Quenching the thermal contribution in laser assisted scanning tunneling microscopySandra Marcela Landi and Oscar Eduardo Martınez Citation: Journal of Applied Physics 88, 4840 (2000); doi: 10.1063/1.1311834 View online: http://dx.doi.org/10.1063/1.1311834 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/88/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Femtosecond laser assisted scanning tunneling microscopy J. Appl. Phys. 88, 4851 (2000); 10.1063/1.1290706 Thermal effects in pulsed laser assisted scanning tunneling microscopy J. Appl. Phys. 87, 2574 (2000); 10.1063/1.372221 Laser-induced thermal expansion of a scanning tunneling microscope tip measured with an atomic forcemicroscope cantilever Appl. Phys. Lett. 73, 2521 (1998); 10.1063/1.122502 Thermal expansion of scanning tunneling microscopy tips under laser illumination J. Appl. Phys. 83, 3453 (1998); 10.1063/1.366556 Transient tunneling current in laser-assisted scanning tunneling microscopy J. Appl. Phys. 82, 4115 (1997); 10.1063/1.366251

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Quenching the thermal contribution in laser assisted scanningtunneling microscopy

Sandra Marcela Landia) and Oscar Eduardo MartınezLaboratorio de Electro´nica Cuantica. Departamento de Fı´sica, Universidad de Buenos Aires,Pabellon I. Ciudad Universitaria C1428EHA Buenos Aires, Argentina

~Received 4 April 2000; accepted for publication 27 July 2000!

When irradiating the sample of a scanning tunneling microscope with a modulated light intensity,light absorption results in tip and sample heating and expansion at the modulation frequency,obscuring other possible laser induced mechanisms. This thermal noise limits the use of lightmodulation when very high spatial resolution is desired in fluorescence or nonlinear optics near fieldexperiments, being an extreme case the measurement of the optical rectification with scanningtunneling microscopes. In this work we describe a method in which the thermal expansion at themodulation frequency can be reduced by orders of magnitude. The method is based on theirradiation of the sample with two interfering laser beams at different frequencies and incidencedirection, giving light fringes traveling in the illuminated zone. Solving the heat diffusion equationwe predict the thermal behavior of sample and find a good agreement with experimental data.© 2000 American Institute of Physics.@S0021-8979~00!02321-5#

I. INTRODUCTION

By combining scanning tunneling microscopy~STM!with optical excitation, light induced effects on surfaces canbe studied with high spatial resolution. Photocurrent andphotovoltage generation at semiconductor surfaces havebeen used as an imaging mechanism,1–5 or alternatively tostudy local carrier recombination,6–9 to determine carrier re-laxation time10 or to study the electrical properties of thephotoexcited tunnel junction between a metal and asemiconductor.11,12 Imaging by means of nonlinear effects,such as wave mixing and rectification of optical frequencies,has also been reported.13–17

Modulating the light intensity is the common techniquefor extracting the light induced information from the back-ground signal and noise by means of a phase sensitive detec-tion. When irradiating the sample with an intensity-modulated beam, nonresonant light absorption causesperiodic heating of tip and sample, leading to thermal expan-sion at the modulation frequency.18 This effect has been usedto modulate the distance gap and to measure workfunctions.19 Due to the high sensitivity of the tunneling cur-rent to tip-sample distances, a subangstrom thermal modula-tion causes a measurable current. This fact limits the use oflight modulation when very high spatial resolution is desiredin fluorescence or nonlinear optics near field experiments,since the amplitude of photothermal current often hides otherpossible laser induced mechanisms. Several prior works haveaddressed this problem. By analyzing the sample thermalexpansion in the frequency domain, the existence of a cutofffrequency has been determined20,21 that depends on the sub-strate thermal properties, with a high frequency rolloff as1/v above the cutoff. This result suggests the convenience ofmodulating at high frequencies in order to reduce the thermal

contribution to the current. However, the use of frequenciesabove a few kilohertz is restricted by the frequency responseof the STM current amplifiers, even in high frequency STMdesigns.22 Alternatively, a detailed study of the spatial be-havior of sample expansion23 has showed that choosingproperly the beam size and tip location in the spot, it ispossible to increase the signal to noise ratio without the needof driving the experiment at high frequencies.

