Radiative Auger Emission

Amplified spontaneous emission was recently observed by Bawendi, Klimov and coworkers for spherical colloidal CdSe QDs in close-packed films where pumping vhth an amplified femtosecond laser source was used to compete with fast non-radiative Auger decay processes [13, 88]. In further studies, films vhth CdSe nanocrystals were deposited on a distributed feed-back grating structure to yield optically pumped lasing that was tunable through the visible range by changing the nanocrystal size [89, 90]. 

Figure 1.10 shows the photon-induced K X-ray spectrum of Zn recorded with a crystal spectrometer, which clearly shows the satellite, hypersatellite, and the RAE (Radiative Auger Effect A broad weak X-ray emission structure with several maxima on the low-energy side of the characteristic X-ray lines which has been interpreted as a radiative K —> transition resulting... 

Auger emission, in which the excess energy is released to an electron (Auger electron), which is emitted (non radiative decay). 

AES was developed in the late 1960s, and in this technique electrons are detected after emission from the sample as the result of a non-radiative decay of an excited atom in the surface region of the sample. The effect was first observed in bubble chamber studies by Pierre Auger (1925), a French physicist, who described the process involved. 

These features of lines of various spectra (X-ray, emission, photoelectron, Auger) are determined by the same reason, therefore they are discussed together. Let us briefly consider various factors of line broadening, as well as the dependence of natural line width and fluorescence yield, characterizing the relative role of radiative and Auger decay of a state with vacancy, on nuclear charge, and on one- and many-electron quantum numbers. 

The different emission products which are possible after photoionization with free atoms lead to different experimental methods being used for example, electron spectrometry, fluorescence spectrometry, ion spectrometry and combinations of these methods are used in coincidence measurements. Here only electron spectrometry will be considered. (See Section 6.2 for some reference data relevant to electron spectrometry.) Its importance stems from the rich structure of electron spectra observed for photoprocesses in the outermost shells of atoms which is due to strong electron correlation effects, including the dominance of non-radiative decay paths. (For deep inner-shell ionizations, radiative decay dominates (see Section 2.3).) In addition, the kinetic energy of the emitted electrons allows the selection of a specific photoprocess or subsequent Auger or autoionizing transition for study. 

Hitherto the discussion of Fig. 5.2 has neglected the possibility of non-radiative decay following 4d shell excitation/ionization. These processes are explained with the help of Fig. 5.2(h) which also reproduces the photoelectron emission discussed above, because both photo- and autoionization/Auger electrons will finally yield the observed pattern of electron emission. (In this context it should be noted that in general such direct photoionization and non-radiative decay processes will interfere (see below).) As can be inferred from Fig. 5.2(h), two distinct features arise from non-radiative decay of 4d excitation/ionization. First, 4d -> n/ resonance excitation, indicated on the photon energy scale on the left-hand side, populates certain outer-shell satellites, the so-called resonance Auger transitions (see below), via autoionization decay. An example of special interest in the present context is given by... 

Recombination is either radiative or non-radiative. The radiative process is accompanied by the emission of a photon, the detection of which is the basis of the luminescence experiment. The radiative transition is the inverse of optical absorption and the two rates are related by detailed balance. Non-radiative recombination is commonly mediated by the emission of phonons, although Auger processes are sometimes important, in which a third carrier is excited high into the band. The thermalization process occurs by the emission of single phonons and is consequently very rapid. Non-radiative electron-hole recombination over a large energy requires the cooperation of several phonons, which suppresses the transition probability. 

The probability of relaxation by radiative emission, i.e. giving rise to the emission of an X-ray photon rather than an Auger electron. For the K series, this probability is low for light elements up to Z = 10 and increases rapidly with atomic number, becoming significant for the heavy elements. For the L series, a curve of the same shape is obtained, shifted towards the heavier atoms. 

The physics of the Z-ray-emission process presents an even more fundamental barrier to the usefulness of EDS in low-Z element analysis. The electron beam incident on a sample excites characteristic Z-rays (as distinct from bremstrahlung) via the radiative decay of core holes created as a primary event within the inner electronic structure of the element in question. However, these core holes can decay via competing channels, the most important of these being the Auger process in this, the energy associated with the neutralization of the core holes is transmitted to another electron in a shallower level, which is then ejected from the atom. The probability of radiative as opposed to Auger decay decreases with Z, so that for sodium the relative probabilities are 1 40, for carbon 1 400. Instrumental factors notwithstanding, this... 

