The morphological evolution of columnar gold electrodeposits grown at 100 nm s −1 by electroreducing a gold oxide layer on a gold cathode has been studied at a nanometer level by scanning tunneling microscopy. The interface thickness (ξ) depends on the scan length (L) as ξ∝ L α with α=0.49±0.07 for L > ds, where ds is the average top columnar size, and α=0.90±0.07 for L s. These results prove that the growing surface can be described as a self-affine fractal for length scales greater than the columnar size. Conversely, the columnar surface approaches the behavior of an Euclidean surface.Instituto de Investigaciones Fisicoquímicas Teóricas y AplicadasFacultad de Ciencias Exacta

Arvia, Alejandro Jorge

Herrasti, P.

Ocón, P.

Salvarezza, Roberto Carlos

Vara, J. M.

Vázquez, L.

English

Servicio de Difusión de la Creación Intelectual

PHYSICAL REVIEW E VOLUME 49, NUMBER 2 FEBRUARY 1994Self-affine fractal electrodeposited gold surfaces:Characterization by scanning tunneling microscopyL. Vazquez, ' R. C. Salvarezza, P. Ocon, P. Herrasti, J. M. Vara, and A. J. ArviaInstituto de Ciencia de Materiales, Consej o Superior de Investigaciones Cientijicas, Departamento de Fisica Aplicada, C XII-,Uniuersidad Auto noma de Madrid 28049, Madrid, SpainDepartamento de Quimica Fisica Aplicada C II, U-niversidad Auto noma de Madrid, 28049 Madrid, Spain'Instituto de Inuestigaciones Fisicoquimicas Teo ricas y Aplicadas,Sucursal 4, Casilla de Correo 16, (1900) La Plata, Argentina(Received 14 July 1993)The morphological evolution of columnar gold electrodeposits grown at 100 nm s ' by electroreduc-ing a gold oxide layer on a gold cathode has been studied at a nanometer level by scanning tunneling mi-croscopy. The interface thickness (g) depends on the scan length (L) as (~L' with a=0.49+0.07 forI.& d„where d, is the average top columnar size, and a=0.90+0.07 for I. &d, . These results provethat the growing surface can be described as a self-afFine fractal for length scales greater than the colum-nar size. Conversely, the columnar surface approaches the behavior of an Euclidean surface.PACS number{s): 81.1S.Lm, 68.5S.Jk, 05.40.+j, 05.70.LnINTRODUCTIONA relatively large number of physical and chemicalprocesses are related to the development of complexstructures involving rough surfaces. This is the case ofmetal electrodeposition from either aqueous solutions orhydrous metal oxide layers on a conducting substrate [1].Depending on the experimental conditions, metal electro-deposits can exhibit diffusion-limited aggregation, ordense radial or columnar patterns. Columnar structuresdevelop at intermediate growth rates in the 15 & v & 150-nm s ' range [2]. The interface of columnar deposits hasbeen described as either self-similar [3] or self-affine frac-tals [4]. As concluded from large-scale computer simula-tions, the Eden model generates compact structures withself-affine fractal surfaces [5], whereas continuum modelspredict compact structures with self-similar surfaces [3].Several attempts to characterize the surfaces of metalelectrodeposits as fractals have been reported [1,6,7]. Re-cently, it has been shown that when the scale length (L)is smaller than the average top columnar size (d, ), the in-terface of two-dimensional (2D) columnar copper electro-deposits behaves as a self-afFine fractal, fulfilling the lawsg~L with tx-=—,', and gcch~ with P&1, where g is theroot-incan-square roughness, and h is the average columnheight. In this particular case d, has been estimated as500 )Mm [8]. The value u= —,' is consistent with that ex-pected from the Eden model [5] used for describing theevolution and properties of different types of aggregates,but this is not the case for the value of P. According tothe Eden model the value P=—,' should be expected in-stead of P & 1 [5]. Nevertheless, as the preceding analysis[8] was restricted to scale length values in the 5 —500-pmrange, a large extrapolation was required to compare theresults to computer simulation data. This inconveniencecan be overcome when high-resolution data become avail-able. These data would offer