Laser Interferometric Endpoint

1. Theory

• Definition: Laser interferometric endpoint detection shines a laser on the wafer during etch or deposition and records the reflected intensity, which oscillates as the film thins because reflections from its top and bottom interfere (Oxford page; US 4,454,001).
• Transparent films: Each cycle at normal incidence removes $\lambda /2n$ of film (Oxford page).
• Patterned and opaque material: Interference between light from the mask top and the etched surface gives one cycle per $\lambda /2$ of depth (US 4,454,001).
• Endpoint: Oscillation stops when the film clears, and the phase predicts remaining thickness before it clears (background knowledge, Heavens).

2. Working Principle

• Laser: He-Ne at 632.8 $\mathrm{nm}$ or diode lasers at 670, 905 or 980 $\mathrm{nm}$ at normal incidence (US 4,454,001; EPFL page).
• Optics: Quarter-wave plate and polarizing beam splitter separate incident and reflected beams onto a photodetector (US 4,454,001).
• Placement: The spot is aimed at a chosen feature or test area before each run (Oxford page).
• Analysis: Fringe counting or sinusoid fitting gives rate, depth and stop time (EPFL page; background knowledge).

3. Applications

• Dielectric etch to remaining thickness: Stopping on a target oxide or nitride thickness (Oxford page; background knowledge).
• Silicon trench depth: Deep etch rate monitoring through masks (US 4,454,001).
• Resist and hard-mask etch: Rate and uniformity monitoring (background knowledge).
• Low open area etches: Where OES signals are too weak (Oxford page; Optical Emission Spectroscopy Endpoint (OES) page).

Fringe Relations

Name	Formula	Related Formulae	Variables/Constants
Transparent-film fringe period	$\Delta d_{cycle}=\frac{\lambda }{2n}$	$d\left(t\right)=d_0-N_{fringe}\frac{\lambda }{2n}$	$\begin{array}{r}\Delta d_{cycle}:thicknessremovedperreflectance\\ cycleatnormalincidence\end{array}$ $n:filmindex$ $\begin{array}{r}{N}_{fringe}:cyclescounted;Oxfordpage:each\\ cyclecorrespondsto\lambda /2n;US4,454,001:\\ the\lambda /2nrelationofearlierworkfor\\ transparentfilms,contrastedwithitsown\\ method\end{array}$ $\begin{array}{r}(assumed:SiO2n=1.456at670\mathrm{nm},1.457\\ at632.8\mathrm{nm},Si3N42.0,resist1.6;\\ computed:230,217,168and209\mathrm{nm}per\\ cycle)\end{array}$
Patterned-area (opaque) fringe period	$\Delta d_{cycle}=\frac{\lambda }{2}$	$\text{depth}=N_{fringe}\frac{\lambda }{2},ER=\frac{\lambda /2}{T_{cycle}}$	$T_{cycle}:timeperperiod$ $\begin{array}{r}ER:etchrate;US4,454,001:normal\\ incidenceonapattern,zeroth-order\\ reflection,oneperiodper\lambda /2ofdepth,\\ He-Neat6328\mathring{\mathrm{A}},about1mmspot,\\ quarter-waveplateandpolarizingbeam\\ splitter,patternsofabout0.5to50\mu \mathrm{m}\\ forvisiblelight,Example1with3.13\\ periodsfor1.025\mu \mathrm{m}inSi(errorunder4\\ percent),Example2with4.26periodsfor\\ 1.27\mu \mathrm{m}(about6percent)\end{array}$ $\begin{array}{r}(computed:316.4\mathrm{nm}perperiod;0.990\mu \mathrm{m}\\ (-3.4percent)and1.348\mu \mathrm{m}(+6.1per\\ cent))\end{array}$
Fringe rate	$f_{fringe}=\frac{2nER}{\lambda }$	$T_{cycle}=\frac{1}{f_{fringe}}$	$\begin{array}{r}{f}_{fringe}:oscillationfrequencyofthe\\ reflectedsignal;relation(background\\ knowledge,Heavens);EPFLpage:theetch\\ ratefollowsfromhalfaperiodofthe\\ sinusoid\end{array}$ $\begin{array}{r}(assumed:SiO2at230nm/minand670\mathrm{nm};\\ computed:0.0167\mathrm{Hz},a60speriod)\end{array}$

