Bulk standing wave intensity

The equation for the standing wave intensity inside the resist has both a periodic and a nonperiodic component. For a resist film that is much thicker than the period X/4 2 of the standing wave, it is customary to think of the nonperiodic component of the standing wave as a bulk intensity, which is averaged over a period of the standing wave (see Fig. 9.13). The bulk intensity is given by 

Normalizing the bulk intensity distribution to the value at z 0, we obtain 

Equation (9.51) is exactly the same as the case for when a single reflection from the resist-substrate interface is added incoherently to the incoming wave. Expanding the normalized bulk intensity in a McLaurin series in z, and truncating 

---

Figure 9.13 Computed normalized intensity and bulk intensity of standing waves in a resist fiim. Simulation parameters X 365 nm, 02 1.71 0.02/, fis...

Because of the addition of the returning wave to the bulk intensity, the intensity drop-off is less steep for more reflective substrates (see Fig. 9.14). This implies that resists will have straighter sidewalls on reflective substrates, provided the standing waves can be diffused out. Also, resists to be used on nonreflective substrates need to be more transparent than those used for highly reflective materials such as aluminum (see Fig. 9.14). 

Sonication allows changing the normal course of the reaction and gives preferentially the latter compound, in amounts depending on the irradiation conditions and the acoustic intensity. s The SrnI pathway is even more important under standing-wave conditions. A direct link is thus established between a particular mechanism and the presence of an acoustic field. A complete interpretation is missing, however, and the presence of by-products derived from the 4-nitrobenzyl radical was not evidenced. Since the nitronate anion is not expected to vaporize, and a reaction in the bulk liquid should exhibit no sonochemical effect, it can be deduced that the sonochemical process takes place at the bubble interface. 

---