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Thermionic emission
From Wikipedia, the free encyclopedia
Close up of the filament on a low pressure
mercury gas discharge lamp showing white
thermionic emission mix coating on the central
portion of the coil. Typically made of a mixture
of barium, strontium and calcium oxides, the
coating is sputtered away through normal use,
often eventually resulting in lamp failure
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 charge
carriers can be electrons or ions, and in older literature are sometimes
referred to as "thermions". After emission, a charge will initially be left behind
in the emitting region that is equal in magnitude and opposite in sign to the
total charge emitted. But if the emitter is connected to a battery, then this
charge left behind will be neutralized by charge supplied by the battery, as the
emitted charge carriers move away from the emitter, and finally the emitter
will be in the same state as it was before emission. The thermionic emission of
electrons is also known as thermal electron emission.
The classical example of thermionic emission is the emission of electrons from
a hot metal cathode into a vacuum (archaically known as the Edison effect) in
a vacuum tube. However, the term "thermionic emission" is now used to refer
to any thermally excited charge emission process, even when the charge is
emitted from one solid-state region into another. This process is crucially
important in the operation of a variety of electronic devices and can be used
for power generation or cooling. The magnitude of the charge flow increases
dramatically with increasing temperature. However, vacuum emission from
metals tends to become significant only for temperatures over 1000 K. The
science dealing with this phenomenon has been known as thermionics, but
this name seems to be gradually falling into disuse.
History
In reading this history, it is necessary to remember that the electron was not
identified as a separate physical particle until the 1897 work ofJ. J. Thomson. One
therefore has to be careful in using the word "electron" when discussing
experiments that took place before this date.
The phenomenon was initially reported in 1873 by Frederick Guthrie in
Britain. While doing work on charged objects, Guthrie discovered that a red-hot iron
sphere with a positive charge would lose its charge (by somehow discharging it into
air). He also found that this did not happen if the sphere had a negative
charge.[1] Other early contributors included Hittorf (1869–1883), Goldstein (1885),
and Elster and Geitel (1882–18
The Edison effect in a diode tube. A diode tube is connected in
two configurations, one has a flow of electrons and the other
does not. Note that the arrows represent electron current, not
conventional current. The effect was rediscovered by Thomas
Edison on February 13, 1880, while trying to discover the reason
for breakage of lamp filaments and uneven blackening (darkest
near one terminal of the filament) of the bulbs in his
incandescent lamps. Edison built several experiment bulbs,
some with an extra wire, a metal plate, or foil inside the bulb
which was electrically separate from the filament. He connected
the extra metal electrode to the lamp filament through a
galvanometer. When the foil was given a more negative charge
than the filament, no charge flowed between the foil and the
filament.
We now know that this was because the cool foil emitted few electrons.
However, when the foil was given a more positive charge than the filament, negative
charge apparently flowed from the filament through the vacuum to the foil. This
one-way current was called the Edison effect (although the term is occasionally used
to refer to thermionic emission itself). He found that the current emitted by the hot
filament increased rapidly with increasing voltage, and filed a patent application for
a voltage-regulating device using the effect on November 15, 1883 (U.S. patent
307,031,[2] the first US patent for an electronic device). He found that sufficient
current would pass through the device to operate a telegraph sounder. This was
exhibited at the International Electrical Exposition in Philadelphia in September
1884. William Preece, a British scientist took back with him several of the Edison
Effect bulbs, and presented a paper on them in 1885, where he referred to
thermionic emission as the "Edison Effect." [3] The British physicist John Ambrose
Fleming, working for the British "Wireless Telegraphy" Company, discovered that the
Edison Effect could be used to detect radio waves. Fleming went on to develop the
two-element vacuum tube known as the diode, which he patented on November 16,
1904. The thermionic diode can also be configured as a device that converts a heat
difference to electric power directly without moving parts (a thermionic converter, a
type of heat engine). Following J. J. Thomson's identification of the electron, the
British physicist Owen Willans Richardson began work on the topic that he later
called "thermionic emission". He received a Nobel Prize in Physics in 1928 "for his
work on the thermionic phenomenon and especially for the discovery of the law
named after him".
Richardson's Law
In any solid metal, there are one or two electrons per atom that are
free to move from atom to atom. This is sometimes collectively referred to as
a "sea of electrons". Their velocities follow a statistical distribution, rather
than being uniform, and occasionally an electron will have enough velocity to
exit the metal without being pulled back in. The minimum amount of energy
needed for an electron to leave a surface is called the work function. The work
function is characteristic of the material and for most metals is on the order of
several electronvolts. Thermionic currents can be increased by decreasing the
work function. This often-desired goal can be achieved by applying various
oxide coatings to the wire.
