Thickness measurement of coatings and characterization of surfaces with surface waves - Part 1: Guide to the determination of elastic constants, density and thickness of films by laser induced surface acoustic waves

This document gives guidance on methods of determining the elastic constants, density and thickness of thin films by laser-induced surface acoustic waves.
It defines terms and described procedures.

Schichtdickenmessung und Charakterisierung von Oberflächen mittels Oberflächenwellen - Teil 1: Leitfaden zur Bestimmung von elastischen Konstanten, Dichte und Dicke von Schichten mittels laserinduzierten Ultraschall-Oberflächenwellen

Dieses Dokument legt einen Leitfaden fest für die mechanische Charakterisierung von Oberflächen mit laserinduzierten Ultraschall-Oberflächenwellen zur Bestimmung von elastischen Konstanten, der Dichte sowie der Dicke von dünnen Schichten.
Es legt Messverfahren und Begriffe fest.

Mesure de l'épaisseur des revêtements et caractérisation des surfaces à l'aide d'ondes de surface - Partie 1 : Guide pour la détermination des constantes élastiques, de la masse volumique et de l'épaisseur des films à l'aide d'ondes acoustiques de surface générées par laser

Le présent document constitue un guide relatif aux méthodes de détermination des constantes élastiques, de
la masse volumique et de l’épaisseur de films fins à l’aide d’ondes acoustiques de surface générées par laser.
Le mode opératoire de mesurage et les termes employés y sont définis.

Merjenje debeline nanosa prevlek in karakterizacija valovitih površin – 1. del: Vodilo za ugotavljanje prožnosti, specifične teže in debeline prevlek z laserjem, ki povzroča valovito akustično površino

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2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Thickness measurement of coatings and characterization of surfaces with surface waves - Part 1: Guide to the determination of elastic constants, density and thickness of films by laser induced surface acoustic wavesMesure de l'épaisseur des revetements et caractérisation des surfaces a l'aide d'ondes de surface - Partie 1 : Guide pour la détermination des constantes élastiques, de la masse volumique et de l'épaisseur des films a l'aide d'ondes acoustiques de surface générées par laserSchichtdickenmessung und Charakterisierung von Oberflächen mittels Oberflächenwellen - Teil 1: Leitfaden zur Bestimmung von elastischen Konstanten, Dichte und Dicke von Schichten mittels laserinduzierten Ultraschall-OberflächenwellenTa slovenski standard je istoveten z:EN 15042-1:2006SIST EN 15042-1:2006en17.040.20ICS:SLOVENSKI

STANDARDSIST EN 15042-1:200601-september-2006

EUROPEAN STANDARDNORME EUROPÉENNEEUROPÄISCHE NORMEN 15042-1April 2006ICS 17.040.20 English VersionThickness measurement of coatings and characterization ofsurfaces with surface waves - Part 1: Guide to the determinationof elastic constants, density and thickness of films by laserinduced surface acoustic wavesMesure de l'épaisseur des revêtements et caractérisationdes surfaces à l'aide d'ondes de surface - Partie 1 : Guidepour la détermination des constantes élastiques, de lamasse volumique et de l'épaisseur des films à l'aided'ondes acoustiques de surface générées par laserSchichtdickenmessung und Charakterisierung vonOberflächen mittels Oberflächenwellen - Teil 1: Leitfadenzur Bestimmung von elastischen Konstanten, Dichte undDicke von Schichten mittels laserinduzierten Ultraschall-OberflächenwellenThis European Standard was approved by CEN on 2 March 2006.CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such nationalstandards may be obtained on application to the Central Secretariat or to any CEN member.This European Standard exists in three official versions (English, French, German). A version in any other language made by translationunder the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the officialversions.CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania,Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATIONCOMITÉ EUROPÉEN DE NORMALISATIONEUROPÄISCHES KOMITEE FÜR NORMUNGManagement Centre: rue de Stassart, 36

