Theoretical study on the effect of H₂ and NH₃ on trimethylgallium decomposition process in GaN MOVPE

Gallium nitride (GaN) has been attracting great attention as the next-generation semiconductor for power devices. ^1,2) GaN is a wide bandgap semiconductor (3.4 eV), which enables high voltage, high speed, and high-temperature operation compared with Si which is the conventional power device material. Therefore, GaN has been actively researched not only for conventional optoelectronic devices but also for future power devices.

Metal-organic vapor phase epitaxy (MOVPE) ^3,4) is widely used for the production of GaN. In MOVPE, hydrogen (H₂) and nitrogen (N₂) carrier gases are used to supply the source gases, trimethyl gallium [TMGa, Ga(CH₃)₃] and ammonia (NH₃), to a substrate with a temperature of 1300 K. However, the detailed TMGa decomposition process has not yet been elucidated. ^5–13) Currently, the most commonly employed reaction pathway to model the gas-phase reaction rate of GaN MOVPE has been proposed by Hirako et al. ¹⁴⁾ This study states that the main reaction pathway is the reaction with ammonia and amino-related molecules undergo polymerization reactions with each other to form polymers such as 3Ga(CH₃)₂NH₂ → [Ga(CH₃)₂NH₂]₂ + Ga(CH₃)₂NH₂ → [Ga(CH₃)₂NH₂]₃. Ravasio et al. suggested that in addition to the polymerization reaction, radical reactions by H atoms and NH₂ molecules have a significant impact on the main reaction pathway ¹⁵⁾ such as Ga(NH₂)₃ + H → Ga(NH₂)₂H + NH₂. Sekiguchi et al. showed that TMGa repeatedly reacts with H₂ and decomposes into GaH ¹⁶⁾ by considering the reaction free energies.

In this study, we present a detailed theoretical discussion of the main reaction pathway of the TMGa decomposition by determining the Gibbs energy of activation including H₂ in addition to the source gases TMGa and NH₃ by ab initio calculations. In this study, we do not consider radicals, since they are very rare chemical species. The content of this paper is as follows. In Sect. 2, we describe the calculation methods. In Sect. 3, calculated results and discussions are shown, and finally, we summarize our findings in Sect. 4.

We used a combination of DFT calculations and transition state theory to analyze chemical reactions during GaN MOVPE growth. The structural optimization of each state, the electronic energy of the ground state, the vibrational frequency calculations and the Gibbs free energy calculations were performed using Gaussian. ^16,17) In this study, we used two exchange correlation functionals used in previous studies. The first is B3LYP, ^18,19) which is the most commonly used in quantum chemical calculations. This calculation method is thought to be a suitable method for estimating TMGa decomposition reaction. ^20–23) The second is the meta-exchange correlation functional M062X. ²⁴⁾ For both calculations, we used 6-311G + (d, p) ²⁵⁾ as the basis set because it allows us to determine the structure and energy of Ga–N with reasonable accuracy. ²⁶⁾

The Gibbs energy of activation is obtained by calculating the difference between the Gibbs free energies of the initial and transition states, and is an important parameter in considering the reaction process. In order to calculate the Gibbs energy of activation, we obtained the transition structure using the following procedure.

First, we searched for structures close to the transition state using Reaction plus, ²⁷⁾ a software program for which the nudged elastic band method is available. This is a method of searching for a minimum energy path between two different energy minimum states, the initial and the final states. ^28,29) Next, we obtained the transition states using Gaussian, ^30,31) and then vibrational analysis was performed on each structure, confirming that it has no imaginary frequency at the stable point and only one imaginary frequency in the reaction direction in the transition state. Finally, to confirm that the obtained transition states are the assumed transition states of the reactants and products, intrinsic reaction coordinate calculations were performed. ^32,33)

