- Email: [email protected]
Surface roughness factor of anodic oxide layer for electrolytic capacitors
Materials Chemistry and Physics 82 (2003) 331–334
Surface roughness factor of anodic oxide layer for electrolytic capacitors Han-Jun Oh a,∗ , Gyeong-Su Park b , Jung-Gu Kim c , Yongsoo Jeong d , Choong-Soo Chi e a Department of Materials Science, Hanseo University, Seosan 352-820, South Korea Samsung Advanced Institute of Technology, P.O. Box 111, Suwon 449-712, South Korea c Department of Metallurgical Engineering, SungKyunKwan University, Suwon 440-746, South Korea d Korea Institute of Machinery and Materials, Changwon 641-010, South Korea e School of Metallurgical and Materials Engineering, Kookmin University, Seoul 136-702, South Korea b
Received 12 September 2002; received in revised form 7 February 2003; accepted 18 February 2003
Abstract The roughness factor of barrier-type anodic oxide layer with low electrical conductivity was evaluated using electrochemical measurement in electrolyte with redox couple. To evaluate the surface roughness factor, the surface of barrier-type oxide layer was covered with thin layer of platinum by sputtering. From the limiting diffusion current method the surface roughness factor of barrier-type Al2 O3 estimated to be 1.03. This factor is in good agreement with the results of the cross-sectional characteristics by using transmission electron microscope. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Electrochemical techniques; Aluminum oxide; Dielectric properties; Capacitance
1. Introduction The barrier-type anodic oxide layer on aluminum are used as a dielectric layer in aluminum electrolytic capacitors and the electrical properties of capacitor in relation to dielectric dimensions are generally expressed using the conventional equation, as given in d=
εε0 Ar C
(1)
where d is the thickness of the barrier-type oxide layer, C the capacitance of the Al2 O3 layer, ε the dielectric constant for aluminum oxide, ε0 the permittivity of free space, A the surface area, and r the geometrical surface roughness factor. To calculate the anodic film thickness from the measured capacitance or obtain the desirable parameter from the known parameters using Eq. (1), the evaluation of the surface roughness factor of oxide layer is important. But there have been few reports that mention the surface roughness factor of barrier-type oxide film. In general, the surface roughness factor is evaluated using a limiting diffusion method, which was based upon the fact that the surface belongs to the electrically conducting materials. Therefore, for the surface of barrier-type Al2 O3 ∗ Corresponding author. E-mail address: [email protected] (H.-J. Oh).
layer with low electrical conductivity, this electrochemical method cannot be direct utilized. Thus, to evaluate the surface roughness factor on oxide layer with nonconductivity, the surface of barrier-type Al2 O3 was covered with thin layer of platinum by sputtering and then the electrochemical measurement in electrolyte with redox couple was performed. To validate this surface roughness factor, the value estimated from electrochemical impedance spectroscopy (EIS) measurement and TEM results were examined.
2. Experimental For oxide layer as a working electrode a sheet of aluminum (99.99 wt.%, Tokai Metals Co., Japan) was electropolished, then the aluminum oxide films were prepared at a constant voltage of 140 V for 10 min in the 150 g/l ammonium adipate (NH4 OCO(CH2 )4 COONH4 ) solution at 65 ◦ C. For this nonconductive Al2 O3 layer formed in anodic process to apply the electrochemical measurement, the sputtered platinum layer on this oxide layer has been deposited. The process was carried out at the working pressure of 8 × 10−2 Torr for 1.8 min using RF magnetron sputtering system. This surface coated with platinum is used as a working electrode. The electrochemical experiment for limiting diffusion current density employed a commercial
0254-0584/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0254-0584(03)00139-1
332
H.-J. Oh et al. / Materials Chemistry and Physics 82 (2003) 331–334
electrochemical analyzer (IM6, Zahner elektrik, Germany). All solutions were prepared with distilled water and deaerated with nitrogen for 15 min. And chemicals, K3 Fe(CN)6 (Merck), K4 Fe(CN)6 H2 O (Merck) and K2 SO4 (Fulka) used were of reagent-grade. All potentials for measurements in present paper are referenced to the Hg/Hg2 SO4 /0.5 M K2 SO4 solution and a platinum sheet was used for the counter electrode. The measurement for limiting diffusion current density was performed in 0.5 M K2 SO4 solution with 1 mM ferri and ferrocyanide as a electroactive species material at 25 ◦ C (pH 6.44). The exposed geometrical area of the sputtered platinum layer on Al2 O3 as the working electrode in electrolyte was 0.95 cm2 .
