Patterned-Wafer Optical Inspection

1. Theory

• Definition: A patterned-wafer optical inspection tool images or scans a processed wafer and finds defects by comparing each die or memory cell with nominally identical neighbours, flagging locations where the signal differs (multi-beam patent; scatter-plot patent).
• Bright field and dark field: Bright field collects specular light with high-resolution optics and small pixels, while dark field collects scattered light with larger pixels and higher throughput (multi-beam patent).
• Comparison: Subtracting aligned images cancels the repeating pattern, so only differences above a noise-based threshold remain (scatter-plot patent).
• Sub-resolution detection: Defects smaller than the optical resolution are still detectable from their scattered or interference signal (Laser-Scattering Particle Inspection page).

2. Working Principle

• Optics: DUV to visible illumination, laser or broadband, with bright-field, dark-field or combined annular modes (multi-beam patent).
• Scanning: Time-delay-integration or multi-beam scanning across dies at high pixel rates (multi-beam patent).
• Detection algorithms: Die-to-die, array cell-to-cell and grey-level-adaptive thresholds (scatter-plot patent).
• Review: Candidate defects are reviewed and classified, for example by SEM (E-Beam Inspection and Defect Review page).

3. Applications

• Memory arrays: Cell-to-cell inspection of repetitive regions (scatter-plot patent).
• Particle and pattern defects: Defects and particles on product wafers (multi-beam patent; scatter-plot patent).

Imaging Modes and Resolution

Name	Formula	Related Formulae	Variables/Constants
Bright-field and dark-field imaging	$I_{BF}\propto {\left|E_{spec}+E_{def}\right|}^2,I_{DF}\propto {\left|E_{scat}\right|}^2$	$\text{BF: small pixels, high resolution; DF: large pixels, high SNR}$	$E_{spec}:specularlyreflectedfield$ $E_{def}:defect-perturbedfield$ $\begin{array}{r}{E}_{scat}:scatteredfield;multi-beampatent:\\ brightfieldcollectsspecularlightwith\\ high-resolutionopticsandverysmall\\ pixels,darkfieldcapturesscattered\\ lightwithrelativelylargepixels,high\\ SNRandthroughput,annularbeamfor\\ simultaneousBFandDF,confocalpinhole\\ suppressingunder-layersignals;field\\ forms(myreading)\end{array}$ $\begin{array}{r}(myreading:inBFasmalldefectappears\\ throughinterferencewiththestrong\\ specularfield,whileinDFthebackground\\ isnearzero)\end{array}$
Optical resolution	$\delta =\frac{0.61\lambda }{NA}$	$p_{pixel}\lesssim \frac{\delta }{2}(\text{sampling})$	$\delta :Rayleighresolution$ $\lambda :wavelength$ $NA:numericalaperture$ $\begin{array}{r}{p}_{pixel}:pixelsizeatthewafer;Basler:\\ d=0.61\lambda /NAandsamplingpitchatmosthalf\\ theresolution;multi-beampatent:very\\ smallBFpixels,pixelaspectratio1:5to\\ 1:10\end{array}$ $\begin{array}{r}(assumed:NA=0.9;computed:180\mathrm{nm}at\\ 266\mathrm{nm}and305\mathrm{nm}at450\mathrm{nm})\end{array}$
Sub-resolution defect signal	$I_{DF}\propto \frac{d^6}{{\lambda }^4}(d\ll \lambda )$	$SNR=\frac{\Delta I}{{\sigma }_{noise}}$	$d:defectsize$ $\Delta I:defectsignalabovebackground$ $\begin{array}{r}{\sigma }_{noise}:noisefrompatternvariationandshot\\ noise;Rayleighscaling(Laser-Scattering\\ ParticleInspectionpage);multi-beam\\ patent:dark-fieldSNRdetecting\\ relativelysmalldefectsathigh\\ throughput\end{array}$ $\begin{array}{r}(computed:adefecthalfthesizegives\\ onesixty-fourthofthedark-fieldsignal)\end{array}$

