X-Ray Fluorescence Spectrometer (XRF and TXRF)

1. Theory

• Definition: An X-ray fluorescence spectrometer excites inner-shell vacancies with X-rays and identifies elements from the characteristic lines emitted as outer electrons fill them; total-reflection XRF (TXRF) illuminates a polished wafer below the critical angle to measure trace surface contamination (Kohno; Diebold et al.).
• Characteristic lines: Line energies scale roughly as the square of atomic number (Moseley), and intensity depends on fluorescence yield and absorption above the edge (background knowledge, Jenkins).
• Total reflection: Below the critical angle the beam penetrates only a few nanometres, so substrate fluorescence and scatter fall sharply while surface atoms are excited by both incident and reflected beams (Kohno; Diebold et al.).
• Quantification: Net line intensities are converted to coverage with standards and relative sensitivities (Diebold et al.; background knowledge).

2. Working Principle

• Source: A monochromatized tube line, such as W-L-beta or Mo-K-alpha, is chosen to excite target elements but not the substrate (Kohno; Diebold et al.).
• Geometry: The beam strikes the wafer at about 1 to 3 $\mathrm{mrad}$, below the critical angle (Diebold et al.; Kohno).
• Detection: An energy-dispersive detector placed close above the wafer collects the fluorescence spectrum (background knowledge, Klockenkamper and von Bohlen).
• Mapping and preconcentration: Sweeping TXRF maps the wafer, and vapour-phase decomposition collects surface metals into a droplet for higher sensitivity (Kohno; background knowledge).

3. Applications

• Metal contamination control: Fe, Ni, Cu and Zn on silicon at $1\times 10^9$ to $1\times 10^{10}$ $atoms/c{\mathrm{m}}^2$ for logic, memory and image sensors (Kohno; Diebold et al.).
• Wide-gap wafers: SiC and GaN contamination with excitation chosen below the Ga-K edge (Kohno).
• Process tool qualification: Cleans, furnaces and implanters checked with monitor wafers (background knowledge).
• Thin-film composition: Conventional XRF for film thickness and composition of metal layers (background knowledge, Jenkins).

Fluorescence Physics

Name	Formula	Related Formulae	Variables/Constants
Characteristic line energy (Moseley)	$E_{K\alpha }\approx \frac{3}{4}{R}_y{\left(Z-1\right)}^2$	$\lambda =\frac{hc}{E}=\frac{12.398}{E\left[\mathrm{keV}\right]}\mathring{\mathrm{A}}$	$E_{K\alpha }:K-alphalineenergy$ $R_y:Rydbergenergy13.606\mathrm{eV}$ $Z:atomicnumber$ $\begin{array}{r}\lambda :wavelength;Moseleyformandconversion\\ (backgroundknowledge,Jenkins);Kohno:\\ W-L\beta excitationat9.67\mathrm{keV},Ga-Kedge\\ 10.386\mathrm{keV},RamanfeaturefromGaNnear\\ 7.0to8.7\mathrm{keV}\end{array}$ $\begin{array}{r}(computed:Si1.72,Fe6.38,Ni7.44and\\ Cu8.00\mathrm{keV}againsttabulated1.74,6.40,\\ 7.48and8.05\mathrm{keV};W-L\beta is1.282\mathring{\mathrm{A}})\end{array}$
Fluorescence yield	${\omega }_K\approx \frac{Z^4}{a+Z^4},a\approx 10^6$	$I_i\propto I_0{\omega }_K{\tau }_i{C}_i\epsilon \left(E_i\right)$	${\omega }_K:K-shellfluorescenceyield$ $I_i:lineintensityofelementi$ $I_0:incidentintensity$ $\begin{array}{r}{\tau }_i:photoabsorptioncrosssectionabovethe\\ edge\end{array}$ $C_i:amountofelement$ $\begin{array}{r}\epsilon :detectorefficiency;approximateforms\\ (backgroundknowledge,Jenkins);Diebold\\ etal.:softwarescalingresponsetoother\\ elementsfromoneNistandardwith\\ fluorescence-yieldcurves\end{array}$ $\begin{array}{r}(computed:{\omega }_{K}is0.037forSi,0.31forFe\\ and0.41forCu,solightelements\\ fluoresceweakly)\end{array}$
Excitation above the absorption edge	$E_0>E_{edge,i}$	$\text{W-L}\beta (9.67\mathrm{keV})\text{excites Fe to Zn but not Ga-K}$	$E_0:excitationenergy$ $\begin{array}{r}{E}_{edge,i}:absorption-edgeenergyofelementi;\\ Kohno:W-L\beta at9.67\mathrm{keV}belowtheGa-K\\ edgeat10.386\mathrm{keV},avoidingGa\\ fluorescenceonGaN;edgeselection\\ (backgroundknowledge,Klockenkamperand\\ vonBohlen)\end{array}$ $\begin{array}{r}(computed:the0.72\mathrm{keV}marginbelowthe\\ Ga-Kedgesuppressesthesubstratepeak)\end{array}$

