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Determination of Sublimation Enthalpy and Vapor Pressure for Inorganic and Metal-Organic Compounds by Thermogravimetric Analysis

Module by: Andrew R. Barron. E-mail the author

Introduction

Metal compounds and complexes are invaluable precursors for the chemical vapor deposition (CVD) of metal and non-metal thin films. In general, the precursor compounds are chosen on the basis of their relative volatility and their ability to decompose to the desired material under a suitable temperature regime. Unfortunately, many readily obtainable (commercially available) compounds are not of sufficient volatility to make them suitable for CVD applications. Thus, a prediction of the volatility of a metal-organic compounds as a function of its ligand identity and molecular structure would be desirable in order to determine the suitability of such compounds as CVD precursors. Equally important would be a method to determine the vapor pressure of a potential CVD precursor as well as its optimum temperature of sublimation.

It has been observed that for organic compounds it was determined that a rough proportionality exists between a compound’s melting point and sublimation enthalpy; however, significant deviation is observed for inorganic compounds.

Enthalpies of sublimation for metal-organic compounds have been previously determined through a variety of methods, most commonly from vapor pressure measurements using complex experimental systems such as Knudsen effusion, temperature drop microcalorimetry and, more recently, differential scanning calorimetry (DSC). However, the measured values are highly dependent on the experimental procedure utilized. For example, the reported sublimation enthalpy of Al(acac)3 (Figure 1a, where M = Al, n = 3) varies from 47.3 to 126 kJ/mol.

Figure 1: Structure of a typical metal β-diketonate complex. (a) acetylacetonate (acac); (b) trifluoro acetylacetonate (tfac), and (c) hexafluoroacetylacetonate (hfac).
Figure 1 (Fig28.jpg)

Thermogravimetric analysis offers a simple and reproducible method for the determination of the vapor pressure of a potential CVD precursor as well as its enthalpy of sublimation.

Determination of sublimation enthalpy

The enthalpy of sublimation is a quantitative measure of the volatility of a particular solid. This information is useful when considering the feasibility of a particular precursor for CVD applications. An ideal sublimation process involves no compound decomposition and only results in a solid-gas phase change, i.e., Equation 1.

graphics2.jpg
(1)

Since phase changes are thermodynamic processes following zero-order kinetics, the evaporation rate or rate of mass loss by sublimation (msub), at a constant temperature (T), is constant at a given temperature, Equation 2. Therefore, the msub values may be directly determined from the linear mass loss of the TGA data in isothermal regions.

graphics3.jpg
(2)

The thermogravimetric and differential thermal analysis of the compound under study is performed to determine the temperature of sublimation and thermal events such as melting. Figure 2 shows a typical TG/DTA plot for a gallium chalcogenide cubane compound (Figure 3).

Figure 2: A typical thermogravimetric/differential thermal analysis (TG/DTA) analysis of [(EtMe2C)GaSe]4, whose structure is shown in Figure 3. Adapted from E. G. Gillan, S. G. Bott, and A. R. Barron, Chem. Mater., 1997, 9, 3, 796.
Figure 2 (graphics4.jpg)
Figure 3: Structure of gallium chalcogenide cubane compound, where E = S, Se, and R = CMe3, CMe2Et, CEt2Me, CEt3.
Figure 3 (graphics5.jpg)

Data collection

In a typical experiment 5 - 10 mg of sample is used with a heating rate of ca. 5 °C/min up to under either a 200-300 mL/min inert (N2 or Ar) gas flow or a dynamic vacuum (ca. 0.2 Torr if using a typical vacuum pump). The argon flow rate was set to 90.0 mL/min and was carefully monitored to ensure a steady flow rate during runs and an identical flow rate from one set of data to the next.

Once the temperature range is defined, the TGA is run with a preprogrammed temperature profile (Figure 4). It has been found that sufficient data can be obtained if each isothermal mass loss is monitored over a period (between 7 and 10 minutes is found to be sufficient) before moving to the next temperature plateau. In all cases it is important to confirm that the mass loss at a given temperature is linear. If it is not, this can be due to either (a) temperature stabilization had not occurred and so longer times should be spent at each isotherm, or (b) decomposition is occurring along with sublimation, and lower temperature ranges must be used. The slope of each mass drop is measured and used to calculate sublimation enthalpies as discussed below.

Figure 4: A typical temperature profile for determination of isothermal mass loss rate.
Figure 4 (graphics6.jpg)

As an illustrative example, Figure 5 displays the data for the mass loss of Cr(acac)3 (Figure 1a, where M = Cr, n = 3) at three isothermal regions under a constant argon flow. Each isothermal data set should exhibit a linear relation. As expected for an endothermal phase change, the linear slope, equal to msub, increases with increasing temperature.