Transition state theory was used to calculate the rate constant, which represents the rate of the reaction. ³⁴⁾ We compared our results with those of other studies, ^15,35) in which the same calculation method was used to calculate the rate constants for the reaction of TMGa with NH₃, and confirmed that our results adequately represent those of previous studies. In addition, to determine which exchange-correlation functional is appropriate, we compared the Gibbs free energies of several molecules in the reaction path using the coupled cluster singles and doubles (CCSD) method, ^36–40) which is a high-precision calculation method. All basis functions in this case, we used aug-c.c.-pVTZ. ^41,42)

In this calculation, the frequency is obtained by approximating the energy surface with a quadratic curve, which tends to be larger than the actual frequency. A scaling factor is sometimes used to bring this into better agreement with the experimental frequencies. In this study, the scaling factors of B3LYP[6-311g + (d,p)], B3LYP(aug-c.c.-pVTZ), M062X[6-311g + (d,p)], M062X(aug-c.c.-pVTZ) and CCSD(aug-c.c.-pVTZ) were calculated as 0.9688, 0.9675 and 0.9520, 0.9557, and 0.9558, respectively. ^43,44)

It is known that frequencies lower than 150 cm⁻¹ are degenerate to rotational motion. Previous studies have improved the accuracy of chemical reactions by considering lower frequencies as rotators when necessary. ^15,35) This low vibrational frequency is mainly associated with the Ga–CH₃ bond, and we replaced this vibration with a one-dimensional free rotor.

For the mole fraction calculation, the species conservation equation was solved in time evolution, considering only the chemical reaction term as in Eq. (1). $\rho$ is the density, ${Y}_{\alpha }$ is the mass fraction of the chemical species $\alpha ,$ and ${\omega }_{\alpha }$ is the rate of formation of the chemical species $\alpha$ and is obtained from the rate constant

$$\begin{eqnarray}&&\displaystyle \frac{\partial \left(\rho {Y}_{\alpha }\right)}{\partial t}={\omega }_{\alpha }.\end{eqnarray} \tag{ 1 }$$

3.1. Reaction of TMGa with H₂ and NH₃ by B3LYP

First, to consider the reactions when one methyl group is removed from TMGa, we calculated the Gibbs energy of activation for each chemical reaction. Table I shows the Gibbs energy of activation and rate constants for each chemical reaction at 1300 K. In our previous work, the main reaction pathway is the one in which H₂ reacts with TMGa to form dimethyl gallium hydrogen [DMGaH, Ga(CH₃)₂H]. However, as shown in Fig. 1, the Gibbs energy of activation of TMGa reacting with H₂ is 3.24 eV at 1300 K [Reaction Eq. (1); Hereafter R1], whereas the Gibbs energies of activation of TMGa reacting with NH₃ first to form an amino group (−NH₂) and then reacting with H₂ to desorb the amino group are 2.96 eV (R2) and 2.84 eV (R3) respectively, which is smaller than that of reacting with only H₂. Calculating the difference in Gibbs energy of activation (3.24 − 2.96 eV = 0.28 eV) using the Eyring equation, it is clear that the reaction with NH₃ is faster because the kinetic constant with NH₃ is about 12 times larger than the kinetic constant with H₂. Therefore, as shown in Fig. 1, the main reaction pathway is not R1, but a combination of R2 and R3.

Table I. Gibbs energy of activation for the TMGa decomposition reaction.

