Raman Spectrometer

1. Theory

• Definition: A Raman spectrometer illuminates a sample with a laser and measures the weak inelastically scattered light, shifted by the energies of vibrational modes (phonons) (background knowledge; EAG).
• Stress: Strain changes phonon frequencies; in silicon the 520 $\mathrm{c}{\mathrm{m}}^{-1}$ optical phonon shifts in proportion to stress, so the shift maps stress (EAG; Kim et al.).
• Composition: In SiGe, the Si-Si, Si-Ge and Ge-Ge modes shift with Ge fraction and strain, so two peaks give both (Kim et al.).
• Structure: Peak widths and positions distinguish crystalline, amorphous and graphitic material (Kim et al.; background knowledge).

2. Working Principle

• Micro-Raman: A microscope focuses the laser to a sub-micrometre spot and collects the backscattered light (background knowledge; EAG).
• Filtering and dispersion: A notch or edge filter blocks the laser line; a grating spectrometer and CCD record the Stokes spectrum (background knowledge).
• Wavelength choice: The laser wavelength sets the sampling depth through the absorption coefficient (EAG; background knowledge).
• Peak fitting: Lorentzian fits locate peaks to a few hundredths of an inverse centimetre, compared with a stress-free reference (background knowledge; Kim et al.).

3. Applications

• Process-induced stress: Stress near trench isolation, through-silicon vias and contacts (Kim et al.; background knowledge).
• Strained silicon and SiGe: Strain and Ge content in channels and buffers (EAG; Kim et al.).
• Carbon hard masks: D and G band analysis of amorphous carbon films (Kim et al.).
• Wide-gap materials: Polytypes and stress in SiC and GaN (background knowledge).

Raman Scattering

Name	Formula	Related Formulae	Variables/Constants
Raman shift	$\Delta \tilde{\nu }=\frac{1}{{\lambda }_0}-\frac{1}{{\lambda }_s}$	${\lambda }_s={\left(\frac{1}{{\lambda }_0}-\Delta \tilde{\nu }\right)}^{-1}(\text{Stokes})$	$\Delta \tilde{\nu }:Ramanshiftininversecentimetres$ ${\lambda }_0:laserwavelength$ $\begin{array}{r}{\lambda }_s:scatteredwavelength;relation\\ (backgroundknowledge);EAG:stress-free\\ siliconnear520\mathrm{c}{\mathrm{m}}^{-1}(520.4inits\\ figure),514.5\mathrm{nm}laser;Kimetal.:520.3\\ \mathrm{c}{\mathrm{m}}^{-1}(seetheQ/A)\end{array}$ $\begin{array}{r}(computed:the520\mathrm{c}{\mathrm{m}}^{-1}lineexcitedat\\ 514.5\mathrm{nm}appearsat528.6\mathrm{nm})\end{array}$
Stokes and anti-Stokes intensities	$\frac{I_{AS}}{I_S}={\left(\frac{{\tilde{\nu }}_0+{\tilde{\nu }}_m}{{\tilde{\nu }}_0-{\tilde{\nu }}_m}\right)}^4\exp \left(-\frac{hc{\tilde{\nu }}_m}{k_{B}T}\right)$	$I\propto {\tilde{\nu }}_s^4(\text{scattering efficiency})$	$I_{AS},I_S:anti-StokesandStokesintensities$ ${\tilde{\nu }}_0:laserwavenumber$ ${\tilde{\nu }}_m:phononwavenumber$ $h:Planckconstant$ $\begin{array}{r}c:speedoflight;forms(background\\ knowledge)\end{array}$ $\begin{array}{r}(computed:forsiliconat300\mathrm{K}with514.5\\ \mathrm{nm}excitationtheratiois0.102)\end{array}$
Sampling depth and spot	$d_s\approx \frac{1}{2\alpha \left({\lambda }_0\right)}$	$d_{spot}=\frac{1.22{\lambda }_0}{NA}$	$\begin{array}{r}{d}_s:samplingdepth(lighttravelsinand\\ backout)\end{array}$ $\begin{array}{r}\alpha :absorptioncoefficientatthelaser\\ wavelength\end{array}$ $d_{spot}:diffraction-limitedspot$ $\begin{array}{r}NA:numericalaperture;forms(background\\ knowledge);EAG:penetrationdepthabout\\ 0.8\mu \mathrm{m}at514.5\mathrm{nm}fora0.1to0.2\mu \mathrm{m}Si\\ epilayeronSiGe;ultravioletlasersprobe\\ about10\mathrm{nm}andredlasersseveral\\ micrometresinsilicon(background\\ knowledge)\end{array}$ $\begin{array}{r}(computed:514.5\mathrm{nm}withNA=0.9givesa\\ 0.70\mu \mathrm{m}spot)\end{array}$