Total Reflection Geometry

Name	Formula	Related Formulae	Variables/Constants
Total reflection condition	${\alpha }_i<{\alpha }_c=\sqrt{2\delta }\propto \lambda \sqrt{{\rho }_e}$	${\alpha }_c\left(\lambda \right)={\alpha }_c\left({\lambda }_0\right)\frac{\lambda }{{\lambda }_0}$	${\alpha }_i:incidenceangle$ ${\alpha }_c:criticalangle$ $\delta :refractivedecrement$ $\begin{array}{r}{\rho }_e:electrondensity;XRRpage:{\alpha }_c=\sqrt{2\delta };\\ Kohno:eachmaterialhasitsowncritical\\ angle,totalreflectionbelowit;Diebold\\ etal.:{\theta }_{c}of6.1\mathrm{arcmin}forSiand5.9\\ \mathrm{arcmin}forSiO2(Moradiation),incidence\\ at1.3\mathrm{mrad}\end{array}$ $\begin{array}{r}(computedfromtheXRRvalues:MoK\alpha gives\\ Si1.78\mathrm{mrad}(6.12\mathrm{arcmin})andSiO21.73\\ \mathrm{mrad}(5.95\mathrm{arcmin});W-L\beta givesSi3.21\\ \mathrm{mrad})\end{array}$
Penetration depth at grazing incidence	$z_p=\frac{\lambda }{4\pi }{\left\{\frac{1}{2}\left[\sqrt{{\left({\alpha }_i^2-{\alpha }_c^2\right)}^2+4{\beta }^2}-\left({\alpha }_i^2-{\alpha }_c^2\right)\right]\right\}}^{-1/2}$	$z_p\left({\alpha }_i\ll {\alpha }_c\right)\approx \frac{\lambda }{4\pi {\alpha }_c}$	$z_p:1/eintensitypenetrationdepth$ $\begin{array}{r}\beta :absorptionindex;explicitform\\ (backgroundknowledge,Klockenkamperand\\ vonBohlen);Dieboldetal.:OCR-garbled\\ versioninX={\alpha }_i/{\alpha }_c,about50\mathring{\mathrm{A}}at1.3\\ \mathrm{mrad}forMo,CuandWradiation,above100\\ \mathrm{nm}reportedelsewhere;Kohno:about5\mathrm{nm}\\ undertotalreflection\end{array}$ $\begin{array}{r}(computed:MoK\alpha onSigives\lambda /(4\pi {\alpha }_c)=3.2\\ \mathrm{nm})\end{array}$
Angle scans: particles against films	$I_{particle}\left({\alpha }_i<{\alpha }_c\right)\approx 2I_{particle}\left({\alpha }_i>{\alpha }_c\right)$	$I_{film}\text{peaks near}{\alpha }_c$	$\begin{array}{r}I:fluorescencefromresidueontopofthe\\ reflectingsurfaceorfromaplatedfilm;\\ Dieboldetal.:particulateintensity\\ roughlyconstantupto{\theta }_{c}andabouthalf\\ aboveit,platedintensityrisingsharply\\ near{\theta }_c,1.3\mathrm{mrad}chosensobothgive\\ nearlyequalsignals;standing-wave\\ doublingfromincidentandreflectedbeams\\ (backgroundknowledge,Klockenkamperand\\ vonBohlen)\end{array}$ $\begin{array}{r}(computed:1.3\mathrm{mrad}is0.73oftheMoK\alpha \\ criticalangleofSi)\end{array}$

