On the limitations of thermal atomic layer deposition of InN using ammonia

Indium nitride (InN) is a semiconducting material with a narrow bandgap of 0.7 eV and high electron mobility and velocity, giving it potential uses in, for example, infrared photovoltaics and high-frequency transistors.^1–3 Conventional chemical vapor deposition (CVD) of InN, using the common precursors trimethyl indium [TMI, In(CH₃)₃] and ammonia (NH₃), is limited by the low thermal stability of the material, which decomposes into metallic indium and nitrogen gas already at 500 °C.⁴ By utilizing low-temperature atomic layer deposition (ALD) as a time-resolved alternative to CVD, low thermal stability could be circumvented as depositions could occur below the decomposition temperature.

Plasma ALD has successfully been used to deposit InN with both N₂ (Refs. 5–7) and NH₃ (Ref. 8) plasma together with TMI at temperatures below the thermal decomposition of InN. Precursors with chelating ligands forming N–In bonds have also been used successfully to deposit InN with NH₃ plasma.^9,10 However, a thermal ALD process has not been shown experimentally. This is in contrast to the other group 13-N semiconductors, both AlN and GaN, which have been grown using thermal NH₃ and trimethyl aluminum [TMA, Al(CH₃)₃] (Refs. 11 and 12) and trimethyl gallium [TMG, Ga(CH₃)₃],^13,14 respectively.

Since plasma ALD of InN gives films with TMI, and since the plasma discharge is not activated when TMI is exposed to the NH_x-covered InN surface, it is reasonable to assume that the limitation to a thermal ALD process for InN is found in the interaction between NH₃ and the –In(CH₃)_x covered InN surface. Although it is thermodynamically favorable for NH₃ to decompose into N₂ and H₂ at the temperatures in the ALD processes, the decomposition is limited by very slow kinetics at these temperatures, making NH₃ stable during the residence time in ALD.¹⁵ Therefore, the majority of NH₃ molecules are expected to arrive at the surface intact in thermal ALD, contrasting plasma ALD processes where the plasma decomposes NH₃ molecules into more reactive species.⁸ 

Ab initio calculations on NH₃ reactive adsorption have been reported earlier on GaN by Krukowski et al.^16,17 In their work, they have shown that upon adsorbing onto a bare GaN surface, NH₃ can form a variety of different NH_x surface species located at different adsorption sites. By thermodynamic analysis, they derived the stability of these species and investigated the prevalence at different partial pressures of NH₃ and H₂. Using a similar approach, we investigated the stability of different NH_x surface species on AlN, GaN, and InN.¹⁸ Here, we also found that there exist different stable configurations of NH_x with similar structures, on all three materials. In these studies, NH₃ is modeled to adsorb on a bare surface allowing it to easily reach an adsorption site. However, after the thermal adsorption of trimethyl metal precursors, the adsorption sites would be blocked by methyl groups, kinetically hindering initial adsorption.

The lack of a thermal ALD process for InN, which is known for AlN and GaN, indicates a reaction path for the adsorption of intact NH₃ on AlN and GaN, that is not accessible on InN. In this study, we use quantum-chemical modeling of NH₃ adsorption on methyl-terminated GaN and InN. By comparison of adsorption energies and barriers, we find that there exists a possible reactive adsorption path of NH₃ on GaN, while a similar path on InN would be orders of magnitude slower. We argue that this huge difference in reaction time would explain why the adsorption of NH₃ is severely limited on InN and, thus, a fully thermal, low-temperature ALD process of InN with TMI and NH₃ would be very challenging.