the possibility of checkingthe validity of models. For this purpose scanning tunnel-ing microscopy (STM) would be an adequate techniquebecause of its high 3D resolution and nondestructivecharacter [9]. In fact, STM has been used recently to an-alyze the fractal roughness of vapor-deposited gold films[10,11]. This type of STM fractal study can be extendedto a number of electrodeposited metal films.In this work the STM fractal analysis of columnar goldQms covering a relatively broad range of film thicknessesis reported. Dynamic scaling analysis of interface growth[12] from STM data has allowed us to prove the self-affine character of electrodeposited gold film surfaces,and to evaluate the exponent a from the logtog vs log, oLrelationships.EXPKRIMKNTGold films on gold cathodes were grown at 100 nm sby electroreducing a hydrous gold oxide layer previouslyformed at 2.5 V (vs the reversible hydrogen electrode) in0.5M aqueous sulfuric acid using a conventional electro-chemical setup at 298 K. Details about gold filmpreparation are given elsewhere [13]. These films exhibita rough surface and a porous mass with a uniform ap-parent density which is close to that of bulk gold oxide[13]. The average gold film thickness 5 becomes propor-tional to q, the electrodeposited charge density defined asthe electrodeposited charge per unit of geometric sub-strate area by the relationship [14]fi=Mq/zFp,where M and p are the molecular weight and the densityof gold oxide, and zF is the corresponding molar charge.From Eq. (1), and taking M =440 g mol ', p = 11g cm, and z =6 for gold oxide, 5 can be estimated fromq values [14). Values of 5 in the 100—12000-nm rangewere obtained by adjusting the amount (thickness) of hy-drous gold oxide previously produced.The surface morphology of gold films was studied inair using two different STM microscopes, namely a Nano-1063-651X/94/49(2)/1507(5)/$06. 00 49 1507 1994 The American Physical Society1508 L. VAZQUEZ et al.scope II STM and a homemade piezotube STM con-trolled through ATQMIs electronics. Both STM's werecalibrated by imaging highly oriented pyrolytic graphite(HOPG) surfaces. To minimize the influence of artifactsdue to tip geometry, different platinum tips were used.These tips were made from 0.5-mm-diam platinum wiresdirectly by cutting. STM measurements were performedusing 0.05-V bias voltage with the tip positive at 1 —2-nAconstant current. Data were acquired in a fully automat-ed work station, and stored as digitized images with400 X 400 pixels.RESULTS AND DISCUSSIONSTM images of electrodeposited gold film surfaces cov-ering the 100(5(12000-nm range are shown in Figs.1(a)—1(c). These images reveal a deposit formed by arounded top columnar structure. As 6 increases, the sur-face becomes rougher due to the preferential growth ofsome columns as compared to other ones, this effect be-ing caused by shadowing. In this case, d, increases with5. The value of gsTM, the root-mean-square roughnessmeasured from STM images, increases initially with both5 and S, the total scan length (Fig. 2), but for 6= 160 nmand S ) 1.5 pm a constant value of gsrM is reached.Furthertnore, for a given 5 value, the deposit surfaceimaged at different magnifications looks very similar, asexpected for a fractal surface [Figs. 3(a)—3(b)].To characterize the Auctuating interfaces of gold elec-trodeposits, dynamic scaling analysis of surface growthhas been applied [5,12]. Accordingly, g'(L), the surfacewidth in the i direction, for a sample of lateral dimensionI., can be defined as the root-mean-square roughnessgiven byg'(L)= (1/L) g [h, —ho]' (2)re!~+jj'~', .'t'ai~~:,:.4Q.where h is the deposit height measured along the i direc-tion at the j position, and ho is the average height of thesample. In addition, g and L are related through theequationg'(L, h) ~ L f(x), (3)where f (x) =lto/Lr. The function f (x) has the follow-ing properties: f (x) =const for x ~, and f (x)=xfor x 0. After a certain critical thickness (growthtime), g' reaches a steady state, and Eq. (3) becomesg'(L) ~L' .These dynamic scaling concepts can be applied to STMdata derived from electrodeposited gold surfaces as30—2„„=X~20-~15-C)10—KOoo 0o-gyD0 I I I I I I I I I ) I I I I I I | I I ) I I I I I I0 500 1000ScanI I I ( 1 I I 1 I I I I I ( I I I I I I I I I i I I I f I I 1 I 11500 2000 2500 3000size nrnFICx. 