Reflectance and Endpoint

Name	Formula	Related Formulae	Variables/Constants
Single-film reflectance	$r=\frac{r_{01}+r_{12}{e}^{-2i\beta }}{1+r_{01}{r}_{12}{e}^{-2i\beta }},\beta =\frac{2\pi nd}{\lambda }$	$r_{ij}=\frac{n_i-n_j}{n_i+n_j},R={\left|r\right|}^2$	$\begin{array}{r}{r}_{01},r_{12}:ambient-filmandfilm-substrate\\ Fresnelcoefficients\end{array}$ $\beta :phasethickness$ $\begin{array}{r}R:reflectance;Airyform(background\\ knowledge,Heavens)\end{array}$ $\begin{array}{r}(assumed:Sin=3.81at670\mathrm{nm};computed:\\ r_{01}=-0.186,r_{12}=-0.447)\end{array}$
Fringe contrast	$R_{max}={\left(\frac{|r_{01}|+|r_{12}|}{1+|r_{01}{r}_{12}|}\right)}^2,R_{min}={\left(\frac{|r_{01}|-|r_{12}|}{1-|r_{01}{r}_{12}|}\right)}^2$	$V=\frac{R_{max}-R_{min}}{R_{max}+R_{min}}$	$\begin{array}{r}V:fringevisibilityforrealindiceswith\\ r_{01}and{r}_{12}ofthesamesign;relations\\ (backgroundknowledge,Heavens)\end{array}$ $\begin{array}{r}(computed:SiO2onSiat670\mathrm{nm}:Rswings\\ between0.341,equaltobareSi,and\\ 0.081,V=0.62)\end{array}$
Endpoint signature	$\frac{dR}{dt}\to 0\text{when}d\to 0$	$R_{final}=R_{substrate}$	$\begin{array}{r}{R}_{substrate}:reflectanceoftheexposed\\ underlayer;Oxfordpage:interferometry\\ tracksremainingthicknessandneedsthe\\ spotplacedbeforeeachrunoradedicated\\ waferarea;US4,454,001:controlsample\\ atleast90percentreflective\\ underneath,thickerthan\lambda /2,etching\\ stoppedbeforereaching\lambda /2;EPFLpage:\\ 670,905and980\mathrm{nm}lasersatnormal\\ incidence\end{array}$ $\begin{array}{r}(myreading:interferometrycanstop\\ beforeclearing,bypredictingthetimeto\\ atargetremainingthickness,whichOES\\ cannot)\end{array}$

