Free excitons

We adopt a simplified microscopic quantum-mechanical model of a 2D Wannier-Mott exciton, in which the polarization (eqn C.3) can be taken to vanish for L Lw/2 and inside the well to be given by the product of the Is-wave function of the relative motion of the electron and hole at the origin, with the lowest subband envelope functions for the electron and hole in the approximation of 

The corresponding electric field E(r) = — V (r) can be obtained from the solution of the Poisson equation for the potential f (r) (the charge density being Pi r) = —VP(r)) 

the electric field penetrating the organic material is given by 

Now we simply substitute this electric field into (C.7) and get the decay rate  

(a) Free L-exciton lifetime r (ns) versus the in-plane wavevector k (cm-1) for three well widths Lw = 20 A (dotted line), Lw = 40 A (dashed line), Lw = 60 A (solid line), other parameters being Lb 40 A, q, = 6, 1 = 4+3i. (b) Free L-exciton (solid line) and Z-exciton (dashed line) lifetime r (ns) versus the barrier width Lb 

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Figure 3 shows different forms of chemisorption for a C02 molecule. In the weak form of chemisorption the C02 molecule is bound to the surface by two valency bonds, as shown in Fig. 3a. This is an example of adsorption on a Mott exciton which is a pair of free valencies of opposite sign (i.e., an electron-hole pair). This may be either a free exciton wandering about the crystal or a virtual exciton generated in the very act of adsorption. As seen from Fig. 3a, in the case of the C02 molecule the weak form of chemisorption is a valency-saturated and electrically neutral form. As a result of electron capture, this form is transformed into a strong acceptor form shown in Fig. 3b, while as a result of hole capture it becomes a strong donor form shown in Fig. 3c. Both these forms are ion-radical ones. It should, however, be noted that the ion-radicals formed in these two cases are quite different and, having entered into a reaction, may cause it to proceed in different directions.

Another type of absorption is also possible, i.e., exciton absorption which enriches the crystal in free excitons if the latter annihilate then on the lattice defects, causing a change in the charged state of the defects and leading to the appearance of free carriers in the crystal. In this case photoconduction arises as a secondary effect. 

At low temperatures, donors and acceptors remain neutral when they trap an electron hole pair, forming a bound exciton. Bound exciton recombination emits a characteristic luminescence peak, the energy of which is so specific that it can be used to identify the impurities present. Thewalt et al. (1985) measured the luminescence spectrum of Si samples doped by implantation with B, P, In, and T1 before and after hydrogenation. Ion implantation places the acceptors in a well-controlled thin layer that can be rapidly permeated by atomic hydrogen. In contrast, to observe acceptor neutralization by luminescence in bulk-doped Si would require long Hj treatment, since photoluminescence probes deeply below the surface due to the long diffusion length of electrons, holes, and free excitons. 

Bulk silicon is a semiconductor with an indirect band structure, as schematically shown in Fig. 7.12 c. The top of the VB is located at the center of the Brillouin zone, while the CB has six minima at the equivalent (100) directions. The only allowed optical transition is a vertical transition of a photon with a subsequent electron-phonon scattering process which is needed to conserve the crystal momentum, as indicated by arrows in Fig. 7.12 c. The relevant phonon modes include transverse optical phonons (TO 56 meV), longitudinal optical phonons (LO 53.5 meV) and transverse acoustic phonons (TA 18.7 meV). At very low temperature a splitting (2.5 meV) of the main free exciton line in TO and LO replicas can be observed [Kol5]. 

The photoluminescence (PL) spectrum in Figure 1.7 shows a number of lines related to nitrogen-bound excitons and free excitons. SiC has an indirect bandgap, thus the exciton-related luminescence is often assisted by a phonon. Bound exciton luminescence without phonon assistance can, however, occur because conservation in momentum can be accomplished with the help of the core or the nucleus of the nitrogen atom. That is why the zero phonon lines of the nitrogen atom are seen, denoted and Q , in the spectrum but not the zero phonon line of the free exciton. 

Figure 1.7 Near-band-edge photoluminescence spectrum of 4H-SIC showing the bound exciton-related luminescence denoted and (where h is the energy in meV of the phonon involved in the transition) and free exciton-related luminescence denoted /. (Data provided by Docent Anne Henry at Linkoping University.)...

