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Synthetic semiconductor diamond electrodes: elucidation of the equivalent circuit for the case of frequency-dependent impedance
ELSEVIER
Journal of Electroanalytical
Chemistry
413 (1996)
105-l
10
Synthetic semiconductor diamond electrodes: elucidation of the equivalent circuit for the case of frequency-dependent impedance Yu.V. Pleskov a9* , V.V. Elkin a, M.A. Abaturov a, M.D. Krotova a, V.Ya Mishuk a, V.P. Vamun b, I.G. Teremetskaya b a A.N. Frumkin b Institute
Institute of Electrochemistry, Russian Academy of Sciences, I1 7071 Moscow, Russia of Physical Chemistry, Russian Academy of Sciences, 117915, Moscow, Rassia Received
24 November
1995; revised
19 February
1996
Abstract Analysis of the frequency dependence of the impedance of boron-doped equivalent circuit. The latter generally comprises a frequency-independent
diamond thin film electrodes resulted in elucidation of their capacitance (or a constantphaseelement)and a resistance,
connectedin parallel,with a series-connected “bulk” resistance.For electrodeswhoseimpedancecontainsa constantphaseelement,a frequency-dependent Mott-Schottky plot enabledus to determinethe flat-band potential.The constantphaseelementwas shownto describepropertiesof the spacechargeregionin diamond,rather than thoseof surfacestates.The behaviourof diamondelectrodesis often affectedby a series(“Helmholtz”) capacitance,which may be comparedwith the spacechargecapacitanceof a semiconductor. Keywords:
Diamond;
Boron;
Equivalent
circuits;
Frequency
analysis
1. Introduction In an earlier publication [l] we showed that the impedance of chemical vapour deposition (CVD) grown polycrystalline diamond thin film electrodes is essentially determined, depending on the nature of the samples,by either a frequency-independent spacecharge layer capacitance or a constant phase angle element (CPE) whose impedancecan be written as
zCPE= u-‘(jtoen where j = ( - 1)‘12 and w is the angular frequency. We showed [1,2] that some samples(below we shall refer in particular to a sample denoted 306) demonstratedpractically ideal behaviour of a semiconductor electrode: no CPE in its equivalent circuit; and parallel capacitance practically frequency-independent in the 1 to 91 kHz range (and equal to ca. 0.5pFcm-‘). On the contrary, the behaviour of other samples,e.g. denoted below as 419 and 420 (and somesamplesstudied in Ref. [3]) was essentially determined by the presence of CPEs in their equivalent circuits. A tentative explanation of this difference in the
* Corresponding
author.
0022.0728/96/$15.00 Copyright PII SOO22-0728(96)04620-7
0 1996 Elsevier
behaviour of the sampleswill be given in the last section of this paper. In the present work, using frequency analysis of data published in Ref. [l] (for samples306 and 419) and new experimental data (sample 420) on the impedance spectroscopy of diamond electrodes, we shall elucidate their equivalent electrical circuit and discussthe physico-chemical nature of the elements of the circuits.
2. Experimental Polycrystalline diamond films were deposited on W or heavily doped p-type Si substratesfrom an activated acetone + methane+ hydrogen gasmixture. They were doped with boron (acceptor) in the courseof growth; the resulting free carrier (hole) concentration ranged from 10” to 3 X 10” cme3. This doping level enables us to consider the samples under study as a moderately doped wide gap p-type semiconductor. The working area of the samples was ca. 0.4cm’; the film thicknesses 1.5, 2.3 and 10km for samples419, 420 and 306 respectively. In what follows, all capacitance and resistancevalues will be given per square centimetre of a geometrical surface of electrodes. The roughnessfactor (which was estimated as ca.
Science S.A. All rights reserved.
Yu.V.Pleskovetal./Jownal ofElectroanalytical Chemistry 413 (1996)105-110
106 2.5) is thus neglected sion). We measured
(see Ref. [I] the impedance
for a detailed discususing an a.c. bridge
R-568 at frequencies of 0.61 to 91 kHz in the potential region where a depletion layer emerged in diamond. For details of the experimental conditions (concerning the film growth and impedance measurements), see Ref. [l]. All measurements were taken in 1 M KC1 solution at room temperature; the potential values are given versus the saturated calomel electrode.
3. Results and discussion
40-
Yi$ 30c ;3 & I ZO-
3.1. The series (‘ ‘Helmholtz’ ‘) capacitance
To analyse the experimental data on impedance of diamond electrodes, we use the simple but versatile equivalent circuit shown in Fig. 1. Here R, is the cell resistance including resistances of the diamond film and solution bulk; C,, is the frequency-independent capacitance of the space charge region in diamond; CPE is the frequency-dependent element (in our case with constant phase angle), which describes the relaxation processes occurring on the electrode surface and/or in the space charge region; R, is the resistance of a faradaic process at the electrodelsolution interface; and C,, is the capacitance related to elements which are located outside the semiconductor (e.g. the Helmholtz layer, surface films, etc.). Usually, C, is an order of magnitude higher than C,, or the capacitance related to the CPE, and hence it does not contribute to the electrode impedance. Also note that the “parallel” resistance R measured in the solution of a background electrolyte QKCl) was of the order of 1 Ma cm2; this large value of R, enables us to neglect this element of the equivalent circuit (Fig. l), in the absence of redox couples in solution, as compared with other resistances (see below). As we have already mentioned in the Introduction, samples 419 and 420 cannot be characterised by a frequency-independent capacitance. Indeed, when their impedance is presented on a complex plane (Fig. 2; also compare figure 3 of Ref. [l]), the dependence of the imaginary component on the real component is (in the high-frequency region) a line whose slope is somewhat less than 7r/2, corresponding (see IQ. (1)) to a value of
lo-
OV
circuit
of electrode.