1. 3D STM images of gold electrodepo sits. (a)650X650 nm, 6=160 nm. (b) 700X700 nm, 5=560 nm. (c)700X 700 nm, 6=9100 nm. Note that the z scale is the same inthe three images.FIG. 2. Dependence of gsTM, the rms roughness of the STMimage, on S, the total scan length, for 6=9100 (5) and 5=160nm (0).49 SELF-AFFINE FRACTAL ELECTRODEPOSITED GOLD. . . 1509(b)p4?.: C;, i&$-'FIG. 3. STM top view images at different magnifications of agold film with 5=9100 nm. (a) 300X300 nm; (b) 1280X 1280nm .g'=gsTM, where gsTM is the root-mean-square roughnessdetermined from the STM scans in the i direction (i =xand y}. Accordingly, we have evaluated the value of gsTMover each STM scan segment of length L, along the x andy directions after the standard plane correction. Moreexplicitly, we have usedlog, ogTM vs log, g, plots for each STM image.It should be noted that although for computer-simulated fractals data covering four to five orders ofmagnitude in scale length are usually required for loga-rithmic fittings [1],for experimental systems the situationis less ambitious, as frequently the fractal behavior is re-stricted to a certain scale length. Accordingly, fractalstructures of real objects are characterized by log-logplots covering scale lengths of at least one order of rnag-nitude or thereabouts [16).Typical plots obtained for electrodeposited gold filmswith 5=160 nm for three different STM images, and5= 12000 nm for four different STM images, are shownin Fig. 4. In the former case (Fig. 4, plot A} two linearregions with slopes a&&=0.83+0.06 and a2&=0. 5420.06, respectively, and a crossing point at log, pLp =2.5,can be observed. Similarly, in the latter case (Fig. 4, plot8) slopes a,s =0 79+0. 06 a.nd a2s =0 41+. 0 06 .are ob-tained for log, g, values smaller and greater thanLa=2.9, respectively. In both cases the value of Lo wason the order of d, . However, as already reported [17] thedynamic scaling method applied to STM images with256X256 size underestimates the value of a for a) 0.6.Thus in our case a& must be corrected to obtain a&, thetrue value of a„in contrast to the value of a2, whichcoincides with a2, the true value of az.Average values of a&, a2, and Lo, as well as N, and N2,the number of averaged STM images for each sample, aresummarized in Table I. Data demonstrate that the valueof a becomes independent of 5, at least within the experi-mental errors. These results, which were taken usingdifferent tips, have allowed us to discard some apprecia-ble effects of the tip on the fractal analysis of STM im-ages. The average c7 values are (a, )=0.90+0.07(N& =153) and (a2) =0.49+0.07 (N2= 128).Thus for L, &d„(a,) =—1. This fact suggests that aEuclidean behavior of the surface is attained as thecolumnar surface becomes smoother. Otherwise, for&?,„=0.11andksTM(L, ) ~ (1!L,) g [h,.—h, ]Jks™Ls(sa)(5b)Io~FXI1.8n A=&&. ;ygwhere h, is the average height of the surface profile oflength L, measured by STM in either the x or y direc-tions. For each scan 360 data pairs (L„gsTM)have beenobtained, L, being varied from S/64 to almost S. Final-ly, for each L, the corresPonding g'srM value rePresentsthe average of 400 scans of the same image. However, asalready reported [10,15], log, ogsTM vs log, +, plots ob-tained in the y direction sometimes presented anomalousa values due to either drift effects or noise arising fromlow-frequency mechanical vibrations. For this reason,the dynamic scaling analysis was restricted to those STMscans made in the fast x direction, and presented asA II):0.70.31.0CX I„——0.0;3'JP 3.0 4.0 5.0log?o t L, ( A )FIG. 4. log, ogTM vs log, ~, plots calculated for 5= 160 (plotA) and 9100 nxn (plot 8). Values of a below (a&) and above(a2) the crossing point (Lp) are given.1510 L. VAZQUEZ et al.TABLE I. Values of al, K„andI 0 resulting from gold filmsof different values of 5. Nl and N2 denote the number