Simulation Study of Crystalline Al₂O₃ Thin Films Prepared at Low Temperatures: Effect of Deposition Temperature and Biasing Voltage

Abstract

In this paper, classical molecular dynamics simulations were used to explore the impact of deposition temperature and bias voltage on the growth of Al2O3 thin films through magnetron sputtering. Ion energy distributions were derived from plasma mass spectrometer measurements. The fluxes of deposited particles (Ar+, Al+, and O−) were categorized into low, medium, and high energies, and the results show that the films are dominated by amorphous Al2O3 at low incident energies without applying bias. As the deposition temperature increased, the crystallinity of the films also increased, with the crystals predominantly consisting of γ-Al2O3. The crystal content of the deposited films increased when biased with −20 V compared to when no bias was applied. Crystalline films were successfully obtained at a deposition temperature of 773 K with a −20 V bias. When biased with −40 V, crystals could be obtained at a lower deposition temperature of 573 K. Increasing the bias enables the particles to have higher energy to overcome the nucleation barrier of the crystallization process, leading to a greater degree of film crystallization. At this stage, the average bond length between Al-O is measured to be approximately 1.89 Å to 1.91 Å, closely resembling that of the crystal.

1. Introduction

Alumina (Al₂O₃) is commonly used in industrial production and other areas, including optics, electronics, catalysis, and coatings, due to its superior hardness, remarkable wear resistance, exceptional optical transparency, and thermal stability [1,2,3]. In addition to stable α-Al₂O₃ (corundum), it contains various transition phases, such as γ-, κ-, and δ- [4]. Among the various phases, the geometrical arrangement of ions in the amorphous Al₂O₃ structure is more similar to γ-Al₂O₃ than to other phases. Consequently, upon heating, amorphous Al₂O₃ films undergo crystallization into the γ-phase, which then transforms into the α-phase at elevated temperatures [5]. Therefore, it is possible to synthesize γ-Al₂O₃ crystals at low temperatures. Moreover, γ-Al₂O₃ plays a crucial role in industrial production as both a catalyst [6,7] and a protective coating material [8,9].

High power impulse magnetron sputtering (HiPIMS), among the various ionized physical vapor deposition (PVD) techniques, has garnered substantial attention over recent decades [10]. HiPIMS was developed in 1999 by Kouznetsov et al. [11]. In particular, HiPIMS has a low duty cycle (<5%) and low repetition frequency (50–500 Hz). This results in an elevated peak power density of the HiPIMS discharge, exceeding 0.5 kW·cm⁻², leading to an increased dissociation rate of particles during sputtering. As a result, these properties benefit the modulation of film microstructure and properties. Recently, Ferreira et al. [12] investigated the effect of depositing Al₂O₃ thin films at different sputtering parameters by HiPIMS and medium frequency (MF). The results show that film quality is correlated with the energy of the deposition process (i.e., higher energy leads to higher film density and refractive index).

Recent studies have conducted various experiments and simulations to investigate the production of Al₂O₃ thin films through magnetron sputtering. These studies also aim to analyze how deposition parameters influence the structure and properties of the films. The focus is often on understanding the impact of factors such as particle energy distribution and deposition temperature on the films’ characteristics. The factors affecting the growth of Al₂O₃ films can be attributed to two aspects. On the one hand, Al₂O₃ thin films, in various phases encompassing a broad spectrum of applications, can be fabricated by adjusting external parameters such as sputtering power [13], bias voltage [14], and heating temperature [12]. On the other hand, film growth is actually influenced by internal factors, including bombardment particle content flux [15], energy flux composition [16], and surface temperature [17]. In Ref. [18], the structural transformation of Al₂O₃ thin films under irradiation with various energy fields was investigated. The study revealed that thin films experience an amorphous transition to γ-Al₂O₃ when assisted by an energy field at 300 °C. Current research has focused on simulating the production of thin films through magnetron sputtering. In Ref. [19], classical molecular dynamics (MD) were employed to systematically describe the growth of Al₂O₃ under different sputtering parameters. The results show that there is an optimal crystallization temperature for the growth of Al₂O₃ thin films that is influenced by the deposition energy and that low deposition energies are detrimental to the crystallization of the films. Pham et al. [20] explored the formation of Cu_x(FeAlCr)_100-x thin films on Ni(001) substrates using MD, where an elevation in deposition temperature led to a reduction in roughness but a decrease in the percentage of thin film crystallization when the film structure was Cu₂₅Fe₂₅Al₂₅Cr₂₅.

