March 1984 / Vol. 9, No. 3 / OPTICS LETTERS 93

Thermal diffusivity in thin films measured by noncontactsingle-ended pulsed-laser-induced thermal radiometry

Wing P. Leung* and Andrew C. Tam

IBM Research Laboratory, Son Jose, California 95193

Received November 14, 1983; accepted December 30, 1983

A pulsed nitrogen laser is used to induce a sharp thermal gradient in a thin film, and the infrared thermal radiationfrom the irradiated region is monitored from the same side as the excitation beam (i.e., single-ended detection).We show that the profile of this pulsed phqtothermal radiometry signal can be analyzed to provide the thermal dif-fusivity or thickness of the sample as well as information on subsurface modifications or the degree of thermal con-tact with a substrate. We present data for several important classes of film, including metal, polymer, and paper(e.g., in currency) and show the important features of the present technique for thin-film characterization, namely,nondestructive, fast, and remote sensing.

Thermal diffusivity in materials is traditionally mea-sured,1' 2 by contact methods, requiring attachment ofelectrical and thermocouple leads to a sample. Non-contact methods, using all-optical means for excitationand for probing, are also possible for a gaseous sample 3

as well as for a condensed sample. 4 However, mostprevious techniques are doubled ended (i.e., measure-ment devices are on both sides of the sample), makingthem difficult to use on samples in which the back sidesare inaccessible, e.g., remote, bulky, or mounted. Wereport here a new noncontact single-ended techniqueto measure thin-film thermal diffusivity D, if itsthickness I is known (actually, it is 12 /D that is mea-sured, so I can also be measured if D is known). Thissingle-ended pulsed photothermal radiometry (PPTR)technique 5 is shown to be quite useful for remotemonitoring of the properties thin films and their ther-mal contacts with surroundings.

Our experimental arrangement is shown in Fig. 1. Apulsed laser of pulse duration TL (full width at halfmaximum) is incident upon a thin-film sample in air.The laser wavelength XL is chosen such that the sampleis highly opaque at AL (i.e., absorption length <c samplethickness /); pulse width T L must be much shorter thanthe characteristic thermal diffusion time ti. We haveused a short-pulsed ultraviolet laser for this experiment(Molectron UV12 nitrogen laser with T

L = 8 nsec andXL = 337 nm). The laser energy emitted is about 1 mJ;and it is suitably attenuated (by up to a factor of 100)so that sample damage does not occur within the irra-diated area, which is about 0.2 cm2. The pulsed laserincident upon the opaque sample produces a sharpspatial temperature profile f(z) at time t = 0, with zbeing the distance into the sample (z = 0 is the irradi-ated top surface and z = 1 is the back surface). Thisinitial temperature profile f(z) causes heat diffusionfrom the irradiated surface into the sample, thus re-ducing the top surface temperature 00(t) (above ambi-ent temperature To). However, when the heat diffusionreaches the back surface, further cooling of the topsurface is hindered; i.e., the decay of 00(t) with t char-

acteristically slows down after the critical time tI, givenby

t, = 12/(4D). (1)

We monitor 00 (t) by observing the broadband in-frared (IR) gray-body thermal emission5-9 from the ir-radiated surface, using a liquid-nitrogen-cooled Hd-Cd-Te detector (New England Research, ModelMPP-12-2-JI) sensitive to 8-12-gm radiation with a risetime of 0.5 gsec. For simplicity in the present discus-sion, we assume that the sample is opaque in the IR(true for the metal films studied). The detected tran-sient IR signal S(t) is

S(t) = Groj[To + Oo(t)]4 - T04} (2)

or

S(t) - 4GeTo 3G0 (t), (3)

where G is a constant depending on the electronic gainand the detector spectral bandwidth, e is the emissivity

Concave (a)mirror Laser beam

for single-endedradiometTy

Tektronix7854 Oscilloscopewith 7D20 plug-in

Sample /supportring

1 -.0l-8 nsec

N2 Laser

* ., I Laser beamI i M . it,1* for transmissionp -| radiornetry

Thin filmsample

Fig. 1. Experimental apparatus for thin-film measurementusing PPTR technique. The pulsed N2 laser beam repre-sented by solid lines indicates the present single-ended PPTRtechnique, and the N2 laser beam represented by dashed lines(when three mirrors, represented also by dashed lines, areinstalled) indicates the double-ended transmission thermalradiometry method used in Refs. 4 and 10.

0146-9592/84/030093-03$2.00/0 © 1984, Optical Society of America

94 OPTICS LETTERS / Vol. 9, No. 3 / March 1984

of the sample surface averaged over the detectorbandwidth, and cr is the Stefan-Boltzmann constant.Approximation (3) [true in our experiments since typ-ically Oo(0) - 10'Cl indicates that the observed IR ra-diometry signal S(t) is proportional59 to the top surfacetemperature 00(t).

