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Transformation kinetics for low temperature post-deposition crystallization of TiO₂ thin films prepared via atomic layer deposition (ALD) from tetrakis(dimethylamino) titanium(IV) (TDMAT) and water

Jamie P. Wooding,¹ Shawn A. Gregory,¹ Amalie Atassi,¹ Guillaume Freychet,² Kyriaki Kalaitzidou,^3,1 Mark D. Losego¹

¹School of Materials Science and Engineering, Georgia Institute of Technology

Atlanta, GA 30332, United States

²Energy  Sciences   Directorate/Photon   Science  Division, NSLS-II, Brookhaven National Laboratory

Upton, NY 11973, United States

³George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology 

Atlanta, GA 30332, United States

Received July 15 2022. Accepted Sept 24 2022

Abstract

Background: We report on the fundamental crystallization kinetics of atomic layer deposited (ALD) TiO₂ thin films undergoing a post-deposition anneal (PDA) at low temperatures to probe differences in the as-deposited film microstructure.

Methods: The system of study is ALD TiO₂ thin films prepared from tetrakis(dimethylamino)titanium(IV) (TDMAT) and water at 120 °C, 140 °C and 160 °C followed by ex situ low temperature annealing at temperatures ranging from 140 °C to 220 °C. All as-deposited TiO₂ thin films are amorphous by X-ray diffraction (XRD). Post-deposition annealing (PDA) produces large grain anatase crystals, confirmed by XRD and top-view scanning electron microscopy (SEM). A detailed SEM study is performed to quantify the nucleation and growth kinetics by fitting microstructural data to the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation. Finally, a time-temperature-transformation (TTT) diagram is constructed to summarize the differences in crystallization behavior at different ALD deposition temperatures. 

Results and Conclusions: Fitting microstructural data to the JMAK equation reveals an Avrami exponent close to 3 with continuous nucleation, suggesting two-dimensional, plate-like crystal growth. Applying an Arrhenius relationship to the phase transformation data, the combined activation energy for nucleation and growth is found to be 1.40–1.58 eV atom^-1. Nucleation rates are determined, and an Arrhenius relationship is used to calculate the critical Gibbs free energy for nucleation (~1.3-1.4 eV atom^-1). As such, nucleation is the rate-limiting step for the amorphous to anatase phase transformation. ALD growth temperature is found to dictate film microstructure with lower deposition temperatures reducing the nucleation rate and leading to larger grain sizes irrespective of PDA conditions. The nucleation rate pre-exponential frequency factor increases with increasing deposition temperature, thereby increasing the likelihood for nucleation. Interestingly, it is this difference in the vibrational modes of the amorphous structure, as indicated by the variation in the nucleation rate pre-exponential frequency factor, that alters the phase transformation rates and not a change in the activation energies for the transformation. 

1. Introduction

Titanium dioxide (TiO₂) is a wide-bandgap semiconductor with phase-dependent high refractive index and high dielectric constant.^1,2 While the anatase phase is preferred for photocatalysis³ and gas sensing,⁴ rutile is preferred for high-k applications.⁵ Amorphous TiO₂ is preferred for diffusion barriers⁶ and corrosion prevention.⁷ TiO₂ has also been applied in nanolaminates with Al₂O₃ in optical thin film applications,^8,9 and with HfO₂ for increased dielectric permittivity in capacitors.¹⁰ Many applications require uniform TiO₂ thin films that are conformal with precise thickness control.¹¹ Atomic layer deposition (ALD) is a well-known growth process to achieve such thin films. As such, understanding TiO₂ phase control in ALD films is important.

TiO₂-ALD has been studied extensively using TiCl₄ and H₂O as co-reactants.^12-14 For TiCl₄/H₂O ALD chemistry, films are typically reported as being amorphous when deposited at temperatures less than 150 °C, with the onset of anatase phase crystallization around 150 °C^5,14,15  and rutile phase crystallization requiring temperatures of 350 °C¹⁴ or greater.^5,16 ALD TiO₂ films deposited from tetrakis(dimethylamino)titanium(IV) (TDMAT) and H₂O are well-studied but to a lesser extent. TDMAT can be preferred as a precursor over TiCl₄ due to lack of chlorine contamination in the deposited film^17,18 and its so-called “electrically leaky TiO₂” property.¹⁹ However, TDMAT/H₂O films are nearly always amorphous as-deposited,^18,20,21 given that the ALD deposition temperature window is limited by TDMAT’s decomposition temperature of approximately 220 °C.²² Studies on ALD TiO₂ deposited from TDMAT/H₂O report a variety of electronic properties,^7,23 inspiring a report from Babadi et al. probing the gas phase reactions and ALD cycle time.²⁴ However, few studies exist on post-deposition crystallization of TDMAT/H₂O-based ALD TiO₂ thin films,^25-28 and these studies do not go into microstructural detail at low annealing temperatures.

