Localized Electrodeposition Using a Scanning Tunneling

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Localized Electrodeposition Using a Scanning Tunneling

Transcript Of Localized Electrodeposition Using a Scanning Tunneling

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Journal of The Electrochemical Society, 148 ͑2͒ C124-C130 ͑2001͒
0013-4651/2001/148͑2͒/C124/7/$7.00 © The Electrochemical Society, Inc.
Localized Electrodeposition Using a Scanning Tunneling Microscope Tip as a Nanoelectrode
W. Schindler,a,z D. Hofmann, and J. Kirschner
Max-Planck-Institut fu¨r Mikrostrukturphysik, D-06120 Halle, Germany
The mechanism of localized electrodeposition on the nanometer scale is studied using the tip of an electrochemical scanning tunneling microscope as a ‘‘nanoelectrode,’’ which is retracted from the substrate ͑working electrode͒ during growth of the clusters. The system chosen exemplarily is Au͑111͒/Co2ϩ, which shows a relatively weak substrate/deposit interaction compared to the strong interaction characteristic of underpotential deposition systems. The width and height of the clusters, which can be grown with diameters even below 10 nm, are determined by the diameter of the tip apex, the distance between tip and substrate, the substrate potential, and by the amount of Co transferred to the substrate via the tip. The influence of these parameters on the cluster growth can be well understood assuming diffusion as the mechanism of Co transfer from the tip to the substrate. Field and charging effects of either tip or substrate can be excluded due to the large distance of approximately 20 nm between both electrodes. © 2001 The Electrochemical Society. ͓DOI: 10.1149/1.1343107͔ All rights reserved.
Manuscript submitted June 19, 2000; revised manuscript received September 26, 2000.

The preparation of structures with lateral dimensions on the nanometer-scale attracts an increasing interest, since it has been shown that the physical and chemical properties of such nanostructures can strongly deviate from the properties of the corresponding bulk material.1-3 Thus, nanotechnology opens up the promising possibility for tailoring novel properties of materials by varying the lateral structure size, and for exploiting even quantum effects for novel applications, e.g., quantum logic circuits.4 An example is the single electron transistor which operates at room temperature if its lateral structure size is confined to below 20 nm. This has been realized recently by a special nano-oxidation process using the tip of an atomic force microscope.5,6 Nanostructures are also of great interest in other fields like, e.g., magnetism7-10 or electrocatalysis.11-13
In view of studying the size-dependent properties of model nanostructures it would be desirable to generate these structures at precisely, preset substrate positions. At present, scanning-probe-based nanostructure techniques seem to be suitable to fabricate nanostructures with lateral sizes below 20 nm, which is currently hard to achieve with existing lithographic techniques. However, it is most important that the generation of nanostructures is not accompanied by unwanted irreversible modifications of either the substrate, the nanostructure, or the scanning probe. Otherwise, the physical and chemical properties of nanostructures may be expected to be determined by the particular defects rather than by their intrinsic structure, particularly surface structure which increasingly determines the properties of ever smaller structures.
So far, a variety of scanning-probe-based methods have been reported in the literature.14 They are on the one hand based on the specific pregeneration of defects which act as nucleation centers,15-17 or on the other hand correlated with parasitic effects like field effects which may result in unwanted modification of either the substrate surface or the probe surface.18-20 The mechanisms of all techniques which are applied with the probe in tunneling distance to the substrate is not very clear at present, and has been shown to be a superposition of different electrochemical and field effects,21,22 even if mechanical contact can be excluded at all. An exception from these methods is the so-called ‘‘jump to contact’’ method by Kolb and co-workers,23-25 which is not affected by unwanted field effects, but rather based on a controlled approach of the scanning tunneling microscope ͑STM͒ tip against the substrate. However, this technique seems to be applicable only in systems with a strong substrate/deposit interaction, i.e., underpotential deposition ͑UPD͒ systems.26 Recently, we have developed a technique which
a Present address: Institut fu¨r Hochfrequenztechnik und Quantenelektronik, Universita¨t Karlsruhe ͑TH͒, D-76131 Karlsruhe, Germany.
z E-mail: [email protected]

