Scanning Joule expansion microscopy at nanometer scalesJ. Varesi and A. Majumdar Citation: Applied Physics Letters 72, 37 (1998); doi: 10.1063/1.120638 View online: http://dx.doi.org/10.1063/1.120638 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/72/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Enabling low-noise null-point scanning thermal microscopy by the optimization of scanning thermal microscopeprobe through a rigorous theory of quantitative measurement Rev. Sci. Instrum. 85, 114901 (2014); 10.1063/1.4901094 Temperature measurements of heated microcantilevers using scanning thermoreflectance microscopy Rev. Sci. Instrum. 84, 034903 (2013); 10.1063/1.4797621 Imaging Joule heating in a conjugated-polymer light-emitting diode using a scanning thermal microscope Appl. Phys. Lett. 84, 4890 (2004); 10.1063/1.1762988 High-resolution scanning thermal probe with servocontrolled interface circuit for microcalorimetry and otherapplications Rev. Sci. Instrum. 75, 1222 (2004); 10.1063/1.1711153 Study of the hot spot of an in-plane gate transistor by scanning Joule expansion microscopy J. Appl. Phys. 84, 6917 (1998); 10.1063/1.368989

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.6.218.72

On: Tue, 09 Dec 2014 13:16:18

Scanning Joule expansion microscopy at nanometer scalesJ. VaresiDepartment of Mechanical Engineering, University of California, Santa Barbara, California 93106

A. Majumdara)

Department of Mechanical Engineering, University of California, Berkeley, California 94720

~Received 27 May 1997; accepted for publication 31 October 1997!

We report a new technique called scanning Joule expansion microscopy that can simultaneouslyimage surface topography and material expansion due to Joule heating with vertical resolution in the1 pm range and lateral resolution similar to that of an atomic force microscope. By coating thesample with a polymer film, we demonstrate that sample temperature distribution can be directlymeasured without the need of fabricating temperature-sensing scanning probes. ©1998 AmericanInstitute of Physics.@S0003-6951~98!01401-6#

The inventions of the scanning tunneling microscope1

~STM! and the atomic force microscope2 ~AFM! have led tothe development of numerous scanning probe microscopes~SPMs! that image surface topography and other surfaceproperties with nanometer-scale spatial resolution. The scan-ning thermal microscope~SThM! was first developed by fab-ricating a coaxial thermocouple at the end of a sharp metaltip.3 Since then researchers using SThM have usually fabri-cated thermocouples or other temperature sensors on the veryend of AFM cantilever tips.4–12 To increase SThM spatialresolution, much effort has been focused towards reducingsensor size to submicrometer scales. This, however, hascome at the cost of fabrication difficulty, particularly for sen-sor diameters below 0.5mm.6–12 In addition, the best reso-lution reported so far has been about 25 nm, which is limitedby the size of the tip–sample liquid film bridge.12 In re-sponse to increased fabrication difficulty as well as to furtherimprove the resolution, we propose a new technique calledscanning Joule expansion microscopy~SJEM! which elimi-nates the need for sensor nanofabrication while having a po-tential spatial resolution of 1–10 nm.

Figure 1 shows the schematic diagram of our SJEM sys-tem. An AFM is used to bring a sharp tip into force-controlled contact with the sample surface and perform araster scan. Applied to an electrically conducting sample is asinusoidal or pulsed voltage which produces sample Jouleheating and temperature rise, resulting in sample thermal ex-pansion. The AFM photodiode detects the cantilever deflec-tion due to both expansion and sample topography. Since thefeedback controller of the AFM has a bandwidth of 20 kHz,the photodiode signal below 20 kHz is processed for feed-back control of the z-piezo to image surface topography. TheJoule heating frequency is kept above 20 kHz to avoid feed-back response. The lock-in amplifier is tuned to the Jouleheating frequency which detects only the expansion signaland provides this to an auxiliary AFM channel to form theexpansion image. The system can also be operated withoutfeedback in which case the heating frequency can be belowthe controller bandwidth. Detection of sample expansion due

to Joule heating in electronic circuits was first demonstratedusing optical interferometry for expansion measurement.13

The spatial resolution of such far-field optical techniques isdiffraction-limited to about the optical wavelength which ison the order of 1mm. Material expansion was also addressedby Weaveret al.14 who measured optical absorption using anSTM. However, due to lack of sufficiently high resolution,they did not report any images. We demonstrate here thatone can obtain expansion images with spatial resolution onthe order of 10 nm. Since the expansion signal is a convolu-tion of surface topography, expansion coefficient, and tem-perature rise, we propose a scheme for directly extracting thetemperature distribution from the expansion signal.