20 Re Z I Rcm2
Fig. 2. The electrode impedance Z on a complex plane with no allowance for the series capacitance C,, (I-8) and with due allowance for C, (9). Sample 419. Potential E/V: 0.40 (l), 0.35 (2). 0.30 (31, 0.25 (4). 0.20 (5). 0.15 (6). 0.10 (7). 0.05 (8). Values of frequency (kHz) are shown at the points (for E = OMV).
LY< 1. Moreover, the slope (and hence the CY value) depends on the electrode potential E. To determine particular values of LY, we plotted the imaginary component versus the frequency (in logarithmic coordinates) (Fig. 3(a)); the calculated CTvalues, for samples 419 and 420, are given in the second and sixth columns of Table 1. The observed E-dependence of (Y can hardly be given a reasonable explanation; in particular, it cannot be caused by a faradaic current flow because of the negligibly small current value. Another difficulty we have met in our discussion of the CPEs is the discrepancy between the above-determined cr value and the phase shift cp between the real and imaginary components of a CPE; this shift, as follows from Eq. (11, can be written as 2cp/lr=a
Fig. 1. Equivalent
10
(2)
This relation is not fulfilled, as can be seen from a comparison of the second and third, or sixth and seventh, columns of the table; this implies that the studied impedance has a more complicated structure. In further discussions of the impedance, we shall allow for results of the analysis of the potential dependence, in Mott-Schottky coordinates, of the capacitive component
Yu.V. Pleskov
et al./Journal
of Electroanalytical
f/kHz Fig. 3. Dependence of nent of the impedance potentials: (a) with no due allowance for C,. 0.30 (3). 0.25 (41, 0.20
the logarithm of the measured imaginary compoon the logarithm of the frequency f for different allowance for the series capacitance C,, (b) with Sample 419. Potential E/V: 0.40 (I), 0.35 (21, (51, 0.15 (61, 0.10 (7), 0.05 (8).
of the measured impedance. Below we show that this analysis detects, in the impedanceof sample419, a series capacitance C, = 2.3 l.~Fcrn-*. It turns out that, with due allowance for this capacitance, we succeededin eliminating the above-mentioned difficulties related to the CPE. Indeed, the sheaf of lines 1 to 8 in Fig. 2 reduces to a single line 9; whereas the diverging lines in Fig. 3(a) become a family of parallel lines (Fig. 3(b), which proves the absenceof any tangible potential dependenceof (Y (see fourth column of Table 1). Moreover, the relation between cr and cp now obeys Eq. (2) (cf. fourth and fifth columns of Table 1).
Table 1 Calculated E/V
parameters
413 (1996)
105-110
107
A similar analysisof the Mott-Schottky plot for sample 420 revealed a seriescapacitanceC, = 1.5 ~.LF cm-*, whose allowance resulted in a decrease,however smaller,in the (Y values (cf. sixth and eighth columns of Table 1). To complete the discussionof the complex-plane presentation of the impedance,we turn to its real component. By extrapolating the lines (Fig. 2) to an infinite frequency, we obtain the series resistances R, = 4.4, 8.6 and 10.8 fi cm* for samples419, 420 and 306 respectively. These values are practically potential-independent, which enables us to relate them essentially to the ohmic resistance of a diamond film and electrolyte in the cell. We estimated the resistance of a diamond film proper for sample 420 (thickness 2.3 X 10U4cm>, by measuring its resistancein a solid-state system ‘film between two ohmic contacts’, as 2.0 0 cm*. The specific resistancevalue of the order of lo4 R cm* was thus determined for the diamond films under study. We now turn to the analysisof Mott-Schottky plots. In Fig. 4(a) and Fig. 5(a) we show the potential dependences of the reciprocal of the capacitancesquared,Cm2, obtained from the impedance measurementsat frequencies of 0.61 to 91 kHz. The plots can be, with due reservation, approximated by lines whose slope has a pronounced frequency dependence,increasing with frequency. This type of C-‘, E-dependence can often be met within the literature on semiconductor electrodes (see, for example, Ref. [4]); it has also been observed for a polycrystalline diamondlmetal contact [5]. No plausible explanation has been given for it so far. It is usually believed that the capacitance thus measuredis the sum of a frequency-independent space charge layer (more precisely depletion layer) capacitance C,, and a frequency-dependent capacitance of surface states (which can be represented by a CPE in the equivalent circuit, Fig. 11, connected in parallel. The surface statesmay be assumedto be distributed in energy in such a way that their capacitance also gives a linear C-*, E-dependence.Then, owing to the finite relaxation time of the charges trapped in the surface
of CPE
Sample 419 No allowance
0.05 0.10 0.15 0.175 0.2 0.25 0.30 0.35 0.40
Chemistry
Sample 420 for C,
Due allowance for C, = 2.3 p,Fcm-*
No allowance
for C,
Due allowance for C,= 1.5kFcm-’
a
TV/T
a
2cp/m
a
2lp/r
(Y
TV/T
0.78 0.79 0.79
0.80 0.80 0.8 1
0.70 0.7 1 0.7 1
0.69 0.69 0.70
0.93
0.93
0.89
0.89
0.93
0.94
0.89
0.90
0.79 0.80 0.8 1 0.83 0.85
0.82 0.83 0.85 0.86 0.89
0.71 0.70 0.70 0.7 1 0.71
0.70 0.70 0.71 0.71 0.71
0.94
0.94
0.90
0.91
0.93
0.94
0.89
0.91
108
Yu.V. Pleskoo
et al./Journd
of Electroanalytical
E/V Fig. 4. The Mott-Schottky plot for sample 419 (a) with no allowance for the series capacitance C, and (b) with due allowance for C,. Frequency f/kHz: 0.61 (1). 1.1 (2). 2.1 (3), 4.1 (4), 6.1 (5),9.1 (61, 13.7 (7). 17 (8). 21 (91, 41 (IO), 61 (Ii), 91 (12).