B-1050 Brussels© 2006 CENAll rights of exploitation in any form and by any means reservedworldwide for CEN national Members.Ref. No. EN 15042-1:2006: E

EN 15042-1:2006 (E) 2 Contents Page Foreword..............................................................................................................................................................3 1 Scope......................................................................................................................................................4 2 Normative references............................................................................................................................4 3 Terms and definitions...........................................................................................................................4 4 Symbols and abbreviations..................................................................................................................5 5 Description of the method....................................................................................................................6 6 Determination of the elastic constants, density thickness of the film...........................................16 7 Test report............................................................................................................................................19 Annex A (informative)

Material data..............................................................................................................21 Annex B (informative)

Other methods for determining Young's modulus of film materials...................23 Bibliography......................................................................................................................................................26

EN 15042-1:2006 (E) 3 Foreword This document (EN 15042-1:2006) has been prepared by Technical Committee CEN/TC 262 “Metallic and other inorganic coatings”, the secretariat of which is held by BSI. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by October 2006, and conflicting national standards shall be withdrawn at the latest by October 2006.

According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

EN 15042-1:2006 (E) 4 1 Scope This document gives guidance on methods of determining the elastic constants, density and thickness of thin films by laser-induced surface acoustic waves. It defines terms and described procedures. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. EN ISO 11145:2001, Optics and optical instruments — Laser and laser-related equipment — Vocabulary and symbols (ISO 11145:2001) International Vocabulary of Basic and General Terms in Metrology, 2nd Edition 1994, Beuth Verlag GmbH Berlin Wien Zürich 3 Terms and definitions For the purposes of this document, the terms and definitions given in the International Dictionary of Metrology (VIM), EN ISO 11145:2001 and the following apply.

3.1 surface acoustic waves ultrasonic wave propagating along the surface of the material NOTE An important property of this wave is the penetration depth into the material, which depends on frequency. 3.2 phase velocity velocity at which the phase of the wave propagates 3.3 group velocity

velocity at which the surface acoustic wave impulse induced by the laser propagates 3.4 dispersion dependence of the phase velocity on the frequency of the wave 3.5 dispersion relation ratio of angular frequency to the amount of the wave vector (wave number) 3.6 dispersion degree difference between phase and group velocity NOTE The dispersion degree is expressed as a percentage. 3.7 bandwidth

frequency range of the amplitude spectrum

EN 15042-1:2006 (E) 5 3.8 measuring length distance between the positions at which the dispersion curve is measured 3.9 thermo-elastic inducing inducing a surface acoustic wave by locally rapid heating of the test material as the result of absorbing a pulsed laser radiation 4 Symbols and abbreviations a half length of the side of membrane for the membrane deflection technique;

c phase velocity of the surface acoustic wave; c(E', E, ν', ν, ρ ', ρ, d, fk) theoretical values of the phase velocity (calculated for example according [2]); c(fk) phase velocity of the measured dispersion curve; C1, C2 constants (functions of the Poisson’s ratio ν); d

film thickness; dS substrate thickness; dN
nitriding depth; δ
indentation depth;
∆f frequency shift;

∆d uncertainty of the film thickness; ∆E uncertainty of Young’s modulus of the film;

uncertainty of Poisson’s ratio of the film;
uncertainty of the density of the film; ∆E’

uncertainty of Young’s modulus of the substrate; ∆ν’ uncertainty of Poisson’s ratio of the substrate; ∆ρ’ uncertainty of the density of the substrate; E*

Young’s modulus; E Young’s modulus of the film; E' Young’s modulus of the substrate; Eo Young’s modulus of the indenter;

EI Young’s modulus determined by indenter test; ELA Young’s modulus determined by the laser-acoustic method; fk frequency values of the measured dispersion curve; f frequency; f0 resonance frequency of the resonance test method; F force;

h deflection of membrane deflection technique;

hp plastic indentation depth of the indenter test; k magnitude of the wave vector; light wavelength of the light of Brillouin-scattering technique; p pressure of the membrane deflection technique;