Figure 2 shows the vibration spectrum of a 200mmlong, 0.6mm thick, and 36mm wide SiNx AFM cantilever incontact with a gold interconnect. Such a cantilever has afree-standing resonant frequency of about 20 kHz which in-creases during surface contact to about 80 kHz as shown.This resonance is highly damped, perhaps due to the pres-ence of a water film. Applied across the interconnect were100 ns voltage pulses at a repetition rate of 36 kHz whichproduce the peaks in the spectrum at the harmonics of thefundamental frequency. One can tune to any of these peaksto obtain SJEM images.

a!Author to whom correspondence should be addressed. Electronic mail:majumdar@me.berkeley.edu

FIG. 1. Schematic diagram of the experimental setup used for scanningJoule expansion microscopy~SJEM!.

37Appl. Phys. Lett. 72 (1), 5 January 1998 0003-6951/98/72(1)/37/3/$15.00 © 1998 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.6.218.72

On: Tue, 09 Dec 2014 13:16:18

Figure 3 shows an image obtained by SJEM. Thissample was composed of two parallel 160-nm-thick goldlines patterned by electron-beam lithography on a SiO2 sub-strate. A sinusoidal bias of amplitude 1.4 V at 30 kHz wasapplied to the sample. The expansion image cross sectionshows an expansion signal of about 1.6 V after a 66 dB gain.With a photodiode sensitivity of 30 nm/V, the deflectionmeasured in this case was 24 pm. Using the spectrum shownin Fig. 2, the vertical resolution limit for the SJEM systemcan be estimated. The noise floor in the range of 60–80 kHzis approximately2100 dB or 1025 V/AHz. With a lock-inamplifier bandwidth of 26 Hz and a photodiode sensitivity of30 nm/V, the noise was 1.5 pm. This results in signal-to-noise ratios of 16:1 for the expansion image in Fig. 3.

The deflection of the cantilever in response to an acsample bias could be due to several reasons, namely:~1!sample expansion due to Joule heating of the sample;~2!thermally induced cantilever bending resulting from a bima-terial effect due to the presence of the metal coating on thebackside of the cantilever;~3! a pressure wave resulting fromthermal expansion of the surrounding gas;~4! electrostaticforces between the tip and the sample; and~5! piezoelectricdeformation of the sample. To remove the possibility of bi-material effect, the Au–Cr coating on the AFM cantileverwas etched away. However, removal of the metal film wasnot entirely necessary since the thermal time constant of such

bimaterial cantilevers was calculated and measured15 to beabout 0.17–0.33 ms—an order of magnitude lower than thecorresponding frequencies used in this study. With the probein contact with a Joule heated sample in a vacuum of 1025

Torr, the expansion signal remained unchanged thus elimi-nating acoustic excitation as the signal source. When thedemetallized cantilever tip was taken out of contact but stillwithin a few nanometers away from the sample, the expan-sion signal was absent. This eliminated electrostatic forceinteractions. The choice of gold as the sample eliminates thepossibility of piezoelectric effect since gold is not a piezo-electric material. Moreover, since the piezoelectric effect de-pends on the electric field, it would require the expansionsignal to be linear with applied voltage. TheV2 dependenceof the expansion signal shown in Fig. 4 strongly indicatesthat it is most likely due to Joule heating since power dissi-pation and temperature rise are proportional toVrms

2 /R,whereVrms is the root-mean-square applied voltage andR isthe sample electrical resistance.

The local expansion signal,l (r , f ), at vector position,r ,on the sample surface and frequency,f , can be written asl (r , f )5a(r )L(r )DT(r , f ), wherea(r ) is the local thermalexpansion coefficient,L(r ) the local sample height, andDT(r , f ) the local temperature rise at frequency,f . Since thelocal height,L(r ), is already contained in the topography,the expansion signal can be used to obtain local materialcharacteristics througha(r ) or temperature rise throughDT(r , f ). We now demonstrate howl (r , f ) can be deconvo-luted to directly obtainDT(r , f ). To remove material and

FIG. 5. Comparison of the experimental measurements and theoretical pre-dictions of the expansion signal of a poly~methyl methacrylate! ~PMMA!film coating a gold interconnect fabricated on a glass substrate. The inter-connect was biased at a frequency of 20 kHz.

FIG. 2. Vibrational spectrum of the 200mm long, 0.6mm thick, and 36mmwide SiNx AFM cantilever in contact with gold interconnect across which100 ns voltage pulses were applied at a repetition rate of 36 kHz. Note thehighly damped resonance at 80 kHz for the in-contact cantilever. Superim-posed on the white noise background are the expansion signals at the har-monics of the pulsed bias.

FIG. 3. Topographical and Joule expansion images~4 mm 3 4 mm! of two160 nm thick gold lines patterned by electron-beam lithography on a SiO2

substrate. An ac bias of 1.4 V and current density of 5.93 1010 A/m2at 30kHz was applied to the lines. The expansion signal was measure by a lock-inamplifier tuned to 60 kHz with a bandwidth of 26 Hz.