Resolution and Practical Limits

Name	Formula	Related Formulae	Variables/Constants
Thickness resolution	$\delta d=\frac{\delta \varphi }{2\pi }\frac{\lambda }{2n}$	$\delta \varphi \approx \frac{2\pi }{20}\text{(fitted)}$	$\begin{array}{r}\delta \varphi :phaseuncertaintyofthefitted\\ sinusoid;relation(backgroundknowledge,\\ Heavens)\end{array}$ $\begin{array}{r}(assumed:onetwentiethofacycle;\\ computed:11.5\mathrm{nm}forSiO2at670\mathrm{nm})\end{array}$
Mixed signals (beats)	$R\left(t\right)\approx R_1\left(t\right)+R_2\left(t\right)$	$\text{envelope at}\left|f_1-f_2\right|$	$\begin{array}{r}{R}_1,R_2:contributionsoftwoetching\\ materialsinthespot;US4,454,001:\\ amplitudechangesinExample2readas\\ beatsfromsuperposedinterferenceof\\ siliconandsilicondioxideetching\\ (initialoxide4150\mathring{\mathrm{A}},final1125\mathring{\mathrm{A}},Cl2\\ at10mTorr,300V,0.15W/c{\mathrm{m}}^{2}for32min;\\ Example1CF3Clat1.5kWand0.4\mathrm{Torr}for\\ 10min);incoherent-sumapproximation\\ (backgroundknowledge)\end{array}$ $\begin{array}{r}(computed:oxideremoved3025\mathring{\mathrm{A}}in32min\\ is9.5nm/min,and1.27\mu \mathrm{m}ofSiin32min\\ is40nm/min)\end{array}$
Spot placement and open area	$A_{spot}=\pi \frac{w^2}{4}$	$\text{pattern pitch}\ll w\text{for a stable zeroth order}$	$\begin{array}{r}w:spotdiameter;US4,454,001:about1mm\\ spotoverthepattern;Oxfordpage:OES\\ needsseveralsquarecentimetresofopen\\ areawhileinterferometryneedsonlythe\\ spotplacedontherightfeature;geometry\\ (backgroundknowledge)\end{array}$ $\begin{array}{r}(computed:a1mmspotcovers0.785square\\ mm,soitaveragesoverthousandsof10\mu \mathrm{m}\\ features)\end{array}$

Important Questions

Ques: How does laser interferometry measure etch rate?

By counting oscillations in reflected intensity. Light reflected from the top of a transparent film interferes with light from its bottom interface, and at normal incidence each full cycle corresponds to $\lambda /2n$ of film removed (Oxford page). For oxide at 670 $\mathrm{nm}$ with an assumed index of 1.456, this is 230 $\mathrm{nm}$ per cycle; for nitride with an assumed 2.0, 168 $\mathrm{nm}$ (computed). At an assumed 230 $nm/min$ the signal has a 60 s period (computed), so rate is the cycle thickness divided by the measured period. The EPFL page describes deriving etch rate from half a period of the sinusoid, which is half a cycle and $\lambda /4n$ of film. The EPFL tools use 670, 905 or 980 $\mathrm{nm}$ lasers at normal incidence. Reference: Oxford Instruments Plasma Technology, ‘Optical end point detectors’ upgrade page (fetch-tool summary); EPFL Center of MicroNanoTechnology, ‘Etch End-Point Detection (EPD) Capabilities’ (fetch-tool summary); O. S. Heavens, Optical Properties of Thin Solid Films, Dover 1991, and E. D. Palik (ed.), Handbook of Optical Constants of Solids, Academic Press 1985 (background knowledge; not opened).

Ques: Is one fringe lambda/2n or lambda/2?

Both are right, for different structures. For a transparent film the optical path inside the film sets the period, giving $\lambda /2n$ (Oxford page), and US 4,454,001 cites this relation from earlier work. That patent instead measures etch depth into opaque silicon through a patterned mask, where the interfering beams travel in the ambient, and states one period per $\lambda /2$, 316.4 $\mathrm{nm}$ for its He-Ne laser (computed). Its examples bear this out: 3.13 periods give 0.990 $\mu \mathrm{m}$ against a profiler depth of 1.025 $\mu \mathrm{m}$, and 4.26 periods give 1.348 $\mu \mathrm{m}$ against 1.27 $\mu \mathrm{m}$, errors of -3.4 and +6.1 per cent (computed), consistent with its stated 4 and 6 per cent. Using $\lambda /2n$ for trench depth would be wrong (my reading). Reference: Oxford Instruments Plasma Technology, ‘Optical end point detectors’ upgrade page (fetch-tool summary); ‘Interferometric method and apparatus for measuring etch rate and fabricating devices’, US patent 4,454,001 (fetch-tool summary; title from the search listing, bibliographic data not in the text).

Ques: How large is the interference signal for oxide on silicon?

