Measurement of the thickness of thin layers by ultrasonic interferometryM. Houze, B. Nongaillard, M. Gazalet, J. M. Rouvaen, and C. Bruneel Citation: Journal of Applied Physics 55, 194 (1984); doi: 10.1063/1.332863 View online: http://dx.doi.org/10.1063/1.332863 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/55/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Direct measurement of ultrasonic velocity of thin elastic layers J. Acoust. Soc. Am. 101, 626 (1997); 10.1121/1.417965 Remote ultrasonic measurement of the thickness of thin films J. Acoust. Soc. Am. 84, 1094 (1988); 10.1121/1.396695 Feasibility of Thin Film Thickness Monitoring by Holographic Interferometry J. Vac. Sci. Technol. 9, 1080 (1972); 10.1116/1.1316994 Thickness Measurements of Thin Permalloy Films: Comparison of X-Ray Emission Spectroscopy, Interferometry,and Stylus Methods J. Vac. Sci. Technol. 2, 203 (1965); 10.1116/1.1492425 The Thickness Measurement of Thin Films by Multiple Beam Interferometry J. Appl. Phys. 21, 843 (1950); 10.1063/1.1699770

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Measurement of the thickness of thin layers by ultrasonic interferometry M. Houze, B. Nongaillard, M. Gazalet, J. M. Rouvaen, and C. Bruneel Laboratoire d'Opto-acousto-electronique (ERA No. 593 c'N.R.S.) Universite de Valenciennes, 59326 Valenciennes Cedex, France

(Received 28 April 1983; accepted for publication 19 July 1983)

An ultrasonic interferometer working in a pulsed mode is described in this paper. It allows for the measurement of coating thicknesses as thin as 5 flm with a 5% precision over different substrates at a very high rate (up to 1000 times per second). The optimal conditions for this interferometric measurement are defined theoretically and the probe characteristics have been optimized technologically. This, together with the design of a very large frequency bandwidth (from 90 to 510 MHz) electronic setup, leads to interesting performances. The advantages of the system for achieving thickness measurements are discussed and comparisons are made with other systems.

PACS numbers: 68.60. + q, 06.70.Mx, 43.35.Ns, 43.35.Yb

I. INTRODUCTION

The thickness of a coating is directly related to its phys­ical and mechanical properties, such as the appearance and rigidity. Its evaluation is therefore crucial in many industrial applications. Many different physical parameters may be used to measure the thickness of a material. A number of apparatuses are commercially available for this purpose, which rely on the propagation of ionizing radiation, the ca­pacitance variation of a condensor, the reluctance variation of a magnetic circuit, or the losses by eddy currents. The ultrasonic methods prove to be advantageous owing to the fast measurement time, the ability to test coatings over non­metallic substrates and the ability to perform automated continuous measurements. In this later application, a nonri­gid contacting method may be used to test the sample through a single accessible face. The ultrasonic systems which are actually available are based upon a round trip time measurement method 1 and as such are not well suited for thicknesses less than 100 flm if a reasonable limit is kept for the ultrasonic pulses duration. 2 In order to remedy the lack of apparatus for this thickness range, an interferometric ul­trasonic system has been worked out. It allows measurement at very high rate (up to 1000 times per second) of coating thicknesses between 5 and 20 flm over very different sub­strates (aluminum, steel, lucite ... ). Moreover, the coating thickness is set to a predetermined value, the measurement system can be used for continuous monitoring and feedback control. The interferometer technique is harder to imple­ment than the round trip time one, but it must be considered for small thicknesses. In order to design the system several problems have been solved, first to theoretically define the optimal conditions for the interferometric measurement and second to design the ultrasonic probe and the electronic set­up.

preclude the direct transposition to the testing of moving parts. Therefore, our system will use pulse modulated sig­nals and water coupling for the contact. The water thickness between the probe and the sample to be measured is chosen so that the significant echoes 2 and 3 (see Fig. 1) which come from the front and back faces of the sample, are time separat­ed from those parasitic ones due to multiple reflection inside water. The pulse duration must be taken longer than the

II. PRINCIPLE OF THE MEASUREMENT: THEORETICAL RESULTS

Ultrasonic interferometry is a well known method, which is mainly used to measure phase velocities at low fre­quencies. 3

-5 However, the experimental conditions often

used in this case, namely, a rigid contact between the probe and the sample and a continuous wave mode of operation,

coating

:d~ fused silica substrate

sducer ~ 1 I-

water , tran

a) Z1 Z2 Z3

~/\I

b)

c)

FIG. 1. Geometry and timing for the thickness measurement. (a) Water­coating-substrate system. (b) Amplitude maximum for the constructive in· terference of two echoes (2 and 3) at a/ = 207.6·MHz frequency. (c) Ampli­tude minimum for the destructive interference of two echoes (2 and 3) at a f = 254.5-MHz frequency.

