Absorbed energy density

The fundamental parameters necessary to determine profile shape are the absorbed energy density and its dependence on spatial position within the resist film. The situation is depicted in Figure 28 where the absorbed energy density E(r,z) within a given volume element at point r,z resulting... 

Figure 6. Calculated absorbed energy density due to forward and backward scattered electrons. Zq is the penetration depth in a 0.4-nm PMMA film which is coated on an Al substrate. The electron energy used is 20 keV. (Reproduced with permission from Ref. 4j...

Figure 7. Calculated absorbed energy density as a function of radial distance for an infinitessimal beam. The energy density at the midpoint in a 0.5imaging resist layer in SLR and various MLR configurations is plotted. (Reproduced with permission from Ref. 6J...

The absorbed energy density. Eg, required to destroy the gel completely in pre-crosslinked resists can be predicted as follows. Assume that the density of the material is pkg/m, the monomer molecular weight is Mo and that Avogadro s number is Na/(kg.mole). The number of monomer units per m i Na-p/Mo- If the crosslink density (i.e. the fraction of monomer units which are crosslinked) is do, then the number of crosslinks per unit volume is... 

Second, the rapid laser-induced thermal expansion causes [103] a pressure rise, given by the product of the Griineisen coefficient, T, and the absorbed energy density... 

Figure A3.13.il. Illustration of the time evolution of redueed two-dimensional probability densities I I and I I for the exeitation of CHD between 50 and 70 fs (see [154] for further details). The full eurve is a eut of tire potential energy surfaee at the momentary absorbed energy eorresponding to 3000 em during the entire time interval shown here (as6000 em, if zero point energy is ineluded). The dashed eurves show the energy uneertainty of the time-dependent wave paeket, approximately 500 em Left-hand side exeitation along the v-axis (see figure A3.13.5). The vertieal axis in the two-dimensional eontour line representations is...

We can sample the energy density of radiation p(v, T) within a chamber at a fixed temperature T (essentially an oven or furnace) by opening a tiny transparent window in the chamber wall so as to let a little radiation out. The amount of radiation sampled must be very small so as not to disturb the equilibrium condition inside the chamber. When this is done at many different frequencies v, the blackbody spectrum is obtained. When the temperature is changed, the area under the spechal curve is greater or smaller and the curve is displaced on the frequency axis but its shape remains essentially the same. The chamber is called a blackbody because, from the point of view of an observer within the chamber, radiation lost through the aperture to the universe is perfectly absorbed the probability of a photon finding its way from the universe back through the aperture into the chamber is zero. 

The energy densities of laser beams which are conventionally used in the production of thin films is about 10 — 10 Jcm s and a typical subsU ate in the semiconductor industry is a material having a low drermal conductivity, and drerefore dre radiation which is absorbed by dre substrate is retained near to dre surface. Table 2.8 shows dre relevant physical properties of some typical substrate materials, which can be used in dre solution of Fourier s equation given above as a first approximation to dre real situation. 

It is clear from Equation (1.15) that the emitted intensity is linearly dependent on the incident intensity and is proportional to both the quantum efficiency and the optical density (this only for low optical densities). A quantum efficiency of < 1 indicates that a fraction of the absorbed energy is lost by nonradiative processes. Normally, these processes (which are discussed in Chapters 5 and 6) lead to sample heating. The proportionality to OD, which only holds for low optical densities, indicates that the excitation spectra only reproduce the shape of absorption spectra for samples with low concentrations. 

The sealed nickel—metal hydride battery has characteristics very similar to those of the sealed NiCd battery. The main difference is that the NiMH battery uses hydrogen, absorbed in a metal alloy, for the active negative material in place of the cadmium used in the NiCd battery. The NiMH batteries have a higher energy density and are considered more environmentally friendly than the NiCd battery. The sealed NiMH battery, however, does not have the very high rate capability of NiCd battery, and is less tolerant of overcharge. 

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