FIG. 4. Expansion signal of gold line as a function of applied bias.

38 Appl. Phys. Lett., Vol. 72, No. 1, 5 January 1998 J. Varesi and A. Majumdar This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.6.218.72

On: Tue, 09 Dec 2014 13:16:18

topography nonuniformity, the samples were uniformlycoated with a thin layer of a polymer, specifically polymeth-ylmethacrylate~PMMA!. The thermal expansion coefficientof polymers is typically about 1024 K21, which is an orderof magnitude higher than that of metals and two orders ofmagnitude larger than that of most ceramics. Hence, if thePMMA film thickness is on the same order as the metal filmthickness, the expansion signal of the PMMA film will domi-nate. Figure 5 shows a comparison between experimentaldata of the polymer expansion and theoretical predictions16,17

of the normalized temperature distribution of a gold inter-connect deposited on a glass substrate and biased at 20 kHz.

To demonstrate the potential of this technique for highresolution expansion microscopy, Fig. 6 shows topographyand expansion images of an indium tin oxide~ITO! resistorcontaining grains ranging from 50 to 100 nm in lateral size.As shown in the cross section, the higher grains result in alarger expansion signal in accordance with the relationl5aLDT. It is clear that not only can the single grains beresolved, but that there does not appear to be any loss ofspatial resolution between the topographical and expansionimages. This is certainly promising and suggestive that ther-mal and expansion imaging may now be possible at the spa-tial resolution of the AFM, which is in the range of 1–10 nmand perhaps even sub-1 nm.

This work was funded by National Science Foundation~Grant No. CTS-9796166!. The authors’ sincere appreciationgoes out to E. Caine~UCSB! for fabricating line samples andK. Hijikata of Tokyo Institute of Technology for providingITO samples. Thanks also are extended to F. Milstein and P.

Hansma of UCSB for careful reading and insightful com-ments.

1G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Phys. Rev. Lett.49, 57~1982!.

2G. Binnig, C. F. Quate, and Ch. Gerber, Phys. Rev. Lett.56, 930 ~1986!.3C. C. Williams and H. K. Wickramasinghe, Appl. Phys. Lett.49, 1587~1986!; in Photoacoustic and Photothermal Phenomena, edited by P. Hessand J. Peizl, Series on Optical Sciences,~Springer, Berlin, 1987!, p. 364;Proc. SPIE897, 129 ~1988!.

4A. Majumdar, J. P. Carrejo, and J. Lai, Appl. Phys. Lett.62, 2501~1993!;A. Majumdar, J. Lai, M. Chandrachood, O. Nakabeppu, Y. Wu, and Z.Shi, Rev. Sci. Instrum.66, 3584~1995!.

5J. B. Xu, K. Lauger, K. Dransfeld, and I. H. Wilson, Rev. Sci. Instrum.65,2262 ~1994!.

6M. Maywald, R. J. Pylkii, and L. J. Balk, Scanning Microsc.8, 181~1994!.

7R. J. Pylkki, P. J. Moyer, and P. E. West, Jpn. J. Appl. Phys., Part 133,3785 ~1994!; A. Hammiche, D. J. Hourston, H. M. Pollock, M. Reading,and M. Song, J. Vac. Sci. Technol. B, Part 114, 1486~1996!.

8M. Stopka, L. Hadjiiski, R. Oeterschulze, and R. Kassing, J. Vac. Sci.Technol. B13, 2153~1995!.

9G. Fish, O. Bouevitch, S. Kokotov, and K. Lieberman, Rev. Sci. Instrum.66, 3300~1995!.

10R. C. Davis, C. C. Williams, and P. Neuzil, Appl. Phys. Lett.66, 2309~1995!.

11K. Luo, Z. Shi, and A. Majumdar, Appl. Phys. Lett.68, 325 ~1996!.12K. Luo, Z. Shi, J. Varesi, and A. Majumdar, J. Vac. Sci. Technol. B15,

349 ~1997!.13Y. Martin and H. K. Wickramasinghe, Appl. Phys. Lett.50, 167 ~1987!.14J. M. R. Weaver, L. M. Walpita, and H. K. Wickramasinghe, Nature

~London! 342, 783 ~1989!.15J. Lai, T. Perazzo, Z. Shi, and A. Majumdar, Sens. Actuators A58, 113

~1997!.16J. Varesi, MS Thesis, Department of Mechanical Engineering, University

of California, Santa Barbara, 1997.17J. Varesi and A. Majumdar~unpublished!.

FIG. 6. Topographical and Joule expansion images of a polycrystalline indium-tin-oxide~ITO! resistor.

39Appl. Phys. Lett., Vol. 72, No. 1, 5 January 1998 J. Varesi and A. Majumdar This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.6.218.72

On: Tue, 09 Dec 2014 13:16:18