Absorption depth

A very important attribute of light sensitive materials is their absorption depth. The absorption depth is the length of material that will absorb 63.2% of the radiation (1/e of the energy is not absorbed). After two absorption depths, 87% of the light has been absorbed, and after three absorption depths, 95% has been absorbed. To make an efficient detector of light, the material thickness should be several times the absorption depth. 

Figure 8. Absorption depth of photons in silicon. Notice the tremendous variation in penetration depth, from 8 nm in the UV to more than 100 /um in the far-red.

In comparison to infrared detectors, it is much more difficult for silicon-based optical detectors to achieve high QE over a wide bandpass. The main challenge is the tremendous variation of absorption depth shown in Fig. 8. In addition, the index of refraction varies significantly for A = 0.32-1.1 m, as shown in Fig. 10, making it difficult to optimize anti-reflection coatings for broad bandpass. 

The backside passivation processes are most critical for the blue and UV wavelengths. For 0.5-0.7 pm light, high QE is more easily attained - the absorption depth is a few microns, and photons penetrate beyond the backside... 

The challenges of achieving high QE over the 0.3-1.1 m band is summarized in Eig. 14, which shows the optical absorption depth of photons in silicon with the range of thickness of different regions of a CCD. Figure 14, which we like to call the beautiful plot captures the information needed for understanding the QE of silicon CCDs. 

Figure 14. Optical absorption depth of photons in silicon with the thickness of different regions of a CCD overlaid. Figure courtesy of P. Amico, Keck Observatory.

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... 

One can also infer in turn from these arguments that the relative absorption depth of a Mossbauer line should not exceed 10-15%, because of the increasing thickness broadening and the related line distortions. 

Very thick absorbers may be required for applied-field measurements to achieve reasonable absorption depths and measuring times because the Mossbauer spectra are usually split into several hyperfine components. Here the iron content may be as large as 100 pg Fe per cm (1.75 pmol Fe per cm ), which would correspond to t 1 for a two-line spectrum. For smdies of frozen solutions, Fe concentrations of 1 mM are desirable for each nonequivalent iron site [35]. 

Absorption effects combine with this to make the beam attenuate more rapidly. In the absence of extinction, the absorption depth t is given by... 

Some shift of the Py maximum is observed in both cases of Fig. 13. This wavelength shift may be due to self-absorption and re-emission. In the case of Fig. 13a, the absorption depth increases with increasing crystal size despite of the constant ppy. In Fig. 13b, self-absorption and re-emission increases with increasing Py loading, which is easily comprehensible. This phenomenon has been discussed more quantitatively in Ref. 3. 

In xerographic measurements, as illustrated in Fig. 5.3, the sample is corona-charged to a voltage Vq and then exposed to a short wavelength (absorption depth S L) step illumination. At the end of the illumination, there is a measurable surface potential, termed the residual potential V because of the bulk trapped charges. If positive charging is used, then is due to trapped holes in the bulk of the specimen. 

We have selected the most appropriate lines suitable for use for the ions observed in SN 1987A, and they are listed in Table 1 together with the relevant atomic data for the transitions and the observed absorption depths. The f-values have been taken from the sources referenced. 

If the absorption depth L within the sample decreases exponentially according to the Lambert-Beer law, the density of populated excited states N(z) obeys... 

This expression can be analysed in two ways depending on the nature of the sample. In the case of a thin film [in comparison with the absorption depth of the pump light (D transmission changes (aNoD [Pg.18]

Figure 8 Expanded view of the pump-probe geometry and the sample jet. The pumped volume is 200 pm in diameter. The depth of the pumped volume is equal to the absorption depth of the liquid sample, typically 20-50 pm. The probed volume includes some sample that is not pumped, which is minimized by minimizing the jet thickness. (From Ref. 96.)... 

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