ν* Poisson’s ratio;
EN 15042-1:2006 (E) 6 ν Poisson’s ratio of the film;
ν’ Poisson’s ratio of the substrate; νo Poisson’s ratio of the indenter;

scattering angle of the Brillouin-scattering method; ρ* density; ρ density of the film;

ρ’ density of the substrate; σE residual stress; ω

angular frequency; TA annealing temperature; U voltage amplitude. 5 Description of the method 5.1 General principles The elastic modulus (Young's modulus) of the film essentially determines the mechanical behaviour of the coated material, the development of residual stresses, the mechanical energy induced by externally loading the coated surface, influencing creation and growth of cracks in the film and, therefore, influencing essentially the failure behaviour of the coated material. Especially for hard coatings, Young's modulus correlates with hardness that can be measured only with increasing error for reducing film thickness. The structure of coatings can vary within a wide range, depending on the deposition process. This accompanies a Young's modulus of the film which varies considerably. The value tabulated for the bulk material therefore is only a very rough estimation for the material deposited as film. They are given for some selected materials in Annex A. Consequently, measuring the film modulus is a method for controlling the film quality and monitoring the technological process. For measuring Young's modulus of the film, several static and dynamic techniques are used, such as the membrane deflection test, indentation test, Brillouin-scattering, ultrasonic microscopy and resonance vibration test. An overview of the principles of these alternatives is given in Annex B.

These methods are characterised to require special sample preparation, to be time-consuming, or to fail for films of sub-micrometer and nano-meter thickness. The laser-acoustic technique is a practicable method for reproducibly determining Young's modulus of films with thickness down to less than 10 nm without special sample preparation. The technique also enables the film thickness to be measured and provides access to the film density. The method can also be used to characterise layers with gradually varying properties perpendicular to the surface as created by transition hardening and nitriding steels or machining the surface of semiconductor materials. The applicability of the method can be limited by the ultrasonic attenuation of the test material. 5.2 Surface acoustic waves 5.2.1 Properties The test method is based on measuring the dispersion of surface acoustic waves that have a vibration component perpendicular to the surface.

Surface acoustic waves propagate along the surface of the test sample. For isotropic media, their penetration depth is defined to be the distance to the surface where the wave amplitude is decreased to 1/e of the amplitude at the surface A (Figure 1). Approximately, the penetration depth can be equated with the

EN 15042-1:2006 (E) 7 wavelength λ. The penetration depth of the surface acoustic wave reduces with increasing frequency, following the relation:

fc=λ (1) where c
is the
phase velocity,
in m/s; f
is the

frequency, in Hz. The phase velocity depends on the elastic constants and the density of the material.

For a homogeneous isotropic half-space, the following approximation is used ()∗∗∗∗∗+++=vEvvc1112,187,0ρ (2) where v∗ is the

Poisson's ratio; E∗ is the Young's modulus, in N/m2; ∗ is the density, in kg/m3. Equation (2) does not apply to anisotropic materials which are more complex as described in [2]. Key 1

film 2
substrate 3
amplitude within the material A

amplitude at the surface AλA/e = 0,37A123λ123AA/e = 0,37A 1a) — Low frequency: long wavelength, high penetration depth, little effect of the film 1b) — High frequency: short wavelength, low penetration depth, large effect of the film Figure 1 — Properties of the surface acoustic waves

EN 15042-1:2006 (E) 8 5.2.2 Surface acoustic waves in coated materials The surface wave velocity of a material varies by coating with a film with physical properties deviating from the substrate (see Figure 1). It also depends on the elastic properties and the density of film and substrate material and the ratio of film thickness to wavelength. For a homogeneous isotropic film on homogeneous isotropic substrate, the following general relation applies:

