Thermodynamic and experimental studies of β-Ga₂O₃ growth by metalorganic vapor phase epitaxy

Thermodynamic analysis of β-Ga₂O₃ growth by MOVPE using TEG and O₂ as precursors ^19–21) was conducted. It is assumed that a mixture of an inert gas (IG) such as He, Ar, or N₂ and H₂ is used as the carrier gas. TEG is irreversibly decomposed by the homogeneous reaction of β-hydrogen elimination at temperatures above 400 °C, which forms gallane (GaH₃) and ethylene (C₂H₄) gases, even without H₂ in the carrier gas. ²⁵⁾ Therefore, for thermodynamic analysis at a temperature of 500 °C or higher, the starting gaseous species are GaH₃, C₂H₄, O₂, where IG and H₂ are used as the carrier gas. Under the thermal equilibrium above the β-Ga₂O₃ substrate, the following 16 gaseous species coexist: GaH₃, GaH₂, GaH, Ga, Ga(OH), GaO, Ga₂O, C₂H₄, C₂H₂, C₂H₆, CO₂, CO, O₂, H₂O, H₂ and IG. These gaseous species are associated by the following equilibrium reactions:

$$\begin{eqnarray}&&{{\rm{GaH}}}_{3}\left({\rm{g}}\right)={{\rm{GaH}}}_{2}\left({\rm{g}}\right)+\displaystyle \frac{1}{2}{{\rm{H}}}_{2}\left({\rm{g}}\right),\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{{\rm{GaH}}}_{3}\left({\rm{g}}\right)={\rm{GaH}}\left({\rm{g}}\right)+{{\rm{H}}}_{2}\left({\rm{g}}\right),\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{{\rm{GaH}}}_{3}\left({\rm{g}}\right)={\rm{Ga}}\left({\rm{g}}\right)+\displaystyle \frac{3}{2}{{\rm{H}}}_{2}\left({\rm{g}}\right),\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{{\rm{GaH}}}_{3}\left({\rm{g}}\right)+{{\rm{O}}}_{2}\left({\rm{g}}\right)={\rm{Ga}}({\rm{OH}})\left({\rm{g}}\right)+{{\rm{H}}}_{2}{\rm{O}}\left({\rm{g}}\right),\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&2\mathrm{Ga}\left({\rm{g}}\right)+\frac{3}{2}{{\rm{O}}}_{2}\left({\rm{g}}\right)=\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}\left({\rm{s}}\right),\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{\rm{Ga}}\left({\rm{g}}\right)+\displaystyle \frac{1}{2}{{\rm{O}}}_{2}\left({\rm{g}}\right)={\rm{GaO}}\left({\rm{g}}\right),\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&2{\rm{Ga}}\left({\rm{g}}\right)+\displaystyle \frac{1}{2}{{\rm{O}}}_{2}\left({\rm{g}}\right)={{\rm{Ga}}}_{2}{\rm{O}}\left({\rm{g}}\right),\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{{\rm{C}}}_{2}{{\rm{H}}}_{4}\left({\rm{g}}\right)={{\rm{C}}}_{2}{{\rm{H}}}_{2}\left({\rm{g}}\right)+{{\rm{H}}}_{2}\left({\rm{g}}\right),\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&{{\rm{C}}}_{2}{{\rm{H}}}_{4}\left({\rm{g}}\right)+{{\rm{H}}}_{2}\left({\rm{g}}\right)={{\rm{C}}}_{2}{{\rm{H}}}_{6}\left({\rm{g}}\right),\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{{\rm{C}}}_{2}{{\rm{H}}}_{4}\left({\rm{g}}\right)+3{{\rm{O}}}_{2}\left({\rm{g}}\right)=2{{\rm{CO}}}_{2}\left({\rm{g}}\right)+2{{\rm{H}}}_{2}{\rm{O}}\left({\rm{g}}\right),\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{{\rm{C}}}_{2}{{\rm{H}}}_{4}\left({\rm{g}}\right)+2{{\rm{O}}}_{2}\left({\rm{g}}\right)=2{\rm{CO}}\left({\rm{g}}\right)+2{{\rm{H}}}_{2}{\rm{O}}\left({\rm{g}}\right),\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{{\rm{H}}}_{2}\left({\rm{g}}\right)+\displaystyle \frac{1}{2}{{\rm{O}}}_{2}\left({\rm{g}}\right)={{\rm{H}}}_{2}{\rm{O}}\left({\rm{g}}\right).\end{eqnarray} \tag{ 12 }$$

