all values of T between the lowest binding energy, E0 and the incident energy, one obtains the result that the total cross section for collision is inversely proportional to the incident energy , and proportional to 1/E0 – 1/E. Generally, E >> E0, so the result is essentially inversely proportional to the binding energy. By using the same integration approach, but over the range 2E0 to E, one obtains by comparing cross-sections that half of the inelastic collisions of the incident electrons produce electrons with kinetic energy greater than E0. These secondary electrons are capable of breaking bonds (with binding energy E0) at some distance away from the original collision. Additionally, they can generate additional, lower energy electrons, resulting in an electron cascade. Hence, it is important to recognize the significant contribution of secondary electrons to the spread of the energy deposition. In general, for a molecule AB: e− + AB → AB− → A + B− This reaction, also known as "electron attachment" or "dissociative electron attachment" is most likely to occur after the electron has essentially slowed to a halt, since it is easiest to capture at that point. The cross-section for electron attachment is inversely proportional to electron energy at high energies, but approaches a maximum limiting value at zero energy. On the other hand, it is already known that the mean free path at the lowest energies (few to several eV or less, where dissociative attachment is significant) is well over 10 nm, thus limiting the ability to consistently achieve resolution at this scale. Resolution capability With today's electron optics, electron beam widths can routinely go down to a few nanometers. This is limited mainly by aberrations and space charge. However, the feature resolution limit is determined not by the beam size but by forward scattering (or effective beam broadening) in the resist, while the pitch resolution limit is determined by secondary electron travel in the resist. This point was driven home by a 2007 demonstration of double patterning using electron beam lithography in the fabrication of 15 nm half-pitch zone plates. Although a 15 nm feature was resolved, a 30 nm pitch was still difficult to do due to secondary electrons scattering from the adjacent feature. The use of double patterning allowed the spacing between features to be wide enough for the secondary electron scattering to be significantly reduced. The forward scattering can be decreased