of STMimages used to derive a& and 0.2 values, respectively.6 (nm}50'1605005602800910011 5000.96+0.070.89+0.090.91+0.060.89+0.040.93+0.070.90+0.060.86+0.06332329172328210.43+0.090.41+0.050.50+0.060.50+0.060.52+0.070.51+0.080.45+0.061793218162412Lo (nm}24253032495079(a, l =0.9o+o.o7 (a, l=o.49+o.o7 128'This sample was prepared by electroreducing a 50-nm gold ox-ide layer formed on 850-nm-thick vapor-deposited gold film byelectro-oxidation in 0.5M H&SO& at 2 V with respect to the re-versible hydrogen electrode.I., &d, a rough self-affine fractal surface is approached(see Fig. 5).It has been reported that gold electrodeposits im-mersed in aqueous solution exhibit a roughness relaxationthat fits the kinetics of particle coalescence controlled bysurface diffusion [13,18], i.e.,(d, i2) =2ya Dt lkT,where y is the gold surface tension, a is the lattice param-eter, k is Boltzmann's constant, and D is the surfacediffusion coefficient of deposited particles. Takinga =4X10 cm, y=1000 ergcm ', D=10 ' cm s[13,19], and T=298 K for t =100 s, it results thatd, -=20 nm, a figure which is close to the columnar topsize of these gold films as imaged by STM. Accordingly,irregularities at the deposit surface which are smallerthan the diffusion length, i.e., of sizes close to d„arelev-eled off by surface diffusion of gold atoms during thepreparation time interval. According to these results,one must conclude that the self-affine character of thecolumnar structure ((a2) =——,' for L, )d, ) must be due tocolumn height fluctuations (Fig. 1). This conclusion con-trasts with that recently derived from columnar Cu elec-trodeposit surfaces [8], which exhibited a self-affine char-acter only for those surfaces involving sizes of columns inthe micrometer range. Our data provide evidence thatthose columns imaged by optical microscopy [8] can bedescribed as a collection of small nanometer-size columnswhich can be resolved only through STM imaging. Thisis clearly seen in Fig. 6, where nanometer-size columnsagglomerate yielding micrometer-size structures. Thusthe irregularities which give self-affine character to thesurface are actually caused by height fluctuations of smallcolumns, as earlier concluded from vapor-deposited goldfilms [10,17], rather than by fluctuations of their owncolumnar surfaces.Recently, a value of n which is consistent with theEden model [5] has been reported for 2D copper electro-deposits [8]. However, the value (a 2 ) =——,' for L, )d, ob-tained in this work for 3D gold electrodeposits differsfrom the value of a predicted for 3D large-scale computersimulations of the Eden model [5]. Similar discrepanciesbetween experimental data and theoretical expectationsfor other growth processes have been previously found[11]. Thus further work is still necessary for acomprehensive understanding of the meaning of the (a2)value.Finally, 2), the local fractal dimension of the depositedgold surface, can be obtained from=3 Q1.0—o.o -t0.6—0.4—0.2 -'0.00 4000 8000Thic1~nr ss ( tat~& )12000I5 awkFIG. 5. The a& vs 6 (top values) and ez vs 6 (bottom values)plots. Error bars are indicated. For each plot the dashed linescorrespond to the error of the final averaged value.FIG, 6. Top view STM image (1230X1230 nm } of a goldfilm with 6=160 nm. Note that micrometer-size structures areformed by a large number of nanometer-size elements.49 SELF-AFFINE FRACTAL ELECTRODEPOSITED GOLD. . . 1511Thus it results that 2), =2 and 2)2=2. 5 for the two re-gimes, respectively. The value of 2)2 agrees with valuesearlier reported for gold deposits using the perimeter-area method applied to STM images [20], and by study-ing diffusion-controlled electrochemical reactions in thistype of gold surface [21]. This confirms the capability ofSTM to characterize the dynamics of rough conductingsurfaces at high-resolution levels.[1]P. Meakin, Crit. Rev. Solid State Mater. Sci. 13, 147(1987).[2] B. Movchan and A. V. Demchishin, Fiz. Met. Metalloved.28, 653 (1969) [Phys. Met. Metallogr. (USSR) 28, 83(1969)].[3]R. P. U. Karunasiri, R. Bruinsma, and J. Rudnick, Phys.Rev. Lett. 62, 788 (1989).