allows the solely electrochemical growth of Co clusters with diameters as small as 15 nm, as measured by STM, at the solid/liquid interface.27,28
In this paper, we present a detailed study of the different parameters of this localized electrocrystallization mechanism, using the STM tip as a nanometer-sized electrochemical electrode ͑Fig. 1͒. In contrast to the various nanostructuring techniques applied with the tip in the tunneling mode, we avoid parasitic effects or defect generation in either the substrate surface or at the STM probe by a large distance between STM tip and substrate surface during cluster growth. This simplifies the interpretation of the results, and allows a detailed discussion of the influence of different parameters on scanning-probe-based nanoscale electrocrystallization.
Experimental
The experiments have been performed with the electrochemical version of the Nanoscope III scanning tunneling microscope ͑Digital Instruments͒, which has been modified to vary the tip potential Etip by external voltages independently of the substrate potential EWE . Cathodic and anodic tip charges were determined by integration of
the tip current Itip . During the whole deposition sequence Itip was monitored by a digitizing oscilloscope. The maximum tip current was limited by the modified current-voltage converter of our STM to 520 nA. During cluster deposition the STM tip was withdrawn from the substrate surface by means of the STM scanner piezoelements, and the feedback loop was disabled. The deposition experiments were performed in a conventional four-electrode electrochemical STM cell providing an electrolyte volume of about 100 ␮L. All potentials were measured vs. a saturated calomel reference electrode ͑SCE͒ ͑B 3105, Schott͒ which has been connected to the cell by a glass capillary, and are quoted in this paper with respect to the standard hydrogen electrode. The counter electrode was made from polycrystalline Pt wire. STM tips were prepared from Au wires of 0.25 mm diam by electrochemical etching in a lamella of HCl ͑32%͒, and then manually coated with Apiezon wax. These tips have been found to be well suited as electrochemical nanoelectrodes showing an electrochemical background current in the double layer regime of the current-voltage characteristics of smaller than 100 pA ͑Fig. 2͒ due to the small unisolated tip area which is of the order of 10 ␮m2, as measured by scanning electron microscopy ͑SEM͒. As substrates Au͑111͒ single crystals were chosen showing atomically flat terraces of several hundreds of nanometers after several cycles of flame-annealing. The aqueous electrolyte was made from ultrapure water ͑Milli-Q plus, Millipore͒, suprapure grade Na2SO4 ͑0.25 M͒, and CoSO4 ͑1 mM͒, and was deaerated by purified nitrogen ͑99.999%, 5 N͒ prior and during the experiments. No additional additives were used in order to avoid any influence on the mechanism of cluster formation. The STM images were recorded in the

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Figure 1. Schematic representation of the mechanism of Co cluster growth using the STM tip as a nanoelectrode. ͑I͒ Co deposition from the electrolyte onto the uncovered part of tip. ͑II͒ Co covered tip. ͑III͒ Co emitting tip during Co dissolution and localized cluster growth underneath the tip onto the substrate. ͑IV͒ Imaging of deposited clusters. The STM tip is retracted from the substrate during the whole deposition procedure.

constant current mode of the STM. The cluster width is specified as the full width at half maximum ͑fwhm͒ of the peak in the line profile through the center of the cluster.
Using the scanning probe tip as a nanoelectrode is a derivative of the concept of the scanning electrochemical microscope ͑SECM͒,29,30 but it shows several important advantages. The electrochemical processes at the nanoelectrode are essentially reversible, and the nanoelectrode is electrochemically inert; its diameter is small compared to typical diameters of ultramicroelectrodes, or even capillaries; and it easily allows imaging in situ of the previously deposited structures by the scanning tunneling microscopy.
The Deposition Procedure
The deposition of Co clusters has been achieved by a two-step process using the STM tip as a nanoelectrode as shown schematically in Fig. 1. The distance of the STM tip from the substrate surface is between 10 and 30 nm during the deposition procedure. It is most important to avoid any mechanical contact of STM tip and subtrate. Thus, one can be sure not to induce irreversible modifications at either the substrate or the STM tip.