In this work, we present a method that reduces the ther-mal contribution by many orders of magnitude, based on theirradiation of the sample with two interfering laser beams.When two light beams propagating with different directionsare superimposed on an absorbent medium, the interferencepattern gives rise to spatially periodic temperature variations~thermal gratings!. If the frequency of one of the beams isslightly shifted from that of the other beam, the phase of theinterference pattern will move, giving light fringes travelingin the illuminated zone. In this manner the total thermal loadon the sample is kept constant, while each point is subjectedto a modulated intensity at the difference between the twofrequencies. Solving the heat diffusion equation we com-puted the thermal contribution to the tunneling current due tothe thermal expansion of the sample, showing several ordersof magnitude decrease as compared to the intensity modula-tion scheme. Experimental results on a gold sample arepresented, showing a good agreement with the theoreticalanalysis.

II. THEORY

The proposed setup is shown in Fig. 1. We assume aGaussian spatial profile of equal size and intensity for bothbeams, that superimpose completely on the sample surface.By choosing the angle between the two beams, the gratingperiod L is set along thex axis, and accordingly its wavea!Electronic mail: landi@df.uba.ar

JOURNAL OF APPLIED PHYSICS VOLUME 88, NUMBER 8 15 OCTOBER 2000

48400021-8979/2000/88(8)/4840/5/$17.00 © 2000 American Institute of Physics

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vectorq52p/L. If one of the beams has a carrier frequencyf and the other onef 1D f , with D f ! f , the intensity distri-bution at the sample surface (z50) is

I ~r ,t !5I 0@11cos~qx2vDt !#e2(x21y2)/2s2~1!

being vD52p D f the angular frequency difference,s thebeam half width ate21/2 of the maximum valueI 0 .

For the calculations of the thermal contribution to thetip-sample distance modulation, only the sample expansionis considered. Grafstro¨m et al.24 have discussed the contribu-tion arising from the tip expansion, for the case of intensitymodulation. In our experiment longer tips and larger spotsizes were used, so that the tip expansion has a much lowercutoff frequency and can be neglected.

To obtain the thermal expansion induced by this travel-ing wave scheme, we must first calculate the time evolutionof the laser induced temperature distributionu(r ,t), whichdevelops when heat is deposited on the sample surface. As-suming thermal equilibrium between the electrons and thelattice, which is established after a few picoseconds,25 theheat diffusion model can be used. Then

]u

]t2DrS ]2u

]x21

]2u

]y2D 2Dz

]2u

]z2 5~12R!a

rce2azI ~r ,t !,

~2!

whereR is the surface reflectivity,r is the sample density,cis its specific heat,a is the optical absorption coefficient, andDr and Dz are the lateral and depth thermal diffusivity, re-spectively.

We restrict the calculations to both optically and ther-mally thick samples, satisfying the condition

a21!d!L, ~3!

whered andL are thermal diffusion length and sample thick-ness, respectively. Assuming that condition~3! is valid, we

can infer that no boundary condition at the rear surface mustbe taken into account. Besides the focused light beam istypically much smaller than the sample dimensions. Hence,we consider the sample as a semi-infinite slab of materialwith a boundary at the planez50.

The solution of the heat diffusion equation@Eq. ~2!#,using expression~1! for the intensity distribution, can bewritten as a sum of two terms:u(r ,t)5u0(r )1uv(r ,t). Thefirst one is the stationary solution and can be evaluated bynumerical integration of the following expression:

u0~r !5~12R!P

p k r d0E

0

`

e2u ~z/d0!J0~2ur8!e2u2/2du, ~4!

where P is the incident power,J0 is the 0th order Besselfunction of the first kind,k r is the lateral sample thermalconductivity,r 8 is the distance from center of the spot insunits, andd0 is a parameter defined asd05sADz /Dr .

The parameteru0 is the increase of temperature given bythe constant thermal load on the sample due to this illumina-tion scheme. It will produce a constant thermal expansionthat will be followed by the STM feedback loop. Its valuedepends on the thermal properties of the sample, the incidentpower, and the spot size. For example, when the beam isfocused to 100mm of diameter, for each milliwatt of power,the increment of temperature on surface sample and center ofspot is around 0.01 °C for gold and 0.02 °C for highly ori-ented pyrolytic graphite.

