coatings

Article Simulation of Acoustic Propagation in Aluminium Coatings for Material Characterization

Eva Grünwald 1, René Hammer 1, Robert Nuster 2, Philipp Aldo Wieser 1, Martin Hinderer 3, Ingo Wiesler 3, Rudolf Zelsacher 4, Michael Ehmann 4 and Roland Brunner 1,*

1 Materials Center Leoben Forschung GmbH (MCL), Leoben 8700, Austria; [email protected] (E.G.); [email protected] (R.H.); [email protected] (P.A.W.) 2 Institute of Physics, Karl-Franzens University of Graz (KFU), Graz 8010, Austria; [email protected] 3 PVA TePla Analytical Systems GmbH (PVA AS), 73463 Westhausen, Germany; [email protected] (M.H.); [email protected] (I.W.) 4 Infineon Technologies Austria AG (IFAT), Villach 9500, Austria; Rudolf.Zelsacher2@infineon.com (R.Z.); Michael.Ehmann@infineon.com (M.E.) * Correspondence: [email protected]; Tel.: +43-3842-459-48

Academic Editors: Timon Rabczuk, Michael Nolan and Alessandro Lavacchi Received: 28 September 2017; Accepted: 4 December 2017; Published: 14 December 2017

Abstract: Aluminium coatings and their characterization are of great interest in many fields of application, ranging from aircraft industries to microelectronics. Here, we present the simulation of acoustic wave propagation in aluminium coatings via the elastodynamic finite integration technique (EFIT) in comparison to experimental results. The simulations of intensity (I)–defocus (z) curves, obtained by scanning acoustic microscopy (SAM), were first carried out on an aluminium bulk sample, and secondly on a 1 µm aluminium coating deposited on a silicon substrate. The I(z) curves were used to determine the Rayleigh wave velocity of the aluminium bulk sample and the aluminium coating. The results of the simulations with respect to the Rayleigh velocity were corroborated by non-destructive SAM measurements and laser ultrasonic measurements (LUS).

Keywords: aluminium coatings; acoustic simulation; scanning acoustic microscopy; V(z); acoustic material signature; Rayleigh wave velocity, integrated computational material engineering

1. Introduction Aluminium coatings offer a variety of favourable properties, including high reflectivity, high conductivity, high corrosion resistance, and low costs. The benefits of aluminium coatings render them attractive candidates for large-scale applications in aircraft industries, and also for implementation in small-scale devices, concerning micro- and nano-electronics [1]. The frequent use of aluminium coatings increases the demand for their precise characterization. However, some state-of-the-art methods show drawbacks concerning thin film characterization; e.g., they require the direct loading of the sample [2]. Alternatively, ultrasonic can be used in order to determine thin film properties; e.g., via laser-induced (LUS) [3–6] or via scanning acoustic microscopy (SAM) [7,8]. SAM represents a well-established tool in state-of-the-art failure and material characterization, providing high potential regarding automation [9], allowing fast and accurate failure detection. With commercially available SAM set-ups, the challenge lies mainly in (1) the necessary specific hardware for the measurement (e.g., emitter/sensor), high time resolution (ps), and accurate movement of emitter/sensor over the sample, and (2) in the interpretation of the SAM data—which can be quite cumbersome due to the presence of various wave modes in thin films.

Coatings 2017, 7, 230; doi:10.3390/coatings7120230 www.mdpi.com/journal/coatings Coatings 2017, 7, 230 2 of 11