Crystalline as-deposited ALD films often show columnar grains through the film thickness. The grain size is typically less than the film thickness given a high density of nuclei during the initial stage of film growth.²⁹ However, TiO₂ ALD films grown from TiCl₄/H₂O chemistry have been shown to exhibit anatase crystals greater in diameter than the film thickness.^30-32 Large-grained anatase can have improved photoelectrochemical performance^16,33 and photocatalytic activity due to its small grain boundary volume.^3,34 Highly defected grain boundary regions do not contribute to the functional performance of the crystalline film, and so maximizing grain size and minimizing grain boundary volume is essential to optimizing material performance. A literature review of the crystal size to TiO₂ film thickness ratio as a function of deposition temperature for TiCl₄/H₂O and TDMAT/H₂O ALD processes is presented in Figure 1. Reported large-grain TiO₂ processes require deposition temperatures between 200 °C and 300 °C. These reports are primarily for as-deposited films from TiCl₄/H₂O chemistry on both silicon and amorphous-Al₂O₃. Here the resultant TiO₂ anatase grain size to film thickness ratio for films on amorphous-Al₂O₃^30,32 is an order of magnitude greater than for films deposited on silicon,^{15,30,32,35-37} with maximum reported ratio values of 40 and 5 respectively. Large anatase crystal growth is heavily substrate³⁰ and surface energy^31,38 dependent. This phenomenon has yet to be reported using TDMAT/H₂O ALD; as such, in Figure 1, we highlight this work’s contribution to forming large grain anatase from TDMAT/H₂O chemistry by PDA.

Figure 1. Plot of the crystal-size-to-film-thickness ratio as a function of the crystallization temperature compiled from various TiO₂ ALD literature reports. All reports use thermal-ALD with water as the co-reactant. Varying titanium precursor and substrate chemistries are noted by data point shape as indicated in the legend.  Conditions reported include: TiCl₄/H₂O on Si as deposited (black square), TiCl₄/H₂O on Al₂O₃ as deposited (green square), TiCl₄/H₂O on Al₂O₃ with PDA (circled green square), TDMAT/H₂O on Si as deposited (red circle), and TDMAT/H₂O on Si with PDA, which are the results from this study (circled red star). Films that undergo PDA are all circled in blue.

Other reports have probed resultant ALD-TiO₂ film structure with post-deposition annealing (PDA).^5,14,33,37 PDA temperatures are typically higher than those used for the ALD growth process. Amorphous as-deposited films are crystallized to anatase at PDA temperatures of 700 °C or lower.  PDA of films at temperatures ranging from 300 to 800 °C have been reported to decrease impurity concentrations and increase crystalline phases.³⁹ Annealing atmosphere is also significant. Jogi et al. found that annealing at 750 °C in 1 atm O₂ for 10 min promoted crystallization into the anatase phase.⁵ Luka et al. performed the most comprehensive PDA study at 160 – 220 °C on thick films (4000, 7000, and 10000 ALD cycles) in N₂ environment and proposed that anatase regions in the as-deposited film grow into the surrounding amorphous regions to transform the films during PDA. However, Aarik et al. found that annealing amorphous films at 400 °C in air and N₂ for 6 hours did not cause a phase transformation, attributing this to chlorine residue in the film.¹⁴ Iancu et al., annealing 30 nm amorphous TiO₂ films from TDMAT/H₂O found that O₂ PDA at 700 °C and higher was more effective in forming rutile than N₂ PDA.²⁷

Here, we describe the first detailed study of anatase formation in TiO₂ thin films deposited on a silicon wafer substrate from TDMAT/H₂O thermal ALD and post-deposition annealing (PDA) in air. This study provides new information on TiO₂ crystal growth during post-deposition annealing and challenges the present understanding of the temperatures required for crystallization to occur. The temperature-dependent crystallization kinetics presented are determined from an array of deposition and annealing temperatures. Using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation, the Avrami exponent is calculated and the low-temperature anatase crystal growth mode is identified. Further, the activation energy for anatase nucleation and growth is calculated, nucleation rates are determined, and the critical Gibbs free energy for nucleation is deconvoluted from the activation energy for crystal growth. This study advances understanding of the amorphous to crystalline phase transformation in ALD TiO₂ thin films and identifies how the as-deposited amorphous structure of a film can influence crystallization kinetics and final film microstructure. 