[4] P. Meakin, P. Ramanlal, L. M. Sander, and R. C. Ball,Phys. Rev. A 34, 509 (1986);J. Krug and P. Meakin, Phys.Rev. A 43, 900 (1991).[5] T. Vicsek, Fractal Growth Phenomena (World Scientific,Singapore, 1989).[6] F. Sagues, F. Mas, M. Villarrasa, and J. Costa, J. Electro-anal. Chem. 278, 351 (1990),and references therein.[7] R. de Levie, J. Electroanal. Chem. 281, 1 (1990).[8] G. L. M. K. S. Kahanda, X. Zou, R. Farrell, and P. Wong,Phys. Rev. Lett. 68, 3741 (1992).[9] G. Binning, H. Rohrer, Ch. Gerber, and E. Weibel, Phys.Rev. Lett. 49, 57 (1982).[10]R. C. Salvarezza, L. Vazquez, P. Herrasti, P. Ocon, J. M.Vara, and A. J. Arvia, Europhys. Lett. 20, 727 (1992).[11]J. Krim, I. Heyvaert, C. Van Haesendonck, and Y. Bruyn-seraede, Phys. Rev. Lett. 70, 57 (1993).[12]F. Family, Physica A 168, 561 (1990).[13]C. Alonso, R. C. Salvarezza, J. M. Vara, A. J. Arvia, L.Vazquez, A. Bartolome, and A. M. Baro, J. Electrochem.Soc. 137, 2161 (1990).[14] L. Vazquez, A. Bartolome, A. M. Baro, C. Alonso, R. C.Salvarezza, and A. J. Arvia, Surf. Sci. 215, 171 (1989).[15]M. W. Mitchell and D. A. Bonnel, J. Mater. Res. 5, 2244(1990).[16]B. H. Kaye, in The Fractal Approach to HetereogeneousChemistry, edited by D. Avnir (Wiley, New York, 1990).[17]L. Vazquez, R. C. Salvarezza, P. Herrasti, P. Oc6n, J. M.Vara, and A. J. Arvia, Appl. Surf. Sci. 70/71, 413 (1993).[18]M. Zinke-Allmang and L. C. Feldman, Appl. Surf. Sci. 52,357 (1991).[19]P. Garcia, M. G6mez, R. C. Salvarezza, and A. J. Arvia,J. Electroanal. Chem. (to be published).[20] J. M. Gomez Rodriguez, L. Vazquez, A. M. Bar6, C.Alonso, R. C. Salvarezza, J. M. Vara, and A. J. Arvia, J.Phys. Chem. 96, 347 (1992).[21] P. Oc6n, P. Herrasti, L. Vazquez, R. C. Salvarezza, J. M.Vara, and A. J. Arvia, J. Electroanal. Chem. 319, 101(1991).

Self-affine fractal electrodeposited gold surfaces : Characterization by scanning tunneling microscopy

SEDICI - Repositorio de la UNLP

PHYSICAL REVIEW E VOLUME 49, NUMBER 2 FEBRUARY 1994
Self-affine fractal electrodeposited gold surfaces:
Characterization by scanning tunneling microscopy
L. Vazquez, ' R. C. Salvarezza, P. Ocon, P. Herrasti, J. M. Vara, and A. J. Arvia
Instituto de Ciencia de Materiales, Consej o Superior de Investigaciones Cientijicas, Departamento de Fisica Aplicada, C XII-,
Uniuersidad Auto noma de Madrid 28049, Madrid, Spain
Departamento de Quimica Fisica Aplicada C II, U-niversidad Auto noma de Madrid, 28049 Madrid, Spain
'Instituto de Inuestigaciones Fisicoquimicas Teo ricas y Aplicadas,
Sucursal 4, Casilla de Correo 16, (1900) La Plata, Argentina
(Received 14 July 1993)
The morphological evolution of columnar gold electrodeposits grown at 100 nm s ' by electroreduc-
ing a gold oxide layer on a gold cathode has been studied at a nanometer level by scanning tunneling mi-
croscopy. The interface thickness (g) depends on the scan length (L) as (~L' with a=0.49+0.07 for
I.& d„where d, is the average top columnar size, and a=0.90+0.07 for I. &d, . These results prove
that the growing surface can be described as a self-afFine fractal for length scales greater than the colum-
nar size. Conversely, the columnar surface approaches the behavior of an Euclidean surface.
PACS number{s): 81.1S.Lm, 68.5S.Jk, 05.40.+j, 05.70.Ln
INTRODUCTION
A relatively large number of physical and chemical
processes are related to the development of complex
structures involving rough surfaces. This is the case of
metal electrodeposition from either aqueous solutions or
hydrous metal oxide layers on a conducting substrate [1].
Depending on the experimental conditions, metal electro-
deposits can exhibit diffusion-limited aggregation, or
dense radial or columnar patterns. Columnar structures
develop at intermediate growth rates in the 15 & v & 150-
nm s ' range [2]. The interface of columnar deposits has
been described as either self-similar [3] or self-affine frac-
tals [4]. As concluded from large-scale computer simula-
tions, the Eden model generates compact structures with
self-affine fractal surfaces [5], whereas continuum models
predict compact structures with self-similar surfaces [3].