The characteristic of this system is that there are species with different ratios of Ga and O (β-Ga₂O₃(s), GaO(g), and Ga₂O(g)), and unlike the MOVPE growth of III–V compounds, the combustion of hydrocarbons (C₂H₄(g), C₂H₂(g), and C₂H₆(g)) and H₂ must be considered. The law of mass action for equilibrium reactions (1)–(12) can be written as:

$$\begin{eqnarray}&&{K}_{1}\left(T\right)=\displaystyle \frac{{P}_{{{\rm{GaH}}}_{2}}{P}_{{{\rm{H}}}_{2}}^{\displaystyle \frac{1}{2}}}{{P}_{{{\rm{GaH}}}_{3}}},\end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray}&&{K}_{2}\left(T\right)=\displaystyle \frac{{P}_{{\rm{GaH}}}{P}_{{{\rm{H}}}_{2}}}{{P}_{{{\rm{GaH}}}_{3}}},\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&{K}_{3}\left(T\right)=\displaystyle \frac{{P}_{{\rm{Ga}}}{P}_{{{\rm{H}}}_{2}}^{\displaystyle \frac{3}{2}}}{{P}_{{{\rm{GaH}}}_{3}}},\end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}&&{K}_{4}\left(T\right)=\displaystyle \frac{{P}_{{\rm{Ga}}({\rm{OH}})}{P}_{{{\rm{H}}}_{2}{\rm{O}}}}{{P}_{{{\rm{GaH}}}_{3}}{P}_{{{\rm{O}}}_{2}}},\end{eqnarray} \tag{ 16 }$$

$$\begin{eqnarray}&&{K}_{5}\left(T\right)=\frac{{a}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}}{{P}_{\mathrm{Ga}}^{2}{P}_{{{\rm{O}}}_{2}}^{\displaystyle \frac{3}{2}}},\end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray}&&{K}_{6}\left(T\right)=\displaystyle \frac{{P}_{{\rm{GaO}}}}{{P}_{{\rm{Ga}}}{P}_{{{\rm{O}}}_{2}}^{\displaystyle \frac{1}{2}}},\end{eqnarray} \tag{ 18 }$$

$$\begin{eqnarray}&&{K}_{7}\left(T\right)=\displaystyle \frac{{P}_{{{\rm{Ga}}}_{2}{\rm{O}}}}{{P}_{{\rm{Ga}}}^{2}{P}_{{{\rm{O}}}_{2}}^{\displaystyle \frac{1}{2}}},\end{eqnarray} \tag{ 19 }$$

$$\begin{eqnarray}&&{K}_{8}\left(T\right)=\displaystyle \frac{{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{2}}{P}_{{{\rm{H}}}_{2}}}{{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{4}}},\end{eqnarray} \tag{ 20 }$$

$$\begin{eqnarray}&&{K}_{9}\left(T\right)=\displaystyle \frac{{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{6}}}{{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{4}}{P}_{{{\rm{H}}}_{2}}},\end{eqnarray} \tag{ 21 }$$

$$\begin{eqnarray}&&{K}_{10}\left(T\right)=\displaystyle \frac{{P}_{{{\rm{CO}}}_{2}}^{2}{P}_{{{\rm{H}}}_{2}{\rm{O}}}^{2}}{{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{4}}{P}_{{{\rm{O}}}_{2}}^{3}},\end{eqnarray} \tag{ 22 }$$

$$\begin{eqnarray}&&{K}_{11}\left(T\right)=\displaystyle \frac{{P}_{{\rm{CO}}}^{2}{P}_{{{\rm{H}}}_{2}{\rm{O}}}^{2}}{{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{4}}{P}_{{{\rm{O}}}_{2}}^{2}},\end{eqnarray} \tag{ 23 }$$

$$\begin{eqnarray}&&{K}_{12}\left(T\right)=\displaystyle \frac{{P}_{{{\rm{H}}}_{2}{\rm{O}}}}{{P}_{{{\rm{H}}}_{2}}{P}_{{{\rm{O}}}_{2}}^{\displaystyle \frac{1}{2}}}.\end{eqnarray} \tag{ 24 }$$

