Field enhancement factor

Fig. 13. Electric-field dependence of the emission current obtained for a carefully aligned MWCNT film [38], Inset Fowler-Nordheim plot, where y is the field-enhancement factor.

Figure 1.2 Modulus of the field enhancement factor versus the aspect ratio a = b and wavelengths X for SPM tips of different materials (a) gold, (b) platinum, (c) silver, (d) p-doped silicon, (e) tungsten. Reprinted with permission from J. Jersch, Applied Physics A, 66, 29 (1998). Copyright 1998, Springer-Verlag.

Pettinger et al. observed a TERS spectrum of monolayer-thick brilliant cresyl blue (BCB) adsorbed on a smooth Au film surface by using a Ag tip, while no STM image of the adsorbed surface was shovm [23]. The Raman intensity increased when the tip was in the tunneling position, meaning that the tip-surface distance was around 1 nm. They calculated the field enhancement factor by the method described by... 

Interesting nanostructures, that may present an interaction among nanoclusters, with consequent increase of local field enhancement factor are obtained by irradiating AuCu alloy clusters with Ne ions at 190 keV [30]. 

Calculations for TE polarized light give similar results42, but the maximum induced 8/Vell in the PWEF waveguide is about three times smaller than for the TM mode. This difference is largely due to the absence of the surface field enhancement factor of (9.5), since the electric field of the TE mode is parallel to the waveguide surface and hence there is no electric field discontinuity. 

Here, cp (eV) is the barrier height, F is the local field, and a and b are constants. The typical field required for emission from solids is of order 1000 V/pm. The easiest way to create such a high field is by field enhancement at a sharp tip, so that the local field F is many times larger than the applied field F, F = ( /. (1 is a dimensionless geometrical field enhancement factor given by h/r for a tip, where h is the height and r is its radius. 

Nilsson et al. [26,27] showed how the total emission current from a less than perfect array of CNT emitters will depend on the distribution of the field enhancement factors, p. The p probability distribution follows a roughly bell-shaped distribution. Clearly, the high p values matter most, so that these follow an effectively exponential decreasing probability distribution (Fig. 13.4),... 

Fig. 13.4 Distribution of field enhancement factors in a CNT emitting, showing exponential decay at high enhancement factors.

The field emission properties of carbon nanotube forests and single nanotubes are described. Controlled emission is possible for aligned CNT arrays where the spacing is twice the CNT height, as grown by plasma enhanced chemical vapor deposition. This leads to the maximum field enhancement factor. For random forests, the field enhancement obeys an exponential distribution, leading to a lower emission site density and imperfect current sharing. Ballast resistors can help alleviate this problem. Random nanocarbons perform less well than CNTs. Some applications are covered. Elec-... 

Field enhancement factors observed in Raman scattering from molecules adsorbed on nanosurfaces are even larger. The intensity of Stokes component in Raman scattering is proportional to the square of dipole momentum on that frequency [61] ... 

The problem now reduces to finding how ra is related to the experimental parameters. The gas supply functions for different tip geometry have already been discussed in Section 2.1.2 and they are given by eqs (2.9), (2.11) and (2.12). zs is the total gas supply function Z multiplied by sa/A where sA is the cross-section of a surface atom in capturing an incoming gas atom, and A is the total area of the gas supply function. For a large field enhancement factor, = aF2/2kT, zs can be approximated by... 

Figure 10.1. Comparison of normal (top) and surface-enhanced (bottom) Raman scattering. The top panel shows the conversion of incident laser light of intensity /(vl) into Stokes scattered light /NRS, which is proportional to the Raman cross section and the number of target molecules N in the probed volume. In the bottom panel

Figure 19.19 Left side Variation of the photoluminescence intensity E (b) of the PEG-functionalized Au and CdTe nanoparticles depending on the temperature (a) (c) shows the calculated photon-field enhancement factor P of the CdTe nanoparticles as a function of time. Right side Schematic representation of a dynamic nanothermometer based on a nanoparticle superstructure. This superstructure consists of two types of nanoparticles (gold and CdTe) connected by polymeric spacers.118 (Reprinted with permission from J. Lee et al., Angew. Chem. Int. Ed., 2005, 44, 7439-7442. Copyright Wiley-VCH Verlag GmbH Co. KGaA.)...

The local field enhancement factor, characterizing the modification of absorption. This results, in most cases of interest, in an enhancement, and possibly a very large enhancement up to = 10. ... 

Moreover, it is possible to show that the local field enhancement factor and the radiative enhancement factor Mnjj(ty) are in many cases... 

A larger modification is predicted when the resonance occurs beyond the free-space fluorescence peak (case D of Fig. 2.2(b)). The MEF signal is however much smaller because of the small local field enhancement factor at. ... 

The incident polarization only affects the coupling to the LSP resonances at the laser frequency, i.e. the local field enhancement factor at... 

Here M are the field enhancement factors and is the modified quantum yield given by... 

To examine the role of the LDOS modification near a metal nanobody and to look for a rationale for single molecule detection by means of SERS, Raman scattering cross-sections have been calculated for a hypothetical molecule with polarizability 10 placed in a close vicinity near a silver prolate spheroid with the length of 80 nm and diameter of 50 nm and near a silver spherical particle with the same volume. Polarization of incident light has been chosen so as the electric field vector is parallel to the axis connecting a molecule and the center of the silver particle. Maximal enhancement has been found to occur for molecule dipole moment oriented along electric field vector of Incident light. The position of maximal values of Raman cross-section is approximately by the position of maximal absolute value of nanoparticle s polarizability. For selected silver nanoparticles it corresponds to 83.5 nm and 347.8 nm for spheroid, and 354.9 nm for sphere. To account for local incident field enhancement factor the approach described by M. Stockman in [4] has been applied. To account for the local density of states enhancement factor, the approach used for calculation of a radiative decay rate of an excited atom near a metal body [9] was used. We... 

Okada and coworkers investigated the nonlinear optical response of silver triangular nanoprisms by pump-probe femtosecond spectroscopy [197]. They reported a different x/ value at the In-plane dipole and quadrupole plasmon resonances, which they showed to correspond to the difference in local field enhancement factors. In both cases, the spectral dispersion of the nonlinear susceptibility exhibits similar behaviour, that is negative and positive values at the low-energy and high-energy sides of the plasmon band, respectively. 

One-dimensional conducting polymer nanomaterials have been utilized as the field emission electron sources for flat panel displays [365-367]. Conducting polymer nanotubes or nanowires were mostly prepared by the electrochemical polymerization within the cylindrical pores of alumina membranes, and the field emission characteristics were evaluated. As a typical example, a field emission cell was composed of PEDOT nanowire (conductivity, 3.4 x 10 S cm ) tips (cathode) and ITO (anode). The turn-on field of PEDOT nanowire was 3.5-4.0 jiAcm at 10V jim , and the current density increased up to 100 xAcm at 4.5 V jim . The field enhancement factor of the PEDOT nanowire tips was 1200 and this value was comparable to that of CNT. PPy nanowire and PANI nanotube was also prepared using nanoporous template, and their field emission characteristics were investigated [365]. PPy nanowire and PANI nanotubes showed the turn-on fields of 3.5-4.0 and 5.0 jjlA cm at 6 and 8 V im . These studies offered a great feasibility of conducting polymers as the building blocks for all-polymer field emission displays. 

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