Normal versus anomalous roughening in electrodeposited Prussian Blue layers

Electrochemistry Communications 13 (2011) 1455–1458

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Normal versus anomalous roughening in electrodeposited Prussian Blue layers M.F. Alamini a, R.C. da Silva a, V.C. Zoldan a, E.A. Isoppo b, U.P. Rodrigues Filho c, F.D.A. Aarão Reis d, A.N. Klein e, A.A. Pasa a,⁎ a

Departamento de Física, UFSC, 88.040-900 Florianópolis, SC, Brazil LCME, UFSC, 88.040-900 Florianópolis, SC, Brazil Instituto de Química de São Carlos, USP, 13.564-970 São Carlos, SP, Brazil d Instituto de Física, UFF, Niterói, RJ, Brazil e Laboratório de Materiais, UFSC, Florianópolis, SC, Brazil b c

a r t i c l e

i n f o

Article history: Received 21 July 2011 Received in revised form 20 September 2011 Accepted 22 September 2011 Available online 5 October 2011 Keywords: Prussian Blue Electrodeposition Kinetic roughening

a b s t r a c t Electrochemical deposition of Prussian Blue shows a time increase of adsorption rate and produces films with faceted surfaces and smooth morphology at short length scales. Roughness scaling suggests anomalous roughening. However, an interpretation of normal Family–Vicsek scaling provides exponents consistent with roughening dominated by surface diffusion and time-dependent deposition rate characteristic of electrodeposition. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The study of surface morphology is an important tool for fundamental and applied research on thin films. Currently, it is of particular interest in electrochemical deposition because the growth significantly differs from the widely studied physical deposition processes. In this work, electrochemical growth of Prussian Blue (PB) films is analyzed by surface imaging methods and kinetic roughening concepts. Prussian Blue Fe4[Fe(CN)6]3 is a material with increasing interest for applications such as molecular magnets, electrochromic devices, and electrochemical sensors [1–5]. Here, PB films up to 650 nm thick are deposited by cyclic voltammetry and studied by atomic force and transmission electron microscopy (AFM, TEM). Typical features of anomalous roughening are observed [6], similar to electrodeposition of metals and alloys [7–12]. AFM images suggest a type of faceted anomalous scaling observed in metal dissolution [13] and statistical models [14]. However, a novel interpretation of normal Family–Vicsek (FV) scaling [15,16] with time increasing adsorption rate is proposed. Exponents of the Mullins-Herring class [17,18] are obtained from the experimentally measured anomalous exponents. This is consistent with roughening dominated by surface diffusion, while particular electrodeposition features determine the time evolution of adsorption rates and possibly spatial inhomogeneity. Comparison with related models [19] suggests large mobility of

⁎ Corresponding author. Tel.: + 55 48 84061547; fax: + 55 48 32340599. E-mail addresses: [email protected] (F.D.A.A. Reis), pasa@fisica.ufsc.br (A.A. Pasa). 1388-2481/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.elecom.2011.09.025

the adsorbed species, which explains the smooth surface at molecular scale with sharp facets at larger length scales. 2. Experimental The electrodeposition of PB films is performed in a conventional three-electrode cell with Au (50 nm) on (100) Si n-type (1–10 Ω cm) as working electrode, platinum foil as counter-electrode, and a saturated calomel electrode (SCE) as reference. The electrolyte at pH 1.5 consisted of 0.5 mM of K3Fe(CN)6, 0.5 mM FeCl3, 1.0 M KCl and 0.01 M HCl. The layer formation was promoted by sweeping sequentially the potential, for two different scan rates ν and a maximum number of 80 cycles. The surface topography close to the center of each sample was measured with contact mode AFM. Low and high-resolution TEM images of cross sections of the thickest samples were also obtained. 3. Results and discussion Fig. 1a shows cyclic voltammograms for potentials in the range from −0.25 to 0.7 V, with scan rates 50 and 100 mV/s, after 20 and 80 cycles. Current peaks were observed at 0.18 and 0.31 V, corresponding to reduction and oxidation reactions, respectively. Reduction forms Prussian White (PW) K4Fe4[Fe(CN)6]3 with K + ions entrapped in the solid structure for charge compensation. A global electrochemical reaction describing the reduction of species on the electrode surface (corresponding to the cathodic peak) could be 4Fe 3+ + 3[Fe(CN)6] 3- + 4 K + + 7e- → K4Fe4[Fe(CN)6]3. PW is

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Fig. 1. (a) Cyclic voltammograms for scan rates 50 and 100 mV/s after 20 and 80 cycles. (b) Reduced charge per cycle.

