Surface structures from NH3 chemisorption in CVD and ALD of AlN, GaN and InN films

Aluminum nitride (AlN), gallium nitride (GaN) and indium nitride (InN) form a family of technologically important semiconductors of high importance to light-emitting diodes and high frequency electronics. Although thin films of these materials are routinely manufactured by chemical vapor deposition (CVD) and atomic layer deposition (ALD), the methods are far from optimal and knowledge of the underlaying chemical processes are lacking. In this work we performed ab-initio investigations of the surface coverage of these materials under an ammonia rich atmosphere. Periodic density functional theory (DFT) calculations were used to test probable surface structures, their electronic and thermal energies were used to calculate their contribution to the surface composition at temperature and pressure conditions relevant for CVD and ALD processes of these materials. The results show similarities between the group of materials with similar NHx surface structure present for all three. Comparison of the coverage showed that at low growth temperatures the surface is expected to be covered by NH2 while at high temperatures most surface sites would be vacant. The surface structures where all found to be most stable on AlN and least stable on InN. These results are important for further investigations of the material growth mechanisms.


Introduction
The group 13 nitrides (13Ns), aluminum (AlN), gallium (GaN) and indium nitride (InN) are important materials in the semiconductor industry [1]. They range in bandgap from the wide gap of 6.0 eV for AlN [2], to the narrow 0.7 eV for InN [3] with GaN at an intermediate gap of 3.4 eV [4]. This bandgap range covers ultra-violet to infra-red and thus contains the full visible spectrum making the 13Ns well suited for optoelectronics such as LEDs [5,6]. InN has also a very high electron mobility and electron saturation velocity making it suited for high frequency transistors [7,8].
To use the 13Ns in these applications they need to form thin films with high crystalline quality, conformity, and low impurity levels. One common method to achieve such films for AlN and GaN is chemical vapor deposition (CVD). CVD of AlN and GaN is routinely done at temperatures around 800-1100 °C. For InN, conventional CVD is problematic to use as InN decomposes into metallic indium and nitrogen gas at around 500 °C [1], well below the temperatures needed to activate the decomposition chemistry of ammonia which is used as nitrogen precursor in the growth process [9]. Atomic layer deposition (ALD) is a low temperature CVD method with a time-resolved supply of the precursors, leading to a deposition fully governed by surface chemical reactions. ALD has the potential to circumvent the high temperature required in CVD of 13Ns and at the same time increase the ability to uniformly coat substrates with very high aspect ratios. ALD has already been demonstrated to be superior to continuous CVD for deposition of the temperature sensitive InN films [10,11].
Insight from modeling can be used to better understand the surface chemical processes in ALD and CVD. One of the foundations for the surface chemistry are the surface structures of the substrates covered with the adsorbates. From the possible surface terminations of the 13Ns, the reactivity of the different possible surfaces can be estimated. The surface structures are also needed to be able to investigate adsorption pathways as well as adatom diffusion. Earlier theoretical studies of NH3 adsorption and decomposition on GaN [12,13] and InN [13,14] have shown that NH3 can decompose into a variety of NHx adatoms upon adsorption on the 13Ns, often with surface NH2 being one of the most prominent species. The adsorption and decomposition on AlN have not previously been investigated in detail.
Most of the studies are performed at a low coverage with only a single or few NHx adatoms in the computational cell giving a coverage of up to around 0.25 ML. At higher coverage, lateral effects can modify the structures and shift the surface energies, changing which configuration is the most favorable. The structures from the earlier works were used as a basis and we extend them by increasing the coverage to the limiting 1 ML as expected by a complete ALD process.
We further extend these works by comparing the possible adsorbate-surface structures in the whole family of 13Ns as well as employing a statistical mechanical approach investigate the mixing of the different surface-coverage structures and view the dependence of the mixing on temperature, gas mixture and pressure. We find that the most probable surface NHx specie at low temperatures is the on-top NH2 for AlN, GaN and InN. At high temperatures, no NHx species are stable on the surface and will desorb, leaving a bare surface. The transition temperatures between these two follows a clear trend where AlN has the highest transition temperature and InN the lowest with GaN in between.