One outstanding attribute of acoustic microscopy is the possibility to monitor the intensity I of the reflected sound waves as a function of the defocus position z—also called V(z) curves or acoustic material signatures (AMS) [7,8]—from which the Rayleigh wave velocity of the analysed material can be obtained. The I(z) measurement relies on the excitation of Rayleigh waves that propagate on the sample surface and leak back to the piezoelectric transducer. Decreasing the distance between lens and sample, the Rayleigh contribution interferes with the acoustic field reflected from the sample—alternating destructively and constructively, resulting in an oscillation of the measured intensity I as function of the defocus position z. The Rayleigh wave velocity can be used directly for material characterization or material monitoring [10,11], or alternatively, material properties can be extracted [3–8]. In layered media, the Rayleigh velocity depends on if the analysed coatings are thinner than approximately 1–2 [12,13]. Considering a broad-band Rayleigh wave, the lower frequency part of the wave propagates more in the substrate, whereas higher frequency components travel mainly in the coating due to their lower penetration depth. Consequently, the Rayleigh wave velocity becomes dispersive (i.e., depends on frequency); this effect has been extensively studied in the past (e.g., [13–15]). The dispersion of the Rayleigh wave can be used to extract elastic mechanical parameters like the Young´s modulus, because the Rayleigh wave velocity depends on the density as well as the elastic constants. In this sense, the determination of the Rayleigh wave velocities is of high interest for the characterization of materials—especially of coatings—and was studied via LUS in, e.g., [3–6] and via SAM in, e.g., [8,16–19]. In the past, I(z) measurements have been investigated analytically via ray theory [7,20,21] and via wave theory approaches [7,22]. For general numerical elastic wave propagation, finite element [23–25], spectral element [26,27], pseudospectral [28,29], finite volume methods [30], finite difference [31–34], and the elastodynamic finite integration technique (EFIT) [35,36] can be found in the literature. It is a common feature of all real-space numerical schemes for elastic wave propagation in higher dimensions that the linear dispersion relation of the wave equation is not reproduced exactly, but numerical dispersion errors are introduced. Severe dispersive errors and even spurious solutions force standard finite element methods (FEMs) with low-degree ansatz functions to use excessively high mesh densities [23–25]. In this work, to access the I(z) curves we use EFIT for the full elastic wave propagation, because of its good compromise in terms of accuracy relative to its computational cost. The field variables, velocity and stress, are placed in a staggered manner onto the computational grid, which greatly improves the dispersion relation of the scheme. Interestingly, this property is also exploited in electrodynamics, where the finite difference time domain (FDTD) scheme is unsurpassed for inhomogeneous domains [37], and recently also for the relativistic wave equation [38]. The elastic wave discretization using a staggered grid and the EFIT are related, with the difference being that the material properties are placed differently on the grid, allowing the EFIT to more accurately describe material inhomogeneities [35]. We simulated the I(z) curve for an aluminium bulk sample for calibration, because bulk values for aluminium can be found in the literature (e.g., [7]). In addition, the Rayleigh wave velocity can be measured very accurately via LUS [3–6]. After this calibration step, the I(z) curve of an aluminium-coated silicon sample was simulated and directly compared to results obtained from SAM measurements. The Rayleigh wave velocity—as a material parameter—was obtained from the EFIT simulation and from the SAM measurement, using a 400 MHz acoustic lens. The SAM and the LUS measurements corroborated the EFIT simulation results regarding the Rayleigh wave velocity of the aluminium sample and the aluminium coating. The use of full wave simulation as tested here on aluminium bulk and coated samples allows for arbitrarily varying real thickness and material property distribution up to complex geometrical structures like microelectronics components. Although ray theory approaches outperform the EFIT simulation of I(z) curves with respect to time-efficiency in general, the EFIT simulation provides more possibilities with respect to: (a) depicting Coatings 2017, 7, 230 3 of 11 the sound field propagation for various time-steps in the measurement, (b) creating an A-scan equivalent, (c) analysing the influence of, e.g., anti-reflective coating (ARC) or damping of the coupling liquid, and (d) most notably, complex multi-layered structures—relevant for, e.g., micro- and nanoelectronicCoatings 2017 devices—can, 7, 230 be conveniently analysed via state-of-the-art EFIT simulations.

2. Materialscoupling and liquid, Methods and (d) most notably, complex multi‐layered structures—relevant for, e.g., micro‐ and nanoelectronic devices—can be conveniently analysed via state‐of‐the‐art EFIT simulations. 2.1. Sample 2. Materials and Methods The analysed sample was a 4 × 2 cm2 segment of an aluminium-coated silicon wafer with (100) 2.1. Sample crystallographic orientation. The aluminium layer was deposited via physical vapour deposition, and its thicknessThe analysed was determinedsample was a 4 via × 2 cm profilometry.2 segment of an In aluminium addition,‐coated the silicon density wafer of with 2.709 (100) g/cm 3 of the aluminiumcrystallographic thin film orientation. was determined The aluminium via layer X-ray was diffraction deposited via (XRD) physical using vapour a deposition, D8 Discover and system its thickness was determined via profilometry. In addition, the density of 2.709 g/cm3 of the (Bruker,aluminium Billerica, thin MA, film USA). was determined via X‐ray diffraction (XRD) using a D8 Discover system (Bruker, Billerica, MA, USA). 2.2. Scanning Acoustic Microscopy (SAM) 2.2. Scanning Acoustic Microscopy (SAM) In scanning acoustic microscope measurements, piezoelectric transducers (emitter/sensor) are used to generateIn scanning ultrasonic acoustic waves microscope (see Figure measurements,1), e.g., [ piezoelectric7]. The sound transducers waves are (emitter/sensor,) focused onto are or below the surfaceused ofto generate the investigated ultrasonic waves sample (see via Figure an 1), acoustic e.g. [7]. lens.The sound At the waves sample–water are focused onto interface, or below part of the surface of the investigated sample via an acoustic lens. At the sample–water interface, part of the the acoustic field is reflected and propagates back to the transducer. At the transducer, the reflected acoustic field is reflected and propagates back to the transducer. At the transducer, the reflected acousticacoustic field is field converted is converted into into a time-variant a time‐variant electric electric signal signal which which is presented is presented in time in domain time domain and and commonlycommonly referred referred to as to A-scan as A‐scan (see (see e.g., e.g., [39 [39]).]).

