of work function for various solid materials with the tables of electron affinity and ionization energy for atomic species, it is clear that many combinations would result in a neutral atom, however some specific combinations would result in the atom preferring an ionized state: e.g., a halogen atom in a ytterbium box, or a cesium atom in a tungsten box. At room temperature this situation is not stable since the atom tends to adsorb to the exposed lining of the box instead of floating freely. At high temperatures, however, the atoms are evaporated from the surface in ionic form; this spontaneous surface ionization effect has been used as a cesium ion source. At room temperature, this example finds application in semiconductors, where the ionization of a dopant atom is well described by this ensemble. In the semiconductor, the conduction band edge plays the role of the vacuum energy level (replacing ), and is known as the Fermi level. Of course, the ionization energy and electron affinity of the dopant atom are strongly modified relative to their vacuum values. A typical donor dopant in silicon, phosphorus, has ; the value of in the intrinsic silicon is initially about , guaranteeing the ionization of the dopant. The value of depends strongly on electrostatics, however, so under some circumstances it is possible to de-ionize the dopant. Meaning of chemical potential, generalized "particle number" In order for a particle number to have an associated chemical potential, it must be conserved during the internal dynamics of the system, and only able to change when the system exchanges particles with an external reservoir. If the particles can be created out of energy during the dynamics of the system, then an associated term must not appear in the probability expression for the grand canonical ensemble. In effect, this is the same as requiring that for that kind of particle. Such is the case for photons in a black cavity, whose number regularly change due to absorption and emission on the cavity walls. (On the other hand, photons in a highly reflective cavity can be conserved and caused to have a nonzero .) In some cases the number of particles is not conserved and the represents a more abstract conserved quantity: Chemical reactions: Chemical reactions can convert one type of molecule to another; if reactions occur then the must be defined such that they do not change during