Overlay Metrology Tool

1. Theory

• Definition: An overlay metrology tool measures the lateral misregistration between a pattern and the layer beneath it, using dedicated targets in the scribe line or in-die, so lithography can be corrected wafer to wafer (Levinski et al.; Xu et al.).
• Image-based overlay (IBO): A microscope images nested box or bar targets from both layers and compares their centres (Levinski et al.).
• Diffraction-based overlay (DBO): Stacked gratings diffract unequally into +1 and -1 orders when shifted; pads with programmed biases calibrate this asymmetry into overlay (Xu et al.).
• Accuracy: Tool-induced shift, target asymmetry and process damage cause errors that must be separated from true overlay (Levinski et al.; Xu et al.).

2. Working Principle

• IBO: Bright-field imaging of box-in-box or advanced imaging targets, measured at 0 and 180 degree wafer rotations to remove TIS (Levinski et al.).
• DBO: Measuring diffracted intensities from biased grating pads at selected wavelengths and polarizations (Xu et al.).
• Sampling: Several fields per wafer and wafers per lot feed a wafer and field model of translation, scaling and rotation (Levinski et al.; Adel et al.).
• Recipe optimization: Wavelength chosen away from swing-curve zero crossings for high sensitivity (Xu et al.).

3. Applications

• Lithography feedback: Scanner corrections for offset, rotation and scale (Adel et al.).
• Process monitoring: Detecting mark asymmetry from CMP or etch (Xu et al.).
• Tool matching: TIS and TMU tracking across metrology tools (Levinski et al.).

Image-Based Overlay and Uncertainty

Name	Formula	Related Formulae	Variables/Constants
Image-based overlay (box-in-box)	$O{V}_x=\frac{1}{2}\left[\frac{c_1+c_3}{2}-\frac{c_2+c_4}{2}\right]$	$O{V}_x=x_{c,top}-x_{c,bottom}$	$\begin{array}{r}O{V}_x:overlayerroralongx,c_{1}to{c}_4:\\ edge-to-edgeseparationsbetweeninnerand\\ outerboxedgesontheleftandright\\ sides\end{array}$ $\begin{array}{r}{x}_c:centreofeachlaye{r}^{\prime }smark;Levinski\\ etal.:halfthedifferenceofaveraged\\ separations,20by20\mu \mathrm{m}targetina40by\\ 40\mu \mathrm{m}field,8by8samplinggrid,25-wafer\\ lots;Adeletal.:overlayasthe\\ misregistrationbetweenthecentresof\\ symmetryofthetwolayers\end{array}$ $\begin{array}{r}(assumed:leftseparationsaverage5.006\mu \mathrm{m}\\ andright4.994\mu \mathrm{m};computed:O{V}_x=6\mathrm{nm})\end{array}$
Tool-induced shift	$TIS=\frac{OV\left(0^{\circ }\right)+OV\left(180^{\circ }\right)}{2}$	$O{V}_{true}=\frac{OV\left(0^{\circ }\right)-OV\left(180^{\circ }\right)}{2}$	$\begin{array}{r}TIS:tool-inducedshift,OV(0),OV(180):\\ overlaymeasuredwiththewaferat0and\\ 180degrees;Levinskietal.:TIS\\ quantifiesopticalaberrationeffects,is\\ targetdependent,andisisolatedby\\ averagingbecausetrueoverlaychanges\\ signonrotation;Adeletal.:TISasthe\\ averagebeforeandafterrotation;true\\ overlayashalfthedifference(computed,\\ sincetrueoverlayreversessign)\end{array}$ $\begin{array}{r}(assumed:3.2and-2.4\mathrm{nm};computed:TIS=\\ 0.4\mathrm{nm}andO{V}_{t}rue=2.8\mathrm{nm})\end{array}$
Total measurement uncertainty	$TMU=\sqrt{{\sigma }_{prec}^2+{\sigma }_{TIS}^2+{\sigma }_{match}^2}$	${\sigma }_{TIS}=\mathrm{std}\left[\frac{OV\left(0^{\circ }\right)+OV\left(180^{\circ }\right)}{2}\right]$	${\sigma }_{prec}:repeatability$ ${\sigma }_{TIS}:TISvariability$ ${\sigma }_{match}:tool-to-toolmatching$ $\begin{array}{r}\mathrm{std}:standarddeviationoverrepeated\\ targets;Bringoltzetal.:precision,TIS\\ andmatchingcomprisethetotal\\ measurementuncertainty;quadraturesum\\ (myreading);Adeletal.:TISvariability\\ definedseparately;Xuetal.:DBOTMUin\\ thesub-nanometrerangecitingpriorwork\end{array}$ $\begin{array}{r}(assumed:0.3,0.4and0.3\mathrm{nm};computed:\\ TMU=0.58\mathrm{nm})\end{array}$