Detection and Quantification

Name	Formula	Related Formulae	Variables/Constants
Detection limit	$DL=\frac{3\sqrt{N_B}}{N_S}{C}_{std}$	$DL\propto \frac{1}{\sqrt{t}}$	$DL:detectionlimit$ $N_B:backgroundcounts$ $N_S:netcountsfromastandard$ $C_{std}:standardcoverage$ $\begin{array}{r}t:countingtime;3-sigmaform(background\\ knowledge,Jenkins);Kohno:TXRF1\times 10^9\\ atoms/c{\mathrm{m}}^2,VPD-ICP-MSandAAS1\times 10^7,logic\\ controlnear1\times 10^{10}andmemoryorCIS1\times 10^9;\\ Dieboldetal.:below1\times 10^{10}atoms/c{\mathrm{m}}^{2}for\\ FeandCu,2percentreproducibilityin\\ thelow1\times 10^{10}range(seetheQ/A)\end{array}$ $\begin{array}{r}(assumed:N_S=1\times 10^{4}froma1\times 10^{12}atoms/c{\mathrm{m}}^2\\ standard,N_B=400;computed:DL=6\times 10^9\\ atoms/c{\mathrm{m}}^2)\end{array}$
Calibration and quantification	$C_x=C_{std}\frac{I_x}{I_{std}}\frac{S_{std}}{S_x}$	$S_x\propto {\omega }_K\tau \left(E_0\right)\epsilon \left(E_x\right)$	$C_x:unknowncoverage$ $I:netintensity$ $\begin{array}{r}S:relativeelementalsensitivity;Diebold\\ etal.:NiandCudosestandardsof\\ 20.4\times 10^{12}and23.0\times 10^{12}atoms/c{\mathrm{m}}^2,afactor\\ 1.5moreCuononeinstrumentthan\\ another;relative-sensitivityscaling\\ (backgroundknowledge,Klockenkamperand\\ vonBohlen)\end{array}$ $\begin{array}{r}(myreading:thefactor-1.5offsetshows\\ whystandardsmustmatchthedeposittype)\end{array}$
Local TXRF against wafer-average VPD	${\bar{C}}_{VPD}=\frac{1}{A_w}\int C\left(x,y\right)dA$	$D{L}_{VPD-TXRF}\approx D{L}_{TXRF}\frac{A_{spot}}{A_w}(\text{ideal})$	$\begin{array}{r}{\bar{C}}_{VPD}:wafer-averagecoverageafter\\ vapour-phasedecomposition\end{array}$ $A_w:waferarea$ $\begin{array}{r}{A}_{spot}:analysedarea;Kohno:1\times 10^{10}atoms/c{\mathrm{m}}^2\\ Featonespotreadingas1\times 10^{8}by\\ VPD-ICP-MS,sweepingTXRFcoveringa6\\ inchwaferinabout30minutes,edge\\ measurement,4and6inchSiC;collection\\ relation(backgroundknowledge,\\ KlockenkamperandvonBohlen)\end{array}$ $\begin{array}{r}(assumed:1\mathrm{c}{\mathrm{m}}^{2}spot;computed:a300\mathrm{mm}\\ waferis707\mathrm{c}{\mathrm{m}}^2,ideallylowering1\times 10^{9}to\\ 1.4\times 10^{6}atoms/c{\mathrm{m}}^2)\end{array}$

Important Questions

Ques: How does XRF identify elements?

