The kinetic roughening of Ar+ ion-sputtered Pd(001) surface was investigated. The facet formation on the sputtered surface was studied by tracing the extradiffraction peaks or satellites around the diffraction peaks corresponding to the sample surface. The morphological evolution of the sputtered Pd(001) surface was also investigated by an scanning tunneling microscopy (STM). It was shown that the nanoscale adatom islands form and grow with increasing sputter time.open313

Chang, YJ

Chung, JW

Ghim, Cheol-Min

Kahng, B

Kim, DH

Kim, HJ

Kim, JS

Kim, ND

Kim, TC

Noh, DY

Noh, TW

Yang, JS

Physical Review Letters

We investigate the kinetic roughening of Ar+ ion-sputtered Pd(001) surface both experimentally and theoretically. In situ real-time x-ray reflectivity and in situ scanning tunneling microscopy show that nanoscale adatom islands form and grow with increasing sputter time t. Surface roughness W(t) and lateral correlation length xi(t) follow the scaling laws W(t)similar tot(beta) and xi(t)similar tot(1/z) with the exponents betasimilar or equal to0.20 and 1/zsimilar or equal to0.20, for an ion beam energy epsilon=0.5 keV, which is inconsistent with the prediction of the Kuramoto-Sivashinsky (KS) model. We thereby extend the KS model by applying the coarse-grained continuum approach of the Sigmund theory to the order of O(del(4),h(2)), where h is the surface height, and derive a new term of the form del(2)(delh)(2) which plays a decisive role in describing the observed morphological evolution of the sputtered surface.open1141sciescopu

Ghim, CM

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Kinetic roughening of ion-sputtered Pd(001) surface: Beyond the Kuramoto-Sivashinsky model