In this paper, molecular dynamics were used to analyze the influence of deposition parameters, in particular the deposition temperature and bias voltage (V_b) on the structure of Al₂O₃ thin films. The crystal transformation (radial distribution function and coordination number), crystal type (bond statistics), and surface roughness in thin films are discussed based on the plasma mass spectrometer test results to classify the energy flux of the incident particles, and the influence law of sputtering parameters on the transformation of the film crystal structure during magnetron sputtering is explored to explain the low-temperature crystallization transformation mechanism of Al₂O₃ thin films.

2. Method

2.1. Simulation Method

The MD simulations in this paper utilize the LAMMPS (Large Scale Atomic/Molecular Massively Parallel, version-2 Aug 2023, Sandia National Laboratories, Albuquerque, NM, USA) [21] open-source code. The model consists of two parts: α-Al₂O₃ substrate and deposited Al and O particles. Figure 1a shows a schematic diagram of the cell of α-Al₂O₃, with Al particles in grey and O particles in red. The type of Al₂O₃ cell is a rhombic cell and the crystal system is tripartite. Following Sigumonrong’s recommendation [22], the crystal system was then transformed into an orthorhombic system with its z-axis aligned along the (001) direction. The substrate was obtained by cell expansion of an orthorhombic crystal system with a substrate size of 33.3 Å × 28.8 Å × 13.2 Å and a total number of substrate atoms of 1440 (Figure 1b). The substrate was partitioned into three regions: the bottom three atomic layers were fixed to prevent movement during deposition; the middle ten atomic layers were temperature controlled using the NVT ensemble to maintain a constant temperature; and the top five atomic layers were free layers, employing the NVE ensemble for heat transfer and energy exchange with the deposited particles. Furthermore, periodic boundary conditions were applied to x- and y-axes and the non-periodic boundary condition was applied to z-axes. The Ar particle incidence and elimination regions were set at 40~45 Å and 45~50 Å from the substrate surface, respectively. The generation regions of Al and O particles were set at 50~60 Å from the substrate surface. The boundary in the z-direction of the model was set to be the reflective layer of Al and O particles. The time step was set to 1 fs and the following rules were followed during deposition:

(1)

The substrate (α-Al₂O₃) was subjected to a “thermalization campaign” of 1 ps at a given temperature of 1300 K (using Nose-Hoover temperature control) before growth was initiated.

(2)

Random generation of new atoms was at a rate consistent with the distribution of energy in the deposition particle generation zone, using the NVE ensemble.

(3)

Generation of atoms was followed by 5 ps collisional deposition for heat exchange with the substrate and energy dissipation.

(4)

The deposition was followed by a 1 ps thermalization run (microcanonical ensemble) to remove the remaining energy.

(5)

Ar particles were inserted for collision rebound during Al, O deposition.

(6)

There was a return to step (2) and the process was repeated. In order to show whether crystallization can occur, steps (2–6) were cycled until the number of particles deposited was not less than 2200 for Al and O, and not less than 320 for Ar particles for sputtering collisions (based on the ratio of the number of O to Ar in the mass spectrometry data).

It is widely recognized that the selection of interaction potential plays a crucial role in ensuring the accuracy of classical MD simulations. For thin film growth, it has been shown [19,23] that the role of Coulomb forces needs to be taken into account (remote ordering of atoms requires interactions between remote atoms). In this paper, the choice of the potential function for alumina film deposition is based on the partial-charge (Al^+1.4175, O^−0.945) Buckingham interaction potential (U = Ae^−r/ρ − Cr⁻⁶ (r < r_c), where ρ is an ionic-pair dependent length parameter, and r_c is the cutoff on both terms) proposed in reference [24], which has been proved [19,23] to meet the requirements of this paper, and the parameters are shown in

Table 1. Matsui (data from [24]) potential function parameters.

