Editing Photolithography (section)

== Resolution in projection systems ==
{{Main|Optics#Diffraction and optical resolution|Diffraction|Optical resolution}}
[[Image:Yellow fluorescent light spectrum.png|thumb|right|250px|The filtered [[fluorescent lighting]], yellow LED or low-pressure sodium lighting in photolithography cleanrooms contains no ultraviolet or blue light in order to avoid exposing photoresists. The spectrum of light emitted by such fixtures gives virtually all such spaces a bright yellow color.]]
[[File:Diffraction_order_spectrum_with_range_of_illumination.png|thumb|left|200px|'''Diffraction order spectrum with partial coherence.''' The diffraction order spectrum (up to 3rd order) of a line-space pattern (pitch<3 wavelength/NA) is shown with different colors indicating different illumination angles in a partial coherence setting.]]
The ability to project a clear image of a small feature onto the wafer is [[diffraction limit|limited]] by the [[wavelength]] of the light that is used, and the ability of the reduction lens system to capture enough diffraction orders from the illuminated mask. Current state-of-the-art photolithography tools use deep ultraviolet (DUV) light from [[excimer laser]]s with wavelengths of 248 (KrF) and
193 (ArF) [[Nanometre|nm]] (the dominant lithography technology today is thus also called "'''excimer laser lithography'''"), which allow minimum feature sizes down to '''50'''&nbsp;nm. Excimer laser lithography has thus played a critical role in the continued advance of the [[Moore's Law]] for the last 20 years (see below<ref name=LaFontaine>La Fontaine, B., "Lasers and Moore's Law", SPIE Professional, Oct. 2010, p. 20; http://spie.org/x42152.xml</ref>).

The minimum feature size that a projection system can print is given approximately by:

:<math>CD = k_1 \cdot\frac{\lambda}{NA}</math>
where <math>\,CD</math> is the '''minimum feature size''' (also called the '''critical dimension''', '''target design rule''', or "'''half-pitch'''"), <math>\,\lambda</math> is the wavelength of light used, and <math>\,NA</math> is the [[numerical aperture]] of the lens as seen from the wafer.

<math>\,k_1</math> (commonly called ''k1 factor'') is a coefficient that encapsulates process-related factors and typically equals 0.4 for production. (<math>\,k_1</math> is actually a function of process factors such as the angle of incident light on a reticle and the incident light intensity distribution. It is fixed per process.) The minimum feature size can be reduced by decreasing this coefficient through [[computational lithography]].[[File:From_on-axis_to_off-axis_illumination.png|thumb|left|300px|'''Illumination direction impact.''' On-axis illumination provides higher contrast, but only off-axis illumination resolves the smallest pitch.]]
[[File:Pitch_widening_below_Rayleigh_criterion.png|thumb|right|300px|The Rayleigh criterion defines the minimum separation for preserving the distance between two points in the projected image.]]
According to this equation, minimum feature sizes can be decreased by decreasing the wavelength, and increasing the numerical aperture (to achieve a tighter focused beam and a smaller spot size). However, this design method runs into a competing constraint. In modern systems, the [[depth of focus]] is also a concern:

:<math>D_F = k_2 \cdot\frac{\lambda}{\,{NA}^2}</math>

Here, <math>\,k_2</math> is another process-related coefficient. The depth of focus restricts the thickness of the photoresist and the depth of the topography on the wafer.  [[Chemical mechanical polishing]] is often used to flatten topography before high-resolution lithographic steps.

