Molecular dynamics simulations and experimental studies on low-temperature growth of GaN

Growth mechanisms of (0001) wurtzite GaN films at low temperature are investigated by molecular dynamics simulations and experiments. The crystallization properties of GaN films deteriorate dramatically at low temperature due to the limited energy available for atomic surface migration and incorporation into the perfect lattice sites. In our simulation, growth interruption stage is periodically introduced and the as-deposited GaN films are treated with energy-carrying argon ions at this stage. The surface atoms located at the weak binding sites can acquire energy from the argon ions for secondary migration and incorporation into the perfect lattice sites. As a result, the crystallization properties of GaN films are significantly improved. GaN films are experimentally grown on sputtered AlN/sapphire substrates at 600 °C via inductively coupled plasma metal organic chemical vapor deposition along with periodic argon plasma treatment. The as-deposited film acquires energy from the plasma, leading to significant improvement of the crystalline properties. The surface morphology of the GaN film demonstrates a noticeable smoothing effect, with an evident increase in grain size from submicron to micron level. Additionally, GaN film with the optimized surface morphology exhibits high c-axis and in-plane orientations, and the full width half maximums of (002) and (102) x-ray diffraction rocking curves are 0.25° and 0.32°, respectively. These results provide effective guidance for the growth of GaN films at low temperature.


Introduction
Large-scale semiconductor films have received significant attention in many fields, including display devices, solar cells, and flexible devices [1][2][3].Semiconductor films with high crystalline quality usually exhibit better electrical and optical properties.To date, semiconductor films are commonly grown on single crystal substrates with limited size [4].Due to the need for sufficient energy to dissociate the precursors and enhance the ability of atoms for surface migration, the growth is typically carried out at high temperature, thereby improving the crystalline quality of the deposited film [5].For instance, the typical growth temperature for gallium nitride (GaN) using metal organic chemical vapor deposition (MOCVD) exceeds 1000 °C [6].
The high growth temperature results in many limitations and difficulties in the development of high crystalline quality semiconductor films.Firstly, substrates which can endure high temperature are usually expensive and have limited size.Large-scale low cost amorphous substrates typically have very low melting points.For instance, the melting point of float glass typically does not exceed 600 °C [5].Secondly, the growth of high quality ternary and quaternary III-nitrides with a high indium composition is extremely challenging, which is primarily attributed to the low vapor pressure and decomposition temperature of indium nitride (InN) [7].In addition, excessive growth temperature often leads to thermal mismatch between the deposited films and the substrates [8].Therefore, low temperature growth of high-quality semiconductor films on large-scale amorphous substrates is particularly attractive for the development of large-area electronic devices.
Taking the low-temperature growth of III-nitrides as an example, the following two problems need to be solved.Firstly, ammonia is usually difficult to be pyrolyzed at a temperature as low as 600 °C.Secondly, the adatoms deposited at such temperature likely lack sufficient energy to effectively migrate on the growth surface and incorporate into the perfect lattice sites.A variety of low-temperature plasma enhanced epitaxy have been proposed to address the first problem, including plasma-assisted molecular beam epitaxy (PA-MBE) [9], pulsed laser deposition (PLD) [10], pulsed sputtering deposition (PSD) [4,11], remote plasma-MOCVD (RP-MOCVD) [12], electron cyclotron resonance-MOCVD (ECR-MOCVD) [13] and inductively coupled plasma-MOCVD (ICP-MOCVD) [14,15].In RP-MOCVD, group V precursor is ionized by an ECR plasma source operating at 2.45 GHz.The advantage of ECR is the high energy conversion rate, although there is a possibility of mode hopping.The substrate is positioned at a distance of ∼25 cm from the plasma source outlet.The kinetic energy and number density of ions will gradually decrease on the way to the substrate, thereby reducing the bombardment of high-energy ions on the deposited film.In ICP-MOCVD, a planar coil driven by radio frequency (RF) power source operating at 13.56 MHz, is utilized to ionize the group V precursor.The advantage of ICP is its ability to easily generate high-density and large-area uniform plasma.It has been demonstrated that the showerhead structure can effectively reduce the bombardment of high-energy ions reaching the substrate on the deposited film [14].For the second problem, numerical simulation is an effective approach to investigate the growth mechanism.As a dynamic microscopic process, the migration of adatoms on the growth surface and their incorporation into the lattice, is difficult to characterize directly.Among the common simulation methods in material science, molecular dynamics (MD) simulation is an important method to investigate the dynamics of film growth [16][17][18][19][20].However, there are few reports on MD simulation related to energy compensation at low temperature.
In this paper, low-temperature growth of GaN films are investigated by molecular dynamics simulations and experiments.The effects of growth temperature on the crystallization properties of GaN films are investigated.The mechanisms of energy compensation by argon (Ar) ion treatment are then investigated.Moreover, the effects of periodic growth interruption and Ar plasma treatment for low-temperature growth of GaN films are investigated experimentally via ICP-MOCVD.The GaN film with micron grain size as well as high c-axis and inplane orientations is obtained on sputtered AlN/sapphire substrates at 600 °C.