Interacting Particles	A (eV)	ρ (Å)	C (eV·A6)
O-O	6463.4	0.276	85.22
Al-O	28,480	0.172	34.63
Al-Al	31,574,470	0.068	14.07

. The non-film-forming Ar⁺ is only involved in the bombardment of the film; therefore, the Lennard–Jones (L-J) potential was chosen with the parameters shown in

Table 2. Lennard–Jones potential parameters (data from [25,26]).

Potential Function Coefficients	Ar	Al	O
ε	0.00978 eV	0.39217 eV	0.00844 eV
σ	3.465 Å	2.62 Å	3.541 Å

.

In the process of high-power pulsed magnetron sputtering deposition, the applied bias voltage is positively correlated with the particle energy hitting the substrate. Bubenzer [27] proposed an equation for the relationship between bias voltage and particle energy:

$$E={\displaystyle \frac{K{V}_{bias}}{pm}};0\le m\le 1$$

(1)

where $V_{bias}$denotes the applied bias amplitude, K is a constant, p is the discharge voltage, and m is a coefficient. As described in Equation (1), the energy of the particles impacting the substrate is proportional to the amplitude of the applied bias, while ensuring that the other parameters remain constant. However, in this paper, O⁻ is used as a simulation object to have a deceleration effect under negative bias conditions. Therefore, the effect of low- and medium-energy O⁻ that disappears due to bias on the film is ignored, according to

Table 3. Substrate temperature and bias voltage for deposition of different thin film samples.

Samples	1	2	3	4	5
Substrate temperature (K)	300	573	773	773	773
Substrate bias (V)	−40	−40	−40	−20	0

.

2.2. Calculation and Analysis Methods

The radial distribution function g(r) describes the ratio of ρ(r), the average atomic number density in a spherical shell with a distance to the atom of r and a thickness of Δr, to the average atomic number density of the whole system, ρ₀:

$$g\left(r\right)={\displaystyle \frac{\rho \left(r\right)}{{\rho }_0}}={\displaystyle \frac{V{\sum }_{i=1}^N{N}_i\left(r\right)}{4\pi r^2∆r{N}^2}}$$

(2)

where V is the volume of the system, N is the number of atoms in the system, and N_i(r) is the number of atoms in the spherical shell at a distance r from atom i.

The coordination number refers to the number of atoms within a specific range (first nearest neighbor) surrounding a given atom, serving as a tool for structural analysis. It offers insight into the atomic density of the atom within its immediate surroundings. This study utilizes the Al-O cutoff radius as the designated distance limit. The quantity of O atoms present around the Al atom within this cutoff distance plays a crucial role in determining the structure and indicating the level of crystal crystallization. Al atoms exhibiting a coordination number of 6 are classified as octahedral structures, while those with a coordination number of 4 are identified as tetrahedral structures.

Common neighbor analysis (CNA) [28] was used to describe the bonding correlations between neighboring atoms. CNA uses three statistical parameters (jkl): where j is the number of co-neighbors of two bonded atoms; k is the number of bonds between these neighboring atoms; and l is the maximum length consisting of these bonds. The structural characteristics of FCC are 6 ternary 421 per atom, while the structural characteristics of HCP are a combination of 3 ternary 421 and 3 ternary 422 per atom.

For deposition, surface roughness is an important parameter. On the atomic scale, it means the measurement of the maximum and minimum average surface height somewhere on the surface. The root mean square roughness, R_q, is calculated as follows:

$$R_q=\sqrt{{\displaystyle \frac{\sum _{i=1}^N{\left(z_i-\overline{z}\right)}^2}{N}}}$$

(3)

where N is the number of atoms on the surface of the film, $\overline{z}$ is the average height of surface atoms, and $z_i$ is the height of the ith atom.