In 1901 Richardson published the results of his experiments: the
current from a heated wire seemed to depend exponentially on the
temperature of the wire with a mathematical form similar to the Arrhenius
equation. Later, he proposed that the emission law should have the
mathematical form
where J is the emission current density [SI unit: A/m2], T is the
thermodynamic temperature of the metal [SI unit: Kelvin (K)], W is the work
function of the metal, k is the Boltzmann constant, and AG is a parameter
discussed next.
In the period 1911 to 1930, as physical understanding of the behavior
of electrons in metals increased, various different theoretical expressions
(based on different physical assumptions) were put forwards for AG, by
Richardson, Dushman, Fowler, Sommerfeld and Nordheim. Over 60 years
later, there is still no consensus amongst interested theoreticians as to what
the precise form of the expression for AG should be, but there is agreement
that AG must be written in the form
where λR is a material-specific correction factor that is typically of order
0.5, and A0 is a universal constant given by
where m and −e are
and h is Planck's constant.
the
mass
and
charge
of
an
electron,
In fact, by about 1930 there was agreement that, due to the wave-like
nature of electrons, some proportion rav of the outgoing electrons would be
reflected as they reached the emitter surface, so the emission current density
would be reduced, and λR would have the value (1-rav). Thus, one sometimes
sees the thermionic emission equation written in the form
.
However, a modern theoretical treatment by Modinos assumes that
the band-structure of the emitting material must also be taken into account.
This would introduce a second correction factor λB into λR, giving AG = λB(1
− rav)A0. Experimental values for the "generalized" coefficient AG are generally
of the order of magnitude of A0, but do differ significantly as between
different emitting materials, and can differ as between different
crystallographic faces of the same material. At least qualitatively, these
experimental differences can be explained as due to differences in the value
of λR.
Considerable confusion exists in the literature of this area because: (1)
many sources do not distinguish between AG and A0, but just use the
symbol A (and sometimes the name "Richardson constant") indiscriminately;
(2) equations with and without the correction factor here denoted by λR are
both given the same name; and (3) a variety of names exist for these
equations, including "Richardson equation", "Dushman's equation",
"Richardson-Dushman equation" and "Richard-Laue-Dushman equation". The
nomenclature preferred by the editor writing this paragraph is that the
equation with only A0 in should be called the "elementary Richardson-type
equation", and the equation with the "generalized" coefficient AG should be
called the "generalized Richardson-type equation". In the literature, the
elementary equation is sometimes given in circumstances where the
generalized equation would be more appropriate, and this in itself can cause
confusion. To avoid misunderstandings, the meaning of any "A-like" symbol
should always be explicitly defined in terms of the more fundamental
quantities involved.
Because of the exponential function, the current increases rapidly with
temperature when kT is less than W. (For essentially every material, melting
occurs well before kT=W.)
Schottky emission
In electron emission devices, especially electron guns, the thermionic electron
emitter will be biased negative relative to its surroundings. This creates an
electric field of magnitude F at the emitter surface. Without the field, the
surface barrier seen by an escaping Fermi-level electron has height W equal to
the local work-function. The electric field lowers the surface barrier by an
amount ΔW, and increases the emission current. This is known as the
"Schottky effect" or field enhanced thermionic emission. It can be modeled by
a simple modification of the Richardson equation, by replacing W by
(W − ΔW). This gives the equation[4][5]
where ε0 is the electric constant (also, formerly, called the vacuum
permittivity).
Electron emission that takes place in the field-and-temperature-regime where
this modified equation applies is often called Schottky emission. This equation
is relatively accurate for electric field strengths lower than about 10 8 V m−1.
For electric field strengths higher than 108 V m−1, so-called Fowler-Nordheim
(FN) tunneling begins to contribute significant emission current. In this
regime, the combined effects of field-enhanced thermionic and field emission
can be modeled by the Murphy-Good equation for thermo-field (T-F)
emission.[6] At even higher fields, FN tunneling becomes the dominant
electron emission mechanism, and the emitter operates in the so-called "cold
field electron emission (CFE)" regime.