Chemistry
413
(1996)
105-110
states, there must exist a limiting frequency when the surface states cease to contribute to the measured capacitance. However, the highest frequency accessible to us (91 kHz) appears to be still lower than the limiting one. A flat-band potential (for which the space charge capacitance tends to infinity) can be obtained by extrapolating the Mott-Schottky lines to their intersection with the potential axis. It is particularly remarkable that the extrapolation of the lines plotted for different frequencies (see Fig. 4(a) and Fig. 5(a)) gives a common intersection point which, however, is located somewhat above the potential axis, as if a series-connected capacitance constrained the capacitance of the system which otherwise would tend to infinity at a .flat-band potential. By subtracting this hypothetical capacitance C, (2.3 FFcm-’ for sample 419, 1.5 p,F cm-* for sample 420) from the measured impedance data, we succeeded in locating the intersection points exactly on the potential axis, thus obtaining the flat-band potential values Efb = 0.45 V (Fig. 4(b)), 0.75 V (Fig. 5(b)) for samples 419 and 420 respectively. This subtraction changes the appearance of the plots, but not significantly. The small (ca. 0.3 V) difference in values of the flat-band potentia1 can be caused by occasional differences in the growth and pretreatment conditions. These Eh values are in reasonable agreement with those measured earlier [6,7]. Below we shall describe another approach to the determination of the series capacitance C, in a CPE-containing equivalent circuit of an electrode. As will be shown, the impedance of electrode 419 can be modelled by three series-connected elements, namely (see Fig. 1) resistance R,, capacitance C, and a CPE with its two characteristic parameters o and (Y. The impedance of this circuit can be written as Z= R, + l/(jwC,)
+ l/[(jw)mo]
= 1 R,+c0s(a~/2)(~%)-‘1 - j[ l/( wCO) + sin( arr/2)(
w&)-l
I
(3)
We now introduce a specific function S = (Z= [l/C,
R,)jw
= l/C,
+ (jo)lea/a
+ sin( an/2)(
+ j[cos( cmr/2)(
00
’
I
1
E/V Fig. 5. The Mott-Schottky plot for sample 420 (a) with no allowance for the series capacitance C, and (b) with due allowance for C,. Frequency f/kHz: 15(1). 41 (21, 61 (3). 91 (4).
(4)
CO-“/CT)]
,
I
w’-“/a)]
I 2 Re S / pF-i cm2
Fig. 6. Plot of the function S @q. (4)). Series resistance R, = 4.4 fl cm’.
Sample 419. Potential
E = 0.2 V.
Yu.V. Pleskov
Re P I
et al./Jourd
pF-Q-69
Fig. 7. Plot of the function P (Eq. (5)). Sample E (V) are shown at the groups of points.
SPJl
ofElectroandytica1
cd
419. Values
of potential
whose diagram is shown in Fig. 6. We see that, for the fitted value of R, = 4.4 fi cm2, the entire set of impedance data falls, even with a spread, onto a single line whose slope gives (Y = 0.68. By extrapolating the line to an intersection with the Re S axis, we obtained the “series” value of S, namely S, = l/C, where C, = 2.4 pFcrns2. Recall that the above-described approach to the impedance analysis gave similar values: R, = 4.4 fl cm2, cr = 0.70, Co = 2.3 bFcme2. The parameters R,, C, and CY appeared to be, within 5% accuracy, potential-independent. On the contrary, the parameter cr of CPE does depend on the potential. To obtain values of l/u for different potentials, we averaged over frequency the real component of a complex function P: P= [Z-R,-
l/(jwC,)](jw)“=
l/cr
(5) which is plotted in Fig. 7. The plot comprises eight groups of dots relating to eight potential values, each group comprising nine dots relating to different frequencies. This plot is essentially significant methodologically because it enables one to judge, by the extent of the scatter of points, the validity of the equivalent circuit adopted for sample 419, comprising three series-connected elements, namely resistance, capacitance and CPE character&d by a single potential-dependent parameter g. By using the values of parameters C, and a, together with the (+ values for different potentials, we can model the plot of Fig. 4 (that is the Mott-Schottky plot) and compare it with experiment. The Mott-Schottky ordinate is the real component of the function S (Eq. (4)) squared: Ce2 = (Re S)’ = [l/C,
+ sin( (Y?r/2)( o’-“/a)]2
(6)
In Fig. 8 we plotted the potential dependence of the dimensionless quantity ((T 1E= 0.25v/(+ )-2, this plot being essentially similar to the Mott-Schottky plot. We obtain a line whose extrapolation to its intersection with the potential axis gives us the flat-band potential &,, = 0.43 V, i.e. close to the value previously determined by the traditional approach. To complete this topic, we note that the two approaches described are essentially different: the first is based on an
Chemistry
413 (1996)
105-110
109
assumption that the potential dependence of the capacitance obeys the Mott-Schottky formula and the intersection point for lines related to different frequencies (Fig. 4(a) and Fig. 5(a)) is the flat-band potential; whereas the second approach is based on an assumption that the frequency-dependent element of the equivalent circuit is essentially a CPE. The very presence of the finite series capacitance, irrespective of its physico-chemical nature (to be discussed below), can introduce an error into the determination of the flat-band potential by extrapolating Mott-Schottky plots (see, for example, Ref. [4]). Indeed, the extrapolation points are shifted by 0.1 to 0.2 V relative to the true flat-band potential (cf. Fig. 4(a) and Fig. 4(b), Fig. 5(a) and Fig. 5(b)). 3.2. The parallel (“semiconductor”)
capacitance
By allowing for the series capacitance, we have thus isolated the CPE in a diamond electrode impedance. We shall now try to isolate the parallel frequency-independent capacitance C, which relates to the Schottky barrier at a semiconductorlelectrolyte interface. To do this, we plotted the capacitive part of the measured impedance (upon subtracting the series capacitance C, and series resistance R,) as a function of frequency to the power of - (1 - (Y>. Use of these coordinates enabled us to straighten the lines for different E values, and to extrapolate them further to infinite frequency. In Fig. 9 a sheaf of such lines is shown for sample 419; the value of ff = 0.70 was taken from the fourth column of Table 1. It is particularly remarkable that they all give a zero intercept on the capacitance axis, which proves the absence of any parallel capacitance in the equivalent circuit of Fig. 1. In this particular feature the case of the electrodes whose impedance contained a CPE (samples 419 and 420) differs from the case of sample 306 exam-
N c9 w” b -F-
Fig. 8. Potential
dependence
of (uIE=
0.25~ /CT-~.
