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Space charge is a concept in which excess electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 is treated as being a continuum
Continuum

Continuum can refer to:* Continuum , anything that goes through a gradual transition from one condition, to a different condition, without any abrupt changes or "discontinuities"....
 of charge distributed over a region of space (either a volume or an area) rather than distinct point-like charges. This model typically applies when charge carriers have been emitted from some region of a solid—the cloud of emitted carriers can form a space charge region if they are sufficiently spread out or the charged atoms, or molecules left behind in the solid can form a space charge region.






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Space charge is a concept in which excess electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 is treated as being a continuum
Continuum

Continuum can refer to:* Continuum , anything that goes through a gradual transition from one condition, to a different condition, without any abrupt changes or "discontinuities"....
 of charge distributed over a region of space (either a volume or an area) rather than distinct point-like charges. This model typically applies when charge carriers have been emitted from some region of a solid—the cloud of emitted carriers can form a space charge region if they are sufficiently spread out or the charged atoms, or molecules left behind in the solid can form a space charge region. Space charge usually only occurs in dielectric
Dielectric

A dielectric is a nonconducting substance, i.e. an Insulator . The term was coined by William Whewell in response to a request from Michael Faraday....
 media (including vacuum
Vacuum

A vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty," but in reality, no volume of space can ever be perfectly empty....
) because in a conductive medium the charge tends to be rapidly neutralized or screened
Electric field screening

Screening is the damping of electric fields caused by the presence of mobile electric charge carriers. It is an important part of the behavior of charge-carrying fluids, such as ionized gases and electrical conduction electrons in semiconductors and metals....
. The sign of the space charge can be either negative or positive. This situation is perhaps most familiar in the area near a metal
Metal

In chemistry, a metal is a chemical element whose atoms readily lose electrons to form positive ions , and form metallic bonds between other metal atoms and ionic bonds between nonmetal atoms....
 object when it is heated to incandescence
Incandescence

Incandescence is the emission of light from a hot body due to its temperature. The term derives from the verb incandesce, to grow white....
 in a vacuum
Vacuum

A vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty," but in reality, no volume of space can ever be perfectly empty....
. This effect was first observed by Thomas Edison
Thomas Edison

Thomas Alva Edison was an American inventor and businessman who developed many devices that greatly influenced life around the world, including the phonograph and the long-lasting, practical electric light bulb....
 in light bulb filaments, where it is sometimes called the Edison Effect, but space charge is a significant phenomenon in many vacuum and solid-state electronic devices.

Cause


Physical explanation

When a metal object is placed in a vacuum and is heated to incandescence, the energy is sufficient to cause electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
s to "boil" away from the surface atom
Atom

|-! bgcolor=gray | Properties|-||}The atom is a basic unit of matter consisting of a dense, central atomic nucleus surrounded by a electron cloud of electric charge electrons....
s and surround the metal object in a cloud of free electrons. This is called thermionic emission
Thermionic emission

Thermionic emission is the heat-induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal energy given to the carrier overcomes the forces restraining it....
. The resulting cloud is negatively charged, and can be attracted to any nearby positively charged object, thus producing an electrical current which passes through the vacuum.

Mathematical explanation

If the "vacuum
Vacuum

A vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty," but in reality, no volume of space can ever be perfectly empty....
" has a pressure
Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
 of 10-6 mm or less, the main vehicle
Vehicle

Vehicles, derived from the Latin word, vehiculum, are non-living means of transport. Most often they are manufactured , although some other means of transport which are not made by humans also may be called vehicles; examples include icebergs and floating tree trunks....
 of conduction is electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
s. The emission current density (J) from the cathode
Cathode

A cathode is an electrode through which electric charge flows out of a polarized electrical device. Mnemonic: CCD .From an electrochemical point of view, positively charged ion invariably move toward the cathode and/or negatively charged ion move away from it to balance the electrons arriving from external circuitry....
, as a function
Function (mathematics)

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed Set , such as the real numbers , although different inputs may have the same output....
 of its thermodynamic temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 T, in the absence of space-charge, is given by:

where
A0 = 1.2 × 106 A m-2 K-2
e = elementary positive charge (i.e., magnitude of electron charge),
m = electron mass,
k = Boltzmann's constant = 1.38 x 10-23J/K,
h = Planck's constant = 6.55 x 10-34 J s,
φ = work function
Work function

In solid state physics, the work function is the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface ....
 of the cathode,
r = mean electron reflection coefficient.


The reflection coefficient can be as low as 0.105 but is usually near 0.5. For Tungsten
Tungsten

Tungsten , also known as wolfram , is a chemical element that has the symbol W and atomic number 74.A steel-gray metal, tungsten is found in several ores, including wolframite and scheelite....
, (1 - r)A0 = 0.6 to 1.0 × 106 A m-2 K-2, and φ = 4.52 eV. At 2500 °C, the emission is 3000 A/m2.