2.3. Sample Preparation and Characterization

Al₂O₃ films were deposited on (100) single-crystal silicon wafers using a twin-target reactive high-power impulse magnetron sputtering system. The system was equipped with two identical Al targets, and during each discharge cycle, both target electrodes were converted once. This configuration allows the two targets to alternately function as the anode and cathode. The average power applied to the target in each pulse cycle was 180 W. The pulse frequency and width of the power supply were 2000 Hz and 40 µs, respectively. The target material was a 99.999% pure round aluminum target with a 100 mm diameter and 6 mm thickness. The angle between the target and the central axis of the sample stage was set at 45°, with a distance of 100 mm. Before deposition, the single-crystal silicon (100) substrate was continuously ultrasonically cleaned with alcohol and petroleum ether for 10 min each for later use. The vacuum chamber background vacuum was 1.0 × 10⁻³ Pa. During the deposition process, the argon flow rate was 50 sccm, and the oxygen flow rate was 14 sccm. The working pressure and deposition time were 0.2 Pa and 3 h, respectively. A resistance heater was used to regulate the substrate temperature, which was measured with a k-type thermocouple. The substrate bias and temperature parameters are shown in Table 3.

The mass spectrometer, model PSM003 from Hiden Analytical in the UK (PSM003, Hiden Analytical, Warrington, UK), was connected to the vacuum chamber to obtain an Ion Energy Distribution Function (IEDF). The connection was made through the side transfer port of the vacuum chamber, with the front detector positioned at a distance of r = −40 mm below the target, as illustrated in Figure 2. Prior to testing, the mass spectrometer was evacuated to a pressure below 2 × 10⁻⁵ Pa using a vacuum pump. To prevent counter saturation, the isotope ³⁶Ar⁺ of Argon, with relatively low content, was used to calibrate the electrostatic lens system of the mass spectrometer for optimal sensitivity. The energy sweep range during testing was set from 0–80 eV in increments of 0.1 V, with a test time of 100 ms for each energy step to maximize signal strength.

The crystal structure of the deposited thin films was measured by Empyrean X-ray diffraction (XRD) produced by Panalytical in the Netherlands (GIXRD; Empyrean, PANalytical, Almelo, Holland). The device used a Cu target (λ = 0.15418 nm) as the X-ray source, and the operating voltage and current were set to 40 kV and 40 mA, respectively. Since the sample in this study was a thin film, the grazing incidence method (GIXRD) was used to set the incidence angle to 1°.

3. Results

Based on the scanning results of the mass spectrometer, the positive ions ³⁶Ar⁺ and ²⁷Al⁺ and the negative ion ¹⁶O⁻ were selected for the simulation study, and the results obtained are shown in Figure 3a–c.

The categorization of ²⁷Al⁺ and ¹⁶O⁻ ions into high, medium, and low energy levels is determined by Breilmann’s division of ion energy distribution functions (IEDFs) [29]. The contribution of ³⁶Ar⁺ was averaged across the IEDFs due to its minimal involvement in film formation and low concentration. During simulation, the average value and proportion of each energy interval for ²⁷Al⁺ and ¹⁶O⁻ ions were calculated, and they are detailed in

Table 4. Percentage of each ion in IEDFs and average energy values.

Energy Division	27Al+	16O−	36Ar+
low energy	0~3.15 eV	0~8 eV
percentage	35%	80%
average	1.2 eV	2.45 eV
moderate energy	3.15~13.2 eV	8~34 eV
percentage	55%	17%	3.5 eV
average	7.5 eV	18.6 eV
high energy	13.2~25.5 eV	34~60 eV
percentage	10%	3%
average	16.9 eV	48 eV

.

The growth of the films was investigated at different bias voltages (0 V, −20 V, and −40 V) in the range of substrate temperature T = 300 K~773 K (Figure 4). When no bias is applied (Figure 4a), the rise in temperature does not significantly impact the film structure (300–673 K), which remains amorphous. As the temperature nears 773 K, some regularity in the atomic arrangement at the film’s interface starts to appear, although most atoms in the film remain irregularly arranged. This is due to the low energy of the ions upon impact, with the substrate temperature increase unable to compensate for the lack of particle energy. Consequently, Al atoms are unable to move to the octahedral positions typical of crystalline Al₂O₃ (similarly for O). When a −20 V bias voltage is applied (Figure 4b), the film maintains an amorphous structure at 300 K−673 K. In contrast, the film structure shows a more orderly atomic arrangement at T = 773 K compared to that shown in Figure 4a. This suggests the development of a distinct crystalline structure in the film, promoting the formation of a continuous crystalline film. Since the negative bias is able to attract positive ions, this increases the energy for particles to bombard the substrate. When these high-energy particles bombard the surface of the substrate, they transfer energy to the substrate, which creates additional temperature on the substrate surface. The increase in temperature promotes the migration of particles, which increases the degree of crystallization of the Al₂O₃ film. Figure 4c illustrates the atomic structure of Al₂O₃ thin films with a bias increased to −40 V. The continuous growth of crystalline alumina films is observed at deposition temperatures near T = 573 K. Essentially, the deposition temperature required for the formation of continuously grown films decreases with an increase in bias. However, excessively high temperatures (T = 773 K) can lead to damage to the film structure. This is attributed to the substrate’s high temperature causing excessive particle migration, leading to defects accumulating faster than they can be repaired.

