Laser-Scattering Particle Inspection

1. Theory

• Definition: A laser-scattering particle inspection tool scans an unpatterned wafer with a focused laser spot and counts localized light scatterers from particles, pits and crystal-originated defects, reporting their sizes as latex sphere equivalents (SEMI M53; Hattori).
• Rayleigh scattering: For particles much smaller than the wavelength, scattered intensity scales as $d^6/{\lambda }^4$, so sensitivity falls steeply with size and improves at shorter wavelength (Hattori; Prahl).
• Background: Surface roughness and organic films scatter uniformly as haze, setting the noise floor (Hattori; Eckhardt Optics).
• Calibration: Certified PSL sphere depositions map signal to LSE diameter so tools agree (SEMI M53).

2. Working Principle

• Illumination: UV or visible lasers, for example 266 $\mathrm{nm}$, at normal or oblique p-polarized incidence (Hattori; patent).
• Collection: Several dark-field collectors at different angles separate particles, pits and scratches (patent).
• Scanning: Spiral or raster scanning of a 50 by 120 $\mu \mathrm{m}$ spot across the whole wafer (patent).
• Qualification: Capture rate and false-count rate are measured with repeated-scan overlay methods (SEMI M50).

3. Applications

• Incoming wafer qualification: Light point defects and haze on prime, epitaxial and SOI wafers (Hattori; SEMI M53).
• Cleaning and process tool monitoring: Particle adders from wet cleans, furnaces and deposition (Hattori).
• Crystal defect screening: COP classification on polished wafers (Hattori).
• Film inspection: Blanket films after deposition (SEMI M53).

Scattering Physics and Size Calibration

Name	Formula	Related Formulae	Variables/Constants
Rayleigh scattering by a small particle	$I_s=I_i\frac{\left(1+{\cos }^2\theta \right)}{2R^2}{\left(\frac{2\pi }{\lambda }\right)}^4{\left(\frac{d}{2}\right)}^6{\left(\frac{n^2-1}{n^2+2}\right)}^2$	$I_s\propto \frac{d^6}{{\lambda }^4}$	$I_s:scatteredintensity$ $I_i:incidentintensity$ $\theta :scatteringangle$ $R:distancetothedetector$ $\lambda :wavelength$ $d:particlediameter$ $\begin{array}{r}n:particlerefractiveindex;Prahl\\ (miepython):thisRayleighformfor\\ spheresmuchsmallerthanthewavelength;\\ Hattori:equationwithsixth-powersize,\\ inversefourth-powerwavelengthand\\ inverse-squaredistancedependence\end{array}$ $\begin{array}{r}(computed:halvingdcutsthesignalto\\ 1.6percent,afactorof64)\end{array}$
Wavelength scaling of sensitivity	$d_{min}\propto {\lambda }^{2/3}(\text{fixed signal threshold})$	$\lambda =266,355,405,488,532\mathrm{nm}$	$\begin{array}{r}{d}_{min}:smallestdetectablediameter;scaling\\ computedfromPrah{l}^{\prime }s{I}_s\propto d^6/{\lambda }^4;Hattori:\\ 266\mathrm{nm}Nd:YAGfourthharmonicat100mW\\ withnoisebelow0.3percentrms,\\ detecting30\mathrm{nm}onbulkSiand40\mathrm{nm}on\\ SOI,commercialsensitivitiesof48,50\\ and60\mathrm{nm}PSL,othersourcesat355,405,\\ 488and532\mathrm{nm};patent:532\mathrm{nm}Nd:YVO4and\\ otherlasers(seetheQ/A)\end{array}$ $\begin{array}{r}(computed:48\mathrm{nm}at488\mathrm{nm}scalesto32\mathrm{nm}\\ at266\mathrm{nm}and39\mathrm{nm}at355\mathrm{nm})\end{array}$
Latex sphere equivalent size	$d_{LSE}:I_s\left(d_{LSE},n_{PSL}\right)=I_{s,measured}$	$d_x=d_{PSL}{\left(\frac{K_{PSL}}{K_x}\right)}^{1/3},K=\frac{n^2-1}{n^2+2}$	$\begin{array}{r}{d}_{LSE}:diameterofaPSLspheregivingthe\\ samesignal\end{array}$ $\begin{array}{r}K:Clausius-Mossottifactor;SEMIM53:\\ calibrationofdark-fieldchannelsso\\ matchedtoolsassignthesameLSEdiameter\\ toalocalizedlightscatterer,PSL\\ spheresandDUV-stablesilicadepositions\\ asintensityreferencesonpolished,\\ epitaxialorfilmedwafers;equivalence\\ relationcomputedfromthe{K}^2{d}^{6}dependence\\ inPrah{l}^{\prime }sform\end{array}$ $\begin{array}{r}(assumed:n=1.59PSL,1.46SiO2,2.0\\ Si3N4;computed:asilicaparticlemustbe\\ 7.2percentlargerandanitrideparticle\\ 12.3percentsmallerthanPSLforthe\\ samesignal)\end{array}$