From classical optics, k1=0.61 by the [[Angular resolution#The_Rayleigh_criterion|Rayleigh criterion]].<ref>{{cite web| url = https://www.linkedin.com/pulse/lithography-resolution-limits-paired-features-frederick-chen/| title = Lithography Resolution Limits: Paired Features}}</ref> The image of two points separated by less than 1.22 wavelength/NA will not maintain that separation but will be larger due to the interference between the [[Airy disc]]s of the two points. It must also be remembered, though, that the distance between two features can also change with defocus.<ref>{{cite web| url = https://www.linkedin.com/pulse/impact-defocus-illumination-imaging-pitch-frederick-chen| title = Impact of Defocus and Illumination on Imaging of Pitch}}</ref>
[[File:Illumination impact on pitch.png|thumb|left|250px|Illumination can significantly impact the apparent pitch of the image of the same object (a pair of bright lines in this case).]]
[[File:Sub-0.5 k1 brick pattern.png|thumb|left|300px|Straight edges of shortened features are distorted into bowed edges as pitch is reduced in both directions.]]
[[File:Gap k1 vs hp k1.png|thumb|right|300px|'''Gap width vs. half-pitch.''' The tighter the line pitch, the wider the gap between the ends of the lines (perpendicular to the pitch).]]
Resolution is also nontrivial in a two-dimensional context. For example, a tighter line pitch results in wider gaps (in the perpendicular direction) between the ends of the lines.<ref>{{cite web| url = https://www.linkedin.com/pulse/how-line-cuts-became-necessarily-separate-steps-lithography-chen| title = How Line Cuts Became Necessary}}</ref><ref>M. Eurlings et al., Proc. SPIE 4404, 266 (2001).</ref> More fundamentally, straight edges become rounded for shortened rectangular features, where both x and y pitches are near the resolution limit.<ref>{{cite web| url = https://www.youtube.com/watch?v=En5K33mLv0k| title = 1D vs 2D Patterning Limits in Advanced Lithography| website = [[YouTube]]| date = 29 August 2021}}</ref><ref>{{cite web| url = https://www.youtube.com/watch?v=V7l9Im9zneg| title = Vanishing of Half the Fourier Coefficients in Staggered Arrays| website = [[YouTube]]| date = 10 October 2021}}</ref><ref>{{Cite web|url=https://www.youtube.com/watch?v=9_Q8E9uyr4Q|title=Pitch Walking From Corner Rounding in Lithography|date=31 March 2022 |via=www.youtube.com}}</ref><ref>E. S. Wu et al., J. Microlith., Microfab., Microsyst. 4, 023009 (2005).</ref>

For advanced nodes, blur, rather than wavelength, becomes the key resolution-limiting factor. Minimum pitch is given by blur sigma/0.14.<ref>{{cite web| url = https://www.linkedin.com/pulse/blur-wavelength-determines-resolution-advanced-nodes-frederick-chen| title = Blur not Wavelength Determines Resolution at Advanced Nodes}}</ref> Blur is affected by dose<ref>A. Narasimhan  et al., Proc. SPIE 9422, 942208 (2015).</ref><ref>P. de Schepper et al., Proc. SPIE 9425, 942507 (2015).</ref><ref>{{cite journal| url = https://escholarship.org/uc/item/4t5908f6| title = Determination of effective attenuation length of slow electrons in polymer films| year = 2020| doi = 10.1063/5.0007163| last1 = Ma| first1 = J. H.| last2 = Naulleau| first2 = P.| last3 = Ahmed| first3 = M.| last4 = Kostko| first4 = O.| journal = Journal of Applied Physics| volume = 127| issue = 24| page = 245301| bibcode = 2020JAP...127x5301M| osti = 1782149| s2cid = 221935438| doi-access = free}}</ref> as well as quantum yield,<ref>{{cite web| url = http://euvlsymposium.lbl.gov/pdf/2007/RE-08-Gallatin.pdf| title = Resolution, LER, and Sensitivity Limitations of Photoresist}}</ref> leading to a tradeoff with stochastic defects, in the case of EUV.<ref>P. De Bisschop and E. Hendrickx, Proc. SPIE 10583, 105831K (2018).</ref><ref>{{cite web| url = https://www.linkedin.com/pulse/revisiting-euv-lithography-post-blur-stochastic-frederick-chen| title = Revisiting EUV Lithography: Post-Blur Stochastic Distributions}}</ref><ref>A. De Silva et al., Proc. SPIE 10957, 109570F (2019).</ref>