The first principle density functional theory (DFT) was used to investigate the adsorption of NH₃ during the second step of the thermal ALD cycle using the Vienna Ab initio Simulation Package (VASP),^19–21 with optimizers extended by the VTST package.²² The General Gradient Approximation (GGA) functional PBE (Ref. 23) together with the third version of Grimme’s dispersion correction²⁴ was used with a plane wave basis set with cut-off energy of 700 eV and projector augmented wave (PAW)²⁵ potentials. The valence electron configuration used for different elements were 1s¹ for H, 2s² 2p² for C, 2s² 2p³ for N, 3d¹⁰ 4s² 4p¹ for Ga, and 4d¹⁰ 5s² 5p¹ for In. The electronic convergence was set to 10⁻⁶ eV for geometry optimization and 10⁻⁸ eV for phonon calculations.

As the surface model, seven-layer slabs with around 20 Å of vacuum padding, along the $[0001]$-direction were created from optimized unit cells of wurtzite-structured GaN and InN. The optimized cell parameters, $a=3.199Å$ and $c=5.173Å$ for GaN and $a=3.563Å$ and $c=5.762Å$ for InN, are in close agreement with experimental values, $a=3.197Å$ and $c=5.207Å$ for GaN (Ref. 26) and $a=3.533Å$ and $c=5.693Å$ for InN.²⁷ To allow the adsorption of NH₃, rectangular $(2×2)$ supercells along the $[224¯0]$ and $[1¯100]$ directions were constructed. This gave the cells the dimensions $a=6.40Å$⁠, $b=5.54Å$⁠, and $c=44.4Å$ for GaN and $a=7.13Å$⁠, $b=6.17Å$⁠, and $c=49.0Å$ for InN with $α=β=γ=90°$ for both structures, allowing four adsorption sites per cell. The dangling bonds at the N atoms at the bottom of the slab were saturated with four H atoms, one atom for each N. The effect on bottom termination was tested against the saturation of four pseudo-H with a 0.75 charge,²⁸ and with three ordinary H, not fully occupying all the N sites. The noted difference in the reactive adsorption energy was less than 1 kJ mol⁻¹, indicating that the slab was large enough for the bottom to not affect the surface reactions. In terms of a chemical formula, the composition of the slabs was Ga₂₈N₂₈H₄ and In₂₈N₂₈H₄. A $3×3×1$ Γ-centered k-point mesh was used for surface calculations. Calculations on gas species were accomplished by placing the molecule in a $10×10×10Å3$ cube, with the Γ-point as the only k-point. The relative energies were calculated by taking the energy for the surface with the surface species $(Esurf+ads)$ subtracted by the energy for the initial methyl-terminated surface $(Esurf)$ and ammonia in the gas phase $(ENH3)$⁠, Eq. (1),

For the relative energy of structure E, the energy of the surface species in Eq. (1) is replaced by the sum of energies of the surface with NH₂ substituting one methyl group $(Esurf+NH2)$ and gas phase methyl $(ECH4)$⁠.

All structures were optimized until the forces on all atoms were less than 10⁻² eV Å⁻¹. For surface structures, the positions of atoms at the lower five layers were kept fixed after optimization of the initial structure. Transition State (TS) structures were found by the Nudged Elastic Band (NEB) method, with an improved tangent definition and climbing image formulation as implemented in VTST.²² After structural optimization, harmonic phonon calculations were performed using finite displacements. The structures were confirmed to have no imaginary frequencies, except for the TS structures, which were confirmed to have a single imaginary mode in the direction of the reaction. Thermodynamic potentials for the nongas phase species were calculated using only vibrational contribution to free energy, Eq. (2),

For gaseous species, translational and rotational contributions were included as well. Thermochemical calculations were performed at STP (298.15 K, 1 atm) and at 500–800 K, i.e., temperatures of interest for the ALD of GaN and InN. The free energies were calculated at a pressure of 1 atm to be able to directly use them for calculations and discussions of rate constants by the Eyring equation and to relate them to equilibrium constants.

The investigated adsorption pathway for GaN (Fig. S1 in the supplementary material²⁹) and InN (Fig. 1) follow a very similar path, starting from the methyl-terminated surface, previously found as the final product after a self-limited adsorption cycle of TMG/TMI.³⁰ This surface has a methyl group on top of each surface metal atom, a total of four per cell, with a bond length of 1.97 Å for GaN and 2.18 Å for InN, pointing almost perpendicular to the surface. Desorption energies for methyl groups on GaN and InN are given in Table SI in the supplementary material. Most of the methyl groups are assumed to be still attached to the surface as the desorption energy is positive.

