SPONTANEOUS EMISSION AND LEVEL LIFETIME

An atom at an excited state will eventually drop to a lower level and in doing so will emit a photon of radiation in a process called spontaneous emission. Excited electrons will not stay at the excited level forever since nature favors a low energy level and so will emit the photon spontaneously after an average time of τ_sp called the spontaneous lifetime of the level. This time depends on the atomic species involved and can be measured for a given species; some levels have long lifetimes measured in seconds, whereas others are relatively short, on the order of nanoseconds or less. This lifetime determines the ability of the emitting atom to store energy and will affect the efficiency of sources. In lasers, it also factors prominently in determining the probability that laser action can be coaxed from a particular atomic species. Consider Figure 1.1, in which two atoms with different spontaneous lifetimes are excited at a start time t =0. The top atom, with a relatively short lifetime, emits a

Figure 1.1. Spontaneous lifetime.

photon spontaneously at a time t = τ₁, while the second atom, with a longer lifetime, waits until an elapsed time of t = τ₂ before emitting a photon. Radiation is not always emitted from a transition. An electron can lose energy by colliding with tube walls. Such non-radiative events are rare, though, in a gas at low pressure (such as that in a discharge tube or neon sign), so we shall not discuss them here. This non-radiative mechanism is important, however, as it is used to depopulate certain energy levels in lasers (including the common helium neon laser) and so will be dealt. In addition to losing energy in collisions (primarily in a gas, where atoms are treated essentially as independent entities), electrons that are trapped in a crystal lattice can lose energy by causing vibrations in the crystal. A vibration resulting from a transition, called a phonon, produces heat in the crystal and occurs commonly in semiconductor materials.