Detection Algorithms

Name	Formula	Related Formulae	Variables/Constants
Die-to-die difference image	$D\left(x,y\right)=I_{test}\left(x,y\right)-I_{ref}\left(x,y\right)$	$\text{defect if}\left|D\right|>T,{\sigma }_D=\sqrt{2}\sigma$	$D:differenceimage$ $I_{test},I_{ref}:alignedtestandreferencedieimages$ $T:threshold$ $\begin{array}{r}\sigma :single-imagenoise;scatter-plot\\ patent:differenceimagebysubtracting\\ greylevels,eachpixelcomparedwitha\\ thresholdwindowsuchas\pm 50or\pm 40;\\ multi-beampatent:comparisonofadie\\ withanotherdieinsteadofareference\\ image,adjacentdiesinaroworcolumn;\\ noiserelation(computedforindependent\\ noiseinthetwoimages)\end{array}$ $\begin{array}{r}(computed:a\pm 50grey-levelwindowsetat\\ 3{\sigma }_{D}implies\sigma of11.8greylevelsper\\ image)\end{array}$
Array (cell-to-cell) mode	$D_{array}\left(x,y\right)=I\left(x,y\right)-I\left(x+P_{cell},y\right)$	$\text{same-die comparison removes die-to-die process variation}$	$\begin{array}{r}{P}_{cell}:repeatperiodofthememorycell;\\ scatter-plotpatent:arraymodecomparesa\\ diesectionwithanotheridenticalsection\\ ofthesamedie;shift-by-periodform(my\\ readingofthearraymode)\end{array}$ $\begin{array}{r}(myreading:comparingneighboursafew\\ micrometresapartavoidsthewafer-scale\\ filmandfocusvariationthatinflates\\ die-to-dienoise)\end{array}$
Scatter-plot (adaptive) thresholding	$\left(g_{ref},g_{test}\right)\text{histogram, }256\times 256$	$T=T\left(g_{ref}\right)$	$\begin{array}{r}g:greylevel;scatter-plotpatent:\\ test-pixelgreylevelplottedagainst\\ alignedreferencegreylevelina256by\\ 256array,outliersfromthediagonal\\ clusterasdefects,noisemodulation\\ varyingwithgreylevel,20000-pixel\\ histogramexample\end{array}$ $\begin{array}{r}(myreading:agrey-level-dependent\\ thresholdallowstighterlimitsinquiet\\ regionswithoutfloodingnoisybright\\ regionswithnuisance)\end{array}$

Throughput and Review

Name	Formula	Related Formulae	Variables/Constants
Throughput and data rate	$DR=\frac{n{N}_{PL}}{\tau }$	$t_{wafer}=\frac{A_{wafer}}{p_{pixel}^{2}DR}$	$DR:pixelspersecond$ $n:numberofbeams$ $N_{PL}:pixelsperline$ $\tau :linetime$ $\begin{array}{r}{A}_{wafer}:inspectedarea;multi-beampatent:\\ data-raterelation,Dammanngratingbeam\\ brushwithn=4,beamspacingD=\\ HFOV/(n-1),2000-pixel35-lineCCD\\ example;timerelation(computed)\end{array}$ $\begin{array}{r}(assumed:n=4,N_{PL}=2000,\tau =1\mu \mathrm{s};\\ computed:8\times 10^{9}pixelspersecond,59\\ minutesper300\mathrm{mm}waferat50\mathrm{nm}pixels\\ and35sat0.5\mu \mathrm{m}pixels)\end{array}$
Multi-beam geometry	$D=\frac{HFOV}{n-1},\sin \alpha =\frac{D}{N_{PL}}$	$T=\frac{P}{\sin \alpha }=\frac{P\left(n-1\right)N_{PL}}{HFOV}$	$HFOV:horizontalfieldofview$ $\alpha :beam-arraytilt$ $P:pixelpitch$ $\begin{array}{r}T:resultinglinespacing;multi-beam\\ patent:Eqs.1to3withn>1,\\ equal-intensitybeamsfromaDammann\\ grating\end{array}$ $\begin{array}{r}(computed:n=4beamsspreadacrossthe\\ fieldatonethirdoftheHFOVeach)\end{array}$
Capture, nuisance and review	$\text{capture}=\frac{N_{DOI,detected}}{N_{DOI}}$	$\text{nuisance fraction}=\frac{N_{nuisance}}{N_{detected}}$	$\begin{array}{r}DOI:defectsofinterest,nuisance:real\\ butharmlessornoiseevents;definitions\\ (myreading);reviewontheE-Beam\\ InspectionandDefectReviewpage;\\ scatter-plotpatent:thresholdwindows\\ tradingsensitivityagainstfalse\\ detections;multi-beampatent:\\ high-throughputdarkfieldagainst\\ high-resolutionbrightfield\end{array}$ $\begin{array}{r}(myreading:opticalinspectionflags\\ candidatesandSEMreviewclassifiesthem,\\ sorecipesaretunedonreviewedsamples)\end{array}$

Important Questions

Ques: How do bright-field and dark-field inspection differ?

By which light they collect and what that does to resolution and speed. The multi-beam patent describes bright field as collecting specularly reflected light with very high-resolution optics and very small pixels, giving detailed images, and dark field as capturing scattered light with relatively large pixels and high signal-to-noise, so small defects are found at high throughput. In bright field, a small defect appears through interference with the strong specular field; in dark field the patterned background is largely rejected (my reading). An annular beam can collect both simultaneously, and a confocal pinhole suppresses signals from under-layers. The resolution $0.61\lambda /NA$ is 180 $\mathrm{nm}$ at 266 $\mathrm{nm}$ and NA 0.9 (assumed; computed), so both modes detect defects well below resolution. Reference: ‘Multi beam scanning with bright/dark field imaging’, US patent 7,049,155 (continuation of an application filed 2002) (fetch-tool summary).

Ques: How does die-to-die comparison find a defect?

