FTIR Spectrometer

1. Theory

• Definition: A Fourier-transform infrared spectrometer passes infrared light through a Michelson interferometer and the sample, records the interferogram and Fourier transforms it into a spectrum (background knowledge, Griffiths and de Haseth).
• Impurity bands: Interstitial oxygen absorbs at about 1107 $\mathrm{c}{\mathrm{m}}^{-1}$ and substitutional carbon at about 605 $\mathrm{c}{\mathrm{m}}^{-1}$ in silicon; the absorption is proportional to concentration (Bruker; PerkinElmer).
• Calibration factors: Fixed factors convert absorption coefficient to concentration, defined by standards (PerkinElmer; SEMI MF1188).
• Reflectance mode: Interference fringes between the surface and the epi-substrate interface give epitaxial layer thickness (background knowledge).

2. Working Principle

• Interferometer: A moving mirror varies the path difference; resolution is set by its travel (background knowledge).
• Reference subtraction: A float-zone silicon spectrum removes the lattice phonon bands (Bruker; PerkinElmer).
• Baseline: The absorption coefficient is calculated from the peak and baseline transmissions and the thickness (PerkinElmer).
• Low temperature: Cooling to 77 $\mathrm{K}$ sharpens the carbon band and lowers detection limits; below 10 $\mathrm{K}$ shallow dopants become visible (Bruker).

3. Applications

• Wafer specification: Oxygen and carbon in Czochralski silicon, which control gettering and thermal donors (PerkinElmer; background knowledge).
• Solar silicon: Carbon and oxygen in multicrystalline and mono-like ingots (Bruker).
• Epitaxy: Epitaxial layer thickness on heavily doped substrates (background knowledge).
• Dielectrics: Bonding and hydrogen content of oxide and nitride films (background knowledge).

Interferometry and Absorption

Name	Formula	Related Formulae	Variables/Constants
Interferogram and spectrum	$I\left(\delta \right)={\int }_0^{\infty }B\left(\tilde{\nu }\right)\cos \left(2\pi \tilde{\nu }\delta \right)d\tilde{\nu }$	$B\left(\tilde{\nu }\right)={\int }_{-\infty }^{\infty }I\left(\delta \right)\cos \left(2\pi \tilde{\nu }\delta \right)d\delta$	$\begin{array}{r}I(\delta ):interferogram(ACpart)against\\ opticalpathdifference\delta ,B(\tilde{\nu }):spectrum\\ againstwavenumber\tilde{\nu };Michelson\\ interferometerandFouriertransform\\ relations(backgroundknowledge,Griffiths\\ anddeHaseth)\end{array}$ $\begin{array}{r}(computed:1107\mathrm{c}{\mathrm{m}}^{-1}isawavelengthof\\ 9.03\mu \mathrm{m})\end{array}$
Spectral resolution	$\Delta \tilde{\nu }\approx \frac{1}{{\delta }_{max}}$	${\delta }_{max}=2x_{max}(\text{mirror travel }{x}_{max})$	$\Delta \tilde{\nu }:resolution$ $\begin{array}{r}{\delta }_{max}:maximumpathdifference;relation\\ (backgroundknowledge,Griffithsandde\\ Haseth);PerkinElmer:4\mathrm{c}{\mathrm{m}}^{-1}with32scans;\\ Bruker:4\mathrm{c}{\mathrm{m}}^{-1}atroomtemperatureand1\mathrm{c}{\mathrm{m}}^{-1}\\ atlowtemperature,routinemeasurement\\ under1minute,spotabout8\mathrm{mm}\end{array}$ $\begin{array}{r}(computed:4\mathrm{c}{\mathrm{m}}^{-1}needs0.25\mathrm{cm}path\\ differenceand1.25\mathrm{mm}ofmirrortravel;1\\ \mathrm{c}{\mathrm{m}}^{-1}needs5\mathrm{mm}oftravel)\end{array}$
Absorption coefficient	$\alpha =\frac{1}{d}\ln \frac{T_0}{T}$	$T=\frac{{\left(1-R\right)}^2{e}^{-\alpha d}}{1-R^2{e}^{-2\alpha d}}(\text{multiple reflections})$	$\alpha :absorptioncoefficient$ $d:samplethickness$ $T_0:baselinetransmissionatthepeak$ $T:transmissionatthepeak$ $\begin{array}{r}R:surfacereflectance(about0.30for\\ siliconintheinfrared);PerkinElmer:\alpha \\ fromthebaselineandpeaktransmission\\ withdincentimetresaftersubtractinga\\ float-zonereference;Bruker:Lambert-Beer\\ proportionalityofpeakareato\\ concentration;multiple-reflectionform\\ (backgroundknowledge,Schroder)\end{array}$ $\begin{array}{r}(computed:\alpha =2.61\mathrm{c}{\mathrm{m}}^{-1}ina500\mu \mathrm{m}wafer\\ meansT/T_0=0.878,a12percentdip)\end{array}$