Large enough for robust detection. With assumed indices of 1.456 for oxide and 3.81 for silicon at 670 $\mathrm{nm}$, the Fresnel coefficients are -0.186 and -0.447 (computed). Reflectance then swings between 0.341, equal to bare silicon, at half-wave thicknesses and 0.081 at quarter-wave thicknesses, a fringe visibility of 0.62 (computed; background knowledge, Heavens). When the oxide clears, reflectance settles at the bare silicon value and stops oscillating, which marks endpoint. US 4,454,001 notes that a control area needs a reflective underlayer and a film thicker than $\lambda /2$ to give a full cycle. With phase fitted to one twentieth of a cycle, remaining thickness is resolved to about 11.5 $\mathrm{nm}$ (assumed; computed). Reference: O. S. Heavens, Optical Properties of Thin Solid Films, Dover 1991, and E. D. Palik (ed.), Handbook of Optical Constants of Solids, Academic Press 1985 (background knowledge; not opened); ‘Interferometric method and apparatus for measuring etch rate and fabricating devices’, US patent 4,454,001 (fetch-tool summary; title from the search listing, bibliographic data not in the text).

Ques: Why does the interferometer signal sometimes show beats?

Because two materials etching at once each contribute an oscillation. In Example 2 of US 4,454,001, silicon was etched through an oxide mask for 32 min in Cl2 at 10 mTorr; the mask thinned from 4150 to 1125 $\mathring{\mathrm{A}}$ while 1.27 $\mu \mathrm{m}$ of silicon was removed. The patent attributes amplitude changes to beats between the silicon and oxide interference signals. The average rates were 9.5 $nm/min$ for oxide and 40 $nm/min$ for silicon (computed), so their fringe frequencies differ and the envelope varies at the difference frequency (background knowledge). This is why the example’s error, about 6 per cent, exceeds Example 1’s under 4 per cent with an aluminium mask, which does not etch (my reading). Fitting both components separates them. Reference: ‘Interferometric method and apparatus for measuring etch rate and fabricating devices’, US patent 4,454,001 (fetch-tool summary; title from the search listing, bibliographic data not in the text).

Ques: When is interferometry preferred to OES endpoint?

When open area is small or the process must stop on remaining thickness. The Oxford page notes that OES typically needs several square centimetres of etched area, while interferometry depends only on placing the spot on the right feature, either by aiming before each run or using a dedicated wafer area. A 1 $\mathrm{mm}$ spot, as in US 4,454,001, covers 0.785 square millimetres and averages over thousands of 10 $\mu \mathrm{m}$ features (computed). Because interferometry tracks phase continuously, it can predict when a target thickness will be reached and stop before clearing, which OES cannot since it only sees the change when the film is gone (my reading). Its weakness is that it samples one location rather than the whole wafer (Optical Emission Spectroscopy Endpoint (OES) page). Reference: Oxford Instruments Plasma Technology, ‘Optical end point detectors’ upgrade page (fetch-tool summary); ‘Interferometric method and apparatus for measuring etch rate and fabricating devices’, US patent 4,454,001 (fetch-tool summary; title from the search listing, bibliographic data not in the text).

References

1. Oxford Instruments Plasma Technology, “Optical end point detectors.” Available: https://plasma.oxinst.jp/service-support/upgrades/optical-end-point-detectors
2. EPFL Center of MicroNanoTechnology, “Etch End-Point Detection (EPD) Capabilities.” Available: https://www.epfl.ch/research/facilities/cmi/process/etching/end-pointing-capabilities/
3. O. S. Heavens, Optical Properties of Thin Solid Films, Dover, 1991; E. D. Palik (ed.), Handbook of Optical Constants of Solids, Academic Press, 1985 (cited from background knowledge).
4. “Interferometric method and apparatus for measuring etch rate and fabricating devices,” US patent 4,454,001. Available: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/4454001

Related pages in this vault: Optical Emission Spectroscopy Endpoint (OES), Spectral Reflectometer, Spectroscopic Ellipsometer, White-Light Interferometer, Optical CD Scatterometer (OCD), Quartz Crystal Microbalance (QCM).