Stress and Composition

Name	Formula	Related Formulae	Variables/Constants
Stress in silicon	${\sigma }_{uni}\left[\mathrm{MPa}\right]\approx -500\Delta \omega ,{\sigma }_r+{\sigma }_{\theta }=\left(470\mathrm{MPa}\mathrm{cm}\right)\Delta \omega$	${\sigma }_{biax}\left[\mathrm{MPa}\right]\approx -250\Delta \omega (\text{each component, (001) Si})$	$\begin{array}{r}\Delta \omega :peakshiftfromthestress-free\\ positionininversecentimetres\end{array}$ $\begin{array}{r}{\sigma }_{uni}:uniaxialstress,{\sigma }_r,{\sigma }_{\theta }:in-plane\\ stresscomponents\end{array}$ $\begin{array}{r}{\sigma }_{biax}:equalbiaxialstress;Kimetal.:\\ in-planesum470MPaperinverse\\ centimetreafterChandrasekharetal.\\ (1978)andAnastassakisetal.(1990),\\ signconventionsstatedinconsistently\\ (seetheQ/A);EAG:a9.5\mathrm{c}{\mathrm{m}}^{-1}redshiftof\\ astrainedSiepilayerreadasabout2.4\\ \mathrm{GPa}tensilepercomponentunderbiaxial\\ stress,shiftproportionaltostrain;\\ uniaxialandbiaxialcoefficients\\ (backgroundknowledge,DeWolf)\end{array}$ $\begin{array}{r}(computed:EA{G}^{\prime }s2.4\mathrm{GPa}percomponentfor\\ 9.5\mathrm{c}{\mathrm{m}}^{-1}is253\mathrm{MPa}perinversecentimetre\\ percomponent,or505forthesum)\end{array}$
Phonon deformation potentials	$\left|\begin{array}{ccc}p{\epsilon }_{11}+q\left({\epsilon }_{22}+{\epsilon }_{33}\right)-\lambda & 2r{\epsilon }_{12}& 2r{\epsilon }_{13}\\ 2r{\epsilon }_{12}& p{\epsilon }_{22}+q\left({\epsilon }_{11}+{\epsilon }_{33}\right)-\lambda & 2r{\epsilon }_{23}\\ 2r{\epsilon }_{13}& 2r{\epsilon }_{23}& p{\epsilon }_{33}+q\left({\epsilon }_{11}+{\epsilon }_{22}\right)-\lambda \end{array}\right|=0$	${\lambda }_j={\omega }_j^2-{\omega }_0^2\approx 2{\omega }_0\Delta {\omega }_j$	$p,q,r:phonondeformationpotentials$ ${\epsilon }_{ij}:straincomponents$ $\begin{array}{r}{\lambda }_j:eigenvaluesforthethreeoptical\\ phonons\end{array}$ $\begin{array}{r}{\omega }_0:unstrainedfrequency;secularequation\\ (backgroundknowledge,DeWolf;Kimetal.\\ citeGanesanetal.1970);backscattering\\ from(001)Siseesonlythethirdphonon\end{array}$ $\begin{array}{r}(computed:\Delta \omega =1\mathrm{c}{\mathrm{m}}^{-1}at520\mathrm{c}{\mathrm{m}}^{-1}\\ correspondsto\lambda =1040\mathrm{c}{\mathrm{m}}^{-1}squared)\end{array}$
SiGe composition and strain	${\omega }_{SiSi}=520.5-62x-815\epsilon$	${\omega }_{SiGe}=400.5+14.2x-575\epsilon$	${\omega }_{SiSi},{\omega }_{SiGe}:Si-SiandSi-Gemodefrequencies$ $x:Gefraction$ $\begin{array}{r}\epsilon :in-planestrain;Kimetal.:these\\ relationsafterTsangetal.(1993),Ge\\ contentsof17to32percentstudied,\\ Si-Si,Si-GeandGe-Gebands;EAG:Si-Si\\ substratepeakat499.9\mathrm{c}{\mathrm{m}}^{-1}(499.7inits\\ figure)for30percentGeandstrainedSi\\ epilayerat510.9\mathrm{c}{\mathrm{m}}^{-1}\end{array}$ $\begin{array}{r}(computed:relaxedSi0.7Ge0.3gives501.9\\ \mathrm{c}{\mathrm{m}}^{-1}fromtheformula,2.0\mathrm{c}{\mathrm{m}}^{-1}aboveEA{G}^{\prime }s\\ 499.9;SionrelaxedSi0.7Ge0.3has1.25\\ percenttensilestrain,apredictedshift\\ of-10.2\mathrm{c}{\mathrm{m}}^{-1}andabout2.26\mathrm{GPa}biaxial\\ stress,againstEA{G}^{\prime }smeasured-9.5\mathrm{c}{\mathrm{m}}^{-1}\\ and2.4\mathrm{GPa})\end{array}$