3. Results and discussion 3.1. Diffusion limiting current analysis Fig. 1 shows the current–time response obtained in constant anodic overpotential and the change of It1/2 with time at a constant potential. In this measurement the constant anodic overpotential of 100 mV was applied to the electrode surface, where the oxidation of Fe(CN)6 −4 occurs at an electrode Fe(CN)6 −4 = Fe(CN)6 −3 + e− , the decrease of current density with time associated with depletion of chemical species at the surface represented. In Fig. 1 the point represented the measured data and the solid line indicates average value of It1/2 over all measured time. This figure indicates that the measured current is diffusion controlled since the It1/2 product is fairly constant [1]. The average of product It1/2 for ferrocyanide system is 1.34 × 10−4 (As1/2 ); this standard deviation of 3.0 × 10−6 indicates that the potential step measurement is nearly satisfactory. Therefore the effective surface area can be evaluated by the Eq. (2), the Cottrell equation.
Fig. 1. The current–time response obtained at constant anodic overpotential of >100 mV in 0.5 M K2 SO4 solution with 1 mM ferri and ferrocyanide at 25 ◦ C (pH 6.44) and the change of It1/2 with time at a constant potential at I–t transient measurement.
Amea
√ I πDt = nFDC0
(2)
where Amea is the surface area of measured electrode, I the measured diffusion limiting current, D the diffusion coefficient, n the number of electrons, F the Faraday’s constant, and C0 the concentration of chemical species. Taking the diffusion coefficient [2] for ferrocyanide in K2 SO4 solution, D(Fe[CN]6 −4 ) = 6.32 × 10−6 cm2 /s, and the concentration of Fe(CN)6 −4 , 10−6 M/cm3 , we estimated the effective surface area to be 0.98 cm2 . Although the test was performed for sputter-deposited platinum layer on barrier-type Al2 O3 , it is possible to calculate a surface roughness factor of barrier-type Al2 O3 by substitution of calculated surface area, 0.98 cm2 , corresponds to a simple geometrical area, 0.95 cm2 . From the expression, r = Amea /Ageo , the surface roughness factor was estimated to be 1.03. 3.2. Cross-sectional morphology To investigate the cross-sectional morphology characteristics of both surface for barrier-type Al2 O3 as substrate and for platinum sputter-deposited surface thickness on this substrate, the sectioned specimens by ion milling (PIPS 691, Gatan) were observed at accelerating voltage of 300 kV, using TEM (H-9000NA, Hitachi). The cross-sectional morphology characteristics of both surface for barrier-type Al2 O3 as substrate and for platinum sputter-deposited surface 70 nm thickness on this substrate have been investigated by using TEM. The Fig. 2 shows the cross-sectional morphology for barrier-type Al2 O3 and for platinum deposited layer on barrier-type Al2 O3 . The observed dummy materials on platinum layer were used for preparing TEM specimens. Fig. 2 also shows that the no distinct morphological changes on platinum deposited layer revealed compared to on barrier-type Al2 O3 substrate.
Fig. 2. TEM micrograph of the cross-sectional surface characteristics for aluminum substrate, barrier-type Al2 O3 layer on substrate and platinum-deposited layer on barrier-type Al2 O3 .