()λρρω/,,,,,,dvEvEckc′′′== (3) where c is the phase velocity, in m/s;

is the circular frequency, in Hz; k is the magnitude of wave vector, in 1/m; E' is the Young's modulus of the substrate, in N/m2; v'

is the Poisson's ratio of the substrate; '

is the density of the substrate, in kg/m3; E is the Young's modulus of the film, in N/m2; v is the

Poisson's ratio of the film;
is the density of the film, in kg/m3; d is the thickness of the film in m;

is the wavelength, in m. Equation (3) is the dispersion relation for the surface wave propagating in coated materials. The implicit form of this relation is deduced from the boundary conditions of stress and displacement components at the surface and the interface between film and substrate [2].

For anisotropic film and substrate materials, the elastic constants Cij are used instead of Young's modulus and Poisson ratio.

The effect of the film on the wave propagation increases with increasing frequency of the wave due to its reducing penetration depth. This makes the wave velocity dependent on frequency. Figure 2 shows three characteristic cases.

EN 15042-1:2006 (E) 9 Key X axis = f, in MHz Y axis = c, in m/s 1 Silicon (100) without film 2 Film of amorphous carbon on silicon: E = 411 Gpa ρ = 2,69 g/cm3 d = 5,58 µm 3 Film of polyamide on silicon:

E = 3,8 GPa ρ = 1,4 g/cm3
d = 1,85 µm
Measured Calculated

Figure 2 — Two cases of dispersion of the surface acoustic wave in coated material compared to the case of non-coated material

The film properties in Figure 2 (Young's modulus, density, film thickness) were deduced from the measured curve by the inverse solution of the dispersion relation (3). The curves can be explained as follows. The velocity is independent on the frequency for the non-coated silicon substrate.

The diamond-like carbon film on the silicon makes the dispersion curve to increase. The wave velocity is higher for the film than for the substrate. The dispersion curve decreases with frequency for the silicon coated by a polyamide. The wave velocity is lower for the film than for the substrate. The shape of the dispersion curve characterises the film-substrate-compound. The intersection with the velocity axis at the frequency f = 0 defines the wave velocity of the substrate depending on the elastic parameters and the density of the substrate as given in relation (2) for isotropic materials.

The shape of the curve itself depends on the ratio of the elastic constants and the ratio of the density of film and substrate and on the film thickness as well. The test method consists in measuring the dispersion curve and deducing the material parameters from the inverse solution of the dispersion relation.

For a given combination of film and substrate material, a generalised dispersion curve can be defined, depending on the film thickness normalised to the wavelength.

For the same material, all measuring points fit the same generalised curve independent of the film thickness. Figure 3 shows an example for the case of diamond-coated silicon.

EN 15042-1:2006 (E) 10 Key X axis = c, in m/s Y axis = d/ 5900m/s5800570056000,005500540053005200510050000,020,040,060,080,100,120,140,165XY1234 4321 d = 0,08 µm, measured d = 0,95 µm, measured d = 3,7 µm, measured Theoretical dispersion curve calculated for d = 3,7 µm, E’ = 1 029 GPa and ρ = 3,54 g/cm3

5 Velocity of the surface acoustic waves for (100)-Silicon in [011]-direction Figure 3 — Generalized dispersion curve for diamond films on silicon single crystals depending on the ratio d/

The curve shown in Figure 3 was measured for three samples with different film thickness. The measured segments of curve nearly exactly fit the theoretical curve. The restriction that the dispersion can only be measured with limited bandwidth, 200 MHz in this case, prevent one from measuring the complete dispersion for all film thickness. Therefore, the several measurements cover only a limited segment of the theoretical curve calculated for a wide range. Figure 3 reveals the measured curve to contain less information with reducing film thickness so that less film parameters can be obtained for thinner films.