FigureFigure 1. Schematic 1. Schematic of of scanning scanning acousticacoustic microscopy microscopy (SAM) (SAM) principle. principle.

If the opening angle of the lens exceeds the critical Rayleigh angle θ, If the opening angle of the lens exceeds the critical Rayleigh angle θ , R θ sin (1)   −1 v0 θR = sin (1) Rayleigh waves can be excited at the surface of thev Rsample (Equation (1)). Here, ν0 denotes the sound velocity in water, which is approximately 1500 m/s at room temperature. Once excited, the RayleighRayleigh waves wave propagates can be excited along the at surface the surface and leaks of theenergy sample back to (Equation the lens and (1)). subsequently Here, ν0 todenotes the soundthe velocitytransducer. in At water, the piezoelectric which is approximately element of the transducer, 1500 m/s atthe room phase temperature. and amplitude Onceof the excited, the Rayleighlongitudinal wave sound propagates wave reflected along thefrom surface the sample and and leaks the leaky energy Rayleigh back wave to the are lens summed and subsequently up [7]. The two wave modes (Rayleigh and ) interfere alternating constructively and to the transducer. At the piezoelectric element of the transducer, the phase and amplitude of the destructively, depending on the defocus position of the transducer. According to [7], the periodicity longitudinal∆z of the sound oscillation wave depends reflected on fromthe Rayleigh the sample sound andvelocity the ν leakyR of the Rayleigh investigated wave sample are via summed up [7]. The two wave modes (Rayleigh and longitudinal wave) interfere alternating constructively and λ destructively, depending on the defocus position∆ of the transducer. According to [7], the periodicity(2) ∆z 2 1 cosθ of the oscillation depends on the Rayleigh sound velocity νR of the investigated sample via where λ0 denotes the of the sound wave in water, see Equation (2). λ ∆z = 0 (2) 2 × (1 − cos θR) Coatings 2017, 7, 230 4 of 11

where λ0 denotes the wavelength of the sound wave in water, see Equation (2). A SAM can be operated in either pulsed or tone-burst mode [22]. The generally longer excitation time in tone burst mode results in signals which are very narrow in the frequency domain, allowing precise frequency-dependent measurements. In the work reported here, a commercially available SAM 400 (PVA, Analytical Systems GmbH, Westhausen, Germany) was operated in reflection mode, equipped with a custom-built tone-burst set-up, to perform precise frequency-dependent measurements. For the calibration measurement on bulk aluminium, an acoustic objective (AO) was used with a transducer of 400 MHz nominal centre frequency andCoatings an 2017 opening, 7, 230 angle of 120◦ (PVA, Analytical Systems GmbH, Westhausen, Germany). The resonance frequencyA SAM can be of operated the transducer in either pulsed was or found tone‐burst at mode approximately [22]. The generally 430 longer MHz. excitation In the case of the aluminium coating,time in tone an burst acoustic mode results objective in signals with which an openingare very narrow angle in the of frequency 60◦ was domain, applied allowing (PVA, Analytical precise frequency‐dependent measurements. Systems GmbH,In Westhausen, the work reported Germany). here, a commercially Operated available in tone-burst SAM 400 (PVA, mode, Analytical the transducer Systems GmbH, was addressed at approximatelyWesthausen, 400 MHz, Germany) at the was resonance operated in frequency reflection mode, of the equipped transducer. with a custom The ‐Ibuilt(z) curve tone‐burst was monitored with a step sizeset‐up, of to 2 performµm in precise the case frequency of the‐dependent calibration measurements. measurement For the calibration and in measurement the case ofon the coating bulk aluminium, an acoustic objective (AO) was used with a transducer of 400 MHz nominal centre measurement.frequency From theand periodicityan opening angle∆z ofof 120° the (PVA,I(z) Analytical curves, theSystems Rayleigh GmbH, waveWesthausen, velocities Germany). were extracted. The resonance frequency of the transducer was found at approximately 430 MHz. In the case of the 2.3. Elastodynamicaluminium Finite coating, Integration an acoustic Technique objective with (EFIT) an opening angle of 60° was applied (PVA, Analytical Systems GmbH, Westhausen, Germany). Operated in tone‐burst mode, the transducer was addressed The descriptionat approximately of ultrasonic 400 MHz, at sound the resonance field propagationfrequency of the simulation transducer. The in I( isotropicz) curve was linear elastic materials, discretizedmonitored with via a the step elastodynamic size of 2 μm in the finitecase of integrationthe calibration measurement technique, and can in be the found case of the in [35]. coating measurement. From the periodicity Δz of the I(z) curves, the Rayleigh wave velocities were The underlyingextracted. set of differential equations is given by the kinetics * 2.3. Elastodynamic Finite Integration Technique∂ v (EFIT)* ρ = ∇ × σ The description of ultrasonic sound ∂fieldt propagation simulation in isotropic linear elastic materials, discretized via the elastodynamic finite integration technique, can be found in [35]. the kinematics The underlying set of differential equations* is given by* the kineticsT d 1 ∂ * * ≈ [(∇ρ ⊗ v ) σ + ( ∇ ⊗ v ) ] dt 2 ∂ the kinematics and the constitutive (or material) law relatingdϵ 1 them by σ ≈ E ·  * ⊗v ⊗v ρ is the mass density, v is the particled velocity2 field (being the first derivative of the displacement * field u with respectand the constitutive to time), (or material)is the (second law relating rank) them strainby σ∙ tensor, σ is the (second rank) stress tensor, and E is the (forthρ rank)is the mass stiffness density, tensor. is Asthe shownparticle velocity in Figure field2 ,(being the velocities the first derivative and stress of fieldthe variables displacement field with respect to time), is the (second rank) strain tensor, σ is the (second rank) are discretizedstress in atensor, staggered and E is mannerthe (forth rank) on the stiffness spatial tensor. grid As togethershown in Figure with 2, a the leap-frog velocities and updating stress procedure in time (c.f. Figurefield variables2)[ 35 are]. Itdiscretized is shown in a in staggered [35] that manner the schemeon the spatial can grid be writtentogether with for a arbitrary leap‐frog anisotropy and inhomogeneityupdating ofprocedure the elastic in time material (c.f. Figure behaviour. 2) [35]. It is shown in [35] that the scheme can be written for arbitrary anisotropy and inhomogeneity of the elastic material behaviour.

