Pair emission

Benyoucef, M., Ulrich, S.M., Michler, P., Wiersig, J., Jahnke, F., andForchel, A., 2004, Enhanced correlated photon pair emission from a pillar microcavity. New J. Physics 6 91. 

FIGURE 9.1 Schematic of emissive transitions of electrons in semiconductors (a) band-band emission (b) a free electron recombines with a trapped hole (c) a trapped electron recombines with a free hole (d) donor-acceptor pair emission. 

The single electron detection rate C+ at the same electron energy depends on both the pair emission rate and on the single ionization rate N iEi) ... 

Another type of recombination in semiconductors is donor-acceptor pair emission. In this type of emission an electron trapped at a donor and a hole trapped at an acceptor recombine. Again GaP is a very nice example (Fig. 3.24). The donor-acceptor pair emission in this figure is due to a Sp-Zncg pair transition. The lines are due to the fact that the di.stance between the donor Sp and the acceptor Znca varies due to their statistical distribution over the lattice, so that the binding energy of electron and hole varies with the distance between the centers where they are trapped. 

Also in other semiconductors such donor-acceptor pair emissions have been found. A well-known example is ZnS Cu,Al where Alzn is the donor and Cuzo the acceptor. This material is used as the green-emitting phosphor in color television tubes. The blue emission of ZnS Al is due to recombination in an associate consisting of a zinc vacancy (acceptor) and Alzn (donor). Since these centres occur as coupled defects, their distance is restricted to one value only (this is sometimes called a molecular center). Due to strong electron-lattice coupling the emissions from ZnS consist of broad bands. 

Fig. 3.24. The Sp-Znoa donor-accepior pair emission in GaP at 1.6 K. At the bottom R indicates he donor-acceptor distance of the relevant emitting pair. The lines are indicated by their shell number (shell I means nearest-neighbour pairs, etc.). On the right-hand side we see the zero-phonon lines of the individual lines on the left-hand side we sec mainly vibronic lines (in the semiconductor field often called replicas) due to coupling with host-laiiicc modes. Modifted from A.T. Vink, thesis, Technical University Eindhoven, 1974...

Fig. 3.25. Emission tran.sitions in a semiconductoi (schemalical representation). The band gap Eg separates the valence band (VB) and the conduction band (CB). Excitation over the band gap (/) creates electrons in CB and holes in VB. Optical recombination is shown in processes 2-6 (2) a free hole recombines with an electron trapped in a shallow trap level (near-edge emission) (3) the same with a deep electron-trapping level (4) a free electron recombines with a trapped hole (5) donor-acceptor pair emission (6) electron-hole recombination in an associate of a donor and an acceptor...

Finally nonradiative transitions which are specific for semiconductors are mentioned. In order to do so, we consider a specific radiative transition, viz. the donor-acceptor-pair emission (Sect 3.3.9). In the excited. state the donor and acceptor are occupied (Fig. 4.14). This excited luminescent center may show radiative and nonradiative transitions within the center itself (similar to the discussion in Sect. 4.2). In addition, however, there are other processes which are related to the valence and/or conduction band. 

Fig. 4.14. Nonradiativc transitions in a semiconductor. The donor-acceptor pair emission (DA) can be quenched by thermal ionization of one of the centers (a) or by an Auger process (6). In the latter case a conduction electron is promoted high into the conduction band...

Fig. 7.6. Rneigy level scheme for the donor-acceptor pair emission of ZnS Ag. The valence and conduction bands of ZnS are indicated by VB and CB, respectively. D is the shallow donor (aluminium or chlorine), A is the acceptor (silver)...

Right Monomer and pair emission (mini-exciton). The 0,0-transition of the phosphorescence of C- oHg as a guest molecule in a CioDg host crystal is shown. The spectra from crystals with 0.2, 2, 5, 10 and 20 mole % C- oHg are shifted vertically for... 

No low level of / = 0 is predicted by these schemes other than the ground state, but it arises naturally as a dilational state in the alpha particle model. This model (Sect. 4) also predicts the 2 state but requires low lying states of J = y and 1" which have not been identified. The 0" state can also be obtained by double nucleon excitation, e.g. in the configuration pfj p i - The transition probability of the O " state for pair emission to the ground state can be estimated from the cross section for excitation of this state with electrons. Schiff claims that the value obtained is too small to be explained by the alpha particle model and too large to be accounted for by a // coupling model with excitation of two -particles he suggests that a collective model intermediate in properties between the two extreme models is necessary. 

If the energy of the transition is greater than 1.022 MeV, the nucleus may lose its excitation energy also by internal electron-positron pair emission. The probability of this mechanism is low it is usually more than 10 times smaller than the probability of y-ray emission. In contrast with the internal conversion electron emission, the internal pair formation coefficient increases with increasing y-ray energy and decreases with increasing atomic number and multipolarity of transition. A review of internal pair formation was given by Wilson (1965). 

The other well-known emission bands in GaN, in lower energy regions such as donor-acceptor pair emission together with its phonon replicas, as well as the blue-green, yellow, and red emission bands, have also been observed in GaN films with nonpolar orientations and their origin was, in principle, related to the same defects as the respective emissions in polar materials [95, 99]. 

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