Diffraction-Based Overlay

Name	Formula	Related Formulae	Variables/Constants
Diffraction-based overlay signal	$Asy=I_{+1}-I_{-1}$	$\Delta R=R\left(x+d\right)-R\left(x-d\right)\approx d\frac{\partial R}{\partial x}$	$\begin{array}{r}Asy:asymmetrybetween+1and-1\\ diffractedorders\end{array}$ $d:overlayshift$ $\begin{array}{r}R:reflection;Xuetal.:asymmetry\\ definitionandreflection-difference\\ relation,1:1denseline-spacegratings\\ withhorizontallinesforyandvertical\\ linesforx,effectivelyzeroTISforDBO\end{array}$ $\begin{array}{r}(myreading:aperfectlyalignedsymmetric\\ gratingstackdiffractsequallyinto+1\\ and-1,soanyasymmetrymeasuresthe\\ shift)\end{array}$
Biased pads and overlay extraction	$\Delta I_{\pm d}=k\left(d\pm d^{\prime }\right)$	$d=d^{\prime }\frac{\Delta I_{+d}+\Delta I_{-d}}{\Delta I_{+d}-\Delta I_{-d}},k=\frac{\Delta I_{+d}-\Delta I_{-d}}{2d^{\prime }}$	$\begin{array}{r}\Delta I_{\pm d}:asymmetryofthe+d^{\prime }and-d^{\prime }biased\\ pads,d^{\prime }:programmedbias\end{array}$ $\begin{array}{r}k:overlaysensitivity;Xuetal.:linear\\ model\Delta I=kdwithksetbystackand\\ measurementparameters,overlayrelation,\\ kprintedas(\Delta I_{+d}-\Delta I_{-d})/d^{\prime }(seetheQ/A)\end{array}$ $\begin{array}{r}(assumed:d^{\prime }=20\mathrm{nm},\Delta I_{+d}=0.30,\Delta I_{-d}=\\ -0.10;computed:d=10\mathrm{nm}andk=0.010\\ pernm)\end{array}$
Bottom-mark asymmetry error	$\Delta I_{\pm d}=k\left(d\pm d^{\prime }\right)+\Delta I_{BMA}$	$\Delta OV=\frac{\Delta I_{BMA}}{k}$	$\begin{array}{r}\Delta I_{BMA}:asymmetryfromadeformedbottom\\ grating\end{array}$ $\begin{array}{r}\Delta OV:resultingoverlayerror;Xuetal.:\\ relations,largerkreducingtheerror,\\ FDTDona1by1\mathrm{n}{\mathrm{m}}^{2}grid,400to800\mathrm{nm}\\ wavelengthsweep,offsetsfrom-24to+24\\ \mathrm{nm},avoidingswing-curvezerocrossings\end{array}$ $\begin{array}{r}(assumed:\Delta I_{BMA}=0.005;computed:0.5\mathrm{nm}\\ erroratk=0.010pernm,halvedifk\\ doubles)\end{array}$