Figure 5 shows the radial distribution function between Al-O (cutoff radius 8 Å) in the films at different substrate temperatures and bias voltage. In Figure 5a,b, only the first peak (short-range ordering) is evident, and the rest of the long-range peaks are weak, indicating that the films are in an amorphous state at T = 300 K and 500 K, −40 V bias. Upon reaching a substrate temperature of 573 K (Figure 5c) and V_b = −40 V, not only is the first peak clear, but the subsequent long-range peaks are also prominent, indicating ordering between Al-O in the film. Figure 5d (T = 673 K) shows similar results to Figure 5c, with the noteworthy observation that at V_b = −40 V, the half-width of the first peak increases, the average distance between Al-O atoms increases, and particle migration ability improves. Upon further increasing the substrate temperature to 773 K, multiple peaks are evident at V_b = −20 V, indicating successful crystallization of the thin film. This suggests that raising the substrate temperature can decrease the energy required for particle bombardment. Figure 5f provides a more intuitive illustration of the temperature’s impact on thin film crystallization. When combined with Figure 4, it can be qualitatively concluded that crystalline thin films can be achieved at a lower temperature of T = 573 K with a bias voltage of −40 V.

It is well known that the high-density α-Al₂O₃ phase is composed of complete octahedral (coordination number = 6) coordination Al atoms and the γ-Al₂O₃ phase is defined by a blend of predominantly octahedrally coordinated and a minor fraction of tetrahedrally coordinated (coordination number = 4) Al atoms, while most tetrahedrally coordinated Al atoms are present in the non-crystalline phase [5,10,30].

In order to quantitatively determine the crystal structure of Al₂O₃ films with substrate bias, Figure 6a–e shows the structural proportion of coordinated Al atoms in Al₂O₃ films deposited under different bias voltage in the range of T = 300 K~773 K. It is evident that as the applied bias value increases, there is a rise in the content of octahedral coordination Al atoms, accompanied by a decline in tetrahedral counterparts, particularly notable when the bias shifts from −20 V to −40 V. In particular, the octahedral content increased from 17% to 36% at the deposition temperature of 573 K, indicating that the crystal content in the film increased significantly. It is worth mentioning that at T = 773 K, the content of octahedrally coordinated Al atoms increases more for the 0–20 V bias than for the 20–40 V bias, which is due to the slow amorphization in the films caused by the bombardment of energetic particles. Figure 6f illustrates this point more intuitively. When the bias voltage is −40 V, the octahedra increases from 20% to 40%, and the tetrahedron decreases from 48% to 33% as the substrate temperature rises from 300 K to 673 K. Nevertheless, at T = 773 K, the octahedral content decreased by 2%. At the atomic level, the lower deposition temperature requires the bombardment of high-energy particles to provide energy for the film-forming particles so that the crystal velocity formed is higher than the damage caused by the bombardment. Once the temperature is high (T = 773 K), the high-energy particle bombardment (with a −40 V bias applied) causes the defects to accumulate faster than the crystals formed by diffusion, which leads to slow amorphization of the film.

Figure 7 shows the average coordination number of Al atoms in the Al₂O₃ film, showcasing varying coordination numbers, including 4, 6, 5, and 3. The results indicate that with increased temperature under the same bias voltage, the average coordination value of Al rises. However, at a bias voltage of −40 V, the average Al coordination decreases by 0.2 from 673 K to 773 K at the substrate temperature. This aligns with the conclusion from Figure 6, suggesting that crystallization in the film is not strongly correlated with Al atoms of coordination 4 and 6. The presence of defects in the film is indicated by most Al atomic coordination numbers being below 5. Possible reasons for these defects include the influence of Al⁺ and Ar⁺ promotion and O⁻ inhibition during negative bias application, as well as the presence of Al vacancies in γ-Al₂O₃ itself.