194 J. Appl. Phys. 55 (1),1 January 1984 0021-8979/84/010194-05$02.40 © 1983 American Institute of Physics 194

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round trip time of ultrasound inside the coating, in order to allow for the overlapping of the significant echoes.

A theoretical study has been carried to deduce the var­iations of the interferometric electric signal B against the frequency J, with mechanical impedances ZI' Z2' Z3 for the three media (water coating substrate) and pulse duration as parameters. Taking the reflection and transmission coeffi­cient at the interfaces II' and 12, into account, the amplitudes for successively reflected and transmitted ultrasonic waves may be computed.

The balance is obtained by summing over a finite num­ber n of echoes, which depends directly on the pulse dura­tion. The reflection coefficient Rn at the interface II may be expressed as:

R~ = [R~ +R~ +(1-R~fR~(n-I)R~n+2RIR2COS¢

+2( -l)nR~-IR~+I(l-Rf)cos{(n -1)¢ J

+ 2( - 1 n 1 - R ~ )(R IR 2 )n cos n¢ ]I

where,

RI = (Z2 - Zd/(Z2 + Zd,

R2 = (Z3 - Z2)1(Z3 + Z2) ,

(1)

(2)

(3)

are, respectively, the reflection coefficients at interfaces II and 12 and

¢ = 41Tel/v, (4)

stands for the phase lag due to a round trip of the ultrasonic wave inside the coating with thickness e, at the velocity v.

The prime derivative of Rn with respect to ¢ may be written as

(5)

It follows that the extrema of the reflection coefficient Rn versus the variable ¢ /21T occur at frequencies or thicknesses such that

(i) sin ¢ = 0,

(ii) Xn (¢ ) = 0 .

The solutions ofEq. (6) are evidently given by

4e1= kv,

where k is a positive integer.

(6)

(7)

(8)

They don't depend on the number n of overlapping ech­oes. The frequency gaps 111m and 111M corresponding to two successive minima and maxima, respectively, are given by

e = v/2J1lm = v/2J1/M . (9)

The measurements of the frequency gaps allows for the de­termination of the (e/v) ratio, and, consecutively, of the thickness if the velocity is known. So, for given material, the thinner the coating the higher the frequency gaps will be.

The second Eq. (7) gives (n-2) solutions, if n > 2, over a frequency range of width V/4e' corresponding to a single solution ofEq. (6). Let us consider the most useful case where the reflection coefficients at the interfaces II and 12 are of the same order of magnitude. This corresponds well to the mea­surement of a paint coating over a metallic substrate with water coupling. By studying the curvature of the function

195 J. Appl. Phys., Vol. 55, No.1, 1 January 1984

Rn (¢), it may be pointed out that the secondary extrema from Eq. (7) are only sensible around the main maxima from Eq. (6). So they cannot perturb the thickness measurement if the main minima are detected and frequency gap 111m is used.

The variations ofR n versus¢ /21Tare shown in Fig. 2 for different pulse duration using mechanical impedances corre­sponding to a paint coating over a steel base.

III. EXPERIMENTAL SETUP

The first step of the experimental realization is a choice of an operating frequency bandwidth, which is a function of the thickness range to be measured. Let I1lmax stand for the maximum value of 111m obtained for the minimal value emin of the thickness to be measured. The ratio of the maximal (stop) h to minimal (start) II frequencies for the sweeping ratio frequency generator is given by

12/11 = 5(3 I1lmax + 2 (/)/(3 I1lmax - 10 (/), (10)

where 0 I has been allowed to join the minima precisely. For obtaining Eq. (10) it has been assumed that two

minima, at least, must be found over the measurement range for all thicknesses greater than emin . An upper limit is im-

0.5 1.5 2 C1J vr

FIG. 2. Theoretical variations of Rn vs,p 12rr for different pulse durations using mechanical impedances corresponding to a paint coating over a steel base. Z, = 1.5 X 106 kg!m2 s. Z2 = 5.6 X 106 kg!m2 s. Z, = 40 X 106 kg! m2 s.

