Space charge is an interpretation of a collection of electric charges 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 effects are most pronounced in dielectric media (including vacuum); in highly conductive media, 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. 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 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 electric current which passes through the vacuum. Space charge can result from a range of phenomena, but the most important are:
Combination of the current density and spatially inhomogeneous resistance Ionization of species within the dielectric to form heterocharge Charge injection from electrodes and from a stress enhancement Polarization in structures such as water trees. "Water tree" is a name given to a tree-like figure appearing in a water-impregnated polymer insulating cable. It has been suggested that in alternating current (AC) most carriers injected at electrodes during a half 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 direct current (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 near "vacuum" has a pressure of 10−6 mmHg or less, the main vehicle of conduction is electrons. The emission current density, J {\displaystyle J} , from the cathode, as a function of its thermodynamic temperature, T {\displaystyle T} , in the absence of space-charge, is given by Richardson's law:
J = ( 1 − r ~ ) A 0 T 2 e ( − ϕ k T ) {\displaystyle J=(1-{\tilde {r}})A_{0}T^{2}e^{\left({\frac {-\phi }{kT}}\right)}}
where
A 0 = 4 π e m e k 2 h 3 ≈ 1.2 ⋅ 10 6 A ⋅ m − 2 ⋅ K − 2 = {\textstyle A_{0}={\frac {4\pi em_{\mathrm {e} }k^{2}}{h^{3}}}\approx 1.2\cdot 10^{6}\mathrm {A{\cdot }m^{-2}{\cdot }K^{-2}} =} a chemical constant of the electron gas,
e = 1.6 ⋅ 10 − 19 C = {\textstyle e=1.6\cdot 10^{-19}{\text{ C}}=} elementary positive charge (i.e., magnitude of electron charge),
m e = 9.11 ⋅ 10 − 31 kg = {\textstyle m_{e}=9.11\cdot 10^{-31}{\text{ kg}}=} electron mass,
k = 1.38 ⋅ 10 − 23 J ⋅ K − 1 = {\textstyle k=1.38\cdot 10^{-23}{\text{ J}}\cdot {\text{K}}^{-1}=} Boltzmann constant,
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