Figure 2. The staggered discretization of field variables velocity v and stress σ in the elastodynamic Figure 2. Thefinite staggered integration discretization technique (EFIT). of field variables velocity v and stress σ in the elastodynamic finite integration technique (EFIT). Figure 3 shows EFIT results for the SAM measurement of a coated sample at nine time‐steps. In accordance with the SAM measurement, an anti‐reflective coating (ARC) on the lens was Figure3 implemented.shows EFIT The results ultrasonic for field the is SAMdepicted measurement by the normalized of magnitude a coated of samplethe z‐component at nine of time-steps. In accordancethe withvelocity the field SAMin Figure measurement, 3. The sound wave anis excited anti-reflective by the transducer coating in Figure (ARC) 3, time‐steps on the 1 lens was implemented. The ultrasonic field is depicted by the normalized magnitude of the z-component of the velocity field in Figure3. The sound wave is excited by the transducer in Figure3, time-steps 1 Coatings 2017, 7, 230 5 of 11 Coatings 2017, 7, 230 and 2, and propagates from top to bottom through the lens body (time (time-step‐step 3) towards the surface of the sample (time (time-step‐step 4). At At the the surface (time (time-step‐step 5), 5), part of the sound field field is transmitted into the sample (time-step(time‐step 6).6). The remainingremaining soundsound field field is is reflected reflected and and travels travels back back to to the the lens lens at at time-steps time‐steps 7 7and and 8. At8. At time-step time‐step 9, the 9, reflectedthe reflected sound sound waves waves reach thereach transducer. the transducer. The artificial The artificial A-scan is A obtained‐scan is obtainedby summing by summing up the z-component up the z‐component of the velocity of the field velocity along field the width along of the the width transducer of the at transducer the position at theof the position transducer. of the transducer.

Figure 3. EFITEFIT simulation simulation of SAM measurement, time steps 1–9.

