Thermodynamic study of CVD–ZrO2 phase diagrams

Journal of Alloys and Compounds 483 (2009) 394–398

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Thermodynamic study of CVD–ZrO2 phase diagrams A.M. Torres-Huerta a,∗ , J.R. Vargas-García b , M.A. Domínguez-Crespo a , J.A. Romero-Serrano b a b

Research Center for Applied Science and Advanced Technology, Altamira-IPN, Altamira C.P.89600 Tamaulipas, Mexico Dept of Metallurgical Eng., ESIQIE-IPN, Mexico 07300 D.F., Mexico

a r t i c l e

i n f o

Article history: Received 30 August 2007 Received in revised form 23 July 2008 Accepted 2 August 2008 Available online 14 November 2008 Keywords: Zirconia CVD Zr(acac)4 reaction Thermodynamics

a b s t r a c t Chemical vapor deposition (CVD) of zirconium oxide (ZrO2 ) from zirconium acetylacetonate Zr(acac)4 has been thermodynamically investigated using the Gibbs’ free energy minimization method and the FACTSAGE program. Thermodynamic data Cp◦ , H◦ and S◦ for Zr(acac)4 have been estimated using the Meghreblian–Crawford–Parr and Benson methods because they are not available in the literature. The effect of deposition parameters, such as temperature and pressure, on the extension of the region where pure ZrO2 can be deposited was analyzed. The results are presented as calculated CVD stability diagrams. The phase diagrams showed two zones, one of them corresponds to pure monoclinic phase of ZrO2 and the other one corresponds to a mix of monoclinic phase of ZrO2 and graphite carbon. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Zirconia (ZrO2 ) films have been widely studied for thermal barrier coatings, high-temperature optical filters, oxygen sensors and fuel cells applications, due to their low thermal conductivity, high refraction index and high ionic conductivity [1]. Pure ZrO2 exists at atmospheric pressure in three different phases. The monoclinic phase (Baddeleyite) is stable up to 1170 ◦ C, and then a reversible martensitic transformation to the tetragonal form occurs, which is stable up to 2370 ◦ C. Above this temperature (2370 ◦ C) up to the melting point at 2680 ◦ C, the cubic phase exists, which is the phase required in electrochemical devices because of its higher ionic conductivity [1]. To stabilize the cubic phase at room temperature, some cations such as Ca2+ , Mg2+ , and Y3+ are added during the synthesis of the ZrO2 thin films [1,2]. Some groups have reported the stabilization of a mix of cubic and tetragonal phases [3–8]. However, cubic phase without foreign cations has been obtained in spite of instability at room temperature [9–11]. This has been explained by the presence of internal stress and/or ultrafine grain size produced during films formation. Many different techniques such as sol–gel, evaporation, sputtering, atomic layer deposition (ALD), and chemical vapor deposition (CVD) [12] have been used to produce ZrO2 thin films. Quality and properties of the ZrO2 thin films strongly depend on deposition method and the process parameters. CVD has been used to produce ZrO2 thin films for electrochemical devices

∗ Corresponding author. Tel.: +52 55 57 29 6000x87523. E-mail addresses: [email protected], [email protected] (A.M. Torres-Huerta). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.08.128

and thermal barriers coatings [1] and seems to be a very promising and competitive method for electronic and optical device applications. Because the chemistry and growth mechanisms during the CVD film synthesis are complicated processes, a CVD thermodynamic study will help to predict the nature of the solid species that will form the films, under given conditions of temperature, pressure and initial reagent quantities [13,14]. Furthermore, CVD optimization will be difficult to attain the desirable product yield, composition, surface morphology or thickness. A great number of experiments are required to determine the optimal operation conditions such as deposition temperature, total pressure, and partial pressures. Therefore, the thermodynamic simulation is a method to optimize the CVD process avoiding experimentation based on trial and error [15]. All of the three phases of ZrO2 (monoclinic, tetragonal and cubic) are reported in the literature but only a few models of thermodynamic ZrO2 CVD films have been published [16,17]. In previous works [4,5], ZrO2 , IrO2 and Pt thin films have been synthesized by CVD process and now, as a continuation of these works, a thermodynamic study to explain the phase and the conditions that promote the formation of pure ZrO2 from a ␤-diketonate precursor (Zr-acetylacetonate, Zr(acac)4 ) and oxygen (O2 ) as carrier/reactive gas, is carried out from the estimation of thermodynamic data (Cp◦ , H◦ and S◦ at 298 K). 2. Thermodynamic calculations The thermodynamic calculations (FACTSAGE software [18]) are based on the Gibbs free energy minimization method, in which the concentration of the chemical species at equilibrium is