Here, ${K}_{n}(T),$ ${P}_{{\rm{i}}},$ and ${a}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ are the equilibrium constant of the equilibrium reaction (n) depending on the growth temperature (T), the equilibrium partial pressures of gaseous species i, and the activity of β-Ga₂O₃, respectively, where the value of ${a}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ can be assumed to be 1 in this case. ${K}_{n}(T)$ can be calculated using the thermochemical tables ^34–36) and can be fitted by the following equation:

$$\begin{eqnarray}&&{\mathrm{log}}_{10}{K}_{n}\left(T\right)=a+\displaystyle \frac{b}{T}+c\cdot {\mathrm{log}}_{10}T,\end{eqnarray} \tag{ 25 }$$

where a, b, and c are fitting parameters, and their best fit values for each chemical reaction are summarized in Table I. The total pressure (${P}_{{\rm{tot}}}$) given by the sum of the equilibrium partial pressures for each gaseous species is constant; therefore, the following equation is satisfied:

$$\begin{eqnarray}\begin{array}{lll}{P}_{{\rm{tot}}} & = & {P}_{{{\rm{GaH}}}_{3}}+{P}_{{{\rm{GaH}}}_{2}}+{P}_{{\rm{GaH}}}+{P}_{{\rm{Ga}}}+{P}_{{\rm{Ga}}({\rm{OH}})}+{P}_{{\rm{GaO}}}\\ & & +\,{P}_{{{\rm{Ga}}}_{2}{\rm{O}}}+{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{4}}+{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{2}}+{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{6}}+{P}_{{{\rm{CO}}}_{2}}+{P}_{{\rm{CO}}}\\ & & +\,{P}_{{{\rm{O}}}_{2}}+{P}_{{{\rm{H}}}_{2}{\rm{O}}}+{P}_{{{\rm{H}}}_{2}}+{P}_{{\rm{IG}}}.\end{array}\end{eqnarray} \tag{ 26 }$$

The stoichiometric relationship for the formation of β-Ga₂O₃ satisfies the following equation:

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{1}{2}\left[{P}_{{\rm{TEG}}}^{{\rm{o}}}-\left({P}_{{{\rm{GaH}}}_{3}}+{P}_{{{\rm{GaH}}}_{2}}+{P}_{{\rm{GaH}}}+{P}_{{\rm{Ga}}}+{P}_{{\rm{Ga}}\left({\rm{OH}}\right)}+{P}_{{\rm{GaO}}}+2{P}_{{{\rm{Ga}}}_{2}{\rm{O}}}\right)\right]\\ =\,\displaystyle \frac{2}{3}\left[{P}_{{{\rm{O}}}_{2}}^{{\rm{o}}}-\left({P}_{{{\rm{O}}}_{2}}+\displaystyle \frac{1}{2}{P}_{{\rm{Ga}}({\rm{OH}})}+\displaystyle \frac{1}{2}{P}_{{\rm{GaO}}}+\displaystyle \frac{1}{2}{P}_{{{\rm{Ga}}}_{2}{\rm{O}}}+{P}_{{{\rm{CO}}}_{2}}+\displaystyle \frac{1}{2}{P}_{{\rm{CO}}}+\displaystyle \frac{1}{2}{P}_{{{\rm{H}}}_{2}{\rm{O}}}\right)\right].\end{array}\end{eqnarray} \tag{ 27 }$$

Here, ${{P}}_{{\rm{TEG}}}^{{\rm{o}}}$ and ${P}_{{{\rm{O}}}_{2}}^{{\rm{o}}}$ are the input partial pressures of TEG and O₂, respectively. The left side of Eq. (27) gives half the number of Ga atoms lost from the vapor phase due to β-Ga₂O₃ growth, which is equal to the driving force for β-Ga₂O₃ growth (${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$). Furthermore, the atomic numbers of hydrogen, carbon, and IG in the vapor phase are invariant; therefore, the following two equations are introduced:

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{\displaystyle \frac{15}{2}{P}_{{\rm{TEG}}}^{{\rm{o}}}+{P}_{{{\rm{H}}}_{2}}^{{\rm{o}}}}{\displaystyle \frac{27}{2}{P}_{{\rm{TEG}}}^{{\rm{o}}}+{P}_{{{\rm{H}}}_{2}}^{{\rm{o}}}+{P}_{{\rm{IG}}}^{{\rm{o}}}}\\ =\,\displaystyle \frac{\displaystyle \frac{3}{2}{P}_{{{\rm{GaH}}}_{3}}+{P}_{{{\rm{GaH}}}_{2}}+\displaystyle \frac{1}{2}{P}_{{\rm{GaH}}}+\displaystyle \frac{1}{2}{P}_{{\rm{Ga}}({\rm{OH}})}+2{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{4}}+{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{2}}+3{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{6}}+{P}_{{{\rm{H}}}_{2}{\rm{O}}}+{P}_{{{\rm{H}}}_{2}}}{\displaystyle \frac{3}{2}{P}_{{{\rm{GaH}}}_{3}}+{P}_{{{\rm{GaH}}}_{2}}+\displaystyle \frac{1}{2}{P}_{{\rm{GaH}}}+\displaystyle \frac{1}{2}{P}_{{\rm{Ga}}({\rm{OH}})}+4{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{4}}+3{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{2}}+5{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{6}}+{P}_{{{\rm{H}}}_{2}{\rm{O}}}+{P}_{{{\rm{H}}}_{2}}+{P}_{{{\rm{CO}}}_{2}}+{P}_{{\rm{CO}}}+{P}_{{\rm{IG}}}},\end{array}\end{eqnarray} \tag{ 28 }$$