oxidized to PB through the reaction K4Fe4[Fe(CN)6]3 − 4e − → Fe4[Fe (CN)6]3 + 4 K + [20], where Fe 2+ ions are re-oxidized to Fe 3+ and K + ions are released to the solution. Fig. 1a also shows that the area of the 20th cycle (charge exchanged at the electrode) is smaller than that of the 80th cycle, thus the rate of production of PB increases in time, in agreement with a concomitant increase in the surface roughness of the growing deposit [21]. Fig. 1b shows the reduction charge per cycle as a function of the number of cycles for both scan rates. This quantity is proportional to the deposited mass per cycle, as was observed experimentally by measuring the thickness of the layers with a profilometer as a function of the total reduced charge Q, where a growth rate of 4 nm/mC was observed for samples prepared at 50 mV/s (results not shown). The fit in Fig. 1b gives a growth rate dH/dt ~ t Ω, with Ω = 0.35, where H is the average film thickness, thus Het

Ωþ1

;

with Ω þ 1 ¼ 1:35:

ð1Þ

The typical surface morphology of PB films is shown by the AFM image of Fig. 2a. From AFM images, the surface roughness w(l,H) = [b(h(H)- b h(H)N) 2N] 1/2 is measured in square boxes of various sizes

l for each film thickness (here H replaces the usual time variable). Fig. 2b shows w versus l for deposition at 50 mV/s, with a typical feature of anomalous scaling: for small and fixed l, the roughness continuously increases in time. Analogous data were obtained from samples deposited at 100 mV/s. Fig. 2c shows the local roughness wl, measured at l = 50 nm, as a function of the total reduced charge Q (assumed proportional to H). It gives κ

κ

wl e Q e H ;

with

κ ¼ 0:33;

ð2Þ

where κ is the local slope exponent [6]. For small l, a linear increase of w with l (Fig. 2b) gives α ; w e l loc

with

αloc ¼ 1:0;

ð3Þ

where α loc is the local roughness exponent. This exponent is also found in systems with faceted or grainy surface structures, which is a geometric effect of box counting and related methods [22].

Fig. 2. (a) AFM image of the PB film deposited at 50 mV/s after 80 scanning cycles. (b) Surface roughness as a function of box size for five film thicknesses deposited at 50 mV/s. (c) Local (l = 50 nm) and saturation roughness and (d) correlation length as a function of integrated reduction charge for films deposited at 50 and 100 mV/s.

M.F. Alamini et al. / Electrochemistry Communications 13 (2011) 1455–1458

The roughness in Fig. 2b reaches a saturation value ws for large l. Fig. 2c shows ws versus Q, giving β0

ws e H ;

with

0

β ¼ 0:5:

ð4Þ

This value of β' is also obtained in epitaxial films of Cu [23] and Ag [24] with mounded morphology and in some lattice growth models [25]. It is associated with large step-edge barriers that prevent interlayer transport, but those systems have constant deposition rates, in contrast to the present one. The shape of voltammograms in Fig. 1a and the high concentration of supporting electrolyte suggest that diffusion in solution dominates reactant migration towards the electrode surface, where the electric field is small [26]. These features do not explain the increase of adsorption rate, instead, slow diffusion might eventually reduce it. Thus, that increase is probably related to the increase of the electroactive surface area in time, which is directly connected to the increase in roughness (Eq. (4)). This also contrasts with the constant rates of vapor deposition. The intersection of the linear fits of scaling and saturation regimes (Fig. 2b) gives the correlation length ξ for each thickness. Fig. 2d shows that ω

ξ e Qω e H ;

with

0

ω ¼ 1=z ¼ 0:18:

ð5Þ

Here, z' = 5.6 may be interpreted as a dynamic exponent. This is supported by AFM image in Fig. 2a showing the growth of pyramidal grains of order ξ. Given that α loc = α'-z'κ, the global roughness exponent is α' = 2.85. Fig. 3a shows a remarkable data collapse with roughness scaled by ws and box size scaled by ξ, for ν = 50 mV/s. This follows the anomalous scaling relation [6] w ¼ ws f ðl=ξÞ;

ð6Þ

where f is a scaling function. Similar results are obtained for ν = 100 mV/s. Additional insight on the growth dynamics is provided by TEM cross section images displayed in Fig. 3b and c, respectively with low and high resolution. They confirm the formation of single crystalline pyramidal grains and reveal lattice fringes with d-spacing of 0.359 nm of the (220) planes of the cubic structure of PB. The pyramids become sharper as the film grows, as indicated by the rapid increase of the local roughness (Eq. (2)). TEM images also show pyramids with very smooth faces at atomic length scales. This is possible only if surface diffusion of adsorbed species is rapid, so that molecules and radicals can migrate to distant points with small activation energy barriers (large barriers are found only in highly packed configurations).