Computational method Quantum chemical calculation
All quantum chemical calculations were performed using density functional theory (DFT) as implemented in the VASP software [15][16][17], extended by the VTST package [18]. Electronic energies, geometry optimized structures and normal vibrations were all calculated using the GGA functional PBE [19] with Grimme's version 3 dispersion correction [20]. A plane wave basis set and the projector augmented wave method (PAW) [21] were used for core electrons.
For Ga and In, 3d and 4d-electrons respectively were treated as valence electrons. To model the surface, a slab of each respective 13N compound was made from an optimized unit cell. First the unit cell was reoriented to make a conventional cell with axis along the [101 ̅ 0] and [12 ̅ 10] direction, containing 4 primitive cells. The conventional cell was then repeated in the [0001] direction and padded with vacuum. The number of layers and vacuum separation as well as cutoff energy and number of k-points were checked to be converged with respect to the surface energy. Dangling bonds on the bottom of the slab were passivated by hydrogen atoms to limit artificial charges across the slab and vacuum padding.
During optimization, all atoms were allowed to relax, and the optimization criteria was set to 0.01 eV/Å. Normal mode frequencies were calculated using the harmonic approximation and the finite displacement method were used to get the force constants using the Phonopy software [22]. During frequency calculations, the atoms below the 2 nd topmost layer were frozen. The normal mode frequencies were then used to calculate the vibrational part of the partition function and used to get thermodynamic properties for the surface system.
Calculations on gas phase molecules were performed by placing the molecule in a cubic cell with side 10 Å to ensure separation from the neighboring cells. For gaseous molecules, modes corresponding to translational and rotational movement were removed from the vibrations and the translational and rotational contributions to the partition function were calculated separately.
These were then, together with the vibrational contribution, used to get the thermochemical properties of the molecules.

Equilibrium composition calculation
According to statistical mechanics, a system in the isothermal-isobaric ensemble will minimize its Gibbs energy (eq. 1) at equilibrium.
where the summation goes over all species defined to be present in the system.
This gives an optimization problem for the equilibrium composition minimize ( ) (2) subject to = and ≥ 0 where is the matrix of the elemental composition of the species and is a vector of the amount of the elements. The chemical potential was calculated using the Gibbs energy of the pure species at the total pressure ∘ ( ∘ ) and the chemical activity ( ) as the sum For gas species the activity was approximated by the partial pressure = ∘ while for surface species the activity was defined as the coverage ratio = . The Gibbs energies of the pure species were calculated from the partition function derived from the quantum chemical calculations. Optimization were performed using Optimization Toolbox from Matlab R2021a.

Adsorption of NHx species and surface reconstructions
To investigate the different possible surface structures of 13Ns under an ammonia ambient atmosphere, NHx (x=0-3) molecules or radicals were introduced to the surface slab. The NHx species were placed in proximity of possible adsorption sites and the structures were optimized to find stable adsorption configurations. The four different adsorption sites considered, viewed along the (0001) axis, were: top (directly above a metal site), bridge (between two neighboring metal sites), hcp hollow (between three neighboring metal sites, above the top layer nitrogen), and fcc hollow (between three neighboring metal sites, above the empty site in hexagonal packing), see Figure 1. No adsorbate was found to adsorb to the hcp hollow site, probably due to the close proximity to, and repulsion from, the surface layer nitrogen. As a model for the possible surface after an ideal ALD half cycle, reconstructions were investigated assuming a  fcc hollow, between three neighboring metal sites above the empty site in hexagonal packing.

NH3 adsorption structure
Undecomposed NH3 was found to adsorb on the top site, Figure 2. After a coverage of 0.5 monolayer of NH3, additional NH3 only weakly physisorb at a large distance above the surface layer. This can be seen as a saturation of the NH3 coverage, since when an ammonia molecule binds to a metal site, it will contribute with two valence electrons to the surface metals. At a 0.5 ML NH3 coverage, the number of valence electrons will form a full octet for each surface metal by forming a bond to the ammonia on half of the sites and a free electron pair on the other half.
This free electron pair would then in turn repel the free pair of additional NH3 causing them not to adsorb.

N adsorption structures
Full coverage of N atoms was also investigated, and similar to the NH terminated surfaces N terminations was also found to form both N monomer and N2 dimers on the surface.

Other adsorption structures
Structures for two other terminations were also investigated; a surface terminated by H, Figures   10 Table I.