1. Experimental

2.1 ALD conditions

ALD was conducted in a home-built, hot-walled, flow-tube reactor with custom LabVIEW control software.⁴⁰ Nitrogen (99.999% purity, Airgas) was used as the carrier gas at a constant flow rate of 90 sccm, resulting in a chamber pressure of 1.15 Torr. For all ALD processing, the deposition region was held, as specified, at 120 °C, 140 °C, or 160 °C and all gas process lines were maintained at 110 ˚C. Depositions were performed on 1 cm x 1 cm Si substrates containing their native oxide layer (WRS Materials, P/Boron<100>, 0-100 Ω). All silicon surfaces were first cleaned with a 5-minute air plasma treatment (Expanded Plasma Cleaner PDC-001, Harrick Plasma) with RF level high, to remove the adventitious carbon and leave a native oxide thickness of approximately 1.7 nm as determined by spectroscopic ellipsometry.

Tetrakis(dimethylamino)titanium(IV) (TDMAT, 99% purity) from Strem Chemicals, Inc. (Newburyport, MA, USA) and deionized water were used as the precursor and co-reactant for ALD of TiO₂ films. TDMAT was dosed in a bubbler configuration with delivery lines to the reactor heated to 82 °C. Each ALD cycle used a deposition sequence of 1.0 s TDMAT / 5 s N₂ purge / 0.4 s H₂O / 85 s N₂ purge. For all conditions, 1120 ALD cycles were deposited to yield 50 nm to 58 nm TiO₂ films. ALD growth per cycle (GPC) values varied from 0.44 Å to 0.54 Å and are presented in SI Figure 1a. The GPC decreased with increasing ALD temperature, which is consistent with literature reports for TDMAT/H₂O thermal ALD.^36,41 SI Figure 1b presents index of refraction, n, values measured at 550 nm for the as-deposited and annealed films. For TiO₂ films deposited at each ALD temperature, annealing increased the refractive index, as expected. Refractive index values measured at 550 nm approached 2.55 after PDA, which is close to literature reported refractive index values of 2.6 for anatase.⁴² As detailed in Table 1, in this work two experimental parameters were explored: (1) varying the deposition temperature between 120 °C and 160 °C and (2) varying the ex situ post deposition anneal (PDA) temperature from 140 °C to 220 °C. PDA was performed in an oven in air at atmospheric pressure. Room temperature TiO₂ films on Si were placed into a pre-heated oven at the target annealing temperature. At the end of the desired anneal period, the TiO₂ films were removed from the oven and passively cooled to room temperature. The TiO₂ films were imaged by SEM periodically throughout the annealing process to measure the increasing percent crystallinity. Once the film achieved >95% percent crystallinity by image analysis of SEM micrographs, we defined that as “apparent full crystallinity” and stopped continuing the annealing process.

Table 1. The range of ALD temperatures (120 °C, 140 °C, and 160 °C)  and subsequent PDA temperatures (140 °C to 220 °C ) studied in this work

1. Characterization

Spectroscopic ellipsometry (alpha-SE, J.A. Woollam) was used to measure film thickness and index of refraction at 550 nm. A CodyLor model was used to describe the TiO₂ layer on top of the native oxide layer on a Si substrate. Before ALD, the measured SiO₂ native oxide layer on Si was approximately 1.7 nm, determined by modeling a native oxide layer on Si in J.A. Woollam’s CompleteEASE software. Grazing incidence X-ray diffraction (GIXRD) was used to identify the crystalline phase of the deposited films. GIXRD was conducted on a PANalytical Empyrean system using Cu-Kα radiation, a BBHD source optic, and a PIXcel 2-dimensional detector. 2q-w scans were taken. Additionally, grazing incidence wide-angle X-ray scattering (GIWAXS) measurements were performed on a TiO₂ film set for as-deposited, short PDA, and long PDA conditions. GIWAXS was used to verify that the initial crystal growth viewed in SEM is indeed the TiO₂ anatase crystalline phase that is measurable by GIXRD upon further transformation. Measurements were performed at the Soft Matter Interfaces Beamline at the National Synchrotron Light Source II with an incident energy of 12 keV and an incident angle of 0.15 degrees. Scattering patterns were recorded on a Pilatus 900 K−W detector, consisting of 0.172 mm square pixels, mounted at a fixed distance of 0.279 m from the sample position. The range of scattering angles was acquired by moving the detector horizontally on a fixed arc and post-processing the images using Xi CAM software.⁴³ Both the samples holder and the detector were enclosed in a vacuum chamber. 

A Hitachi SU8230 field emission SEM (FE-SEM) operated at 1 kV accelerating voltage and 15-20 µA emission current was used to image microstructure and crystal growth from the secondary electron (SE) signal. In the images, amorphous regions appear dark while crystalline regions tend to appear bright. For each condition, at least two TiO₂ films were prepared and imaged, and images were taken top down at three different lateral locations on the film surface. Image analysis was performed with ImageJ to quantify the crystalline fraction transformed and to determine crystalline area density and size.