By the energies of characteristic X-ray lines. An incident photon above an element’s absorption edge ejects an inner electron, and an outer electron fills the hole, emitting a photon whose energy is fixed by the atom (background knowledge, Jenkins). Moseley’s law, $E_{K\alpha }\approx \frac{3}{4}{R}_y(Z-1{)}^2$, gives Fe at 6.38, Ni at 7.44 and Cu at 8.00 $\mathrm{keV}$, within 1 per cent of the tabulated 6.40, 7.48 and 8.05 $\mathrm{keV}$ (computed). Light elements are harder because the fluorescence yield falls steeply: about 0.037 for Si against 0.31 for Fe (computed approximation). Kohno chose W-L-beta at 9.67 $\mathrm{keV}$, which excites transition metals but lies 0.72 $\mathrm{keV}$ below the Ga-K edge, so GaN substrates do not swamp the spectrum (computed). Reference: R. Klockenkamper and A. von Bohlen, Total-Reflection X-Ray Fluorescence Analysis and Related Methods, 2nd ed., Wiley 2015, and R. Jenkins, X-Ray Fluorescence Spectrometry, 2nd ed., Wiley 1999 (background knowledge; not opened); H. Kohno, ‘Evaluation of contamination of power semiconductor device wafers by total reflection X-ray fluorescence spectrometer’, The Rigaku Journal 29(1), 9 (2013) (fetch-tool summary).

Ques: Why is TXRF so much more sensitive than ordinary XRF?

Because total reflection removes most of the substrate background. Below the critical angle the beam enters the wafer only a few nanometres: Kohno gives about 5 $\mathrm{nm}$, and Diebold et al. about 50 $\mathring{\mathrm{A}}$ at 1.3 $\mathrm{mrad}$. The limiting depth $\lambda /(4\pi {\alpha }_c)$ is 3.2 $\mathrm{nm}$ for Mo K-alpha on silicon (background knowledge, Klockenkamper and von Bohlen; computed). Substrate fluorescence and Compton scatter therefore drop by orders of magnitude, while atoms on the surface see both the incident and reflected beams, nearly doubling their excitation (background knowledge). The detector can sit close to the wafer, collecting a large solid angle. Diebold et al. also note reports of penetration above 100 $\mathrm{nm}$, which applies at or above the critical angle (my reading). Reference: H. Kohno, ‘Evaluation of contamination of power semiconductor device wafers by total reflection X-ray fluorescence spectrometer’, The Rigaku Journal 29(1), 9 (2013) (fetch-tool summary); A. C. Diebold, P. Maillot, M. Gordon, J. Baylis, J. Chacon, R. Witowski, H. Arlinghaus, J. A. Knapp and B. L. Doyle, ‘Evaluation of Surface Analysis Methods for Characterization of Trace Metal Surface Contaminants Found in Silicon IC Manufacturing’, Sandia report SAND-91-1083C (about 1991) (fetch-tool summary; OCR-degraded); R. Klockenkamper and A. von Bohlen, Total-Reflection X-Ray Fluorescence Analysis and Related Methods, 2nd ed., Wiley 2015, and R. Jenkins, X-Ray Fluorescence Spectrometry, 2nd ed., Wiley 1999 (background knowledge; not opened).

Ques: Do Diebold’s critical angles agree with the reflectometry values?