Several attempts to characterize the surfaces of metal
electrodeposits as fractals have been reported [1,6,7]. Re-
cently, it has been shown that when the scale length (L)
is smaller than the average top columnar size (d, ), the in-
terface of two-dimensional (2D) columnar copper electro-
deposits behaves as a self-afFine fractal, fulfilling the laws
g~L with tx-=—,', and gcch~ with P&1, where g is the
root-incan-square roughness, and h is the average column
height. In this particular case d, has been estimated as
500 )Mm [8]. The value u= —,' is consistent with that ex-
pected from the Eden model [5] used for describing the
evolution and properties of different types of aggregates,
but this is not the case for the value of P. According to
the Eden model the value P=
—,
' should be expected in-
stead of P & 1 [5]. Nevertheless, as the preceding analysis
[8] was restricted to scale length values in the 5 —500-pm
range, a large extrapolation was required to compare the
results to computer simulation data. This inconvenience
can be overcome when high-resolution data become avail-
able. These data would offer the possibility of checking
the validity of models. For this purpose scanning tunnel-
ing microscopy (STM) would be an adequate technique
because of its high 3D resolution and nondestructive
character [9]. In fact, STM has been used recently to an-
alyze the fractal roughness of vapor-deposited gold films
[10,11]. This type of STM fractal study can be extended
to a number of electrodeposited metal films.
In this work the STM fractal analysis of columnar gold
Qms covering a relatively broad range of film thicknesses
is reported. Dynamic scaling analysis of interface growth
[12] from STM data has allowed us to prove the self-
affine character of electrodeposited gold film surfaces,
and to evaluate the exponent a from the logtog vs log, oL
relationships.
EXPKRIMKNT
Gold films on gold cathodes were grown at 100 nm s
by electroreducing a hydrous gold oxide layer previously
formed at 2.5 V (vs the reversible hydrogen electrode) in
0.5M aqueous sulfuric acid using a conventional electro-
chemical setup at 298 K. Details about gold film
preparation are given elsewhere [13]. These films exhibit
a rough surface and a porous mass with a uniform ap-
parent density which is close to that of bulk gold oxide
[13]. The average gold film thickness 5 becomes propor-
tional to q, the electrodeposited charge density defined as
the electrodeposited charge per unit of geometric sub-
strate area by the relationship [14]
fi=Mq/zFp,
where M and p are the molecular weight and the density
of gold oxide, and zF is the corresponding molar charge.
From Eq. (1), and taking M =440 g mol ', p = 11
g cm, and z =6 for gold oxide, 5 can be estimated from
q values [14). Values of 5 in the 100—12000-nm range
were obtained by adjusting the amount (thickness) of hy-
drous gold oxide previously produced.
The surface morphology of gold films was studied in
air using two different STM microscopes, namely a Nano-
1063-651X/94/49(2)/1507(5)/$06. 00 49 1507 1994 The American Physical Society
1508 L. VAZQUEZ et al.
scope II STM and a homemade piezotube STM con-
trolled through ATQMIs electronics. Both STM's were
calibrated by imaging highly oriented pyrolytic graphite
(HOPG) surfaces. To minimize the influence of artifacts
due to tip geometry, different platinum tips were used.
These tips were made from 0.5-mm-diam platinum wires
directly by cutting. STM measurements were performed
using 0.05-V bias voltage with the tip positive at 1 —2-nA
constant current. Data were acquired in a fully automat-
ed work station, and stored as digitized images with
400 X 400 pixels.
RESULTS AND DISCUSSION
STM images of electrodeposited gold film surfaces cov-
ering the 100(5(12000-nm range are shown in Figs.
1(a)—1(c). These images reveal a deposit formed by a
rounded top columnar structure. As 6 increases, the sur-
face becomes rougher due to the preferential growth of
some columns as compared to other ones, this effect be-
ing caused by shadowing. In this case, d, increases with
5. The value of gsTM, the root-mean-square roughness
measured from STM images, increases initially with both
5 and S, the total scan length (Fig. 2), but for 6= 160 nm
and S ) 1.5 pm a constant value of gsrM is reached.
Furthertnore, for a given 5 value, the deposit surface
imaged at different magnifications looks very similar, as
expected for a fractal surface [Figs. 3(a)—3(b)].
To characterize the Auctuating interfaces of gold elec-
trodeposits, dynamic scaling analysis of surface growth
has been applied [5,12]. Accordingly, g'(L), the surface
width in the i direction, for a sample of lateral dimension
I., can be defined as the root-mean-square roughness
given by
g'(L)= (1/L) g [h, —ho]' (2)
re!~+jj'~', .
't'ai~~:,
:.4Q.
where h is the deposit height measured along the i direc-
tion at the j position, and ho is the average height of the
sample. In addition, g and L are related through the
equation
g'(L, h) ~ L f(x), (3)
where f (x) =lto/Lr. The function f (x) has the follow-
ing properties: f (x) =const for x ~, and f (x)=x
for x 0. After a certain critical thickness (growth
time), g' reaches a steady state, and Eq. (3) becomes
g'(L) ~L' .
