode, variable reactance diode or tuning diode is a type of diode which has a variable capacitance that is a function of the voltage impressed on its terminals....

article.

## Electrostatics

For a p–n junction Poisson's equation
Poisson's equation
In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in electrostatics, mechanical engineering and theoretical physics...

becomes $\Delta \varphi =-\frac\left\{\rho \right\}\left\{\varepsilon \right\}=\frac\left\{q\right\}\left\{\varepsilon \right\}\left\left( \underbrace \left\{\left\{lowercase\right\}\right\}$
A p–n junction is formed at the boundary between a P-type
P-type semiconductor
A P-type semiconductor is obtained by carrying out a process of doping: that is, adding a certain type of atoms to the semiconductor in order to increase the number of free charge carriers ....

and N-type
N-type semiconductor
N-type semiconductors are a type of extrinsic semiconductor where the dopant atoms are capable of providing extra conduction electrons to the host material . This creates an excess of negative electron charge carriers....

semiconductor created in a single crystal of semiconductor by doping
Doping (semiconductor)
In semiconductor production, doping intentionally introduces impurities into an extremely pure semiconductor for the purpose of modulating its electrical properties. The impurities are dependent upon the type of semiconductor. Lightly and moderately doped semiconductors are referred to as extrinsic...

, for example by ion implantation
Ion implantation
Ion implantation is a materials engineering process by which ions of a material are accelerated in an electrical field and impacted into another solid. This process is used to change the physical, chemical, or electrical properties of the solid...

, diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...

of dopant
Dopant
A dopant, also called a doping agent, is a trace impurity element that is inserted into a substance in order to alter the electrical properties or the optical properties of the substance. In the case of crystalline substances, the atoms of the dopant very commonly take the place of elements that...

s, or by epitaxy
Epitaxy
Epitaxy refers to the deposition of a crystalline overlayer on a crystalline substrate, where the overlayer is in registry with the substrate. In other words, there must be one or more preferred orientations of the overlayer with respect to the substrate for this to be termed epitaxial growth. The...

(growing a layer of crystal doped with one type of dopant on top of a layer of crystal doped with another type of dopant). If two separate pieces of material were used, this would introduce a grain boundary
Grain boundary
A grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material...

between the semiconductors that severely inhibits its utility by scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

the electrons and holes.{{Citation needed|date=April 2010}}. P–N junctions are elementary "building blocks" of most semiconductor electronic devices
Semiconductor device
Semiconductor devices are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductors. Semiconductor devices have replaced thermionic devices in most applications...

such as diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

s, transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

s, solar cell
Solar cell
A solar cell is a solid state electrical device that converts the energy of light directly into electricity by the photovoltaic effect....

s, LEDs
LEDS
LEDS can be initials for:* Law Enforcement Data System* Link Eleven Display System* Low Energy Dislocation Structure* Land Electronic Defence System * LEDs * Life-Events and Difficulties Schedule...

, and integrated circuit
Integrated circuit
An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

s; they are the active sites where the electronic action of the device takes place. For example, a common type of transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

, the bipolar junction transistor
Bipolar junction transistor
|- align = "center"| || PNP|- align = "center"| || NPNA bipolar transistor is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons...

, consists of two p–n junctions in series, in the form n–p–n or p–n–p. The discovery of the p–n junction is usually attributed to American physicist Russell Ohl
Russell Ohl
Russell Shoemaker Ohl was an American engineer who is generally recognized for patenting the modern solar cell ....

of Bell Laboratories. A Schottky junction is a special case of a p–n junction, where metal serves the role of the n-type semiconductor.

## Properties of a p–n junction

The p–n junction possesses some interesting properties that have useful applications in modern electronics. A p-doped semiconductor is relatively conductive. The same is true of an n-doped semiconductor, but the junction between them can become depleted
Depletion region
In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region or the space charge region, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers have diffused away, or have been forced away by an...

of charge carriers, and hence non-conductive, depending on the relative voltages of the two semiconductor regions. By manipulating this non-conductive layer, p–n junctions are commonly used as diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

s: circuit elements that allow a flow of electricity
Electricity
Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire...

in one direction but not in the other (opposite) direction. This property is explained in terms of forward bias and reverse bias, where the term bias refers to an application of electric voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

to the p–n junction.