Sample 419.
110
Yu.V. Pleskou
et d/Journal
ofElectroanalytica1
4r
0
0.2
0.4
0.6
f-o.3 / m-o.3 Fig. 9. Dependence of the measured capacitance (with the series capacitance C, and series resistance R,) on power of - 0.3. Sample 419. Potential E/V: 0.40 (11, 0.25 (4), 0.2 (5), 0.15 (61, 0.10 (7), 0.05 (8). Values of are shown at the dots.
due allowance for frequency f to the 0.35 (21, 0.30 (31, frequency f(kHz)
ined in Refs. [1,2], where the frequency-independent space charge layer capacitance actually exists. Thus, the equivalent circuit of samples 419 and 420 comprises (see Fig. 1): an ohmic resistance of the bulk of the contacting phases R,, a frequency-dependent element (the CPE), and a series capacitance C,. (Recall that the parallel resistance R, is not included because of negligibly small faradaic currents in our experiments.) For sample 306, the equivalent circuit comprises a resistance R, and a space charge layer capacitance C, (the series capacitance C, is likely to be very large and thus has little, if any, effect on the flat-band potential determination).
4. Concluding
remarks
The reason for the difference in a frequency behaviour of the impedance of the samples remains obscure. The technology of diamond film growth has not been fully standardised so far, therefore weakly controllable factors in film growth and surface preparation can affect electrode behaviour markedly. Concerning the samples under study, we note that they differ in their surface morphology, in particular sample 306 is a coarse-grained film with crystallites as large as a few micrometres, whereas samples 419 and 420 are fine-grained, composed of crystallites of submicrometre size. Correspondingly, the proportion of disordered carbon material which constitutes intercrystalline boundaries is substantially higher in these latter samples; and this we may regard as the reason for the more pronounced frequency dependence of the impedance. Only preliminary conclusions can be drawn at this stage on the physico-chemical nature of some elements of the equivalent circuit. The series capacitance C,, which we called “Helmholtz”, is too small to be unambiguously
Chemistry
413 (1996)
105-110
identified as a capacitance of the Helmholtz layer at the diamondlsolution interface; however, it has been argued on occasions that the Helmholtz capacitance of semiconductor electrodes can be as low as 3 to 6 ~Fcm-* [8]. The series capacitance C, can be caused by a thin, tunnel-transparent film possessing particular properties, which forms on the surface of a CVD grown diamond film when the activation of the gas phase is stopped, during cooling of the reactor. Assuming E = 5 for the permittivity of this layer, we estimated its thickness as ca. 2 nm. The potential-sensitive frequency dependence of the CPE-containing impedance obviously cannot be ascribed to surface states but reflects some relaxation processes occurring in the space charge region in diamond; their nature remains unclear, however. Possibly, the impedance of samples 419 and 420 (but not 306) is affected by slow ionisation of boron, a relatively deep acceptor, and this is reflected in the characteristic appearance of the MottSchottky plots, see Fig. 4 (also compare figs. 1 and 2 of Ref. [5]). One way or another, processes of this type should be taken into account in discussions of frequencydependent Mott-Schottky plots.
Acknowledgements We are indebted to B.M. Grafov for valuable discussions. The constructive criticism raised by the referee is acknowledged. This study was supported in part by the Russian Foundation for Basic Research, Project No. 96-0334133a.
References [ll
Yu.V. Pleskov, V.Ya. Mishuk, M.A. Abaturov, V.V. Elkin, M.D. Krotova, V.P. Vamin and LG. Teremetskaya, J. Electroanal. Chem., 396 (1995) 227. Dl Yu.V. Pleskov, A.V. Churikov, V.P. Vamin and I.G. Teremetskaya, submitted to J. Electrochem. Sot. L. Nyikos and Yu. Pleskov, Electrochim. Acta, 37 [31 A. Sakharova, ( 1992) 973. in B.E. Conway, R.E. White [41 Yu.V. Pleskov and Yu.Ya. Gurevich, and J.O’M. Bockris (Eds.), Modern Aspects of Electrochemistry, Vol. 16. Plenum Press, New York, 1985, Chap. 3, p. 189. [51 G. Zhao, E. Charlson, T. Stacy and E.J. Charlson, in A. Feldman, Y. Tseng, W.A. Yarbrough, M. Yoshikawa and M. Murakawa (I%.), Applications of Diamond Films and Related Materials: Proc. Third Int. Conf., 1995, p. 141. [61 Yu.V. Pleskov, A.Ya. Sakharova, M.D. Krotova, L.L. Bouilov and B.V. Spitsyn, J. Electroanal. Chem., 228 (1987) 19. Yu.V. Pleskov, F. Di Quarto, S. Piazza, C. Sunseri, [71 A.Ya. Sakharova. I.G. Teremetskaya and V.P. Vamin, J. Electrochem. Sot., 142 (1995) 2704. B.E. Conway and E. Yeager [81 Yu.V. Pleskov, in J.O’M. Bock& @Is.), Comprehensive Treatise of Electrochemistry, Vol. 1, Plenum Press, New York, 1985, p. 291.