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P H Y S I C A L R E V I E W L E T T E R S week ending18 JUNE 2004VOLUME 92, NUMBER 24Kinetic Roughening of Ion-Sputtered Pd(001) Surface:Beyond the Kuramoto-Sivashinsky ModelT. C. Kim,1 C.-M. Ghim,2,* H. J. Kim,1 D. H. Kim,1 D.Y. Noh,1 N. D. Kim,3 J.W. Chung,3 J. S. Yang,4 Y. J. Chang,4T.W. Noh,4 B. Kahng,2 and J.-S. Kim5,†1Department of Materials Science and Engineering, Gwangju Institute of Science and Technology, Gwangju, 500-712, Korea2School of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea3Department of Physics and BSRI, Pohang University of Science and Technology,Pohang 790-784, Korea4School of Physics and Research Center for Oxide Electronics, Seoul National University, Seoul 151-747, Korea5Department of Physics, Sook-Myung Women’s University, Seoul 140-742, Korea(Received 3 September 2003; revised manuscript received 10 February 2004; published 17 June 2004)246104-1We investigate the kinetic roughening of Ar ion-sputtered Pd(001) surface both experimentally andtheoretically. In situ real-time x-ray reflectivity and in situ scanning tunneling microscopy show thatnanoscale adatom islands form and grow with increasing sputter time t. Surface roughness Wt andlateral correlation length t follow the scaling laws Wt  t and t  t1=z with the exponents  ’0:20 and 1=z ’ 0:20, for an ion beam energy "  0:5 keV, which is inconsistent with the prediction ofthe Kuramoto-Sivashinsky (KS) model. We thereby extend the KS model by applying the coarse-grained continuum approach of the Sigmund theory to the order of Or4; h2, where h is the surfaceheight, and derive a new term of the form r2rh2 which plays a decisive role in describing theobserved morphological evolution of the sputtered surface.DOI: 10.1103/PhysRevLett.92.246104 PACS numbers: 68.55.–a, 05.45.–a, 64.60.Cn, 79.20.Rfroughness and growth exponents  and  are related via results.Recently, the observation of ordered nanostructuressuch as ripples and two-dimensional patterns on ion-sputtered surfaces has attracted much attention due tothe demonstration of the possibility of fabrication ofordered nanoscale structures in a relatively easy andaffordable way [1–3]. Such experimental results havemotivated extensive theoretical investigations. A linearmodel, proposed by Bradley and Harper (BH) [4], hasbeen successful in predicting the formation of the ripplestructure. The wavelength, orientation, and amplitude ofthe ripples can be predicted in terms of experimentalparameters such as the incident angle of the ion beamand substrate temperature [5]. The BH theory, however,fails to explain a number of experimental observationssuch as the saturation of the ripple amplitude [6] or theappearance of kinetic roughening [7,8]. To remedy suchshortcomings, the noisy Kuramoto-Sivashinsky (KS)equation [9] was introduced based on the Sigmund theoryof sputter erosion [10]. In addition to the linear terms ofthe BH model, it contains a nonlinear term proportionalto rh2, known as the Kardar-Parisi-Zhang (KPZ) term[11], where h is surface height. Because of the nonlinearterm, the surface roughness or ripple amplitude is asymp-totically saturated into a constant value [12].Kinetic roughening behavior is described by the scal-ing theory [13]. The surface roughness of the sample, LL in size, at sputter time t is defined as W 	1=L2Prhr; t  h2q, where h  1=L2Prhr; t. Itfollows the scaling relation, WL; t  Lgt=L=,where gu  u for u 1 and gu! 1  const. The0031-9007=04=92(24)=246104(4)$22.50scaling relations to give the dynamic exponent, z  =,which determines the scaling of the saturation time withthe system size L. Below, we deal with the inverse dy-namic exponent, 1=z, called the coarsening exponent, inanalyzing the experimental results.In this Letter, we study the kinetic roughening of thesputter-eroded Pd(001) surface via novel experimentaltechniques combined with the stochastic continuumtheory. Both in situ real-time x-ray reflectivity (XRR)and in situ scanning tunneling microscopy (STM) showthat nanoscale islands are formed on the surface, evolvingwith increasing sputter time t following the scaling func-tion WL; t. In particular, we obtain  ’ 0:2 and 1=z ’0:2 for ion beam energy   0:5 keV, which are neither inagreement with the KS values, KS  0:22–0:25 and1=zKS  0:25–0:33 [14], nor with the KPZ values,KPZ  0:25 and 1=zKPZ  0:63 [13]. To resolve this in-consistency, we investigate theoretically the erosion pro-cess by applying the