$$\begin{eqnarray}&&\begin{array}{c}\begin{array}{l}\displaystyle \frac{6{P}_{{\rm{TEG}}}^{{\rm{o}}}}{\displaystyle \frac{27}{2}{P}_{{\rm{TEG}}}^{{\rm{o}}}+{P}_{{{\rm{H}}}_{2}}^{{\rm{o}}}+{P}_{{\rm{IG}}}^{{\rm{o}}}}\\ =\,\displaystyle \frac{2{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{4}}+2{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{2}}+2{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{6}}+{P}_{{{\rm{CO}}}_{2}}+{P}_{{\rm{CO}}}}{\displaystyle \frac{3}{2}{P}_{{{\rm{GaH}}}_{3}}+{P}_{{{\rm{GaH}}}_{2}}+\displaystyle \frac{1}{2}{P}_{{\rm{GaH}}}+\displaystyle \frac{1}{2}{P}_{{\rm{Ga}}({\rm{OH}})}+4{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{4}}+3{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{2}}+5{P}_{{{\rm{C}}}_{2}{{\rm{H}}}_{6}}+{P}_{{{\rm{H}}}_{2}{\rm{O}}}+{P}_{{{\rm{H}}}_{2}}+{P}_{{{\rm{CO}}}_{2}}+{P}_{{\rm{CO}}}+{P}_{{\rm{IG}}}},\end{array}\end{array}\end{eqnarray} \tag{ 29 }$$

where ${P}_{{{\rm{H}}}_{2}}^{{\rm{o}}}$ and ${P}_{{\rm{IG}}}^{{\rm{o}}}$ are the input partial pressures of H₂ and IG, respectively. Equation (28) is the ratio of the number of hydrogen atoms to the number of hydrogen, carbon and IG atoms in the system, and Eq. (29) is the ratio of the number of carbon atoms to the number of hydrogen, carbon and IG atoms in the system.

Table I. Fitting parameters for calculation of the equilibrium constants as a function of T (in Kelvin).