Yes, once scaled for wavelength. Diebold et al. give critical angles of 6.1 $\mathrm{arcmin}$ for silicon and 5.9 $\mathrm{arcmin}$ for SiO2 with molybdenum radiation. Since ${\alpha }_c=\sqrt{2\delta }$ is proportional to wavelength (XRR page), the Cu K-alpha values of 0.221 and 0.215 ${}^{\circ }$ scale to 1.78 $\mathrm{mrad}$ (6.12 $\mathrm{arcmin}$) and 1.73 $\mathrm{mrad}$ (5.95 $\mathrm{arcmin}$) at 0.7107 $\mathring{\mathrm{A}}$ (computed), matching within 0.5 per cent. Their 1.3 $\mathrm{mrad}$ incidence is 0.73 of the silicon critical angle (computed), safely in total reflection. For W-L-beta at 1.282 $\mathring{\mathrm{A}}$, as Kohno used, silicon’s critical angle rises to 3.21 $\mathrm{mrad}$ (computed), so incidence angles must be reset when the excitation line changes. Reference: A. C. Diebold, P. Maillot, M. Gordon, J. Baylis, J. Chacon, R. Witowski, H. Arlinghaus, J. A. Knapp and B. L. Doyle, ‘Evaluation of Surface Analysis Methods for Characterization of Trace Metal Surface Contaminants Found in Silicon IC Manufacturing’, Sandia report SAND-91-1083C (about 1991) (fetch-tool summary; OCR-degraded); X-Ray Reflectometer (XRR) page of this vault; H. Kohno, ‘Evaluation of contamination of power semiconductor device wafers by total reflection X-ray fluorescence spectrometer’, The Rigaku Journal 29(1), 9 (2013) (fetch-tool summary).

Ques: Is the TXRF detection limit $1\times 10^9$ or $1\times 10^{10}$ atoms per square centimetre?

Kohno lists $1\times 10^9$ $atoms/c{\mathrm{m}}^2$ for TXRF, while Diebold et al. report below $1\times 10^{10}$ $atoms/c{\mathrm{m}}^2$ for Fe and Cu with 2 per cent reproducibility in the low $1\times 10^{10}$ range. The difference is mainly instrumental generation: Diebold’s evaluation dates from about 1991, and Kohno’s from 2013 with monochromatized W-L-beta excitation (my reading). The 3-sigma limit $3\sqrt{N_B}{C}_{std}/N_S$ gives $6\times 10^9$ $atoms/c{\mathrm{m}}^2$ for an assumed $1\times 10^4$ net counts from a $1\times 10^{12}$ standard over 400 background counts (computed), and it improves as the square root of counting time, so a few-fold longer count reaches the mid-$1\times 10^9$ range. For current tools $1\times 10^9$ is more likely, matching Kohno’s control targets for memory and image sensors. Reference: H. Kohno, ‘Evaluation of contamination of power semiconductor device wafers by total reflection X-ray fluorescence spectrometer’, The Rigaku Journal 29(1), 9 (2013) (fetch-tool summary); A. C. Diebold, P. Maillot, M. Gordon, J. Baylis, J. Chacon, R. Witowski, H. Arlinghaus, J. A. Knapp and B. L. Doyle, ‘Evaluation of Surface Analysis Methods for Characterization of Trace Metal Surface Contaminants Found in Silicon IC Manufacturing’, Sandia report SAND-91-1083C (about 1991) (fetch-tool summary; OCR-degraded); R. Klockenkamper and A. von Bohlen, Total-Reflection X-Ray Fluorescence Analysis and Related Methods, 2nd ed., Wiley 2015, and R. Jenkins, X-Ray Fluorescence Spectrometry, 2nd ed., Wiley 1999 (background knowledge; not opened).

Ques: How can angle scans tell particles from films?

By how fluorescence changes across the critical angle. Diebold et al. found that residue or particles on top of the wafer give roughly constant intensity up to the critical angle and about half above it, because below it they sit in both incident and reflected beams (background knowledge, Klockenkamper and von Bohlen). Plated or uniformly distributed contamination instead rises sharply as the angle approaches the critical angle and falls beyond it, since the evanescent field at the interface peaks there. They chose 1.3 $\mathrm{mrad}$ for Mo radiation so both types give nearly equal fluorescence, letting residue standards calibrate plated samples. Diebold et al. also report a factor of 1.5 difference in Cu between two instruments, so calibrations must match the deposit form. Reference: A. C. Diebold, P. Maillot, M. Gordon, J. Baylis, J. Chacon, R. Witowski, H. Arlinghaus, J. A. Knapp and B. L. Doyle, ‘Evaluation of Surface Analysis Methods for Characterization of Trace Metal Surface Contaminants Found in Silicon IC Manufacturing’, Sandia report SAND-91-1083C (about 1991) (fetch-tool summary; OCR-degraded); R. Klockenkamper and A. von Bohlen, Total-Reflection X-Ray Fluorescence Analysis and Related Methods, 2nd ed., Wiley 2015, and R. Jenkins, X-Ray Fluorescence Spectrometry, 2nd ed., Wiley 1999 (background knowledge; not opened).

