Acceptor Transitions

The OSs for shallow acceptor transitions between ground state (0) with degeneracy go and final state (/) in cubic semiconductor can be expressed as  

OSs of the first transitions of the p3/2 spectrum in silicon and germanium obtained using different calculations are shown in Tables 5.22 and 5.23. 

In group-IV semiconductors, donors like P and As and acceptors like Al are monoisotopic, but others show an isotopic distribution (see appendix D). Beyond EMT, calculations of the isotopic splitting of the ground state of 

The OSs of the transitions calculated in [14], where a( ) corresponds to (( ), are compared with some of the ones in [46]. There are differences in the attributions for the highly excited states. The original OSs have been multiplied by 104. The energies (final states) are in meV a[14],b[46] 

The energy (meV) indicated is that of the final state. The original OSs values have been multiplied by 104 a[14],b[16] 

---

Figure 6.10 Energy-level diagram showing the coupling of donor and acceptor transitions of equal energy required for long-range nonradiative transfer...

Equation (4.79) shows that Ro, and consequently the transfer rate, is independent of the donor oscillator strength but depends on the acceptor oscillator strength and on the spectral overlap. Therefore, provided that the acceptor transition is allowed (spin conservation) and its absorption spectrum overlaps the donor fluorescence spectrum, the following types of energy transfer are possible ... 

When the absorption spectra of 2, 26 and 27 in the region around 300 nm are compared 26 shows a band at 297 nm, whereas 2 has a less intense shoulder at 302 nm. 27 lacks an absorption band in this region, which suggests that the 302-nm band of 26 is associated with an electron donor-acceptor transition, i.e. a tz-tz transannular interaction in an electron-withdrawing 7t-acidic 39> tetrafluorophenylene ring. 

The pH of deposition (adjusted by adding NH4OH, therefore pH increased but free Cd decreased) affected the PL spectra of the CdS films deposited from a standard solution [31]. A broad, red luminescence (ca. 1.2-2.0 eV with peak at 1.68 eV) was characteristic of all the spectra, regardless of deposition pH. At pH = 11.5, a narrow (0.18 eV half-width) green peak (2.255 eV) appeared, but it did not occur above or below this pH value). This peak, ca. 0.2 eV less than the bandgap, could be either a shallow-donor-to-shallow-acceptor transition or a band-to-fairly shallow interband state transition. 

Because of the Stokes shift for vibrationally relaxed systems (the rate of transfer < the rate of vibrational relaxation), transfer between like molecules is less efficient than that between unlike molecules when acceptor is at a lower energy level (exothermic transfer). No transfer is expected if the acceptor level is higher than the donor level. If (i) the acceptor transition is strong (Emaz —- 10,000), (ii) there is significant spectral overlap, and (iii) the donor emission yields lie within 0.1 — 1.0, then R0 values of 50-100 A are predicted. 

The solvent effect on V° can be significant. It derives from the modification of the donor and acceptor transitions densities by the medium, and is in effect regardless of whether or not the molecules interact with each other. V° is therefore the solvent-modified electronic coupling described in Equation (3.139), and as such, can be explicitly dissected into contributions from Coulombic and short-range interactions as well as electron correlation effects. According to the results reported in ref. [47], the solvent modification of Vshort is minor but VCoul is strongly influenced by the medium. In Figure 3.49 we plot results reported in ref. [47] to illustrate that. 

In contrast, EET has been historically modelled in terms of two main schemes the Forster transfer [15], a resonant dipole-dipole interaction, and the Dexter transfer [16], based on wavefunction overlap. The effects of the environment where early recognized by Forster in its unified theory of EET, where the Coulomb interaction between donor and acceptor transition dipoles is screened by the presence of the environment (represented as a dielectric) through a screening factor l/n2, where n is the solvent refractive index. This description is clearly an approximation of the global effects induced by a polarizable environment on EET. In fact, the presence of a dielectric environment not only screens the Coulomb interactions as formulated by Forster but also affects all the electronic properties of the interacting donor and acceptor [17],... 