Structure and Artefacts

Name	Formula	Related Formulae	Variables/Constants
Amorphous and crystalline fractions	$X_c=\frac{I_c}{I_c+y{I}_a}$	${\omega }_{a\text{-}Si}\approx 480\mathrm{c}{\mathrm{m}}^{-1}(\text{broad}),{\omega }_{c\text{-}Si}\approx 520\mathrm{c}{\mathrm{m}}^{-1}$	$X_c:crystallinefraction$ $\begin{array}{r}{I}_c,I_a:crystallineandamorphous\\ integratedintensities\end{array}$ $\begin{array}{r}y:cross-sectionratio(about0.8to1);\\ forms(backgroundknowledge)\end{array}$ $\begin{array}{r}(assumed:I_c=I_a,y=0.9;computed:X_c=\\ 0.53)\end{array}$
Carbon D and G bands	$\frac{I_D}{I_G}=\frac{C\left({\lambda }_0\right)}{L_a}(\text{nanocrystalline graphite})$	$D:1320\text{to}1440\mathrm{c}{\mathrm{m}}^{-1},G:1480\text{to}1580\mathrm{c}{\mathrm{m}}^{-1}$	$I_D,I_G:DandGbandintensities$ $\begin{array}{r}{L}_a:in-planecrystallitesize,C({\lambda }_0):\\ constant,about4.4\mathrm{nm}at514\mathrm{nm}\\ (Tuinstra-Koenig,backgroundknowledge);\\ Kimetal.:thesebandrangesfor\\ amorphouscarbonhard-maskfilms\end{array}$ $\begin{array}{r}(computed:I_D/I_G=1gives{L}_a=4.4\mathrm{nm}at\\ 514\mathrm{nm})\end{array}$
Laser heating	$\Delta {\omega }_T\approx \chi \Delta T$	$T=\frac{hc{\tilde{\nu }}_m}{k_B\ln \left[{\left(\frac{{\tilde{\nu }}_0+{\tilde{\nu }}_m}{{\tilde{\nu }}_0-{\tilde{\nu }}_m}\right)}^4\frac{I_S}{I_{AS}}\right]}$	$\Delta {\omega }_T:thermalshift$ $\begin{array}{r}\chi :temperaturecoefficient,about-0.02\\ \mathrm{c}{\mathrm{m}}^{-1}perkelvinforsiliconnearroom\\ temperature(backgroundknowledge)\end{array}$ $\begin{array}{r}\Delta T:localheating;temperaturefromthe\\ anti-Stokesratio(rearrangedfromthe\\ intensityrow)\end{array}$ $\begin{array}{r}(computed:25\mathrm{K}oflaserheatingmimicsa\\ 0.5\mathrm{c}{\mathrm{m}}^{-1}shift,about125\mathrm{MPa}ofbiaxial\\ stress)\end{array}$

Important Questions

Ques: How does a Raman spectrometer measure phonons?