Oxygen and Carbon in Silicon

Name	Formula	Related Formulae	Variables/Constants
Interstitial oxygen	$\left[O_i\right]=3.14\times 10^{17}{\alpha }_{1107}\mathrm{c}{\mathrm{m}}^{-3}$	${\left[O_i\right]}_{ppma}=6.28{\alpha }_{1107}$	$[O_i]:interstitialoxygenconcentration$ $\begin{array}{r}{\alpha }_{1107}:absorptioncoefficientatthe1107\mathrm{c}{\mathrm{m}}^{-1}\\ Si-O-Siband;PerkinElmer:thesefactors,\\ example\alpha =2.61giving8.20\times 10^{17}\mathrm{c}{\mathrm{m}}^{-3}and\\ 16.4\mathrm{ppma},SEMIMF1188-1105short-baseline\\ method,NISTreferencematerialsnolonger\\ available;Bruker:about1107\mathrm{c}{\mathrm{m}}^{-1},1720\mathrm{c}{\mathrm{m}}^{-1}\\ overtoneforthickingots,1.0\times 10^{18}\mathrm{c}{\mathrm{m}}^{-3}=\\ 20.1\mathrm{ppma}example;otherhistorical\\ factors(seetheQ/A)\end{array}$ $\begin{array}{r}(computed:3.14\times 10^{17}x2.61=8.20\times 10^{17}\mathrm{c}{\mathrm{m}}^{-3};\\ 1\mathrm{ppma}=5.0\times 10^{16}\mathrm{c}{\mathrm{m}}^{-3}insilicon)\end{array}$
Substitutional carbon	$\left[C_s\right]=8.2\times 10^{16}{\alpha }_{605}\mathrm{c}{\mathrm{m}}^{-3}$	${\left[C_s\right]}_{ppma}=1.64{\alpha }_{605}$	$[C_s]:substitutionalcarbonconcentration$ $\begin{array}{r}{\alpha }_{605}:absorptioncoefficientattheC-Si\\ band;PerkinElmer:thesefactors,607\mathrm{c}{\mathrm{m}}^{-1}\\ inthecalculationand605\mathrm{c}{\mathrm{m}}^{-1}inthe\\ spectrumdiscussion,\alpha =0.384giving\\ 3.15\times 10^{16}\mathrm{c}{\mathrm{m}}^{-3},SEMIMF1391andJEITA\\ EM-3503;Bruker:about605\mathrm{c}{\mathrm{m}}^{-1}atroom\\ temperatureandabout608\mathrm{c}{\mathrm{m}}^{-1}at77\mathrm{K}(see\\ theQ/A)\end{array}$ $\begin{array}{r}(computed:8.2\times 10^{16}x0.384=3.15\times 10^{16}\mathrm{c}{\mathrm{m}}^{-3}=\\ 0.63\mathrm{ppma})\end{array}$
Detection limits and thickness	${\left[X\right]}_{min}\propto \delta {\alpha }_{min}=\frac{\delta \left(\ln T\right)}{d}$	$d_{opt}\approx 1.5\mathrm{mm}(\text{room temperature}),3\text{to}3.5\mathrm{mm}(77\mathrm{K})$	$[X{]}_{min}:detectionlimit$ $\begin{array}{r}\delta {\alpha }_{min}:smallestresolvableabsorption\\ change;scaling(backgroundknowledge);\\ Bruker:room-temperaturedetectionlimit\\ oforder1\times 10^{16}\mathrm{c}{\mathrm{m}}^{-3}(200ppba)on\\ double-polished1.5\mathrm{mm}samples,thickness\\ 0.4to2\mathrm{mm}(thinnerforoxygenonly),\\ low-temperaturecarbonaccuracyabout\\ 5\times 10^{14}\mathrm{c}{\mathrm{m}}^{-3}(10ppba)withanLN2MCT\\ detector,2.3\times 10^{15}\mathrm{c}{\mathrm{m}}^{-3}exampleon3.4\mathrm{mm}at\\ 77\mathrm{K},samplesuptoabout4\mathrm{mm},\\ far-infraredboronandphosphorusbelow10\\ \mathrm{K}\end{array}$ $\begin{array}{r}(computed:a500\mu \mathrm{m}waferhasthreetimes\\ fewerabsorbersperareathana1.5\mathrm{mm}\\ sample,raisingthedetectionlimitabout\\ threefold)\end{array}$

