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The ground state configuration for the erbium atom is [Xe)4fi^5s^5p^6s^5d^.

W hen it becomes ionised, the final four shells become 4 fi^5 s^5 p ^, the 5 d and 6s

shells being empty. The first two terms in Eq.(2.1.1) determ ine the electronic structure. The approach to treating is to em ploy the central field approximation^ (Chapter 3). The solutions to the problem can be split into a product of radial and angular functions. While the radial function depends upon the potential formed by the nucleus and all other electrons in the shell, the spherical symmetry ensures that the angular component is identical to that of the hydrogen atom and can therefore be expressed as a sum of spherical harmonics. The solutions are labelled by the quantum numbers, L and 5. L is the total orbital quantum number and S is the total spin quantum number. Linear conibinations of states described by L and S serve as the basis states for evaluating the electron-electron interaction. This interaction splits the single-electron configuration into separate levels The allowed values of L, which are 0, 1, 2, 3...6, are expressed by the capital letters S, P, D , F, G, H , and I,

respectively. The electronic structure of rare earth ions is dominated by this factor followed by the spin-orbit interaction next in importance. Spin-orbit interaction lifts the degeneracy in total angular momentum and splits the L S terms into J multiplets (where J is the total spin)^.

This splitting into multiplets means that the energy of a state depends upon the total momentum quantum number J, where J=(L+S), (L+S-1), (L+S-2), ...(L-5). The level notation is based upon the 'Russell-Saunders' nomenclature, and provides the symbol characterising each level. This is calculated from W hile both the electrostatic and spin-orbit interactions increase with rising atomic number, spin-orbit increases more rapidly, so that LS mixing is more significant for high-Z rare earths such as Er^+.

The maximum capacity of th e /s h e ll is 14 electrons. In the case of the Er^+ ion the / shell contains 11 electrons and 3 holes. It is convenient to calculate the electronic configuration using the 3 vacancies rather than the 11 electrons^. The only

difference arises when ordering the levels, as holes possess a positive charge. The ground state of an atom is the state with the highest value of S and L, in this order. For the ground state o f Er^+, the sum of the individual spins for each vacancy is

S = S ] + S 2 + S 3 = \ / 2 + \ / 2 + \ / 2 = 3 / 2 . The highest value of L compatible with the exclusion principle is L=/7+/2+ / i= l+2+3=6. According to Hund's rule, if an atom has more electrons than vacancies in the valence shell, the ground state has the highest value of y, where y=L+5=15/2. The ground state is "^1,5/2- The other levels of the multiplet are, in ascending energy, 7=13/2, 11/2, and 9/2.

The complete configuration of Er^+ can be calculated from all the possible values of L = l, 2, 3, 4, 5, 6, with 6"= 1/2 and 3/2. Multiplets of close levels can overlap to a certain extent. The energy level diagram of Er^+ is shown in Fig.2.2.1. The energy levels are labelled by their Russell-Saunders S U terms^.

7 / 2 1/2 3 / 2 9 / 2 1 3 / 2 1 5 / 2 Spin- No ► electron electron interaction repulsion orbit coupling

Figure 2.2.1. The energy levels of the isolated Er^+^^1.

For each of the 1 levels there are several degenerate states. The number of states is equal to (2J+1). It is found that counting all the I levels will result in a total of fifty-six possible states. In Chapter 3, the effect of crystal symmetry in relieving some of these degeneracy's is examined.

C hapter 2: Properties of the rare earths

2.2.1 Pump wavelengths

The first four levels have all been successfully used as optical pump levels for Er^+ in glass. The most efficient pump is in the 980nm range, corresponding to the third, \ ^ i2 level (Fig 2.2.2). An ion in the ground state is excited by 980nm to the third excited level. It then decays nonradiatively to the ^ Ii3 /2 metastable state. This is the initial level for the transition producing gain at 1500nm. Any process which removes ions from this state, other than by stim ulated em ission, decreases the luminescence efficiency. When the rare earth is in silicon, however, the case is different. The pump wavelengths used must be within the host band-gap to ensure absorption i.e. 514nm , 488nm , 476nm , and 457nm . The only one of these corresponding to direct optical excitation of the Er^+ is 476nm thus, excitation in silicon is believed to occur by indirect means^. The exact mechanism is not known, but as m entioned in C hapter 1, the excitation is believed to result from the recombination of an electron and hole at, or near, a rare earth ion.

4 1/2 S 3 / 2

490 nm

520 nm

550 nm

650 nm

_{800 nm}

Pump At

980 nm

\

980 nmNon Radiative

Transition

1535 nm

/ \ / v

Ground State

F igure 2.2.2 Energy levels of Er^+ labelled with Russell-Saunders ^Lj terms. For each state, the Ground State Absorption (GSA) column lists the wavelength of the excited-state absorption terminating on it^.