Equilibrium surface terminations
To create phase diagrams, we consider the different adsorption types as different surface species and we assume that the different surface species can form a homogeneous mixture on the surface, i.e., a 2D analogue of an ideal solution. A distinct surface one-phase region was assumed to be the region where a certain set of surface species are present at significant amounts, arbitrarily set to at least 1 % of all surface species. The equilibrium amounts of each surface species was obtained from minimization of the systems Gibbs free energy at different combinations of temperature, total pressure, and initial composition.
Temperature-pressure phase diagrams were constructed between 200-1800 K and 0.001-1 bar total pressure to model a large set of possible conditions, containing the expected temperatures and pressures during CVD and ALD. A ratio of 1000:1 between gas and adsorption sites was used as an estimation of a surface covered by a free-flowing gas. The initial amount of NH3 compared to N2 in the gas was set to 2:15 and the surface was assumed initially to be bare.       A limitation of the equilibrium model is that it predicts the full decomposition of NH3 into N2 and H2 at higher temperatures. According to recent kinetic simulations, this decomposition is too slow to occur during CVD or ALD [9]. This would lead to a too low amount of NH3 in the gas and change the surface phase diagrams. To solve this problem additional pseudoequilibrium calculations were performed with N2 excluded from the possible decomposition products of NH3. N2 is kept as a carrier gas and is allowed to adsorb as N2 dimers but not decompose or abstract hydrogen.
The removal of decomposition to N2 changes the phase diagrams significantly as expected. For AlN, Figure 16 Figure S13.  and only at the highest temperatures does it climb above it, Figure S14. For InN the phase diagram, Figure 18, without NH3 decomposition exhibits fewer phases compared to those of AlN and GaN, as in the case with NH3 decomposition included ( Figure   15). At low temperatures, the surface is covered by a mixture of NH2(tp) and bare sites. There is a region at high pressure and low temperature where NH2(br) also reaches above the  Figure S15.   The ternary phase diagram for GaN shows many similarities to that of AlN, in the low temperature and pressure case, Figure S16. The main difference is the absence of phases containing N2 surface dimers. At high temperature and pressure, the surface becomes covered by a mix of H(tp) and bare sites terminations at all compositions under the condition that there is enough hydrogen present in the system. InN also show similarities with AlN and GaN in the low temperature limit, Figure S17. The lack of adsorption onto InN can be explained by the low reactivity of ammonia onto the surface. At temperatures above 320 K at CVD and ALD pressures even the most stable termination, NH2(tp), is less thermodynamically stable than ammonia in gas phase at normal pressures and bare In sites. According to the HSAB theory In is, compared to Al and Ga, a soft acid while the nitrogen in ammonia is a hard base [24]. As hard bases prefer to react with hard acids and soft bases prefer soft acids, ammonia would prefer to react with the harder acid Al or Ga than with In. This is also shown in the ratio of NH3 to 13-precursor used in CVD of 13Ns, where AlN requires a ratio of around 100, GaN a ratio of 1000 and InN a ratio of up to 100 000.
The high stability of N2 and H2 gas at equilibrium causes the surface to become uncovered at higher temperatures. This is a challenge for the CVD and ALD growth as the surfaces would decompose during a high temperature process if enough time is passed. This equilibrium decomposition is most noticeable for InN where the surface is bare already at room temperature, a temperature much lower than the one needed for CVD and ALD growth. Overcoming this problem leads to the need to shift the process from the thermal equilibrium, either by not allowing enough time for the NHx to decompose into N2 and H2 or by using a plasma enhanced process.

Conclusions
Structures and energies of different NHx surface structures on the three 13Ns, AlN, GaN and InN were investigated by DFT. Their stability at different temperature and pressures were determined by a minimization of the systems Gibbs energy. We have shown that the surface terminations are dependent on temperature with a hydrogen bonding NH2(tp) surface structure being the dominating structure at low temperatures and a bare surface being dominating at high temperatures for all three 13Ns. The NH2(tp) surface structure forms a good candidate for growth of 13Ns films since the availability of lone electrons pairs on the surface nitrogen can act as adsorption sites for a metal precursor containing a Lewis-acidic metal-atom. We also show that stability of the nitrogen containing surface structures decreases as the atomic number of the metal moves downwards in group 13, indicating that the growth process would be easier on AlN compared to GaN and hardest on InN, in agreement with experimental findings. The obtained structures can also be used to further develop models to investigate the atomistic processes during CVD and ALD growth as a basis for the adsorption mechanics of a metal precursors.