By detecting light scattered with a small change of energy. Most laser light scatters elastically, but about one photon in a million or fewer gives up or gains the energy of a lattice vibration, appearing at a shift $\Delta \tilde{\nu }=1/{\lambda }_0-1/{\lambda }_s$ from the laser (background knowledge). Silicon’s optical phonon near 520 $\mathrm{c}{\mathrm{m}}^{-1}$, excited at 514.5 $\mathrm{nm}$ as in EAG’s measurements, appears at 528.6 $\mathrm{nm}$ (computed). A filter removes the laser line and a grating spectrometer records the Stokes spectrum; the weaker anti-Stokes side, 0.102 of the Stokes intensity for silicon at 300 $\mathrm{K}$ (computed), gives the temperature. Because the shift depends on bond stiffness and mass, it reflects stress, composition and crystallinity. Reference: EAG Laboratories, ‘Semiconductor Stress Measurements by Raman Spectroscopy’, application note M-005016 (fetch-tool summary); I. De Wolf, ‘Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits’, Semicond. Sci. Technol. 11, 139 (1996) (background knowledge; not opened).

Ques: How is stress obtained from the silicon peak?

From the shift relative to stress-free silicon, using a coefficient that depends on the stress state. Compressive stress raises the frequency and tensile stress lowers it; for uniaxial stress the coefficient is about -500 $\mathrm{MPa}$ per inverse centimetre, and for equal biaxial stress in (001) silicon about -250 per component (background knowledge, De Wolf). EAG measured a strained silicon epilayer at 510.9 $\mathrm{c}{\mathrm{m}}^{-1}$, a red shift of about 9.5 $\mathrm{c}{\mathrm{m}}^{-1}$, and reported about 2.4 $\mathrm{GPa}$ tensile per component, or 253 $\mathrm{MPa}$ per inverse centimetre (computed). Backscattering from (001) silicon sees only one phonon, so a single shift cannot separate stress components; the full analysis uses the phonon deformation potentials p, q and r in the secular equation (background knowledge, De Wolf). Reference: EAG Laboratories, ‘Semiconductor Stress Measurements by Raman Spectroscopy’, application note M-005016 (fetch-tool summary); I. De Wolf, ‘Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits’, Semicond. Sci. Technol. 11, 139 (1996) (background knowledge; not opened).

Ques: Is the conversion 470 or about 500 MPa per inverse centimetre, and which sign is compressive?

Kim et al. give the in-plane stress sum as 470 $\mathrm{MPa}\mathrm{cm}$ times the shift, after Chandrasekhar and Anastassakis, while EAG’s numbers imply about 505 for the sum (computed from 2.4 $\mathrm{GPa}$ per component and 9.5 $\mathrm{c}{\mathrm{m}}^{-1}$) and De Wolf’s biaxial factor of about 250 per component implies 500 (background knowledge). The 7 per cent spread comes from different deformation-potential sets; the about 500 value is more widely used, but either is within their uncertainty (my reading). On sign, Kim et al.’s slide says a positive shift means compressive, while its text says tensile. The slide is correct: compression stiffens bonds and raises the frequency, as EAG’s tensile epilayer with its red shift confirms (background knowledge; EAG). Reference: J. H. Kim, C. H. Lee, K. H. Bae and S. M. Han, ‘Application of Raman Spectroscopy for Local Stress Methodology and Characterization of Amorphous Carbon and SiGe Films in Semiconductor Process Development’, NIST-hosted presentation (year not stated) (fetch-tool summary); EAG Laboratories, ‘Semiconductor Stress Measurements by Raman Spectroscopy’, application note M-005016 (fetch-tool summary); I. De Wolf, ‘Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits’, Semicond. Sci. Technol. 11, 139 (1996) (background knowledge; not opened).

