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4. Electrochemistry of Diamond: Semiconductor and Structural Aspects Yuri V. Pleskov 4.1. Introduction Being extraordinarily stable and corrosion-resistant, diamond is an attractive electrode material for use in theoretical and applied electrochemistry [1]. In particular, diamond electrodes have been reported to be stable and effective electrodes for environmentallyoriented [2] and analytical [3,4] purposes. As with many insulators, diamond can be transformed into a wide-gap semiconductor by appropriate doping. Boron practically is the only “shallow” acceptor dopant that makes diamond conducting at room temperature (most other dopants have too large an ionization energy) [5]. Recently, sulfur was suggested as an equally shallow donor dopant [6]. Depending on the doping level, diamond exhibits properties either of a semiconductor (e.g., at boron content from 10 to 1000 ppm) or a “poor metal” (with up to 10,000 ppm of B or even higher). It is the heavily doped diamond that is used as an electrode material in electrosynthesis, electroanalysis, etc. However, in this chapter we shall focus our attention on moderately doped diamond, because it is most suitable for revealing effects of the semiconductor nature and crystal structure on the electrochemical properties of this material. 4.2. Effects of the Semiconductor Nature of Diamond 4.2.1. Current—Voltage Curves It is known that one of the characteristic features of semiconductor/metal contacts is the rectification of electric current. The asymmetry of current—voltage semiconductor/metal contact is curves at a quite pronounced: the “direct” current passing the contact can be rather large, while the reverse (blocking) current is very small. The current—voltage characteristics at some “ideal” semiconductor electrodes do follow this law (e.g., anodic dissolution of n-type germanium, etc.) [7]. For p-type boron-doped diamond electrodes, the blocking direction of current is cathodic; for n-type sulfur-treated diamond, anodic. The asymmetrical current—voltage characteristics have indeed occasionally been observed in redox electrolytes with lightly doped diamond samples [1, 8 , 9 ] (Fig. 4.1). However, more abundant are symmetrical cyclic voltammograms, the more so for heavily doped diamond (Fig. 4.2 [10]). Different redox systems differ in their peak-to-peak potential difference Ep on the cyclic voltammograms: the faster is the electrochemical reaction, the smaller isEp. For reversible reactions, Ep ≈ 59 mV [11]. An extensive qualitative study of the dependence of Ep on the Fig. 4.1. a - Cyclic voltammogram for a boron-doped diamond electrode in 0.008 M K3Fe(CN)6 solution [1]; b - potentiodynamic curves for a sulfur-treated diamond electrode: cathodic in 0.1 M K3Fe(CN)6, anodic in 0.1 M K4Fe(CN)6 solution, at a potential scan rate of (1) 5, (2) 10, (3) 20, (4) 50, and (5) 100 mV s -1 [9]. Supporting electrolyte: 0.5 M H2SO4. Fig. 4.2. Cyclic voltammogram for a {111} face of a HTHP single crystal in 0.5 M H2SO4 + 0.01 M Fe(CN)63- + 0.01 M Fe(CN)64 solution. The potential scan rate was 5 mV s-1 [10]. properties of diamond and electrolyte [12] showed that (1) outersphere reactions are more reversible than inner-sphere ones1; (2) redox systems with more positive equilibrium potentials are more reversible than those having negative equilibrium potentials, which is but natural for a p-type semiconductor electrode (see [7]); and (3) on heavily doped (metal-like) diamond electrodes, the We recall that outer-sphere reactions involve the outer coordination sphere of reacting ions; thus, little if any change occurs inside the ion solvate shell. These reactions proceed without breaking up intramolecular bonds,whereas in inner-sphere reactions, involving the inner coordination sphere, the electron transfer is accompanied by the breaking up or formation of such bonds. Inner-sphere reactions are often complicated by the adsorption of reactants and/or reaction products on the electrode surface. 