Journal of Electroanalytical
Chemistry
413 (1996)
105-l
10
Synthetic semiconductor diamond electrodes: elucidation of the equivalent circuit for the case of frequency-dependent impedance Yu.V. Pleskov a9* , V.V. Elkin a, M.A. Abaturov a, M.D. Krotova a, V.Ya Mishuk a, V.P. Vamun b, I.G. Teremetskaya b a A.N. Frumkin b Institute
Institute of Electrochemistry, Russian Academy of Sciences, I1 7071 Moscow, Russia of Physical Chemistry, Russian Academy of Sciences, 117915, Moscow, Rassia Received
24 November
1995; revised
19 February
1996
Abstract Analysis of the frequency dependence of the impedance of boron-doped equivalent circuit. The latter generally comprises a frequency-independent
diamond thin film electrodes resulted in elucidation of their capacitance (or a constantphaseelement)and a resistance,
connectedin parallel,with a series-connected “bulk” resistance.For electrodeswhoseimpedancecontainsa constantphaseelement,a frequency-dependent Mott-Schottky plot enabledus to determinethe flat-band potential.The constantphaseelementwas shownto describepropertiesof the spacechargeregionin diamond,rather than thoseof surfacestates.The behaviourof diamondelectrodesis often affectedby a series(“Helmholtz”) capacitance,which may be comparedwith the spacechargecapacitanceof a semiconductor. Keywords:
Diamond;
Boron;
Equivalent
circuits;
Frequency
analysis
1. Introduction In an earlier publication [l] we showed that the impedance of chemical vapour deposition (CVD) grown polycrystalline diamond thin film electrodes is essentially determined, depending on the nature of the samples,by either a frequency-independent spacecharge layer capacitance or a constant phase angle element (CPE) whose impedancecan be written as
zCPE= u-‘(jtoen where j = ( - 1)‘12 and w is the angular frequency. We showed [1,2] that some samples(below we shall refer in particular to a sample denoted 306) demonstratedpractically ideal behaviour of a semiconductor electrode: no CPE in its equivalent circuit; and parallel capacitance practically frequency-independent in the 1 to 91 kHz range (and equal to ca. 0.5pFcm-‘). On the contrary, the behaviour of other samples,e.g. denoted below as 419 and 420 (and somesamplesstudied in Ref. [3]) was essentially determined by the presence of CPEs in their equivalent circuits. A tentative explanation of this difference in the
* Corresponding
author.
0022.0728/96/$15.00 Copyright PII SOO22-0728(96)04620-7
0 1996 Elsevier
behaviour of the sampleswill be given in the last section of this paper. In the present work, using frequency analysis of data published in Ref. [l] (for samples306 and 419) and new experimental data (sample 420) on the impedance spectroscopy of diamond electrodes, we shall elucidate their equivalent electrical circuit and discussthe physico-chemical nature of the elements of the circuits.
2. Experimental Polycrystalline diamond films were deposited on W or heavily doped p-type Si substratesfrom an activated acetone + methane+ hydrogen gasmixture. They were doped with boron (acceptor) in the courseof growth; the resulting free carrier (hole) concentration ranged from 10” to 3 X 10” cme3. This doping level enables us to consider the samples under study as a moderately doped wide gap p-type semiconductor. The working area of the samples was ca. 0.4cm’; the film thicknesses 1.5, 2.3 and 10km for samples419, 420 and 306 respectively. In what follows, all capacitance and resistancevalues will be given per square centimetre of a geometrical surface of electrodes. The roughnessfactor (which was estimated as ca.
Science S.A. All rights reserved.
Yu.V.Pleskovetal./Jownal ofElectroanalytical Chemistry 413 (1996)105-110
106 2.5) is thus neglected sion). We measured
(see Ref. [I] the impedance
for a detailed discususing an a.c. bridge
R-568 at frequencies of 0.61 to 91 kHz in the potential region where a depletion layer emerged in diamond. For details of the experimental conditions (concerning the film growth and impedance measurements), see Ref. [l]. All measurements were taken in 1 M KC1 solution at room temperature; the potential values are given versus the saturated calomel electrode.
3. Results and discussion
40-
Yi$ 30c ;3 & I ZO-
3.1. The series (‘ ‘Helmholtz’ ‘) capacitance
To analyse the experimental data on impedance of diamond electrodes, we use the simple but versatile equivalent circuit shown in Fig. 1. Here R, is the cell resistance including resistances of the diamond film and solution bulk; C,, is the frequency-independent capacitance of the space charge region in diamond; CPE is the frequency-dependent element (in our case with constant phase angle), which describes the relaxation processes occurring on the electrode surface and/or in the space charge region; R, is the resistance of a faradaic process at the electrodelsolution interface; and C,, is the capacitance related to elements which are located outside the semiconductor (e.g. the Helmholtz layer, surface films, etc.). Usually, C, is an order of magnitude higher than C,, or the capacitance related to the CPE, and hence it does not contribute to the electrode impedance. Also note that the “parallel” resistance R measured in the solution of a background electrolyte QKCl) was of the order of 1 Ma cm2; this large value of R, enables us to neglect this element of the equivalent circuit (Fig. l), in the absence of redox couples in solution, as compared with other resistances (see below). As we have already mentioned in the Introduction, samples 419 and 420 cannot be characterised by a frequency-independent capacitance. Indeed, when their impedance is presented on a complex plane (Fig. 2; also compare figure 3 of Ref. [l]), the dependence of the imaginary component on the real component is (in the high-frequency region) a line whose slope is somewhat less than 7r/2, corresponding (see IQ. (1)) to a value of
lo-
OV
circuit
of electrode.