## Equilibrium (zero bias)

In a p–n junction, without an external applied voltage, an equilibrium condition is reached in which a potential difference is formed across the junction. This potential difference is called built-in potential $V_\left\{\rm bi\right\}$. After joining p-type and n-type semiconductors, electrons near the p–n interface tend to diffuse into the p region. As electrons diffuse, they leave positively charged ions (donors
Donor (semiconductors)
In semiconductor physics, a donor is a dopant atom that, when added to a semiconductor, can form n-type regions.For example, when silicon , having four valence electrons, needs to be doped as an n-type semiconductor, elements from group V like phosphorus or arsenic can be used because they have...

) in the n region. Likewise, holes near the p–n interface begin to diffuse into the n-type region, leaving fixed ions (acceptors
Acceptor (semiconductors)
In semiconductor physics, an acceptor is a dopant atom that when added to a semiconductor can form p-type regions.For example, when silicon , having four valence electrons, needs to be doped as a p-type semiconductor, elements from group III like boron or aluminium , having three valence...

) with negative charge. The regions nearby the p–n interfaces lose their neutrality and become charged, forming the space charge region or depletion layer (see figure A).
The electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

created by the space charge region opposes the diffusion process for both electrons and holes. There are two concurrent phenomena: the diffusion process that tends to generate more space charge, and the electric field generated by the space charge that tends to counteract the diffusion. The carrier concentration profile at equilibrium is shown in figure A with blue and red lines. Also shown are the two counterbalancing phenomena that establish equilibrium.
The space charge region is a zone with a net charge provided by the fixed ions (donors
Donor (semiconductors)
In semiconductor physics, a donor is a dopant atom that, when added to a semiconductor, can form n-type regions.For example, when silicon , having four valence electrons, needs to be doped as an n-type semiconductor, elements from group V like phosphorus or arsenic can be used because they have...

or acceptors
Acceptor (semiconductors)
In semiconductor physics, an acceptor is a dopant atom that when added to a semiconductor can form p-type regions.For example, when silicon , having four valence electrons, needs to be doped as a p-type semiconductor, elements from group III like boron or aluminium , having three valence...

) that have been left uncovered by majority carrier diffusion. When equilibrium is reached, the charge density is approximated by the displayed step function. In fact, the region is completely depleted of majority carriers (leaving a charge density equal to the net doping level), and the edge between the space charge region and the neutral region is quite sharp (see figure B, Q(x) graph). The space charge region has the same magnitude of charge on both sides of the p–n interfaces, thus it extends farther on the less doped side (the n side in figures A and B).

## Forward bias

In forward bias, the p-type is connected with the positive terminal and the n-type is connected with the negative terminal. With a battery connected this way, the holes
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...

in the P-type region and the electrons in the N-type region are pushed toward the junction. This reduces the width of the depletion zone. The positive charge applied to the P-type material repels the holes, while the negative charge applied to the N-type material repels the electrons. As electrons and holes are pushed toward the junction, the distance between them decreases. This lowers the barrier in potential. With increasing forward-bias voltage, the depletion zone eventually becomes thin enough that the zone's electric field cannot counteract charge carrier motion across the p–n junction, as a consequence reducing electrical resistance. The electrons that cross the p–n junction into the P-type material (or holes that cross into the N-type material) will diffuse in the near-neutral region. Therefore, the amount of minority diffusion in the near-neutral zones determines the amount of current that may flow through the diode. Only majority carriers (electrons in N-type material or holes in P-type) can flow through a semiconductor for a macroscopic length. With this in mind, consider the flow of electrons across the junction. The forward bias causes a force on the electrons pushing them from the N side toward the P side. With forward bias, the depletion region is narrow enough that electrons can cross the junction and inject into the P-type material. However, they do not continue to flow through the P-type material indefinitely, because it is energetically favorable for them to recombine with holes. The average length an electron travels through the P-type material before recombining is called the diffusion length, and it is typically on the order of microns
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...