5.2.3 Surface acoustic waves in non-homogeneously coated materials The dispersion of surface acoustic waves can also be used to characterise surface modifications with gradually varying properties perpendicular to the surface instead of the step-like behaviour of the properties of coating. Figure 4 shows the example of a nitrided steel with three different nitriding depths. The surface treatment makes a diffusion layer with continually decreasing hardness into the material.

If a suitable theory for the surface wave propagating in gradient layers is not available, the measuring method can be calibrated by samples with known hardening depth. This enables the hardening depth to be determined non-destructively for nitrided components.

EN 15042-1:2006 (E) 11 m/s3140312031003060025751001251503160308050MHzYX123 Key X axis = f, in MHz Y axis = c, in m/s

321 dN = 105 µm dN = 80 µm dN = 60 µm Figure 4 — Dispersion curves for nitrided steel samples with different nitriding depth

The dispersion curve has a characteristic form for a special gradient of the microstructure, which can be used for controlling the technological process. These characteristic curves should be defined, belonging to the upper and lower limit for the tolerable quality.

5.3 Measuring technique 5.3.1 Principles Obtaining reliable information on coatings or micro-structural gradients perpendicular to the surface requires measurement of the dispersion curve with a bandwidth as wide as possible. Therefore, a spectral measuring method is used.

Short laser pulses generate thermo-elastically wide-band surface acoustic wave impulses. Having passed the distance x, these impulses are received by a suitable detector, for example, a piezoelectric transducer or an interferometric technique.

Figure 5 presents two surface acoustic wave pulses received at two different distances x1 and x2 between the focus line of the laser beam and a piezoelectric detector. The different shape of the waveform at position x2 compared to position x1 reveals the dispersion of the surface acoustic wave. It contains the information of the film properties.

EN 15042-1:2006 (E) 12 The detected impulses uj(t) (j = 1 and 2) are Fourier-transformed tdtitufU××=∫∞∞−)(exp)()(jjω (4) and the phase spectrum calculated as follows πφ2nfUfUf+=)(Re)(Imarctan)(jjj (5) The ambiguity of the phase value n2π is determined from the dispersion degree following the procedure described in [3].

123X1 X2123 Key X axis = t, in µs Y axis =
u, in V 1 laser beam

2 detector 3 sample u1(t) signal, detected at distance x1 u2(t) signal, detected at distance x2 X3,23,33,43,53,63,7µsu

(t)1v0,40,20,0-0,2-0,4YX4,44,54,4v0,2u

(t)20-0,24,64,74,8YFigure 5 — Laser-acoustic signals for two different distances x1 and x2

The phase velocity is obtained from the relation )()()()(1212ffxxfcΦ−Φ−=ω

(6) The distance (x2 – x1) represents the measuring length. The final result is a spectrum of values of the phase velocity depending on frequency. Its frequency range is determined by the bandwidth of the surface acoustic wave impulse, illustrated in Figure 6.

EN 15042-1:2006 (E) 13 Key X axis =
f, in MHz Y axis =
c, in m/s Z axis =

u, in V 1 Amplitude spectrum 2 Phase velocity 3 Frequency range of the measurement 5220m/s52005180516005140512051005080506050100150200250300MHz3X10,112YZ Figure 6 — Deducing the frequency range of the measured dispersion curve from the amplitude spectrum of the impulse

The measurement provides reliable values for the phase velocity only in the frequency range of a high enough amplitude []{}[]{}2j2jj)(Im)(Re)(fUfUfU+=. This frequency range is defined by the 3 dB-bandwidth of the amplitude spectrum.

Taking into account at least two impulses received at different distances between the source of the ultrasound (position of the focused laser beam) and the detector enables a difference measuring method to be performed. In this way, the effect of the measuring device is eliminated.

5.3.2 Example of realising a measuring equipment An example of a measuring equipment is shown in Figure 7. A nitrogen pulse laser (wavelength: 337 nm, pulse duration: 0,5 ns, pulse energy: 0,4 mJ) generates thermo-elastically surface acoustic wave impulses. The laser beam is focused by a cylindrica

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