1. Results and Discussion

3.1 Controlling grain size in post-deposition annealed films

Figure 2a presents SEM micrographs of as-deposited TiO₂ films compared to PDA films. As-deposited TiO₂ films appear grey in SEM. Small, white surface features, herein called nuclei, are routinely observed and mimic literature reports for very small crystals in otherwise amorphous thin films.^30,32 Films deposited at 160 °C have a higher density of these nuclei compared to films deposited at lower temperatures. Upon post-deposition annealing (PDA) at 200 °C, films deposited at 160 °C develop a fine grain structure with average grain size of 540 nm, while films deposited at 140 °C and 120 °C develop larger grains with average sizes of 1.2 µm and 4.6 µm, respectively. Figure 2b reports representative GIXRD data for the as-deposited and PDA TiO₂ thin films, confirming that as-deposited films are amorphous and PDA films are the anatase crystalline phase. Note here that the small, white features in the amorphous film do not purport a crystalline signature in GIXRD or in the GIWAXS data collected at a synchrotron light source (SI Figure 2). Nor do these small, white surface features seem to be correlated to the subsequent crystal growth; i.e., we do not observe one-to-one matching between nuclei and grains. This is unlike the report from Luka et al. that described TiO₂ anatase expansion from crystalline seeds³⁷ or from Macco et al. that described hydrogen-doped In₂O₃ isotropic crystal growth from a low density of embedded crystallites in a mostly amorphous film.  Thus, these features may be sub-critical nuclei or not nuclei at all, but they are clearly different from prior reports.

Figure 2. a) SEM micrographs for ALD films grown at 120 °C, 140 °C, and 160 °C: as-deposited (left) vs. post-deposition annealed at 200 °C in air (right).  Anneal times to achieve apparent full crystallinity are listed on micrographs. Note the scale bar is different in the 120 °C PDA 200 °C micrograph to capture the large grain size.  b) GIXRD scans for as-deposited and annealed (PDA at 200 °C in air) films deposited at 120 °C, 140 °C, and 160 °C. The three primary TiO₂-anatase peaks are labeled: 2θ = 25.3°, 37.8°, 48.0°. 

Regardless, such large grain growth (>1 mm grain size in ~50 nm thick films) has not been observed before in ALD TiO₂ films using the TDMAT/H₂O chemistry. Further, it is surprising that the resultant microstructure varies so significantly depending on deposition temperature, with grain size decreasing from 4.6 µm to 540 nm with a 40 °C increase in temperature. To provide further insights into this crystallization process and to determine why resultant, annealed microstructure is determined by ALD temperature, we undertake a comprehensive time-dependent study of the crystalline transformation kinetics to understand the underlying activation energies.

3.2 Amorphous to crystalline transformation kinetics

Crystallization kinetics are studied over a range of ALD temperatures and post-deposition annealing (PDA) temperatures. Specifically, TiO₂ films deposited at substrate temperatures of 140 °C and 160 °C are annealed in air at 160 °C, 180 °C, and 200 °C, while TiO₂ films deposited at 120 °C are annealed in air at 180 °C, 200 °C, and 220 °C. Figure 3 presents a representative selection of micrographs used for tracking crystal growth during PDA. Here, the brighter regions are crystalline while the darker regions are amorphous. SI Figure 3 provides a representative crystal growth series for TiO₂ films deposited at 120 °C. SI Figure 4 presents an SEM image and explains the ImageJ processing steps to quantify the percent crystalline phase. Figure 4a-c plots the crystalline fraction transformed determined from this image analysis for TiO₂ films deposited at 120 °C, 140 °C and 160 °C and then annealed at 160 °C, 180 °C, 200 °C, and 220 °C. These data series exhibit the expected S-curve shape and can be fit to the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation.^44-46 The general form of the JMAK equation (Equation 1) is applied to model the fraction transformed to the crystalline phase over PDA time :

Here, is the reaction rate for combined anatase nucleation and growth and is the Avrami exponent, which often characterizes the mechanism and dimensionality of the phase transformation. The JMAK equation as presented in Equation 1 is linearized to the following form:

In plotting vs. , the slope of this line is equal to the Avrami exponent and the y-intercept is equal to . Applying this linearization to both deposition temperatures at each of the three PDA temperatures (Figure 4d-f), and are calculated for each experimentally measured transformation curve. These values are presented in Table 2. 

Figure 3. SEM micrographs for TiO₂ films deposited at a) 140 °C and post-deposition annealed (PDA) at 200 °C for i) 0 h, ii) 3.9 h, and iii) 10 h, at 180 °C for iv) 0 h, v) 12 h, and vi) 47 h, and at 160 °C for vii) 0 h, viii) 110 h, and ix) 327 h. SEM micrographs for TiO₂ films deposited at b) 160 °C and post-deposition annealed (PDA) at 200 °C for i) 0 h, ii) 3.9 h, and iii) 5.9 h, at 180 °C for iv) 0 h, v) 12 h, and vi) 25 h, and at 160 °C for vii) 0 h, viii) 67 h, and ix) 109 h. Annealing time in hours is for the specified time, t, duration.

