Editing Electron-beam lithography (section)

===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>