Optics, Haze and Scanning

Name	Formula	Related Formulae	Variables/Constants
Haze and surface roughness	$\text{haze (ppm)}=\frac{P_{scattered}}{P_{incident}}\times 10^6$	$TIS\approx {\left(\frac{4\pi \sigma \cos {\theta }_i}{\lambda }\right)}^2$	$P:opticalpower$ $TIS:totalintegratedscatter$ $\sigma :rmsroughness$ $\begin{array}{r}{\theta }_i:incidenceangle;EckhardtOptics:\\ TIS=R_0[1-\exp (-(4\pi R_q\cos {\theta }_i/\lambda {)}^2)],shorter\\ wavelengthsscatteringmore;\\ small-roughnessformperunitreflectance\\ andppmdefinition(computed);Hattori:\\ organichazeandmicro-roughnessreducing\\ sensitivity,roughnessrisingafterO3\\ oxidationandDHFetchcleaning,\\ micro-roughnesssensitivitiesof80,60\\ and48\mathrm{nm};patent:hazeanddefectscatter\\ portions,P-polarizedcollectorsplacedat\\ hazeminima\end{array}$ $\begin{array}{r}(computed:0.1\mathrm{nm}rmsgivesabout22\mathrm{ppm}\\ at266\mathrm{nm}and6.6\mathrm{ppm}at488\mathrm{nm})\end{array}$
Oblique incidence and collectors	${\theta }_i\approx 65^{\circ }(\text{p-polarized})$	$\text{wing collectors at}\sim 26^{\circ },\text{back collectors at}55^{\circ }\text{azimuth}$	$\begin{array}{r}{\theta }_i:incidencefromthenormal;patent:\\ P-polarizedlightat65degrees,wing\\ collectorsuptoabout40degrees\\ (preferably26),backcollectorsatabout\\ 55degreesazimuth,collectorplacementat\\ hazeminima,scratchsignalschangingwith\\ waferrotation;normalandoblique\\ channelsforparticleandpit\\ discrimination(myreading)\end{array}$ $\begin{array}{r}(myreading:p-polarizedobliquelight\\ suppressessubstrateroughnessscatter\\ relativetoparticlescatter,raising\\ signal-to-hazeratio)\end{array}$
Scan speed and sensitivity	${\left(\sqrt{R}\right)}^{1/6}=\frac{d_f}{d_s}$	$SNR\propto \sqrt{t_{dwell}}{d}^6$	$R:ratiooffulltoslowscanspeed$ $\begin{array}{r}{d}_f,d_s:discerniblediametersatfulland\\ slowspeed\end{array}$ $\begin{array}{r}{t}_{dwell}:dwelltime;patent:relation\\ (renderinggarbled),spotabout50by120\\ \mu \mathrm{m},20\mu \mathrm{s}AODscanwith16\mu \mathrm{s}active,4scan\\ lengthsand4cross-scanpitchesgiving16\\ speeds;shot-noiseSNR(myreading)\end{array}$ $\begin{array}{r}(computed:slowing16timesimprovesdby\\ 16^{1/12}=1.26,about26percent;a300\mathrm{mm}\\ waferholds1.2\times 10^{7}spotareas)\end{array}$

