Editing Electron-beam lithography (section)

===Resolution capability===
[[File:Electron_travel_(Monte_Carlo).png|thumb|300px|left|'''Low energy electron migration.''' The distance (r) traveled by a low energy electron affects the resolution and can be at least several nanometers.]]
With today's electron optics, electron beam widths can routinely go down to a few nanometers. This is limited mainly by [[Optical aberration|aberration]]s 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 electrons|secondary electron]] travel in the [[resist]].<ref name="broers">{{cite journal|title=Electron beam lithography—Resolution limits|author=Broers, A. N.|journal=Microelectronic Engineering|volume=32|issue=1–4|year=1996|pages=131–142|doi=10.1016/0167-9317(95)00368-1|display-authors=etal}}</ref><ref>{{cite journal|bibcode=2009JKPS...55.1720L |title=Secondary electron generation in electron-beam-irradiated solids:resolution limits to nanolithography |url=http://www.kps.or.kr/home/kor/journal/library/downloadPdf.asp?articleuid=%7BDBBE4A45-2FC0-4127-BF2D-3081FAE2CE37%7D |author=K. W. Lee |journal=	J. Korean Phys. Soc. |volume=55 |page=1720 |year=2009 |doi=10.3938/jkps.55.1720 |issue=4 |url-status=dead |archiveurl=https://web.archive.org/web/20110722141849/http://www.kps.or.kr/home/kor/journal/library/downloadPdf.asp?articleuid=%7BDBBE4A45-2FC0-4127-BF2D-3081FAE2CE37%7D |archivedate=2011-07-22 |url-access=subscription }}</ref> This point was driven home by a 2007 demonstration of double patterning using electron beam lithography in the fabrication of 15&nbsp;nm half-pitch zone plates.<ref>[http://spie.org/x8367.xml SPIE Newsroom: Double exposure makes dense high-resolution diffractive optics]. Spie.org (2009-11-03). Retrieved on 2011-08-27.</ref> Although a 15&nbsp;nm feature was resolved, a 30&nbsp;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 [[Poly(methyl methacrylate)|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 [[phonon]]s and [[polaron]]s. Although the latter is basically an ionic lattice effect,<ref>{{cite journal|author=Dapor, M.|journal= J. Micro/Nanolith. MEMS MOEMS|volume=9|issue= 2|page= 023001|year=2010|doi=10.1117/1.3373517|title=Monte Carlo modeling in the low-energy domain of the secondary electron emission of polymethylmethacrylate for critical-dimension scanning electron microscopy |display-authors=etal}}</ref> polaron hopping can extend as far as 20&nbsp;nm.<ref>{{cite journal|author=P. T. Henderson|journal= Proc. Natl. Acad. Sci. U.S.A. |volume=96|pages= 8353–8358|doi=10.1073/pnas.96.15.8353 |year=1999|display-authors=1|title=Long-distance charge transport in duplex DNA: The phonon-assisted polaron-like hopping mechanism|issue=15|pmid=10411879|last2=Jones|first2=D|last3=Hampikian|first3=G|last4=Kan|first4=Y|last5=Schuster|first5=GB|pmc=17521|bibcode = 1999PNAS...96.8353H |doi-access= free }}</ref> 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&nbsp;eV. This is necessary since the energy distribution of secondary electrons peaks well below 10&nbsp;eV.<ref name="seiler">{{cite journal|title=Secondary electron emission in the scanning electron microscope|author=H. Seiler|journal=J. Appl. Phys.|volume=54|year=1983|pages=R1–R18|doi=10.1063/1.332840|bibcode = 1983JAP....54R...1S|issue=11 }}</ref> Hence, the resolution limit is not usually cited as a well-fixed number as with an optical diffraction-limited system.<ref name="broers" /> 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&nbsp;nm of resist thickness  in PMMA or a commercial resist. Furthermore dielectric breakdown discharge is possible.<ref>{{cite web |first1=G. |last1=Denbeaux |first2=J. |last2=Torok |first3=R. |last3=Del Re |first4=H. |last4=Herbol |first5=S. |last5=Das |first6=I. |last6=Bocharova |first7=A. |last7=Paolucci |first8=L.E. |last8=Ocola |first9=C. |last9=Ventrice Jr. |first10=E. |last10=Lifshin |first11=R.L. |last11=Brainard |title=Measurement of the role of secondary electrons in EUV resist exposures |date=2013 |work=International Workshop on EUV Lithography |url=https://www.euvlitho.com/2013/P29.PDF}}</ref> More recent studies have indicated that 20&nbsp;nm resist thickness could be penetrated by low energy electrons (of sufficient dose) and sub-20&nbsp;nm half-pitch electron-beam lithography already required double patterning.<ref>[https://semiwiki.com/lithography/294565-the-complexities-of-the-resolution-limits-of-advanced-lithography/ Complexities of the Resolution Limits of Advanced Lithography]</ref><ref>[https://www.linkedin.com/pulse/complexities-resolution-limits-advanced-lithography-frederick-chen Resolution Limits]</ref>

As of 2022, a state-of-the-art electron multi-beam writer achieves about a 20&nbsp;nm resolution.<ref>{{cite video |url=https://www.youtube.com/watch?v=WWF3VdI2E7A |title=Electron Blur Impact on Electron Beam and EUV Lithography |first=Frederick |last=Chen |date=2023}}</ref><ref>{{cite conference |first1=M. |last1=Chandramouli |first2=B. |last2=Liu |first3=Z. |last3=Alberti |first4=F. |last4=Abboud |first5=G. |last5=Hochleitner |first6=W. |last6=Wroczewski |first7=S. |last7=Kuhn |first8=C. |last8=Klein |first9=E. |last9=Platzgummer |title=Multibeam mask requirements for advanced EUV patterning |book-title=Photomask Technology |volume=12293 |series=SPIE Proceedings |date=2022  |doi=10.1117/12.2645895 |pages=122930O }}</ref>