The II((zz)) measurement, measurement, carried carried out out via via SAM, SAM, was was simulated simulated for the for case the caseof (1) of an (1) aluminium an aluminium block 3 ofblock approximately of approximately 40 × 50 40 × 3× mm50 ×, referred3 mm3, to referred as bulk to aluminium, as bulk aluminium, and (2) an and aluminium (2) an aluminium coating of approximatelycoating of approximately 1 μm thickness, 1 µm thickness,deposited depositedon a silicon on wafer a silicon (100). wafer In accordance (100). In accordance with the SAM with measurement,the SAM measurement, we implemented we implemented a transducer a transducer of approximately of approximately 430 MHz 430 centre MHz frequency centre frequency and a lensand‐ aopening lens-opening angle of angle 120° of in 120 the◦ simulationin the simulation for case for (1). case For (1). the For simulation, the simulation, isotropic isotropic linear elastic linear material behaviour was assumed, in accordance with [13]. The assumption of isotropy is made for aluminium because its Zener anisotropy ratio is close to one [40]. Literature values for the longitudinal Coatings 2017, 7, 230 6 of 11

Coatings 2017, 7, 230 elastic material behaviour was assumed, in accordance with [13]. The assumption of isotropy is madeand transversal for aluminium sound because velocity its and Zener the anisotropy density of ratioaluminium is close were to one used [40 ].as Literature input values values [7,40]. for theThe longitudinalsimulation was and transversalcarried out soundfor more velocity than and30 defocus the density positions, of aluminium and the were A‐scan used data as input was valuesassembled [7,40 for]. The each simulation of them. From was carried the A‐scan out fordata, more the thanrelevant 30 defocus time window positions, was and identified, the A-scan and data the wasintensity assembled was computed for each of and them. integrated From the over A-scan the identified data, the relevanttime interval. time windowFor case was(2), the identified, aluminium and thecoating intensity on a was silicon computed substrate, and literature integrated values over the for identified the longitudinal time interval. and transversal For case (2), sound the aluminium velocity coatingand the ondensity a silicon of substrate,aluminium literature as well valuesas silicon for thewere longitudinal used as input and values, transversal taken sound from velocity [7,40]. andThe thesimulation density ofwas aluminium carried out as wellfor a as transducer silicon were of used400 MHz as input centre values, frequency taken from and [ a7 ,40lens]. ‐Theopening simulation angle wasof 60°. carried For more out for than a transducer 30 defocus of positions, 400 MHz centre the A frequency‐scan data and were a lens-openingcomputed and angle the ofintensity 60◦. For of more the thanacoustic 30 defocus signal as positions, a function the A-scanof the datadefocus were position computed z was and computed. the intensity The of thefrequency acoustic‐dependent signal as a functiondamping of of the the defocus coupling position liquidz was was computed. implemented The frequency-dependent via an exponential dampingdamping of factor the coupling in the liquidsimulation, was implemented and due to viathe an spherical exponential focus damping of the factorlens used in the in simulation, the SAM andmeasurement, due to the sphericalan axial focussymmetric of the simulation lens used inalong the SAMthe z‐axis measurement, was performed an axial [36]. symmetric simulation along the z-axis was performed [36]. 2.4. Laser Ultrasound (LUS) 2.4. LaserThe laser Ultrasound ultrasonic (LUS) measurement is described in [3–6]. Here, a pulsed laser is focused via a cylindricalThe laser lens ultrasonic on the sample measurement surface, exciting is described a Rayleigh in [3 –wave.6]. Here, A second, a pulsed continuous laser is focused wave laser via is a cylindricalused in order lens to on detect the sample the Rayleigh surface, wave, exciting using a Rayleigh a beam deflection wave. A second, approach. continuous A schematic wave of laser the isset used‐up is in shown order in to Figure detect the4. From Rayleigh the measurement wave, using at a beam two detection deflection points, approach. the phase A schematic velocity of the set-upRayleigh is shownwave v inR as Figure function4. From of frequency the measurement f (Equation at two 3) can detection be determined points, the via phase [3–6]: velocity of the

Rayleigh wave vR as function of frequency f (Equation 3)2π can be determined via [3–6]: (3) Φ Φ (x2 − x1) 2 π f vR( f ) = (3) In Equation (3), x2 − x1 is the distance betweenΦ2( fthe) − detectionΦ1( f ) points and Φ denotes the phases of the Fourier‐transformed laser‐induced signals.

Figure 4. Schematic of laser-inducedlaser‐induced ultrasound (LUS) set-up;set‐up; CW laser denotes a continuous wave laser, SAW denotesdenotes aa surfacesurface acousticacoustic wave.wave.