Models, Recipes and Budgets

Name	Formula	Related Formulae	Variables/Constants
Wafer-level overlay model	$dx=T_x+M_{x}x-R_{x}y+r_x$	$dy=T_y+M_{y}y+R_{y}x+r_y$	$T:translation$ $M:magnification(scaling)inppm$ $R:rotationinmicroradians$ $\begin{array}{r}r:residual;Adeletal.:offset,rotation\\ andscaleascorrectables;explicitlinear\\ form(myreading);Levinskietal.:\\ measurementsperlotandperfield\\ location\end{array}$ $\begin{array}{r}(computed:0.1\mathrm{ppm}scalingat150\mathrm{mm}\\ radiusgives15\mathrm{nm},and0.1\mu \mathrm{rad}rotation\\ gives15\mathrm{nm})\end{array}$
Swing curve and wavelength choice	$k\left(\lambda \right)=\frac{\partial Asy}{\partial d}$	$k\left(\lambda \right)\approx 0\Rightarrow \text{avoid}$	$\begin{array}{r}k(\lambda ):sensitivityasafunctionof\\ wavelength;Xuetal.:zero-crossingareas\\ oftheswingcurvetobeavoided,high-k\\ recipeslesssensitivetomarkasymmetry;\\ OCDpage:samerigoroussolversas\\ scatterometry\end{array}$ $\begin{array}{r}(computed:withfixed\Delta I_{BMA},theerror\\ growsas1/k,tenfoldwhenkfallstoone\\ tenth)\end{array}$
Overlay budget and metrology share	$O{V}_{total}=\sqrt{{\sum }_{i}O{V}_i^2}$	$O{V}_{meas}^2=O{V}_{true}^2+TM{U}^2$	$\begin{array}{r}O{V}_i:independentcontributors(scanner,\\ process,mask,metrology);root-sum-square\\ budget(myreading);Levinskietal.:TIS\\ correctionaspartofaccurateoverlay;Xu\\ etal.:sub-nmDBOTMU\end{array}$ $\begin{array}{r}(computed:a0.58\mathrm{nm}TMUona3\mathrm{nm}true\\ overlayreadsas3.06\mathrm{nm},a2percent\\ inflation)\end{array}$

Important Questions

Ques: How does box-in-box overlay measurement work?

By comparing the centres of nested marks from two layers. Levinski et al. describe the overlay along x as half the difference between the averaged inner-to-outer edge separations on the two sides, $O{V}_x=\frac{1}{2}[(c_1+c_3)/2-(c_2+c_4)/2]$, with an example target of 20 by 20 $\mu \mathrm{m}$ in a 40 by 40 $\mu \mathrm{m}$ field. If the left separations average 5.006 $\mu \mathrm{m}$ and the right 4.994 $\mu \mathrm{m}$, the overlay is 6 $\mathrm{nm}$ (assumed values; computed). The same logic in y uses the top and bottom edges. Because edges are found by imaging, the result depends on edge contrast and optical aberrations, which is why tool-induced shift must be removed and why measurement is repeated over sampling grids, 8 by 8 positions in their example. Reference: V. Levinski et al., ‘Apparatus and methods for reducing tool-induced shift during overlay metrology’, US patent 7,433,039 (priority 2004) (fetch-tool summary); M. Adel et al., ‘Optimized Overlay Metrology Marks: Theory and Experiment’, IEEE Trans. Semicond. Manuf. 17(2), 2004: overlay as misregistration between the centres of symmetry of the two layers, TIS as the average of measurements before and after 180 degree rotation, dynamic precision and TIS variability, offset, rotation and scale correctables (fetch-tool summary).

Ques: How is tool-induced shift removed?

By measuring at 0 and 180 degree wafer rotations. Levinski et al. define $TIS=[OV(0^{\circ })+OV(180^{\circ })]/2$: rotating the wafer reverses the true overlay but leaves the tool’s aberration-induced offset unchanged, so averaging isolates TIS. The true overlay is half the difference (computed), consistent with Adel et al.’s definition of TIS as the average of the two measurements. Measurements of 3.2 and -2.4 $\mathrm{nm}$ give a TIS of 0.4 $\mathrm{nm}$ and a true overlay of 2.8 $\mathrm{nm}$ (assumed values; computed). They note TIS depends on optical aberrations and is target dependent, so it must be characterized per layer. Xu et al. describe DBO as having effectively zero TIS, which is likely an idealization, since Bringoltz et al. list target asymmetries that still bias overlay (my reading). Reference: V. Levinski et al., ‘Apparatus and methods for reducing tool-induced shift during overlay metrology’, US patent 7,433,039 (priority 2004) (fetch-tool summary); M. Adel et al., ‘Optimized Overlay Metrology Marks: Theory and Experiment’, IEEE Trans. Semicond. Manuf. 17(2), 2004: overlay as misregistration between the centres of symmetry of the two layers, TIS as the average of measurements before and after 180 degree rotation, dynamic precision and TIS variability, offset, rotation and scale correctables (fetch-tool summary); B. Xu, Q. Wu, L. Dong and Y. Wei, ‘Selection of DBO measurement wavelength for bottom mark asymmetry based on FDTD method’, J. Semicond. 40, 122403 (2019) (fetch-tool summary); B. Bringoltz, T. Marciano et al. (KLA), ‘Accuracy In Optical Overlay Metrology’, Semiconductor Engineering, 18 Jan 2017: precision, TIS and matching taken to comprise the total measurement uncertainty; target asymmetries include sidewall-angle asymmetry, top and bottom tilts, fin-depth asymmetries and pad-to-pad variations (fetch-tool summary).