Reactions	a	b	c
${{\rm{GaH}}}_{3}\left({\rm{g}}\right)={{\rm{GaH}}}_{2}\left({\rm{g}}\right)+\displaystyle \frac{1}{2}{{\rm{H}}}_{2}\left({\rm{g}}\right)$	−1.10 × 101	−2.12 × 103	4.87 × 100
${{\rm{GaH}}}_{3}\left({\rm{g}}\right)={\rm{GaH}}\left({\rm{g}}\right)+{{\rm{H}}}_{2}\left({\rm{g}}\right)$	−9.36 × 100	−4.75 × 103	5.08 × 100
${{\rm{GaH}}}_{3}\left({\rm{g}}\right)={\rm{Ga}}\left({\rm{g}}\right)+\displaystyle \frac{3}{2}{{\rm{H}}}_{2}\left({\rm{g}}\right)$	−9.45 × 100	−7.72 × 103	5.78 × 100
${{\rm{GaH}}}_{3}\left({\rm{g}}\right)+{{\rm{O}}}_{2}\left({\rm{g}}\right)={\rm{Ga}}({\rm{OH}})\left({\rm{g}}\right)+{{\rm{H}}}_{2}{\rm{O}}\left({\rm{g}}\right)$	−1.38 × 101	2.66 × 104	4.56 × 100
$2\mathrm{Ga}\left({\rm{g}}\right)+\frac{3}{2}{{\rm{O}}}_{2}\left({\rm{g}}\right)=\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}\left({\rm{s}}\right)$	−3.75 × 101	8.59 × 104	2.66 × 100
${\rm{Ga}}\left({\rm{g}}\right)+\displaystyle \frac{1}{2}{{\rm{O}}}_{2}\left({\rm{g}}\right)={\rm{GaO}}\left({\rm{g}}\right)$	−1.45 × 100	6.55 × 103	−2.88 × 10−1
$2{\rm{Ga}}\left({\rm{g}}\right)+\displaystyle \frac{1}{2}{{\rm{O}}}_{2}\left({\rm{g}}\right)={{\rm{Ga}}}_{2}{\rm{O}}\left({\rm{g}}\right)$	−4.64 × 100	3.35 × 104	−1.28 × 100
${{\rm{C}}}_{2}{{\rm{H}}}_{4}\left({\rm{g}}\right)={{\rm{C}}}_{2}{{\rm{H}}}_{2}\left({\rm{g}}\right)+{{\rm{H}}}_{2}\left({\rm{g}}\right)$	3.42 × 100	−9.14 × 103	1.02 × 100
${{\rm{C}}}_{2}{{\rm{H}}}_{4}\left({\rm{g}}\right)+{{\rm{H}}}_{2}\left({\rm{g}}\right)={{\rm{C}}}_{2}{{\rm{H}}}_{6}\left({\rm{g}}\right)$	−5.24 × 100	7.19 × 103	−5.00 × 10−1
${{\rm{C}}}_{2}{{\rm{H}}}_{4}\left({\rm{g}}\right)+3{{\rm{O}}}_{2}\left({\rm{g}}\right)=2{{\rm{CO}}}_{2}\left({\rm{g}}\right)+2{{\rm{H}}}_{2}{\rm{O}}\left({\rm{g}}\right)$	2.73 × 10−1	6.89 × 104	−5.07 × 10−1
${{\rm{C}}}_{2}{{\rm{H}}}_{4}\left({\rm{g}}\right)+2{{\rm{O}}}_{2}\left({\rm{g}}\right)=2{\rm{CO}}\left({\rm{g}}\right)+2{{\rm{H}}}_{2}{\rm{O}}\left({\rm{g}}\right)$	1.15 × 101	3.92 × 104	−1.14 × 100
${{\rm{H}}}_{2}\left({\rm{g}}\right)+\displaystyle \frac{1}{2}{{\rm{O}}}_{2}\left({\rm{g}}\right)={{\rm{H}}}_{2}{\rm{O}}\left({\rm{g}}\right)$	2.28 × 10−2	1.26 × 104	−8.37 × 10−1

The equilibrium partial pressures of gaseous species can be calculated by solving the set of simultaneous equations under certain growth conditions: T, ${P}_{{\rm{tot}}},$ ${P}_{\mathrm{TEG}}^{{\rm{o}}},$ the input VI/III ratio (= $2{P}_{{{\rm{O}}}_{2}}^{{\rm{o}}}/{P}_{{\rm{TEG}}}^{{\rm{o}}}$), and the mole fraction of H₂ in the carrier gas (${F}^{{\rm{o}}}={{P}}_{{{\rm{H}}}_{2}}^{{\rm{o}}}/\left({{P}}_{{{\rm{H}}}_{2}}^{{\rm{o}}}+{{P}}_{{\rm{IG}}}^{{\rm{o}}}\right)$). Under thermal equilibrium, i.e. under mass transportation limited growth, the growth rate (GR) is given as:

$$\begin{eqnarray}&&{\rm{G}}{\rm{R}}={K}_{{\rm{g}}}\cdot {\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}},\end{eqnarray} \tag{ 30 }$$

where ${K}_{{\rm{g}}}$ is the mass transfer coefficient. ^32,33)

Figure 1(a) shows the growth temperature dependence of the equilibrium partial pressures of gaseous species over β-Ga₂O₃ under conditions with ${P}_{{\rm{tot}}}$ = 20 Torr, ${P}_{{\rm{TEG}}}^{{\rm{o}}}$ = 2.0 × 10^–2 Torr, VI/III = 10, and ${F}^{{\rm{o}}}$ = 0 (inert carrier gas). The vapor pressure of pure Ga metal (${P}_{{\rm{Ga}}}^{{\rm{V}}}$) is also included as a dotted line. ³⁷⁾ The equilibrium partial pressures of C₂H₄, C₂H₂, and C₂H₆ are very low and decrease with an increase in the growth temperature, whereas those of H₂, CO, CO₂, and H₂O remain high over the entire temperature range investigated. This indicates that hydrocarbons and H₂ cause combustion reactions with O₂ by chemical reactions (8)–(12). In the MOVPE growth of GaN, a high concentration of carbon has been reported to be incorporated into a grown layer by the simultaneous supply of hydrocarbons. ³⁸⁾ Therefore, if the presence of CO and CO₂ in the system does not cause carbon contamination (this will be mentioned again later in this study), high-temperature growth is considered to be preferable because the equilibrium partial pressures of hydrocarbons in the system become low. Another aspect to consider is that the equilibrium partial pressure of gaseous Ga is below ${P}_{{\rm{Ga}}}^{{\rm{V}}}$ over the entire temperature range investigated, which indicates that metal Ga droplets are not formed on the β-Ga₂O₃ surface.