Houzeetal. 195

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posed on the frequency h by the ultrasonic attenuation in the diffe~ent media and a lower one by the need of significant relative frequency bandwidth for the transducer. From the previous criteria, a frequency variation from 90 to 510 MHz is needed to measure paint thicknesses down to 4 f..lm (v = 2500 mls for typical paints).

The next step is to design optimal geometry for the ul­trasonic probe and the water coupling column. The water thic~nes.s has been chosen equal to 100 f..lm in order to sepa­rate III time the useful echoes 2 and 3 (see Fig. 1) from the parasitic ones due to multiple reflections inside water. Fused silica has been used for the acoustic delay line material of the probe, since the transmission losses from water amounts to only 4.4 dB.

The ultrasonic interferometric measurement of thick­ness calls for the overlapping of echoes 2 and 3 and time separation of echoes 1 and 2 (see Fig. 1). This leads to the inequalities

2elv<T<2Iwlvw ' (11)

Is> (/jvw + 2elv) Vs , (12)

where Iw, Is and e are the thicknesses of, respectively, the water, silica rod, and paint coating, Vw ' v,, and v being the respective velocities in the same media, and T is the pulse duration.

The maximal value of paint (v = 2500 m/s) thickness to be measured is, in our case, equal to 20 f..lm. The pulse dura­tion lies therefore between 16 and 133 ns. In order to keep the thickness Is to technologically compatible minimum, it has been fixed to 1 mm. The transducer has been worked out from a lithium niobate (360 rotated Y cut), lapped and thinned to a 1= 7.4-f..lm thickness. An active area (A of 0.8 mm2

) has been chosen in order to get a flat response curve for echo 2 (see Fig. 3). This arises from a close compensation between the variations in electromechanical coupling effi­ciencies, those in the ultrasonic transmission and propaga­tion losses inside the different media and in the electronic receiver gain. The electronic setup is shown in Fig. 4. It is designed to fulfill the severe requirements imposed by the very large frequency bandwidth used. For this purpose, a constant electronic detection in frequency is utilized, like for

losses (dB)

., .... '"""'-. __ .,_,.,_.' a '.'-'.'- ............. _ .... --... - ... -- ... -

100 200 300 400 510 f(MHZ)

FIG. 3. Performances of the system: (a) frequency response for echo 2 (Fig. I); (bl attenuation losses inside fused silica; (c) attenuation losses inside wa­ter; (d) transmission losses at the silica-water interface; (e) frequency re­sponse of electronic setup; (f) frequency response of transducer.

196 J. Appl. Phys., Vol. 55, No.1, 1 January 1984

FIG. 4. Electronic setup.

spectrum analyzers. At the emission stage, an output leveled sweeping generator covering the 90-51O-MHz frequency range is used. Its output is then pulse modulated and fed to the ultrasonic transducer through a directional coupler. From this coupler, the reflected echoes may be received. Us­ing a delayable gate, the useful overlapping echoes 2 and 3 may be picked up and the parasitic ones rejected, so that the electronic receiver may have an appreciable gain without being saturated. A tracking local oscillator, whose output frequency is at each time shifted by a constant value from that of the sweeping generator, is realized using an electronic mixer and a low pass filter.

The detected signal is fed to a sample and hold circuit whose gate is synchronized with the emission pulse, delayed and set inside the overlapping signal. The output of the sam­ple and hold circuit is passed through a low pass filter, whose cutoff frequency is a function of the frequency slope of the sweeping generator. The output signal is fed to the vertical amplifier of an oscilloscope or a plotter and the synchroniz­ing sawtooth from the sweeping generator is applied to the horizontal amplifier. The frequencies at different places in the setup are given in Table I.

IV_ EXPERIMENTAL RESULTS

Several curves have been drawn on a plotter, giving the amplitUde of the overlapping signal for different runs of paint thickness measurement (5, 10, and 20 f..lm) over differ­ent base (aluminum, galvanized steel). They are shown in Fig. 5, where a close agreement with the theoretical ones

TABLE I. Frequencies at different places in the setup.