. Although the electrons penetrate only a short distance into the P-type material, the electric current continues uninterrupted, because holes (the majority carriers) begin to flow in the opposite direction. The total current (the sum of the electron and hole currents) is constant in space, because any variation would cause charge buildup over time (this is Kirchhoff's current law). The flow of holes from the P-type region into the N-type region is exactly analogous to the flow of electrons from N to P (electrons and holes swap roles and the signs of all currents and voltages are reversed). Therefore, the macroscopic picture of the current flow through the diode involves electrons flowing through the N-type region toward the junction, holes flowing through the P-type region in the opposite direction toward the junction, and the two species of carriers constantly recombining in the vicinity of the junction. The electrons and holes travel in opposite directions, but they also have opposite charges, so the overall current is in the same direction on both sides of the diode, as required. The Shockley diode equation models the forward-bias operational characteristics of a p–n junction outside the avalanche (reverse-biased conducting) region.

## Reverse bias

Reverse-biased usually refers to how a diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

is used in a circuit
Electronic circuit
An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow...

. If a diode is reverse-biased, the voltage at the cathode is higher than that at the anode. Therefore, no current will flow until the diode breaks down. Connecting the P-type region to the negative terminal of the battery and the N-type region to the positive terminal corresponds to reverse bias. The connections are illustrated in the following diagram: Because the p-type material is now connected to the negative terminal of the power supply, the 'holes
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...

' in the P-type material are pulled away from the junction, causing the width of the depletion zone to increase. Likewise, because the N-type region is connected to the positive terminal, the electrons will also be pulled away from the junction. Therefore, the depletion region
Depletion region
In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region or the space charge region, is an insulating region within a conductive, doped semiconductor material where the mobile charge carriers have diffused away, or have been forced away by an...

widens, and does so increasingly with increasing reverse-bias voltage. This increases the voltage barrier causing a high resistance to the flow of charge carriers, thus allowing minimal electric current to cross the p–n junction. The increase in resistance of the p–n junction results in the junction behaving as an insulator. The strength of the depletion zone electric field increases as the reverse-bias voltage increases. Once the electric field intensity increases beyond a critical level, the p–n junction depletion zone breaks down and current begins to flow, usually by either the Zener or the avalanche breakdown
Avalanche breakdown
Avalanche breakdown is a phenomenon that can occur in both insulating and semiconducting materials. It is a form of electric current multiplication that can allow very large currents within materials which are otherwise good insulators. It is a type of electron avalanche...

processes. Both of these breakdown processes are non-destructive and are reversible, as long as the amount of current flowing does not reach levels that cause the semiconductor material to overheat and cause thermal damage. This effect is used to one's advantage in Zener diode
Zener diode
A Zener diode is a special kind of diode which allows current to flow in the forward direction in the same manner as an ideal diode, but will also permit it to flow in the reverse direction when the voltage is above a certain value known as the breakdown voltage, "Zener knee voltage" or "Zener...

regulator circuits. Zener diodes have a certain - low - breakdown voltage. A standard value for breakdown voltage is for instance 5.6 V. This means that the voltage at the cathode can never be more than 5.6 V higher than the voltage at the anode, because the diode will break down - and therefore conduct - if the voltage gets any higher. This in effect regulates the voltage over the diode. Another application where reverse biased diodes are used is in Varicap
Varicap
In electronics, a varicap diode, varactor diode, variable capacitance diode, variable reactance diode or tuning diode is a type of diode which has a variable capacitance that is a function of the voltage impressed on its terminals....

diodes. The width of the depletion zone of any diode changes with voltage applied. This varies the capacitance of the diode. For more information, refer to the Varicap
Varicap
In electronics, a varicap diode, varactor diode, variable capacitance diode, variable reactance diode or tuning diode is a type of diode which has a variable capacitance that is a function of the voltage impressed on its terminals....

article.

## Electrostatics

For a p–n junction Poisson's equation
Poisson's equation
In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in electrostatics, mechanical engineering and theoretical physics...

becomes $\Delta \varphi =-\frac\left\{\rho \right\}\left\{\varepsilon \right\}=\frac\left\{q\right\}\left\{\varepsilon \right\}\left\left( \underbrace\left\{\left\{\left\{n\right\}_\left\{0\right\}\right\}-\left\{\left\{p\right\}_\left\{0\right\}\right\}\right\}_\left\{\begin\left\{smallmatrix\right\} \text\left\{equilibrium concentration\right\} \\ \text\left\{difference of free charges \left(\right\}\approx \text\left\{0\right)\right\} \end\left\{smallmatrix\right\}\right\}+\underbrace\left\{\left\{\left\{N\right\}_\left\{A\right\}\right\}-\left\{\left\{N\right\}_\left\{D\right\}\right\}\right\}_\left\{\begin\left\{smallmatrix\right\} \text\left\{concentration difference\right\} \\ \text\left\{of acceptor and donor atoms\right\} \end\left\{smallmatrix\right\}\right\} \right\right)$ where $\varphi$ is the electric potential
Electric potential
In classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...