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The growth temperature dependence of ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ calculated from the results in Fig. 1(a) is shown in Fig. 1(b), together with ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ calculated for various ${F}^{{\rm{o}}}$ under the same growth conditions as in Fig. 1(a) except for ${F}^{{\rm{o}}}.$ When ${F}^{{\rm{o}}}$ is 0, ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ is almost equal to ${P}_{{\rm{TEG}}}^{{\rm{o}}}/2$ up to 900 °C, but decreases sharply as the temperature increases above 900 °C, and then becomes negative above 1020 °C indicating the decomposition (etching) of β-Ga₂O₃. Figure 1(a) shows that even when ${F}^{{\rm{o}}}$ is 0, H₂ derived from TEG is present in the system at a high equilibrium partial pressure; therefore, β-Ga₂O₃ is considered to react with H₂ and decompose at high temperatures. At around 1200 °C, the equilibrium partial pressures of H₂O and Ga₂O become very high, and the ratio of the equilibrium partial pressure of Ga₂O and H₂O is almost 1:2. Therefore, β-Ga₂O₃ decomposes by the same net reaction as the decomposition reaction in H₂ atmosphere heat treatment, as shown by: ³⁹⁾

$$\begin{eqnarray}&&\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}\left({\rm{s}}\right)+2{{\rm{H}}}_{2}({\rm{g}})={\mathrm{Ga}}_{2}{\rm{O}}\left({\rm{g}}\right)+2{{\rm{H}}}_{2}{\rm{O}}\left({\rm{g}}\right).\end{eqnarray} \tag{ 31 }$$

In addition, as ${F}^{{\rm{o}}}$ increases, the temperature at which ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ becomes 0 shifts to a lower temperature. If ${F}^{{\rm{o}}}$ is 0.01, i.e. the carrier gas contains 1% H₂, then β-Ga₂O₃ cannot be grown at 1000 °C. Therefore, it can be concluded that ${F}^{{\rm{o}}}$ = 0, i.e. the use of IG as a carrier gas, is preferable for the MOVPE growth of β-Ga₂O₃ at high temperatures. A similar conclusion has been drawn for the HVPE growth of β-Ga₂O₃. ³²⁾

Figure 2 shows the equilibrium partial pressures of gaseous species over β-Ga₂O₃ and the resultant ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ when the input VI/III ratio is changed under growth conditions of T = 900 °C, ${P}_{{\rm{tot}}}$ = 20 Torr, ${P}_{\mathrm{TEG}}^{{\rm{o}}}$ = 2.0 × 10^–2 Torr, and ${{F}}^{{\rm{o}}}$ = 0. Near the input VI/III ratio of 20, the equilibrium partial pressures of gaseous species, except IG, change suddenly. On the side where the input VI/III ratio is lower than 20, the equilibrium partial pressures of H₂, CO, C₂H₂, C₂H₄, and C₂H₆ increase due to incomplete combustion of hydrocarbons and H₂. At the same time, as the input VI/III ratio decreases, the equilibrium partial pressure of Ga₂O increases and exceeds ${P}_{{\rm{TEG}}}^{{\rm{o}}},$ so that ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ becomes negative and β-Ga₂O₃ is decomposed (etched). Therefore, if there is insufficient O₂ in the system, then O₂ is preferentially consumed for the combustion of hydrocarbons and H₂, and the H₂ remaining due to incomplete combustion decomposes (etches) β-Ga₂O₃ by reaction (31). On the other hand, on the side where the input VI/III ratio is higher than 20, the equilibrium partial pressures of O₂, H₂O, and CO₂ become high, while those of H₂, CO, C₂H₂, C₂H₄, C₂H₆, and gaseous species containing Ga decrease. Therefore, when there is sufficient O₂ in the system, hydrocarbons and H₂ combust completely, and the remaining O₂ contributes to the growth of β-Ga₂O₃. The complete combustion of hydrocarbons and H₂ can also be confirmed by the equilibrium partial pressures of CO₂ and H₂O being almost equal to $6{P}_{{\rm{TEG}}}^{{\rm{o}}}$ and $7.5{P}_{{\rm{TEG}}}^{{\rm{o}}},$ respectively. Furthermore, the ${P}_{{{\rm{O}}}_{2}}^{{\rm{o}}}$ required for the complete combustion of carbon and hydrogen derived from TEG is equal to $9.75{P}_{{\rm{TEG}}}^{{\rm{o}}};$ therefore, the input VI/III ratio at which combustion is completed is 19.5. This is the reason why the equilibrium partial pressures of gaseous species change suddenly near the input VI/III ratio of 20. When the input VI/III ratio is increased, ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ is rapidly increased to a positive value in the input VI/III ratio range of 7–20 and then becomes saturated at almost half the value of ${P}_{{\rm{TEG}}}^{{\rm{o}}}.$ Therefore, it is essential to use a high input VI/III ratio that allows sufficient O₂ to remain, even after complete combustion of the hydrocarbons and H₂, for the MOVPE growth of β-Ga₂O₃. It should also be noted that the equilibrium partial pressure of Ga is lower than ${P}_{{\rm{Ga}}}^{{\rm{V}}}$ throughout this figure and no Ga droplets are generated on the β-Ga₂O₃ surface.

