Space charge
This situation is perhaps most familiar in the area near a metal object when it is heated to incandescence in a vacuum.
Space charge is a significant phenomenon in many vacuum and solid-state electronic devices.
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.
However, a small fraction of the carriers can be trapped at levels[clarification needed] deep enough to retain them when the field is inverted.
The amount of charge in AC should increase slower than in direct current (DC) and become observable after longer periods of time.
The emission current density (J) from the cathode, as a function of its thermodynamic temperature T, in the absence of space-charge, is given by Richardson's law:
The emission current as given above is many times greater than that normally collected by the electrodes, except in some pulsed valves such as the cavity magnetron.
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 led to further innovations such as the vacuum tube tetrode.
It allowed the construction of space charge tubes for car radios that required only 6 or 12 volts anode voltage (typical examples were the 6DR8/EBF83, 6GM8/ECC86, 6DS8/ECH83, 6ES6/EF97 and 6ET6/EF98).
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.
First proposed by Clement D. Child in 1911, Child's law states that the space-charge-limited current (SCLC) in a plane-parallel vacuum diode varies directly as the three-halves power of the anode voltage
[3] For electrons, the current density J (amperes per meter squared) is written:
Child originally derived this equation for the case of atomic ions, which have much smaller ratios of their charge to their mass.
Irving Langmuir published the application to electron currents in 1913, and extended it to the case of cylindrical cathodes and anodes.
Child's law was further generalized by Buford R. Conley in 1995 for the case of non-zero velocity at the cathode surface with the following equation:[5]
In recent years, various models of SCLC current have been revised as reported in two review papers.
The Mott–Gurney law offers some crucial insight into charge-transport across an intrinsic semiconductor, namely that one should not expect the drift current to increase linearly with the applied voltage, i.e., from Ohm's law, as one would expect from charge-transport across a metal or highly doped semiconductor.
Using the Mott–Gurney law for characterizing amorphous semiconductors, along with semiconductors containing defects and/or non-Ohmic contacts, should however be approached with caution as significant deviations both in the magnitude of the current and the power law dependence with respect to the voltage will be observed.
In those cases the Mott–Gurney law can not be readily used for characterization, and other equations which can account for defects and/or non-ideal injection should be used instead.
In the case where the electron/hole transport is limited by trap states in the form of exponential tails extending from the conduction/valence band edges,
is the effective density of states of the charge carrier type in the semiconductor, i.e., either
Note that the equation describing the current in the low voltage regime follows the same thickness scaling as the Mott–Gurney law,
When a very large voltage is applied across the semiconductor, the current can transition into a saturation regime.
In the ballistic case (assuming no collisions), the Mott–Gurney equation takes the form of the more familiar Child–Langmuir law.
is the effective density of states of the charge carrier type in the semiconductor.
The slowing carriers also increases the space charge density and resulting potential.
In addition, the potential developed by the space charge can reduce the number of carriers emitted.
[16] When the space charge limits the current, the random arrivals of the carriers are smoothed out; the reduced variation results in less shot noise.
