Excitation volume

The spatial resolution of the CI SEM mode depends mainly on the electron-probe size, the size of the excitation volume, which is related to the electron-beam penetration range in the material (see the articles on SEM and EPMA), and the minority carrier diffusion. The spatial resolution also may be afiFected by the signal-to-noise ratio, mechanical vibrations, and electromagnetic interference. In practice, the spatial resolution is determined basically by the size of the excitation volume, and will be between about 0.1 and 1 pm ... 

Fig. 18.9 Single molecule fluorescence detection in LC ARROW chip, (a) Top view of experi mental beam geometry of dye molecule in sub picoliter excitation volume (dotted ellipse) (2exc excitation beam, dF fluorescence signal) (b) fluorescence signal as function of molecules in excitation volume symbols, different experimental runs, dashed line linear fit...

The irradiation of a polymer surface with the high intensity, pulsed, fer-UV radiation of the excimer laser causes spontaneous vaporization of the excited volume. This phenomenon was first described by Srinivasan (1) and called ablative photodecomposition. The attention of many researchers was drawn to the exceptional capabilities of photoablation (2). Etching is confined to the irradiated volume, which can be microscopic or even of submicron dimensions, on heat-sensitive substrates like polymers. In most experimental conditions, there is no macroscopic evidence of thermal damage, even when small volumes are excited with pulses of... 

Because the excitation intensity varies as the square of the distance from the focal plane, the probability of two-photon absorption outside the focal region falls off with the fourth power of the distance along the z optical axis. Excitation of fluorophores can occur only at the point of focus. Using an objective with a numerical aperture of 1.25 and an excitation beam at 780 nm, over 80% of total fluorescence intensity is confined to within 1 pm of the focal plane. The excitation volume is of the order of 0.1-1 femtoliter. Compared to conventional fluorometers, this represents a reduction by a factor of 1010 of the excitation volume. 

G(t) decays with correlation time because the fluctuation is more and more uncorrelated as the temporal separation increases. The rate and shape of the temporal decay of G(t) depend on the transport and/or kinetic processes that are responsible for fluctuations in fluorescence intensity. Analysis of G(z) thus yields information on translational diffusion, flow, rotational mobility and chemical kinetics. When translational diffusion is the cause of the fluctuations, the phenomenon depends on the excitation volume, which in turn depends on the objective magnification. The larger the volume, the longer the diffusion time, i.e. the residence time of the fluorophore in the excitation volume. On the contrary, the fluctuations are not volume-dependent in the case of chemical processes or rotational diffusion (Figure 11.10). Chemical reactions can be studied only when the involved fluorescent species have different fluorescence quantum yields. 

Tj-hem TD = to2/4Dt the chemical relaxation time is much larger than the characteristic diffusion time so that there is no chemical exchange during diffusion through the excitation volume. The autocorrelation function is then given by... 

The point is now to estimate the maximum number of photons that can be detected from a burst. The maximum rate at which a molecule can emit is roughly the reciprocal of the excited-state lifetime. Therefore, the maximum number of photons emitted in a burst is approximately equal to the transit time divided by the excited-state lifetime. For a transit time of 1 ms and a lifetime of 1 ns, the maximum number is 106. However, photobleaching limits this number to about 105 photons for the most stable fluorescent molecules. The detection efficiency of specially designed optical systems with high numerical aperture being about 1%, we cannot expect to detect more than 1000 photons per burst. The background can be minimized by careful dean-up of the solvent and by using small excitation volumes ( 1 pL in hydrodynamically focused sample streams, 1 fL in confocal exdtation and detection with one- and two-photon excitation, and even smaller volumes with near-field excitation). 

Confocal microscopes (see Section 11.2.1.1) are well suited to the detection of single molecules. A photon burst is emitted when the molecule diffuses through the excitation volume (0.1-1 fL). An example is given in Figure 11.16. 

Single-molecule detection in confocal spectroscopy is characterized by an excellent signal-to-noise ratio, but the detection efficiency is in general very low because the excitation volume is very small with respect to the whole sample volume, and most molecules do not pass through the excitation volume. Moreover, the same molecule may re-enter this volume several times, which complicates data interpretation. Better detection efficiencies can be obtained by using microcapillaries and micro structures to force the molecules to enter the excitation volume. A nice example of the application of single-molecule detection with confocal microscopy is... 

Under the same optical configuration, FCS (Fluorescence Correlation Spectroscopy) measurements (see Section 11.3) can be carried out on samples at the singlemolecule level under conditions where the average number of fluorescent molecules in the excitation volume is less than 1. It should be noted that at low fluorophore concentrations, the time required to obtain satisfactory statistics for the fluctuations may become problematic in practical applications (e.g. for a concentration of 1 fM, a fluorophore crosses a confocal excitation volume every 15 min). 

Qualitative analysis is manifested in the identification of the elements present. It is based on Moseley s law, which points out that the energies of a pre-selected line-type (e.g. Kai) lie on a monotonic, smooth curve as a function of the atomic number. Simultaneous read-out of the positions of the many lines present in the EDS spectrum acts as identifying fingerprints and results in a list of the element present in the excited volume. 

In summary, the intensity of the analytical line of any of the elements present in the excited volume to the sample is determined by four groups of data. The first ( Sample ) is only dependent on the sample as a whole (density, local thickness), so being common for all elements in the excited volume. The second ( FactovAf) only depends on atomic data, the third is the fraction of the given element (ca) and the fourth is the detection efficiency at the energy of the detected line. (Mass fractions appear in these formulas, as explained in the Appendix.)... 

The probability of ionization is given by the geometrical probability, i.e. by the ratio of that effective area to the total area considered, which is unit. That is why (3b) gives the ionization probability of the i element per incident electron for the excited volume of our thin layer. Although the concentration dependence described in (3a) is identical to that given in (3b), it is expressed simpler in (3b), which describes a linear dependence on its variable (c ) than how it is expressed in (3a) where both the numerator and the denominator depends on the variable (c ). 

We will assume that all the incident fields are polarized in the x-direction. The pump and Stokes focal fields, which each look like the complex fields depicted in Figure 9.1, set up an effective CARS excitation field E = (r) (r). The anti-Stokes polarization in the excitation volume induced by the effective excitation field can be considered as a collection of radiating dipoles. The resulting CARS amplitude at any far-field point Q with coordinates R = (R, 6, (j)) is a sum of the amplitude contributions form all these dipoles and is given by... 

FIGURE 9.2 Sketch of far-field detection of CARS waves generated in the focal volume. The figure shows the yz cross-section of the excitation volume. O is the origin of the coordinate system and also the center of the focal volume and O is a far-field point on the optical axis. The coordinates of the points in the near-field are represented by (x,y,z) and those of the points in the far-field by (X,Y,Z) in cartesian coordinate system. The outgoing arrows around the near-field points represent the CARS waves generated in the focal volume. The incoming arrows at the far-field points represent the contributions from the individual points in the focal volume. 

In Figure 10.12, the TE-CARS signal intensity largely surpasses the background because the number of molecules in the excited volume is enough to induce the large signal. It, however, depends on experimental conditions such as the number of molecules, excitation laser power, and optical density of samples. In other cases, the... 

Figure 2.12. Primary excitation volume within the sample due to electron beam-sample interactions.

---