Sigmund theory to higher order,finding that the relevant higher order term is of theform r2rh2, referred to as the conserved KPZ(CKPZ) term. In fact, preceding studies anticipated theCKPZ term induced by the instability at step edges[15,16]. However, there has been no explicit derivationthereof starting from the microscopic nature of sputtererosion. Thus, the coefficient was also not to be derivedfrom experimental parameters, but only has been given adhoc. Here applying the Sigmund theory, we derive theCKPZ term and the coefficient as well explicitly in termsof experimental parameters, which enables us to directlyassess the theoretical predictions against experimental 2004 The American Physical Society 246104-10.0 0.1 0.2 0.3 0.4 0.5 0.610-310-210-1100 t (sec)Intensity(counts/sec)qz(Å-1)0358147810483FIG. 1. Specular x-ray reflectivity (symbols) as a function ofthe momentum transfer, qz, for increasing sputter times with"  0:5 keV and f  2:0 1013 ions=cm2=s. The solid linesare the theoretical prediction by the Parratt formula.1000 100001100 1 2 3 4 50369122.5×10 13f (ions/cm /sec)2W(Å)fluence (10  ions/cm  )ε (keV)W(Å)t (sec)2.01.50.51.5×10130.5×10 1317 2FIG. 2. The surface roughness W as a function of sputter timet for different ion energies, "  0:5 (), 1.5 (), and 2.0 (4)keV, but with a fixed ionic flux, f  2:0 1013 ions=cm2=s. Theinset shows that the roughness evolution for a given " followsthe same fluence dependence, irrespective of f.P H Y S I C A L R E V I E W L E T T E R S week ending18 JUNE 2004VOLUME 92, NUMBER 24Experiment.—A Pd(001) sample was cleaned by severalcycles of Ar ion sputtering around 300 K and annealingup to 920 K. The clean Pd(001) surface exhibited anaverage terrace size of about 3000 A˚ and little surfacemodulation or defects by contaminants as judged by STMimages. The initial surface roughness of the sample wasless than 2 A˚ , and the miscut from surface normal direc-tion was 0:3, as determined, respectively, by XRR andx-ray diffraction spot-profile analysis. Sputtering experi-ments were performed for Pd(001) around 300 K with Arion beam incident normally to the sample surface. Toavoid possible contamination during sputtering, freshAr gas (purity of 99.999%) was continuously made toflow through the chamber with Ar partial pressure main-tained around 2:0 105 Torr.The morphological evolution of the Pd(001) duringsputtering was observed in situ by both XRR and STM.The XRR experiment was performed in a custom-de-signed UHV chamber at the 5C2 GIST beamline of thePohang Light Source in Korea. The base pressure of thechamber was kept below mid-1010 Torr. The incidentx rays were vertically focused by a mirror to 1 mm insize, and a double-bounce Si(111) monochromator wasemployed to both focus the beam in the horizontal direc-tion and monochromatize the incident x ray to a wave-length of 1.24 A˚ , which corresponded to the x-ray energyof 10 keV. The x-ray reflectivity was measured in realtime while Pd(001) was sputtered. The incident Ar beamenergy, ", ranged from 0.5 to 2.0 keV, and the ionbeam flux, f, measured from the ion current collectedat the sample, ranged from 0:5 1013 to 2:51013 ions=cm2=s. Sputtering started with the sample atroom temperature measured by a thermocouple directlyattached to the back end of the sample. After sputteringfor more than 10 h, the sample temperature rose only lessthan 30 K.To observe the sputter-induced morphological evolu-tion in real space, a commercial STM (Omicron VT-STM) was also used. The base pressure was kept in thelow 1011 Torr. STM tips were electrochemically etchedpolycrystalline W wires that were annealed and sputteredin a UHVchamber. In all the STM measurements, the tip-sample voltage was kept as 80 mV, and the tunnelingcurrent was at 1 nAwith the sample at room temperature.Sputtering was performed with "  0:5 keV and f 0:5 1013 ions=cm2=s. During sputtering, the sampletemperature was around 300 K. Sputtering and STMmeasurement were alternated, and the sputter time re-ferred to in this Letter is the total sputter time determinedby summing all the previous sputtering periods. X-rayreflectivity indicated that there was no significant changein the surface roughness for 10 h after the interruption ofsputtering. Thus, the interruption of sputtering for theSTM measurement was not expected to result in addi-tional relaxation of the sputtered surface.Experimental results.