by using higher energy electrons or thinner resist, but the generation of secondary electrons is inevitable. It is now recognized that for insulating materials like PMMA, low energy electrons can travel quite a far distance (several nm is possible). This is due to the fact that below the ionization potential the only energy loss mechanism is mainly through phonons and polarons. Although the latter is basically an ionic lattice effect, polaron hopping can extend as far as 20 nm. The travel distance of secondary electrons is not a fundamentally derived physical value, but a statistical parameter often determined from many experiments or Monte Carlo simulations down to < 1 eV. This is necessary since the energy distribution of secondary electrons peaks well below 10 eV. Hence, the resolution limit is not usually cited as a well-fixed number as with an optical diffraction-limited system. Repeatability and control at the practical resolution limit often require considerations not related to image formation, e.g., resist development and intermolecular forces. A study by the College of Nanoscale Science and Engineering (CNSE) presented at the 2013 EUVL Workshop indicated that, as a measure of electron blur, 50-100 eV electrons easily penetrated beyond 10 nm of resist thickness in PMMA or a commercial resist. Furthermore dielectric breakdown discharge is possible. More recent studies have indicated that 20 nm resist thickness could be penetrated by low energy electrons (of sufficient dose) and sub-20 nm half-pitch electron-beam lithography already required double patterning. Scattering In addition to producing secondary electrons, primary electrons from the incident beam with sufficient energy to penetrate the resist can be multiply scattered over large distances from underlying films and/or the substrate. This leads to exposure of areas at a significant distance from the desired exposure location. For thicker resists, as the primary electrons move forward, they have an increasing opportunity to scatter laterally from the beam-defined location. This scattering is called forward scattering. Sometimes the primary electrons are scattered at angles exceeding 90 degrees, i.e., they no longer advance further into the resist. These electrons are called backscattered electrons and have the same effect as long-range flare in optical projection systems. A large enough dose of backscattered electrons can lead to complete exposure of resist over an area much larger than defined by the beam spot. Proximity effect The smallest features produced by electron-beam lithography have generally been isolated features, as nested features exacerbate the