Figure 8 quantified the medium-range order in the film and analyzed it using common neighbor statistics [28], showing the statistical data of the O lattice structure. Notably, α-Al₂O₃ consists of a local HCP arrangement of O, while γ-Al₂O₃ consists of a local FCC arrangement [31].

Firstly, with the increase of bias voltage, the content of ternary 421 bonding pairs increases and 422 bonding pairs decreases. This suggests that increasing the bias leads to a higher number of FCC structures of O in the film, generating crystalline Al₂O₃ dominated by the γ phase. The influence of substrate temperature on the type of thin film crystal is evident, as shown in Figure 8a. At a temperature of 773 K with no bias applied, the content of ternary 421 bonding pairs is 11.5%, which is 2~3% higher than that at lower temperatures. However, with a bias voltage of −40 V, the content of 421 bonding pairs at 773 K decreases to 15.6%, lower than at 673 K (18.2%). This suggests that slow amorphization resulting from high-energy particle bombardment primarily impacts the formation of γ-Al₂O₃. Additionally, the presence of α-Al₂O₃ (Figure 8b) in the film may indicate epitaxial growth of a small fraction of Al₂O₃, a phenomenon that has been previously observed [32]. With the increase of γ-phase content, the α-phase shows a decreasing trend, which may be attributed to (1) part of the α-phase being transformed to the γ-phase [33]; and (2) the increase of the migration energy of film-forming particles weakens the epitaxial growth effect, resulting in a decrease in the content, which is the same as the conclusion that the bombardment will induce local epitaxial growth to be terminated during the formation of the film in Ref. [17].

Figure 9 shows a top view of the deposition of a thin film at different temperatures with a −40 V bias applied, providing information on the effect of the simulated conditions on the morphology of the film. As the deposition temperature increases, there are some differences in the atomic structure of the films formed on the substrate surface, especially in terms of atomic height. Under the bias voltage of −40 V, there are no large bumps and pits on the surface of the Al₂O₃ film, the peak-to-valley distance is between 4.7 Å~6.3 Å, and the surface is relatively smooth. The surface roughness is shown in

Table 5. Surface roughness at different deposition temperatures at a bias voltage of −40 V.

Temperature	300 K	500 K	573 K	673 K	773 K
Rq (Å)	1.39 ± 0.05	1.37 ± 0.02	1.42 ± 0.03	1.36 ± 0.03	0.92 ± 0.02

. In addition, an analysis of the atomic surface height shows that as the substrate temperature increases, the film’s compactness is enhanced and the atomic surface height diminishes. This phenomenon is particularly pronounced at T = 673 K (Figure 9d) and T = 773 K (Figure 9e).

The XRD patterns of the Al₂O₃ films prepared at different deposition parameters are shown in Figure 10. The green vertical line in the figure is the standard diffraction peak of γ-Al₂O₃ (PDF#29-0063). Figure 10a shows the XRD results with a bias voltage of 0 V, −20 V, and −40 V at T = 773 K. The diffraction peaks correspond to the (400), (440), and (311) crystal planes of the Al₂O₃ phases, respectively. This result shows that crystalline Al₂O₃ films can be obtained at a substrate temperature of 773 K and a bias voltage of 0 V. As the bias voltage increases from 0 V to −40 V, the intensity of each diffraction peak increases, and the peaks become sharper. This indicates that the increase in bias improves the crystallinity of Al₂O₃ films. The changing trend of the crystallinity of Al₂O₃ films is similar to the simulation results. Figure 10b is an XRD image of 300 K, 573 K, and 773 K at a bias voltage of −40 V. When the temperature rises, the intensity of the diffraction peak increases significantly, and the crystallinity of the Al₂O₃ film is the highest when the temperature is 773 K. The intensity of the diffraction peak increases with the substrate temperature, indicating that increasing the substrate temperature is beneficial for the crystallization of the film, which is basically consistent with previous publications [34].

