Picosecond Ultrasonic Film Metrology

1. Theory

• Definition: Picosecond ultrasonic metrology uses a femtosecond pump pulse to launch a strain pulse into a film and a delayed probe pulse to detect its echoes from buried interfaces through small reflectivity changes, giving thickness from echo time and sound velocity (pulse-echo patent; Onto paper).
• Opaque films: It measures metals that ellipsometry cannot, because the strain pulse, not light, crosses the film (pulse-echo patent).
• Interfaces: Echo amplitude and sign follow the acoustic impedance contrast of each interface (schoolphysics; sign my reading).
• Transparent films: Oscillations at the Brillouin frequency give sound velocity and modulus (Onto paper).

2. Working Principle

• Laser: About 100 $\mathrm{MHz}$ train of femtosecond pulses split into pump and probe (pulse-echo patent; Onto paper).
• Delay: A mechanical delay line scans the probe arrival time after the pump (pulse-echo patent; range computed in the delay row).
• Detection: Pump modulation near 50 $\mathrm{kHz}$ and lock-in detection of parts-per-million reflectivity changes (pulse-echo patent).
• Analysis: Echo times and amplitudes fitted with literature sound velocities, without external calibration (Onto paper).

3. Applications

• Metal film thickness: Barrier, seed, liner and interconnect metals in production (pulse-echo patent; Onto paper).
• RF filters: Mo/AlN/Mo bulk-acoustic-wave stacks before and after trimming (Onto paper).
• Multilayer stacks: Up to eight layers on product-sized pads (Onto paper).
• Film properties: Sound velocity, Young’s modulus (Onto paper).

Acoustic Echoes

Name	Formula	Related Formulae	Variables/Constants
Thickness from echo time	$d=\frac{v_L\Delta t}{2}$	$\Delta t=t_{n+1}-t_n$	$d:filmthickness$ $v_L:longitudinalsoundvelocity$ $\begin{array}{r}\Delta t:intervalbetweensuccessiveechoes;\\ pulse-echopatent:thicknessequalsthe\\ speedtimeshalftheintervalbetweenthe\\ firstandsecondechoes,96\mathrm{nm}Tiwith\\ echoesatabout28and60\mathrm{ps},180\mathrm{nm}Ti\\ withafirstechoatabout58\mathrm{ps};Onto\\ paper:thicknessfromechotransittime\\ withaliteraturesoundvelocityandno\\ externalcalibration\end{array}$ $\begin{array}{r}(computed:6.0nm/psfromthe32\mathrm{ps}\\ interval,6.9nm/psfromthe28\mathrm{ps}first\\ echo,6.2nm/psfrom58\mathrm{ps}at180\mathrm{nm})\end{array}$
Acoustic reflection at an interface	$r=\frac{Z_2-Z_1}{Z_2+Z_1},Z=\rho v_L$	$A_n\propto r^n$	$\begin{array}{r}r:strainreflectioncoefficientfora\\ waveinmedium1meetingmedium2\end{array}$ $Z:acousticimpedance$ $\rho :density$ $\begin{array}{r}{A}_n:amplitudeofthen-thecho;\\ schoolphysics:Z=\rho vandtheintensity\\ ratio(Z_2-Z_1{)}^2/(Z_2+Z_1{)}^2,thesignedamplitude\\ form(myreading);densitiesand\\ velocitiesfromtheacoustic-properties\\ tableandIoffe;A_{n}relation(myreading)\end{array}$ $\begin{array}{r}(Ti4540kgpercubicmetreand6230m/s,\\ Cu8900and4700,Al2700and6320,quartz\\ glass2600and5570fromthetable,Si\\ 2329and8430fromIoffe;computed:Z=\\ 28.3,41.8,17.1,14.5and19.6\mathrm{MRayl};r=\\ -0.18TionSi,-0.49Cuonsilicaglass,\\ +0.07AlonSi)\end{array}$
Elastic modulus from velocity	$C_{11}=\rho v_L^2$	$E=\rho v_L^2\frac{\left(1+\nu \right)\left(1-2\nu \right)}{1-\nu }$	$C_{11}:longitudinalmodulus$ $E:Youn{g}^{\prime }smodulus$ $\begin{array}{r}\nu :Poisso{n}^{\prime }sratio;Ontopaper:Youn{g}^{\prime }s\\ moduluscalculatedfromthemeasuredsound\\ velocity;UWEMA611:v^2=C_{1111}/\rho and\\ C_{1111}=E(1-\nu )/[(1+\nu )(1-2\nu )](garbledin\\ extraction),rearrangedforE(computed)\end{array}$ $\begin{array}{r}(computed:C_{11}=176\mathrm{GPa}forTiand197\mathrm{GPa}\\ forCufromthetablevalues)\end{array}$