The presence of a shallow acceptor level in GaN has been attributed to C substituting on an N site by Fischer et al [7], In luminescence experiments on GaN from high temperature vapour phase epitaxy in a C-rich environment donor-acceptor and conduction-band-to-acceptor transitions have been distinguished in temperature dependent experiments. From the separation of both contributions an optical binding energy of 230 meV close to the value of effective mass type acceptors was obtained. Hole concentrations up to 3 x 1017 cm 3 were achieved by C doping with CCU by Abernathy et al [10], In addition Ogino and Aoki [17] proposed that the frequently observed yellow luminescence band around 550 nm should be related to a deep level of a C-Ga vacancy complex. The identification of this band, however, is still very controversial. 

Hwang et al. [19] reported that the acceptor energy level of the phosphorus (P) impurity was estimated to be located at 0.127 eV above the valence band on the study of the free electron to the acceptor transition at 3.310 eV from the photoluminescence spectra of P-doped p-type ZnO films grown by rf-frequency magnetron sputtering. They also suggested that the emission lines at 3.310 and 3.241 eV of the photoluminescence spectra could be attributed to a conduction band to the P-related acceptor transition and a donor to the acceptor pair transition, respectively. 

The exchange term is usually dominant at close approach of M d and Ma, and allows triplet exciton transfer to occur when the donor and acceptor transitions are spin-forbidden. Therefore, four energy transfer processes from a singlet (1M [) excited molecule and triplet (3Mp excited molecule to an unexcited molecule in the singlet state (1Ma) are possible ... 

The relatively low values of yss and Ds in quasi-amorphous solids might be underlain by disorder (see Sec. 2.4.3) and/or a contribution of triplet excitons in quenching of fluorescent singlets (cf. Sec. 2.5.1.2). The diffusion coefficient of triplets is expected to be lower than of singlets since both energy donor and acceptor transitions are disallowed. A low value of yss has been found for the triplet-triplet annihilation rate constant from biexcitonic quenching... 

The most studied acceptor dopant up to now, by far, is N, and this element has been shown by electron paramagnetic resonance data to go predominantly onto the O site and have acceptor nature. It has an acceptor transition at 90 meV, for [N] lO cm, and this energy can be estimated to be about 130 - 150 meV at infinite dilution ". Thus, it is perhaps not surprising that p-type ZnO can be produced with N doping however, it is still somewhat of a mystery as to why As, P, and Sb also work. In any case, the recent success in creating p-type ZnO bodes well for the future of the ZnO LED industry, although much more research will be necessary before the situation is well understood. 

Luminescence can also arise from a trapped exciton or from a transition between two centers (donor-acceptor transitions). 

For electric multipolar interactions, the transfer rate IFda is proportional to the probability of the donor and acceptor transitions, to the overlap between the emission and absorption bands of the donor and acceptor, and to an inverse power of the donor-acceptor separation, with = 6, 8, 10 for dipole-dipole, dipole-quadrupole, or quadrupole-quadrupole interaction. For electric dipole-dipole interaction, the transfer rate is proportional to... 

The probability of the donor-acceptor transition decreases with increasing intrapair separation ... 

An approximate expression for the F factor appearing above is given by equation 17, where yi is the ligand state band width at half-height and A is the difference between the donor and acceptor transition energies involved in the transfer process . 

The parameter in Equation 8 is referred to as the orientation factor of FRET. This factor represents the angular dependence of the interaction energy between the acceptor transition dipole and the oscillating dipole electric field of the donor, is the source of much debate and many misunderstandings. It is the most difficult factor to control and usually the hardest to determine with confidence (28, 48). Therefore, we will spend more time discussing this factor. 

For forbidden donor and acceptor transitions the Coulomb term vanishes and the exchange term will predominate. If both transitions are allowed and the distance is not too small, the dipole-dipole interactions will prevail. The higher multipole terms are important only at very short distances, where, however, the essential contributions arise again from the exchange interaction, unless it vanishes due to the spin symmetry. 

Different complicating factors led to the development of a more generalized approach [22, 23] in which the Coulomb interaction is now considered in terms of local interactions between donor and acceptor transition densities. This is... 

The back-electron-transfer step is identical to the band-to-molecular state charge-transfer process involving minority-carrier injection (Section 2.3.5). This step is sensitive to defects that would act as donors with smaller activation barriers than a single regeneration step involving band-to-molecular acceptor transitions. Optimally the surface should have low defect densities and the cation level should lie as high above the valence band as possible (electrochemical determinations of the redox potential of the cation radical are needed). 

---