Practice and Thickness

Name	Formula	Related Formulae	Variables/Constants
Reference subtraction	$A_{diff}\left(\tilde{\nu }\right)=A_{sample}\left(\tilde{\nu }\right)-\frac{d_s}{d_r}{A}_{FZ}\left(\tilde{\nu }\right)$	$A=-{\log }_{10}T$	$A:absorbance$ $A_{FZ}:float-zonereferenceabsorbance$ $\begin{array}{r}{d}_s,d_r:sampleandreferencethicknesses;\\ Bruker:FZreferencewithnegligible\\ carbonandoxygenremoveslatticephonon\\ absorption,thicknessandsurfacefinish\\ ideallymatched;PerkinElmer:zero-oxygen\\ FZreferencespectrumsubtracted;\\ thicknessscaling(backgroundknowledge)\end{array}$ $\begin{array}{r}(computed:a2percentthicknessmismatch\\ leaves2percentofthestrong610\mathrm{c}{\mathrm{m}}^{-1}\\ phononband,whichoverlapsthecarbon\\ peak)\end{array}$
Epitaxial-layer thickness by IR reflectance	$d_{epi}=\frac{\Delta m}{2\Delta \tilde{\nu }\sqrt{n^2-{\sin }^2\theta }}$	$\Delta {\tilde{\nu }}_{fringe}=\frac{1}{2nd}(\text{normal incidence})$	$d_{epi}:epitaxiallayerthickness$ $\begin{array}{r}n:infraredindexoftheepi(about3.42\\ forsilicon)\end{array}$ $\begin{array}{r}\Delta m:fringesinspan\Delta \tilde{\nu };interference\\ betweenthesurfaceandtheepi-substrate\\ interface,contrastfromtheheavilydoped\\ substrat{e}^{\prime }sfree-carrierindex(background\\ knowledge,Schroder);samefringerelation\\ astheSpectralReflectometerpage\end{array}$ $\begin{array}{r}(computed:a5\mu \mathrm{m}siliconepihasfringes\\ 292\mathrm{c}{\mathrm{m}}^{-1}apart)\end{array}$
Mapping uniformity	$RSD=\frac{\sigma }{\bar{x}}\times 100\text{per cent}$	${\bar{x}}_O=6.99\times 10^{17},{\sigma }_O=7.54\times 10^{16};{\bar{x}}_C=3.03\times 10^{16},{\sigma }_C=1.67\times 10^{15}\mathrm{c}{\mathrm{m}}^{-3}$	$RSD:relativestandarddeviation$ $\sigma :standarddeviation$ $\begin{array}{r}\bar{x}:meanovermappoints;PerkinElmer:\\ 17-pointmapofa6\mathrm{in},500\mu \mathrm{m}double-side\\ polishedCZwafer,RSD10.78percentfor\\ oxygenand5.52percentforcarbon\end{array}$ $\begin{array}{r}(computed:7.54\times 10^{16}/6.99\times 10^{17}=10.8per\\ cent,1.67\times 10^{15}/3.03\times 10^{16}=5.5percent;\\ thesecombinetrueradialvariationand\\ measurementnoise)\end{array}$

Important Questions

Ques: How does an FTIR spectrometer obtain a spectrum?