Generation and Detection

Name	Formula	Related Formulae	Variables/Constants
Strain pulse generation	$\zeta =\frac{\lambda }{4\pi \kappa },{\tau }_s\approx \frac{\zeta }{v_L}$	${\tau }_{pump}\ll {\tau }_s$	$\zeta :opticalabsorptiondepth$ $\kappa :extinctioncoefficient$ ${\tau }_s:strainpulseduration$ $\begin{array}{r}{\tau }_{pump}:pumppulseduration;pulse-echo\\ patent:femtosecondpulses,durations\\ belowabout10\mathrm{ps}claimed,absorption\\ lengthbelow70\mathring{\mathrm{A}}inAlat0.5\mu \mathrm{m};Onto\\ paper:100\mathrm{fs}pump;relations(myreading)\end{array}$ $\begin{array}{r}(assumed:\zeta =7\mathrm{nm}inAl;computed:{\tau }_s=\\ 1.1\mathrm{ps};a5\mathrm{nm}Tifilmhasa1.6\mathrm{ps}round\\ trip)\end{array}$
Reflectivity detection	$\frac{\Delta R}{R}=\frac{\partial \ln R}{\partial \eta }\eta \left(t\right)$	$\Delta R/R\sim 10^{-6}\text{to}10^{-5}$	$\Delta R/R:probereflectivitychange$ $\begin{array}{r}\eta :strainnearthesurface;Ontopaper:\\ probedetectsthereturningwavethrough\\ strain-inducedreflectivitychange;\\ pulse-echopatent:optical-constant\\ changesofafewpartspermillion,\\ modulationnear50\mathrm{kHz}forlock-in\\ detection;relation(myreading)\end{array}$ $\begin{array}{r}(myreading:lock-inmodulationat50\mathrm{kHz}\\ liftsthepart-per-millionsignalabove\\ laserintensitynoise)\end{array}$
Brillouin oscillation in transparent films	$v=\frac{\lambda }{2n\tau \cos \phi }$	$f_B=\frac{1}{\tau }=\frac{2nv\cos \phi }{\lambda }$	$\tau :oscillationperiod$ $n:refractiveindex$ $\phi :refractionangle$ $\lambda :probewavelength$ $\begin{array}{r}{f}_B:Brillouinfrequency;Ontopaper:sound\\ velocityfromtheoscillationperiodwith\\ thisequation\end{array}$ $\begin{array}{r}(assumed:\lambda =800\mathrm{nm},AlNn=2.15andv=\\ 11,000m/s,normalincidence;computed:\tau \\ =16.9\mathrm{ps},59\mathrm{GHz})\end{array}$