1 reactions proceed in a more reversible manner than on moderately doped electrodes (which demonstrate semiconductor behavior). The latter statement was corroborated quantitatively [ 13 ] by juxtaposing the charge-transfer (faradaic) resistance RF of diamond/redox electrolyte interfaces and the diamond bulk resistivity . This resistance can be measured using the electrochemical-impedance method, as a low-frequency cut-off on the real-component axis in the complex-plane presentation of impedance spectra taken in redox solutions of different concentrations (Fig. 4.3a [13])2. It can be also determined from the slope of the current—voltage curves recorded in these solutions. We emphasize that both the impedance spectra and the voltammetric curves should be taken at or near the reversible potential of the redox systems. The faradaic resistance is essentially equal to the reciprocal of the exchange current j0 (up to a factor of RT / F), which is a measure of the reaction rate: RF = RT / (nFj0) (4.1) Here R is the gas constant, T is the absolute temperature, and F is the Faraday constant. The RF vs. dependence is presented in Fig. 4.4. We conclude that the reaction proceeds at a higher rate at readily conducting diamond electrodes. More precisely, the low-frequency cut-off equals RF + Rs where Rs is the “series” (Ohmic) resistance in the equivalent circuit of the electrode (Fig. 4.6 below). 2 Fig. 4.3. (a) Complex-plane plots of impedance spectra measured for a polycrystalline diamond electrode at the equilibrium potential in 1 M KCl + x M K3Fe(CN)6 + x M K4Fe(CN)6 solution at a value of x: (1) 3.3 10-3; (2) 10-2; (3) 5 10-2; (4) 10-1; (5) 2 10-1. Frequency f (Hz) is shown in the figure. (b) Dependence of the faradaic resistance on the K4Fe(CN)6 concentration (the K3Fe(CN)6 concentration being kept constant) [13]. Fig. 4.4. Dependence of the faradaic resistance measured at the equilibrium redox potential for polycrystalline diamond electrodes on their resistivity for (1) Fe(CN)63-/4- and (2) quinone/hydroquinone redox systems [13]. At first glance, the proportionality between RF and reflects the fundamental law of the electrochemical kinetics at semiconductor electrodes, namely, the exchange current of a semiconductor electrode must be proportional to the surface concentration of charge carriers participating in the redox reaction. However, a closer look into the problem, based on reference [14], allows one to conclude that it is the potential distribution at the diamond/redox electrolyte solution interface, rather than the surface concentration of the charge carriers, that depends on the diamond doping level, the more so, for more heavily doped samples. More precisely, the potential drop in the Helmholtz layer in a redox electrolyte increases with increasing doping. Therefore, the reaction rate reflects the Helmholtz potential drop, rather than the charge carrier concentration. This is the reason why the behavior of semiconductor diamond is far from “ideal”; in particular, no current rectification is typically observed on (rather heavily doped) diamond electrodes, as mentioned above. In addition to the Ep quantity, the electrode kinetics can be characterized by the transfer coefficients (for cathodic reactions) and (for anodic reactions). The transfer coefficients can be found, e.g., from the slope of the dependence of the voltammetric current peak potential Ep on the logarithm of the potential scanning rate v (compare Fig. 4.1b): Ep = const - (RT / 2nF) ln v (4.2) They can also be obtained from the slope of the dependence of the faradaic resistance on the logarithm of the redox electrolyte concentration at the equilibrium potential (see Fig. 4.3b). Indeed, as shown above, the faradaic resistance RF, measured in a redox solution at its equilibrium potential, equals the reciprocal of the exchange current j0. By measuring the dependence of j0 on the concentration of the oxidized form cox in the solution, while the concentration of the reduced form cred has been kept constant (or vice versa), the transfer coefficient (or, respectively, ) can be calculated by the formula [11]: j0 = nFk0 cox 1- cred , where k0 is the rate constant of the reaction. (4.3) On metal electrodes, the transfer coefficients typically approach 0.5. Generally, the transfer coefficients for redox reactions on moderately doped diamond electrodes are smaller than 0.5; their sum +, less than 1. We recall that an ideal semiconductor electrode must demonstrate a rectification effect; in particular, on p-type semiconductors, reactions proceeding via the valence band have the transfer coefficients = 0, = 1, and thus, + = 1 [7]. Actually, the ideal behavior is rarely the case even with single crystal semiconductor materials manufactured by use of advanced technologies ( like germanium, silicon, gallium arsenide, etc.). The departure from the “ideal” semiconductor behavior is likely to be caused by the fact that the interfacial potential drop appears essentially localized, even in part, in the Helmholtz layer, due, e.g., to a high density of surface states, or the surface states directly participate in the electrochemical reactions. As a result, the transfer coefficients and have intermediate values, between those characteristic of semiconductors (0 or 1) and metals (0.5). Semiconductor diamond falls in with this peculiarity. However, for heavily doped electrodes, the redox reactions often proceed as reversible, and the transfer coefficients approach 0.5 ( “metal-like” behavior). 