Modeling of electrochromic processes

Electrochimica Acta 44 (1999) 3177±3184

Modeling of electrochromic processes Junichi Nagai*, Graham D. McMeeking Chemistry Research Laboratory, Asahi Glass Co., Ltd, 1150 Hazawa-cho, Kanagawa-ku, Yokohama 221-8755, Japan Received 25 September 1998

Abstract Over the last decade, there has been great interest in electrochromic technology for smart windows. Various kinds of electrochromic materials were examined and their electrochromic processes were analyzed in terms of optical and electrochemical properties. For glazing applications, there are still two systems: one is all solid state whilst the other is a laminated system that utilizes an organic electrolyte. The response of an electrochromic system is a complicated function of the sheet resistance of ITO, and the ionic transport of the electrolyte, charge storage layer and electrochromic ®lm. In this paper, analysis of electrochromic process is focused on the ionic transport in the electrochromic thin ®lms using ®nite di€usion model. # 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction There are many analytical tools that can be used to elucidate the electrochromic reactions in materials such as WO3, NiO, etc., particularly when they are based on the di€usion of ions (cf. Fig. 1). For instance, voltammetry analysis is widely used, but it is rather dicult to deduce the kinetic parameters such as di€usion coecient, because of the complicated nature of the current, that is dependent on the thickness of the ®lm, the resistance of the system, the chemical potential, scan rate, etc. For these reasons, this method is only utilized for qualitative analysis. However, if we use switching chronopotentiometry, we can determine the di€usion coecient of the material easily, without knowing the chemical potential of the material which requires the analysis of its chemical composition. For WO3 the relationship between potential and the charge injected/extracted is shown in Fig. 2. In this case, the charge (electron) is injected into the ®lm from the time t=0 to t and at t=t, the charge is extracted by reversing the polarity of the current. At time t=t+t , the

* Corresponding author.

electrode potential theoretically becomes in®nite, leading to the breakdown of the electrode because ionic transport is insucient to maintain a constant current. This phenomenon has been previously reported but only for semi®nite di€usion occurring in an electrolyte (Ref. [1,2]). In this paper, by re®ning the ®nite di€usion model, a novel technique to determine the di€usion coecients of ions in the electrochromic thin ®lms is presented.

2. Experimental 2.1. Fabrication of WO3, NiOx and (CeO2)x (TiO2)1ÿx ®lms WO3 and NiOx ®lms are deposited by electron beam (EB) evaporations of the corresponding WO3 (99.9%) and NiO (99.9%) on ITO coated glass (10 O/q) as previously reported (Ref. [3,4]). Prior to the depositions, the vacuum chamber is evacuated to the pressure less than 2  10ÿ5 Torr. During the evaporation, O2 gas is introduced to keep a constant pressure of 1  10ÿ4 and 8  10ÿ5 Torr for WO3 and NiOx, respectively and the substrates are heated at 1208C. Deposition rates are

0013-4686/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 3 - 4 6 8 6 ( 9 9 ) 0 0 0 3 5 - 3

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J. Nagai, G.D. McMeeking / Electrochimica Acta 44 (1999) 3177±3184

ÿ4NiO…OH ÿ †x …or NiO ‡ xOHÿ ‡ xp‡ ÿ ÿ NiO ‡ xOHÿ ÿ ÿ4NiO…OH† ÿ x ‡ xe †

…2†

…CeO2 †y …TiO2 †1ÿy ‡ xeÿ ‡ xLi‡ ÿ ÿ4Li ÿ x …CeO2 †y  …TiO2 †1ÿy ,

…3†

where eÿ and p+ denote electrons and holes, respectively. In any case, mobilities of electrons and holes are so high that the total reactions are limited by the di€usion of ions (Li+ and OHÿ). Motions of ions, electrons and holes are depicted in Fig. 1. The transport of ions is a di€usion process, governed by Fick's law: D@ 2 C…z,t† @ C…z, t† ˆ @ z2 @t Fig. 1. Schematic illustration of electrochromic process for WO3.

around 1 nm/s for WO3 and 0.1±0.2 nm/s for NiOx ®lms, respectively. As a reference, WO3 ®lm annealed at 1508C for 1 h was also used. (CeO2)x (TiO2)1ÿx ®lms were formed by cosputtering method (Ref. [5]) using Ti (99.99%) and Ce (99.99%). Prior to the sputtering the chamber was evacuated to 1  10ÿ6 Torr and then a mixed gas of Ar and O2 (Ar:O2=45:5 sccm) was introduced and a pressure of 6  10ÿ2 Torr was maintained. Film thickness was measured using surface pro®lometer (Dektak 3030, Sloan). The thicknesses were 500.0, 680.3 and 855.0 nm for WO3, NiOx and (CeO2)y(TiO2)1ÿy, respectively.