Figure 3. ͑a͒ Voltage and ͑b͒ current transients during deposition of Co onto the STM tip ͑load tip͒, and its subsequent dissolution from the STM tip
͑unload tip͒. Qcat denotes the predeposited cathodic charge onto the STM tip. ͑From Ref. 28.͒

Figure 2. Cyclic voltammogram of the Co deposition onto the uncovered
part of the Au STM tip. ⌬Et(i1p) denotes the potential jump in order to initiate Co deposition onto the tip, ⌬Et(i2p) the potential jump followed by an immediate Co dissolution from the tip. The arrows indicate the cycling direction of the potential with a sweep rate of 10 mV sϪ1. ͑From Ref. 27.͒

During the first step of the deposition procedure Co is deposited from the electrolyte onto the uncoated part of the STM tip ͑Fig. 1, I͒ until the tip is covered with a preset amount of Co ͑Fig. 1, II͒. This is typically of the order of 10 to 20 monolayers of Co. The second step is the complete dissolution of Co from the STM tip ͑Fig. 1, III͒, which results in an increase of the Co2ϩ concentration around the
STM tip, and particularly in the gap between the STM tip and the substrate. The increase of the Co2ϩ concentration around the STM tip results in an increase of the Co2ϩ concentration at the substrate
surface opposite to the STM tip, which then causes an increase of the Nernst potential for Co2ϩ deposition within a certain area on the substrate underneath the STM tip. Co2ϩ will nucleate within this particular substrate area ͑Fig. 1, III, IV͒ at a properly adjusted substrate potential, positive to the bulk deposition equilibrium potential
of the electrolyte, but smaller than the increased Nernst potential
due to the Co dissolution from the STM tip.
The detailed potentials at the STM tip during deposition and
dissolution of Co onto and from the tip, respectively, are shown in
Fig. 2, the corresponding potential and current transients are plotted
in Fig. 3. The deposition sequence starts with the uncovered tip at a
tip potential of Etip ϭ Ϫ360 mV. Co deposition is achieved by a potential jump ⌬Et(i1p) into the cathodic potential regime. The measured current to the STM tip is diffusion limited during Co growth
on the uncovered tip area. After deposition of a preadjusted amount of cathodic charge Qcat , Etip is switched by ⌬Et(i2p) into the anodic regime to dissolve Co from the STM tip. As is seen in Fig. 3, the measured Co2ϩ current during dissolution is limited to approxi-
mately 520 nA by the current-voltage converter of our STM, and
lasts for about 2-3 ms depending on the preadjusted charge Qcat .

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Figure 4. STM image of two Co clusters on Au͑111͒ deposited by a twofold
application of the deposition procedure with Qcat ϭ 400 pC. The fwhm of the clusters is 15 Ϯ 1 nm, and the height 7.5 Ϯ 0.5 nm as measured by
STM. EWE ϭ Ϫ530 mV, ⌬z ϭ 15 nm. The lower baselines of the STM scans across the clusters, compared to the substrate surface, are a scan artifact. ͑From Ref. 28.͒

The procedure is reversible, since the Co film covering the STM tip is completely dissolved, except for unknown submonolayer alloying phenomena at the Au STM tip, and can hence be repeated many times without alteration of the shape of the Au STM tip. This feature also allows a subsequent in situ imaging of the deposited structures. Such an imaging would not be possible in the case of a pure Co nanoelectrode, because the Co dissolution would change the shape of this electrode.
Figure 4 shows two Co clusters on a Au͑111͒ terrace imaged after a twofold application of the described procedure. The width of the clusters is 15 nm, as measured by STM.

The Mechanism
In order to understand the mechanism of the cluster formation on
the substrate surface opposite to the STM tip, we consider the influence of the local variation of the Co2ϩ concentration during the
anodic dissolution from the tip on the Nernst potential at the sub-
strate surface in a model calculation. Since the thickness of the
electrochemical double layer at the tip and the substrate surfaces is approximately 1 nm in a 0.5 M NaSO4-1 mM Co2ϩ solution,31 and hence much smaller than the typical tip substrate distance of 10-30 nm during the deposition procedure, the transfer of Co2ϩ from the tip to the substrate is determined by diffusion of Co2ϩ. Ion migra-
tion may be excluded, since the voltage drop at both substrate and
STM tip essentially occurs across the electrochemical double layer.
Thus the electric field in the remaining gap between tip and sub-
strate may be assumed to be zero. Hence, the problem can be reduced to solving the diffusion equationb for Co2ϩ at appropriate
boundary conditions, analogous to similar problems described in the literature.32,33 The main contribution to the local variation of the Co2ϩ concentration at the substrate surface originates mainly from
the STM tip apex, which is modeled as a hemisphere with a radius
of a ϭ 50 nm in agreement with a variety of SEM micrographs of different STM tips. During the short time of a few milliseconds of Co2ϩ emission from the STM tip ͑Fig. 3͒, this hemisphere represents a continuously Co2ϩ emitting surface source with a constant Co2ϩ emission rate. The emission rate is constant due to the constant Co2ϩ current during Co2ϩ emission from the STM tip, which is limited to
approximately 520 nA by the current-voltage converter of our STM
scanner, as shown by the current transient in Fig. 3.