20 Re Z I Rcm2
Fig. 2. The electrode impedance Z on a complex plane with no allowance for the series capacitance C,, (I-8) and with due allowance for C, (9). Sample 419. Potential E/V: 0.40 (l), 0.35 (2). 0.30 (31, 0.25 (4). 0.20 (5). 0.15 (6). 0.10 (7). 0.05 (8). Values of frequency (kHz) are shown at the points (for E = OMV).
LY< 1. Moreover, the slope (and hence the CY value) depends on the electrode potential E. To determine particular values of LY, we plotted the imaginary component versus the frequency (in logarithmic coordinates) (Fig. 3(a)); the calculated CTvalues, for samples 419 and 420, are given in the second and sixth columns of Table 1. The observed E-dependence of (Y can hardly be given a reasonable explanation; in particular, it cannot be caused by a faradaic current flow because of the negligibly small current value. Another difficulty we have met in our discussion of the CPEs is the discrepancy between the above-determined cr value and the phase shift cp between the real and imaginary components of a CPE; this shift, as follows from Eq. (11, can be written as 2cp/lr=a
Fig. 1. Equivalent
10
(2)
This relation is not fulfilled, as can be seen from a comparison of the second and third, or sixth and seventh, columns of the table; this implies that the studied impedance has a more complicated structure. In further discussions of the impedance, we shall allow for results of the analysis of the potential dependence, in Mott-Schottky coordinates, of the capacitive component
Yu.V. Pleskov
et al./Journal
of Electroanalytical
f/kHz Fig. 3. Dependence of nent of the impedance potentials: (a) with no due allowance for C,. 0.30 (3). 0.25 (41, 0.20
the logarithm of the measured imaginary compoon the logarithm of the frequency f for different allowance for the series capacitance C,, (b) with Sample 419. Potential E/V: 0.40 (I), 0.35 (21, (51, 0.15 (61, 0.10 (7), 0.05 (8).
of the measured impedance. Below we show that this analysis detects, in the impedanceof sample419, a series capacitance C, = 2.3 l.~Fcrn-*. It turns out that, with due allowance for this capacitance, we succeededin eliminating the above-mentioned difficulties related to the CPE. Indeed, the sheaf of lines 1 to 8 in Fig. 2 reduces to a single line 9; whereas the diverging lines in Fig. 3(a) become a family of parallel lines (Fig. 3(b), which proves the absenceof any tangible potential dependenceof (Y (see fourth column of Table 1). Moreover, the relation between cr and cp now obeys Eq. (2) (cf. fourth and fifth columns of Table 1).
Table 1 Calculated E/V
parameters
413 (1996)
105-110
107
A similar analysisof the Mott-Schottky plot for sample 420 revealed a seriescapacitanceC, = 1.5 ~.LF cm-*, whose allowance resulted in a decrease,however smaller,in the (Y values (cf. sixth and eighth columns of Table 1). To complete the discussionof the complex-plane presentation of the impedance,we turn to its real component. By extrapolating the lines (Fig. 2) to an infinite frequency, we obtain the series resistances R, = 4.4, 8.6 and 10.8 fi cm* for samples419, 420 and 306 respectively. These values are practically potential-independent, which enables us to relate them essentially to the ohmic resistance of a diamond film and electrolyte in the cell. We estimated the resistance of a diamond film proper for sample 420 (thickness 2.3 X 10U4cm>, by measuring its resistancein a solid-state system ‘film between two ohmic contacts’, as 2.0 0 cm*. The specific resistancevalue of the order of lo4 R cm* was thus determined for the diamond films under study. We now turn to the analysisof Mott-Schottky plots. In Fig. 4(a) and Fig. 5(a) we show the potential dependences of the reciprocal of the capacitancesquared,Cm2, obtained from the impedance measurementsat frequencies of 0.61 to 91 kHz. The plots can be, with due reservation, approximated by lines whose slope has a pronounced frequency dependence,increasing with frequency. This type of C-‘, E-dependence can often be met within the literature on semiconductor electrodes (see, for example, Ref. [4]); it has also been observed for a polycrystalline diamondlmetal contact [5]. No plausible explanation has been given for it so far. It is usually believed that the capacitance thus measuredis the sum of a frequency-independent space charge layer (more precisely depletion layer) capacitance C,, and a frequency-dependent capacitance of surface states (which can be represented by a CPE in the equivalent circuit, Fig. 11, connected in parallel. The surface statesmay be assumedto be distributed in energy in such a way that their capacitance also gives a linear C-*, E-dependence.Then, owing to the finite relaxation time of the charges trapped in the surface
of CPE
Sample 419 No allowance
0.05 0.10 0.15 0.175 0.2 0.25 0.30 0.35 0.40
Chemistry
Sample 420 for C,
Due allowance for C, = 2.3 p,Fcm-*
No allowance
for C,
Due allowance for C,= 1.5kFcm-’
a
TV/T
a
2cp/m
a
2lp/r
(Y
TV/T
0.78 0.79 0.79
0.80 0.80 0.8 1
0.70 0.7 1 0.7 1
0.69 0.69 0.70
0.93
0.93
0.89
0.89
0.93
0.94
0.89
0.90
0.79 0.80 0.8 1 0.83 0.85
0.82 0.83 0.85 0.86 0.89
0.71 0.70 0.70 0.7 1 0.71
0.70 0.70 0.71 0.71 0.71
0.94
0.94
0.90
0.91
0.93
0.94
0.89
0.91
108
Yu.V. Pleskoo
et al./Journd
of Electroanalytical
E/V Fig. 4. The Mott-Schottky plot for sample 419 (a) with no allowance for the series capacitance C, and (b) with due allowance for C,. Frequency f/kHz: 0.61 (1). 1.1 (2). 2.1 (3), 4.1 (4), 6.1 (5),9.1 (61, 13.7 (7). 17 (8). 21 (91, 41 (IO), 61 (Ii), 91 (12).