H.-J. Oh et al. / Materials Chemistry and Physics 82 (2003) 331–334
Thus, this cross-sectional characteristics by TEM were in good agreement with the value of roughness factor obtained the potential step experiment. 3.3. Electrochemical impedance spectroscopy To validate this surface roughness factor, the calculated oxide layer thickness by Eq. (1) was compared with the value determined from TEM. In general, capacitance can be measured from EIS and can be directly converted to an oxide thickness by conventional equation, as given in Eq. (1), where ε = 8.5 [3] for Al2 O3 , ε0 = 8.85 × 10−12 F/m, A = 0.95 cm2 and r = 1.03 that obtained in the present results. Thus, for this purpose experiments for electrochemical impedance spectroscopy were performed using commercially available equipment (IM6, Zahner-Elektrik, Germany) at open-circuit potential at 25 ◦ C in 0.5 M K2 SO4 , an unstirred electrolyte. After the measurement of the complex impedance as a function of frequency the capacitance of the barrier-type oxide layer as impedance parameter can be analyzed with fitting of equivalent circuit. This is performed by a computer simulation and fitting program [4]. EIS measured results in this research can be analyzed by using the simple equivalent circuits in Fig. 3. In the circuit model, the layer impedance corresponds to that of an equivalent circuit containing two branches. One can be associated with the bulk resistance of the oxide layer and the other with the capacitive component of the passive layer which behaves like an ideal capacitor or an inhomogeneous dielectric The impedance characteristic of equivalent circuit model A in Fig. 3 shows a frequency dependent impedance, ZA . ZA = RE +
i2πfR21 C R1 − 2 1 + (2πfR1 C) 1 + (2πfR1 C)2
(3)
However, the impedance of circuit model B can be determined by the frequency range. The Young impedance in model B converges with decreasing frequency asymptotically to a resistance [5,6]. 1 τp lim ZY = RY = exp − 1 (4) ω→0 CY p
333
depends on the effective range between the charge carrier concentration and oxide thickness. If p is small, i.e. it can be associated with the rapid decrease of carrier concentration density or the relatively large thickness of the oxide layer, in these cases, the Young impedance for the fit is especially valid. The validity of these parameters was proven by an earlier investigation [6]. And with increasing frequency the Young impedance of model B converges to a capacitance lim ZY =
ω→∞
1 iωCY
(5)
Thus, at very low frequencies, the circuit impedance according to Eq. (4) is given by Eq. (6) ZB ω→0
−1 −1 = RE + (R−1 Y + R1 )
(6)
but in higher frequency ranges, the circuit impedance according to Eq. (5) can be described by Eq. (7). ZB = RE +
ω→∞
i2πfR21 CY R1 − 2 1 + (2πfR1 CY ) 1 + (2πfR1 CY )2
(7)
For fitting impedance spectra of Al2 O3 with variable stoichiometry in this study a model with Young impedance (Fig. 3, model B) instead of pure capacitance (Fig. 3, model A) was used. The physical meaning of this circuit model B was properly described in previous investigations [5,6]. The measured impedance spectra and fitted result of barrier oxide layer formed in ammonium adipate solution are shown in Fig. 4. From fitted capacitance in EIS measurement and surface roughness factor estimated in limiting diffusion current density, we estimated the thickness of oxide layer to be 149 and 151 nm. In order to compare the oxide film thickness with the value calculated from impedance spectroscopy, the film thicknesses of the aluminum oxide layers were examined by TEM (100 kV, JEM1210). The calculated film thicknesses evaluated by EIS, as shown in Table 1, are in agreement to the thickness of oxide layer determined by using TEM.
where RY is the resistance and CY the capacitance for the aluminum oxide layer with a vertical decay of conductivity, τ the time constant, and p the relative penetration depth which
Fig. 3. Equivalent circuit model for evaluation of capacitance from measured impedance spectra on barrier-type oxide layer.
