Optical absorption depth

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.

Operating Temperature. The calculations in the previous sections assumed that only fluctuations in the rate of arrival of photons from the forward hemisphere were important. This is evidenced by the employment of M(v, 7 ), which applies to a hemisphere. If the sensitive element of the detector is at the same temperature as the background, it will receive radiation not only from the forward hemisphere but from the reverse as well. Even though the back side of the element is mounted on a substrate, radiation will enter either through or from the substrate. Whether or not this is important is determined by whether the detector responds only to radiation incident on the front surface. In most photovoltaic detectors the back surface is much farther from the junction than the sum of the optical absorption depth and the carrier diffusion length. Thus most photovoltaic detectors have a preferred surface, and the background limit does not depend upon the mode of operation. 

This distance or a multiple thereof is generally known as the thermal diffusion distance for the particular problem and is a handy quantity to use when scaling the effects of laser heating. It is often useful to know how the optical absorption depth compares with the thermal diffusion distance during a laser irradiation. To see the meaning of the thermal diffusion depth more clearly, consider the following particular solutions of Eq. (32) ... 

When a is very large or the optical absorption depth 0 is very small compared to the thermal diffusion depth (/cip) /. Here ip is the duration of the irradiation. 

A detailed theoretical description of photoacoustic spectroscopy has been given by Rosencwaig and Gersho [4]. They defined the optical absorption depth of a solid sample pp as the reciprocal of the linear absorption coefficient, [i.e., pp = l/a(v)]. They examined several different cases, of which the most important in practice are when the sample thickness, I, is greater than L and pp. Only these cases are discussed here. 

The values of the linear absorption coefficient a(v) and the optical absorption depth pp at the peak of the strongest bands in three spectral regions are also given in Table 20.2. Clearly, > pp for each of these bands, which is the condition for photoacoustic saturation for spectra taken at the lowest optical velocity, so that these three bands in the PE spectmm all have about the same intensity. 

PAS signals are generated as a result of the absorption of radiation by the sample, thus causing a periodic temperature fluctuation within the optical absorption depth. Consequently, as the absorbed radiation from within a thermal diffusion length is released to the surface, there is an increase in the pressure of the ambient gas surrounding the sample. The pressure change is then detected by a microphone and subsequently converted to an electric signal. 

In each of these approaches, imaging is confined to the top of a single polymeric film by adjusting optical absorption. The penetration depth of the silylation agent and the attendant swelling of the polymer film must also be controlled to avoid distortion of the silylated image. Resists of this type are capable of very high resolution (Fig. 37). 

Depth resolution depends on the (spectrally dependent) optical absorption coefficient of the material. Near-surface analysis (first 50 nm) frequendy can be per-... 

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. 

While planar optical sensors exist in various forms, the focus of this chapter has been on planar waveguide-based platforms that employ evanescent wave effects as the basis for sensing. The advantages of evanescent wave interrogation of thin film optical sensors have been discussed for both optical absorption and fluorescence-based sensors. These include the ability to increase device sensitivity without adversely affecting response time in the case of absorption-based platforms and the surface-specific excitation of fluorescence for optical biosensors, the latter being made possible by the tuneable nature of the evanescent field penetration depth. 

Now for the photon flux. As the altitude increases, the atmosphere looks thinner so the light has to pass through a smaller amount of atmosphere dependent on the zenith angle, which is related to the latitude on the planet and the angle that its axis of rotation makes with the plane of the solar system, the season of the year and hence the position of the planet in its orbit. The depth of atmosphere through which the Sun s rays pass is given by dz sec0. Hence the optical absorption is ... 

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