ͭ ͩ ͪ ͩ ͪ ͮ b The diffusion equation in spherical coordinates is given by

‫ץ‬C 1 ‫ץ‬

‫ץ‬C

1‫ץ‬

‫ץ‬C

D ‫ץ‬2C

‫ץ‬t ϭ r2 ‫ץ‬r Dr2 ‫ץ‬r ϩ sin ⌰ ‫ ⌰ץ‬D sin ⌰ ‫ ⌰ץ‬ϩ sin2 ⌰ ‫␾ץ‬2

with the spherical coordinates r,⌰,␾, the ion concentration C, and the

constant D.

diffusion

Figure 5. Schematic of the STM tip geometry assumed for the model calculation: The tip apex is modeled by a hemisphere of radius aជ . The diffusion profile is calculated by integration of point sources across the surface of the hemisphere as indicated in the graph.

Thus, the radial Co2ϩ concentration profile underneath the emit-
ting STM tip is obtained by solving the diffusion equation for these particular boundary conditions. Integration of Co2ϩ emitting point sources across the hemisphere of the tip apex ͑Fig. 5͒ leads to the
concentration profile C(R,t0) at distance r ϭ ͉Rជ Ϫ aជ ͉ from the STM tip apex surface ͑Fig. 5͒ at time t ϭ t0

͵ ͭ ͩ ͪ ajCo2ϩ
C͑R,t0͒ ϭ eRͱ␲D ϫ

t0 1

͑R Ϫ a͒2

0 ͱt exp Ϫ 4Dt

ͩ ͪ ͮ R2 ϩ a2
Ϫ exp Ϫ 4Dt dt

with e ϭ 1.602 ϫ 10Ϫ19 A s, the Co2ϩ diffusion constant D ϭ 7 ϫ 10Ϫ6 cm2 sϪ1,34 and the Co2ϩ emission current density jCo2ϩ ϭ 520 nA ϫ (Stip)Ϫ1, where Stip denotes the total unisolated tip area. For the numerical calculations an unisolated tip area of Stip ϭ 10 ␮m2 was used. The influence of the substrate on the forma-
tion of the concentration profile underneath the STM tip has not
been considered in this model calculation, but is addressed in the
Discussion section. Figure 6 shows the calculated time dependence of the Co2ϩ con-
centration at two distances r ϭ 5 nm and r ϭ 40 nm from the STM tip apex during Co2ϩ emission. A constant Co2ϩ concentration is

Figure 6. Calculated time dependence of the generation of the Co2ϩ con-
centration profile for different distances r ϭ 5 nm and r ϭ 40 nm from the STM tip surface for an emission time t0 ϭ 5 ms using Eq. 1. Co2ϩ emission current ICo2ϩ ϭ 520 nA, total uncovered tip area Stip ϭ 10 ␮m2. The concentration c0 denotes the 1 mM Co2ϩ electrolyte concentration (r ϭ ϱ).

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Figure 7. Calculated increase ⌬N P of the Co2ϩ/Co Nernst potential at the
substrate surface for a tip substrate distance ⌬z ϭ 20 nm with respect to the Co2ϩ/Co Nernst potential of the 1 mM Co2ϩ solution. ICo2ϩ ϭ 520 nA, Stip ϭ 10 ␮m2. The solid lines of constant Co2ϩ concentration are calculated, the dashed lines of constant Co2ϩ concentration are extrapolated according to
the STM tip shape. The diameter of the growth area is exemplarily shown
assuming EWE adjusted 34 mV below the maximum of the effective Nernst potential. ͑From Ref. 28.͒

reached within 100-200 ␮s, which means that the Co2ϩ diffusion

profile around the STM tip can be considered stationary during the Co2ϩ emission time of 2-3 ms ͑Fig. 3b͒.

