Editing Electron-beam lithography (section)

===Proximity effect===
The smallest features produced by electron-beam lithography have generally been isolated features, as nested features exacerbate the [[Proximity effect (electron beam lithography)|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.e., difference between maximum and minimum intensity. Hence, nested feature resolution is harder to control. For most resists, it is difficult to go below 25&nbsp;nm lines and spaces, and a limit of 20&nbsp;nm lines and spaces has been found.<ref name="liddle">{{cite journal|title=Resist Requirements and Limitations for Nanoscale Electron-Beam Patterning|author=J. A. Liddle|journal=Mater. Res. Soc. Symp. Proc.|volume=739|issue=19|year=2003|pages=19–30|url=http://www.mrs.org/s_mrs/sec_subscribe.asp?CID=2557&DID=118066&action=detail|display-authors=1|author2=<Please add first missing authors to populate metadata.>}}{{Dead link|date=March 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> In actuality, though, the range of secondary electron scattering is quite far, sometimes exceeding 100&nbsp;nm,<ref>{{cite journal|doi=10.1016/S0167-9317(02)00531-2|title=The inclusion of secondary electrons and Bremsstrahlung X-rays in an electron beam resist model|year=2002|last1=Ivin|first1=V|journal=Microelectronic Engineering|volume=61–62|page=343 }}</ref> but becoming very significant below 30&nbsp;nm.<ref>{{cite journal|doi=10.1143/JJAP.36.7552|title=Novel Proximity Effect Including Pattern-Dependent Resist Development in Electron Beam Nanolithography|year=1997|last1=Yamazaki|first1=Kenji|last2=Kurihara|first2=Kenji|last3=Yamaguchi|first3=Toru|last4=Namatsu|first4=Hideo|last5=Nagase|first5=Masao|journal=Japanese Journal of Applied Physics|volume=36|issue=12B|page=7552 |bibcode = 1997JaJAP..36.7552Y |s2cid=250783039 }}</ref>

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.<ref>{{cite journal|doi=10.1088/0953-8984/10/26/010|year=1998|last1=Renoud|first1=R|last2=Attard|first2=C|last3=Ganachaud|first3=J-P|last4=Bartholome|first4=S|last5=Dubus|first5=A|journal=Journal of Physics: Condensed Matter|volume=10|page=5821|bibcode = 1998JPCM...10.5821R|issue=26|title=Influence on the secondary electron yield of the space charge induced in an insulating target by an electron beam |s2cid=250739239 }}</ref>

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 [[convolution|convolved]] by the scattering distribution [[point spread function]] ''PSF(x,y)''. However, it must be remembered that an error in the applied dose (e.g., from shot noise) would cause the proximity effect correction to fail.