		B3LYP[6-311g + (d,p)]		M062X[6-311g + (d,p)]
Reaction		Gibbs energy of activation at 1300 K (eV)	Kinetic constant at 1300 K (m3 mol−1 s−1)	Gibbs energy of activation at 1300 K (eV)	Kinetic constant at 1300 K (m3 mol−1 s−1)
1	Ga(CH3)3 + H2 → Ga(CH3)2H + CH4	3.240	0.806	3.228	0.892
2	Ga(CH3)3 + NH3 → Ga(CH3)2NH2 + CH4	2.965	9.410	2.676	124.129
3	Ga(CH3)2NH2 + H2 → Ga(CH3)2H + NH3	2.840	28.515	2.806	38.802
4	Ga(CH3)2H + NH3 → Ga(CH3)2NH2 + H2	2.811	37.160	2.556	362.661
5	Ga(CH3)2NH2 + H2 → GaCH3HNH2 + CH4	3.526	0.063	3.515	0.069
6	Ga(CH3)2NH2 + NH3 → GaCH3(NH2)2 + CH4	3.175	1.439	2.851	25.907
7	GaCH3(NH2)2 + H2 → GaCH3HNH2 + NH3	3.029	5.317	2.925	13.377
8	GaCH3HNH2 + NH3 → GaCH3(NH2)2 + H2	2.998	6.956	2.708	93.146
9	Ga(CH3)2H + H2 → GaCH3H2 + CH4	3.192	1.237	3.184	1.322
10	Ga(CH3)2H + NH3 → GaCH3HNH2 + CH4	2.942	11.530	2.665	136.413
11	GaCH3HNH2 + H2 → GaCH3H2 + NH3	2.817	35.003	2.779	49.536
12	GaCH3H2 + NH3 → GaCH3HNH2 + H2	2.791	44.390	2.551	376.803
13	GaCH3(NH2)2 + H2 → GaH(NH2)2 + CH4	3.980	0.001	3.850	0.003
14	GaCH3(NH2)2 + NH3 → Ga(NH2)3 + CH4	3.441	0.134	3.073	3.577
15	Ga(NH2)3 + H2 → GaH(NH2)2 + NH3	3.124	2.270	3.342	0.323
16	GaH(NH2)2 + NH3 → Ga(NH2)3 + H2	3.258	0.684	2.918	14.282
17	GaCH3HNH2 + H2 → GaH2NH2 + CH4	3.516	0.068	3.501	0.079
18	GaCH3HNH2 + NH3 → GaH(NH2)2 + CH4	3.063	3.897	2.760	58.627
19	GaH(NH2)2 + H2 → GaH2NH2 + NH3	3.058	4.093	2.973	8.718
20	GaH2NH2 + NH3 → GaH(NH2)2 + H2	3.024	5.526	2.755	61.339
21	GaCH3H2 + H2 → GaH3 + CH4	3.157	1.687	3.161	1.628
22	GaCH3H2 + NH3 → GaH2NH2 + CH4	2.937	12.041	2.684	115.093
23	GaH2NH2 + H2 → GaH3 + NH3	2.837	29.276	2.807	38.364
24	GaH3 + NH3 → GaH2NH2 + H2	2.768	54.206	2.550	379.258
25	GaH2NH2 + H2 → GaNH2 + 2H2	3.610	0.030	3.917	0.002
26	GaH3 + H2 → GaH + 2H2	3.861	0.003	4.056	0.001
27	GaCH3H2 + H2 → GaCH3 + 2H2	3.931	0.002	4.139	0.0003
28	GaCH3 + H2 → GaH + CH4	2.666	135.244	2.851	26.010
29	GaCH3 + NH3 → GaNH2 + CH4	2.608	227.222	2.534	438.763

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Considering the reaction of TMGa as well as the subsequent reactions, 29 chemical reactions are possible, as shown in Table I. The polymerization reactions between NH₂ related molecules are not taken into account, and obviously unstable radical molecules and atoms such as NH₂ and H are not generated in our considered 29 reactions. We do not consider the reverse reaction in which two hydrogens are desorbed, such as the reaction in which monomethyl gallium (MMGa, GaCH₃) is formed (R27; GaCH₃H₂ + H₂ → GaCH₃ + 2H₂), and the reactions in which GaNH₂ and GaH are formed (R25; GaH₂NH₂ + H₂ → GaNH₂ + 2H₂, R26; GaH₃ + H₂ →GaH + 2H₂). These reactions are called three-body reactions, and in general the probability of three chemical species colliding and reacting is negligibly small.