Ques: What is the stress-free silicon peak, 520.0, 520.3, 520.4 or 520.5 inverse centimetres?

All appear: EAG writes about 520 $\mathrm{c}{\mathrm{m}}^{-1}$ with 520.4 in its figure, Kim et al. use 520.3 $\mathrm{c}{\mathrm{m}}^{-1}$, and the Tsang formula Kim et al. quote has an intercept of 520.5 $\mathrm{c}{\mathrm{m}}^{-1}$. The differences reflect spectrometer calibration and laser heating rather than physics: silicon’s peak shifts about -0.02 $\mathrm{c}{\mathrm{m}}^{-1}$ per kelvin (background knowledge), so 10 $\mathrm{K}$ of laser heating moves it 0.2 $\mathrm{c}{\mathrm{m}}^{-1}$, the size of the spread. The most likely value at room temperature without heating is near 520.5 $\mathrm{c}{\mathrm{m}}^{-1}$, but no absolute value should be trusted; each measurement must use an unstressed silicon reference measured on the same instrument at the same power (my reading). A 0.2 $\mathrm{c}{\mathrm{m}}^{-1}$ error is about 50 $\mathrm{MPa}$ of biaxial stress (computed). Reference: EAG Laboratories, ‘Semiconductor Stress Measurements by Raman Spectroscopy’, application note M-005016 (fetch-tool summary); J. H. Kim, C. H. Lee, K. H. Bae and S. M. Han, ‘Application of Raman Spectroscopy for Local Stress Methodology and Characterization of Amorphous Carbon and SiGe Films in Semiconductor Process Development’, NIST-hosted presentation (year not stated) (fetch-tool summary).

Ques: How does Raman give SiGe composition and strain?

From two peaks at once. Kim et al. quote Tsang’s relations ${\omega }_{SiSi}=520.5-62x-815\epsilon$ and ${\omega }_{SiGe}=400.5+14.2x-575\epsilon$, so measuring both modes gives two equations for Ge fraction and strain. For relaxed Si0.7Ge0.3 the Si-Si mode is predicted at 501.9 $\mathrm{c}{\mathrm{m}}^{-1}$, while EAG measured 499.9 $\mathrm{c}{\mathrm{m}}^{-1}$ on a 30 per cent substrate, 2.0 $\mathrm{c}{\mathrm{m}}^{-1}$ lower (computed), suggesting slight tension or a composition a little above 30 per cent (my reading). A silicon layer grown on relaxed Si0.7Ge0.3 takes 1.25 per cent tensile strain from the lattice mismatch, predicting a shift of -10.2 $\mathrm{c}{\mathrm{m}}^{-1}$ and about 2.26 $\mathrm{GPa}$ (computed), close to EAG’s -9.5 $\mathrm{c}{\mathrm{m}}^{-1}$ and 2.4 $\mathrm{GPa}$. Reference: J. H. Kim, C. H. Lee, K. H. Bae and S. M. Han, ‘Application of Raman Spectroscopy for Local Stress Methodology and Characterization of Amorphous Carbon and SiGe Films in Semiconductor Process Development’, NIST-hosted presentation (year not stated) (fetch-tool summary); EAG Laboratories, ‘Semiconductor Stress Measurements by Raman Spectroscopy’, application note M-005016 (fetch-tool summary).

Ques: How do the laser wavelength and objective set what is probed?

Wavelength sets depth and the objective sets lateral size. Light must enter and return, so the sampling depth is about $1/(2\alpha )$; EAG gives about 0.8 $\mu \mathrm{m}$ for silicon at 514.5 $\mathrm{nm}$, deeper than its 0.1 to 0.2 $\mu \mathrm{m}$ epilayer, so the spectrum contains both layer and substrate peaks. Ultraviolet excitation probes only about 10 $\mathrm{nm}$ of silicon and isolates thin channels, while red light reaches several micrometres (background knowledge). Laterally, a diffraction-limited spot of $1.22{\lambda }_0/NA$ is 0.70 $\mu \mathrm{m}$ at 514.5 $\mathrm{nm}$ with NA = 0.9 (computed), so stress near isolation trenches can be mapped on a sub-micrometre scale. Stress gradients within the probed depth broaden the peak, so the result is an average. Reference: EAG Laboratories, ‘Semiconductor Stress Measurements by Raman Spectroscopy’, application note M-005016 (fetch-tool summary); I. De Wolf, ‘Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits’, Semicond. Sci. Technol. 11, 139 (1996) (background knowledge; not opened).