Figure 5: Plot of TGA results for Cr(acac)3 performed at different isothermal regions. Adapted from B. D. Fahlman and A. R. Barron, Adv. Mater. Optics Electron., 2000, 10, 223.
Figure 5 (graphics7.jpg)

Note:

Samples of iron acetylacetonate (Figure 1a, where M = Fe, n = 3) may be used as a calibration standard through ΔHsub determinations before each day of use. If the measured value of the sublimation enthalpy for Fe(acac)3 is found to differ from the literature value by more than 5%, the sample is re-analyzed and the flow rates are optimized until an appropriate value is obtained. Only after such a calibration is optimized should other complexes be analyzed. It is important to note that while small amounts (< 10%) of involatile impurities will not interfere with the ΔHsub analysis, competitively volatile impurities will produce higher apparent sublimation rates.

It is important to discuss at this point the various factors that must be controlled in order to obtain meaningful (useful) msub data from TGA data.

  1. The sublimation rate is independent of the amount of material used but may exhibit some dependence on the flow rate of an inert carrier gas, since this will affect the equilibrium concentration of the cubane in the vapor phase. While little variation was observed we decided that for consistency msub values should be derived from vacuum experiments only.
  2. The surface area of the solid in a given experiment should remain approximately constant; otherwise the sublimation rate (i.e., mass/time) at different temperatures cannot be compared, since as the relative surface area of a given crystallite decreases during the experiment the apparent sublimation rate will also decrease. To minimize this problem, data was taken over a small temperature ranges (ca. 30 °C), and overall sublimation was kept low (ca. 25% mass loss representing a surface area change of less than 15%). In experiments where significant surface area changes occurred the values of msub deviated significantly from linearity on a log(msub) versus 1/T plot.
  3. The compound being analyzed must not decompose to any significant degree, because the mass changes due to decomposition will cause a reduction in the apparent msub value, producing erroneous results. With a simultaneous TG/DTA system it is possible to observe exothermic events if decomposition occurs, however the clearest indication is shown by the mass loss versus time curves which are no longer linear but exhibit exponential decays characteristic of first or second order decomposition processes.

Data analysis

The basis of analyzing isothermal TGA data involves using the Clausius-Clapeyron relation between vapor pressure (p) and temperature (T), Equation 3, where ∆Hsub is the enthalpy of sublimation and R is the gas constant (8.314 J/K.mol).

graphics8.jpg
(3)

Since msub data are obtained from TGA data, it is necessary to utilize the Langmuir equation, Equation 4, that relates the vapor pressure of a solid with its sublimation rate.

graphics9.jpg
(4)

After integrating Equation 3 in log form, substituting in Equation 4, and consolidating the constants, one obtains the useful equality, Equation 5.

graphics10.jpg
(5)

Hence, the linear slope of a log(msubT1/2) versus 1/T plot yields ΔHsub. An example of a typical plot and the corresponding ΔHsub value is shown in Figure 6. In addition, the y intercept of such a plot provides a value for Tsub, the calculated sublimation temperature at atmospheric pressure.

Figure 6: Plot of log(msubT1/2) versus 1/T and the determination of the ΔHsub (112.6 kJ/mol) for Fe(acac)3 (R2 = 0.9989). Adapted from B. D. Fahlman and A. R. Barron, Adv. Mater. Optics Electron., 2000, 10, 223.
Figure 6 (graphics11.jpg)

Table 1 lists the typical results using the TGA method for a variety of metal β-diketonates, while Table 2 lists similar values obtained for gallium chalcogenide cubane compounds.

Table 1: Selected thermodynamic data for metal β-diketonate compounds determined from thermogravimetric analysis. Data from B. D. Fahlman and A. R. Barron, Adv. Mater. Optics Electron., 2000, 10, 223.
Compound ΔHsub (kJ/mol) ΔSsub (J/K.mol) Tsub calc. (°C) Calculated vapor pressure @ 150 °C (Torr)
Al(acac)3 93 220 150 3.261
Al(tfac)3 74 192 111 9.715
Al(hfac)3 52 152 70 29.120
Cr(acac)3 91 216 148 3.328
Cr(tfac)3 71 186 109 9.910
Cr(hfac)3 46 134 69 29.511
Fe(acac)3 112 259 161 2.781
Fe(tfac)3 96 243 121 8.340
Fe(hfac)3 60 169 81 25.021
Co(acac)3 138 311 170 1.059
Co(tfac)3 119 295 131 3.319
Co(hfac)3 73 200 90 9.132
Table 2: Selected thermodynamic data for gallium chalcogenide cubane compounds determined from thermogravimetric analysis. Data from E. G. Gillan, S. G. Bott, and A. R. Barron, Chem. Mater., 1997, 9, 3, 796.
Compound ∆Hsub (kJ/mol) ∆Ssub (J/K. mol) Tsub calc. (°C) Calculated vapor pressure @ 150 °C (Torr)
[(Me3C)GaS]4 110 300 94 22.75
[(EtMe2C)GaS]4 124 330 102 18.89
[(Et2MeC)GaS]4 137 339 131 1.173
[(Et3C)GaS]4 149 333 175 0.018
[(Me3C)GaSe)]4 119 305 116 3.668
[(EtMe2C)GaSe]4 137 344 124 2.562
[(Et2MeC)GaSe]4 147 359 136 0.815
[(Et3C)GaSe]4 156 339 189 0.005