4. Discussion

In this paper, Al₂O₃ thin films were deposited using simulated magnetron sputtering to facilitate low-temperature crystallization. The migration of particles is heavily influenced by their energy, requiring sufficient energy to overcome the nucleation potential barrier during crystallization. This energy is necessary for particles to move to lattice positions in crystalline alumina during crystal formation. In a previous study, the effect of deposition temperature on the crystal structure of alumina films without substrate bias was analyzed [35]. The results showed that the grain size increased from 15 nm at 300 °C to 25 nm at 500 °C, indicating that the crystallization degree of the film increased from 300 °C to 500 °C. The growth of crystalline Al₂O₃ films at relatively low substrate temperatures can be attributed to the following reasons: (i) the scattering effect of the particles is weakened at low pressure, and the high-energy bombardment particles are retained; and (ii) the energy provided by energetic ions (Al⁺, Ar⁺, O⁺, O⁻) increases the possibilities for thin film crystallization. Similarly, in the previous simulation, the degree of crystallization of the film increases with increasing temperature when no bias voltage is applied. However, the energy required for crystallization only from the perspective of increasing thermodynamics (without applying bias) requires a very high substrate temperature, which makes the preparation of crystalline Al₂O₃ thin films more expensive and process intensive. When a bias is applied to the substrate, the deposited ions receive additional kinetic energy and bombard the surface of the film with higher energy. High-energy particles bombarding the surface will undergo an energy conversion so that the atoms on the surface of the film will obtain additional energy and this extra energy will promote the orderly arrangement of the atoms and increase the degree of crystallization of the film. In the above circumstances, the simulation and XRD results also show a tendency for the degree of crystallization of the film to increase with increased bias. Figure 11 shows the statistical results of Al-O bond lengths. The Al-O bond lengths in crystalline Al₂O₃ are 1.91 Å to 1.92 Å [19]. In general, thin film crystallization requires a minimum amount of free energy to bring its structure to a stable state. This obtained energy is mainly supplied to the deposited atoms so that they can diffuse to the desired lattice position for crystallization. According to the previous section, applying a bias voltage of −20 V is necessary to obtain crystalline Al₂O₃ films at T = 773 K with an Al-O bond length of 1.90 Å. Applying a bias voltage of −40 V reduces the deposition temperature to 573 K with an Al-O bond length of 1.89 Å, which is close to that of the Al-O in crystalline Al₂O₃. This indicates that the bias increases the diffusion capacity of the atoms, allowing the deposited atoms to diffuse to the desired lattice position for crystallization. In other words, the bias provides additional energy to the incident particles, allowing them to compensate for the crystallization activation energy that would otherwise need to be provided by the thermal energy. From Figure 11, we can see that by setting the substrate temperature, bias, and particle incident energy in the simulation, the statistical bond length can predict the influence of the three parameters on the crystallization of the thin film and predict the appropriate process window for the preparation of crystalline alumina films before an experiment.

5. Conclusions

In this paper, molecular dynamics simulations were used to analyze the growth of Al₂O₃ films under bias and substrate temperature during magnetron sputtering. The principle of low-temperature crystallization was investigated by assigning values to incident particles through ion energy distributions measured by plasma mass spectrometry. The simulation results show that:

(1)

Under low-energy particle deposition conditions, the growth of Al₂O₃ thin film crystals requires high deposition temperatures for optimal results. Without applying bias to the particles during the deposition process, even at 773 K, achieving a well-crystallized Al₂O₃ film is challenging, with only 17.2% octahedral coordination of Al content in the film.

(2)

The bias is conducive to the deposition of crystalline Al₂O₃ films at low temperatures. When the bias of −40 V is applied, the content of octahedral coordination of Al in the Al₂O₃ film is 36.3% and that of ternary 421 increases by 6% at T = 573 K, the crystallinity in the film rises, and the Al₂O₃ crystal is dominated by γ phases. However, the average coordination number in the film remains mostly below 5, indicating a significant presence of defects. This observation may be attributed to the fast deposition of Al+ ions and slow deposition of O- ions.

(3)

The low-temperature preparation of crystalline Al₂O₃ films is attributed to the energy of the particles, and the application of a bias enables the diffusion of the thin particles to be enhanced, compensating for the crystallization energy supplied by the substrate temperature and allowing the films to be prepared at low temperatures.