Despite the high resolution of electron-beam lithography, the generation of defects during electron-beam lithography is often not considered by users. Defects may be classified into two categories: data-related defects, and physical defects. Data-related defects may be classified further into two sub-categories. Blanking or deflection errors occur when the electron beam is not deflected properly when it is supposed to, while shaping errors occur in variable-shaped beam systems when the wrong shape is projected onto the sample. These errors can originate either from the electron optical control hardware or the input data that was taped out.
As might be expected, larger data files are more susceptible to data-related defects.
Physical defects are more varied, and can include sample charging either negative or positive , backscattering calculation errors, dose errors, fogging long-range reflection of backscattered electrons , outgassing, contamination, beam drift and particles. Since the write time for electron beam lithography can easily exceed a day, "randomly occurring" defects are more likely to occur. Here again, larger data files can present more opportunities for defects.
Photomask defects largely originate during the electron beam lithography used for pattern definition. The primary electrons in the incident beam lose energy upon entering a material through inelastic scattering or collisions with other electrons. By using the same integration approach, but over the range 2E 0 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 E 0. These secondary electrons are capable of breaking bonds with binding energy E 0 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: . 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. 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.
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 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. Furthermore dielectric breakdown discharge is possible.
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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. 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. The smallest features produced by electron-beam lithography have generally been isolated features, as nested features exacerbate the proximity effect , whereby electrons from exposure of an adjacent region spill over into the exposure of the currently written feature, effectively enlarging its image, and reducing its contrast, i.
Hence, nested feature resolution is harder to control. The proximity effect is also manifest by secondary electrons leaving the top surface of the resist and then returning some tens of nanometers distance away. Proximity effects due to electron scattering can be addressed by solving the inverse problem and calculating the exposure function E x,y that leads to a dose distribution as close as possible to the desired dose D x,y when convolved by the scattering distribution point spread function PSF x,y.
However, it must be remembered that an error in the applied dose e. Since electrons are charged particles, they tend to charge the substrate negatively unless they can quickly gain access to a path to ground. For a high-energy beam incident on a silicon wafer, virtually all the electrons stop in the wafer where they can follow a path to ground.
However, for a quartz substrate such as a photomask , the embedded electrons will take a much longer time to move to ground.
Optimizing electron beam lithography in the nanometer range
Often the negative charge acquired by a substrate can be compensated or even exceeded by a positive charge on the surface due to secondary electron emission into the vacuum. However, they are of limited use due to their high sheet resistance, which can lead to ineffective grounding. Hence, resist-substrate charging is not repeatable and is difficult to compensate consistently. Negative charging deflects the electron beam away from the charged area while positive charging deflects the electron beam toward the charged area. Due to the scission efficiency generally being an order of magnitude higher than the crosslinking efficiency, most polymers used for positive-tone electron-beam lithography will crosslink and therefore become negative tone at doses an order of magnitude than doses used for positive tone exposure.
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Metal nanowire grating patterns. Nanoscale , 2 10 , Parisse, D. Luciani, A. Santucci, P. Zuppella, P. Tucceri, A. Reale, L. Patterning at the nanoscale: Atomic force microscopy and extreme ultraviolet interference lithography. Materials Science and Engineering: B , 3 , Mohamed, M.