In the case of (1), the calibration measurement on bulk aluminium, Rayleigh waves were excited In Equation (3), x2 − x1 is the distance between the detection points and Φ denotes the phases of via a pulsed laser at 11 positions. The applied Nd:YAG laser has a pulse width of approximately the Fourier-transformed laser-induced signals. 2 ns, a repetition rate of 10 Hz, and a wavelength of 532 nm. For the 11 cases, the excited Rayleigh In the case of (1), the calibration measurement on bulk aluminium, Rayleigh waves were excited waves were detected via a second continuous wave laser. The time at which the Rayleigh waves via a pulsed laser at 11 positions. The applied Nd:YAG laser has a pulse width of approximately 2 ns, passed the detection point are plotted as function of the distance the waves travelled in Figure 5. a repetition rate of 10 Hz, and a wavelength of 532 nm. For the 11 cases, the excited Rayleigh waves For the aluminium coating, the pulsed laser from the calibration measurement was used in were detected via a second continuous wave laser. The time at which the Rayleigh waves passed the order to excite broadband Rayleigh waves on the sample. The measurement was performed in the detection point are plotted as function of the distance the waves travelled in Figure5. frequency range up to 200 MHz. The Rayleigh wave velocity was obtained from the measurement For the aluminium coating, the pulsed laser from the calibration measurement was used in at two detection points via Equation (3). Since the Rayleigh wave velocity depends on frequency order to excite broadband Rayleigh waves on the sample. The measurement was performed in the in the case of a coated sample, a theoretical model for the evaluation of the dispersion curve was frequency range up to 200 MHz. The Rayleigh wave velocity was obtained from the measurement considered [13]. In the theoretical model, isotropic material behaviour is assumed. This assumption at two detection points via Equation (3). Since the Rayleigh wave velocity depends on frequency is valid if the measurement is carried out along a symmetry axis of the silicon [3–6]. Our measurements were performed along the [110] symmetry axis of the silicon sample. Coatings 2017, 7, 230 7 of 11 in the case of a coated sample, a theoretical model for the evaluation of the dispersion curve was considered [13]. In the theoretical model, isotropic material behaviour is assumed. This assumption is valid if the measurement is carried out along a symmetry axis of the silicon [3–6]. Our measurements were performedCoatings 2017, 7 along, 230 the [110] symmetry axis of the silicon sample.

Coatings 2017, 7, 230

Figure 5. LUS measurement on bulk aluminium. Comparison of EFIT result to LUS measurement. Figure 5. LUS measurement on bulk aluminium. Comparison of EFIT result to LUS measurement. 3. ResultsFigure 5. LUS measurement on bulk aluminium. Comparison of EFIT result to LUS measurement. 3. Results 3.3.1. Results Aluminium Bulk Sample for Calibration 3.1. Aluminium Bulk Sample for Calibration In the case of the aluminium sample, the simulated intensity I as function of the defocus In3.1.positions the Aluminium case z ofis shown the Bulk aluminium Sample in Figure for Calibration6, sample, in direct the comparison simulated to intensity the SAM Imeasurement.as function of From the Figure defocus 6, positionsthe z is shownperiodicityIn in the Figure caseof the 6of ,I( in zthe) directoscillation aluminium comparison Δz was sample, determined to thethe SAMsimulated and measurement.used intensityto calculate I From asthe function Rayleigh Figure ofwave6 ,the the velocity defocus periodicity positionsvR via z ≅is shownΔ ,in according Figure 6, into direct[22]. Incomparison [22], the important to the SAM property measurement. of the IFrom(z) curves Figure in 6, the the of the I(z) oscillation ∆z was determined and used to calculate the Rayleigh wave velocity vR via ∼periodicitypevaluation ofof theRayleigh I(z) oscillation wave velocities Δz was is determined appointed to and be Δusedz, not to the calculate amplitude. the Rayleigh However, wave differences velocity vR = f v0∆z, according to [22]. In [22], the important property of the I(z) curves in the evaluation in the amplitudes of the I(z) curves in Figure 6 might stem from actual higher damping coefficients of RayleighvR via wave≅ velocitiesΔ, according is appointed to [22]. In to [22], be ∆thez, important not the amplitude. property of the However, I(z) curves differences in the in evaluation(e.g., for water of Rayleigh we used wave literature velocities values is appointed for the damping to be Δz ,coefficient; not the amplitude. the damping However, in the differences sapphire the amplitudes of the I(z) curves in Figure6 might stem from actual higher damping coefficients inlens the body amplitudes is not includedof the I(z in) curves our simulations). in Figure 6 mightConcerning stem fromthe LUS actual measurement, higher damping the slope coefficients of the (e.g., for water we used literature values for the damping coefficient; the damping in the sapphire (e.g.,linear for fit water in Figure we used5 was literature used to determinevalues for thethe Rayleighdamping wave coefficient; velocity. the The damping EFIT, SAM, in the and sapphire LUS lens bodylensresults body is are not is listed not included includedin Table in 1, in our in our comparison simulations). simulations). to a literature Concerning value the the for LUS the LUS Rayleighmeasurement, measurement, wave velocitythe slope the in slope ofbulk the of the linearlinearaluminium fit in fit Figure in Figure[7].5 was 5 was used used to determineto determine the the Rayleigh Rayleigh wave velocity. velocity. The The EFIT, EFIT, SAM, SAM, and and LUS LUS resultsresults are listedare listed in in Table Table1, 1, in in comparison comparison to to a aliterature literature value value for the for Rayleigh the Rayleigh wave velocity wave velocityin bulk in bulkaluminium [7]. [7 ]. Intensity [a.u.] Intensity Intensity [a.u.] Intensity

Figure 6. EFIT simulation (diamonds) and SAM measurement (circles) of I(z) for the aluminium bulk sample at 430 MHz.