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Table 1 Chemical species considered during thermodynamic calculations. Species H2 H2 O CO2 CH4 CO CH3 COOH CH2 CO O2 C

ZrO2 Zr(acac)4 C graphite(s) C diamond(s2) ZrO2 monoclinic(s) ZrO2 tetragonal(s2) ZrO2 cubic(s3) Zr(s) Zr(s2)

estimated as a function of temperature, total pressure and concentration of reactants. The reactant substances included in the calculations were oxygen (O2(g) ) and the metal–organic precursor zirconium acetylacetonate [Zr(acac)4(s) ], which is attractive for CVD due to its high volatility and thermal stability. As the standard enthalpy of formation (H◦ ), standard entropy (S◦ ) and heat capacity (Cp◦ ) for Zr(acac)4 are not available in the literature, the Meghreblian–Crawford–Parr [19] and Benson’s [20] methods were used to estimate them. The gaseous and solid chemical species considered in the calculations are summarized in Table 1. These include the significant decomposition products of several metalacetylacetonates reported in the literature [21–25]. 2.1. Cp◦ , H◦ and S◦ estimation The heat capacity (Cp◦ ) was estimated by using the Dobratz equation (1) along with the Meghreblian recommendations for the characteristic stretching- and bending-vibrational frequencies ( and ı) and the analysis of Crawford and Parr [19], which leads to the typical equation of the heat capacity as a function of temperature (2). The frequencies ( and ı) are characteristic of the type of bond in a molecule. The low pressure heat capacities of pure vapor and gases may be estimated with good accuracy with this method [19]. Cp◦ = 4R +

 +

m 2

R+



3n − 6 − m −



qi

C␦i can be estimated C␯i , C␦i = A + BT + CT 2

(2)

Fig. 1 shows the Zr(acac)4 formula, together with the kind of bonds in the molecule [25]. The heat capacity constants (A, B and C) and bond frequencies for every bond type in the Zr(acac)4 molecule are summarized in Table 2 [19]. Because of no bond frequency data exist for O–metal bonds, to overcome this problem in the calculations, the constant values of O–H bond were used instead of those of the O–Zr bond, based on the hydrogen-like approximation for higher electronic states. This approximation is found on the fact that as the atom approaches the ionized state, the effective core charge approaches 1, and the structure becomes hydrogen-like.  From the Zr(acac)4 molecule, m = 16, n = 57 and qi = 56. Using, the A, B and C values from Table 2, Cvi and C␦i functions were determined and substituted in Eq. (1). Thus, a typical heat capacity Eq. (3) as a function of temperature for Zr(acac)4 molecule can be obtained: Cp◦ = −24.4438 + 395.3988 × 10−3 T

qi Cvi

 

Fig. 1. Zr(acac)4 formula [26].



qi

−145.0630 × 10−6 T 2 , cal mol−1 K−1 qi C␦i

(1)

where Cp◦ is the gas heat capacity (cal/mol K); R is the gas constant, 1.987 cal/mol K; m is the number of single bonds about which internal rotation of groups can take place (e.g., C–C or C–O in esters or ethers); qi is the number of bonds of the ith type; n is the number of atoms in the molecule; qi is the total number of bonds in the molecule; Cvi , C␦i are the Einstein functions for the bonds of the ith type;  and ı are the characteristic frequencies for longitudinal and transversal vibrations, respectively, s−1 . From Eq. (2), Cvi and

(3)