Quantitative calculation of the transient top andbottom surface temperatures [00(t) and 01(t), respec-tively] has been given by Parker et al. 10 (based on thework of Carslaw and Jaeger 1 1) for large time, i.e., t >g 2/D, where g is the longest of the optical or absorptiondepths, or the thermal diffusion lengths during the laserpulse or the detector rise time:

c(t)l K[1 + 2 E (+1)nexp(-n2co)] X (4)

where K is a constant independent of time and co is adimensionless time given by

i 2 tC =---,4 tU

(5)

with t, being given by Eq. (1). Expressions (3) and (4)indicate that the PPTR signal S(t) monitoring 00(t) ofan isolated homogeneous film at long time has a uni-versal shape once the time-scale parameter t 1 is defined;that is, we should be able to fit the signal S(t) by thetheoretical form of Eq. (4) by optimizing just one freeparameter t1, which defines the dimensionless time co.This indicates that (1) the above PPTR method is a newsingle-ended remote-sensing method to measure eitherthe thermal diffusivity D or the thickness I of a thin filmand (2) we should be able to detect any case of noniso-lation or inhomogeneity of a film (e.g., if the film is at-tached to a backing instead of being freestanding or ifthe film is layered instead of being uniform) by thecharacteristic deviation of the signal S(t) from the shapeof 00 (t) in Eq. (4). These conclusions are supported byour experimental results described below. Further-more, we have also performed the well-known trans-mission radiometry technique 4 "0 [i.e., monitoring 01(t)of Eq. (4), as indicated in Fig. 1], obtaining results in

0 C e1 20 30 10Ial 1. "I 1

(c)

Fig. 2. (a) Observed PPTR signals for five Type 302 stain-less-steel sheets of thicknesses 12.5, 25, 50, 75, and 125 Am.Horizontal scale is 100 ,sec/div. (b) The lower trace is themagnified signal for the 12.5-pm-thick steel, and the uppertrace is due to the instrumental scattering effect (scatteredN2 laser beam onto the detector) obtained by putting a glassslide (to block 8-12-pm radiation) in front of the Hg-Cd-Tedetector. Horizontal scale is 2 psec/div. (c) Theoretical fitof the PPTR signal by Eq. (4) for large t for the 12.5-pm-thickstainless steel.

QuartzBack ngAir

AJ~inU~!~bidSI Backing

Table 1. Thermal Diffusivities of Some Samples

Thermal Diffusivity D a(10-3 cm2/sec)

Single-I Ended Transmission Other

Sample (gm) PPTR Radiometry Methods

Type 302 12.5 36(8) 32(8)stainlesssteel

25.0 39(9) 44(9) 40.5(Ref. 12)

50.0 36(5) 35(5)125.0 41(6) (signal

too weak)Teflon 89.0 0.84 1.0 0.88

(Ref. 13)

a Obtained by fitting the single-ended PPTR signal by Eq. (4) forlarge t, by analyzing our observed transmission radiometry signal asParker et al. did in Ref. 10, and by other methods given in the liter-ature.

Fig. 3. Observed PPTR signal for a free-standing stain-less-steel sheet of 12 5-Mum thickness (lower trace) comparedwith signal for the same film Iying in contact with a quartzsubstrate (upper trace). Horizontal scale is 50 msec/div.

agreement with those from single-ended PPTR (Table1).

The observed PPTR signals for five sheets of Type302 stainless-steel shims of thicknesses 12.5, 25, 50, 75,and 125 Am are shown in Fig. 2. There is an initialsharp decrease in the signal with time and a final flat-tening of the signal after the heat is uniformly distrib-uted across the thickness so that the surface cooling"stops" (i.e., very slow heat loss to the surrounding airand heat conduction along the film). Although theearly signal (i.e., t $ 10 psec) is unchanged for differentthicknesses since it is spectroscopy related5 and notthickness related, the later signal depends character-istically on the thickness of the sample. A computer

-25,,(- 7 5al - 50' - 25!| 12.5

(a)

Scatterece Light

Only- Signal

+ScatterecLight

(b)

l 2

; ,

i .| - Exp- mer

5 T heO !

SIJ

March 1984 / Vol. 9, No. 3 / OPTICS LETTERS 95

program based on Eq. (4) is developed to fit the latersignal; a theoretical fit is shown in Fig. 2(c), and nu-merical results of the fit are listed in Table 1, whereresults by other measurement techniques are also listedfor comparison. If the back surface of the sample is incontact with a substrate, the shape of the signal for t S~1 msec is unchanged, but the signal at very long timesdecays much faster than in the isolated-film case, asshown in Fig. 3.