…4†

where D is the di€usion coecient of corresponding ions, C(z, t ) is the concentration of the ions in the ®lm at the charged state. For the cathodic electrochromic materials such as WO3 and (CeO2)x (TiO2)1ÿy, C(z, t ) denotes the concentrations of LixWO3 and Lix (CeO2)y (TiO2)1ÿy, respectively. Whereas, for anodic electrochromic materials such as NiO, C(z, t ) denotes the concentration of NiO(OH)x, The boundary conditions at z=0 and z=L and the initial conditions are: z ˆ 0: nFD @ C…x, t†=@ z ˆ 2J…t†,

…5†

where the positive sign applies for the cathodic materials and negative sign for anodic materials.

2.2. Electrochemical measurements Electrochemical measurements were reported previously (Ref. [6]). Cyclic voltammograms and acimpedance spectroscopies were measured using a three electrode system with Pt counter and Ag/Ag+ reference electrodes. The electrolyte used was g-butyrolactone with 1 M LiClO4 (ca. 1000 ppm H2O). All data was saved in memory recorder (8806, Hioki) for analysis.

3. Theory of ®nite di€usion The electrochromic phenomena in WO3, NiOx, and (CeO2)y (TiO2)1ÿy can be described by: WO3 ‡ xeÿ ‡ xLi‡ ÿ ÿ4Li ÿ x WO3

…1†

Fig. 2. Switching chronopotentiometry (above) and electrode potential (for WO3).

J. Nagai, G.D. McMeeking / Electrochimica Acta 44 (1999) 3177±3184

z ˆ L: nFD@ C…z, t†=@ z ˆ 0

…6†

t ˆ 0: C…z, t† ˆ C0

…7†

for 0YyYL,

where L is the thickness of the ®lm, C0 the initial concentration of ions in the ®lm, J(t ) the current density, n the number of electrons (or holes) transferred in the electrochromic process, F the Faraday's constant. For the case of switching chronopotentiometry, the stepwise current is described by: J…t† ˆ ‡J0 ˆ ÿJ0

for 0Yt
…8†

for tyt,

3179

H…z, t† ˆ fJ0 …nFD†g‰Dt=L2 ‡ f3…L ÿ z†2 ÿ L2 †g=…6L2 † ÿ …2=p2 † 

1 X f…ÿ1†k =k2 gexp…ÿDk2 p2 t=L2 †

…14†

kˆ1

 cosfkp…L ÿ z†=LgŠ: Or H…z, t† ˆ fJ0 =…nFD†g2…Dt†1=2 

1 X ‰ierfcf…z ‡ 2kL†=…4Dt†1=2 g

…15†

kˆ0

where J0 is the constant current and the t is the time for switching the polarity of the current. Here, note that J0>0 for anodic materials and J0 < 0 for cathodic materials. To solve the di€usion equation, method of Laplace transformation is utilized. For the function F(t ), its transformed function F( p ) is de®ned by: F… p† 

…1 0

F…t†  exp…ÿpt†dt:

…9†

For current density J(t ), the following formula is obtained: J… p† ˆ J0  f1 ÿ 2 exp…ÿpt†g=p:

…10†

Then the Laplace transformation of the concentration C(Z, t ) satisfying the boundary and initial conditions (5)±(7) is obtained as (cf. Refs. [7,8]): C… p† ˆ …C0 =p†3fJ… p†