Counting, Classification and Substrates

Name	Formula	Related Formulae	Variables/Constants
Capture rate and false counts	$CR=\frac{N_{detected,true}}{N_{true}}$	$FCR=\frac{N_{false}}{\text{wafer}}$	$CR:capturerate$ $N_{true}:realscatterersaboveasize$ $\begin{array}{r}FCR:falsecountrate;SEMIM50:\\ determinationofCR,FCRandcumulative\\ FCRagainstLSEsizebytheoverlaymethod\\ (definitionsnotgivenonthescopepage);\\ definitions(myreading)\end{array}$ $\begin{array}{r}(myreading:overlayingrepeatedscans\\ separatesrepeatablerealdefectsfrom\\ randomfalsecounts)\end{array}$
Particle against crystal-defect classification	$\text{accuracy}=\frac{N_{correct}}{N_{total}}$	$\text{normal/oblique and wide/narrow channel ratios}$	$\begin{array}{r}Hattori:classificationofparticles\\ againstCOPs,systemXat100\mathrm{nm}84and85\\ percent,Yat80\mathrm{nm}84and84percent,Z\\ at80\mathrm{nm}53and93percent;multi-channel\\ discrimination(myreading)\end{array}$ $\begin{array}{r}(computed:systemZmisclassifies47per\\ centofparticles,soitsparticlecounts\\ wouldbestronglyunderstated)\end{array}$
SOI and wavelength penetration	${\delta }_{abs}=\frac{1}{\alpha \left(\lambda \right)}$	$\text{buried-oxide interference modulates scatter on SOI}$	${\delta }_{abs}:absorptiondepthinSi$ $\begin{array}{r}\alpha :absorptioncoefficient;Hattori:266\mathrm{nm}\\ penetratinglessthan488\mathrm{nm}andreducing\\ reflectionsfromburiedlayers,30against\\ 40\mathrm{nm}limitsonbulkandSOI,PSLtests\\ from40to152\mathrm{nm}onbondedSOIandSIMOX;\\ PVEducation:absorptiondepth1/\alpha ,blue\\ lightabsorbedwithinafewmicronsin\\ silicon\end{array}$ $\begin{array}{r}(computed:SOIraisesthe266\mathrm{nm}limitby\\ 33percent,from30to40\mathrm{nm})\end{array}$

Important Questions

Ques: Why does particle detection get so hard as particles shrink?

Because Rayleigh scattering scales as the sixth power of diameter. Hattori’s Rayleigh equation shows intensity proportional to $d^6$, $1/{\lambda }^4$ and $1/R^2$; Prahl’s full form also includes $[(n^2-1)/(n^2+2){]}^2$. Halving the diameter therefore cuts the signal to 1.6 per cent, a factor of 64 (computed). Since the substrate’s haze sets a nearly fixed background, smaller particles quickly fall below it. Shorter wavelengths help because the ${\lambda }^{-4}$ term raises particle scatter, which is why Hattori used a 266 $\mathrm{nm}$ laser at 100 mW with noise below 0.3 per cent rms. Roughness scatter also rises at short wavelength, so the gain is partly offset (Eckhardt Optics: shorter wavelengths scatter more). Reference: T. Hattori, ‘Challenges of Smaller Particle Detection on Both Bulk-Silicon and SOI Wafers’, presentation hosted by NIST (2005) (fetch-tool summary; equation garbled); S. Prahl, miepython documentation, ‘Rayleigh Scattering’ (2025): I = I0 (1 + cos^2 theta)/(2R^2) (2 pi/lambda)^4 ((n^2 - 1)/(n^2 + 2))^2 (d/2)^6 for spheres much smaller than the wavelength (fetch-tool summary); Eckhardt Optics, ‘Optical Scattering and Surface Roughness’: TIS = R0[1 - exp(-(4 pi Rq cos theta_i/lambda)^2)], shorter wavelengths scatter more (fetch-tool summary).

Ques: Is the detection limit 30 nm or 48 to 60 nm?