Chemistry
413
(1996)
105-110
states, there must exist a limiting frequency when the surface states cease to contribute to the measured capacitance. However, the highest frequency accessible to us (91 kHz) appears to be still lower than the limiting one. A flat-band potential (for which the space charge capacitance tends to infinity) can be obtained by extrapolating the Mott-Schottky lines to their intersection with the potential axis. It is particularly remarkable that the extrapolation of the lines plotted for different frequencies (see Fig. 4(a) and Fig. 5(a)) gives a common intersection point which, however, is located somewhat above the potential axis, as if a series-connected capacitance constrained the capacitance of the system which otherwise would tend to infinity at a .flat-band potential. By subtracting this hypothetical capacitance C, (2.3 FFcm-’ for sample 419, 1.5 p,F cm-* for sample 420) from the measured impedance data, we succeeded in locating the intersection points exactly on the potential axis, thus obtaining the flat-band potential values Efb = 0.45 V (Fig. 4(b)), 0.75 V (Fig. 5(b)) for samples 419 and 420 respectively. This subtraction changes the appearance of the plots, but not significantly. The small (ca. 0.3 V) difference in values of the flat-band potentia1 can be caused by occasional differences in the growth and pretreatment conditions. These Eh values are in reasonable agreement with those measured earlier [6,7]. Below we shall describe another approach to the determination of the series capacitance C, in a CPE-containing equivalent circuit of an electrode. As will be shown, the impedance of electrode 419 can be modelled by three series-connected elements, namely (see Fig. 1) resistance R,, capacitance C, and a CPE with its two characteristic parameters o and (Y. The impedance of this circuit can be written as Z= R, + l/(jwC,)
+ l/[(jw)mo]
= 1 R,+c0s(a~/2)(~%)-‘1 - j[ l/( wCO) + sin( arr/2)(
w&)-l
I
(3)
We now introduce a specific function S = (Z= [l/C,
R,)jw
= l/C,
+ (jo)lea/a
+ sin( an/2)(
+ j[cos( cmr/2)(
00
’
I
1
E/V Fig. 5. The Mott-Schottky plot for sample 420 (a) with no allowance for the series capacitance C, and (b) with due allowance for C,. Frequency f/kHz: 15(1). 41 (21, 61 (3). 91 (4).
(4)
CO-“/CT)]
,
I
w’-“/a)]
I 2 Re S / pF-i cm2
Fig. 6. Plot of the function S @q. (4)). Series resistance R, = 4.4 fl cm’.
Sample 419. Potential
E = 0.2 V.
Yu.V. Pleskov
Re P I
et al./Jourd
pF-Q-69
Fig. 7. Plot of the function P (Eq. (5)). Sample E (V) are shown at the groups of points.
SPJl
ofElectroandytica1
cd
419. Values
of potential
whose diagram is shown in Fig. 6. We see that, for the fitted value of R, = 4.4 fi cm2, the entire set of impedance data falls, even with a spread, onto a single line whose slope gives (Y = 0.68. By extrapolating the line to an intersection with the Re S axis, we obtained the “series” value of S, namely S, = l/C, where C, = 2.4 pFcrns2. Recall that the above-described approach to the impedance analysis gave similar values: R, = 4.4 fl cm2, cr = 0.70, Co = 2.3 bFcme2. The parameters R,, C, and CY appeared to be, within 5% accuracy, potential-independent. On the contrary, the parameter cr of CPE does depend on the potential. To obtain values of l/u for different potentials, we averaged over frequency the real component of a complex function P: P= [Z-R,-
l/(jwC,)](jw)“=
l/cr
(5) which is plotted in Fig. 7. The plot comprises eight groups of dots relating to eight potential values, each group comprising nine dots relating to different frequencies. This plot is essentially significant methodologically because it enables one to judge, by the extent of the scatter of points, the validity of the equivalent circuit adopted for sample 419, comprising three series-connected elements, namely resistance, capacitance and CPE character&d by a single potential-dependent parameter g. By using the values of parameters C, and a, together with the (+ values for different potentials, we can model the plot of Fig. 4 (that is the Mott-Schottky plot) and compare it with experiment. The Mott-Schottky ordinate is the real component of the function S (Eq. (4)) squared: Ce2 = (Re S)’ = [l/C,
+ sin( (Y?r/2)( o’-“/a)]2
(6)
In Fig. 8 we plotted the potential dependence of the dimensionless quantity ((T 1E= 0.25v/(+ )-2, this plot being essentially similar to the Mott-Schottky plot. We obtain a line whose extrapolation to its intersection with the potential axis gives us the flat-band potential &,, = 0.43 V, i.e. close to the value previously determined by the traditional approach. To complete this topic, we note that the two approaches described are essentially different: the first is based on an
Chemistry
413 (1996)
105-110
109
assumption that the potential dependence of the capacitance obeys the Mott-Schottky formula and the intersection point for lines related to different frequencies (Fig. 4(a) and Fig. 5(a)) is the flat-band potential; whereas the second approach is based on an assumption that the frequency-dependent element of the equivalent circuit is essentially a CPE. The very presence of the finite series capacitance, irrespective of its physico-chemical nature (to be discussed below), can introduce an error into the determination of the flat-band potential by extrapolating Mott-Schottky plots (see, for example, Ref. [4]). Indeed, the extrapolation points are shifted by 0.1 to 0.2 V relative to the true flat-band potential (cf. Fig. 4(a) and Fig. 4(b), Fig. 5(a) and Fig. 5(b)). 3.2. The parallel (“semiconductor”)
capacitance
By allowing for the series capacitance, we have thus isolated the CPE in a diamond electrode impedance. We shall now try to isolate the parallel frequency-independent capacitance C, which relates to the Schottky barrier at a semiconductorlelectrolyte interface. To do this, we plotted the capacitive part of the measured impedance (upon subtracting the series capacitance C, and series resistance R,) as a function of frequency to the power of - (1 - (Y>. Use of these coordinates enabled us to straighten the lines for different E values, and to extrapolate them further to infinite frequency. In Fig. 9 a sheaf of such lines is shown for sample 419; the value of ff = 0.70 was taken from the fourth column of Table 1. It is particularly remarkable that they all give a zero intercept on the capacitance axis, which proves the absence of any parallel capacitance in the equivalent circuit of Fig. 1. In this particular feature the case of the electrodes whose impedance contained a CPE (samples 419 and 420) differs from the case of sample 306 exam-
N c9 w” b -F-
Fig. 8. Potential
dependence
of (uIE=
0.25~ /CT-~.