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Figure 3 shows deposition phase diagrams that summarize ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ obtained for ${P}_{{\rm{TEG}}}^{{\rm{o}}}$ and input VI/III ratios at 700 °C, 900 °C, and 1100 °C under a ${P}_{{\rm{tot}}}$ of 20 Torr and ${F}^{{\rm{o}}}$ of 0 (IG is used as the carrier gas). The input VI/III ratio at which β-Ga₂O₃ can be grown (i.e. where ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ becomes positive) increases with the growth temperature because H₂, CO, and Ga(OH) have high equilibrium partial pressures under high-temperature conditions, so that more O₂ is required for their complete combustion. Furthermore, ${P}_{{\rm{Ga}}}^{{\rm{V}}}$ decreases with the growth temperature; therefore, when ${P}_{{\rm{TEG}}}^{{\rm{o}}}$ is high and the input VI/III ratio is low at 700 °C [lower-right of Fig. 3(a)], ${P}_{{\rm{Ga}}}$ becomes higher than ${P}_{{\rm{Ga}}}^{{\rm{V}}}$ and Ga droplets are formed. From these phase diagrams of deposition, growth conditions favorable to obtain a large positive ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}},$ i.e. a large growth rate, can be determined for the MOVPE growth of β-Ga₂O₃.

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The growth of β-Ga₂O₃ was demonstrated using TEG and O₂ precursors in an in-house-built MOVPE system with a horizontal hot-wall quartz glass reactor. Figure 4 shows a schematic diagram of the MOVPE system. The conditions suitable for growth determined by the thermodynamic analysis were adopted. Argon (Ar) was used as the carrier gas, i.e. ${F}^{{\rm{o}}}$ is 0. The total pressure in the reactor (${P}_{{\rm{tot}}}$) was kept at 20 Torr using a vacuum pump and pressure controller. The total gas flow rate in the reactor was maintained at 1100 sccm, and the TEG was supplied from a bubbler with a molar flow rate of 48.6 μmol min⁻¹, i.e. ${P}_{{\rm{TEG}}}^{{\rm{o}}}$ = 2.0 × 10^–2 Torr. The input VI/III ratio was set to 100. The quartz glass reactor was heated to 800 °C–1000 °C with a multi-zone electric furnace, and a c-plane sapphire substrate was placed in the center to attempt β-Ga₂O₃ growth. The growth time was fixed at 1 h.

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The thickness and surface morphology of the grown layers were evaluated by cross-sectional and surface observations using field emission scanning electron microscopy (FE-SEM; JEOL, JSM-6700F). The concentrations of the impurities (H, C, N, and Si) incorporated in the grown layers were analyzed by secondary ion mass spectrometry (SIMS; CAMECA, IMS-7f) measurements. The optical bandgaps of the grown layers were evaluated by measurement of the external optical transmission spectra in the wavelength range of 200 nm–800 nm with an unpolarized light source using a double-beam spectrophotometer (JASCO, V-7300). A blank sapphire substrate was used as a reference. Interference fringes in the spectra were also used to cross-check the grown layer thickness. The crystal structures of the grown layers were determined by the analysis of high-resolution X-ray diffraction (XRD; Spectris, X'Pert MRD) 2θ–ω profiles.

