recombination of electron-hole pairs are in equipoise. The number of electron-hole pairs in the steady state at a given temperature is determined by quantum statistical mechanics. The precise quantum mechanical mechanisms of generation and recombination are governed by the conservation of energy and conservation of momentum. As the probability that electrons and holes meet together is proportional to the product of their numbers, the product is in the steady-state nearly constant at a given temperature, providing that there is no significant electric field (which might "flush" carriers of both types, or move them from neighbor regions containing more of them to meet together) or externally driven pair generation. The product is a function of the temperature, as the probability of getting enough thermal energy to produce a pair increases with temperature, being approximately exp(−EG/kT), where k is Boltzmann's constant, T is the absolute temperature and EG is bandgap. The probability of meeting is increased by carrier traps – impurities or dislocations which can trap an electron or hole and hold it until a pair is completed. Such carrier traps are sometimes purposely added to reduce the time needed to reach the steady-state. Doping The conductivity of semiconductors may easily be modified by introducing impurities into their crystal lattice. The process of adding controlled impurities to a semiconductor is known as doping. The amount of impurity, or dopant, added to an intrinsic (pure) semiconductor varies its level of conductivity. Doped semiconductors are referred to as extrinsic. By adding impurity to the pure semiconductors, the electrical conductivity may be varied by factors of thousands or millions. A 1 cm3 specimen of a metal or semiconductor has the order of 1022 atoms. In a metal, every atom donates at least one free electron for conduction, thus 1 cm3 of metal contains on the order of 1022 free electrons, whereas a 1 cm3 sample of pure germanium at 20°C contains about atoms, but only free electrons and holes. The addition of 0.001% of arsenic (an impurity) donates an extra 1017 free electrons in the same volume and the electrical conductivity is increased by a factor of 10,000. The materials chosen as suitable dopants depend on the atomic properties of both the dopant and the material to be doped. In general, dopants that produce the desired controlled changes are classified as either electron acceptors or donors. Semiconductors doped with donor impurities are called n-type, while