4.2.2. Impedance Spectroscopy Another specific feature of semiconductor electrodes is the characteristic potential dependence of their differential capacitance. The measuring procedure is known to consist in applying a perturbing harmonic voltage signal of frequency f to the electrochemical cell and measuring the cell response at the same frequency. The differential capacitance rarely is frequencyindependent. Generally, the complex-plane presentation of an impedance spectrum (Fig. 4.5a) has a linear high-frequency segment inclined to a vertical line (Fig. 4.5b [ 15 ]). Such a dependence can be described by introducing a constant-phase element (CPE) into the electrode’s equivalent circuit (Fig. 4.6). The inherent impedance of a CPE is [16]: ZCPE = -1 (i)-a, where i = (1)1/2; = 2f is the ac angular frequency; the power a determines the character of the frequency dependence, and the frequencyindependent quantity is measured in Faa-1cm-2 units. When a approaches 1, the frequency-independent capacitance C can be substituted for with reasonable accuracy. This capacitance can be used in calculating the acceptor (or donor) concentration NA (respectively, ND) in the semiconductor diamond, by using the Schottky theory of semiconductor interfaces [7]. Fig. 4.5. Complex-plane presentation of (a) impedance spectrum for a HTHP single crystal in 2.5 M H2SO4 solution; (b) its high-frequency part [15]. The frequencies (kHz) are shown in the figure. Fig. 4.6. Equivalent circuits for semiconductor electrodes with (a) frequency-independent capacitance Csc and (b) constant-phase element CPE. Rs is the series resistance, and RF is the faradaic resistance. To determine NA (ND), the reciprocal of differential capacitance squared has been plotted versus the electrode potential E; such a graph is called a Mott—Schottky plot (Fig. 4.7). From the slope of the line, NA (ND) can be calculated: ND,A = (2 / e0) [d(C-2) / dE]-1. (4.4) Here and 0 are the permitivity of diamond and free space, respectively, and e is the electron charge; the “+” and “–” signs relate to donors and acceptors, respectively. We recall that equation (4.4) reflects the potential dependence of the thickness of the space-charge layer in the semiconductor. By extrapolating the line to C-2 0, the flat-band potential of the diamond electrode can be found. We note that the slopes of the two lines in Figs. 4.7a and 4.7b have opposite signs, thus unambiguously evidencing the p-type and n-type conductance in the boron-doped and sulfurtreated diamond, respectively. Fig. 4.7. Mott—Schottky plots for (a) {110}-oriented boron-doped ptype and (b) {111}-oriented sulfur-treated n-type CVD epitaxial diamond thin-film electrodes in 0.5 M H2SO4 solution [8, 29]. The Mott—Schottky-plot approach is now widely applied to diamond electrodes as a nondestructive method in studying the bulk and surface properties (through the doping level or flat-band potential, respectively) of synthetic diamond. It should be noted, however, that often the doping level in the diamond may be too high to meet the essential assumption of the Mott—Schottky analysis (primarily, a non-degenerate semiconductor behavior). If such is the case, the values of the acceptor (or donor) concentrations obtained must be referred to as approximations. It is worth mention that, even being frequency-dependent, the Mott—Schottky plot usually remainslinear, thus reflecting the potential dependence of the space-charge layer thickness, for any particular frequency f [17]. This fact allows one to conclude that, whatever is the reason for the frequency dependence of the capacitance, it relates to the space-charge layer, rather than the diamond surface proper. Thus, a slow ionization, in the space charge region of a diamond crystal, of atoms with a relatively deep-lying energy level was assumed [ 18 ] as a tentative explanation for the frequency dispersion of the capacitance of diamond electrodes. In addition to the Mott—Schottky-plot method, based on linear impedance measurements, the dopant concentration can be determined using the amplitude demodulation method (ADM), a version of nonlinear impedance techniques [19]. Unlike the abovediscussed