On the Quasi-equilibrium assumptions in the theory of thermoluminescence (TL)

The phenomenon of thermoluminescence (TL) is governed by a set of simultaneous differential equations. When one studies the properties of a single peak, resulting from the thermal release of electrons from a trap into the conduction band, followed by radiative recombination with holes in centers, the set consists of three non-linear equations. Even in this simple case, the equations cannot be solved analytically. In order to get approximate solutions, the conventional way has been to make the "quasi-equilibrium" assumptions, namely that 9dn_c/dt9 is significantly smaller than 9dn/dt9 and 9dm/dt9, where n and m are the occupancies of traps and centers, respectively, n_c is the concentration of electrons in the conduction band, and n_c{n; n_c{m. We show, using simulations as well as analytical arguments that the former condition often does not occur; however, its consequences are valid. The reason is that the conventional quasi-equilibrium assertion must be replaced by a different condition. As for the smallness of the concentration of free electrons, we show that it may not be fulfilled at the high-temperature end of a single glow peak or in the highest-temperature peak in a series. In some cases, this condition results in a broad high-temperature tail of the TL peak, as previously observed experimentally in several materials.