This stationary concentration profile results in a lateral variation of the Co2ϩ concentration at the substrate surface. According to the Nernst equationc this lateral variation of the Co2ϩ concentration is correlated with a lateral variation ⌬N P(x,y) of the Co2ϩ/Co Nernst potential at the substrate surface, with respect to the Co2ϩ/Co Nernst potential of the 1 mM Co2ϩ electrolyte. Assuming a rotational sym-

metry about the axis of the STM tip, the lateral dependence of

⌬N P(x,y) is considered in the following only in the x direction. Since the Co2ϩ emission from the STM tip results in an increase of
the Co2ϩ concentration at the substrate surface, ⌬N P(x) will be

positive. The calculated increase of ⌬N P(x) as a function of the

lateral distance x from the center of the STM tip, with respect to the Nernst potential of an 1 mM Co2ϩ electrolyte, is shown in Fig. 7.

Since ⌬N P(x) adds to the uniform Nernst potential E1 mM of the 1 mM Co2ϩ electrolyte, the diffusion profile results in a laterally vary-

ing effective Nernst potential Eeff (x) ϭ E1 mM ϩ ⌬N P(x) underneath the STM tip with a maximum Eemffax ϭ E1 mM ϩ ⌬N Pmax at

x ϭ 0 ͑Fig. 7͒.

Adjusting EWE between the Nernst potential E1 mM of the 1 mM Co2ϩ electrolyte and the maximum of this locally increased effective

Nernst

potential

E

max eff

,

the

effective

Nernst

potential

exceeds

E WE

ͩ ͪ c The Nernst potential E is given by the Nernst equation

E ϭ E0 ϩ RT ϫ ln aCo2ϩ

zF

a Co

with the standard potential E0, R ϭ 8.314 J KϪ1 molϪ, T ϭ 298 K, z ϭ 2, F ϭ 96,480 A s, aCo2ϩ ϭ f Co2ϩ ϫ cCo2ϩ , the Co2ϩ activity coefficient f Co2ϩ , and the Co2ϩ con-

centration cCo2ϩ .

Figure 8. ͑a͒ STM image showing the dependence of the cluster height on the preadjusted cathodic charge Qcat . First four deposition cycles: Qcat ϭ 400 pC; deposition cycle five to eight: Qcat ϭ 600 pC; EWE ϭ Ϫ530 mV, ⌬z ϭ 15 nm. The third and the fourth cluster are missing. ͑b͒ Line profile along the white line.
within a particular area underneath the STM tip ͑denoted as growth area in Fig. 7͒, and a localized deposition of Co is initiated.
The Main Parameters
According to the presented model, the height and diameter of the deposited clusters is determined by (i) the radius a of the STM tip apex, (ii) the Co2ϩ emission current density jCo2ϩ, (iii) the tipsubstrate distance ⌬z, (iv) the predeposited tip charge Qcat , and (v) the substrate potential EWE . Thus, the two parameters height and diameter of the clusters are determined by at least five quantities, which are not independent of each other. Therefore, the STM tip diameter, jCo2ϩ, and EWE are held constant in the following, in order to study the influence of Qcat and ⌬z on the shape of the deposited clusters in more detail.
Figure 8 shows a sequence of Co clusters grown by applying the described deposition sequence eight times. Between each sequence the lateral position of the STM tip was changed in linear direction. Whereas the first four sequences were applied with a predeposited cathodic tip charge of Qcat ϭ 400 pC, the sequences five to eight were applied with Qcat ϭ 600 pC. Since the Co deposition onto the tip can be controlled only by measuring the cathodic charge Qcat , this charge was taken as measure for the predeposition of Co onto the STM tip, even if the anodic charges during Co dissolution from the STM tip are the important charges for the cluster formation. However, anodic and cathodic charges are proportional assuming a constant contribution of H2 generation during Co2ϩ deposition onto the tip.35 As is seen in the line profile of Fig. 8b, the height of the clusters scales with the amount of predeposited tip charge. The cluster height is 7.5 Ϯ 0.5 nm in the case of Qcat ϭ 400 pC, and 11.5 Ϯ 1 nm in the case of Qcat ϭ 600 pC. According to our model, the volume of the clusters should scale linearly with Qcat , since the Co2ϩ emission time scales linearly with Qcat due to the constant jCo2ϩ during Co2ϩ emission from the STM tip. However, nucleation of Co can occur only within the growth area on the substrate surface as illustrated in Fig. 7. The growth area depends only on the stationary Co2ϩ concentration profile, which is independent of the time of