Simulation and experimental details
MD simulation is essentially to solve the Newton's equations of motion for all particles in an ensemble at given initial and boundary conditions to obtain their instantaneous positions and velocities.Therefore, it is necessary to determine the interatomic potential of materials, the numerical integration algorithm and the temperature control method before MD simulation.The Tersoff potential suitable for semiconductors [21] is adopted to describe the interaction between atoms in GaN film.The specific model of the Tersoff potential function used is as follows [22]: where E is the total potential energy, f (r) is the cut-off function, V R is the attractive energy between pairs of atoms, V A is the repulsive energy between pairs of atoms, and B is the bond order parameter between atoms.D 0 is the dimer bond energy, r 0 is the dimer bond distance, S is interaction potential parameter, and β is the parameter related ground state vibration frequency.R is cut-off distance, and D is cut-off parameter.γ is the parameter related bond angle distribution, c is bond angle size, d is bond angle strength, θ 0 is the optimal angle for potential energy, and 2μ is cut-off classification parameter.The parameters for the interactions between various types of atoms in GaN are listed in table 1.
The species present in Ar plasma primarily consist of electrons, Ar ions, and neutral Ar atoms.During the deposition and the Ar plasma treatment process, the interaction between electrons and GaN layers can convert the kinetic energy of the electrons into the thermal vibrations energy of the crystal lattice [23].The electron temperature tends to be relatively low in ICP-MOCVD [24].Consequently, the electrons induce slight localized heating effect on the crystal lattice upon reaching the substrate, leading to slight thermal vibrations of the surface atoms.The most efficient channel for energy transfer is facilitated by ions that are accelerated within the plasma sheath [14,23,24].However, these ions are ultimately neutralized on reaching the substrate.As a result, the behavior of the Ar ion during collision with the GaN film is assumed to be similar to that of an Ar atom [25].Due to the significantly greater mass of ions compared to electrons, the momentum transfer becomes apparent as they collide with the atoms in GaN layers.The interaction between Ar atoms and atoms in GaN layers is primarily attributed to van der Waals forces.Therefore, Ar atoms do not form chemical bonds with Ga or N atoms in GaN layers.These Ar atoms will eventually escape from the GaN surface and be vented from the reaction chamber by the pump system.There are two main types of Ar atoms reaching the substrate.One of the types is the metastable Ar atoms with long lifetime, which can transfer potential energy to the GaN lattice.However, this part of the energy is negligible in comparison to the contribution of ions [23].The other type consists of ground state Ar atoms which make up a significant proportion.The kinetic energy of these two types of Ar atoms is relatively low and therefore has little impact on the growth of GaN.The Lennard-Jones potential is employed to describe the interaction between Ar atoms themselves and between Ar atoms and GaN, and the potential function is described as [26]: where ε is the depth of potential well and σ is the distance between two atoms at which the interaction potential energy is zero.The cut-off distance r c is set to 12 Å.The corresponding parameters are listed in table 2. The simulation model is illustrated in figure 1.A wurtzite GaN substrate with dimensions of 3.8 × 3.3 × 1.1 nm 3 , consisting of 720 gallium (Ga) atoms and 576 nitrogen (N) atoms, is constructed using the lattice constants a = 3.19 Å and c = 5.189 Å.The x-, y-, and z-directions are assigned to the [0 − 1 1 0], [−2 1 1 0] and [0 0 0 1] crystalline orientations, respectively.Periodic boundary conditions are used in the x-and y-directions Table 1.The parameters for the three interaction types in GaN [22].to expand the dimensions in these specific directions, whereas a free boundary condition is assumed in the zdirection to simulate the growth on the [0 0 0 1] GaN surface [16].The atoms in the bottom two pairs of Ga and N planes are fixed at their equilibrium positions to prevent crystal drift during the impact.The atomic layers located in the thermostat region are maintained at a constant temperature by adopting the Nose-Hoover method [27].The atomic position and velocity are obtained by solving the Newton's equations of motion at a time step (1 fs) short compared to the highest lattice vibration period based on the Velocity-Verlet numerical integration algorithm [28].The deposited Ga and N atoms are randomly generated from the position of 6.75 ∼ 7.25 nm above the substrate surface at a time interval of 9 ps, and then incident on the substrate at the velocities of 5.4 m s −1 and 10.8 m s −1 , respectively, typical for ICP-MOCVD [15].The incident angle is assumed to be 45°f rom the growth surface.The total number of incident atoms is 6000, with a flux ratio of Ga to N atoms of 1.