…11†

 cosh m…L ÿ z†g=…nFDm  sinh mL†, where m ˆ … p=D†1=2

…12†

‡ ierfcf…2…k ‡ 1†L ÿ z†=…4Dt†1=2 gŠ Eq. (13) is valid irrespective of materials for either cathodic or anodic. Hereafter initial concentration C0 is set to be zero, because prior to the experiments all the ®lms were completely bleached (i.e. discharged). Surface concentration C(0, t ) increases monotonically during the charging process but it decreases after t>t and becomes zero at t=t+t , which means the rate of di€usion can not be sustained to maintain a constant current, whilst the electrode potential increases to in®nity (i.e. breakdown of the electrode). By introducing the following dimensionless parameter Fo, called Fourier's number: Fo ˆ D…t=L2 †

the reversibility factor t/t  can be obtained numerically using Eq. (14) or Eq. (15) and expressed as a function of Fo as shown in Fig. 3. Note that the reversibility factor does not depend upon the value of the current density i0 but on the di€usion constant D, charge injection time t and the ®lm thickness L.For Fo>>1, C(0, t ) is approximated as: C…0, t†ÿ ÿ4fJ ÿ 0 =…nFD†g  ‰Dt=L2 ‡ 1=3 ÿ 2D…t ÿ t†=L2 ÿ 2=3Š:

and the negative sign applies for cathodic materials and the positive for anodic materials. Then the concentration C(z, t ) is obtained taking the inverse of Eq. (10) with current mode Eq. (12) as:

Solution of t  which satis®es C(0, t )=0 is

C…z,t† ˆ C0 ‡ jJ0 j=…nFD†  H…z, t†

Therefore, t  can be obtained:

for 0YtYt

C0 ‡ jJ0 j=…nFD†  fH…z, t† ÿ 2H…z, t ÿ t†g tYt, where

for

t ˆ f2 ÿ 1=…3Fo†gt:

t  =t ˆ …t  ÿt†=t ˆ 1 ÿ 1=…3Fo†: …13†

…16†

…17†

…18†

…19†

As Fo tends to zero (D 4 0 or L 4 1) which is equivalent to the case of semi-in®nite di€usion and the value of t /t becomes exactly 1/3 (Ref. [1,2]). For Fo<<1 using Eq. (15),

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Fig. 3. Relationship between reversibility factor t /t and Fo. (a) Exact solution. (b)Approximate (Fo>>1). (c)Asymptotic limit (Fo<<1).

1=2 C…0, t†ÿ ÿ42fjJ ÿ ÿ 2fD…t ÿ t†g1=2 Š: 0 j=…nFD†g‰…Dt†

…20†

D ˆ L2  Fo=t > 2:5  10ÿ10 cm2 =s:

…22†

Then the solution for C(0, t )=0 is t ˆ …4=3†t and t  =t ˆ …t  ÿt†=t ˆ 1=3:

…21†

These approximated curves for Eqs. (19) and (21) are drawn also in Fig. 3. From the view point of device operation using constant current mode, to avoid the breakdown of the electrode, the ®lm must have a character such that Fo>>10. For example, if the ®lm thickness is 500 nm and charge injection time is 100 s, then the di€usion constant must satisfy:

4. Experimental results 4.1. Results for WO3 ®lms In Fig. 4, voltammograms of as deposited and annealed WO3 ®lms are shown. Due to the dehydration by annealing, the latter ®lm exhibits slower rate of electrochromic reaction. In Fig. 5, relationship between electrode potential E(V vs. Ag/Ag+) and time

Fig. 4. Voltammograms of as deposited and annealed WO3 ®lms (scan rate v=50 mV/s).

J. Nagai, G.D. McMeeking / Electrochimica Acta 44 (1999) 3177±3184

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Fig. 5. Electrode potential of chronopotentiometry for WO3 (J0=ÿ1 mA/cm2).

t(s) is depicted using current density J0=ÿ1 (mA/cm2) and t=10 (s). Breakdown potential was determined such that the electrode potential reaches +2.0 (V vs. Ag/Ag+). Various t  values were obtained by changing the parameters t and J0. In Fig. 6, graphic symbols denote experimental values of t /t as a function

of injection time t and solid lines are corresponding to the plots of di€erent di€usion coecients. The di€usion coecient D estimated for as deposited ®lm is 1±2  10ÿ9 cm2/s, while the annealed one has the value 3±5  10ÿ11 cm2/s. Deviation from the calculated curves at shorter injection time t is observed and this could be

Fig. 6. Analysis of di€usion coecients for WO3 ®lms.