Fig. 4. Impedance plot of fitted data point with circuit model on experimental impedance data for a spectra of barrier oxide layer anodized in ammonium adipate solution.
334
H.-J. Oh et al. / Materials Chemistry and Physics 82 (2003) 331–334
Table 1 Comparison of the calculated film thicknesses from EIS and the values determined from TEM Forming condition
Measured capacitancea (nF/cm2 )
Calculated thicknessb (nm)
Thickness observed TEM (nm)
100 V, 10 min in NH4 H2 PO4 solution 100 V, 10 min in ammonium adipate solution
49.4 48.7
149 151
146 149
a b
The capacitance is evaluated by EIS measurement. The thickness was estimated using Eq. (1) for the measured capacitance and the r = 1.03.
4. Conclusions
References
The surface roughness factor of barrier-type Al2 O3 without electrical conductivity has been estimated by using electrochemical method. From the limiting diffusion current method the surface roughness factor of barrier-type Al2 O3 estimated to be 1.03. This factor is in good agreement with the results of the morphological characteristics by TEM and the calculated thickness determined by interpretation of EIS. The roughness factor of barrier-type Al2 O3 with smooth surface can be evaluated with good agreement by using I–t transient method and for the evaluation of roughness factor of nonconductive dielectric materials this method can be used.
[1] H.E. Zittel, F.J. Miller, Anal. Chem. 37 (1965) 200. [2] I. Hu, D.H. Karweik, T. Kuwana, J. Electroanal. Chem. 188 (1985) 59. [3] A. Kuznetsova, T.D. Burleigh, V. Zhukov, J. Blachere Jr., J.T. Yates, Langmuir 14 (1998) 2502. [4] H. Goehr, Z. Phys. Chem. Neue Folge 148 (1986) 105. [5] H.-J. Oh, J.-G. Kim, Y.-S. Jeong, C.-S. Chi, Jpn. J. Appl. Phys. 39 (2000) 6690. [6] H. Goehr, H.- J Oh, C.-A. Schiller, GDCH Monographie 2 (1995) 341.
Surface roughness factor of anodic oxide layer for electrolytic capacitors Han-Jun Oh a,∗ , Gyeong-Su Park b , Jung-Gu Kim c , Yongsoo Jeong d , Choong-Soo Chi e a Department of Materials Science, Hanseo University, Seosan 352-820, South Korea Samsung Advanced Institute of Technology, P.O. Box 111, Suwon 449-712, South Korea c Department of Metallurgical Engineering, SungKyunKwan University, Suwon 440-746, South Korea d Korea Institute of Machinery and Materials, Changwon 641-010, South Korea e School of Metallurgical and Materials Engineering, Kookmin University, Seoul 136-702, South Korea b
Received 12 September 2002; received in revised form 7 February 2003; accepted 18 February 2003
Abstract The roughness factor of barrier-type anodic oxide layer with low electrical conductivity was evaluated using electrochemical measurement in electrolyte with redox couple. To evaluate the surface roughness factor, the surface of barrier-type oxide layer was covered with thin layer of platinum by sputtering. From the limiting diffusion current method the surface roughness factor of barrier-type Al2 O3 estimated to be 1.03. This factor is in good agreement with the results of the cross-sectional characteristics by using transmission electron microscope. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Electrochemical techniques; Aluminum oxide; Dielectric properties; Capacitance
1. Introduction The barrier-type anodic oxide layer on aluminum are used as a dielectric layer in aluminum electrolytic capacitors and the electrical properties of capacitor in relation to dielectric dimensions are generally expressed using the conventional equation, as given in d=
εε0 Ar C
(1)
where d is the thickness of the barrier-type oxide layer, C the capacitance of the Al2 O3 layer, ε the dielectric constant for aluminum oxide, ε0 the permittivity of free space, A the surface area, and r the geometrical surface roughness factor. To calculate the anodic film thickness from the measured capacitance or obtain the desirable parameter from the known parameters using Eq. (1), the evaluation of the surface roughness factor of oxide layer is important. But there have been few reports that mention the surface roughness factor of barrier-type oxide film. In general, the surface roughness factor is evaluated using a limiting diffusion method, which was based upon the fact that the surface belongs to the electrically conducting materials. Therefore, for the surface of barrier-type Al2 O3 ∗ Corresponding author. E-mail address: [email protected] (H.-J. Oh).