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Figure 9. Model calculation of the dependence of the cluster diameter on the distance ⌬z between STM tip and substrate during the deposition procedure. The graphs show exemplarily two distances ͑a͒ ⌬z ϭ 5 nm and ͑b͒ ⌬z ϭ 40 nm. ICo2ϩ ϭ 520 nA, Stip ϭ 10 ␮m2. c1 denotes the particular Co2ϩ concentration which results in an effective Nernst potential equal to EWE . Nucleation is initiated within the growth area where the effective Nernst potential exceeds EWE .
Co2ϩ emission from the STM tip. Thus, Co growth occurs mainly in the z direction, but is confined laterally to within the growth area. This explains, that Qcat scales linearly with the height of the clusters, and thus linearly with the cluster volume.
According to this explanation, the fwhm of the clusters should be independent of Qcat . However, the STM measurement of Fig. 8 shows also an increase of the cluster fwhm with Qcat from 16 nm at Qcat ϭ 400 pC to 22 nm at 600 pC. This increase of the cluster fwhm, unlike the correct height of the clusters, is due to an artifact of the STM measurement, caused by the convolution of the shape of the tip apex with the real cluster shape. The measured fwhm of clusters is enlarged, the higher the clusters are, even if the real cluster diameter remains constant. The absolute size of this effect depends in general on the actual tip shape and on the real cluster shape. However, the relative effect at objects of different height within a single STM image (i) can be determined if the STM tip remains unchanged during the measurement and (ii) is more or less independent of the actual tip apex diameter if the diameter is in the range of 20-100 nm. Assuming infinitely steep steps of height h and of height 1.5 ϫ h, corresponding to our cluster heights of 7.5 and 11.5 nm ͑Fig. 8͒, the higher step results in an approximately 25% wider fwhm than the lower step. Thus, the observed broadening of the cluster fwhm in Fig. 8 of approximately 35% ͑from 16 nm at Qcat ϭ 400 pC to 22 nm at Qcat ϭ 600 pC in Fig. 8͒ is mainly caused by this artifact. The fwhm of the clusters turns out to be independent of Qcat in good agreement with our model presented above.
As can be seen from Fig. 7, a decrease of ⌬z results in an increase of the Co2ϩ concentration at a fixed lateral position of the substrate surface, and thus, according to the Nernst equation, in an increase of the effective Nernst potential at this particular position. Therefore, the diameter of the growth area is also expected to increase according to our model. This is shown explicitly for two tip-substrate distances ⌬z ϭ 5 nm and 40 nm in Fig. 9. It seems quite surprising that the growth area and hence the cluster diameter should decrease with increasing tip-substrate distance, and vice versa. However, the experimental finding in Fig. 10 proves this prediction. The only parameter which was varied between the deposition of the upper and lower row of clusters was the tip-substrate distance ⌬z. Whereas the measured fwhm of the clusters deposited at ⌬z ϭ 15 nm is 18 Ϯ 1 nm ͑Fig. 10, upper row͒, the fwhm of the clusters deposited at ⌬z ϭ 10 nm is 28 Ϯ 1 nm ͑Fig. 10, lower row͒. Remarkably, all clusters are approximately equal in height due to the constant Qcat during each of the four deposition cycles. Unlike the situation in Fig. 8, the convolution of the tip apex shape with the