The standard enthalpy (H◦ ) and standard entropy (S◦ ) for Zr(acac)4 were estimated using the Benson method [20], which involves both the bond types and the functional groups present in the molecule. This method leads to a good approximation to experimental H◦ and S◦ results for many organic compounds including the Zr(acac)4 [19]. Fig. 1 indicates the functional groups identified in the Zr(acac)4 molecule and Table 3 displays a description of the groups and the H ◦ f 298 K and S ◦ 298 K values considered in the thermodynamic calculations. In this study, (III) group CO–(Cd )(C) was substituted by CO–(C)2 group; (VI) group, O–(Cd )(Zr) was substi-

Table 2 Heat capacity values according to the type of bond [19]. Bond type

C–C C C C–O C O C–H O–Zr

i

910 1200 1030 1740 3000 3500

ıi

C␯i , stretching A

B × 103

C × 106

−0.339 −0.740 −0.458 −0.778 −0.139 0.000

3.564 3.730 3.722 2.721 0.168 −0.240

−1.449 −1.404 −1.471 −0.759 0.447 0.560

O–Zr bond values correspond to O–H bond.

650 910 1120 780 1050 1350

C␦i , bending A

B × 103

C × 106

0.343 −0.339 −0.665 −0.034 −0.579 −0.819

2.707 3.564 3.757 3.220 3.741 3.563

−1.150 −1.449 −1.449 −1.341 −1.471 −1.267

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Table 3 H ◦ f and S ◦ 298 K for the functional groups in Zr(acac)4 molecule. Groups

Nomenclature

Description

Number of groups in the molecule

H ◦ f 298 K (kcal/mol)

S ◦ 298 K (cal/gmol K)

I II III IV V VI VII

C–(CO)(H)3 C–(Cd )(H)3 CO–(Cd )(C) Cd –(CO)(H) Cd –(O)(C) O–(Cd )(Zr) Zr–(O)4

C bonded to a CO group and 3 H C bonded to C with double bond and 3 H CO group bonded to C and C with double bond C with double bond joined to a CO and a H C with double bond joined to an O and C O bonded to a C with double bond and Zr Zr bonded to 4 O

4 4 4 4 4 4 1

−10.1 −10.08 −31.5 8.5 10.3 −23.5 −157.0

30.41 30.41 15.01 – – – –

Cd represents carbon atom that is joined to another carbon atom by a double bond.

tuted by O–(Ti)(C) group; (VII) group, Zr–(O)4 was substituted by Ti–(O)4 group. As the Benson method suggests, groups having the same type of bonds or elements of the same group in the periodic table can be substituted. Thus, using the H◦ values from Table 3, one obtains: H ◦ 298 K = −382, 520 cal mol−1

(4)

A symmetry correction factor for S◦ values is required: (−R ln ). Where  is the total number of independent permutations of identical atoms (or groups) in a molecule that can represent the entire molecule by simple rigid rotations. Inversion is not allowed.  function is separated in two components:  =  ext  int . From Zr(acac)4 molecule,  ext = 4 and  int = 38 . Therefore, using the S◦ values from Table 3 and : S ◦ 298 K = 283.102 cal mol−1 K−1

(5)

Furthermore,



H ◦ T = H ◦ 298.15 K +

T

Cp dT

(6)

298.15 K

H ◦ T = −391, 524.6947 − 24.4438T + 0.1977T 2 −4.8354 × 10−5 T 3 , cal mol−1 and, S

◦

T



=S

◦

298.15 K

T

+ 298.15 K

Cp dT T

(7)

(8)

S ◦ T = 310.9323 − 24.4438 ln T + 395.3988 × 10−3 T −7.2531 × 10−5 T 2 , cal mol−1 K−1

(9)

Fig. 2. ZrO2 –CVD diagrams calculated as a function of partial pressures of Zr(acac)4 and O2 for temperatures: (a) 300 ◦ C; (b) 400 ◦ C; (c) 500 ◦ C; (d) 600 ◦ C; (e) 700 ◦ C; (f) 800 ◦ C and total pressures: 0.1, 1.0, 10.0 and 100.0 Torr.