Hattori reports 30 $\mathrm{nm}$ on bulk silicon with a 266 $\mathrm{nm}$ system, against commercial tools of the time quoted at 48, 50 and 60 $\mathrm{nm}$ PSL. The figures are consistent once wavelength is considered: at a fixed signal threshold $d_{min}\propto {\lambda }^{2/3}$, so 48 $\mathrm{nm}$ at 488 $\mathrm{nm}$ scales to 32 $\mathrm{nm}$ at 266 $\mathrm{nm}$ and 39 $\mathrm{nm}$ at 355 $\mathrm{nm}$ (computed). The 30 $\mathrm{nm}$ value is therefore more likely the deep-UV result and the 48 to 60 $\mathrm{nm}$ values those of visible-laser tools, not a contradiction (my reading). Substrate matters too: Hattori’s limit rose to 40 $\mathrm{nm}$ on SOI, 33 per cent higher (computed), because buried-oxide interference and deeper penetration add background; penetration is set by the absorption depth $1/\alpha$ (PVEducation). Reference: T. Hattori, ‘Challenges of Smaller Particle Detection on Both Bulk-Silicon and SOI Wafers’, presentation hosted by NIST (2005) (fetch-tool summary; equation garbled); S. Prahl, miepython documentation, ‘Rayleigh Scattering’ (2025): I = I0 (1 + cos^2 theta)/(2R^2) (2 pi/lambda)^4 ((n^2 - 1)/(n^2 + 2))^2 (d/2)^6 for spheres much smaller than the wavelength (fetch-tool summary); PVEducation, ‘Absorption Depth’: absorption depth as the inverse of the absorption coefficient, blue photons absorbed within a few microns in silicon (fetch-tool summary).

Ques: What is a latex sphere equivalent size, and why can it mislead?

It is the diameter of a polystyrene sphere that would give the same signal. SEMI M53 calibrates dark-field channels with certified PSL depositions so matched tools assign the same LSE diameter to a scatterer, and adds DUV-stable silica depositions as intensity references. Real particles differ in refractive index: with the Clausius-Mossotti factor $K=(n^2-1)/(n^2+2)$, a silica particle (n = 1.46) must be 7.2 per cent larger than PSL (n = 1.59) to give the same signal, and a nitride particle (n = 2.0) 12.3 per cent smaller (assumed indices; computed). Shape, absorption and pits change the signal further (my reading), so LSE size is a scattering metric, not a physical size. Reference: SEMI M53-0220, ‘Practice for Calibrating Scanning Surface Inspection Systems Using Certified Depositions of Monodisperse Reference Spheres on Unpatterned Semiconductor Wafer Surfaces’, SEMI store scope page (fetch-tool summary); S. Prahl, miepython documentation, ‘Rayleigh Scattering’ (2025): I = I0 (1 + cos^2 theta)/(2R^2) (2 pi/lambda)^4 ((n^2 - 1)/(n^2 + 2))^2 (d/2)^6 for spheres much smaller than the wavelength (fetch-tool summary).

Ques: How do inspection tools separate particles from haze and crystal defects?

With polarization, angle and several collectors. The patent describes p-polarized light at 65 degrees from the normal, wing collectors near 26 degrees and back collectors at 55 degrees azimuth, placed where haze scatter is minimal relative to defect scatter. Haze in parts per million follows roughness as $(4\pi \sigma \cos {\theta }_i/\lambda {)}^2$ (small-roughness limit of Eckhardt Optics’ expression, per unit reflectance; computed): 0.1 $\mathrm{nm}$ rms gives about 22 $\mathrm{ppm}$ at 266 $\mathrm{nm}$ (computed). Particles and crystal-originated pits scatter differently into normal and oblique channels, enabling classification, but Hattori shows wide variation: one system classified 84 per cent of particles correctly at 100 $\mathrm{nm}$, another only 53 per cent at 80 $\mathrm{nm}$, so 47 per cent of particles would be miscounted (computed). Reference: ‘System and method for inspection of a workpiece surface using multiple scattered light collectors’, US patent 8,497,984 (priority 2004) (fetch-tool summary); Eckhardt Optics, ‘Optical Scattering and Surface Roughness’: TIS = R0[1 - exp(-(4 pi Rq cos theta_i/lambda)^2)], shorter wavelengths scatter more (fetch-tool summary); T. Hattori, ‘Challenges of Smaller Particle Detection on Both Bulk-Silicon and SOI Wafers’, presentation hosted by NIST (2005) (fetch-tool summary; equation garbled).