We measured the time-resolved fluorescence from an organic microcrystal, perylene, by using the newly developed fluorescence microscope. Perylene has two types of crystal structure, a-and P- perylene. In a-pcrylene, four molecules exist in a unit cell, whereas two molecules in P-perylene. We chose one a-perylene crystal under the microscope by checking the fluorescence spectrum. At room temperature, a-perylene exhibits very broad fluorescence in the visible region with the intensity maximum around 600 nm. The fluorescence located at 480 nm has been assigned to the emission of the free exciton. The free exciton is relaxed to... 

Therefore the lack of an observable bleach can only be explained by the cancellation of all contributions to the pump-probe signal, which is the case for a perfect harmonic state. It can be shown that the anharmonicity of a vibrational exciton is a direct measure of its degree of delocalization [5]. Thus, we conclude that the free exciton state is almost perfectly delocalized at 90 K. As temperature increases, a bleach signal starts to be observed, pointing to a non-complete cancellation of the different contributions of the total pump-probe signal. Apparently, thermally induced disorder (Anderson localization) starts to localize the free exciton. The anharmonicity of the self-trapped state (1650 cm 1), on the other hand, originates from nonlinear interaction between the amide I mode and the phonon system of the crystal. It... 

Fig.1. (a) Absorption spectra and (b) 2D-IR pump probe spectra of the C=0 mode of crystalline ACN. 2D-IR spectra record the absorption change as a function of probe frequency and the center frequency of a narrow band pump pulse. The contour intervals represent a linear scale. Response of the amide I band upon selective excitation of the self-trapped states (c) and the free exciton peak (d) for two different delay times. The arrows indicate the position of the narrow band pump pulse. 

In a second experiment, narrow band pump pulses (spectral width 30 cm 1, pulse duration 250 fs FWHM) were used to selectively excite individual sub-levels of the NH band (Fig. 2e, g) [4]. On the sub-picosecond time scale, the free-exciton and the lower lying self-trapped states behave distinctly differently. When exciting the free-exciton (Fig 2e), a strong bleach and stimulated emission signal is observed which recovers on a 400 fs time scale. Simultaneously, population is transferred into lower lying self-trapped states. On the other hand, when pumping one of the self-trapped states directly (Fig. 2g), population within all self-trapped states equilibrates essentially instantaneously, but the free exciton peak is not back-populated. This is the direct observation of ultrafast self-trapping Excitation of the free-exciton leads to an irreversible population of self-trapped states, but not vice versa. 

The electronic properties of RGS have been under investigation since seventies [3-7] and now the overall picture of creation and trapping of electronic excitations is basically complete. Because of strong interaction with phonons the excitons and holes in RGS are self-trapped, and a wide range of electronic excitations are created in samples free excitons (FE), atomic-like (A-STE) and molecular-like self-trapped excitons (M-STE), molecular-like self-trapped holes (STH) and electrons trapped at lattice imperfections. The coexistence of free and trapped excitations and, as a result, the presence of a wide range of luminescence bands in the emission spectra enable one to reveal the energy relaxation channels and to detect the elementary steps in lattice rearrangement. 

Radiative decay of free excitons from the bottom of the lowest T(3/2), n= 1 excitonic band produces strong lines FE (Fig.la) in spectra of solid Xe,... 

The commonly used scheme of energy relaxation in RGS includes some stages (Fig.2d, solid arrows). Primary excitation by VUV photons or low energy electrons creates electron-hole pairs. Secondary electrons are scattered inelastically and create free excitons, which are self-trapped into atomic or molecular type centers due to strong exciton-phonon interaction. 

Discrete and continuum free exciton contributions can be identified for each of the band-to-band transitions Eq. Sharp resonance features are superimposed to each of the Eq CP structures because of discrete exciton lines, where the ground and first excited state (n = 1,2) can be seen at RT, and the second... 

Table 3.14. Parameters of the temperature dependence of the transition energy Eq and the discrete free exciton FWHM W20 according to the 2-oscillator model for a ZnO thin filma...

Fig. 3.24. Experimental data (symbols) of the FWHM W of the discrete free exciton together with model calculations (solid line) according to the two-oscillator model (WioiT), 3.30) vs. temperature of a ZnO thin film...

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