—In Born approximation, whichholds above the critical angle, the specular reflectivity246104-2decreases as expW2q2zwith increasing qz [17]. Figure 1shows that the reflectivity decays more steeply as thesputtering proceeds, which indicates that Wt increaseswith t. Quantitatively Wt is determined by fitting theexperimental data according to the Parratt formalism[17,18]. Figure 2 shows Wt thus obtained, as a functionof t for several " but with a fixed f. The linear behavior indouble-logarithmic scale implies power-law behavior,Wt  t. We obtained that  ’ 0:20 0:02 for " 0:5 keV,  ’ 0:23 0:02 for "  1:5 keV, and  ’0:25 0:02 for "  2:0 keV.The inset of Fig. 2 summarizes the surface roughnessWt as a function of fluence (f t) for several differentf’s, but with a fixed ". We find that the roughness evolvesshowing the same fluence dependence, irrespective of f.Such behavior implies that the surface diffusion is notinduced by thermal activation, but rather by the surfacesputtering under the present experimental condition [19].We also study the facet formation on the sputteredsurface by tracing the extradiffraction peaks or satellitesaround the diffraction peak corresponding to the samplesurface, now the (001) plane, because each facet planedefines diffraction rods normal to it. In the inset of Fig. 3,246104-2-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.30.00.20.40.60.81.01.21.4-0.1 0.0 0.10.00.10.20.30.4ε (keV)[115][117]qII(Å-1 )0.52.0qz(Å-1)0.2680.3130.3570.402Intensity(10  counts/monitor)q II (Å-1)-3qz(Å-1 )FIG. 3. X-ray diffraction intensity along 110 for differentqz. The positions of satellite peaks shift to the larger qk for thelarger qz, with a fixed angle to the surface normal, indicatingthat the spots originate from a facet formed by sputtering.Inset: Positions of satellite peaks, qk, as a function of qz.P H Y S I C A L R E V I E W L E T T E R S week ending18 JUNE 2004VOLUME 92, NUMBER 24the diffraction rods defined by the satellite peaks makewell-defined angles with respect to that of the (001) planeas much as the facet plane does to the (001) plane. Fromthe observed angles, we identify the facet formed onsputtering by the 0.5 keV ion beam to be (117) and thatby the 2.0 keV beam to be (115).The morphological evolution of the sputtered Pd(001)surface was also investigated by an STM. Figure 4 showsthe STM images of the sputtered surface at different(total) sputtering times under the same experimentalcondition, "  0:5 keV and f  0:5 1013 ions=cm2.The shape of the island edge looks somewhat irregular,which may be due to random shot noise or the sputter-induced diffusion. This reaffirms that thermal smoothen-ing is inefficient in the present experimental conditions assuggested by the flux-independent scaling behavior. Theinsets of Fig. 4 show the height-height correlation func-tion, Gr; t  hhr; t  h0; 02i, that reveals lateralorder developing on the surface as sputtering proceeds.[110] t = 1030 sec t = 3855 sec  t = 14655 sec t = 50 secFIG. 4. STM images, 200 200 nm2 in size, according totime evolution. The insets at right bottom of each image showthe height-height correlation function obtained from the cor-responding surface profile.246104-3We can see that the island size grows with increasingsputter time. From the height-height correlation function,we determine the lateral correlation length  as theposition giving the first-order maximum, and plot it asa function of t in Fig. 5. It is found that  t1=z with theexponent 1=z ’ 0:20 0:03. The growth exponent deter-mined by the STM measurement is  ’ 0:20 0:03, inagreement with that of the XRR measurement.Theory.—To elucidate the kinetic roughening of thesurface, we systematically expand the Sigmund theoryto obtain the extended KS equation:1c@h@t 1 r2hDr4h 1rh2 2r2rh2  x; y; t; (1)where c is the surface recession rate given by a materialconstant times ionic flux,  the effective surface tensiongenerated by the erosion process, D the ion-induced ef-fective diffusion constant [19], 1 and 2 tilt-dependenterosion rates, and  uncorrelated white noise with zeromean, mimicking the randomness resulting from thestochastic nature of ion arrival at the surface. While thelinear terms may have the origins of thermal diffusionand/or the Ehrlich-Schwoebel instability at step edges[20], their contributions are overwhelmed by ion-inducedeffects under the current experimental conditions, other-wise Wt for various flux conditions could not collapseinto a single curve [19] as shown in the inset of Fig. 2. Thecoefficients , D, and 1 in Eq. (1) were derived in termsof empirical parameters such as ion penetration depth (a)and cascading sizes in transverse and longitudinal direc-tions ( and , respectively), which are determinedexperimentally by ", f, and the incident angle  foroblique incidence. The newly derived CKPZ coefficientis, under normal incidence, given by2  2=2 3=8=42  a2: (2)Using the TRIM Monte Carlo algorithm [21], all the co-efficients in Eq. (1) are determined numerically for ourexperimental parameters, which are tabulated in Table I.In Fig. 6 is shown the estimation of the KPZ and CKPZFIG. 