linear-impedance method, here the perturbing signal applied to the cell is a high-frequency () current signal, modulated in its amplitude at a low frequency (Fig. 4.8, inset); thevoltage response E of the cell is measured at this lower frequency. According to the theory of the method, the response is proportional to the d(C-2)/dE value. This allows direct determining N A: NA = - I02 / 2e02E , (4.5) where I0 is the amplitude of the applied current signal. The potential-independent ADM signal (see Fig. 4.8) is the equivalent of a constant-slope constant(versus depth) Mott—Schottky distribution plot; of the both reflect dopant in a the semiconductor. Fig. 4.8. Potential dependence of the ADM signal for a {111} lateral face of a HTHP single crystal (see Fig. 4.10 below). Inset: form of the perturbing current signal applied to the cell; = 0.5 MHz, = 2 kHz [10]. The ADM measurements were used in determining the doping level in numerous semiconductors, including diamond [18]. A particular application of the ADM method toHTHP (high- temperature, high-pressure) diamond single crystals will be touched on below. 4.2.3. Photoelectrochemistry of Diamond Already in the first paper on the photoelectrochemistry of the diamond electrode [ 20 ], it was shown that the semiconductor nature of diamond manifests itself in generating photocurrent and photopotential. When light is absorbed in diamond, excess charge carriers (electrons and holes) are generated. The electron—hole pairs are separated in the electric field of the space-charge layer; the minority carriers either cross the diamond/solution interface, provided an appropriate electron or hole acceptor (e.g., hydrogen ion) is present in the solution, or, when the interface is of a blocking nature, charge up the electrode surface. Correspondingly, photocurrent or photopotential is observed in the cell. At the first stage, the photoelectrochemistry of diamond was studied using sub-band light, whose quantum energy was less than the diamond band gap width (~ 5.5 eV); therefore, the excess charge carriers were generated via photoionization of some light-sensitive impurities, rather than valence-electron excitation to the conduction band [20, 21 ]. Later, supraband light with higher quantum energy was used [22, 23], which provided band-to-band electron excitation in diamond. Fig. 4.9. Potential dependence of the photocurrent squared for a polycrystalline diamond electrode in 1 M KCl solution [20]. When light is absorbed deep in a semiconductor, that is, the light penetration depth exceeds the (potential-dependent) thickness of the space-charge layer near the electrode surface, the layer where the charge separation proceeds widens with increasing potential applied to the electrode. The photocurrent Iph thus varies with the electrode potential E in much the same way as the differential capacitance C: the photocurrent squared vs. potential plot is linear (Fig. 4.9), resembling the Mott—Schottky plot (compare Fig. 4.7). At the flat-band potential, the electrode is not charged; hence, no charge separation is possible and the photocurrent is zero. Therefore, by extrapolating the plot in Fig. 4.9 to Iph2 0, the flat-band potential can be determined, just as in the Mott—Schottky-plot approach. Other photoelectrochemical methods for the flat-band potential determination, namely, by measuring the photocurrent onset potential or the limiting opencircuit photopotential yielded by very intense illumination, are described in [22]. 4.3. Effects of the Crystal Structure The electrode behavior of diamond can be affected by its crystal structure. Our comparative studies of chemical-vapor-deposited (CVD) single-crystal (homoepitaxial) and polycrystalline diamond thin-film electrodes, as well as amorphous diamond-like carbon electrodes, gave insight into the role of intercrystalline boundaries in the electrochemical behavior of diamond. By comparing the impedance spectra and kinetics of various redox reactions, we concluded that the single-crystal and polycrystalline diamond electrodes are similar in their electrochemical properties. Both the impedance characteristics (the differential capacitance, the CPE parameters a and ) and the kinetic parameters (the transfer coefficients and , the rate constant k0) are similar for the singlecrystal and polycrystalline diamond electrodes. By contrast, the wide-gap diamond-like carbon (assumed to be a model material for the intercrystalline boundaries) appeared to be an inactive electrode in performing the electrochemical redox reactions. Therefore, we