Timing, Range and Stacks

Name	Formula	Related Formulae	Variables/Constants
Pump-probe delay	$L_{stage}=\frac{c{t}_d}{2}\text{(double pass)}$	$t_{rep}=\frac{1}{f_{rep}}$	$L_{stage}:delay-stagetravel$ $t_d:pump-probedelay$ $t_{rep}:pulsespacing$ $\begin{array}{r}{f}_{rep}:repetitionrate;pulse-echopatent:\\ about100\mathrm{MHz}repetition;relation\\ (computed:thefoldeddelaypathdoubles\\ theopticaldelay)\end{array}$ $\begin{array}{r}(computed:10\mathrm{ns}spacing;15\mathrm{cm}travelper\\ 1\mathrm{ns};a12\mu \mathrm{m}Curoundtripof5.1\mathrm{ns}needs\\ 77\mathrm{cm})\end{array}$
Thickness range and repeatability	$\frac{{\sigma }_d}{d}=\sqrt{{\left(\frac{{\sigma }_v}{v}\right)}^2+{\left(\frac{{\sigma }_{\Delta t}}{\Delta t}\right)}^2}$	$d:50\mathring{\mathrm{A}}\text{to}12\mu \mathrm{m}\left(35\mu \mathrm{m}\text{option}\right)$	$\begin{array}{r}\sigma :standarddeviations;Ontopaper:metal\\ films50\mathring{\mathrm{A}}to12\mu \mathrm{m}withanoptionto35\mu \mathrm{m}\\ (also50\mathring{\mathrm{A}}toabout35\mu \mathrm{m}dependingon\\ material),repeatabilitymostlybelow0.10\\ percent(3sigma)for300to9000\mathring{\mathrm{A}},\\ five-layerstackbelow0.1percent,AlN\\ below0.050percent,toolmatchingbetter\\ than0.5percent,uptoeightlayers,\\ spot7by10\mu \mathrm{m},afewsecondspersite;\\ pulse-echopatent:severalhundredmicrons\\ totensofangstroms;errorpropagation\\ (computedforindependenterrors)\end{array}$ $(computed:0.1percentof300\mathring{\mathrm{A}}is0.3\mathring{\mathrm{A}})$
Multilayer stacks	$t_k={\sum }_{i=1}^k\frac{2d_i}{v_i}$	$d_i\text{fitted from echo times and amplitudes}$	$\begin{array}{r}{t}_k:arrivaltimeoftheechofromthek-th\\ interface\end{array}$ $\begin{array}{r}{d}_i,v_i:thicknessandvelocityoflayeri;\\ pulse-echopatent:metallayerovera\\ dielectriconsiliconwithfurtherlayers\\ determinedsimilarly;Ontopaper:\\ Mo/AlN/Moandfive-layerstacks,nearly\\ 400sites;sumrelation(computed)\end{array}$ $\begin{array}{r}(myreading:eachinterfacereturnsan\\ echowhosesignfollowstheimpedance\\ step,solayerorderandcontrastdecide\\ whichlayersareresolvable)\end{array}$

Important Questions

Ques: How does a picosecond ultrasonic tool measure a metal film?

By timing an acoustic echo. A femtosecond pump pulse absorbed near the surface heats a thin layer, whose thermal expansion launches a strain pulse into the film; it reflects at the film-substrate interface, and when it returns the strain changes the optical reflectivity seen by a delayed probe pulse (pulse-echo patent; Onto paper). Thickness is the sound velocity times half the echo interval, $d=v_L\Delta t/2$. The Onto paper notes that a literature velocity gives thickness without external calibration, with a 7 by 10 $\mu \mathrm{m}$ spot and a few seconds per site. Because the measurement uses sound rather than light crossing the film, it works on opaque metals where ellipsometry fails, as the patent notes for Al with an absorption length below 70 $\mathring{\mathrm{A}}$. Reference: ‘Detection of film thickness through induced acoustic pulse-echos’, US patent 6,552,803 (continuation-in-part of US application 09/028,417, filed February 1998, now US 6,108,087) (fetch-tool summary; assignee not in the text); J. Dai, J. Mu, C. Kim and P. Mukundhan, ‘Advantages of Picosecond Ultrasonic Technology for Advanced RF Metrology’, Onto Innovation (CSTIC 2021 paper 6-37 per the file name) (fetch-tool summary).

Ques: What velocity do the titanium echo times imply?

It depends on which times are used, and the patent’s figures differ. For the 96 $\mathrm{nm}$ Ti film the echoes arrive at about 28 and 60 $\mathrm{ps}$; the 32 $\mathrm{ps}$ interval gives $2d/\Delta t$ = 6.0 $nm/ps$, but the 28 $\mathrm{ps}$ first echo alone gives 6.9 $nm/ps$ (computed). The 180 $\mathrm{nm}$ film’s first echo at 58 $\mathrm{ps}$ gives 6.2 $nm/ps$ (computed). Published longitudinal velocities of Ti are 6070, 6100 and 6230 m/s, 6.1 to 6.2 $nm/ps$ (Engineering ToolBox; Olympus; acoustic-properties table), so the interval method is more likely correct: the first echo time includes uncertainty in time zero and the finite depth where the strain is generated, which cancels in the difference between echoes (my reading). This is why the patent defines thickness from the interval between successive echoes. Reference: ‘Detection of film thickness through induced acoustic pulse-echos’, US patent 6,552,803 (continuation-in-part of US application 09/028,417, filed February 1998, now US 6,108,087) (fetch-tool summary; assignee not in the text); Engineering ToolBox, ‘Solids and Metals - Speed of Sound’: titanium 6070 m/s, fused silica 5968 m/s (fetch-tool summary); Olympus (Evident), ‘Material Sound Velocities’: titanium 6100 m/s, copper 4660 m/s (fetch-tool summary); ‘Acoustic Properties of Materials’ table (hosted by Hashemite University): titanium 4.54 g/cm3, 6230 m/s, 28.3e6 kg/(m2 s); copper 8.9, 4700, 41.8; aluminium 2.7, 6320, 17; quartz glass 2.6, 5570, 14.5 (fetch-tool summary).