Next, we considered not only the reaction in which H₂ reacts with DMGaNH₂ to remove the amino group, but also other reactions together. When H₂ and NH₃ react with DMGaNH₂, there are three possible reactions: R3, R5, and R6. When DMGaNH₂ reacts with H₂, the Gibbs energy of activation is smaller and the reaction rate is faster when the amino group is removed (R3) than when the methyl group is removed (R5). The results indicate that DMGaNH₂ reacts with H₂ and changes to DMGaH. This is because the reactivity of H₂ with amino groups is higher than that with methyl groups.

In the decomposition of DMGaH, the Gibbs energy of activation when DMGaH reacts with H₂ is 3.19 eV (R9), whereas the Gibbs energy of activation when DMGaH first reacts with NH₃ to form an amino group and then reacts with H₂ to desorb the amino group is 2.94 eV (R10), 2.82 eV (R11), respectively. Similarly, in the decomposition of MMGaH₂, the Gibbs energy of activation is lower when reacts with NH₃ (R22) and then reacts with H₂ (R23) than when H₂ reacts directly and the methyl group is removed (R21). In this way, TMGa reacts with NH₃ to form an amino group, and then reacts with H₂ to desorb the amino group, and by repeating this reaction, the decomposition proceeds. The reactions that produce GaNH₂ (R25), GaH (R26), and GaCH₃ (R27) are expected to be molecules that are difficult to produce actually because of their high Gibbs energy of activation.

3.2. Reaction of TMGa with H₂ and NH₃ by M062X

3.3. Calculation of mole fractions in MOVPE conditions

We consider the correspondence between the MOVPE conditions and these reactions for which the reaction rates were determined in the previous section. Figs. 2 and 3 show the time evolution of the mole fraction of each chemical species at 1300 K. In this calculation, we used the rate constants shown in Table I. For the initial partial pressure, the conditions of the MOVPE method were used as a reference, with the total pressure being 1.0 atm, the partial pressures of H₂, NH₃, and TMGa being 0.50, 0.16, $1.6\times {10}^{-4}$ atm, respectively, and the remainder being N₂. For both exchange-correlation functions, the mole fraction is almost constant after 0.5 s, indicating that the value after 1 s is almost the same as the value at equilibrium.

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Figures 4 and 5 show the mole fractions of each chemical species after 1 s at 1300 K. In B3LYP, as shown in Fig. 4, GaH₃, in which three methyl groups are decomposed from TMGa, is the most abundant. The calculated GaH₃ ratio is $8.35\times {10}^{-5}.$ In M062X, as shown in Fig. 5, Ga(NH₂)₃, in which three amino groups are formed instead of a methyl group by the reaction with NH₃, is the most abundant at $1.43\times {10}^{-4}.$

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3.4. Main reaction pathway of TMGa decomposition

3.5. Comparison between B3LYP and M062X

The difference in the energies of the molecules calculated is the key to determining the difference between the final products of B3LYP and M062X. Therefore, in order to discuss which exchange-correlation functional is better for this reaction pathway, we calculated the Gibbs free energy of the molecule by using the high precision CCSD method which includes many electron excitations described by the products of single and double electron excitations. ^36–40) The calculations were performed for three molecules, GaH₃, GaH₂NH₂ and GaH(NH₂)₂. Figure 6 shows the change in the Gibbs free energy with respect to GaH₃ at 1300 K. The lower the energy with respect to GaH₃, the easier it is for the reaction with NH₃ to occur. As a result, the Gibbs free energy calculated using the CCSD method took values between B3LYP and M062X, and GaH₃, GaH₂NH₂, and GaH(NH₂)₂ were closer to the CCSD values for B3LYP than for M062X. From this result, the main reaction pathway of B3LYP is more representative of the actual phenomenon, and it can be expected that GaH₃ is actually more abundant in surface reactions than Ga(NH₂)₃.