The adsorption path for NH₃ consists of five steps: initial methyl-terminated metal surface and NH₃ (g) (A) [Figs. 1(a) and S1(a) in the supplementary material], the methyl-terminated surface with physisorbed NH₃ (B) [Figs. 1(b) and S1(b) in the supplementary material], ligand exchange transition state (TS) (C^‡) [Figs. 1(c) and S1(c) in the supplementary material], physisorbed CH₄ above the NH₂ substituted surface (D) [Figs. 1(d) and S1(d) in the supplementary material], and the NH₂ substituted surface with CH₄(g) (E) [Figs. 1(e) and S1(e) in the supplementary material]. The energies of the adsorption paths on GaN and InN are given in Tables I and II, respectively, and graphically in Fig. 2. Transition state C^‡ was confirmed to be the maximum on the minimum energy path (MEP) by optimizing it slightly distorted toward structures B and D. Other reaction paths, such as proton transfer to an adsorbed methyl group via a five-coordinated TS, direct attachment of ammonia to a surface metal, and simultaneous release of methane were investigated. However, no such paths were found to be stable. Simultaneous desorption of two neighboring methyl groups as ethane was also considered, and although the reactions have an overall negative energy, as in Table SI in the supplementary material, the barrier for breaking the two bonds is expected to be of a similar order for the removal of two methyl groups, which is too high to be a viable pathway during ALD timescales.

When NH₃ is introduced to the surface, it is sterically blocked from forming a bond with the Ga/In surface atoms by methyl groups. This causes the NH₃ molecule to form a very weak physisorption, positioned at a large distance above the surface (2.9 Å above the methyl groups). The distance is much larger than the expected distance for a covalent bond and the low adsorption energy indicates only noncovalent interactions between NH₃ and the surface. NH₃ is, therefore, expected to be able to quickly diffuse over the surface as well as easily desorb. Treating translational freedom in the adsorbed NH₃ as a 2D ideal gas, free energy for the species could be lowered by approximately 25 kJ mol⁻¹ at STP and 50–80 kJ mol⁻¹ at ALD temperatures.

As the metal atoms are protected by methyl groups, ligand exchange of CH₃ to NH₂ cannot occur directly. Instead, a methyl group must desorb from the surface, leaving a vacancy onto which NH₃ can adsorb, in a S_N1-like mechanism. While adsorbing, a H atom can be transferred from NH₃ to the released methyl group, allowing it to be released as methane, leaving NH₂ to adsorb onto the vacant site. The H transfer makes the adsorption path differ slightly from a true S_N1 mechanism, as the adsorption kinetics is not fully uncoupled from the second reactant.

After the adsorption of NH₂, the released CH₄ molecule will only be weakly attached to the surface similar to the NH₃ molecule prior to adsorption. The CH₄ molecule is expected to only bind noncovalently with the surface and will quickly desorb after formation. The surface is almost identical to the final structure. The final product after the ligand exchange has one of the CH₃ groups replaced by NH₂ binding on top of the metal site. The bond length between the metal and nitrogen atoms is 1.90 Å for GaN and 2.11 Å for InN.

The low pressure used in ALD processes would cause an increase in free energy for adsorption processes, where the amount of gas molecules decreases, compared to that at standard pressure, and, thus, a smaller fraction of adsorbed species should be obtained at equilibrium. Desorption processes have the opposite effect, being favored by lower pressure. As the reactive adsorption process contains both adsorption and desorption of an equal amount of gas molecules, these effects cancel out and the equilibrium for the overall reaction will be pressure independent. The rate of the adsorption process is dependent on the product of the rate constant and pressure, meaning that for a lower pressure, the rate would be lower than at a higher pressure.