Ga-Ga
To investigate GaN film growth assisted by energy-carrying Ar ions, growth interruption stage is periodically introduced into the growth process.At this stage, the Ga and N fluxes are stopped, and Ar atoms with a designated energy and incident direction are introduced to transfer energy to the GaN film.During each growth cycle, the flux ratio of Ga to N atoms is maintained at 1, and the interval of Ga and N fluxes is set to 9 ps.The number of incident atoms per cycle and the number of growth cycles are adjusted to ensure that the total number of incident atoms is kept at 6000.The energy of Ar atoms varies in the range of 3 ∼ 60.75 eV, and the incident angle varies in the range of 0 ∼ 75°.The incident time interval of Ar atoms is set to 1 ps, as it is much easier to ionize Ar than N 2 .
In the MD simulations, short time step (1 fs) is adopted to accurately simulate high-frequency lattice vibrations, and a large number of atoms are necessary to obtain a reasonable volume to reveal the microstructure [25].As a result, high deposition rates are employed to meet the above requirements [16,25].A GaN film growth rate of ∼0.1 nm ns −1 is adopted during the MD simulations.This is about 10 9 times greater than the typical value (∼0.056 nm s −1 ) in our home made ICP-MOCVD, which significantly reduces the surface migration distance of adatoms before they are buried by newly arriving atoms.The migration distance for adatom on the lattice surface where R is the growth rate, E is the activation energy of surface migration, k B is the Boltzmann constant, and T is the growth temperature [16].In order to overcome the limitation of the unrealistically high growth rate on the atomic surface migration distance, the simulation is carried out at elevated growth temperature [16,29,30].The temperature in the thermostat region is set in the range from 600 °C to 1400 °C at the growth stage.On the other hand, the temperature in the thermostat region is set to 600 °C at the interruption stage, consistent with the growth temperature in ICP-MOCVD.
With the enhanced migration ability of adatoms, the growth of GaN film is more likely to exhibit twodimensional characteristics, resulting in a smoother surface.Therefore, the roughness of simulated GaN film can be used to characterize the migration ability of adatoms and the improved surface morphology indicates enhanced migration ability.The deposited film is divided into 24 × 24 blocks on the xy-plane according to the number of atoms per layer, and the root mean square (RMS) of z-coordinates of the highest points of those blocks is calculated as the RMS roughness (Rq).
The crystallinity parameter ζ, defined in equation (9) [16], is employed to characterize the ability of adatoms to incorporate into the lattice.
where {r k } are the positions of the nearest neighbor atoms of a given atom k. {R k } are the nearest neighbor lattice sites that can be determined according to the crystalline orientation of the substrate and the lattice constants, assuming that the center atom k is located at a lattice site.The scaling factor α is taken to be 0.2 in this paper, while N denotes the atom number in the deposited films.According to equation (9), ζ ranges from 0 ∼ 1 and a greater ζ indicates enhanced atom incorporation into the lattice.In order to reduce the influence of lattice vibration on the crystallization parameters, the temperature in the thermostat region is lowered to room temperature after the deposition process and then the crystallization parameters are calculated.
The nitrogen fraction is defined as where N N denotes the number of nitrogen atoms present in the deposited film.The parameter allows for the measurement of the stoichiometry of the film and facilitates estimating the density of nitrogen and gallium vacancies.
In this work, inductively coupled plasma metal organic chemical vapor deposition (ICP-MOCVD) [14,15] is used to grow GaN at low temperature on sputtered AlN/sapphire substrates.Nitrogen molecules (N 2 ) and triethylgallium (TEG) serve as the group V and III precursors, with flow rates of 320 sccm and 74.5 sccm, respectively.The pressure, the growth temperature and the N 2 plasma power are 1 Pa, 600 °C, and 950 W, respectively.During the growth interruption stage, the Ar flow rate is set to 80 sccm, along with a plasma power of 750 W.During the entire growth process, the rotation speed of the graphite pedestal is maintained at 250 rpm.The surface morphology, the crystalline properties and the impurity properties of GaN films are characterized by atomic force microscope (AFM), x-ray diffraction (XRD), transmission electron microscopy (TEM) and secondary ion mass spectrometry (SIMS) measurements.