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Fig. 7. Voltammograms of NiO with various switching potentials (scan rate v=50 mV/s).

ascribed to the following assumptions: 1. Di€usion coecient does not depend on electrode potential 2. Di€usion is uniform in the ®lm. To improve the present technique, extended research such as modi®cation of current form (e.g. square, sinusoidal, etc.) and/or introduction of a multidi€usion channel are required. 4.2. Results for NiO ®lms In Fig. 7, voltammograms of NiO with various

switching potential are drawn. When the potential exceeds 1.0 V, anodic current shows rapid increase which is a symptom of side reaction such as decomposition of electrolyte or electrode it self Fig. 8 shows the relationship between electrode potential E (V vs. Ag/ Ag+) and time t(s) is depleted using current density J0=+0.5 (mA/cm2) and t=20 (s). Breakdown potential was determined such that the electrode potential reaches ÿ2.0 (V vs. Ag/Ag+) and in this case t =16.1 (s). Various t  values were obtained by changing the parameters t and J0. In Fig. 9, triangular dot denotes experimental values of t /t as a function of injection time t and solid lines are corresponding to the plots of di€erent di€usion coecients. The di€usion coecient D estimated is 2±8  10ÿ10 cm2/s) which is smaller than the previously reported value (Ref. [6]) D=3.8  10ÿ8 cm2/s, but this is presumably due to the fact that the current NiO ®lm is denser (r=3.8 g/cc) than that of previous one (2.6 g/ cc). 4.3. Results for (CeO2)y(TiO2)1ÿy ®lms In Fig. 10, voltammograms of (CeO2)y (TiO2)1ÿy with various scan rates are shown. This material is cathodic electrochromic but peaks are found for both cathodic and anodic processes. Fig. 11 shows the relationship between electrode potential E(V vs. Ag/ Ag+) and time t(s) is depicted using current density J0=ÿ0.1 (mA/cm2) and t=50 (s). Breakdown potential was determined such that the electrode potential reaches +2.0 (V vs. Ag/Ag+) because no sharp rise in potential was found at t>50 (s). Various t  values

Fig. 8. Electrode potential of chronopotentiometry for NiO (J0=+0.5 mA/cm2).

J. Nagai, G.D. McMeeking / Electrochimica Acta 44 (1999) 3177±3184

3183

Fig. 9. Analysis of di€usion coecients for NiO ®lm.

were obtained by changing the parameters t and J0. In Fig. 12, dot denotes experimental values of t /t as a function of injection time t and solid lines are corresponding to the plots of di€erent di€usion coecients. The di€usion coecient D estimated is 4±8  10ÿ11 cm2/s.

5. Conclusions

Fig. 10. Voltammograms of (CeO2)y (TiO2)1ÿy with various scan rates.

Finite di€usion problem was solved for switching chronopotentiometry. It was revealed that during the discharge process electrode potential shows breakdown using constant current density (J0) and the amount of maximum charge extraction (J0  t ) is predicted as a

Fig. 11. Electrode potential of chronopotentiometry for (CeO2)y (tiO2)1ÿy (J0=ÿ0.1 mA/cm2).

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Fig. 12. Analysis of di€usion coecients for (CeO2)y (TiO2)1ÿy ®lm.

function of dimensionless parameter Fo=D(t/L 2), where D is the di€usion constant, t the charge injection time, L, the ®lm thickness. To realize reversible charge injection/extraction. using constant current mode, Fo>>10 is necessary, which requires higher values of D and t with thinner ®lm. Using this relationship, materials design and operation mode can be optimized in terms of D and t. Regarding the validity of the present analysis, the obtained di€usion coecient of WO3 is quite comparable with the value determined by other methods. As for other ®lms such as NiO and (CeO2)y (TiO2)1ÿy, there is no comparable data, therefore, rigorous analysis will be carried out in the future.

References [1] R. Tamamushi, Electrochemistry, Tokyo Kagaku Dojin, Tokyo, 1967. [2] R. Tamamushi, Foundation of Electrode Reaction, Kyoritu Shuppan, Tokyo, 1977. [3] J. Nagai, Proc. SPIE 302 (1988) 28. [4] J. Nagai, Solar Energy Mater. Solar Cells 31 (1993) 291. [5] L. Kullman, A. Azens, C.G. Granqvist, J. Appl. Phys. 81 (1997) 8002. [6] T. Seike, J. Nagai, Solar Energy Mater. 22 (1991) 107. [7] H.S. Carslaw, Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford, 1959. [8] A. Hubbard, F.C. Anson, in: A.J. Bard (Ed.), Electroanalytical Chemistry, vol.4, Marcel Dekker Inc, New York, 1970, p. 214.