Several types of polymer film have been studied bythe PPTR technique, and the result for a Teflon film(0.089 mm thick) is indicated in Fig. 4(a). The signalfor Teflon is somewhat broader than the form predictedby Eq. (4) because Teflon is not highly opaque in theexcitation wavelength (337 nm) or in the detectionwavelength range (8-12,Um).14 The signal 8(t) is nowan integral of IR emission from the bulk of the sampleinstead of only from the top surface, as in the metal-filmcase. By taking this fact into account, 15 we have suc-cessfully fitted the Teflon PPTR signal [Fig. 4(b)] withthe results listed in Table 1.

The observed PPTR signals, when we use a N 2 laserto irradiate 3-mm-diameter regions in various dark-green-colored regions of U.S. currency bills, are indi-cated in Fig. 5. The signal is highly reproducible whendifferent regions of the bill with about the same amountof coloring are irradiated [see Pig. 5(a)], showing thehigh degree of homogeneity of the bill. Also, differentbills produce basically the same signal, showing high

reproducibility of the bills. Other types of paper givedifferent signals; for example, the PPTR signals forthree similar papers (Xerox 4024, Weston bond 25%cotton fiber, and Mead Moistrite XO-2) are given in Fig.5(b). These samples have approximately the samedensity and thickness. The results suggest that PPTRcan be quite useful as a quality-control method forpaper and similar materials.

In conclusion, we have made the first reportedquantitative study of the single-ended PPTR techniquefor noncontact measurement of thermal diffusivities orthickness of an opaque thin film. The examples stud-ied, including metal foils, polymer films, and papers,indicate the wide variety of technologically importantmaterials that can he measured by the present non-contact, fast, and nondestructive technique. We haveshown elsewhere that the early PPTR signal 5"15 is re-lated to the spectroscopic absorption lengths and D.However, the late signal studied here (for t > g2/D) isrelated to the sample thickness and D. Data analysisfor simple cases is discussed here, and details for moregeneral -cases are published elsewhere. 15-

This research is partially supported by the U.S. Officeof Naval Research. We thank G. Sincerbox., B. D.Grant, and H. Coufal for reading this manuscript.

* Permanent address, Department of Physics, TheChinese University of Hong Kong, Shatin, N.T., HongKong.

References

I

(a)

22 6 B -x 1

(b)

Fig. 4. (a) Observed PPTR signal for a Teflon film ofthickness 89Mum. Horizontal scale is 2 msec/div. (b) Fittingof the signal in (a) by theory of Ref. 15.

$< 2

4

(a) MD

Fig. 5. (a) Observed PPTR sig-nal when the N2 1laser is usedto irradiate a dark-green-colored region of a U.S. one-dollarbill: 1 and 2 indicate different regions of a new bill, and 3 and4 indicate different regions of an old bill, showing the highdegree of reproducibility. Horizontal scale, 20 psec/div. (b)Observed PPTR signals for various papers (Xerox 4024,Weston bond 25% cotton fiber, and Mead Moistrite OX-2 fortop, middle, and bottom traces, respectively). Horizontalscale is 2 msec/div.

1. R. P. Tye, ed., Thermal Conductivity (Academic, London,1969).

2. V. V. Mirkovich, ed., Thermal Conductivity 15 (Plenum,New York, 1978).

3. W. Zapka and A. C. Tam, Opt. Lett. 7, 86 (1982).4. H. W. Deem and WV. D. Wood, Rev. Sci. llnstrum. 33,1197

(1962).5. A. C. Tam and B. Sullivan, Appi. Phys. Lett. 43, 333

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(1980).7. P. E. Nordal and S. 0. Kanstad, Phys. Scripta 20, 659

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11. H. S. Carsiaw and J. C. Jaeger, Conduction of Heat in.Solids, 2nd ed. (Claredon, Oxford, 1959).

12. Obtained by using data of thermal conductivity, density,and specific heat of stainless-steel 302 list in C. J. Smi-thells, ed., Mletal Reference Book, 5th ed. (Butterworths,London, 1976).

13. Calculated using thermal conductivity = 2.45 < 10-3W/cm K [T. Ozawa and K. Kanari, Polym. Lett. 5, 767(1967)], heat capacity = 0.29 cal/g K [N. E. Hager, Jr.,Rev. Sci. Instrum. 42, 678 (1971)], and density = 2.28g/CM

3 P4. Brandrup and E. H. Immergut, eds., PolymerHandbook, 2nd ed. (Wiley, New York, 1975), p. V-30.

14. T. Wentink, Jr., and W. G. Planet, Jr., J. Opt. Soc. Am.51, 601 (1971).

15. WV. Leung and A. C. Tam, J. Appl. Phys. (to be pub-lished).