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More importantly, the results of time-of-flight mass spectrometry support the occurrence of a reaction with H₂ to desorb amino groups by the observation of NH₂D molecules under D₂ carrier gas conditions. This observation indicates the reaction described as Ga(CH₃)₂NH₂ + D₂ → Ga(CH₃)₂D + NH₂D. ⁴⁵⁾ Therefore, the experiments also indicate that the main reaction pathway obtained by B3LYP is reasonable

In this study, to examine the main reaction pathway of the TMGa decomposition process, we calculated and compared the decomposition rate from the Gibbs energy of activation and calculated the mole fraction of each chemical species. As a result, in B3LYP, the decomposition pathway of TMGa is the sequential reaction with NH₃ followed by the reaction with H₂. In M062X, the decomposition proceeds through repeated reactions with NH₃ as in the previous study.

Using the reaction rates we obtained, we calculated the mole fractions of each chemical species at 1300 K. It was found that GaH₃ was the most abundant species in B3LYP and Ga(NH₂)₃ in M062X. When we tested the difference between the two exchange-correlation functions using the high precision CCSD method, it was found that the results of the CCSD method were closer to those of B3LYP. Moreover, the experiment also supports the reaction paths obtained by B3LYP. Therefore, the main reaction pathway of TMGa decomposition is as follows

$$\begin{eqnarray*}&&\begin{array}{l}{\rm{Ga}}{\left({{\rm{CH}}}_{3}\right)}_{3}+3{{\rm{H}}}_{2}+{{\rm{NH}}}_{3}\to {\rm{Ga}}{\left({{\rm{CH}}}_{3}\right)}_{2}{{\rm{NH}}}_{2}\\ \,+\,3{{\rm{H}}}_{2}+{{\rm{CH}}}_{4}\to {\rm{Ga}}{\left({{\rm{CH}}}_{3}\right)}_{2}{\rm{H}}+2{{\rm{H}}}_{2}+{{\rm{NH}}}_{3}\\ \,+\,{{\rm{CH}}}_{4}\to {{\rm{GaCH}}}_{3}{{\rm{HNH}}}_{2}+2{{\rm{H}}}_{2}\\ \,+\,2{{\rm{CH}}}_{4}\to {{\rm{GaCH}}}_{3}{{\rm{H}}}_{2}+{{\rm{H}}}_{2}+{{\rm{NH}}}_{3}\\ \,+\,2{{\rm{CH}}}_{4}\to {{\rm{GaH}}}_{2}{{\rm{NH}}}_{2}+{{\rm{H}}}_{2}\\ \,+\,3{{\rm{CH}}}_{4}\to {{\rm{GaH}}}_{3}+{{\rm{NH}}}_{3}+3{{\rm{CH}}}_{4}.\end{array}\end{eqnarray*}$$

The main reaction pathway obtained in our study shows that when H₂ is sufficiently present as a carrier gas, amino groups, which are responsible for the formation of a wide variety of polymers, are difficult to form. Therefore, we were able to reduce the number of chemical reactions considered in conventional fluid simulations. GaH₃ molecules must be considered in the surface reaction of GaN MOVPE. Furthermore, it may be effective to decompose TMGa at a high temperature of about 1300 K for a certain period of time to control carbon contamination.

We greatly thank Dr. Zheng Ye, Prof. Shugo Nitta, and Prof. Hiroshi Amano for an illuminating discussion from the viewpoints of experiments. This work was supported by the MEXT research programs, "Program for Research and Development of Next-Generation Semiconductors to Realize an Energy-Saving Society under contract No. JPJ005357, "Program for Promoting Research on the Supercomputer Fugaku" (Quantum-Theory-Based Multiscale Simulations toward Development of Next-GenerationEnergy-Saving Semiconductor Devices), and also by the grants-in-aid under contract No. 18H03873. Computations were performed on Fugaku, Riken and on other supercomputers at the Supercomputer Center of ISSP, The University of Tokyo, at the Research Center for Computational Science of the National Institutes of Natural Sciences, at the Information Technology Center of Nagoya University, through the HPCI System Research Project (Project ID: hp200122).