Ques: How do scan speed and qualification tests affect results?

Slower scans see smaller particles, and SEMI methods quantify capture. In the patent, sensitivity improves with slower acousto-optic scanning as $(\sqrt{R}{)}^{1/6}=d_f/d_s$, consistent with shot-noise SNR rising with the square root of dwell time and with $d^6$ (my reading); slowing 16 times improves the detectable diameter by 26 per cent (computed). Its spot is about 50 by 120 $\mu \mathrm{m}$, so a 300 $\mathrm{mm}$ wafer holds about $1.2\times 10^7$ spot areas (computed). SEMI M50 determines capture rate and false-count rate against LSE size by overlaying repeated scans: real defects repeat while random counts do not (my reading). Hattori’s cleaning example reduced light point defects from 125,624 to 86 if the labels are read in order, 99.93 per cent removal (computed). Reference: ‘System and method for inspection of a workpiece surface using multiple scattered light collectors’, US patent 8,497,984 (priority 2004) (fetch-tool summary); SEMI M50-0923, ‘Test Method for Determining Capture Rate and False Count Rate for Surface Scanning Inspection Systems by the Overlay Method’, SEMI store scope page (fetch-tool summary); T. Hattori, ‘Challenges of Smaller Particle Detection on Both Bulk-Silicon and SOI Wafers’, presentation hosted by NIST (2005) (fetch-tool summary; equation garbled).

References

1. T. Hattori, “Challenges of Smaller Particle Detection on Both Bulk-Silicon and SOI Wafers,” presentation, 2005. Available: https://www.nist.gov/document/hattori2005pdf
2. S. Prahl, “Rayleigh Scattering,” miepython documentation, 2025. Available: https://miepython.readthedocs.io/en/latest/04_rayleigh.html
3. Eckhardt Optics, “Optical Scattering and Surface Roughness.” Available: https://www.eckop.com/resources/scatterometer-resources/optical-scattering-versus-surface-roughness/
4. PVEducation, “Absorption Depth.” Available: https://pveducation.org/es/fotovoltaica/absorption-depth
5. SEMI M53-0220, “Practice for Calibrating Scanning Surface Inspection Systems Using Certified Depositions of Monodisperse Reference Spheres on Unpatterned Semiconductor Wafer Surfaces,” SEMI. Available: https://store-us.semi.org/products/m05300-semi-m53-practice-for-calibrating-scanning-surface-inspection-systems-using-certified-depositions-of-monodispere-reference-spheres-on-unpatterned-semiconductor-wafer-surfaces
6. “System and method for inspection of a workpiece surface using multiple scattered light collectors,” US patent 8,497,984 (priority December 2004). Available: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/8497984
7. SEMI M50-0923, “Test Method for Determining Capture Rate and False Count Rate for Surface Scanning Inspection Systems by the Overlay Method,” SEMI. Available: https://store-us.semi.org/products/m05000-semi-m50-test-method-for-determining-capture-rate-and-false-count-rate-for-surface-scanning-inspection-systems-by-the-overlay-method

Related pages in this vault: Patterned-Wafer Optical Inspection, Wafer Geometry Gauge, Optical Microscope, Scanning Electron Microscope (SEM), Overlay Metrology Tool, X-Ray Fluorescence Spectrometer (XRF and TXRF), Optical CD Scatterometer (OCD), E-Beam Inspection and Defect Review, Light-Matter Interaction for Optical Inspection, Defect Detection Fundamentals, Defect Sources and Classification, RCA Wet Bench, Megasonic Single-Wafer Cleaner, Spin Rinse Dryer and IPA Vapor Dryer, Defect SPC and Excursion Monitoring.