6DS8/ECH83, 6ES6/EF97 and 6ET6/EF98). 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. In semiconductor physics, space charge layers that are depleted of charge carriers are used as a model to explain the rectifying behaviour of p–n junctions and the buildup of a voltage in photovoltaic cells. Space-charge-limited current In vacuum (Child's law) 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 and inversely as the square of the distance d separating the cathode and the anode. For electrons, the current density J (amperes per meter squared) is written: where is the anode current and S the surface area of the anode receiving the current; is the magnitude of the charge of the electron and is its mass. The equation is also known as the "three-halves-power law" or the Child–Langmuir law. 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. The equation's validity is subject to the following assumptions: Electrons travel ballistically between electrodes (i.e., no scattering). In the interelectrode region, the space charge of any ions is negligible. The electrons have zero velocity at the cathode surface. The assumption of no scattering (ballistic transport) is what makes the predictions of Child–Langmuir law different from those of Mott–Gurney law. The latter assumes steady-state drift transport and therefore strong scattering. In recent years, various models of SCLC current have been revised as reported in two review papers. Child's law was further generalized for the case of non-zero velocity at the cathode surface with the following equation: where is the initial velocity of the particle. This equation reduces to Child's Law for the special case of equal to zero. In semiconductors In semiconductors and insulating materials, an