Figure 10. STM image showing the dependence of the cluster diameter on the distance ⌬z between STM tip and substrate during the deposition procedure. Upper row: ⌬z ϭ 15 nm during deposition; lower row: ⌬z ϭ 10 nm during deposition; Qcat ϭ 800 pC; EWE ϭ Ϫ540 mV. The fwhm of the clusters grown with ⌬z ϭ 15 nm is 18 Ϯ 1 nm, the fwhm of the clusters grown with ⌬z ϭ 10 nm is 28 Ϯ 1 nm, as measured by STM. Each gray scale value corresponds to a height of 1 nm. The lower baselines of the STM scans across the clusters, compared to the substrate surface, are a scan artifact.
real cluster shape would not significantly change the ratio of the cluster fwhms, since all clusters in Fig. 10 are equal in height. Thus, the measured decrease of the cluster fwhm from 28 to 18 nm upon increase of ⌬z from 10 to 15 nm may be assumed to be correct. The volume of the clusters decreases with increasing ⌬z if Qcat is held constant.
Discussion
The localized electrodeposition on the nanometer scale using the tip of a STM as nanoelectrode allows the electrochemical growth of quasi zero-dimensional ͑metal͒ clusters. Even if the threedimensional delocalized nucleation of metal clusters has been widely studied for more than 20 years,36 the active deposition of single clusters on a surface opens up the exciting possibility to investigate the properties of individual clusters. Since the nanoelectrode is made from electrochemically inert Au, and not from, e.g., Co, the technique allows the electrodeposited clusters to be studied simultaneously by in situ STM. The substrate/deposit system Au͑111͒/Co2ϩ shows no underpotential deposition within the measurement accuracy of cyclic voltammetry. Therefore, it is a good example for the universality of the technique. The results may be representative also for other substrate/deposit systems, in particular for underpotential deposition systems. This has been proven by the deposition of Cu clusters on Au surfaces.37
The experimentally observed dependencies of the cluster diameter on the distance ⌬z between the STM tip and substrate during deposition ͑Fig. 10͒, the dependence of the cluster height on the cathodic charge Qcat predeposited onto the STM tip ͑Fig. 8͒, as well as the independence of the cluster diameter on Qcat confirm the predictions of our Co2ϩ diffusion model.
The dependence of the cluster size on the STM tip apex diameter and the dependence on the Co2ϩ current density jCo2ϩ during Co2ϩ emission from the STM tip are difficult to study in situ. An increase of the Co2ϩ current density is expected to result in an increase of the lateral variation ⌬N P of the Co2ϩ/Co Nernst potential at the substrate surface underneath the STM tip. This was optimized in our experiments by changing the current-voltage conversion gain of our current-voltage converter to allow up to 520 nA tip current. A further increase of jCo2ϩ can be achieved either by increasing the Co2ϩ

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Figure 11. STM image showing three Co clusters on Au͑111͒ after deposition with ⌬z ϭ 10 nm and Qcat ϭ 400 pC; EWE ϭ Ϫ535 mV. The height of the clusters is 2.5 Ϯ 0.5 nm, the fwhm is 9.5 Ϯ 0.5 nm, as measured by STM.
emission current or by decreasing the unisolated tip surface area, which was approximately 10 ␮m2 in our experiments. A positive consequence of a further increase of jCo2ϩ would be a less critical adjustment of the substrate potential EWE which had to be adjusted within approximately 40 mV ϭ ⌬N Pmax at our experimental conditions. A rough estimate using Eq. 1 shows that an uncovered tip area of only 1 ␮m2 would result in a maximum increase of the effective Nernst potential by about ⌬N Pmax Ϸ 70 mV. Hence, this range would be available for adjustment of the substrate potential.
Nevertheless, the available potential range ⌬N Pmax between the Nernst potential of the 1 mM Co2ϩ electrolyte solution and the maximum of the effective Nernst potential at the substrate surface
underneath the STM tip is large enough to adjust EWE well above the equilibrium potential for delocalized nucleation on the substrate.
According to our model, the diameter of the nucleation area on
the substrate becomes smaller, if the substrate potential EWE is adjusted to be more positive, because the Co2ϩ/Co Nernst potential is exceeded only within a smaller substrate area. Thus, the cluster di-
ameter could be varied by changing EWE by a few millivolts. It seems to be important that the parameters ⌬z, Qcat , and EWE
can be adjusted independently, thus allowing a nearly independent adjustment of cluster diameter and cluster height. This feature is remarkable, because it allows for tailoring lateral extension and aspect ratio of the structures independently, as may be required for specific applications.
The conical shape of the clusters as seen in the STM images becomes more pronounced with decreasing cluster diameter, as seen from comparison of, e.g., Fig. 10 and 11. This is an artifact of the STM measurement, representing the convolution of the real cluster shape with the shape of the STM tip apex. It becomes increasingly important when studying structures both of lateral sizes in the lower nanometer range, and simultaneously of high aspect ratio.
According to our model, the cluster diameter decreases both with increasing distance between STM tip and substrate and with increas-
ing EWE . These dependencies could compensate large tip diameters, and thus result in the observed small structure sizes. Despite the diameter of our STM tips being approximately 100 nm, clusters with diameters below 10 nm, as measured by STM, could be grown ͑Fig. 11͒. Additionally, small cluster sizes could be achieved by exploiting nucleation overpotentials, which result in a larger ⌬N P necessary for nucleation, and hence a smaller nucleation area on the substrate. Such overpotentials are likely present in our system as seen from the cyclic voltammogram ͑Fig. 2͒.
The absolute value of Etip during loading and emission of Co, as shown in Fig. 2 and 3, are not critical for the diameter of the nucleation area on the substrate, since this area is determined only by the Co2ϩ concentration profile around the STM tip, independent of the particular tip potential. The only essential assumption for the presented model is a constant Co2ϩ emission rate from the STM tip. Qualitatively, the results would remain the same, even if the Co2ϩ