layer with low electrical conductivity, this electrochemical method cannot be direct utilized. Thus, to evaluate the surface roughness factor on oxide layer with nonconductivity, the surface of barrier-type Al2 O3 was covered with thin layer of platinum by sputtering and then the electrochemical measurement in electrolyte with redox couple was performed. To validate this surface roughness factor, the value estimated from electrochemical impedance spectroscopy (EIS) measurement and TEM results were examined.
2. Experimental For oxide layer as a working electrode a sheet of aluminum (99.99 wt.%, Tokai Metals Co., Japan) was electropolished, then the aluminum oxide films were prepared at a constant voltage of 140 V for 10 min in the 150 g/l ammonium adipate (NH4 OCO(CH2 )4 COONH4 ) solution at 65 ◦ C. For this nonconductive Al2 O3 layer formed in anodic process to apply the electrochemical measurement, the sputtered platinum layer on this oxide layer has been deposited. The process was carried out at the working pressure of 8 × 10−2 Torr for 1.8 min using RF magnetron sputtering system. This surface coated with platinum is used as a working electrode. The electrochemical experiment for limiting diffusion current density employed a commercial
0254-0584/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0254-0584(03)00139-1
332
H.-J. Oh et al. / Materials Chemistry and Physics 82 (2003) 331–334
electrochemical analyzer (IM6, Zahner elektrik, Germany). All solutions were prepared with distilled water and deaerated with nitrogen for 15 min. And chemicals, K3 Fe(CN)6 (Merck), K4 Fe(CN)6 H2 O (Merck) and K2 SO4 (Fulka) used were of reagent-grade. All potentials for measurements in present paper are referenced to the Hg/Hg2 SO4 /0.5 M K2 SO4 solution and a platinum sheet was used for the counter electrode. The measurement for limiting diffusion current density was performed in 0.5 M K2 SO4 solution with 1 mM ferri and ferrocyanide as a electroactive species material at 25 ◦ C (pH 6.44). The exposed geometrical area of the sputtered platinum layer on Al2 O3 as the working electrode in electrolyte was 0.95 cm2 .
3. Results and discussion 3.1. Diffusion limiting current analysis Fig. 1 shows the current–time response obtained in constant anodic overpotential and the change of It1/2 with time at a constant potential. In this measurement the constant anodic overpotential of 100 mV was applied to the electrode surface, where the oxidation of Fe(CN)6 −4 occurs at an electrode Fe(CN)6 −4 = Fe(CN)6 −3 + e− , the decrease of current density with time associated with depletion of chemical species at the surface represented. In Fig. 1 the point represented the measured data and the solid line indicates average value of It1/2 over all measured time. This figure indicates that the measured current is diffusion controlled since the It1/2 product is fairly constant [1]. The average of product It1/2 for ferrocyanide system is 1.34 × 10−4 (As1/2 ); this standard deviation of 3.0 × 10−6 indicates that the potential step measurement is nearly satisfactory. Therefore the effective surface area can be evaluated by the Eq. (2), the Cottrell equation.
Fig. 1. The current–time response obtained at constant anodic overpotential of >100 mV in 0.5 M K2 SO4 solution with 1 mM ferri and ferrocyanide at 25 ◦ C (pH 6.44) and the change of It1/2 with time at a constant potential at I–t transient measurement.