A common method used to enhance precursor volatility and corresponding efficacy for CVD applications is to incorporate partially (Figure 1b) or fully (Figure 1c) fluorinated ligands. As may be seen from Table 1 this substitution does results in significant decrease in the ΔHsub, and thus increased volatility. The observed enhancement in volatility may be rationalized either by an increased amount of intermolecular repulsion due to the additional lone pairs or that the reduced polarizability of fluorine (relative to hydrogen) causes fluorinated ligands to have less intermolecular attractive interactions.

Determination of sublimation entropy

The entropy of sublimation is readily calculated from the ΔHsub and the calculated Tsub data, Equation 6.

graphics12.jpg
(6)

Table 1 and Table 2 show typical values for metal β-diketonate compounds and gallium chalcogenide cubane compounds, respectively. The range observed for gallium chalcogenide cubane compounds (ΔSsub = 330 ±20 J/K.mol) is slightly larger than values reported for the metal β-diketonates compounds (ΔSsub = 130 - 330 J/K.mol) and organic compounds (100 - 200 J/K.mol), as would be expected for a transformation giving translational and internal degrees of freedom. For any particular chalcogenide, i.e., [(R)GaS]4, the lowest ΔSsub are observed for the Me3C derivatives, and the largest ΔSsub for the Et2MeC derivatives, see Table 2. This is in line with the relative increase in the modes of freedom for the alkyl groups in the absence of crystal packing forces.

Determination of vapor pressure

While the sublimation temperature is an important parameter to determine the suitability of a potential precursor compounds for CVD, it is often preferable to express a compound's volatility in terms of its vapor pressure. However, while it is relatively straightforward to determine the vapor pressure of a liquid or gas, measurements of solids are difficult (e.g., use of the isoteniscopic method) and few laboratories are equipped to perform such experiments. Given that TGA apparatus are increasingly accessible, it would therefore be desirable to have a simple method for vapor pressure determination that can be accomplished on a TGA.

Substitution of Equation 2 into Equation 4 allows for the calculation of the vapor pressure (p) as a function of temperature (T). For example, Figure 7 shows the calculated temperature dependence of the vapor pressure for [(Me3C)GaS]4. The calculated vapor pressures at 150 °C for metal β-diketonates compounds and gallium chalcogenide cubane compounds are given in Table 1 and Table 2.

Figure 7: A plot of calculated vapor pressure (Torr) against temperature (K) for [(Me3C)GaS]4. Adapted from E. G. Gillan, S. G. Bott, and A. R. Barron, Chem. Mater., 1997, 9, 3, 796.
Figure 7 (graphics13.jpg)

The TGA approach to show reasonable agreement with previous measurements. For example, while the value calculated for Fe(acac)3 (2.78 Torr @ 113 °C) is slightly higher than that measured directly by the isoteniscopic method (0.53 Torr @ 113 °C); however, it should be noted that measurements using the sublimation bulb method obtained values much lower (8 x 10-3 Torr @ 113 °C). The TGA method offers a suitable alternative to conventional (direct) measurements of vapor pressure.

Bibliography

  • P. W. Atkins, Physical Chemistry, 5th ed., W. H. Freeman, New York (1994).
  • G. Beech and R. M. Lintonbon, Thermochim. Acta, 1971, 3, 97.
  • B. D. Fahlman and A. R. Barron, Adv. Mater. Optics Electron., 2000, 10, 223.
  • E. G. Gillan, S. G. Bott, and A. R. Barron, Chem. Mater., 1997, 9, 3, 796.
  • J. O. Hill and J. P. Murray, Rev. Inorg. Chem., 1993, 13, 125.
  • J. P. Murray, K. J. Cavell and J. O. Hill, Thermochim. Acta, 1980, 36, 97.
  • M. A. V. Ribeiro da Silva and M. L. C. C. H. Ferrao, J. Chem. Thermodyn., 1994, 26, 315.
  • R. Sabbah, D. Tabet, S. Belaadi, Thermochim. Acta, 1994, 247, 193.
  • L. A. Torres-Gomez, G. Barreiro-Rodriquez, and A. Galarza-Mondragon, Thermochim. Acta, 1988, 124, 229.

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