By recording an interferogram and Fourier transforming it. A Michelson interferometer splits the infrared beam, sends the halves to a fixed and a moving mirror and recombines them, so the detector sees an intensity that varies with the optical path difference; every wavenumber contributes a cosine, and the transform recovers the spectrum (background knowledge, Griffiths and de Haseth). Resolution is about the inverse of the maximum path difference: 4 $\mathrm{c}{\mathrm{m}}^{-1}$ needs 0.25 $\mathrm{cm}$, or 1.25 $\mathrm{mm}$ of mirror travel (computed). All wavelengths are measured at once, with high throughput, so a silicon impurity measurement at 4 $\mathrm{c}{\mathrm{m}}^{-1}$ takes under a minute (Bruker) and PerkinElmer averages 32 scans. The 1107 $\mathrm{c}{\mathrm{m}}^{-1}$ oxygen band lies at a wavelength of 9.03 $\mu \mathrm{m}$ (computed). Reference: P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry, 2nd ed., Wiley 2007 (background knowledge; not opened); Bruker, Application Note M54, carbon and oxygen in silicon by FT-IR (fetch-tool summary); PerkinElmer, ‘Semi-Automated FT-IR Measurements of Elemental Impurities in Silicon Wafers’ application note (fetch-tool summary).

Ques: How is interstitial oxygen measured in a silicon wafer?

From the absorption coefficient of the 1107 $\mathrm{c}{\mathrm{m}}^{-1}$ Si-O-Si band. The spectrum of a float-zone reference wafer, essentially free of oxygen, is subtracted to remove lattice phonon bands; then $\alpha =(1/d)\ln (T_0/T)$ from the baseline and peak transmissions and the thickness (PerkinElmer). PerkinElmer converts with $[O_i]=3.14$e17$\alpha$, or 6.28$\alpha$ in ppma: its example, $\alpha =2.61$ $\mathrm{c}{\mathrm{m}}^{-1}$ on a 500 $\mu \mathrm{m}$ wafer, gives $8.20\times 10^{17}$ $\mathrm{c}{\mathrm{m}}^{-3}$ and 16.4 $\mathrm{ppma}$ (computed check). That absorption is only a 12 per cent dip in transmission (computed), so baseline choice matters, which is why SEMI MF1188 specifies a short baseline. Bruker uses the weak 1720 $\mathrm{c}{\mathrm{m}}^{-1}$ overtone for thick ingots, where the main band saturates. Reference: PerkinElmer, ‘Semi-Automated FT-IR Measurements of Elemental Impurities in Silicon Wafers’ application note (fetch-tool summary); Bruker, Application Note M54, carbon and oxygen in silicon by FT-IR (fetch-tool summary); SEMI MF1188, ‘Test Method for Interstitial Oxygen Content of Silicon by Infrared Absorption with Short Baseline’, SEMI store listing (title only).

Ques: Which oxygen calibration factor is correct?

Several have been used, which is why oxygen values must always be quoted with their factor. PerkinElmer uses $3.14\times 10^{17}$ $\mathrm{c}{\mathrm{m}}^{-3}$ per inverse centimetre, the factor of SEMI MF1188 and the 1988 international round robin, while older standards used about $4.81\times 10^{17}$ (old ASTM), $2.45\times 10^{17}$ (DIN and the later ASTM F121 revision) and $3.03\times 10^{17}$ (JEIDA) (background knowledge). The same absorption of 2.61 $\mathrm{c}{\mathrm{m}}^{-1}$ therefore reads $8.2\times 10^{17}$ with the current factor but $12.6\times 10^{17}$ with the old ASTM factor, a 53 per cent difference (computed). The $3.14\times 10^{17}$ factor is the more likely correct one today, as it came from comparison with absolute methods and is the basis of current SEMI practice (background knowledge; my reading). Because NIST reference materials are no longer available, standard factors are used (PerkinElmer). Reference: PerkinElmer, ‘Semi-Automated FT-IR Measurements of Elemental Impurities in Silicon Wafers’ application note (fetch-tool summary); SEMI MF1188, ‘Test Method for Interstitial Oxygen Content of Silicon by Infrared Absorption with Short Baseline’, SEMI store listing (title only); D. K. Schroder, Semiconductor Material and Device Characterization, 3rd ed., Wiley 2006 (background knowledge; not opened).