The effects of growth temperature
The effects of growth temperature on the crystallization properties of GaN films are investigated.The atomic structures of the GaN films are shown in figures 2(a)-(f) for growth temperatures of 600 °C, 800 °C, 900 °C, 1000 °C, 1200 °C and 1400 °C.Compared with the GaN films grown at temperatures above 1000 °C, the GaN films grown at 600 °C-900 °C exhibit a higher degree of disorder in their atomic arrangements.This is due to the fact that the deposited atoms lack sufficient energy for surface migration and incorporation into the perfect lattice sites at low temperature.As a result, the growth predominantly occurs in a three-dimensional growth mode.However, the film is primarily grown in two-dimensional growth mode as the growth temperature increases.
Rq and ζ of the simulated GaN films as a function of growth temperature are shown in figure 3.As the growth temperature is raised from 600 °C to 1100 °C, Rq decreases rapidly from 1.079 nm to 0.404 nm and ζ increases significantly from 0.796 to 0.977.However, when the growth temperature is further increased, Rq decreases slowly to 0.322 nm and ζ varies only slightly.These results indicate that the reduced growth temperature is unable to provide sufficient energy for atomic surface migration and incorporation into perfect lattice sites, resulting in poor surface flatness and increased population of defects.

The effects of energy-carrying Ar ion treatment
Energy compensation can be implemented by introducing active ions in the inert gas plasma during lowtemperature growth of GaN film.Shown in figures 4(a)-(f) are the atomic structures of the GaN films grown with periodic Ar ion treatment at a growth temperature of 900 °C.The numbers of treatment cycles are 0, 1, 2, 4, 6, and 12, respectively, and the number of incident Ar ions per cycle is 2000.The energy and the incident angle of the Ar ions are set to 27 eV and 25°, respectively.The resultant crystallization property parameters of GaN films are listed in table 3. It is evident that by increasing the number of treatment cycles while maintaining the total number of incident atoms, the crystallization property parameters of the deposited GaN films can be enhanced.For a treatment cycle of 6, Rq decreases to 0.398 nm, ζ increases to 0.975, and F N reaches 47.2%.However, the crystallization property parameters of the deposited GaN film deteriorate as the number of treatment cycles is further increased to 12.It can be speculated that there exists a specific interaction depth for optimal energy transfer during the Ar ion treatment.arrangements of Ga atoms and N atoms in the sub-outer layer at the starting moment of the Ar treatment stage (at time t s ) from a top view, respectively.Figures 5(c) and (f) show the geometric arrangements of Ga atoms and N atoms in the sub-outer layer at time t e from a top view, where the in-plane trajectories of Ga atoms and N atoms during the entire Ar treatment stage (from t s to t e ) are indicated by red lines, respectively.It can be observed that after the upper layer atoms migrate to the sub-outer layer, they effectively fill up the atomic vacancies within the sub-outer layer.Comparing the results of figures 5(b) and (c), it is evident that the in-plane migration of Ga atoms is significant in the area characterized by a high density of Ga vacancies.On the other hand, those Ga atoms that have been incorporated into the perfect crystal lattice merely undergo slight vibrations around their respective lattice equilibrium positions.Comparing the results of figures 5(e) and (f), it is evident that once the N atoms in the upper layer migrate to the N atomic vacancy areas in the sub-outer layer, they are immediately incorporated into the crystal lattice and undergo minimal further migration.This is consistent with the higher in-plane migration barrier of N atoms on the Ga-terminated (0001) surface compared to that of Ga atoms [31].