, $\rho$ is the charge density
Charge density
The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume, respectively. It is measured in coulombs per meter , square meter , or cubic meter , respectively, and represented by the lowercase Greek letter Rho . Since there are positive as well as...

, $\varepsilon$ is permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

and $q$ is the magnitude of the electron charge. Since the total charge on either side of the depletion region must cancel out it is $\underbrace\left\{\left\{\left\{d\right\}_\left\{p\right\}\right\}\right\}_\left\{\begin\left\{smallmatrix\right\} \text\left\{width of \right\} \\ \text\left\{electric field\right\} \\ \text\left\{within p-side\right\} \end\left\{smallmatrix\right\}\right\}\left\{\left\{N\right\}_\left\{A\right\}\right\}=\underbrace\left\{\left\{\left\{d\right\}_\left\{n\right\}\right\}\right\}_\left\{\begin\left\{smallmatrix\right\} \text\left\{width of \right\} \\ \text\left\{electric field\right\} \\ \text\left\{within n-side\right\} \end\left\{smallmatrix\right\}\right\}\left\{\left\{N\right\}_\left\{D\right\}\right\}$ From the above equations and by deploying basic calculus it can be shown that the total width of the depletion region is $d=\left\{\left\{d\right\}_\left\{p\right\}\right\}+\left\{\left\{d\right\}_\left\{n\right\}\right\}=\sqrt\left\{\frac\left\{2\varepsilon \right\}\left\{q\right\}\frac\left\{\left\{\left\{N\right\}_\left\{A\right\}\right\}+\left\{\left\{N\right\}_\left\{D\right\}\right\}\right\}\left\{\left\{\left\{N\right\}_\left\{A\right\}\right\}\left\{\left\{N\right\}_\left\{D\right\}\right\}\right\}\left\left( \underbrace\left\{\left\{\left\{V\right\}_\left\{bi\right\}\right\}\right\}_\left\{\text\left\{ built-in voltage\right\}\right\}-\underbrace\left\{V\right\}_\left\{\begin\left\{smallmatrix\right\} \text\left\{external applied\right\} \\ \text\left\{voltage\right\} \end\left\{smallmatrix\right\}\right\} \right\right)\right\}$ Furthermore, by implementing the Einstein relation
Einstein relation (kinetic theory)
In physics the Einstein relation is a previously unexpected connection revealed independently by Albert Einstein in 1905 and by Marian Smoluchowski in their papers on Brownian motion...

and assuming the semiconductor is nondegenerate (i.e. the product $\left\{\left\{p\right\}_\left\{0\right\}\right\}\left\{\left\{n\right\}_\left\{0\right\}\right\}$ is independent of the Fermi energy
Fermi energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature....

) it follows that $\left\{\left\{V\right\}_\left\{bi\right\}\right\}=\frac\left\{kT\right\}\left\{q\right\}\ln \left\left( \frac\left\{\left\{\left\{N\right\}_\left\{A\right\}\right\}\left\{\left\{N\right\}_\left\{D\right\}\right\}\right\}\left\{\left\{\left\{p\right\}_\left\{0\right\}\right\}\left\{\left\{n\right\}_\left\{0\right\}\right\}\right\} \right\right)$ where $T$ is the temperature of the semiconductor and $k$ is Boltzmann constant.

## Summary

The forward-bias and the reverse-bias properties of the p–n junction imply that it can be used as a diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

. A p–n junction diode allows electric charges to flow in one direction, but not in the opposite direction; negative charges (electrons) can easily flow through the junction from n to p but not from p to n, and the reverse is true for holes. When the p–n junction is forward-biased, electric charge flows freely due to reduced resistance of the p–n junction. When the p–n junction is reverse-biased, however, the junction barrier (and therefore resistance) becomes greater and charge flow is minimal.