emission rate from the STM tip would not be constant; however, the exact solution of the diffusion equation would be much more complicated than in the presented case.
The influence of the substrate surface on the Co2ϩ diffusion profile has not been taken into account in our model calculation. It is obvious, that the substrate prevents a further Co2ϩ diffusion into the volume of the substrate, which would take place in the case of a missing substrate. Hence, the presence of the substrate should result in an additional increase of Co2ϩ concentration in the gap between tip and substrate, thus resulting in an amplification of the effect. Immediately after initiation of the Co2ϩ nucleation, the growth area on the substrate can be assumed to be a Co2ϩ sink, which reduces the back diffusion of Co2ϩ into the gap between substrate surface and STM tip. This effect would result in a slightly decreasing Co2ϩ concentration in front of the growth area, and thus in a slightly decreasing ⌬N P. In order to maintain the Co2ϩ deposition, the initial enhancement of the Co2ϩ concentration, and hence of the initial ⌬N P, must be large enough to compensate for this effect.
This kind of localized electrochemical deposition is not restricted to STM, but can also be applied in the electrochemical atomic force microscope ͑AFM͒. The only requirement is a conductive probe in order to use the probe as an electrochemical nanoelectrode. A simultaneous lateral translation of the tip during Co2ϩ emission from the tip may be applied to grow continuous lines instead of single clusters. This would open the possibility for fabricating well-defined nanoscale objects in view of nanotechnological applications. In this context, it is important to note, that the repetition rate of the cluster deposition may be at least as high as 10 Hz ͑Fig. 3͒, which would allow one to grow more complicated structures on reasonable time scales.
Summary
The electrochemical deposition of Co clusters, using a STM tip as an electrochemical nanoelectrode poised at a distance of typically 20 nm from the substrate surface, can be described assuming Co transfer from the STM tip to the substrate by diffusion. The influence of the main parameters on the diameter and height of the deposited clusters can be well understood. The scanning probe-based electrochemical deposition, as presented in this paper, allows the active formation of structures at precisely predefined locations on the substrate surface, even in a system showing a relatively weak substrate/deposit interaction compared to the strong interaction of underpotential deposition systems. Therefore, the results seem to be of importance in view of the current variety of reported approaches of scanning probe based nanostructuring techniques. Our results may help to distinguish among different mechanisms which are likely involved in the procedures reported so far in the literature.
Acknowledgments
The authors are indebted to H. Menge for supporting us with high quality Au͑111͒ crystals. Financial support by the Deutsche Forschungsgemeinschaft under contract KI 358/1-2 and SCHI492/ 1-2 is gratefully acknowledged.
Max-Planck-Institut fu¨r Mikrostrukturphysik assisted in meeting the publication costs of this article.
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SubstrateClustersSubstrate SurfacePhysFig