Thin absorber

FIGURE 2.8 Range distribution of 100-eV electrons in the vapor and liquid phases of water. Reproduced from La Verne and Mozumder (1986), with permission of Am. Chem. Soc.  

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Absorption spectroscopy provides a means to study particular details about a monolayer. Transmission spectroscopy is difficult because the film, which is thin, absorbs little. Gaines [1] describes multiple-pass procedures for overcoming this problem. Reflection spectroscopy in the UV-visible range has been reported for lipid monolayers [150,151] and in the IR range for oleic acid [152]. 

Machtie P, Muiier C and Heim C A 1994 A thin absorbing iayer at the center of a Fabry-Perot interferometer J. Physique ii 4 481-500... 

Fig. 3.18 Schematic outline and ideal band diagram of an extremely thin absorber solar cell. The n-Ti02 crystallites are clustered together to form a relatively open, network-like morphology, accommodating a thin layer of CdTe absorber, with p-ZnTe at the back contact. (Reprinted from [270], Copyright 2009, with permission from Elsevier)...

For thin absorbers with t exponential function in the transmission integral can be developed in a series, the first two terms of which can be solved yielding the following expression for the count rate in the detector ... 

Although Lorentzian line shapes should be strictly expected only for Mossbauer spectra of thin absorbers with effective thickness t small compared to unity, Margulies and Ehrman have shown [9] that the approximation holds reasonably well for moderately thick absorbers also, albeit the line widths are increased, depending on the value of t (Fig. 2.7). The line broadening is approximately... 

Fig. 2.8 (a) Fractional absorption of a Mossbauer absorption line as function of the effective absorber thickness t. (b) The depth of the spectrum is determined by fs. The width for thin absorbers, t 1, is twice the natural line width F of the separate emission and absorption lines (see (2.30)). AE is the shift of the absorption line relative to the emission line due to chemical influence... 

The relative absorption depth of the Mossbauer line is determined by the product of the recoU-free fraction/s of the Mossbauer source and the fractional absorption z t) of the sample, abs = fs-e f), where c(t) is a zeroth-order Bessel function ((2.32) and Fig. 2.8). Since c(t) increases Unearly for small values of t, the thin absorber approximation, c(t) t/2, holds up to t 1. On the other hand, values as small as t = 0.2 may cause already appreciable thickness broadening of the Mossbauer lines, according to (2.31), Fexp + 0.135t). In practice, therefore the sample... 

Using the value t = 0.2 for the effective thickness, the amount of resonance nuclei ( Fe) for a good thin absorber can be easily estimated according to the relation = tl(fA-(to)- For a quadrupole doublet with two equal absorption peaks of natural width and a recoil-free fraction of the sample/a = 0.7 one obtains... 

Fig. 3.13 Signal-to-noise ratio of Mossbauer spectra as a function of the area density l of the sample for thin absorbers ( < 1) and negligible nonresonant background, A b A oo...

Conclusions. A Mossbauer sample with a low content of the resonance nuclide has ideal thickness when it attenuates the incident radiation by ca. 63-85% (/ie t = 1-2, C /Co e - e ). However, the optimization should be subordinated to the requirement of a thin absorber having an effective thickness / < 1 to avoid excessive line broadening. 

This paragraph presents a summary of the most relevant expressions provided by Long et al. [1] for the optimization of thin absorbers (effective thickness / high mass absorption. The result of this work is used in Sect. 3.3.2 of the book. Following the approach of [1], we adopt for the signal-to-noise ratio ... 

A relative simple solution can be obtained for absorbers with low signal N, if the background contribution N can be neglected. With equation (2.32) for the fractional absorption in thin absorbers, i.e., s(t) t/2, the signal amplitude can be written as ... 

The intensity of a Mossbauer spectrum depends not only on the recoil-free fractions of the source and the absorber and on the number of absorbing nuclei, but also on the linewidth of the absorption lines and on whether or not saturation effects occur. The following approximate expression is valid for relatively thin absorbers [17] ... 

IJt) is the measured linewidth of a Mossbauer peak 71 is the linewidth of the source ra is the linewidth of the infinitely thin absorber rml is the natural linewidth... 

The molecules form a thin absorbing layer of thickness d, with a complex dielectric constant n(w) = n](exact solution and various approximations.3. For thin films, Bell has obtained a reasonably simple approximation for the absorption of an SEW due to the overlying film. If the SEW are propagated a distance D on the metal substrate, with and without the thin film, the ratio of the SEW intensities is given by... 

The spectrum shown in Figure 4.55 is obtained when there are no hyperhne interactions, that is, the emitter and the absorber have the same energy of emission and absorption. Consequently, the maximum absorption of gamma photons emitted by the source at the thin absorber is v = 0, because of resonant absorption. Subsequently, as the velocity of the source is increased in the positive or the negative directions, the resonance is broken and, therefore, the transmission of gamma photons through the absorber increases [135],... 

For good absorption, the thickness of the absorber in the planar configuration of Fig. 4.3 with normally incident light should be / 1/a. Thin absorbers... 

Absorbance calculations in the above configuration are implemented by introducing the absorbing species as a small perturbation to the initial configuration (see Fig. 2). Either a small extinction coefficient is introduced to the optical properties of the cover material (as shown in Fig. 3) or a thin absorbing layer is introduced between the waveguide and the cover (Fig. 4). A critical assumption for the... 

Relative area. The relative areas of the quadrupole doublets are related to the relative abundance of each component, which can be estimated according to the thin absorber approximation (Eqn. 13, this Chapter) in cases where the approximation is valid. Rancourt et al. (1993) provide a means of estimating how closely the thin absorber approximation is satisfied for a given absorber based on the attenuation of spectral areas for individual lines (see Fig. 3 in their paper). McConnell et al. (2000) used an iron density in the high temperature experiments corresponding to an unenriched concentration of 5 mg Fe/cm, which is equivalent to a dimensionless effective thickness of 2.0. The attenuation of spectral... 

In this chapter, I give an account of the historical development of semiconductor photoelectrochemistry and nanostructured photovoltaic devices in Section 1.2, and then Sections 1.3-1.6 provide a brief introduction to the major cell types discussed in the remainder of the book the ETA (extremely thin absorber) cell, organic and hybrid cells, dye-sensitised solar cells (Gratzel cells) and regenerative solar cells. 

Nanosized TiOi powders are of outstanding importance in this context. Aqueous suspensions of 30 nm particulate TiOi (mostly in the rutile form) are the active agent in many of the photocatalytic systems described by Serpone and Emetine in Chapter 5. Agglomerations of Ti02 nanoparticles into mesoporous films of pore size 2-50 nm which allow the penetration of liquid are the basis of the important dye-sensitised solar cell (DSSC) discussed by Grateel and Durrant in Chapter 8, as well as most of the hybrid devices described by Nelson and Benson-Smith in Chapter 7, and some of the ETA (Extremely Thin Absorber) cells described by Konenkamp in Chapter 6. The term eta-solar cell was actually introduced by Konenkamp and co-workers (Siebentritt et al., 1997), who had earlier used the term sensitisation cell for the same type of device (Wahi and Konenkamp, 1992). Precursors to ETA cells with liquid electrolytes as hole conductors were developed by Vogel et al. (1990), Ennaoui et al. (1992) and Weller (1993). Similar electrolytic cells with RuSa (Ashokkumar et al, 1994) and InP (Zaban et al, 1998) nanoparticle absorbers have also been demonstrated. 

Ernst K., Belaidi A. and Konenkamp R. (2003), Solar cell with extremely thin absorber on highly structured substrate , Semicond. Sci. Technol. 18, 475 79. 

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