Figure 4. a) Amorphous TiO₂ to anatase phase transformation curves for films deposited at (a) 120 °C (solid square marker), (b) 140 °C (solid triangle marker) and (c) 160 °C (solid circle marker) and post-deposition annealed at 160 °C (gold-colored), 180 °C (blue-colored), 200 °C (red-colored), and 220 °C (black-colored). The solid lines are the X(t) model fit for the calculated reaction rate k and Avrami exponent n values. Linearized form of the crystalline fraction transformation curves to extract calculated reaction rate k and Avrami exponent n values for films deposited at (d) 120 °C, (e) 140 °C, and (f) 160 °C.

For the complete experimental set, the values for the Avrami exponent vary from 2.31 to 3.39, with an average value of  . The experimental variation in may be attributed to the nature of these ex situ SEM measurements: the film is removed for imaging, which causes small deviations in time and temperature associated with the cooling and re-heating of the film. The Avrami exponent should remain constant despite changes in temperature given no apparent changes in the crystal nucleation and growth mode. Given the similarity in crystalline microstructures, the crystal nucleation and growth mode at these deposition temperatures appears to be constant. The value for the Avrami exponent is dependent on the dimensionality of the product phase, the time dependence of the nucleation, and the time dependence of the rate limiting growth step. The rate-limiting growth step for an amorphous-to-crystalline transformation is the interfacial reaction. Here, nucleation appears to occur continuously with film annealing, rather than all at once. Given these conditions, an Avrami exponent close to 3 is characteristic of a two-dimensional growth mode, indicative of plate-like microstructure observed here where there are micron-sized grains of only 50 nm thickness.^47,48,16 This post-deposition, ex situ two-dimensional grain growth is notably different than the growth mode often proposed for in situ TiO₂ crystal growth during an ALD process, where nucleation of some crystals occurs and growth continues vertically through the film thickness with subsequent deposition cycles.^15,29,30 

Table 2. Calculated Avrami exponent n and reaction rate k for each ALD and PDA condition.

As shown in Table 2, the combined nucleation-growth reaction rate is temperature dependent, increasing with increasing PDA temperature. This result is consistent with crystalline nucleation and growth being thermally activated processes. Interestingly, at a given PDA temperature, the reaction rate increases with increasing deposition temperature. This indicates that the as-deposited amorphous structures vary at the different deposition temperatures, leading to differences in the energy barriers to nucleation and/or growth. In this study, these transformational reaction rates are greater for films deposited at higher ALD temperatures. As such, transformation from the amorphous phase to the anatase phase is more favorable in amorphous TiO₂ deposited at higher temperatures.

To calculate the combined activation energy for nucleation and growth, an Arrhenius relationship^49,50 is applied to the reaction rates k within a given ALD deposition temperature series as follows:

In Equation 5, is the activation energy for crystal nucleation and growth, is the Boltzmann constant, is the annealing temperature, and is a material-dependent frequency factor. The linearized form of Equation 3 is:

 Figure 5 applies the linearized form Equation 4 to make an Arrhenius plot to extract the activation energy for crystal nucleation and growth and the reaction rate frequency factor for each ALD deposition temperature. As seen in Figure 5, the activation energy for anatase phase nucleation and growth is ~1.5 eV atom^-1, which is in agreement with reported literature.³⁷ Surprisingly, this activation energy is independent of ALD deposition temperature; at 120 °C 1.46 eV atom^-1, at 140 °C 1.58 eV atom^-1, and at 160 °C 1.40 eV atom^-1. This result suggests that the change in the transformation process is the result of the pre-exponential factor, . To evaluate , the activation energy is set to the average value of 1.48 eV atom^-1 for all deposition temperatures and the intercepts are evaluated. The reaction rate frequency factor, ,  is a complex factor dependent upon the vibration frequency of the atoms in the as-deposited structure. The reaction rate frequency factor increases with increasing ALD temperature: s^-1 for 120 °C growth temperature, s^-1 for 140 °C growth temperature, and s^-1 for 160 °C growth temperature. The frequency factor order of magnitude is close to that reported in glass science crystallization kinetics literature⁵¹ and agrees with expectations for molecular vibration.

Figure 5. Arrhenius dependence for reaction rate k, relating to the combined activation energy for crystal nucleation and growth.

To better understand how anatase nucleation and growth rates vary as a function of ALD and PDA temperature, we further consider how the reaction rate k from the JMAK equation is defined (Equation 1). Equation 1 presents the generalized form of the JMAK equation. However, in considering a two-dimensional transforming area with continuous nucleation and growth, as is the case in this experimental work, the equation can be given as:

Here, is defined as the nucleation rate and as the crystal growth rate. This derivation is presented in detail in SI Note 1. As such, the reaction rate k is defined as follows:

Recall that the reaction rate k is determined experimentally from the slope equal to in the linearized JMAK equation (Equation 2). By deconvoluting the reaction rate into nucleation rate and crystal growth rate, we can separate nucleation kinetics and crystal growth kinetics.