Next, the effect of energy transfer by Ar treatment on the secondary migration distance of atoms in each layer of GaN film is analyzed quantitatively.The atomic layers are divided into 10 rectangular blocks along the z-direction, with each rectangular block comprising a pair of Ga and N planes.The average migration distance of Ga and N atoms in each rectangular block is calculated, as shown in figure 6.The average migration distances of Ga atoms in the outer three rectangular blocks are 0.618 nm, 0.338 nm, and 0.110 nm, respectively.In the lower rectangular block, the average migration distances of Ga atoms are in the range of 0.033 nm to 0.045 nm.Similarly, the average migration distances of N atoms in the outer three rectangular blocks are 0.552 nm, 0.256 nm, and 0.090 nm, respectively.In the lower rectangular block, the average migration distances of N atoms are in the range of 0.031 nm to 0.043 nm.It can be seen that the interaction depth of energy-carrying Ar ions is approximately 3 ∼ 4 pairs of Ga and N planes and the average migration distances of Ga atoms are greater than that of N atoms, consistent with the qualitative analysis mentioned above.
To facilitate an intuitive analysis of the effect of Ar treatment on atom incorporation into lattice sites, the geometric arrangement of atoms in GaN films grown with or without Ar treatment are compared in figure 7. It is evident that the arrangement of atoms in GaN film becomes more regular after treatment with energy-carrying Ar ions, and the growth of GaN film tends to follow a two-dimensional mode.On the contrary, the arrangement of atoms in GaN film grown without Ar treatment tends to be relatively disordered due to insufficient energy for  Moreover, the deposited atom number N decreases from 2625 to 2542, which may be attributed to atom expulsion from the GaN film by Ar ion bombardment.Despite this decrease in the deposited atom number, F N increases from 46.1% to 47.2%.This is due to the removal of some of the higher-mass isolated Ga atoms with weak binding in addition to the lighter N atoms by Ar ions with increased incident energy.Moreover, the improvement of Rq and ζ also helps enhance the incorporation efficiency of N atoms.As the incident energy further increases to 60.75 eV, Rq increases from 0.398 nm to 0.520 nm.Simultaneously, there is a noticeable decrease in the ζ, which goes from 0.975 to 0.798.The deposited atom number experiences a rapid decrease, going down from 2542 to 1487.Furthermore, there is a steep decline in F N , with a sharp decrease from 47.2% to 36.6%.It reveals that an excessively high incident energy can lead to severe damage to the GaN lattice, resulting in a significant deterioration of the crystallization property parameters of the deposited GaN film.This indicates that there exists an optimal energy range for crystallization properties.
The crystallization property parameters of the deposited GaN film are shown as a function of ion incident angle at a fixed incident energy of 27 eV in figures 8(c)-(d).The crystallization property parameters only vary slightly for the incident angle ranging from 0°to 75°.Nevertheless, the momentum transfer effect in the horizontal direction becomes more obvious with increased incident angle.The trade-off between energy transfer effect and momentum transfer effect in the horizontal direction leads to optimal crystallization properties at the intermediate incident angle of ∼45°.
Based on the above analysis, it is evident that the energy of the Ar ions has a very significant influence on crystallization properties of the deposited GaN films.A comprehensive comparison of the crystallization property parameters of GaN films optimized by varying the Ar treatment time (t i ) at a fixed incident angle of 25°F is shown in table 4. The number of Ar treatment cycles is 6.It can be observed that for Ar ions with relatively low energy, increasing the treatment time enhance the energy transfer effect.This enhances the ability of weakly bound atoms to migrate and incorporate into the perfect lattice sites, thus improving the crystallization properties of the deposited GaN films.For high Ar ion energy, the treatment time should be reduced as much as possible to prevent excessive bombardment from deteriorating the crystallization properties.