Ques: What does Raman reveal about crystallinity and carbon films?

Peak shapes distinguish structures. Crystalline silicon gives a sharp line at 520 $\mathrm{c}{\mathrm{m}}^{-1}$, amorphous silicon a broad band near 480 $\mathrm{c}{\mathrm{m}}^{-1}$, and the crystalline fraction is $I_c/(I_c+y{I}_a)$; equal intensities with y = 0.9 give 0.53 (background knowledge; computed). Kim et al. use Raman on amorphous carbon hard masks, whose D band lies at 1320 to 1440 $\mathrm{c}{\mathrm{m}}^{-1}$ and G band at 1480 to 1580 $\mathrm{c}{\mathrm{m}}^{-1}$. The G band comes from sp2 bond stretching and the D band from disordered rings; their ratio relates to cluster size, for nanocrystalline graphite by $L_a=C/(I_D/I_G)$ with C about 4.4 $\mathrm{nm}$ at 514 $\mathrm{nm}$, so a ratio of 1 means 4.4 $\mathrm{nm}$ (background knowledge; computed). For amorphous carbon, G position and width track sp3 content and hardness. Reference: J. H. Kim, C. H. Lee, K. H. Bae and S. M. Han, ‘Application of Raman Spectroscopy for Local Stress Methodology and Characterization of Amorphous Carbon and SiGe Films in Semiconductor Process Development’, NIST-hosted presentation (year not stated) (fetch-tool summary); I. De Wolf, ‘Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits’, Semicond. Sci. Technol. 11, 139 (1996) (background knowledge; not opened).

Ques: Why can laser heating fake a stress signal?

Because temperature also shifts the phonon. Silicon’s peak moves about -0.02 $\mathrm{c}{\mathrm{m}}^{-1}$ per kelvin near room temperature (background knowledge), so 25 $\mathrm{K}$ of local heating shifts it 0.5 $\mathrm{c}{\mathrm{m}}^{-1}$, equivalent to about 125 $\mathrm{MPa}$ of biaxial tension (computed). Focused lasers on thin films, membranes or poorly conducting structures can heat them by tens of kelvin. The remedies are low laser power, checks that the peak does not move as power is varied, and identical conditions for the reference. The temperature itself can be measured from the anti-Stokes to Stokes ratio, 0.102 for silicon at 300 $\mathrm{K}$ with 514.5 $\mathrm{nm}$ excitation (computed), or from the shift. Reference: I. De Wolf, ‘Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits’, Semicond. Sci. Technol. 11, 139 (1996) (background knowledge; not opened).

References

1. EAG Laboratories, “Semiconductor Stress Measurements by Raman Spectroscopy,” application note M-005016. Available: https://www.eag.com/wp-content/uploads/2016/09/application-note-semiconductor-stress-measurements-by-raman-spectroscopy-M-005016.pdf
2. I. De Wolf, “Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits,” Semiconductor Science and Technology, vol. 11, pp. 139-154, 1996 (cited from background knowledge).
3. J. H. Kim, C. H. Lee, K. H. Bae and S. M. Han, “Application of Raman Spectroscopy for Local Stress Methodology and Characterization of Amorphous Carbon and SiGe Films in Semiconductor Process Development,” presentation hosted by NIST (year not stated). Available: https://www.nist.gov/document/28kimpdf

Related pages in this vault: FTIR Spectrometer, Photoluminescence Spectrometer, X-Ray Diffractometer (XRD and HRXRD), Scanning Near-Field Optical Microscope (SNOM) and TERS, Confocal Laser Scanning Microscope, Optical Microscope, Spectral Reflectometer, Terahertz Time-Domain Spectrometer, Spectroscopic Ellipsometer, Wafer Curvature Stress Gauge.