The energy profiles, as in Fig. 2, show that the adsorption path for NH₃ follows a similar path with a net lowering of the free energy after ligand NH₂ substitution, indicating that the adsorption process is thermodynamically favorable on both surfaces and that both Ga and In prefers to bond with NH₂ compared to CH₃. At ALD temperatures, 500–700 K, the net free energy is almost independent of changes in temperature, due to only a small change in entropy during the adsorption. However, for adsorption on InN, the relative energies of products D and E, as well as of transition state C, are shifted upward compared to GaN, showing that the process is less favorable on InN. The energies are shifted higher when the initial carbon-metal bond is broken, suggesting that methyl termination is more strongly bound to InN compared to GaN and that the preference to bind with NH₂ instead of CH₃ is much lower for In.

The difference in the free energy of the barrier is even more pronounced than the difference in the net free energy. As the main contribution to the energy of the barrier is the desorption of a CH₃ group from the surface, this is also a clear indicator that InN binds CH₃ more strongly compared to GaN. The difference in the barrier is between 86 and 108 kJ mol⁻¹ at an ALD temperature. The energy of removing CH₃ is lower for GaN compared to InN, possibly due to a larger steric repulsion for the methyl groups in the smaller GaN cell, which could account for the difference in barrier heights. The difference in bond strengths of N to Ga or In do not affect the barrier as the N atom from NH₃ does not interact with the metal until after traversing the transition state. The difference in the total adsorption energy is, however, dependent on the stronger bonds N forms to Ga compared to the bonds formed to In, which agrees with the previously reported results.¹⁸ Comparing the rate constants of adsorption obtained from these barriers by the transition state theory, Table III indicates that the chemisorption of NH₃ is many orders of magnitudes slower on InN compared to GaN, with the ratio of the rate constant for adsorption on InN divided by the constant for adsorption on GaN ranging from $1.0×10−9$ at 500 K to $9.2×10−8$ at 800 K. Furthermore, the rate constant for adsorption on InN at 800 K is of the same magnitude as the rate constant for adsorption on GaN at STP, which is much lower than the temperatures used in thermal GaN ALD. For an ALD process of InN with thermal NH₃ to work in a similar time frame as for GaN, either the temperature of the process must be increased, which is hindered by thermal instability, or the NH₃ pressure must be increased significantly, well outside the possible working pressures for ALD. Overcoming this limitation toward a thermal ALD of InN would require other precursor alternatives to the TMI and NH₃ combination, e.g., an indium precursor that would leave a more reactive surface where NH₃ could adsorb or a nitrogen precursor that would be reactive toward the methyl-terminated surface left by the TMI half-cycle.

In this study, we have compared NH₃ adsorption on GaN and InN using a DFT approach. The adsorption path is very similar for both surfaces, involving a S_N1-like mechanism, in which a methyl group must desorb from the surface initially, allowing NH₃ to adsorb onto the vacant site. The pathway is less energetically favorable for adsorption on InN compared to GaN. The difference in the energy of the adsorption barrier during the ligand exchange indicates that the adsorption process on InN is much slower than on GaN. This slow adsorption rate, many magnitudes slower than on GaN, indicates that thermal ALD using TMI and NH₃ would be almost impossible as the time for the process would be unreasonably long. The limitation of the thermal instability of InN eliminates the possibility of increasing the temperature to allow for shorter deposition times and, as such, the only alternative to a fully thermal ALD process is to use a different precursor system.

This project was funded by the Swedish Foundation for Strategic Research through the project “Time-resolved low temperature CVD for III-nitrides” (No. SSF-RMA 15-0018). L.O. acknowledges financial support from the Swedish Research Council (VR). Supercomputing resources were provided by the Swedish National Infrastructure for Computing (SNIC) and the Swedish National Supercomputer Centre (NSC).

The authors have no conflicts to disclose.

Karl Rönnby: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Henrik Pedersen: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Lars Ojamäe: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.