            To accomplish this deconvolution, crystal nucleation rate is independently determined from short PDA times, prior to impingement of growing crystals. The number of crystals per area in the SEM images are counted at these short PDA times to give a nucleation rate of number of crystals m^-2 s^-1. The instantaneous nucleation rate is plotted on a log scale against PDA temperature as a function of deposition temperature in Figure 6a. For a given annealing temperature at a given deposition temperature, is approximately constant. Nucleation rates increase by just under an order of magnitude with each 20 °C increase in PDA temperature. Films deposited at 160 °C have the greatest nucleation rates and those deposited at 120 °C have the slowest. The nucleation rate, , can be described by an Arrhenius relationship:

In Equation 7,  is the critical Gibbs free energy for nucleation, is the Boltzmann constant, is the PDA temperature, and is the nucleation exponential precursor. Equation 7 is linearized to: 

Here, is equal to where is a frequency factor for the phase transformation and is the concentration of heterogeneous nucleation sites per areal density. The nucleation frequency factor includes the vibrational frequency of the atoms, the area of the critical nucleus, and an activation energy for atomic migration.⁵² This Arrhenius relationship is plotted in Figure 6b to calculate frequency factor for . As presented in Table 2, the critical free energy for nucleation, , for films deposited at 160 °C is 1.32 eV atom^-1,for films deposited at 140 °C is 1.35 eV atom^-1, and for films deposited at 120 °C is 1.41 eV atom^-1. Considering the error presented in Table 2, these critical free energy values for nucleation are roughly equivalent. 

            As seen in Figure 6b, the y-intercept increases with increasing deposition temperature. Therefore, the nucleation frequency factor, , also increases, as with the reaction rate frequency factor, . This increased nucleation frequency factor at higher deposition temperatures is consistent and designates a fundamental difference in the structure between the as-deposited ALD TiO₂ thin films. Previous studies have reported property variations in amorphous TiO₂ films as a function of ALD temperature that could be indicative of thin film structural differences. Piercy et al. found increasing density in amorphous TiO₂ from ALD temperatures 38 °C  to 150 °C⁵³ and DeCoster et al. found thermal conductivity also increased with increasing deposition temperature for amorphous TiO₂ thin films.⁵⁴ Increasing thermal conductivity is indicative of increasing vibrational modes in the material. From the present study, an increased nucleation frequency factor indicates that there is a greater frequency of attempts to form anatase nuclei of critical size, therefore aligning with increased vibrational motion at higher deposition temperatures. This result could also inform a recent literature report that describes how increasing the ALD growth temperature from 100 to 150 °C enables the formation of high-quality, protective anatase TiO₂ coatings at decreased annealing temperatures.³³ The amorphous TiO₂ coating deposited at 150 °C may have a higher degree of vibrational motion causing a greater number of critical nuclei formed per attempt frequency, enabling phase transformation to occur at lower temperature.

Figure 6. a) Log-linear plot of nucleation rates as a function of post-deposition annealing (PDA) temperature for ALD-TiO₂ thin films deposited at 120 °C, 140 °C, and 160 °C. b) Linearized nucleation rate equation for films deposited at 120 °C, 140 °C, and 160 °C with linear regression line of best fit. 

            Experimentally determined values for reaction rate k and nucleation rate are used to calculate the crystal growth rate for each deposition and annealing condition. For two-dimensional, plate-like growth, Equation 6 can be solved for crystal growth rate as follows:

Here, the reaction rate and the average nucleation rate at a given deposition temperature and annealing temperature are used to calculate each crystal growth rate. These instantaneous crystal growth rates are plotted against deposition temperature in Figure 7a. The annealing temperatures presented in Figure 7a are limited to those applicable to all three deposition temperatures and so Figure 7a only includes crystal growth rates for 180 °C and 200 °C PDA. Crystal growth rates are the highest for films deposited at 120 °C, while those for 140 °C and 160 °C films are relatively similar. The crystal growth rate is a stronger function of deposition temperature than PDA temperature.