Thermionic emission can also be enhanced by interaction with other forms of
excitation such as light.[7] For example, excited Cs-vapours in thermionic
converters form clusters of Cs-Rydberg matter which yield a decrease of
collector emitting work function from 1.5 eV to 1.0–0.7 eV. Due to long-lived
nature of Rydberg matter this low work function remains low which
essentially increases the low-temperature converter’s efficiency.[8]
Photon-enhanced thermionic emission
Photon-enhanced thermionic emission (PETE), a process developed by engineers
at Stanford University, that harnesses both the light and heat of the sun to generate
electricity and increases the efficiency of solar power production by more than twice
the current levels. The device developed for the process reaches peak efficiency
after it reaches 200°C; most silicon solar cells become inert after reaching 100°C.
Such device will work best in parabolic trough collectors, which reach temperatures
around 800°C. Although the team used a gallium nitride semiconductor in its "proof
of concept" device, it claims that the use of gallium arsenide can increase the
device's efficiency to 55–60 percent, nearly triple that of existing systems.
Space charge
From Wikipedia, the free encyclopedia
Space charge is a concept in which excess electric charge is treated as
a continuum 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 media (including vacuum) because in a conductive medium the
charge tends to be rapidly neutralized or screened. The sign of the space
charge can be either negative or positive. This situation is perhaps most
familiar in the area near a metal object when it is heated to incandescence in
a vacuum. This effect was first observed by Thomas Edison 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.
Physical explanation
When a metal object is placed in a vacuum and is heated to incandescence,
the energy is sufficient to cause electrons to "boil" away from the
surface atoms and surround the metal object in a cloud of free electrons. This
is called thermionic emission. 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.
Space charge can result from a range of phenomena, but the most important
are:
1. Combination of the current density and spatially inhomogeneous
resistivity
2. Ionization of species within the dielectric to form heterocharge
3. Charge injection from electrodes and from a stress enhancement
4. Polarization in structures such as water trees
It has been suggested that in AC most of carriers injected at electrodes during
a half of cycle are ejected during the next half cycle, so the net balance of
charge on a cycle is practically zero. However, a small fraction of the carriers
can be trapped at levels deep enough to retain them when the field is
inverted. The amount of charge in AC should increase slower than in DC and
become observable after longer periods of time.
Hetero and Homo Charge
Hetero charge means that the polarity of the space charge is opposite to that
of neighboring electrode, and homo charge is the reverse situation. Under
high voltage application, a hetero charge near the electrode is expected to
reduce the breakdown voltage, whereas a homo charge will increase it. After
polarity reversal under ac conditions, the homo charge is converted to hetero
space charge.
Mathematical explanation
If the "vacuum" has a pressure of 10-6 mmHg or less, the main vehicle of
conduction is electrons. The emission current density (J) from the cathode, as
a function of its thermodynamic temperature T, in the absence of spacecharge, 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 of the cathode,
ř = mean electron reflection coefficient.
The reflection coefficient can be as low as 0.105 but is usually near 0.5.
For Tungsten, (1 - ř)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 pulsed valvessuch as the cavity
magnetron. Most of the electrons emitted by the cathode are driven back to it
by the repulsion of the cloud 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 tubes. 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 amplifiers which lead to further innovations such as the
vacuum tube tetrode.
On the other hand, space charge was useful in some tube applications
because it generates a negative EMF 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. 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
Graph showing Child-Langmuir Law. S and d are constant and equal to 1.
Also known as the Child-Langmuir Law or the Three-Halves Power Law, Child's
Law states that the space-charge limited current in a plane-parallel diode
varies directly as the three-halves power of the anode voltage Va and inversely
as the square of the distance d separating the cathode and the anode. That is,
.
Where Ia is the anode current, J the current density, and S the area. This
assumes the following:
The electrodes are planar, parallel, equipotential surfaces of infinite
dimensions.
The electrons have zero velocity at the cathode surface.
In the interelectrode region, only electrons are present.
The current is space-charge limited.
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 J in a planeparallel dielectric sample with electrode separation L is proportional to the
square of the applied voltage V. That is,
This assumes the following:
There is only one type of charge carrier present.
The material has no intrinsic conductivity, but charges are injected into it from
one electrode and captured by the other.
The carrier mobility μ and the dielectric permittivity ε are constant throughout
the sample.
The electric field at the charge-injecting cathode is zero.
As an application example, the steady-state space-charge-limited current
across a piece of silicon with a charge carrier mobility of 1500 cm2/V-s, a
dielectric constant of 11.9, an area of 10-8cm2 and a thickness of 10-4cm can be
calculated by an on line calculator as 1.264-4A at voltage 3V.
Shot noise
Space
charge
tends
to
reduce shot
noise.
Electrons
(and
positive charge carriers) come with their own built-in negative feedback.