Electron-beam lithography (often abbreviated as e-beam lithography or EBL) is the practice of scanning a focused beam of electrons to draw custom shapes on a surface covered with an electron-sensitive film called a resist (exposing). The electron beam changes the solubility of the resist, enabling selective removal of either the exposed or non-exposed regions of the resist by immersing it in a solvent (developing). The purpose, as with photolithography, is to create very small structures in the resist that can subsequently be transferred to the substrate material, often by etching.
The primary advantage of electron-beam lithography is that it can draw custom patterns (direct-write) with sub-10 nm resolution. This form of maskless lithography has high resolution but low throughput, limiting its usage to photomask fabrication, low-volume production of semiconductor devices, and research and development.
There are primarily three methods of EBL techniques used in semiconductor manufacturing, primarily for photomask manufacturing, or more broadly in nanotechnology manufacturing. The three techniques are Gaussian beam (or grey-beam), variable shaped beam (including character projection), and multibeam.
Systems Electron-beam lithography systems used in commercial applications are dedicated e-beam writing systems that are very expensive (> US$1M). For research applications, it is very common to convert an electron microscope into an electron-beam lithography system using relatively low cost accessories (< US$100K). Such converted systems have produced linewidths of ~20 nm since at least 1990, while current dedicated systems have produced linewidths on the order of 10 nm or smaller.
Electron-beam lithography systems can be classified according to both beam shape and beam deflection strategy. Older systems used Gaussian-shaped beams that scanned these beams in a raster fashion. Newer systems use shaped beams that can be deflected to various positions in the writing field (also known as "vector scan").
Electron sources Lower-resolution systems can use thermionic sources (cathode), which are usually formed from lanthanum hexaboride. However, systems with higher-resolution requirements need to use field electron emission sources, such as heated W/ZrO2 for lower energy spread and enhanced brightness. Thermal field emission sources are preferred over cold emission sources, in spite of the former's slightly larger beam size, because they offer better stability over typical writing times of several hours.
Lenses Both electrostatic and magnetic lenses may be used. However, electrostatic lenses have more aberrations and so are not used for fine focusing. There is no known mechanism to make achromatic electron-beam lenses, so extremely narrow dispersions of the electron-beam energy are needed for finest focusing.
Stage, stitching and alignment Typically, for very small beam deflections, electrostatic deflection "lenses" are used; larger beam deflections require electromagnetic scanning. Because of the inaccuracy and because of the finite number of steps in the exposure grid, the writing field is of the order of 100 micrometre – 1 mm. Larger patterns require stage moves. An accurate stage is critical for stitching (tiling writing fields exactly against each other) and pattern overlay (aligning a pattern to a previously made one).
Electron-beam write time The minimum time to expose a given area for a given dose (measured in coulombs/cm2) is given by the following formula:
where is the time to expose the object (can be divided into exposure time/step size), is the beam current (measured in amperes), is the dose, and is the area exposed (in cm2).
E-beam lithography is not suitable for high-volume manufacturing because of its limited throughput. The smaller field of electron-beam writing makes for very slow pattern generation compared with photolithography (the current standard) because more exposure fields must be scanned to form the final pattern area (≤mm2 for electron beam vs. ≥40 mm2 for an optical mask projection scanner). The stage moves in between field scans. The electron-beam field is small enough that a rastering or serpentine stage motion is needed to pattern a 26 mm by 33 mm area for example, whereas in a photolithography scanner only a one-dimensional motion of a 26 mm by 2 mm slit field would be required.
Currently an optical maskless lithography toolFaster and lower cost for 65 nm and 45 nm photomask patterning is much faster than an electron-beam tool used at the same resolution for photomask patterning.
Shot noise As features sizes shrink, the number of incident electrons at fixed dose also shrinks. As soon as the number reaches ~10000, shot noise effects become predominant, leading to substantial natural dose variation within a large feature population. With each successive process node, as the feature area is halved, the minimum dose must double to maintain the same noise level. Consequently, the tool throughput would be halved with each successive process node.
feature diameter (nm) minimum dose for one-in-a-million 5% dose error (μC/cm2) 40 127 28 260 20 509 14 1039 10 2037 7 4158 Note: 1 ppm of population is about 5 standard deviations away from the mean dose.
Ref.: SPIE Proc. 8683-36 (2013)
Shot noise is a significant consideration even for mask fabrication. For example, a commercial mask e-beam resist like FEP-171 would use doses less than 10 μC/cm2, whereas this leads to noticeable shot noise for a target critical dimension (CD) even on the order of ~200 nm on the mask. CD variation can be on the order of 15–20% for sub-20 nm features.The Significance of Point Spread Functions with Stochastic Behavior in Electron-Beam Lithography
Defects in electron-beam lithography 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 error" 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.
Electron energy deposition in matter
The primary electrons in the incident beam lose energy upon entering a material through inelastic scattering or collisions with other electrons. In such a collision the momentum transfer from the incident electron to an atomic electron can be expressed as , where b is the distance of closest approach between the electrons, and v is the incident electron velocity. The energy transferred by the collision is given by , where m is the electron mass and E is the incident electron energy, given by . By integrating over 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.SPIE Newsroom: Double exposure makes dense high-resolution diffractive optics. Spie.org (2009-11-03). Retrieved on 2011-08-27. 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 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 is 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 Nanotechnology, Science, and Engineering 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.Complexities of the Resolution Limits of Advanced LithographyResolution Limits