Ques: When is VPD needed instead of direct TXRF?

When contamination is below the direct limit or must be averaged over the wafer. Kohno lists $1\times 10^7$ $atoms/c{\mathrm{m}}^2$ for VPD-ICP-MS against $1\times 10^9$ for TXRF, but notes that VPD gives only a wafer average: $1\times 10^{10}$ $atoms/c{\mathrm{m}}^2$ of Fe at one spot reads as $1\times 10^8$. Collecting a 300 $\mathrm{mm}$ wafer of 707 $\mathrm{c}{\mathrm{m}}^2$ into a droplet analysed over an assumed 1 $\mathrm{c}{\mathrm{m}}^2$ would ideally lower a $1\times 10^9$ limit to $1.4\times 10^6$ $atoms/c{\mathrm{m}}^2$ (computed); reagent blanks and collection efficiency keep real VPD-TXRF limits higher (my reading). Direct TXRF is non-destructive and needs no pretreatment, and Kohno’s sweeping mode maps a 6 inch wafer in about 30 minutes, keeping spatial information that VPD loses. Reference: H. Kohno, ‘Evaluation of contamination of power semiconductor device wafers by total reflection X-ray fluorescence spectrometer’, The Rigaku Journal 29(1), 9 (2013) (fetch-tool summary); R. Klockenkamper and A. von Bohlen, Total-Reflection X-Ray Fluorescence Analysis and Related Methods, 2nd ed., Wiley 2015, and R. Jenkins, X-Ray Fluorescence Spectrometry, 2nd ed., Wiley 1999 (background knowledge; not opened).

References

1. R. Klockenkamper and A. von Bohlen, Total-Reflection X-Ray Fluorescence Analysis and Related Methods, 2nd ed., Wiley, 2015; R. Jenkins, X-Ray Fluorescence Spectrometry, 2nd ed., Wiley, 1999 (cited from background knowledge).
2. H. Kohno, “Evaluation of contamination of power semiconductor device wafers by total reflection X-ray fluorescence spectrometer,” The Rigaku Journal, vol. 29, no. 1, pp. 9-14, 2013. Available: https://resources.rigaku.com/hubfs/2024%20Rigaku%20Global%20Site/Resource%20Hub/Knowledge%20Library/Rigaku%20Journals/Volume%2029(1)%20-%20Winter%202013/RJ29-1_9-14.pdf
3. A. C. Diebold, P. Maillot, M. Gordon, J. Baylis, J. Chacon, R. Witowski, H. Arlinghaus, J. A. Knapp and B. L. Doyle, “Evaluation of Surface Analysis Methods for Characterization of Trace Metal Surface Contaminants Found in Silicon IC Manufacturing,” Sandia National Laboratories report SAND-91-1083C, about 1991. Available: https://digital.library.unt.edu/ark:/67531/metadc1099222/m2/1/high_res_d/5987145.pdf
4. X-Ray Reflectometer (XRR) page of this vault.

Related pages in this vault: X-Ray Reflectometer (XRR), Auger Electron Spectrometer (AES), X-Ray Photoelectron Spectrometer (XPS), Scanning Electron Microscope (SEM), X-Ray Diffractometer (XRD and HRXRD), Rutherford Backscattering Spectrometer (RBS), Laser-Scattering Particle Inspection, Transmission Electron Microscope (TEM and STEM), Picosecond Ultrasonic Film Metrology, RCA Wet Bench.