concluded that the electrode behavior of polycrystalline diamond films is entirely determined by the diamond crystallites proper, rather than by the intercrystalline boundaries, at least, at moderate electrode polarization [ 24 ]. However, at high anodic potentials (just prior to the onset of oxygen evolution), a minor current peak was observed in the potentiodynamic curves taken with polycrystalline electrodes in a supporting electrolyte solution, which cannot be observed with single-crystal films. The peak was ascribed to the anodic oxidation of sp2-carbon of the intercrystalline boundaries [25], which turned out to be less oxidation-resistant than the diamond crystallites. In the last part of this chapter, our attention will be focused on the electrochemical properties of individual crystal faces of HTHP diamond single crystals, as well as single-crystal (homoepitaxial) CVD-diamond films. Our preliminary studies showed that the HTHP single crystals, on the whole, are similar to the CVD polycrystalline films in terms of their electrode behavior. In particular, both the polycrystalline thin-film electrodes and the HTHP single crystal electrodes are equally characterized by the special type of frequency-dependent capacitance described by the CPE. We dealt with single crystals grown from a Ni—Fe—C—B melt, at pressures and temperatures within the diamond thermodynamic stability range. The growth was performed, using a seed, by temperature gradient techniques (for details, see ref. 26). Boron, an acceptor dopant, was added to the source melt as ferroboron (the boron concentration in the batch was 0.1 wt. %). At the conclusion of the synthesis, the solidified metal was dissolved in a Cr2O7 + H2SO4 mixture at 80100oC and the diamond crystals extracted. This oxidative treatment obviously made the diamond surface oxygen-terminated, unlike as-grown CVD-diamond surfaces which are hydrogen-terminated. The near-seed region of the crystals was then ground off and polished by pressing the crystals against the surface of a rotating cast-iron polishing wheel. One of the crystals is schematically presented in Fig. 4.10. It is a cubo-octahedron with unevenly developed {111} and {100} faces. The orientation of the rear (polished) face also approached {111}. 100 100 111 Fig. 4.10. A HTHP-diamond single crystal (top view). The octahedral and cubic faces (including the polished rear face of the crystal) were consecutively exposed to the electrolyte solution, the rest of the crystal’s surface (including the crystal edges), the ohmic contacts, and the current lead being insulated. To distinguish between like faces, we designated them as “central”, “left”, “right”, “bottom” (see Fig. 4.10), and “rear” (polished). Typical Mott—Schottky plots of the individual faces are given in Fig. 4.11 [10]. The rather positive flat-band potential is due to the fact that the diamond surface had been oxidized during its above-described processing. From the slope of the lines, the uncompensated acceptor concentration was calculated. The NA values thus obtained (coinciding with those determined by the ADM method, see Fig. 4.8) are given in Table 4.1. Fig. 4.11. Mott—Schottky plots for two faces of the crystal shown in Fig. 4.10. in 0.5 M H2SO4 solution [10]. We now turn our attention to the kinetic data. Anodic and cathodic potentiodynamic curves were taken at the faces of the single crystals in the 0.5 M H2SO4 + 0.01 M Fe(CN)63- (or Fe(CN)64) solution. The current vs. potential curves passed through a maximum whose potential depended on the potential scanning rate v (compare the cathodic curves in Fig. 4.1b). The transfer coefficients for the cathodic () and anodic () reactions in the Fe(CN)63-/4- system were determined by using equation (2), as discussed above. The and values are also shown in Table 4.1. Table 4.1. Properties of individual faces of the single crystal (Fig. 4.10) [10]. NA (cm-3) {111} central 2 1019 - 0.11 {111} rear 9 1018 0.5 0.25 1.3 1021 0.6 0.25 {111} lateral (left) 3 1020 0.33 0.43 {100} right 6 1021 - - {100} left 4.8 1021 0.6 0.38 Face {111} lateral (bottom) From these data the following conclusions were drawn: (i) The cast-iron-wheel surface polishing does not affect the capacitance significantly, as no marked difference in C or NA was found between the central (as-grown) and the rear (polished) {111} faces of the crystal shown in Fig. 4.10. In this respect, the semiconductor diamond differs from “traditional” semiconductors (germanium, silicon, etc.), whose mechanical processing, by using abrasives, results in the formation