Amea
√ I πDt = nFDC0
(2)
where Amea is the surface area of measured electrode, I the measured diffusion limiting current, D the diffusion coefficient, n the number of electrons, F the Faraday’s constant, and C0 the concentration of chemical species. Taking the diffusion coefficient [2] for ferrocyanide in K2 SO4 solution, D(Fe[CN]6 −4 ) = 6.32 × 10−6 cm2 /s, and the concentration of Fe(CN)6 −4 , 10−6 M/cm3 , we estimated the effective surface area to be 0.98 cm2 . Although the test was performed for sputter-deposited platinum layer on barrier-type Al2 O3 , it is possible to calculate a surface roughness factor of barrier-type Al2 O3 by substitution of calculated surface area, 0.98 cm2 , corresponds to a simple geometrical area, 0.95 cm2 . From the expression, r = Amea /Ageo , the surface roughness factor was estimated to be 1.03. 3.2. Cross-sectional morphology To investigate the cross-sectional morphology characteristics of both surface for barrier-type Al2 O3 as substrate and for platinum sputter-deposited surface thickness on this substrate, the sectioned specimens by ion milling (PIPS 691, Gatan) were observed at accelerating voltage of 300 kV, using TEM (H-9000NA, Hitachi). The cross-sectional morphology characteristics of both surface for barrier-type Al2 O3 as substrate and for platinum sputter-deposited surface 70 nm thickness on this substrate have been investigated by using TEM. The Fig. 2 shows the cross-sectional morphology for barrier-type Al2 O3 and for platinum deposited layer on barrier-type Al2 O3 . The observed dummy materials on platinum layer were used for preparing TEM specimens. Fig. 2 also shows that the no distinct morphological changes on platinum deposited layer revealed compared to on barrier-type Al2 O3 substrate.
Fig. 2. TEM micrograph of the cross-sectional surface characteristics for aluminum substrate, barrier-type Al2 O3 layer on substrate and platinum-deposited layer on barrier-type Al2 O3 .
H.-J. Oh et al. / Materials Chemistry and Physics 82 (2003) 331–334
Thus, this cross-sectional characteristics by TEM were in good agreement with the value of roughness factor obtained the potential step experiment. 3.3. Electrochemical impedance spectroscopy To validate this surface roughness factor, the calculated oxide layer thickness by Eq. (1) was compared with the value determined from TEM. In general, capacitance can be measured from EIS and can be directly converted to an oxide thickness by conventional equation, as given in Eq. (1), where ε = 8.5 [3] for Al2 O3 , ε0 = 8.85 × 10−12 F/m, A = 0.95 cm2 and r = 1.03 that obtained in the present results. Thus, for this purpose experiments for electrochemical impedance spectroscopy were performed using commercially available equipment (IM6, Zahner-Elektrik, Germany) at open-circuit potential at 25 ◦ C in 0.5 M K2 SO4 , an unstirred electrolyte. After the measurement of the complex impedance as a function of frequency the capacitance of the barrier-type oxide layer as impedance parameter can be analyzed with fitting of equivalent circuit. This is performed by a computer simulation and fitting program [4]. EIS measured results in this research can be analyzed by using the simple equivalent circuits in Fig. 3. In the circuit model, the layer impedance corresponds to that of an equivalent circuit containing two branches. One can be associated with the bulk resistance of the oxide layer and the other with the capacitive component of the passive layer which behaves like an ideal capacitor or an inhomogeneous dielectric The impedance characteristic of equivalent circuit model A in Fig. 3 shows a frequency dependent impedance, ZA . ZA = RE +
i2πfR21 C R1 − 2 1 + (2πfR1 C) 1 + (2πfR1 C)2
(3)
However, the impedance of circuit model B can be determined by the frequency range. The Young impedance in model B converges with decreasing frequency asymptotically to a resistance [5,6]. 1 τp lim ZY = RY = exp − 1 (4) ω→0 CY p