## Non-rectifying junctions

In the above diagrams, contact between the metal wires and the semiconductor material also creates metal-semiconductor junctions called Schottky diode
Schottky diode
The Schottky diode is a semiconductor diode with a low forward voltage drop and a very fast switching action...

s. In a simplified ideal situation a semiconductor diode would never function, since it would be composed of several diodes connected back-to-front in series. But, in practice, surface impurities within the part of the semiconductor that touches the metal terminals will greatly reduce the width of those depletion layers to such an extent that the metal-semiconductor junctions do not act as diodes. These "nonrectifying junction
Nonrectifying junction
In fabricating semiconductor devices, contact between the metal wires and the semiconductor material can create rectifying junctions, also known as Schottky diodes. This is dependent on the difference between the work function of the metal and the electron affinity of the semiconductor...

s" behave as ohmic contact
Ohmic contact
An ohmic contact is a region on a semiconductor device that has been prepared so that the current-voltage curve of the device is linear and symmetric. If the I-V characteristic is non-linear and asymmetric, the contact is not ohmic, but is a blocking or Schottky contact...

s regardless of applied voltage polarity.

## See also

{{Commons category|PN-junction diagrams}} NEWLINE
NEWLINE
• Diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...

and junction diode
• NEWLINE
• Diode modelling
Diode modelling
In electronics, diode modelling refers to the mathematical models used to approximate the actual behavior of real diodes to enable calculations and circuit analysis. A diode's I-V curve is nonlinear...

• NEWLINE
• Semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...

NEWLINE
NEWLINE
• Semiconductor device
Semiconductor device
Semiconductor devices are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductors. Semiconductor devices have replaced thermionic devices in most applications...

• NEWLINE
• N-type semiconductor
N-type semiconductor
N-type semiconductors are a type of extrinsic semiconductor where the dopant atoms are capable of providing extra conduction electrons to the host material . This creates an excess of negative electron charge carriers....

• NEWLINE
• P-type semiconductor
P-type semiconductor
A P-type semiconductor is obtained by carrying out a process of doping: that is, adding a certain type of atoms to the semiconductor in order to increase the number of free charge carriers ....

NEWLINE
• NEWLINE
• Transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

NEWLINE
NEWLINE
• Field effect transistor
• NEWLINE
• Bipolar junction transistor
Bipolar junction transistor
|- align = "center"| || PNP|- align = "center"| || NPNA bipolar transistor is a three-terminal electronic device constructed of doped semiconductor material and may be used in amplifying or switching applications. Bipolar transistors are so named because their operation involves both electrons...

NEWLINE
NEWLINE
• Alloy-junction transistor
Alloy-junction transistor
The germanium alloy-junction transistor, or alloy transistor, was an early type of bipolar junction transistor, developed at General Electric and RCA in 1951 as an improvement over the earlier grown-junction transistor....

• NEWLINE
• p-n-p transistor
• NEWLINE
• n-p-n transistor
NEWLINE
• NEWLINE
• Transistor-transistor logic
Transistor-transistor logic
Transistor–transistor logic is a class of digital circuits built from bipolar junction transistors and resistors. It is called transistor–transistor logic because both the logic gating function and the amplifying function are performed by transistors .TTL is notable for being a widespread...

NEWLINE
• NEWLINE
• Capacitance voltage profiling
• NEWLINE
• Deep-level transient spectroscopy
• NEWLINE
• Solar cell
Solar cell
A solar cell is a solid state electrical device that converts the energy of light directly into electricity by the photovoltaic effect....

• NEWLINE
• Semiconductor detector
Semiconductor detector
This article is about particle detectors. For information about semiconductor detectors in radio, see Diode#Semiconductor_diodes, rectifier, detector and cat's-whisker detector....

NEWLINE

## Junctions

NEWLINE
NEWLINE
• Back junction is a solar cell featuring the formation of a p-n junction at its rear surface
• NEWLINE
• Single-junction
• NEWLINE
• Heterojunction
Heterojunction
A heterojunction is the interface that occurs between two layers or regions of dissimilar crystalline semiconductors. These semiconducting materials have unequal band gaps as opposed to a homojunction...

• NEWLINE
• Multijunction
• NEWLINE
• P-i-n and n-i-p
NEWLINE

## External links

NEWLINE
NEWLINE {{DEFAULTSORT:P-N Junction}}