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Eqs. (3)–(5) as well as those corresponding to all substances considered in the system, are the basis to calculate the concentration of the gaseous and solid chemical species in equilibrium, following the Gibbs free energy minimization method. Considering that Eqs. (3), (7) and (9) were obtained on the basis that equilibrium is reached in the system, which is rarely the case in a CVD process, it is clear that the thermodynamic calculations performed in this work can only give fundamental information that enhance the understanding of CVD process. However this information can be used as a prediction of the trends when experimental conditions are modified [13,14,16].

incorporation in ZrO2 films can be withdrawn with a ratio of PO2 /PZr(acac)4 > 100, due to the formation of CO and CO2 gases by adjusting temperature. This behaviour may be explained if it is considered that Zr(acac)4 molecule contains a large carbon quantity then, in practice to reach a complete reaction an excess of oxygen is required, in addition the molecular decomposition is favoured at greater temperatures. According to the thermodynamic prediction, this study is suitable for a wide total pressure range (0.1–100 Torr) and deposition temperature range (300–800 ◦ C).

2.2. CVD diagrams

3. Conclusions

Fig. 2 shows the ZrO2 –CVD diagrams calculated as a function of partial pressures of Zr(acac)4 and O2 for temperatures between 300 and 800 ◦ C and total pressure range from 0.1 to 100 Torr. For each total pressure and temperature, CVD diagrams display two stability regions; the two-phase area consisted of the monoclinic ZrO2 phase and C (graphite), and the single-phase area corresponding to monoclinic ZrO2 phase. In general, it can be seen that for the pressure between 0.1 and 10.0 Torr, the obtaining of pure ZrO2 shows similar trend before reaching 500 ◦ C. Temperatures higher than 500 ◦ C for 0.1 Torr and 600 ◦ C for 1 and 10 Torr displayed a fairly constant behaviour. i.e., the zones are not changing anymore. On the other hand, at 100 Torr, an opposite behaviour is observed during thermodynamic calculations. A constant shape of the curves was observed at 300, 400 and 500 ◦ C, but important changes can be appreciated from 600 ◦ C (Fig. 2). The results indicate that the ZrO2 films grown under the CVD typical conditions will be invariantly constituted by the monoclinic phase, which is the stable phase at low temperatures. On the other hand, experimental results of several authors, including own results, report the presence of the cubic and tetragonal phases in ZrO2 films [4,5,9–11], obtained without the addition of cations that help to stabilize the cubic phase. The authors agree to report that ZrO2 films are constituted by particles of nanometric size (∼20 nm), and they are attributing the stability of the cubic and tetragonal phases to the ultrafine size of the particles and to the internal stress in the films. The mismatch between the experimental results and the thermodynamic prediction can be associated to the intrinsic nature of the nanostructured materials which present a high density of interfaces. The effects of surface area are not generally taken into consideration when a condensed phase consists of a single mass or a few large pieces so that the ratio of the surface area to the volume is small. However, the effects become important as the surface to volume ratio becomes significantly large for a given amount of a single or multicomponent condensed phases [28]. In this case, the interface of free energy and the surface tension are thermodynamic quantities with great importance. Furthermore, the stresses originated from the presence of coherent interphases in films and multilayer systems can break the rule of the phases of Gibbs and the rule of the common tangent, used to determine the multiphasic equilibrium from the free energy diagrams versus composition [27,28]. In this work, the contribution of the surface thermodynamic quantities to Gibbs free energy was not considered, which could explain the mismatch with reported experimental results. The CVD diagrams indicate that it is possible to deposit pure ZrO2 from O2 and Zr(acac)4 and that the composition of the film is strongly affected by oxygen partial pressure. Consequently, the obtained ZrO2 –CVD diagrams are useful to know the pressure and temperature ranges and the reactant amounts that can promote the growth of pure ZrO2 films. From the diagrams, carbon

ZrO2 –CVD diagrams were obtained using the Gibbs free energy minimization approach. The thermodynamic functions of Zr(acac)4 precursor were estimated by Meghreblian and Benson methods. From the diagrams, it can be predicted that the films will be constituted only by the monoclinic phase, at sufficiently hightemperature or concentration of the oxygen source. Furthermore, they indicate that is possible to obtain pure ZrO2 films when the O2 partial pressure is higher than the gas precursor partial pressure.

Acknowledgements This study was supported by the National Polytechnic Institute (IPN) of Mexico through the projects SIP-IPN 20072176, 20071120 and SNI-CONACyT.

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