Ques: How do biased gratings give overlay in DBO?

By calibrating asymmetry against known offsets. Xu et al. define asymmetry as $I_{+1}-I_{-1}$ and model it as linear in shift, $\Delta I=kd$. Two pads with programmed biases of $+d^{\prime }$ and $-d^{\prime }$ give $\Delta I_{\pm d}=k(d\pm d^{\prime })$, so $d=d^{\prime }(\Delta I_{+d}+\Delta I_{-d})/(\Delta I_{+d}-\Delta I_{-d})$, independent of k. With $d^{\prime }$ = 20 $\mathrm{nm}$ and asymmetries of 0.30 and -0.10, the overlay is 10 $\mathrm{nm}$ and k is 0.010 per nm (assumed values; computed). The method works without a rigorous model because k is measured in situ, whereas OCD-type modelling (OCD page) is needed only to choose robust wavelengths. Their FDTD swept 400 to 800 $\mathrm{nm}$ and offsets of -24 to +24 $\mathrm{nm}$. Reference: B. Xu, Q. Wu, L. Dong and Y. Wei, ‘Selection of DBO measurement wavelength for bottom mark asymmetry based on FDTD method’, J. Semicond. 40, 122403 (2019) (fetch-tool summary); Optical CD Scatterometer (OCD) page of this vault.

Ques: Is the DBO sensitivity k equal to the asymmetry difference divided by d’ or by 2d’?

The summary of Xu et al. gives $k=(\Delta I_{+d}-\Delta I_{-d})/d^{\prime }$, but subtracting their own model $\Delta I_{\pm d}=k(d\pm d^{\prime })$ gives $\Delta I_{+d}-\Delta I_{-d}=2k{d}^{\prime }$, so $k=(\Delta I_{+d}-\Delta I_{-d})/(2d^{\prime })$ (computed). The factor-2 form is more likely correct for pads biased by $\pm d^{\prime }$; the printed form would hold if $d^{\prime }$ denoted the full separation between the pads (my reading). The overlay formula itself is unaffected, since k cancels. The factor matters for error estimates: the bottom-mark error $\Delta OV=\Delta I_{BMA}/k$ is 0.5 $\mathrm{nm}$ for $\Delta I_{BMA}$ = 0.005 at k = 0.010 per nm, but would be misquoted by a factor of two with the other k (assumed values; computed). The full paper should be checked before quoting its k values. Reference: B. Xu, Q. Wu, L. Dong and Y. Wei, ‘Selection of DBO measurement wavelength for bottom mark asymmetry based on FDTD method’, J. Semicond. 40, 122403 (2019) (fetch-tool summary).

Ques: Why must DBO wavelengths avoid swing-curve zero crossings?