Ques: Why are some interfaces easier to measure than others?

Because echo amplitude follows the acoustic impedance step. With $Z=\rho v_L$, schoolphysics gives the reflected intensity ratio as $(Z_2-Z_1{)}^2/(Z_2+Z_1{)}^2$, so the amplitude coefficient is $r=(Z_2-Z_1)/(Z_2+Z_1)$, its sign my reading. With the acoustic-properties table and Ioffe’s silicon values, Cu on silica glass gives -0.49 and a strong inverted echo, Ti on Si -0.18, and Al on Si only +0.07, because their impedances of 17.1 and 19.6 $\mathrm{MRayl}$ nearly match (computed). Each round trip multiplies the echo by $r$, so a low-contrast interface gives a weak first echo and fast decay. The sign also identifies whether the next layer is acoustically harder or softer, which helps assign echoes in multilayer stacks (my reading). Reference: schoolphysics, ‘Acoustic impedance’: Z = density x speed of sound, reflected intensity ratio (Z2 - Z1)^2/(Z2 + Z1)^2 (fetch-tool summary); ‘Acoustic Properties of Materials’ table (hosted by Hashemite University): titanium 4.54 g/cm3, 6230 m/s, 28.3e6 kg/(m2 s); copper 8.9, 4700, 41.8; aluminium 2.7, 6320, 17; quartz glass 2.6, 5570, 14.5 (fetch-tool summary); Ioffe Institute, NSM archive, ‘Si - Silicon: Mechanical properties’: density 2.329 g/cm3, [100] longitudinal velocity 8.43e5 cm/s, C11 16.60e11 dyn/cm2 (fetch-tool summary); University of Wisconsin, EMA 611 ‘Experiment 2. Ultrasonics and Transducers’: v^2 = C1111/rho, C1111 = E(1 - nu)/[(1 + nu)(1 - 2nu)] for isotropic materials (garbled in extraction), pulse-echo path twice the thickness (fetch-tool summary).

Ques: How thin and how thick a film can it measure?

The Onto paper gives metal films from 50 $\mathring{\mathrm{A}}$ to 12 $\mu \mathrm{m}$, with an option to 35 $\mu \mathrm{m}$, and elsewhere 50 $\mathring{\mathrm{A}}$ to about 35 $\mu \mathrm{m}$ depending on material; the patent states tens of angstroms to several hundred microns. The lower limit is set by the strain pulse duration: a 7 $\mathrm{nm}$ absorption depth in Al gives about 1.1 $\mathrm{ps}$ (assumed; computed), comparable to the 1.6 $\mathrm{ps}$ round trip in a 5 $\mathrm{nm}$ Ti film, so echoes overlap and must be fitted (computed). The upper limit is set by attenuation and delay range: a 12 $\mu \mathrm{m}$ Cu round trip takes 5.1 $\mathrm{ns}$, needing 77 $\mathrm{cm}$ of double-pass delay travel, half the 10 $\mathrm{ns}$ pulse spacing at 100 $\mathrm{MHz}$ (computed). The 12 $\mu \mathrm{m}$ standard figure is more likely the routine limit. Reference: J. Dai, J. Mu, C. Kim and P. Mukundhan, ‘Advantages of Picosecond Ultrasonic Technology for Advanced RF Metrology’, Onto Innovation (CSTIC 2021 paper 6-37 per the file name) (fetch-tool summary); ‘Detection of film thickness through induced acoustic pulse-echos’, US patent 6,552,803 (continuation-in-part of US application 09/028,417, filed February 1998, now US 6,108,087) (fetch-tool summary; assignee not in the text).