Figure 6. EFIT simulation (diamonds) and SAM measurement (circles) of I(z) for the aluminium bulk Figure 6. EFIT simulation (diamonds) and SAM measurement (circles) of I(z) for the aluminium bulk sample at 430 MHz. sample at 430 MHz.

Coatings 2017, 7, 230 Coatings 2017, 7, 230 8 of 11 Table 1. Rayleigh wave velocity results for an aluminium sample.

Table 1. RayleighMethod wave velocityΔ resultsz (μm) for anv aluminiumR (m/s) sample. EFIT 13 2896 Method ∆z (µm) vR (m/s) SAM 13 2896 EFIT 13 2896 SAMLUS 13– 2969 2896 LiteratureLUS [7] –– 2906 2969 Literature [7] – 2906 3.2. Aluminium Thin Film on Silicon Substrate 3.2. Aluminium Thin Film on Silicon Substrate Here, Here,the simulation the simulation of I( ofz) Ion(z) an on aluminium an aluminium coating coating with with a a thickness of of approximately approximately 1 µ m1 μm on a siliconon substrate a silicon substrate (100) was (100) performed. was performed. The The simulated simulated results results areare directly directly compared compared to the to SAM the SAM measurementmeasurement in Figure in Figure 7. 7. Intensity [a.u.] Intensity

FigureFigure 7. EFIT 7. EFIT simulation simulation (diamonds) (diamonds) and and SAM SAM measurement measurement (circles) (circles) of I(z) for of an I aluminium(z) for an coating aluminium coatingon on silicon silicon sample sample at 400 at MHz. 400 MHz.

FigureFigure 8 shows8 shows the the RayleighRayleigh phase phase velocity velocityvR as functionvR as offunction frequency. of The frequency. solid line corresponds The solid line correspondsto the theoretical to the theoretical model, predicting model, thepredicting Rayleigh the dispersion Rayleigh curve dispersion of a 1 µm curve aluminium of a coating1 μm aluminium on a coatingsilicon on a substrate. silicon substrate. The dotted The line indotted the frequency line in range the frequency from 50 to 200 range MHz from was obtained 50 to 200 by laserMHz was obtainedultrasonic by laser measurements, ultrasonic measurements, where good agreement where was good found. agreement The empty was diamond found. corresponds The empty to thediamond EFIT simulation result, and the full circle corresponds to the SAM measurement. corresponds to the EFIT simulation result, and the full circle corresponds to the SAM measurement. There is only one data point obtained from the SAM measurement and SAM simulation data Therebecause is only the measurement one data point and simulation obtained were from performed the SAM in tone measurement burst mode in and order SAM to obtain simulation signals data becausewhich the aremeasurement very narrow inand the frequencysimulation domain were (in performed our case at 400in MHz).tone burst The LUS mode measurement in order uses to obtain signalsbroadband which are acoustic very surface narrow waves in inthe a frequencyfrequency range domain from about (in 50our MHz case to 200at MHz.400 MHz). The LUS measurementThe uses wavelengths broadband considered acoustic in this surface work waves are on the in ordera frequency of 10 µm. range This meansfrom about that they 50 do MHz to 200 MHz.penetrate the coating and their propagation is influenced by the substrate. However, the aluminium Thecoating wavelengths has a measurable considered influence in this on the work phase are velocity on the of theorder Rayleigh of 10 wave μm. (seeThis Figure means8). that they do penetrate the coating and their propagation is influenced by the substrate. However, the aluminium coating has a measurable influence on the phase velocity of the Rayleigh wave (see Figure 8). Coatings 2017, 7, 230 9 of 11 Coatings 2017, 7, 230 Phase [m/s] Velocity

FigureFigure 8. 8. RayleighRayleigh wave wave velocity velocity as as function function of of frequency frequency for a 1 μµm aluminium coating on silicon.