In the same way that the rearrangement of charge is crucial to determine the Auger capture rates from the valence band of a metal, it is reasonable to assume that it should also be of great importance to calculate radiative rates from the metal valence band. Nevertheless, the theoretical approach is simpler because the energy associated to the decay is released in the form of photons, and no electronic excitations are created in the medium. The radiative capture process is shown schematically in Fig. 8. We call radiative capture to the process in which the initial state of the electron is a valence-band state, the final state is a bound state of the ion, and the energy balance is compensated by the emission of light. 

If the equilibrium of a semiconductor is disturbed by excitation of an electron from the valence to the conduction band, the system tends to return to its equilibrium state. Various recombination processes are illustrated in Fig. 1.16. For example, the electron may directly recombine with a hole. The excess energy may be transmitted by emission of a photon (radiative process) or the recombination may occur in a radiationless fashion. TTie energy may also be transferred to another free electron or hole (Auger process). Radiative processes associated with direct electron-hole recombination occur mainly in semiconductors with a direct bandgap, because the momentum is conserved (see also Section 1.2). In this case, the corresponding emission occurs at a high quantum yield. The recombination rate is given by... 

Fig. 2 shows a diagram summarizing the various transitions which can be observed in the Mjjj and My spectra of a metal as well as in the 3 d Auger spectra. The Mjjj and My absorption transitions are shown in Fig. 2a and b the energy of the Mjjj discontinuity corresponds to the transfer of an inner 3p i2 electron to the Fermi level and its shape involves the 6d unoccupied distribution the energy of the My absorption line is exactly that of the 5/" -> SJjyj excitation transition. The My emission is shown in Fig. 2e an inner 3 d i2 hole is created and a 5/electron transits to this hole with the emission of a photon. In the corresponding non-radiative transition, there is simultaneously the 5/ electron transition, and the excitation or ionization of a 5/electron (or 6p or 6 s) (Fig. 2f). The My resonance line is represented in 2c the excited 5/electron drops back to the inner hole the corresponding emission line then coincides with an absorption line. The competing non-radiative transition is shown in 2d this is an Auger transition in the excited atom the final state has only one hole in an outer shell and the configuration is the same as in a photoemission process.

Most NEXAFS beamlines measnre soft x-ray absorbance by monitoring the energetic decay of the excited state, which occurs nonradiatively as Auger electron emission and radiatively as photon flnorescence. Auger electron emission provides the most common quantification of soft x-ray absorption into bonnd states. Anger emission occurs when an outer shell electron from the same atom decays into a core hole formed by soft x-ray excitation. The decay energy, which is the difference between onter shell and core orbital energies, is transferred to a second onter shell... 

Fig. n.3 Photoelectric ionization can be followed by either radiative relaxation, causing the emission of characteristic fluorescent X-rays or non-radiative relaxation, involving the emission of Auger electrons. 

The primary purpose of bombarding a specimen with protons or heavier ions in PIXE is to eject bound electrons from the K or L atomic shells. The ejection can also be achieved by means of electrons or photons with energy in the 1-100 keV range. The vacancies will de-excite within 10 s with the emission of characteristic radiation or Auger electrons or both the probability of the radiative relaxation is the fluorescence yield ro. For low-Z elements (Z<30) and for Kvacancies, the production of Auger electrons is more probable than emission of characteristic radiation in the case of Lshell vacancies, this is always the case. Nevertheless, for elements with Z < 20, protons are more efficient than photons or electrons for producing characteristic X-ray. For heavier elements, photon-induced X-ray emission (i.e.. X-ray fluorescence, XRF) is more efficient. 

Equation (3) can be explained in simple terms as follows. The rate of change of the carrier density (i.e., dNc/dt) is equal to the rate at which new carriers are injected, minus the rate at which carriers are removed via nonradiative, radiative, and Auger recombination processes, minus the rate at which carriers are removed via stimulated recombination. Note that the rate of stimulated recombination is proportional to the differential gain given by Eq. (2). This is because the creation of a new photon by stimulated emission (i.e., the gain process) corresponds precisely to the loss of one carrier through stimulated recombination. 

---