Application of Ar plasma treatment in low-temperature growth of GaN films
According to the simulation results in section (3.2), it is found that the crystallization properties of GaN films grown at low temperatures can be significantly improved by periodic Ar ion treatment.We experimentally demonstrate the effectiveness of Ar plasma treatment (APT).The schematic of APT mode is shown in figure 9.Each growth cycle consists of the growth stage and the Ar plasma treatment stage.During the growth stage, the N plasma source and the TEGa source are fed simultaneously for a growth time of t g .Subsequently, the growth is temporarily interrupted for a time of t i , and only the Ar plasma source is introduced during this stage to treat the as-deposited GaN film.The thickness of the deposited GaN film is about 400 nm.
In order to simplify the growth process and improve the growth efficiency of GaN films, we conduct Ar plasma treatment immediately without purging step after the end of growth stage (stage G).However, this approach may result in precursors remaining during Ar plasma treatment stage (stage I), thereby potentially influencing the effectiveness of Ar plasma treatment.Therefore, it is necessary to evaluate the residual status of the precursors during stage I.To confirm the residual status of the precursors, the plasma optical emission spectrums are measured and the results are shown in figures 10(a)-(c).Figure 10(a) shows the set flow rates of N 2 and Ar as a function of time.The optical emission spectrum measured at time t 1 is shown in figure 10(b).The time interval between time t 1 and the starting moment of stage G (time t 0 ) is ∼ 2 s.It can be seen that the spectrum only contains N 2 -related emission peaks.The optical emission spectrum measured at time t 3 is shown in figure 10(c).The time interval between time t 3 and the starting moment of stage I (time t 2 ) is ∼ 1 s.It can be seen that the spectrum only contains Ar-related emission peaks.This suggests that the N 2 precursor remaining during the early stage of stage I is rapidly eliminated from the reaction chamber.In ICP-MOCVD, molecular pump system is employed to control the gas pressure to ∼1 Pa while introducing the precursors.Furthermore, the rotation speed of the graphite pedestal is controlled at 250 rpm to ensure adequate density of active species reaching the graphite pedestal.As a result, the gas velocity within the chamber is accelerated, promoting the rapid expulsion of the precursors from the chamber.Four GaN samples (A ∼ D) are grown on sputtered AlN/sapphire substrates using direct mode and APT mode, and the respective growth conditions for each sample are shown in table 5.The AFM results of the four samples are shown in figures 11(a)-(d), respectively.It is evident that the surface morphologies of GaN films grown in the APT mode demonstrate a noticeable smoothing effect compared to that grown in the direct mode.In addition, the grain size gradually increases from submicron to micron level.
The (002) and (102) XRD rocking curves (XRCs) of Samples A and D are shown in figure 12.The full width half maximums (FWHMs) of (002) and (102) XRCs of Sample A are 0.51°and 0.78°, respectively.In comparison, the (002) and (102) XRCs FWHMs of Sample D are 0.25°and 0.32°, respectively.The narrower FWHMs and stronger diffraction peak intensities of Sample D indicate that the APT method can effectively reduce the defect density and improve the crystallinity.The AFM and XRD results demonstrate that the APT method is a good choice to improve the surface flatness and crystallinity of GaN films grown at low temperature.
According to the results of the MD simulation, the existence of significant vacancy areas indicates that the limited atomic migration ability, and the growth mode tends to be a three-dimensional mode.At the macroscopic scale, it is characterized by the existence of obvious holes in the GaN layers, which can be experimentally validated via TEM.Figures 13(a)-(b) show the TEM measurement results of Samples A and D, respectively.It is evident that Sample A exhibits the significant existence of holes, as can be seen in the area highlighted by the red circles in figure 13(a).Regarding Sample D, apart from the relatively few holes occurring in the GaN layer near the substrate-GaN interface, the GaN layer close to GaN surface demonstrate a noticeable smoothing effect, as can be seen in the continuous area highlighted by the red rectangle in figure 13(b).It can also be observed from the AFM, XRD and TEM results that the GaN film grown at 600 °C using the direct mode exhibits columnar polycrystalline characteristic.However, as shown in figure 2(a), the atomic arrangement of the simulated GaN film grown at 600 °C using direct mode exhibits highly disordered amorphous characteristic, which is not consistent with the experimental results at 600 °C.As shown in figure 2(c), the atomic arrangement of the simulated GaN film grown at 900 °C using direct mode exhibits threedimensional growth with crystalline characteristic, which is consistent with the experimental results at 600 °C.Therefore, the growth temperature of 900 °C is selected to simulate the experimental results at 600 °C.SIMS measurements on Samples A, D and reference GaN are conducted to assess the impurity level.Reference GaN film is grown via MOCVD at 1050 °C.The impurity concentrations (C, O) of the samples are listed in table 6.It can be observed that the impurity concentrations in Samples A and D are four orders of magnitude higher than that of reference GaN.Additionally, the impurity concentrations in Sample D are slightly increased compared to that in Sample A. This can be attributed to the increased density of nitrogen vacancies, leading to a higher incorporation of impurities.
Four GaN samples (E ∼ H) are grown on sputtered AlN/sapphire substrates at 600 °C using periodic H 2 or Ar/H 2 plasma treatment, and the respective growth conditions for each sample are shown in table 7. The AFM results of the four samples are shown in figures 14(a)-(d), respectively.It is evident that H 2 plasma treatment causes an etching effect on the GaN film, thereby deteriorating the surface morphology of the GaN film.Furthermore, it is observed that the etching effect becomes more significant with the increasing proportion of H 2 .The results demonstrate the advantage of utilizing pure Ar plasma treatment for energy compensation.