333
depends on the effective range between the charge carrier concentration and oxide thickness. If p is small, i.e. it can be associated with the rapid decrease of carrier concentration density or the relatively large thickness of the oxide layer, in these cases, the Young impedance for the fit is especially valid. The validity of these parameters was proven by an earlier investigation [6]. And with increasing frequency the Young impedance of model B converges to a capacitance lim ZY =
ω→∞
1 iωCY
(5)
Thus, at very low frequencies, the circuit impedance according to Eq. (4) is given by Eq. (6) ZB ω→0
−1 −1 = RE + (R−1 Y + R1 )
(6)
but in higher frequency ranges, the circuit impedance according to Eq. (5) can be described by Eq. (7). ZB = RE +
ω→∞
i2πfR21 CY R1 − 2 1 + (2πfR1 CY ) 1 + (2πfR1 CY )2
(7)
For fitting impedance spectra of Al2 O3 with variable stoichiometry in this study a model with Young impedance (Fig. 3, model B) instead of pure capacitance (Fig. 3, model A) was used. The physical meaning of this circuit model B was properly described in previous investigations [5,6]. The measured impedance spectra and fitted result of barrier oxide layer formed in ammonium adipate solution are shown in Fig. 4. From fitted capacitance in EIS measurement and surface roughness factor estimated in limiting diffusion current density, we estimated the thickness of oxide layer to be 149 and 151 nm. In order to compare the oxide film thickness with the value calculated from impedance spectroscopy, the film thicknesses of the aluminum oxide layers were examined by TEM (100 kV, JEM1210). The calculated film thicknesses evaluated by EIS, as shown in Table 1, are in agreement to the thickness of oxide layer determined by using TEM.
where RY is the resistance and CY the capacitance for the aluminum oxide layer with a vertical decay of conductivity, τ the time constant, and p the relative penetration depth which
Fig. 3. Equivalent circuit model for evaluation of capacitance from measured impedance spectra on barrier-type oxide layer.
Fig. 4. Impedance plot of fitted data point with circuit model on experimental impedance data for a spectra of barrier oxide layer anodized in ammonium adipate solution.
334
H.-J. Oh et al. / Materials Chemistry and Physics 82 (2003) 331–334
Table 1 Comparison of the calculated film thicknesses from EIS and the values determined from TEM Forming condition
Measured capacitancea (nF/cm2 )
Calculated thicknessb (nm)
Thickness observed TEM (nm)
100 V, 10 min in NH4 H2 PO4 solution 100 V, 10 min in ammonium adipate solution
49.4 48.7
149 151
146 149
a b
The capacitance is evaluated by EIS measurement. The thickness was estimated using Eq. (1) for the measured capacitance and the r = 1.03.
4. Conclusions
References
The surface roughness factor of barrier-type Al2 O3 without electrical conductivity has been estimated by using electrochemical method. From the limiting diffusion current method the surface roughness factor of barrier-type Al2 O3 estimated to be 1.03. This factor is in good agreement with the results of the morphological characteristics by TEM and the calculated thickness determined by interpretation of EIS. The roughness factor of barrier-type Al2 O3 with smooth surface can be evaluated with good agreement by using I–t transient method and for the evaluation of roughness factor of nonconductive dielectric materials this method can be used.
[1] H.E. Zittel, F.J. Miller, Anal. Chem. 37 (1965) 200. [2] I. Hu, D.H. Karweik, T. Kuwana, J. Electroanal. Chem. 188 (1985) 59. [3] A. Kuznetsova, T.D. Burleigh, V. Zhukov, J. Blachere Jr., J.T. Yates, Langmuir 14 (1998) 2502. [4] H. Goehr, Z. Phys. Chem. Neue Folge 148 (1986) 105. [5] H.-J. Oh, J.-G. Kim, Y.-S. Jeong, C.-S. Chi, Jpn. J. Appl. Phys. 39 (2000) 6690. [6] H. Goehr, H.- J Oh, C.-A. Schiller, GDCH Monographie 2 (1995) 341.