These dynamic scaling concepts can be applied to STM
data derived from electrodeposited gold surfaces as
30—
2„„=
X
~
20-
~15-
C)
10—
K
Ooo 0
o
-gyD
0 I I I I I I I I I ) I I I I I I | I I ) I I I I I I
0 500 1000
Scan
I I I ( 1 I I 1 I I I I I ( I I I I I I I I I i I I I f I I 1 I 11500 2000 2500 3000
size nrn
FICx. 1. 3D STM images of gold electrodepo sits. (a)
650X650 nm, 6=160 nm. (b) 700X700 nm, 5=560 nm. (c)
700X 700 nm, 6=9100 nm. Note that the z scale is the same in
the three images.
FIG. 2. Dependence of gsTM, the rms roughness of the STM
image, on S, the total scan length, for 6=9100 (5) and 5=160
nm (0).
49 SELF-AFFINE FRACTAL ELECTRODEPOSITED GOLD. . . 1509
(b)
p4
?.: C
;, i&$-'
FIG. 3. STM top view images at different magnifications of a
gold film with 5=9100 nm. (a) 300X300 nm; (b) 1280X 1280
nm .
g'=gsTM, where gsTM is the root-mean-square roughness
determined from the STM scans in the i direction (i =x
and y}. Accordingly, we have evaluated the value of gsTM
over each STM scan segment of length L, along the x and
y directions after the standard plane correction. More
explicitly, we have used
log, ogTM vs log, g, plots for each STM image.
It should be noted that although for computer-
simulated fractals data covering four to five orders of
magnitude in scale length are usually required for loga-
rithmic fittings [1],for experimental systems the situation
is less ambitious, as frequently the fractal behavior is re-
stricted to a certain scale length. Accordingly, fractal
structures of real objects are characterized by log-log
plots covering scale lengths of at least one order of rnag-
nitude or thereabouts [16).
Typical plots obtained for electrodeposited gold films
with 5=160 nm for three different STM images, and
5= 12000 nm for four different STM images, are shown
in Fig. 4. In the former case (Fig. 4, plot A} two linear
regions with slopes a&&=0.83+0.06 and a2&=0. 54
20.06, respectively, and a crossing point at log, pLp =2.5,
can be observed. Similarly, in the latter case (Fig. 4, plot
8) slopes a,s =0 79+0. 06 a.nd a2s =0 41+. 0 06 .are ob-
tained for log, g, values smaller and greater than
La=2.9, respectively. In both cases the value of Lo was
on the order of d, . However, as already reported [17] the
dynamic scaling method applied to STM images with
256X256 size underestimates the value of a for a) 0.6.
Thus in our case a& must be corrected to obtain a&, the
true value of a„in contrast to the value of a2, which
coincides with a2, the true value of az.
Average values of a&, a2, and Lo, as well as N, and N2,
the number of averaged STM images for each sample, are
summarized in Table I. Data demonstrate that the value
of a becomes independent of 5, at least within the experi-
mental errors. These results, which were taken using
different tips, have allowed us to discard some apprecia-
ble effects of the tip on the fractal analysis of STM im-
ages. The average c7 values are (a, )=0.90+0.07
(N& =153) and (a2) =0.49+0.07 (N2= 128).
Thus for L, &d„(a,) =—1. This fact suggests that a
Euclidean behavior of the surface is attained as the
columnar surface becomes smoother. Otherwise, for
&?,„=0.11
and
ksTM(L, ) ~ (1!L,) g [h,.—h, ]
J
ks™Ls
(sa)
(5b)
I
o~
FX
I
1.8
n A=&&. ;yg
where h, is the average height of the surface profile of
length L, measured by STM in either the x or y direc-
tions. For each scan 360 data pairs (L„gsTM)have been
obtained, L, being varied from S/64 to almost S. Final-
ly, for each L, the corresPonding g'srM value rePresents
the average of 400 scans of the same image. However, as
already reported [10,15], log, ogsTM vs log, +, plots ob-
tained in the y direction sometimes presented anomalous
a values due to either drift effects or noise arising from
low-frequency mechanical vibrations. For this reason,
the dynamic scaling analysis was restricted to those STM
scans made in the fast x direction, and presented as
A II):0.7
0.3
1.0
CX I„——0.0;3
'JP 3.0 4.0 5.0
log?o t L, ( A )
FIG. 4. log, ogTM vs log, ~, plots calculated for 5= 160 (plot
A) and 9100 nxn (plot 8). Values of a below (a&) and above
(a2) the crossing point (Lp) are given.