Sample 419.
110
Yu.V. Pleskou
et d/Journal
ofElectroanalytica1
4r
0
0.2
0.4
0.6
f-o.3 / m-o.3 Fig. 9. Dependence of the measured capacitance (with the series capacitance C, and series resistance R,) on power of - 0.3. Sample 419. Potential E/V: 0.40 (11, 0.25 (4), 0.2 (5), 0.15 (61, 0.10 (7), 0.05 (8). Values of are shown at the dots.
due allowance for frequency f to the 0.35 (21, 0.30 (31, frequency f(kHz)
ined in Refs. [1,2], where the frequency-independent space charge layer capacitance actually exists. Thus, the equivalent circuit of samples 419 and 420 comprises (see Fig. 1): an ohmic resistance of the bulk of the contacting phases R,, a frequency-dependent element (the CPE), and a series capacitance C,. (Recall that the parallel resistance R, is not included because of negligibly small faradaic currents in our experiments.) For sample 306, the equivalent circuit comprises a resistance R, and a space charge layer capacitance C, (the series capacitance C, is likely to be very large and thus has little, if any, effect on the flat-band potential determination).
4. Concluding
remarks
The reason for the difference in a frequency behaviour of the impedance of the samples remains obscure. The technology of diamond film growth has not been fully standardised so far, therefore weakly controllable factors in film growth and surface preparation can affect electrode behaviour markedly. Concerning the samples under study, we note that they differ in their surface morphology, in particular sample 306 is a coarse-grained film with crystallites as large as a few micrometres, whereas samples 419 and 420 are fine-grained, composed of crystallites of submicrometre size. Correspondingly, the proportion of disordered carbon material which constitutes intercrystalline boundaries is substantially higher in these latter samples; and this we may regard as the reason for the more pronounced frequency dependence of the impedance. Only preliminary conclusions can be drawn at this stage on the physico-chemical nature of some elements of the equivalent circuit. The series capacitance C,, which we called “Helmholtz”, is too small to be unambiguously
Chemistry
413 (1996)
105-110
identified as a capacitance of the Helmholtz layer at the diamondlsolution interface; however, it has been argued on occasions that the Helmholtz capacitance of semiconductor electrodes can be as low as 3 to 6 ~Fcm-* [8]. The series capacitance C, can be caused by a thin, tunnel-transparent film possessing particular properties, which forms on the surface of a CVD grown diamond film when the activation of the gas phase is stopped, during cooling of the reactor. Assuming E = 5 for the permittivity of this layer, we estimated its thickness as ca. 2 nm. The potential-sensitive frequency dependence of the CPE-containing impedance obviously cannot be ascribed to surface states but reflects some relaxation processes occurring in the space charge region in diamond; their nature remains unclear, however. Possibly, the impedance of samples 419 and 420 (but not 306) is affected by slow ionisation of boron, a relatively deep acceptor, and this is reflected in the characteristic appearance of the MottSchottky plots, see Fig. 4 (also compare figs. 1 and 2 of Ref. [5]). One way or another, processes of this type should be taken into account in discussions of frequencydependent Mott-Schottky plots.
Acknowledgements We are indebted to B.M. Grafov for valuable discussions. The constructive criticism raised by the referee is acknowledged. This study was supported in part by the Russian Foundation for Basic Research, Project No. 96-0334133a.
References [ll
Yu.V. Pleskov, V.Ya. Mishuk, M.A. Abaturov, V.V. Elkin, M.D. Krotova, V.P. Vamin and LG. Teremetskaya, J. Electroanal. Chem., 396 (1995) 227. Dl Yu.V. Pleskov, A.V. Churikov, V.P. Vamin and I.G. Teremetskaya, submitted to J. Electrochem. Sot. L. Nyikos and Yu. Pleskov, Electrochim. Acta, 37 [31 A. Sakharova, ( 1992) 973. in B.E. Conway, R.E. White [41 Yu.V. Pleskov and Yu.Ya. Gurevich, and J.O’M. Bockris (Eds.), Modern Aspects of Electrochemistry, Vol. 16. Plenum Press, New York, 1985, Chap. 3, p. 189. [51 G. Zhao, E. Charlson, T. Stacy and E.J. Charlson, in A. Feldman, Y. Tseng, W.A. Yarbrough, M. Yoshikawa and M. Murakawa (I%.), Applications of Diamond Films and Related Materials: Proc. Third Int. Conf., 1995, p. 141. [61 Yu.V. Pleskov, A.Ya. Sakharova, M.D. Krotova, L.L. Bouilov and B.V. Spitsyn, J. Electroanal. Chem., 228 (1987) 19. Yu.V. Pleskov, F. Di Quarto, S. Piazza, C. Sunseri, [71 A.Ya. Sakharova. I.G. Teremetskaya and V.P. Vamin, J. Electrochem. Sot., 142 (1995) 2704. B.E. Conway and E. Yeager [81 Yu.V. Pleskov, in J.O’M. Bock& @Is.), Comprehensive Treatise of Electrochemistry, Vol. 1, Plenum Press, New York, 1985, p. 291.