Next, we apply the nucleation rate analysis structure to crystal growth rate. Here, the Arrhenius relationship for crystal growth rate is given as:

With the linearized form:

In Equation 10 and Equation 11, is the Boltzmann constant, is thePDA temperature, and is the exponential pre-factor. PDA temperature is used in Equation 10 and Equation 11 because that is the temperature at which the isothermal grain growth occurs. Figure 7b includes the Arrhenius plot for crystal growth rate for TiO₂ films deposited at 120 °C, 140 °C, and 160 °C with a linear regression line of best fit with 1/ as the abscissa. The reported R-square presented in the Figure 7b caption demonstrates the lack of correlation between grain growth rate and PDA temperature. To verify grain growth rate and PDA temperature are not correlated, we report the p-values for vs. 1/ per deposition temperature. Here, the null hypothesis is that no significant correlation exists between and 1/ per deposition temperature, such that the slope is equal to 0. If the p-value is less than the significance level α = 0.05, then the correlation is statistically significant, and the null hypothesis is rejected. However, if the p-value is greater than α, then the null hypothesis is accepted. The p-values for the correlation between ln(crystal growth rate, ) and 1/ for films deposited at 120 °C, 140 °C, and 160 °C are 0.809, 0.129, and 0.379 respectively. As such, the correlation between crystal growth rate and PDA temperature for a sampling of this size and variation is not statistically significant and so the slope is effectively 0. However, even if we disregard this poor correlation and proceed to calculating the activation energy for crystal growth, , from the linear regression line of best fit, we get values of near-zero: 0.01 eV atom^-1 at 120 °C deposition temperature, 0.1 eV atom^-1 at 140 °C deposition temperature, and 0.05 eV atom^-1 at 160 °C deposition temperature. Thus, we conclude that the crystal growth process is not strongly thermally activated, therefore the crystal growth rate does not vary with increasing PDA temperature. Additional statistical analysis of this crystal growth rate is included in SI Note 2. 

            Calculated values for the critical Gibbs free energy for nucleation, , and the combined activation energy for nucleation and growth, , are reported in Table 3. Anatase nucleation has a significant energy barrier at these lower temperatures and composes most of the combined nucleation and growth activation energy barrier. In fact, the critical Gibbs free energy for nucleation is within error of the activation energy for nucleation and growth for each deposition temperature: 120 °C, 140 °C, and 160 °C. This result informs why the nucleation rates are a strong function of annealing temperature while the crystal growth rates are not. Since crystal growth rate is not found to be correlated to annealing temperature, we expect minimal activation energy for crystal growth. In contrast, the critical Gibbs free energy for nucleation is much higher and requires significant energy input for the phase transformation to occur. Thus, nucleation is the rate-limiting step for this transformation process.

Figure 7. a) Crystal growth rates plotted as a function of deposition temperature for ALD-TiO₂ films deposited at 120 °C, 140 °C, and 160 °C.  b) Arrhenius plot for crystal growth rate for TiO₂ films deposited at 120 °C, 140 °C, and 160 °C with linear regression lines of best fit and 95% confidence intervals. The R-square values for 120 °C, 140 °C, and 160 °C lines respectively are: 0.001, 0.123, and 0.056. 

Table 3. Calculated fundamental activation energies: critical Gibbs free energy for nucleation and combined nucleation-grain growth for each ALD temperature, and reaction rate frequency factor.

3.3 Controlling microstructure

The above analysis deconvolutes the amorphous to anatase phase transformation reaction rate into separate nucleation and growth rates. We can apply this understanding of these fundamental kinetics to understand why the crystalline microstructures after PDA vary with ALD deposition temperature.

Figure 8 presents the calculated grain size, determined using the triple point method,⁵⁵ as a function of the ALD temperature and the post-deposition annealing (PDA) temperature. The grain size after annealing is a strong function of the deposition temperature, increasing almost an order of magnitude with each 20 °C decrease in deposition temperature. Since the Gibb’s free energy for nucleation and the combined activation energy for nucleation and crystal growth do not change considerably with deposition temperature, the pre-exponential factors dominate the rates at which the phase transformation occurs. Because the amorphous TiO₂ films deposited at 160 °C have an order of magnitude higher reaction rate frequency factor compared to amorphous TiO₂ films deposited at 120 °C, more nucleation occurs in the film. This results in a greater nucleation density and a faster time to complete transformation. As such, films with a higher frequency factor form a greater number of crystal nuclei causing a densely packed, fine grain structure (< 1 µm), while films with a lower frequency factor form fewer crystal nuclei, resulting in a large grain structure (> 1 µm). 

To discern the contribution of the crystal growth rate to final grain size, we compare the crystal size of films deposited at 160 °C and annealed at 180 °C (ALD-160 °C / PDA-180 °C) to those deposited at 140 °C and annealed at 200 °C (ALD-140 °C / PDA-200 °C). Referencing Figure 6a, the nucleation rates for these films are roughly equal, while the grain size for ALD-140 °C / PDA-200 °C films is double that of ALD-160 °C / PDA-180 °C films. This is because the crystal growth rate for ALD-140 °C films is greater than for ALD-160 °C films (Figure 7a), resulting in more rapid crystal growth that prevents as much nucleation from occurring. And since the crystal growth rate is not strongly thermally activated, for a given deposition temperature, the grain size only decreases modestly with increasing PDA temperature. So, while raising annealing temperature changes the reaction kinetics and decreases the time to transformation, it does not affect the material frequency factor and so it does not dramatically alter the final crystal microstructure. 