The second term of the solution is the one that yields anoscillation of the temperature at frequencyvD , and results

uv~r ,t !5~12R!P

p k r dqe2r 82/2

e2A12 i ~vD /vq! z/dq

g2A12 i ~vD /vq!ei (qx2vDt),

~5!

where the parameters used have the following definitions:g52p (s/L) takes into account the number of interfer-

ence fringesL within a beam widths,vq5q2Dr the cutoff frequency due to fringes pattern,

determined by the time it takes the heat to diffuse across afringe, and

dq5(1/q)A(Dz /Dr)5A(Dz /vq) the thermal diffusionlength when the modulation frequency isvq .

This oscillating temperature is typically smaller thanu0 .Hence, the temperature rise is sufficiently small to state thatpermanent structural changes in the solid are unlikely to oc-cur, and thatr, c, andk can be assumed to be of constantvalue, as well as the lineal expansion coefficientl. Then, thecorresponding time dependent thermal expansion of thesample (dLz) could be computed from

dLz5lE0

`

uv~r ,t !dz, ~6!

which, after integrating Eq.~5!, yields

dLz5l~12R!P

p k r

e2r 82/2

g2@12 i ~vD /vq!#ei (qx2vDt). ~7!

FIG. 1. Experimental setup. The output of a diode laser~780 nm! is split andfrequency shifted separately by means of two acousto-optic modulators.Both beams are aligned so that they remain parallel to each other. Theinterference is achieved by means of a lens system~focal distance 70 mm!,creating a fringe pattern due to the difference in the incidence angle~shownin the inset!. A lock-in amplifier measures the current at the modulatedfrequency, with a reference signal coming from a photodiode that samplesthe light scattered from the STM junction.

4841J. Appl. Phys., Vol. 88, No. 8, 15 October 2000 S. M. Landi and O. E. Martınez

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Figure 2 shows frequency response ofdLz using g asparameter~i.e., the number of interference fringesL within abeamwidths).

In the limit of no fringes we are in the presence of thestandard modulation scheme, the beam turns on and off atthe frequency difference. The amount of expansion at highfrequency is given by the heat that is absorbed during onemodulation period~one-dimensional model! yielding the 1/vbehavior. At low frequency the lateral diffusion of the heatreduces the thermal expansion variation with frequency. Thechange between these two behaviors is given by the cutofffrequencyv05(2Dr /s2).

As the fringe density increases, the total modulated ther-mal expansion at low frequencies decreases, because the dif-fusion between fringes is the new limiting mechanism. Fortwo fringes per spot size, two orders of magnitude decreasein the low frequency expansion is observed. Hence, increas-ing the number of fringes is an alternative to increasing thefrequency, allowing the work at lower frequencies within thepractical range of the experimental situation~amplifier orlock-in bandwidths!. For this scheme, the cutoff frequency isvq , which is higher thanv0 . For example, the cutoff fre-quency due to the spot size (f 05v0/2p) on gold sample willbe approx. 4.1 kHz if the beamwidth is 100mm, while thecutoff frequency due to the fringe pattern (f q5vq/2p) will

be 0.3 and 8.1 MHz if there are 2 or 10 fringes within thespot, respectively.

III. EXPERIMENTAL SETUP

In order to measure the quenching of the thermal expan-sion with this traveling fringe scheme, the reduction of thesignal due to the optical heating in a scanning tunneling mi-croscope was measured. In the experiment, the two beamsare originated by splitting the output of a diode laser~780nm! and modulated separately using two acousto-opticmodulators. The first one also acts as a beam splitter: whilethe first order is separated, the zero order passes through thesecond acousto-optic modulator. Both modulated beams arealigned so that they remain parallel to each other. Bothbeams are focused overlapping on the sample surface~focaldistance 70 mm!, creating a fringe pattern due to the differ-ence in the incidence angle~as shown in the inset of Fig. 1!.In this way, the grating period can be altered by varying theangle 2w, i.e., varying the distance between both beams be-fore reaching the lens. The spot on the surface sample isabout 100mm in diameter, and the power of each beam istypically 1 mW.

One of the acousto-optic modulator is driven at a fixedfrequencyf 540 MHz, the other one at a variable frequencyf 1D f , with D f between 10 Hz and 100 kHz. Therefore, thepattern moves laterally at a controlled speed giving byD f /L, whereL is the grating period, modulating the illumi-nation at the tunneling junction.

