Editing Electron-beam lithography (section)

==Systems==
Electron-beam lithography systems used in commercial applications are dedicated e-beam writing systems that are very expensive (>&nbsp;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 (<&nbsp;US$100K). Such converted systems have produced linewidths of ~20&nbsp;nm since at least 1990, while current dedicated systems have produced linewidths on the order of 10&nbsp;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 scan|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 emission|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/ZrO<sub>2</sub> 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 currently{{When|date=June 2019}} no mechanism to make achromatic electron beam lenses, so extremely narrow dispersions of the electron beam energy are needed for finest focusing.{{Citation needed|date=June 2019}}{{Update inline|date=June 2019|reason=}}

===Stage, stitching and alignment===
[[File:Feature_stitching_across_fields.png|thumb|right|200px|'''Field stitching.''' Stitching is a concern for critical features crossing a field boundary (red dotted line).]]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&nbsp;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 is given by the following formula:<ref>{{cite journal|author=Parker, N. W.|editor-first1=Elizabeth A. |editor-last1=Dobisz |doi=10.1117/12.390042|title=High-throughput NGL electron-beam direct-write lithography system|journal= Proc. SPIE |volume= 3997|page= 713 |year=2000|display-authors=etal|series=Emerging Lithographic Technologies IV|bibcode=2000SPIE.3997..713P|s2cid=109415718}}</ref>
:<math> D \cdot A = T\cdot I \,</math>

where <math>T</math> is the time to expose the object (can be divided into exposure time/step size), <math>I</math> is the beam current, <math>D</math> is the dose and <math>A</math> is the area exposed.

For example, assuming an exposure area of 1&nbsp;cm<sup>2</sup>, a dose of 10<sup>−3</sup> [[Coulomb|coulombs]]/cm<sup>2</sup>, and a beam current of 10<sup>−9</sup> [[Ampere|amperes]], the resulting minimum write time would be 10<sup>6</sup> seconds (about 12 days). This minimum write time does not include time for the stage to move back and forth, as well as time for the beam to be blanked (blocked from the [[Wafer (electronics)|wafer]] during deflection), as well as time for other possible beam corrections and adjustments in the middle of writing. To cover the 700&nbsp;cm<sup>2</sup> surface area of a 300&nbsp;mm silicon wafer, the minimum write time would extend to 7*10<sup>8</sup> seconds, about 22 years. This is a factor of about 10 million times slower than current optical lithography tools. It is clear that throughput is a serious limitation for electron beam lithography, especially when writing dense patterns over a large area.

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 (≤mm<sup>2</sup> for electron beam vs. ≥40&nbsp;mm<sup>2</sup> 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&nbsp;mm X 33&nbsp;mm area for example, whereas in a photolithography scanner only a one-dimensional motion of a 26&nbsp;mm X 2&nbsp;mm slit field would be required.

Currently an optical [[maskless lithography]] tool<ref>[http://www.micronic.se/site_eng/product/AA65112_Sigma7500-II_product_sheet_A_001.pdf Faster and lower cost for 65&nbsp;nm and 45&nbsp;nm photomask patterning] {{dead link|date=June 2016|bot=medic}}{{cbignore|bot=medic}}</ref> 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.

{| class="wikitable"
|-
! feature diameter (nm)
! minimum dose for one-in-a-million 5% dose error (μC/cm<sup>2</sup>)
|-
| 40
| 127
|-
| 28
| 260
|-
| 20
| 509
|-
| 14
| 1039
|-
| 10
| 2037
|-
| 7
| 4158
|-
|}
'''Note:''' 1 [[Parts-per notation|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/cm<sup>2</sup>,<ref>{{cite journal |last1=Kempsell |first1=M.L. |last2=Hendrickx |first2=E. |last3=Tritchkov |first3=A. |last4=Sakajiri |first4=K. |last5=Yasui |first5=K. |last6=Yoshitake |first6=S. |last7=Granik |first7=Y. |last8=Vandenberghe |first8=G. |last9=Smith |first9=B.W. |title=Inverse lithography for 45-nm-node contact holes at 1.35 numerical aperture |journal=Journal of Micro/Nanolithography, MEMS, and MOEMS |volume=8 |issue=4 |page=043001 |date=2009 |doi=10.1117/1.3263702 }}</ref><ref>{{cite conference |first1=H. |last1=Sunaoshi |first2=Y. |last2=Tachikawa |first3=H. |last3=Higurashi |first4=T. |last4=Iijima |first5=J. |last5=Suzuki |first6=T. |last6=Kamikubo |first7=K. |last7=Ohtoshi |first8=H. |last8=Anze |first9=T. |last9=Katsumata |first10=N. |last10=Nakayamada |first11=S. |last11=Hara |first12=S. |last12=Tamamushi |first13=Y. |last13=Ogawa |title=EBM-5000: electron-beam mask writer for 45-nm node |book-title=Photomask and Next-Generation Lithography Mask Technology XIII |volume=6283 |series=SPIE Proceedings |date=2006 |doi=10.1117/12.681732 |pages=628306 }}</ref> whereas this leads to noticeable shot noise for a target [[Photolithography#Photomasks|critical dimension]] (CD) even on the order of ~200&nbsp;nm on the mask.<ref>{{cite conference |last1=Ugajin |first1=K. |last2=Saito |first2=M. |last3=Suenaga |first3=M. |last4=Higaki |first4=T. |last5=Nishino |first5=H. |last6=Watanabe |first6=H. |last7=Ikenaga |first7=O. |title=1-nm of local CD accuracy for 45-nm-node photomask with low sensitivity CAR for e-beam writer |book-title=Photomask and Next-Generation Lithography Mask Technology XIV |volume=6607 |series=SPIE Proceedings |date=2007 |doi= |pages=90–97 }}</ref><ref>{{cite conference |first1=Frederick |last1=Chen |first2=Wei-Su |last2=Chen |first3=Ming-Jinn |last3=Tsai |first4=Tzu-Kun |last4=Ku |title=Sidewall profile inclination modulation mask (SPIMM): modification of an attenuated phase-shift mask for single-exposure double and multiple patterning |book-title=Optical Microlithography XXVI |volume=8683 |series=SPIE Proceedings |date=2013 |doi=10.1117/12.2008886 |pages=868311 }}</ref> CD variation can be on the order of 15–20% for sub-20&nbsp;nm features.<ref>[https://www.linkedin.com/pulse/significance-point-spread-functions-stochastic-behavior-chen-poduc/ The Significance of Point Spread Functions with Stochastic Behavior in Electron-Beam Lithography]</ref><ref>{{cite conference |first1=Koji |last1=Ichimura |first2=Koji |last2=Yoshida |first3=Hideki |last3=Cho |first4=Ryugo |last4=Hikichi |first5=Masaaki |last5=Kurihara |title=Characteristics of fine feature hole templates for nanoimprint lithography toward 2nm and beyond |book-title=Photomask Technology |volume=12293 |series=SPIE Proceedings |date=2022 |doi=10.1117/12.2643250  |pages=122930F }}</ref>

===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 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.