of a so-called damaged layer rich in dislocations, point defects, and other distortions of the crystal lattice. (Therefore, chemical or electrochemical etching is required to remove the damaged layer, which is necessary for revealing the semiconductor properties.) By contrast, the specific abrasive-free processing of diamond we used, evidently, does not distort its crystal lattice. (ii) The {100} faces appeared more heavily doped than the central {111} face. 3 Interestingly, the lateral {111} faces appeared more heavily doped than the central {111} face of the crystals. These peculiarities may reflect the complicated conditions in the source melt. (iii) Generally, the higher doping level, the less irreversible is the redox reaction. On the most heavily doped {100} “left” face, the reaction kinetics approach that at “metal-like” diamond electrodes. Thus, the known sectorial character of the HTHP diamond crystals [ 27 ] well manifests itself in the electrochemical measurements. On the whole, the difference in the electrochemical behavior of the individual faces can be primarily ascribed to different boron concentration in their adjacent growth sectors, resulting from the different ability of the diamond crystal faces to incorporate the boron dopant during the growth process, rather than to different surface atomic densities or other purely surface properties. We now turn to the homoepitaxial CVD-diamond films deposited onto dielectric single crystal diamond substrates. The three crystal faces, that is, {111}-, {110}-, and {100}-orientated, were studied by differential capacitance measurements [28]. They differ in their capacitance markedly. The Mott—Schottky plots (see, We note that this particular finding is in contrast to the known ability of the {111} face to incorporate boron, during the growth process, more intensely than the {100} face. 3 e.g., Fig. 4.7a for the {110}-oriented film) allowed us to estimate the acceptor concentration in the films (Table 4.2). Their different doping level can be explained by Table 4.2. Acceptor concentration homoepitaxial CVD films [28]. in differently oriented Face {100} {110} {111} Polycrystalline NA (cm-3) (2-3) 1.3 1020 (5-7) 5 1020 1019 1020 the above-mentioned different intensity of boron incorporation into differently orientated diamond crystal faces during the film growth. The results of the kinetic measurements agree with the capacitance data. The voltammetric curves for the polycrystalline film and {111} and {110} faces, taken in Fe(CN)63-/4- and Ru(NH3)2+/3+ redox solutions, are typical of irreversible, however, rather fast electrode reactions. By contrast, on the lightly doped {100} face, the current is very low; the process is under kinetic, rather than diffusion, control (Fig. 4.12). Thus, the electrochemical reactions in the Fe(CN)63-/4- and Ru(NH3)62+/3+ systems are slowed down in the following sequence: polycrystalline ≈ {111} > {110} > {100}. These findings agree with the above-discussed dependence of the electrochemical reaction rate on the diamond doping level. Similar results, for the {111}- and {100}- faces, were obtained in ref. 29. On the whole, the results obtained for the homoepitaxial CVDfilms are in agreement with those found for the individual faces of the HTHP-single crystals. Fig. 4.12. Cyclic voltammograms taken for {110}-, {100}-, and {111}oriented crystal faces of homoepitaxial CVD-diamond films in 0.1 MNaCl + 0.005 M Ru(NH3)6Cl2 + 0.005 М MRu(NH3)6Cl3 solution. The potential scan rate was 10 mV s-1 [28]. 4.4. Conclusions Moderately doped diamond electrodes are well suited for revealing the semiconductor and structural aspects of the diamond electrochemistry. The structural effects often boil down to a difference in the acceptor concentration in the diamond, rather than reflecting the surface atomic density or other purely surface properties. To reveal these fine effects, the electrochemical behavior of individual faces must be compared under the condition of equal doping level. Other studies into the structural effects involved the comparison of the growth and nucleation surfaces of free-standing polycrystalline diamond films [ 31 ], nanodiamond thin-film electrodes [ 32 , 33 ], and the electrochemical polishing of polycrystalline diamond electrode surfaces [34]. 4.5. Acknowledgment The work carried out was financed in part by the NEDO International Joint Research Grant Program, Project 01МВ9, and the Russian Foundation for Basic Research, Project 04-03- 32034. References 1 . Yu. V. 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