Conclusions
In conclusion, growth mechanisms of (0001) wurtzite GaN films at low temperature are investigated by MD simulations and experiments.The crystallization properties of GaN films grown at low temperature are poor due to the low atomic migration rate.By periodically introducing energy-carrying Ar ions with suitable energy to treat the as-deposited GaN film, the weakly bound atoms within the top 3 ∼ 4 pairs of Ga and N planes can acquire sufficient energy and disengage from their original lattice sites.Subsequently, they overcome the surface migration barrier and undergo secondary migration, eventually incorporating into strong binding lattice sites.The incident energy of the energy-carrying Ar ions plays a crucial role in determining the crystallization properties of the grown GaN films.On the other hand, the influence of the incident angle is less significant.The crystallization properties of GaN films can be optimized by adjusting the treatment time of Ar ions with different energies.The GaN film grown via ICP-MOCVD exhibits significant enhancements in surface morphology and crystallinity by employing the APT mode.The effects of H 2 or Ar/H 2 plasma treatment demonstrate the advantage of utilizing pure Ar plasma treatment for energy compensation.These results provide effective guidance for improving the crystallization properties of GaN films grown at low temperature.

Figure 1 .
Figure 1.The simulation model of GaN film growth process: (a) deposition process of Ga and N atoms; (b) GaN film treatment with energy-carrying Ar ions.

Figure 3 .
Figure 3. Rq and ζ of the GaN films as a function of growth temperature.

Figure 5 .
Figure 5.The migration process of atoms in GaN film during energy-carrying Ar ion treatment: (a) the geometric arrangement of atoms in GaN film at the end of the Ar treatment stage from a front view (the trajectories of Ga atoms during the entire Ar treatment stage are indicated by red lines); (b) the geometric arrangement of sub-outer Ga atoms at the starting moment of the Ar treatment stage (at time t s ) from a top view; (c) the geometric arrangement of sub-outer Ga atoms at the end of the Ar treatment stage (at time t e ) from a top view (the in-plane trajectories of Ga atoms during the entire Ar treatment stage are indicated by red lines); (d) the geometric arrangement of atoms in GaN film at time t e from a front view (including the trajectories of N atoms); (e) the geometric arrangement of sub-outer N atoms at time t s from a top view; (f) the geometric arrangement of sub-outer N atoms at time t e from a top view (including the trajectories of N atoms).

Figure 6 .
Figure 6.The average migration distance of atoms in each rectangular block of GaN film treated by energy-carrying Ar ions: (a) the schematic diagram of rectangular blocks divided along the z-direction; (b) the average migration distances of Ga and N atoms in each rectangular block (the z-coordinate of the center point for each block indicates the position of the block in the z-direction).

Figure 7 .
Figure 7.The geometric arrangement of atoms at the same atomic layer position in GaN films grown under two growth modes of (a)-(b) direct growth and (c)-(d) energy-carrying Ar ion treatment.

igure 8 .
The crystallization property parameters of GaN films treated by energy-carrying Ar ions with (a)-(b) different incident energies and (c)-(d) different incident angles.

Figure 9 .
Figure 9.The schematic diagram of (a) direct mode and (b) APT mode.

Figure 10 .
Figure 10.The measurement of plasma optical emission spectrum: (a) the set flow rates of N 2 and Ar as a function of time; (b) plasma optical emission spectrum measured at time t 1 ; (c) plasma optical emission spectrum measured at time t 3 .

Figure 13 .
Figure 13.TEM measurement results of (a) Sample A and (b) Sample D.

Table 2 .
[26]parameters for lennardjones potential employed to describe the interaction between Ar atoms themselves and between Ar atoms and GaN[26].

Table 3 .
The crystallization property parameters of GaN films treated by energy-carrying Ar ions with different number of treatment cycles.

Table 4 .
The crystallization property parameters of optimized GaN films treated by energy-carrying Ar ions with different incident energies at a fixed incident angle of 25°.

Table 5 .
The growth conditions of samples A ∼ D.

Table 7 .
The growth conditions of samples E ∼ H.