Because asymmetry errors are divided by the sensitivity. Xu et al. write the measured asymmetry with a bottom-mark term, $\Delta I_{\pm d}=k(d\pm d^{\prime })+\Delta I_{BMA}$, giving an overlay error $\Delta I_{BMA}/k$. As wavelength changes, thin-film interference in the stack makes k oscillate through zero, the swing curve; near a zero crossing a fixed mark asymmetry produces a huge error, tenfold larger when k falls to one tenth (computed). They therefore recommend avoiding zero-crossing regions and choosing high-k recipes, which are less sensitive to mark asymmetry. Bringoltz et al. list sidewall-angle asymmetry, top and bottom tilts, fin-depth asymmetries and pad-to-pad variations among the asymmetries that bias overlay, so recipes are rechecked whenever upstream processes change. Reference: B. Xu, Q. Wu, L. Dong and Y. Wei, ‘Selection of DBO measurement wavelength for bottom mark asymmetry based on FDTD method’, J. Semicond. 40, 122403 (2019) (fetch-tool summary); B. Bringoltz, T. Marciano et al. (KLA), ‘Accuracy In Optical Overlay Metrology’, Semiconductor Engineering, 18 Jan 2017: precision, TIS and matching taken to comprise the total measurement uncertainty; target asymmetries include sidewall-angle asymmetry, top and bottom tilts, fin-depth asymmetries and pad-to-pad variations (fetch-tool summary).

Ques: How do overlay measurements feed scanner corrections?

Through a wafer and field model. Measured overlay at many sites is fitted with translation, scaling and rotation terms, $dx=T_x+M_{x}x-R_{x}y+r_x$ and similarly for y (Adel et al. name offset, rotation and scale as correctables; the explicit form is my reading). At a 150 $\mathrm{mm}$ wafer radius, 0.1 $\mathrm{ppm}$ of scaling or 0.1 $\mu \mathrm{rad}$ of rotation each produce 15 $\mathrm{nm}$ at the edge (computed), so these terms dominate uncorrected overlay. Levinski et al. describe sampling over lots of typically 25 wafers. Measurement uncertainty adds in quadrature to true overlay: a 0.58 $\mathrm{nm}$ TMU on 3 $\mathrm{nm}$ of true overlay reads as 3.06 $\mathrm{nm}$, a 2 per cent inflation (computed), so TMU must stay well below the overlay being controlled (my reading). Reference: M. Adel et al., ‘Optimized Overlay Metrology Marks: Theory and Experiment’, IEEE Trans. Semicond. Manuf. 17(2), 2004: overlay as misregistration between the centres of symmetry of the two layers, TIS as the average of measurements before and after 180 degree rotation, dynamic precision and TIS variability, offset, rotation and scale correctables (fetch-tool summary); V. Levinski et al., ‘Apparatus and methods for reducing tool-induced shift during overlay metrology’, US patent 7,433,039 (priority 2004) (fetch-tool summary).

References

1. V. Levinski et al., “Apparatus and methods for reducing tool-induced shift during overlay metrology,” US patent 7,433,039 (priority June 2004). Available: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/7433039
2. M. Adel, M. Ghinovker, B. Golovanevsky, P. Izikson, E. Kassel, D. Yaffe, A. M. Bruckstein, R. Goldenberg, Y. Rubner and M. Rudzsky, “Optimized overlay metrology marks: theory and experiment,” IEEE Trans. Semicond. Manuf., vol. 17, no. 2, 2004. Available: https://freddy.cs.technion.ac.il/wp-content/uploads/2017/12/Optimized-Overlay-Metrology-Marks.pdf
3. B. Bringoltz, T. Marciano et al., “Accuracy in Optical Overlay Metrology,” Semiconductor Engineering, Jan. 18, 2017. Available: https://semiengineering.com/accuracy-in-optical-overlay-metrology
4. B. Xu, Q. Wu, L. Dong and Y. Wei, “Selection of DBO measurement wavelength for bottom mark asymmetry based on FDTD method,” Journal of Semiconductors, vol. 40, no. 12, 122403, 2019. Available: https://www.researching.cn/ArticlePdf/m00098/2019/40/12/122403.pdf
5. Optical CD Scatterometer (OCD) page of this vault.

Related pages in this vault: Optical CD Scatterometer (OCD), Wafer Geometry Gauge, CD-SEM, Optical Microscope, Patterned-Wafer Optical Inspection, Laser-Scattering Particle Inspection, E-Beam Inspection and Defect Review, Gauge Repeatability and Reproducibility (Gauge R&R), Statistical Process Control (SPC), Tool Matching and Total Measurement Uncertainty (TMU), High-NA DUV Immersion Scanner, Resolution Enhancement and Multiple Patterning, Nanoimprint Lithography Tool.