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Anomalous scaling is predicted in some systems whose normal roughening mechanisms have time-dependent couplings [27]. Thus hereafter we consider the incorporation of surface diffusion effects and varying growth rate in normal (in opposition to anomalous) dynamic scaling relations. When surface diffusion of adsorbed species affects film morphology, the main parameter is the ratio R = D/F between the average diffusion coefficient D and the flux F of incoming species (additional energy barriers play a role when a range of temperature is studied). That ratio is interpreted as an average number of random steps of an adsorbed molecule when the thickness H increases of one molecular layer [28]. During PB film growth, the temperature is fixed (fixed D) and the adsorption rate (F) varies, thus Eq. (1) gives ReF

−1

−1

e ðdH=dt Þ

eH

−Ω=ð1þΩÞ

:

ð7Þ

The normal FV scaling relation [16] is w = t βg(l/ξ), where g is a scaling function. When R is constant, the correlation length is ξ ~ t 1/z ~ H 1/z and measures the lateral spread of fluctuations by surface processes (reactions, diffusion, surface tension, etc.). When R changes, the number of random steps of an adsorbed molecule changes by the same factor, thus ξ ~ (RH) 1/z is expected from the above interpretation of R. On the other hand, the factor t β (alternatively H β) in the FV relation measures the amplitude of height fluctuations. Increasing R helps to smooth the surface, reducing that amplitude by an overall factor R Δ (Δ N 0) that depends on the roughening mechanism. Thus   β Δ 1=z w ¼ H =R g ðl=ξÞ; ξ e ðRHÞ :

ð8Þ

This form resembles that of a model with irreversible adatom aggregation to step edges [19] and those of models with competitive aggregation dynamics [17]. Substituting Eq. (7) in Eq. (8), the roughness is given as a function of l and H, similarly to the anomalous relation (6). Using Eqs. (4) and (5), the exponents β, z, and Δ are related to the experimentally measured exponents κ, Ω, and ω as z ¼ 1=½ωð1 þ ΩÞ; Δ ¼ ðκ−ωΩÞð1 þ ΩÞ=Ω;

ð9Þ ð10Þ

and 0

β ¼ β −κ þ ωΩ:

ð11Þ

The roughness (Hurst) exponent is α = αloc = 1.0 because the scaling on l does not involve time effects. Eqs. (9) and (11) give z = 4.11 and β = 0.23. These exponents are consistent with the

Fig. 3. (a) Normalized plot for the surface width (w/ws) as a function of scale length (l/ξ). (b) Cross section TEM image and (c) lattice fringes with d-spacing 0.359 nm relative to (220) lattice plane of the cubic PB lattice.

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Mullins-Herring (MH) equation [15,18] for roughening dominated by surface diffusion, whose exact values are α = 1, β = ¼, z = 4. From Eq. (10), Δ = 1.03 is obtained. This large exponent is consistent with large surface mobility suggested by TEM image analysis. For comparison, a much smaller exponent Δ = 0.3 is obtained in a model with highly restricted adatom mobility [19]. Thus, the factor R Δ of Eq. (8) is certainly related to energy barriers for surface diffusion in a variety of microscopic environments (these barriers can be distinguished only with growth at different temperatures). The increasing growth rate (Eq. (1)) continuously reduces the smoothing role of surface diffusion, since molecular layers deposited after many cycles are buried faster than the ones deposited in the beginning of the process. This explains the large difference between exponents from the two interpretations: β' N β because the smoothing effect is continuously reduced, z' N z because the propagation of lateral correlations is slower. We have also tried to use the FV relation (8) with the time t replacing the thickness H, as usual. However, it gives z = 2.67, β = 0.36 and Δ = 0.95, which does not agree with any known theory of surface roughening [15], besides not being consistent with the interpretation of R. 4. Conclusions The scaling of surface roughness and inspection of surface images of electrochemically deposited PB films suggested a novel example of faceted anomalous roughening. However, accounting for the time increase of adsorption rate, which reduces surface diffusion lengths as the film grows, the scenario of a diffusion-dominated growth in the Mullins-Herring class emerges. A significant effect of the diffusionto-deposition ratio on the roughness scaling is found, consistent with the closely packed configurations and formation of a film with single crystalline grains. Particular features of electrodeposition, such as spatial inhomogeneity and time-dependence of reaction rates, explain the time increase of adsorption rate, while surface diffusion of adsorbed species govern film roughening. Acknowledgements The authors acknowledge support from CNPq (Namitec), CAPES, FAPESC, FINEP and Faperj.

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