The STM tip is approached without light illuminationuntil the desired tunneling current is obtained at a set tip-sample distance. The time constant of the feedback loop isset to correct drifts of low frequency but does not respond tofrequencies used for the light modulation. A lock-in ampli-fier measures the current at the modulated frequency, with areference signal coming from a photodiode, that samples thelight scattered from the STM junction. The STM current–voltage converter has a well-known frequency dependence,therefore all the modulated signals have been corrected tak-ing into account this response.

IV. EXPERIMENTAL RESULTS

The technique was tested in a gold sample in order toshow the validity and accuracy of the predictions. To ensurethe photoinduced current were principally of thermal origin,light impinging to STM junction iss polarized. Then, thephotothermal signaldI therm will be proportional to the aver-age tunnelingI t , following the equation:21

dI therm522bdLzI t , ~8!

whereb is a decay constant anddLz the thermal expansionof the sample given by Eq.~7!.

The results are displayed in Fig. 3. According to Eq.~8!the photothermal current is divided by the average tunnelingcurrent in order to obtain a magnitude proportional to thesample expansion@Fig. 3~a!#. The grating period was 8mmapproximately, yielding about 12 fringes within the spot. Inorder to compare with the standard technique of illumination,data measured with each beam modulated in intensity are

FIG. 2. Theoretical results for thermal expansion of a sample illuminated bya modulated Gaussian beam~open squares! and by the traveling wavescheme~filled symbols!. The number of interference fringes of periodLwithin a beam widths is used as parameter.~a! Absolute value and~b!phase shift vs modulation frequency.

4842 J. Appl. Phys., Vol. 88, No. 8, 15 October 2000 S. M. Landi and O. E. Martınez

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plotted together with the signal arising from the method de-scribed in this work. The corresponding theoretical predic-tions are superimposed. Notice that the photoinduced signalis very low when the traveling wave scheme is used, reach-ing in some cases, the limit of our detection sensitivity. Thisexplains the increment of noise in the phase shift measure-ments@Fig. 3~b!#.

As it was pointed out before, the major contribution tophotothermal current arises from the sample expansion. Thefrequency response of the tip expansion was studied in detailby Grafstrom,24 and following the model proposed there weestimated that when standard illumination is used, the tipthermal expansion is negligible as compared to that of thesample. However, with the traveling wave scheme, the endof the tip would see an intensity modulation, as with thestandard scheme and its thermal expansion would be thesame. The signal reduction measured is due to the quenchingof sample thermal expansion. In fact, a remnant modulationis observed at low frequencies@Fig. 3~a!#, which could bedue to the tip contribution.

V. CONCLUSIONS

A scheme for light modulation in an STM junction hasbeen presented that quenches the tip-sample distance modu-lation due to the thermal expansion of the sample. Themethod is based on the irradiation of the sample with twointerfering laser beams at different frequencies and incidentdirection. In this manner, the interference light fringes travelwithin the spot, keeping constant the total thermal load onthe sample, while each point is subjected to a modulatedintensity at the difference between the two frequencies.

Solving the heat diffusion equation we predict the ther-mal contribution to the current based on thermal expansionof the sample, showing several orders of magnitude decreaseas compared to the intensity modulation scheme. The amountof this expected reduction depends on the grating period~given by the angle between the two beams! and frequencydifference. An experimental setup was described and using agold sample we found a good agreement between experi-mental data and theoretical predictions.

ACKNOWLEDGMENTS

The authors wish to acknowledge partial support fromgrants from the CONICET, the Universidad de BuenosAires, and the Agencia Nacional de Produccio´n Cientıfica yTecnologica.

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FIG. 3. Photothermal frequency response for a gold sample when two 1 mWbeams are focused down to a 100mm spot diameter.~a! Absolute value and~b! phase shift. The thermal signal obtained when each beam is used sepa-rately and modulated in intensity is plotted together with the signal arisingfrom the method described in this work. Theoretical results for 10 and 12.5fringes within the spot are superimposed for a qualitative comparison. Up tothree orders of magnitude reduction in the thermal signal is obtained.

4843J. Appl. Phys., Vol. 88, No. 8, 15 October 2000 S. M. Landi and O. E. Martınez

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4844 J. Appl. Phys., Vol. 88, No. 8, 15 October 2000 S. M. Landi and O. E. Martınez

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