Ques: Is the carbon band at 605, 607 or 608 inverse centimetres?

All three appear. PerkinElmer calculates the carbon absorption at 607 $\mathrm{c}{\mathrm{m}}^{-1}$ but cites 605 $\mathrm{c}{\mathrm{m}}^{-1}$ in its spectrum discussion; Bruker gives about 605 $\mathrm{c}{\mathrm{m}}^{-1}$ at room temperature and about 608 $\mathrm{c}{\mathrm{m}}^{-1}$ at 77 $\mathrm{K}$. These are consistent: the band is broad at room temperature and sits on the edge of the strong 610 $\mathrm{c}{\mathrm{m}}^{-1}$ lattice phonon band, so the apparent peak shifts by a few inverse centimetres with reference subtraction, resolution and baseline, and it sharpens and shifts upward on cooling (background knowledge; my reading). The 605 $\mathrm{c}{\mathrm{m}}^{-1}$ value is the conventional room-temperature assignment, and 608 $\mathrm{c}{\mathrm{m}}^{-1}$ the low-temperature one. With 4 $\mathrm{c}{\mathrm{m}}^{-1}$ resolution, a 2 $\mathrm{c}{\mathrm{m}}^{-1}$ difference is half a resolution element and does not change the result if the same convention is used for the calibration factor of $8.2\times 10^{16}$. Reference: PerkinElmer, ‘Semi-Automated FT-IR Measurements of Elemental Impurities in Silicon Wafers’ application note (fetch-tool summary); Bruker, Application Note M54, carbon and oxygen in silicon by FT-IR (fetch-tool summary).

Ques: How low can carbon be measured?

About $1\times 10^{16}$ $\mathrm{c}{\mathrm{m}}^{-3}$ at room temperature and $5\times 10^{14}$ $\mathrm{c}{\mathrm{m}}^{-3}$ at 77 $\mathrm{K}$. Bruker gives a room-temperature detection limit of order $1\times 10^{16}$ $\mathrm{c}{\mathrm{m}}^{-3}$, 200 ppba, for double-side polished samples about 1.5 $\mathrm{mm}$ thick, and a low-temperature carbon accuracy of about $5\times 10^{14}$ $\mathrm{c}{\mathrm{m}}^{-3}$, 10 ppba, with a liquid-nitrogen-cooled MCT detector on samples ideally 3 to 3.5 $\mathrm{mm}$ thick; its example shows $2.3\times 10^{15}$ $\mathrm{c}{\mathrm{m}}^{-3}$ on a 3.4 $\mathrm{mm}$ sample. A 500 $\mu \mathrm{m}$ production wafer has three times fewer absorbers per area than 1.5 $\mathrm{mm}$, so its limit is about three times worse (computed). PerkinElmer measured $3.15\times 10^{16}$ $\mathrm{c}{\mathrm{m}}^{-3}$ on such a wafer, from $\alpha =0.384$ $\mathrm{c}{\mathrm{m}}^{-1}$ (computed check). Below 10 $\mathrm{K}$, far-infrared spectra also reveal boron and phosphorus (Bruker). Reference: Bruker, Application Note M54, carbon and oxygen in silicon by FT-IR (fetch-tool summary); PerkinElmer, ‘Semi-Automated FT-IR Measurements of Elemental Impurities in Silicon Wafers’ application note (fetch-tool summary).

Ques: Why does the reference wafer need to match the sample?

Because the lattice absorbs strongly where the impurity bands sit. The float-zone reference removes silicon’s own phonon absorption, which near 610 $\mathrm{c}{\mathrm{m}}^{-1}$ is much stronger than the carbon band; Bruker therefore recommends matching thickness and surface finish. If thickness differs, the reference must be scaled by $d_s/d_r$; a 2 per cent mismatch leaves 2 per cent of the phonon band, enough to distort a low carbon reading (background knowledge; computed). Surface roughness changes scattering and multiple reflections, and silicon’s infrared reflectance of about 0.30 means that transmission involves multiple passes, handled by the multiple-reflection formula (background knowledge, Schroder). Bruker accepts room-temperature samples from 0.4 to 2 $\mathrm{mm}$, thinner for oxygen only. Reference: Bruker, Application Note M54, carbon and oxygen in silicon by FT-IR (fetch-tool summary); D. K. Schroder, Semiconductor Material and Device Characterization, 3rd ed., Wiley 2006 (background knowledge; not opened).