By subtracting an aligned image of a neighbouring die. The scatter-plot patent generates a difference image by subtracting grey levels and compares each pixel with a threshold window such as plus or minus 50 grey levels. If the window is set at three standard deviations of the difference, the single-image noise is 11.8 grey levels, since independent noise adds as $\sqrt{2}$ (computed). The multi-beam patent compares adjacent dies in a row or column instead of a reference image. With two dies, a difference does not reveal which die is defective; comparing with dies on both sides and assigning the defect to the die that differs from both would resolve this, and is more likely what production tools do (my reading). Reference: ‘Two-dimensional scatter plot technique for defect inspection’, US patent 6,912,304 (related applications filed 1999) (fetch-tool summary); ‘Multi beam scanning with bright/dark field imaging’, US patent 7,049,155 (continuation of an application filed 2002) (fetch-tool summary).

Ques: Why use cell-to-cell comparison in memory arrays?

Because neighbouring cells within a die are more alike than distant dies. The scatter-plot patent describes array mode comparing a section of a die with another identical section of the same die. Shifting by the cell period, $D=I(x,y)-I(x+P_{cell},y)$ (my reading of the array mode), compares features a few micrometres apart, avoiding wafer-scale variation in film thickness, focus and colour that inflates die-to-die noise (my reading). Lower noise allows a tighter threshold and smaller detectable defects. The scatter-plot method adds grey-level-dependent thresholds: plotting test against reference grey levels in a 256 by 256 array separates defects as outliers from the diagonal, accounting for noise that varies with brightness. Reference: ‘Two-dimensional scatter plot technique for defect inspection’, US patent 6,912,304 (related applications filed 1999) (fetch-tool summary).

Ques: Why is bright-field inspection slower than dark field?

Because throughput scales with pixel area. Pixel rate follows $DR=n{N}_{PL}/\tau$ (multi-beam patent): an assumed 4 beams of 2000 pixels at a 1 $\mu \mathrm{s}$ line time give $8\times 10^9$ pixels per second (computed). A 300 $\mathrm{mm}$ wafer then needs about 59 minutes at 50 $\mathrm{nm}$ bright-field pixels but 35 s at 0.5 $\mu \mathrm{m}$ dark-field pixels, a factor of 100 (computed). The patent’s Dammann-grating beam brush with n = 4 equal beams, spaced HFOV/(n - 1), raises throughput by scanning several lines at once. The patent itself links small bright-field pixels with high resolution and large dark-field pixels with high SNR and throughput, so bright field suits sensitivity and dark field speed (my reading). Reference: ‘Multi beam scanning with bright/dark field imaging’, US patent 7,049,155 (continuation of an application filed 2002) (fetch-tool summary).

Ques: How small a defect can optical inspection catch?

Much smaller than the resolution, but with rapidly falling signal. A sub-resolution defect scatters roughly as $d^6/{\lambda }^4$ (Laser-Scattering Particle Inspection page), so halving its size reduces dark-field signal 64 times (computed), and detection depends on signal-to-noise against pattern noise. Shorter wavelengths and higher NA improve both resolution and signal: Basler’s $0.61\lambda /NA$ gives 124 $\mathrm{nm}$ for 193 $\mathrm{nm}$ at NA 0.95 (computed). The multi-beam patent emphasizes high-SNR dark-field detection for relatively small defects, and the scatter-plot patent adaptive thresholds to keep false detections in check. Optical tools flag candidates, and review confirms defects of interest and separates nuisance (E-Beam Inspection and Defect Review page). Reference: Laser-Scattering Particle Inspection page of this vault; Basler AG, ‘What Really Limits Microscopy Resolution? Diffraction, Rayleigh, Aberrations, and Nyquist Explained’: d = 0.61 lambda/NA, effective sampling pitch at most half the optical resolution (fetch-tool summary); ‘Multi beam scanning with bright/dark field imaging’, US patent 7,049,155 (continuation of an application filed 2002) (fetch-tool summary); ‘Two-dimensional scatter plot technique for defect inspection’, US patent 6,912,304 (related applications filed 1999) (fetch-tool summary); E-Beam Inspection and Defect Review page of this vault.

References

1. “Multi beam scanning with bright/dark field imaging,” US patent 7,049,155 (continuation of US application 10/078,542, filed February 2002). Available: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/7049155
2. Basler AG, “What Really Limits Microscopy Resolution? Diffraction, Rayleigh, Aberrations, and Nyquist Explained.” Available: https://www.baslerweb.com/en/learning/microscopy-resolution-limits/
3. “Two-dimensional scatter plot technique for defect inspection,” US patent 6,912,304 (related applications filed 1999). Available: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/6912304
4. Laser-Scattering Particle Inspection page of this vault.

Related pages in this vault: Laser-Scattering Particle Inspection, Optical Microscope, Scanning Electron Microscope (SEM), Confocal Laser Scanning Microscope, Overlay Metrology Tool, Optical CD Scatterometer (OCD), Wafer Geometry Gauge, CD-SEM, E-Beam Inspection and Defect Review, Optical Emission Spectroscopy Endpoint (OES), High-NA DUV Immersion Scanner, Photoresist and Process Window, Light-Matter Interaction for Optical Inspection, Defect Detection Fundamentals, Yield Models and Critical Area, Megasonic Single-Wafer Cleaner, Wafer-Map Spatial Signature Analysis, Defect Inspection Workflow and Sampling Plans.