Figure 8. Calculated grain size from SEM micrograph analysis as a function of ALD temperature (120 °C, 140 °C, and 160 °C) and post-deposition annealing temperature (160 °C, 180 °C, 200 °C, 220 °C).

3.4 Time-Temperature-Transformation (TTT) diagrams for plate-like anatase crystal growth

With the presented phase transformation study for TiO₂ thin films, isothermal time-temperature-transformation (TTT) diagrams can be developed to describe the TiO₂ amorphous to anatase solid-state phase transformation via post-deposition annealing (PDA). TTT diagrams can offer useful information for metal oxide thin films where the crystallization is heating-rate dependent and occurs in the solid state.⁵⁶ Figure 9 includes TTT diagrams for 5%, 50%, and 95% TiO₂-anatase transformation at ALD growth temperatures a) 120 °C, b), 140 °C, and c) 160 °C. Lower ALD temperatures suppress the amorphous to anatase phase transformation and require additional time for the transformation to occur; this is evident from the shifting in the percent crystallized curves to longer required annealing times. Higher deposition temperatures enable faster transformation to the anatase phase at each isothermal PDA temperature. These TTT diagrams for amorphous thin films crystallizing via isothermal PDA provide a guide for evaluating deposition temperature effects on the nucleation and grain growth kinetics of amorphous ALD thin films. 

Figure 9. Time-temperature-transformation (TTT) diagrams for TiO₂ amorphous to anatase phase transformation via isothermal post-deposition anneals for 1120 cycle ALD films deposited at temperatures: (a) 120 °C, (b) 140 °C, (c) 160 °C.  Transformation curves are labeled for 5%, 50%, and 95% transformation to the TiO₂-anatase phase. The abscissa axis is in base-10 log time.

1. Conclusions

We report an atomic layer deposition (ALD) process with a PDA step to grow large grain TiO₂ anatase on a Si substrate from TDMAT/H₂O chemistry. Large-grained anatase minimizes grain boundary volume and enables a greater proportion of the film to contribute its functional performance. The TiO₂-ALD is deposited from 120 °C to 160 °C with ex situ annealing in air from 140 – 220 °C. A detailed SEM study of the TiO₂-amorphous to TiO₂-anatase phase transformation is presented to extract fundamental nucleation and growth kinetics values and to highlight structural differences in the as-deposited film structure as a function of deposition temperature. The JMAK equation is used to determine an average Avrami exponent close to 3 for the transforming volume, consistent with a two-dimensional, plate-like anatase growth mode with continuous nucleation. The critical Gibbs free energy for anatase nucleation is 1.32–1.41 eV atom^-1 and the combined activation energy for nucleation and growth is 1.40–1.58 eV atom^-1, while the activation energy for crystal growth is near zero. Thus, nucleation appears to be the rate-limiting step. Interestingly, in studying the nucleation rate at different PDA temperatures as a function of ALD temperature, we identify the nucleation frequency factor, not the activation energy, as the differentiating quantity between the as-deposited TiO₂ films. Amorphous TiO₂ films deposited at higher temperatures have an increased nucleation frequency factor compared to those deposited at lower temperatures, potentially indicating that as-deposited higher temperature films have increased vibrational modes to attempt nuclei formation. As a result, ALD deposition temperature has a significant effect on the resultant grain size, with 20 °C increases in temperature decreasing the grain size by almost an order of magnitude. Finally, a time-temperature-transformation (TTT) diagram architecture has been applied to highlight the differences in crystallization behavior between ALD temperatures.

In this work, we present a method to study differences in an as-deposited, amorphous TiO₂ film as a function of ALD deposition temperature and introduce the nucleation rate frequency factor as an indicator of resultant nucleation and microstructure. Further, we separate the nucleation and growth kinetics for the amorphous to anatase phase transformation, demonstrating that nucleation is the rate-limiting step for the phase transformation under standard ALD process conditions. Finally, we demonstrate a practical low-temperature route to grow large-grained anatase films which expand their use in applications requiring temperature-sensitive substrates and devices.

1. Acknowledgements

J.P.W. acknowledges this material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-2039655. A significant portion of this work was performed at the Georgia Tech Institute for Electronics and Nanotechnology, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the National Science Foundation (ECCS-2025462). Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors recognize Proposal GU-309504 for scattering measurements at Beamline 12-ID at National Synchrotron Light Source-II at Brookhaven National Lab. A.A. appreciates the support of the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1650044. S.A.G. acknowledges financial support from a Link Foundation Energy Fellowship. J.P.W. thanks D. Tavakoli, T. Walters, and R. Monikandan for assistance with XRD and SEM.

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