Ques: How is epitaxial layer thickness measured by FTIR?

From interference fringes in infrared reflectance. A lightly doped epitaxial layer on a heavily doped substrate has an interface where the refractive index changes, because free carriers in the substrate lower its infrared index; light reflected there interferes with light from the surface (background knowledge, Schroder). The fringe spacing is $1/(2nd)$ at normal incidence, so a 5 $\mu \mathrm{m}$ silicon layer, with an infrared index of about 3.42, gives fringes 292 $\mathrm{c}{\mathrm{m}}^{-1}$ apart (computed), and the thickness follows from the fringe count over a span, as on the Spectral Reflectometer page. The method needs enough doping contrast, typically a substrate above about $1\times 10^{19}$ $\mathrm{c}{\mathrm{m}}^{-3}$, and becomes difficult for layers below about 1 $\mu \mathrm{m}$ (background knowledge). Reference: D. K. Schroder, Semiconductor Material and Device Characterization, 3rd ed., Wiley 2006 (background knowledge; not opened).

Ques: How uniform is oxygen across a wafer?

It varies by several per cent, which a map reveals. PerkinElmer’s 17-point map of a 6 $\mathrm{in}$, 500 $\mu \mathrm{m}$ Czochralski wafer gave a mean oxygen concentration of $6.99\times 10^{17}$ $\mathrm{c}{\mathrm{m}}^{-3}$ with a standard deviation of $7.54\times 10^{16}$, an RSD of 10.8 per cent, and carbon $3.03\times 10^{16}$ with $1.67\times 10^{15}$, 5.5 per cent (computed check). These figures combine true radial variation, from oxygen incorporation during crystal pulling, and measurement scatter (background knowledge), so they do not by themselves give the instrument’s repeatability, which requires repeated measurements at one point. Oxygen matters because it controls precipitation and gettering and forms thermal donors that shift resistivity after annealing near 450 ${}^{\circ }\mathrm{C}$ (background knowledge). Reference: PerkinElmer, ‘Semi-Automated FT-IR Measurements of Elemental Impurities in Silicon Wafers’ application note (fetch-tool summary); D. K. Schroder, Semiconductor Material and Device Characterization, 3rd ed., Wiley 2006 (background knowledge; not opened).

References

1. P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry, 2nd ed. Hoboken, NJ: Wiley, 2007 (cited from background knowledge).
2. Bruker Optics, “Carbon and oxygen in silicon,” Application Note M54. Available: https://www.bruker.com/en/meta/fileadmin/_jcr_content/root/contentpar/search.download-asset.pdf/0f8ddc78-78fe-4e61-8334-5f277720b16b/AN_M54_Carbon_Oxygen_EN.pdf
3. PerkinElmer, “Semi-Automated FT-IR Measurements of Elemental Impurities in Silicon Wafers,” application note. Available: https://resources.perkinelmer.com/lab-solutions/resources/docs/APP-Semi-Automated-FT-IR-Measurements-of-Elemental-Impurities-in-Silicon-Wafers-213362.pdf
4. SEMI, “SEMI MF1188: Test Method for Interstitial Oxygen Content of Silicon by Infrared Absorption with Short Baseline,” SEMI store listing. Available: https://store-us.semi.org/products/mf118800-semi-mf1188-test-method-for-interstitial-oxygen-content-of-silicon-by-infrared-absorption-with-short-baseline
5. D. K. Schroder, Semiconductor Material and Device Characterization, 3rd ed. Hoboken, NJ: Wiley, 2006 (cited from background knowledge).

Related pages in this vault: Spectral Reflectometer, Raman Spectrometer, Spectroscopic Ellipsometer, Lifetime Testers, Terahertz Time-Domain Spectrometer, UV-Vis Spectrophotometer, Secondary Ion Mass Spectrometer (SIMS and ToF-SIMS), White-Light Interferometer.