Ques: How are transparent films such as AlN measured?

Through Brillouin oscillations rather than echoes. In a transparent film, the probe light reflected from the moving strain pulse interferes with light reflected at the surface, producing oscillations whose period gives the sound velocity, $v=\lambda /(2n\tau \cos \phi )$ (Onto paper). For AlN with an assumed refractive index of 2.15 and velocity of 11,000 m/s at 800 $\mathrm{nm}$, the period is 16.9 $\mathrm{ps}$, a 59 $\mathrm{GHz}$ oscillation (assumed; computed). Knowing the velocity, thickness follows from the echo time, and Young’s modulus from velocity and density; for comparison, Ti has $C_{11}=\rho v^2$ of 166 $\mathrm{GPa}$ (computed). The Onto paper reports AlN site repeatability below 0.050 per cent for both thickness and velocity. Reference: J. Dai, J. Mu, C. Kim and P. Mukundhan, ‘Advantages of Picosecond Ultrasonic Technology for Advanced RF Metrology’, Onto Innovation (CSTIC 2021 paper 6-37 per the file name) (fetch-tool summary).

Ques: Why is picosecond ultrasonics used for RF filter stacks?

Because filter frequency depends on layer thicknesses that must be controlled to about 0.1 per cent. The Onto paper gives a 3 sigma frequency target of 0.1 per cent or better, while deposition uniformity is no better than 2 per cent across wafers, which is why the stack is trimmed and measured before and after trimming. It measures all layers of Mo/AlN/Mo and a five-layer metal and AlN stack in one measurement, with repeatability below 0.1 per cent for each layer, tool matching better than 0.5 per cent, and nearly 400 sites per wafer. On a 300 $\mathring{\mathrm{A}}$ film, 0.1 per cent is 0.3 $\mathring{\mathrm{A}}$ (computed). Opaque electrodes and a transparent piezoelectric are measured together, which optical methods cannot do (my reading). Reference: J. Dai, J. Mu, C. Kim and P. Mukundhan, ‘Advantages of Picosecond Ultrasonic Technology for Advanced RF Metrology’, Onto Innovation (CSTIC 2021 paper 6-37 per the file name) (fetch-tool summary).

References

1. “Detection of film thickness through induced acoustic pulse-echos,” US patent 6,552,803 (continuation-in-part of US application 09/028,417, filed February 24, 1998, now US 6,108,087). Available: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/6552803
2. J. Dai, J. Mu, C. Kim and P. Mukundhan, “Advantages of Picosecond Ultrasonic Technology for Advanced RF Metrology,” Onto Innovation (CSTIC 2021, paper 6-37, per the file name). Available: https://ontoinnovation.com/writable/files/Resources/CSTIC-2021_6-37_Johnny-Dai.pdf
3. “Acoustic Properties of Materials,” table hosted by Hashemite University. Available: https://eis.hu.edu.jo/acuploads/10526/UT%20Mat%20Prop.pdf
4. Ioffe Physico-Technical Institute, “Si - Silicon: Mechanical properties,” New Semiconductor Materials. Available: https://www.ioffe.ru/SVA/NSM/Semicond/Si/mechanic.html
5. Engineering ToolBox, “Solids and Metals - Speed of Sound.” Available: https://engineeringtoolbox.com/sound-speed-solids-d_713.html
6. Olympus (Evident), “Material Sound Velocities,” thickness-gauge tutorial appendix. Available: https://www.olympus-ims.com/en/ndt-tutorials/thickness-gage/appendices-velocities/
7. schoolphysics, “Acoustic impedance.” Available: https://schoolphysics.co.uk/age16-19/Sound/text/Acoustic_impedance/index.html
8. University of Wisconsin-Madison, EMA 611 Advanced Mechanical Testing, “Experiment 2. Ultrasonics and Transducers.” Available: https://lakeslab.ep.wisc.edu/EMA611Lab2.pdf

Related pages in this vault: Spectroscopic Ellipsometer, X-Ray Reflectometer (XRR), X-Ray Fluorescence Spectrometer (XRF and TXRF), Four-Point Probe, Wire Resistance and Size Effects, Contacts and Vias, Spectral Reflectometer, Terahertz Time-Domain Spectrometer, Nanoindenter, Quartz Crystal Microbalance (QCM).