electric field causes charged particles, electrons, to reach a specific drift velocity that is parallel to the direction of the field. This is different from the behavior of the free charged particles in a vacuum, in which a field accelerates the particle. The proportionality factor between the magnitudes of the drift velocity, , and the electric field, , is called the mobility, : Drift regime (Mott–Gurney law) The Child's law behavior of a space-charge-limited current that applies in a vacuum diode doesn't generally apply to a semiconductor/insulator in a single-carrier device, and is replaced by the Mott–Gurney law. For a thin slab of material of thickness , sandwiched between two selective Ohmic contacts, the electric current density, , flowing through the slab is given by: where is the voltage that has been applied across the slab and is the permittivity of the solid. 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. Since the only unknown quantity in the Mott–Gurney law is the charge-carrier mobility, , the equation is commonly used to characterize charge transport in intrinsic semiconductors. 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. During the derivation of the Mott–Gurney law, one has to make the following assumptions: There is only one type of charge carrier present, i.e., only electrons or holes. The material has no intrinsic conductivity, but charges are injected into it from one electrode and captured by the other. The carrier mobility, , and the permittivity, , are constant throughout the sample. The current flow is not limited by traps or energetic disorder. The current is not predominantly due to doping. The electric field at the charge-injecting electrode is zero, meaning that the current is governed by drift only. Derivation Consider a crystal of thickness carrying a current . Let be the electric