1510 L. VAZQUEZ et al.
TABLE I. Values of al, K„andI 0 resulting from gold films
of different values of 5. Nl and N2 denote the number of STM
images used to derive a& and 0.2 values, respectively.
6 (nm}
50'
160
500
560
2800
9100
11 500
0.96+0.07
0.89+0.09
0.91+0.06
0.89+0.04
0.93+0.07
0.90+0.06
0.86+0.06
33
23
29
17
23
28
21
0.43+0.09
0.41+0.05
0.50+0.06
0.50+0.06
0.52+0.07
0.51+0.08
0.45+0.06
17
9
32
18
16
24
12
Lo (nm}
24
25
30
32
49
50
79
(a, l =0.9o+o.o7 (a, l=o.49+o.o7 128
'This sample was prepared by electroreducing a 50-nm gold ox-
ide layer formed on 850-nm-thick vapor-deposited gold film by
electro-oxidation in 0.5M H&SO& at 2 V with respect to the re-
versible hydrogen electrode.
I., &d, a rough self-affine fractal surface is approached
(see Fig. 5).
It has been reported that gold electrodeposits im-
mersed in aqueous solution exhibit a roughness relaxation
that fits the kinetics of particle coalescence controlled by
surface diffusion [13,18], i.e.,
(d, i2) =2ya Dt lkT,
where y is the gold surface tension, a is the lattice param-
eter, k is Boltzmann's constant, and D is the surface
diffusion coefficient of deposited particles. Taking
a =4X10 cm, y=1000 ergcm ', D=10 ' cm s
[13,19], and T=298 K for t =100 s, it results that
d, -=20 nm, a figure which is close to the columnar top
size of these gold films as imaged by STM. Accordingly,
irregularities at the deposit surface which are smaller
than the diffusion length, i.e., of sizes close to d„arelev-
eled off by surface diffusion of gold atoms during the
preparation time interval. According to these results,
one must conclude that the self-affine character of the
columnar structure ((a2) =——,' for L, )d, ) must be due to
column height fluctuations (Fig. 1). This conclusion con-
trasts with that recently derived from columnar Cu elec-
trodeposit surfaces [8], which exhibited a self-affine char-
acter only for those surfaces involving sizes of columns in
the micrometer range. Our data provide evidence that
those columns imaged by optical microscopy [8] can be
described as a collection of small nanometer-size columns
which can be resolved only through STM imaging. This
is clearly seen in Fig. 6, where nanometer-size columns
agglomerate yielding micrometer-size structures. Thus
the irregularities which give self-affine character to the
surface are actually caused by height fluctuations of small
columns, as earlier concluded from vapor-deposited gold
films [10,17], rather than by fluctuations of their own
columnar surfaces.
Recently, a value of n which is consistent with the
Eden model [5] has been reported for 2D copper electro-
deposits [8]. However, the value (a 2 ) =——,' for L, )d, ob-
tained in this work for 3D gold electrodeposits differs
from the value of a predicted for 3D large-scale computer
simulations of the Eden model [5]. Similar discrepancies
between experimental data and theoretical expectations
for other growth processes have been previously found
[11]. Thus further work is still necessary for a
comprehensive understanding of the meaning of the (a2)
value.
Finally, 2), the local fractal dimension of the deposited
gold surface, can be obtained from
=3 Q
1.0—
o.o -t
0.6—
0.4—
0.2 -'
0.0
0 4000 8000
Thic1~nr ss ( tat~& )
12000
I
5 awk
FIG. 5. The a& vs 6 (top values) and ez vs 6 (bottom values)
plots. Error bars are indicated. For each plot the dashed lines
correspond to the error of the final averaged value.
FIG, 6. Top view STM image (1230X1230 nm } of a gold
film with 6=160 nm. Note that micrometer-size structures are
formed by a large number of nanometer-size elements.
49 SELF-AFFINE FRACTAL ELECTRODEPOSITED GOLD. . . 1511
Thus it results that 2), =2 and 2)2=2. 5 for the two re-
gimes, respectively. The value of 2)2 agrees with values
earlier reported for gold deposits using the perimeter-
area method applied to STM images [20], and by study-
ing diffusion-controlled electrochemical reactions in this
type of gold surface [21]. This confirms the capability of
STM to characterize the dynamics of rough conducting
surfaces at high-resolution levels.
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Self-affine fractal electrodeposited gold surfaces: Characterization by scanning tunneling microscopy

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Self-affine fractal electrodeposited gold surfaces: Characterization by scanning tunneling microscopy

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