5. Plot of the lateral correlation length  () and thesurface roughness W () for "  0:5 keV obtained from theSTM images as a function of sputter time t.246104-3TABLE I. Numerical estimations of the coefficients in Eq. (1)under the experimental conditions we performed." a (  A)  (  A) D (  A3) 1 2 (  A2)0.5 keV 9 2.72 33.35 0:50 12.21.5 keV 16 5.12 184.32 0:54 33.62.0 keV 18 5.44 266.78 0:50 49.0P H Y S I C A L R E V I E W L E T T E R S week ending18 JUNE 2004VOLUME 92, NUMBER 24terms, for a typical profile of the eroded surface. Thenumerical values in Fig. 6 include the contributionsfrom the coefficients, 1 and 2, as well as from tilt-dependent terms themselves. We find that the CKPZterm should be more relevant to the morphological evo-lution than the KPZ term in a finite system. The contri-butions from other terms allowed by symmetry and oforder Or4; h2, such as r2h2, are found to be negli-gible. Then, for "  0:5 keV, the extended KS equation isreduced to the CKPZ equation that gives the growthexponent cKPZ ’ 0:20 [22] for two dimensions, in agree-ment with the measured value. As the ion energy in-creases, the coefficient D increases very rapidly incomparison with the magnitudes of 1 and 2 as seen inTable I. Thus, for   2:0 keV, the erosion process ismainly governed by the so-called Mullins term, Dr4h[23]. In this case, it is known that the growth exponentMullins ’ 0:25 for two dimensions, again consistent withthe experimental value for "  2:0 keV. The sputter-induced palladium atoms form adatom islands withwell-defined facets as observed in Fig. 3. Then,   1and the coarsening exponent, 1=z, should be equal to following the scaling relation 1=z  =. This predic-tion is confirmed in the present experiment by the obser-vation of 1=z    0:2 for "  0:5 keV. Furthermore,by plugging the numerical values for, say, "  0:5 keV, inTable I into Eq. (1), we estimate the typical lateral sizeand amplitude of islands to be 22 and 3 A˚ , respectively,which are compatible with the experimental resultsshown in Fig. 5.Conclusions.—We have studied the kinetic rougheningof the sputter-eroded Pd(001) surface both experimen-tally and theoretically. The experimental data suggestthat the extended KS model with additional CKPZ termcould properly describe the kinetic roughening behavior.-0.040.000.04 KPZcKPZsurface profileFIG. 6. Comparison of the KPZ and the CKPZ terms for aprototypical profile of eroded surface.246104-4To this end, we apply the Sigmund theory, a coarse-grained continuum approach of collision cascade, toextract the coefficient of each term as a function ofexperimentally controllable parameters, which makes itpossible to systematically improve our understanding ofkinetic roughening on the experimental bases. We expectthat the model sheds light on recent experimental real-ization of self-organized surface nanostructures inducedby ion sputtering.This work is supported by the KRF Grant No.2002-015-CP0087 through SMU and KOSEF GrantsNo. 2002-2-11200-002-3 through SNU and No. R01-2002-000-00469-0 through GIST.*Electronic address: cmghim@phya.snu.ac.kr†Electronic address: jskim@sookmyung.ac.kr[1] S. Facsko et al., Science 285, 1551 (1999).[2] F. Frost, A. Schindler, and F. Bigl, Phys. Rev. Lett. 85,4116 (2000).[3] S. Rusponi et al., Phys. Rev. Lett. 81, 2735 (1998); 81,4184 (1998).[4] R. M. Bradley and J. M. E. Harper, J. Vac. Sci. Technol. A6, 2390 (1988).[5] I. Koponen, M. Hautala, and O.-P. Sievanen, Phys. Rev.Lett. 78, 2612 (1997).[6] K. Wittmaack, J. Vac. Sci. Technol. A 8, 2246 (1990);J. Erlebacher et al., Phys. Rev. Lett. 82, 2330 (1999); J. J.Vajo et al., J. Vac. Sci. Technol. A 6, 76 (1988).[7] E. A. Eklund et al., Phys. Rev. Lett. 67, 1759 (1991).[8] H.-N. Yang, G.-C. Wang, and T.-M. 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Kinetic roughening of ion-sputtered Pd(001) surface: Beyond the Kuramoto-Sivashinsky model

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