4. Discussion Discussion and and Conclusions In this work, SAM I((z)) measurements were were simulated simulated via via EFIT, EFIT, where (1) an aluminium bulk sample for calibration calibration and (2) (2) an an aluminium aluminium-coated‐coated silicon silicon wafer were were analysed. analysed. From From the the II((zz)) curves, curves, the Rayleigh wave velocity of samples (1) and (2)(2) werewere determined.determined. The simulated results were corroborated viavia non-destructivenon‐destructive SAM SAM and and LUS LUS measurements. measurements. The The obtained obtained results results demonstrate demonstrate that thatthe presented the presented approach approach is highly is highly useful useful for the for material the material characterization characterization of coatings. of coatings. The results summarized in Tables 1 1 and and2 2give give integer integer values values for for the the I(z) periodicity Δ∆z,, because the SAM measurement is is limited limited by the the number of oscillations and and the the 2 2 μµm steps of defocus positions. Moreover, the number of evaluable A‐scans is restricted due to multi‐reflected signals in positions. Moreover, the number of evaluable A-scans is restricted due to multi-reflected signals the measurement and in the simulation. Nevertheless, the Rayleigh wave velocities evaluated via in the measurement and in the simulation. Nevertheless, the Rayleigh wave velocities evaluated via EFIT simulations and SAM measurements are corroborated via the LUS method. The error in the EFIT simulations and SAM measurements are corroborated via the LUS method. The error in the determined Rayleigh velocity of the LUS measurements lies in the range of ±10 m/s. determined Rayleigh velocity of the LUS measurements lies in the range of ±10 m/s.

Table 2. Rayleigh wave velocity results at 400 MHz for 1 μm aluminium coating on silicon. Table 2. Rayleigh wave velocity results at 400 MHz for 1 µm aluminium coating on silicon.

Method Δz (μm) vR (m/s) Method EFIT ∆z (µm)38 4775v R (m/s) EFITSAM 3840 4899 4775 SAMTheoretical Model 40– 4819 4899 Theoretical Model – 4819 The advantages of the performed EFIT simulation tackle the challenges of state‐of‐the‐art SAM measurements—namely,The advantages of the accurate performed data EFITinterpretation simulation and tackle the choice the challenges of the most of state-of-the-art suitable transducer. SAM Inmeasurements—namely, addition, the most effective accurate lens datafor a interpretationspecific sample and can the be designed choice of via the EFIT most simulation suitable transducer. support. In addition, the most effective lens for a specific sample can be designed via EFIT simulation support. Acknowledgments: The authors thank Jördis Rosc (MCL) for valuable discussions and Manfred Wießner (MCL) forAcknowledgments: the XRD measurements.The authors PVA thank TePla Jördis Analytical Rosc (MCL)Systems for GmbH, valuable (Westhausen, discussions Germany) and Manfred is gratefully Wießner acknowledged,(MCL) for the XRD especially measurements. Peter Czurratis, PVA TePla Peter Analytical Hoffrogge Systems and Tatjana GmbH, Djuric (Westhausen,‐Rissner Germany)for their contribution is gratefully regardingacknowledged, the SAM especially equipment. Peter This Czurratis, work Peterhas received Hoffrogge funding and Tatjana from ENIAC Djuric-Rissner Joint undertaking for their contribution under FP7 researchregarding (No. the 621270) SAM equipment. and FFG (No. This 843740) work hasand received partly from funding the EU, from H2020 ENIAC (No. Joint 688225). undertaking Financial support under FP7 by research (No. 621270) and FFG (No. 843740) and partly from the EU, H2020 (No. 688225). Financial support theby Austrian the Austrian Federal Federal Government Government (in particular (in particular from Bundesministerium from Bundesministerium für Verkehr, für Innovation Verkehr, und Innovation Technologie und andTechnologie Bundesministerium and Bundesministerium für Wissenschaft, für Wissenschaft, Forschung Forschung und undWirtschaft) Wirtschaft) represented represented by by Österreichische Österreichische Forschungsförderungsgesellschaft mbH mbH and and the the Styrian Styrian and and the the Tyrolean Tyrolean Provincial Government, represented by Steirische Wirtschaftsförderungsgesellschaft mbH mbH and and Standortagentur Standortagentur Tirol, Tirol, within the framework of the COMET Funding Programme (No. 837900) is also gratefully acknowledged. Author Contributions: Roland Brunner conceived and designed the experiments; Eva Grünwald (LUS&SAM), Author Contributions: Roland Brunner conceived and designed the experiments; Eva Grünwald (LUS&SAM), Philipp Aldo Wieser (SAM) and Robert Nuster (LUS) performed experimental work; René Hammer and Philipp Aldo Wieser (SAM) and Robert Nuster (LUS) performed experimental work; René Hammer and Eva Grünwald performed simulations for the experimental work; Rudolf Zelsacher and Michael Ehmann manufactured Coatings 2017, 7, 230 10 of 11

Eva Grünwald performed simulations for the experimental work; Rudolf Zelsacher and Michael Ehmann manufactured the samples; Martin Hinderer and Ingo Wiesler developed the tone burst device for the SAM. Eva Grünwald and Roland Brunner wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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