Thick resists electron scattering

Figure 26. Three-dimensional electron scattering model for a resist on a thick substrate with a scanning electron beam of zero diameter.

For thick substrates, backscattered electrons from the substrate decrease contrast and the minimum dimension increases to about 20 nm. For thick resists, and samples thick compared to the primary electron penetration range, electron scattering in the resist (forward scattering) and backscattering of electrons from the substrate, become more important than the electron interaction range. In these cases, exposure dose is sometimes altered according to the local pattern density to compensate for variations in the backscattered... 

It is clear from Equation 11.3 that resistivity should approach within 10% of the bulk value when the film thickness exceeds about four times the mean free path. The better the conductor, the smaller the mean free path. Thus, the resistivity approaches the bulk value as the film thickness reaches typical values of 100-200 nm for metallic conductors, or perhaps as much as several micrometers for semiconductors, depending on the intrinsic or doped carrier density. For sufficiently thick metallic films with K 1, the temperature coefficient of resistivity becomes positive, as bulk electron-phonon scattering becomes the primary contribution to resistivity [5]. Conduction in semiconductor films remains activation-limited, and retains a negative temperature coefficient. Figure 11.1 illustrates the dependence of resistivity on film thickness for sputtered... 

Thick organic polymer resist films are used for the conventional lithography. Their thicknesses are dozens to hundreds of nanometers. When a processing size becomes small and enters nanometer order in electron beam lithography, scattering of electrons in a resist causes various problems, such as the proximity effect. The variation in molecular mass of each molecule which forms the resist also reduces the resolution. If the ultrathin resist film of several nanometers thickness will be realized, the lithography of higher resolution will become possible. 

In order to check the resist thickness dependence on formation of very fine pitch dot arrays using 30 keV electrons, we calculated electron energy deposition distribution (EDD) using Monte Carlo simulation. As considering the EDD due to electron forward scattering (FS), at least, the miniaturization of the bit size, the deviation value is very crucial. The deviations calculated for PMMA are about 2 nm, about 3 nm and about 8 nm ata resist thickness of 15 mm, 70 nm and 200 nm, respectively. As the resist thickness decreases, the value becomes small. Therefore, we have to use resist films as thin as possible for very fine pitch arrays formation. 

The increase in resistivity at narrow fine widths has been attributed to surface scattering and grain-boundary scattering. The Fuchs and Sondheimer (FS) model attributes the resistivity increase in thin and narrow fines to diffuse scattering of electrons at the exterior surfaces with a probability of 1 — p, where p is the specular scattering coefficient. The length scales in the FS model are the thickness and line width of the conductor and the mean free path A. The simplified expression for resistivity as a function of thickness (T) and linewidth (W) of the conductor is given by ... 

A fairly large number of studies have demonstrated high power outputs up to 1100 and 1329 mW cm" at 600The OCV varies unsystematically in the range 0.72-0.92 V. No correlation can be found between the OCV of the SOFC and the power output. The theoretical voltage at 600 °C for Hg humidified with 3% water is 1.11 V. None of the cells reached the theoretical OCV value due to the internal electronic short circuit. The huge scatter in OCV is consistent with the fact that it is a complex function of the thickness of the electrolyte, electrode polarization resistances, and electrical contact to the cell as illustrated in Fig. 12.19. Some of the studies listed in Tables 12.3 and 12.4 are discussed in more detail below. 

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