Sweeping generator

Local oscillator (/0)

After mixer MX I

After the low-pass filter

After mixer MX2

After selective amplifier and before detection

Frequencies (MHz)

90-510

290

380-800 and DC-200

DC-200

290 and DC-7JO

290

Houzeetal. 196

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a)

b)

c)

FIG. 5. XY recorder trace of the amplitude of the interferometric output signal. Three illustrations of thickness measurements of paint coating. (a) Measurement of paint (v = 2325 m/s) on aluminum base: e = 19 p.m. (b) Measurement of finition paint (v = 2200 m/s) on cold laminated steel: e = IO.S p.m. (c) Measurement of primary paint (v = 2250 m/s) on galvan­ized steel base: e = 4.3 p.m.

TABLE II. Relative thickness variations.

Foucault Foucault's Thickness

thickness ratio

Paint Base (p.m) r,

Metallized Aluminum IS.8

paint 18.3 1.027

Finition Cold 18.5 paint laminated 1.054

steel 19.5

Finition Cold 11 paint laminated 1.1

steel 10

Primary Galvanized 5 paint steel 6 1.2

197 J. Appl. Phys., Vol. 55, No.1, 1 January 1984

may be seen. Secondary maxima occur near the principal ones, so that the minima must be used, as deduced before theoretically, for the thickness measurement. The frequen­cies corresponding to the first and last detected minima have been measured using a frequency meter. The precision of the thickness measurement increases linearly with the number of minima detected over the sweeping frequency range.

A mean velocity value, deduced from some ten mea­surements over one squared centimeter around the tested points is obtained by assuming the correctness of the thick­ness derived from Foucault's method. On the curves of Fig. 5, the frequency gap between two consecutive minima is giv­en together with the values of the thickness deduced from a Foucault's method measurement and from our setup. The measured velocity inside the point material is also given. Detailed results are given in Table II, which gives a compari­son of relative, measurements done using eddy currents and our ultrasonic setup. The maximum discrepancies between ultrasonic interferometry and Foucault's method arise for the small thickness case, where the absolute variations in the paint layer thickness are important. The ultrasonic probe used in our setup does not integrate over a very large area, unlike Foucault's a measurement apparatus, which inte­grates over a ten to twenty times higher area. In order to perform dynamic measurement over moving parts (up to a 100 m per min velocity), an automatic electronic system has been designed. The measurement rate may reach a thousand per second figure, which allows the real time monitoring of paint thickness. In order to perform such a task, this system must be now included in a fabrication unit.

CONCLUSION

In the actual nondestructive thickness measurement apparatuses, a rigid contact is often needed between the probe and the coating to be measured. Moreover, some of these systems rely upon the physical properties of the base material, like the Foucault's eddy current ones, which give a

Ultrasonic interferomet!J: Relative

Interminima Thickness difference

frequency ratio R= 2\72 - rii T2 - r 1

gap (MHz) r2 (%)

62.9 63.4

1.007 2

55.3 1.058 0.38

52.3

85 1.055 4.2

89.7

225 198.5 1.13 6

Houze etal. 197

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systematic error, arising from the existence of a protecting layer deposited using galvanoplasty. The setup reported here allows measurements with a light fluid contact and gives the information needed for monitoring the coating system. A 5% precision is obtained for a thickness of 5 flm, so that our ultrasonic interferometry apparatus performs its measure­ment as well as more complex and less flexible, time consum­ing systems.

Such results have been obtained after optimizing the probe characteristics over a very large frequency bandwidth. Moreover, an electronic system has been designed, which can deliver the digital informations about thickness at a rate

198 J. Appl. Phys., Vol. 55, No.1, 1 January 1984

of 1000 measurements per second. These informations may be scaled to the acoustic wavelength in the general case, or directly to micrometers if the acoustic velocity is known.

'Lawrence C. Lynnworth, IEEE Trans. Sonics Ultrason. SU-22 (1975). 2Sidney Lees, IEEE Trans. Sonics Ultrason. SU·lS (1971). 'Jack G. Parks, Rev. Sci. Instrum. 41 (1970). 4J. Paul Day, Paul S. Ho, and ArthurL. Ruoff, Rev. Sci. Instrum. 44 (1973). 5R. G. Leisure and R. W. Moss, Rev. Sci. Instrum. 40 (1969).

Houze etal. 198

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