The emission current as given above is many times greater than that normally collected by the electrodes, except in some pulse
Pulse

In medicine, a person's pulse is the throbbing of their artery. It can be palpated in any place that allows for an artery to be compressed against a bone, such as at the neck , at the wrist , behind the knee , on the inside of the elbow , and near the ankle joint ....
d valves such as the cavity magnetron
Cavity magnetron

A cavity magnetron is a high-powered vacuum tube that generates coherence microwaves. They are commonly found in microwave ovens, as well as various radar applications....
. Most of the electrons emitted by the cathode are driven back to it by the repulsion
Repulsion

Repulsion is a 1965 in film film directed by Roman Polanski on a scenario by Gerard Brach and Roman Polanski. It was Polanski's first English language film, and was filmed in United Kingdom....
 of the cloud
Cloud

A cloud is a visible mass of Drop or frozen crystals floating in the Celestial body atmosphere above the surface of the Earth or another planetary body....
 of electrons in its neighborhood. This is called the space charge effect. In the limit of large current densities, J is given by the Child-Langmuir equation below, rather than by the thermionic emission equation above.

Occurrence

Space charge is an inherent property of all vacuum tube
Vacuum tube

In electronics, a vacuum tube, electron tube , thermionic valve, or just valve is a device used to amplifier, switch, otherwise modify, or create an Electricity signal by controlling the movement of electrons in a low-pressure space....
s. This has at times made life harder or easier for electrical engineers who used tubes in their designs. For example, space charge significantly limited the practical application of triode
Triode

A triode is an electronic amplifier device having three active electrodes. The term most commonly applies to a vacuum tube with three elements: the Electrical filament or cathode, the control grid, and the Plate electrode or anode....
 amplifier
Amplifier

Generally, an amplifier or simply amp, is any machine that changes, usually increases, the amplitude of a Signal . The "signal" is usually voltage or current....
s because the addition of the grid electrode impedes the flow of electrons from cathode
Cathode

A cathode is an electrode through which electric charge flows out of a polarized electrical device. Mnemonic: CCD .From an electrochemical point of view, positively charged ion invariably move toward the cathode and/or negatively charged ion move away from it to balance the electrons arriving from external circuitry....
 to anode
Anode

An anode is an electrode through which electric charge flows into a polarized electrical device. Mnemonic: ACID . Electrons flow in the opposite direction to the positive electric current....
 depending on fluctuations in grid voltage. These voltages were thus able to control the amount of space charge able to flow within the envelope. While this allowed for more precise control over current flow, it reduced the gain
Gain

In electronics, gain is a measure of the ability of a electrical network to increase the Power or amplitude of a Signal . It is usually defined as the mean ratio of the Signalling of a system to the Signalling of the same system....
 that could be achieved by such tubes.

On the other hand, space charge was useful in some tube applications because it generates a negative EMF
Electromotive force

Electromotive force is a term used to characterize electrical devices, such as voltaic cells, Thermoelectric effects, electrical generators and transformers, and even resistors....
 within the tube's envelope, which could be used to create a negative bias on the tube's grid. Grid bias could also be achieved by using an applied grid voltage in addition to the control voltage. This could improve the engineer's control and fidelity of amplification.

Space charges can also occur within dielectrics
Dielectric

A dielectric is a nonconducting substance, i.e. an Insulator . The term was coined by William Whewell in response to a request from Michael Faraday....
. For example, when gas near a high voltage electrode begins to undergo dielectric breakdown, electrical charges are injected into the region near the electrode, forming space charge regions in the surrounding gas. Space charges can also occur within solid or liquid dielectrics that are stressed by high electric fields. Trapped space charges within solid dielectrics are often a contributing factor leading to dielectric failure within high voltage power cables and capacitors.

Child's Law

Also known as the Child-Langmuir Law or the Three-Halves Power Law, Child's Law states that the space charge-limited current (SCLC) in a plane-parallel diode varies directly as the three-halves power of the anode voltage and inversely as the square of the distance separating the cathode and the anode. That is,

.

Where is the anode current, the current density, and the area. This assumes the following:
  1. The electrodes are planar, parallel, equipotential surfaces of infinite dimensions.
  2. The electrons have zero velocity at the cathode surface.
  3. In the interelectrode region, only electrons are present.
  4. The current is space-charge limited.
  5. The anode voltage remains constant for a sufficiently long time so that the anode current is steady.


Mott's steady-state space-charge-limited conduction model

The steady-state space-charge-limited conduction-current density in a plane-parallel dielectric sample with electrode separation is proportional to the square of the applied voltage . That is,

This assumes the following:
  1. There is only one type of charge carrier present.
  2. The material has no intrinsic conductivity, but charges are injected into it from one electrode and captured by the other.
  3. The carrier mobility and the dielectric permittivity are constant throughout the sample.
  4. The electric field at the charge-injecting cathode is zero.


Shot noise

Space charge tends to reduce shot noise
Shot noise

Shot noise is a type of electronic noise that occurs when the finite number of particles that carry energy, such as electrons in an electronic circuit or photons in an optical device, is small enough to give rise to detectable statistical fluctuations in a measurement....
. Electrons (and positive charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 carriers) come with their own built-in negative feedback
Feedback

Feedback describes the situation when output from an event or phenomenon in the past will influence the same event/phenomenon in the present or future....
.

See also

  • Thermionic emission
    Thermionic emission

    Thermionic emission is the heat-induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal energy given to the carrier overcomes the forces restraining it....
  • Vacuum tube
    Vacuum tube

    In electronics, a vacuum tube, electron tube , thermionic valve, or just valve is a device used to amplifier, switch, otherwise modify, or create an Electricity signal by controlling the movement of electrons in a low-pressure space....
  • Grid leak
    Grid leak

    Grid leak is the small Electric current through the grid of a Vacuum tube into the circuit which feeds the grid. It is an inherent operating characteristic of triodes and other vacuum tubes....