Figure 5 shows the growth rate at growth temperatures of 800 °C, 900 °C, and 1000 °C. A growth rate of ca. 1.4 μm h⁻¹ was confirmed at growth temperatures of 800 °C and 900 °C, whereas the growth rate dropped to ca. 0.8 μm h⁻¹ at 1000 °C. The dashed line in Fig. 5 is the result of fitting the experimental growth rate with Eq. (30) using ${\rm{\Delta }}{P}_{\beta \mbox{-} {\mathrm{Ga}}_{2}{{\rm{O}}}_{3}}$ obtained by the thermodynamic analysis under the same conditions as the growth experiment. Here, K_g = 145 μm h⁻¹ Torr⁻¹ was used; this is 4–5 times larger than the value reported for the HVPE growth of β-Ga₂O₃ using GaCl and O₂ as source gases, ^32,33) which suggests high utilization efficiency of TEG. In the range of 800 °C–900 °C, the experimental growth rate and the thermodynamically calculated growth rate show good agreement, and the growth rate is almost constant, regardless of the growth temperature. However, at 1000 °C, the experimental growth rate is much lower than the thermodynamically calculated growth rate. The reason for this is currently unclear, but it is possible that the sticking coefficient decreases at high temperatures, or that the effective VI/III ratio on the substrate surface is lower than the input VI/III ratio due to insufficient O₂ diffusion. Figure 3 indicated that when the effective VI/III ratio was ca. 20, the thermodynamically calculated growth temperature dependence of the growth rate was in good agreement with the growth temperature dependence of the experimental growth rate in Fig. 5. Further details will be clarified in future work.

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Surface FE-SEM micrographs of the layers grown at each growth temperature are shown in Fig. 6. While the layers grown at 800 °C and 900 °C had smooth surfaces, the surface of the layer grown at 1000 °C was rough and grain boundaries were clearly visible. These grain boundaries are along three directions equivalent to 〈11$\bar{2}$0〉 of the c-plane sapphire substrate, which is a typical arrangement of β-Ga₂O₃($\bar{2}$01) layers grown on c-plane sapphire substrates. ⁴⁰⁾

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Table II shows the results of SIMS measurements of the concentration of impurities incorporated in the layers grown at each growth temperature. The incorporation of both hydrogen and carbon impurities was observed in the order of 10¹⁸ cm⁻³ in the layer grown at 800 °C, but the concentrations in the layers grown at 900 °C and 1000 °C were below the respective background (B.G.) levels of these impurities. In the previous section, we reported that when growth is performed at high temperatures and high input VI/III ratios, CO₂ and H₂O are generated with high equilibrium partial pressures by the complete combustion of hydrocarbons and H₂ derived from TEG. Therefore, these experimental results suggest that the complete combustion of hydrocarbons and H₂ can reduce the incorporation of carbon and hydrogen into the grown layer. However, the reductions may be due to the increase in growth temperature. We will investigate the details in future work. Nitrogen concentrations were also below the B.G. level in layers grown at all growth temperatures. In the layers grown at 900 °C and 1000 °C, impurity incorporation was detected only for Si, both showing almost the same Si impurity concentration, and this was higher than that in the layer grown at 800 °C. No Si-containing gas was used in this growth experiment; therefore, it is considered that the origin of the Si impurities was the reaction of the quartz glass (SiO₂) reactor wall with H₂ present in the growth system to generate gaseous SiO. ^33,41) However, the incorporation of Si impurities is expected to be suppressed in the future through the careful selection of reactor materials; therefore, it is not considered to be a serious problem.

Finally, Fig. 7 shows the results of external optical transmittance measurements and the XRD 2θ–ω scan profile of the layer grown at 900 °C for 1 h. The smooth surface of the grown layer, as shown in Fig. 6(b), resulted in high transmittance of 90%–95% and clear interference fringes in the visible light region. The thickness of the grown layer estimated from these fringes using the refractive index calculated from the Cauchy dispersion model ⁴²⁾ was 1.19 μm, which is consistent with the grown layer thickness obtained by cross-sectional FE-SEM observations. The optical bandgap was estimated to be 4.84 eV (= 256 nm) from the absorption edge of the transmittance, which is close to the previously reported values for β-Ga₂O₃. ^2–4,43) In the XRD 2θ–ω profile, a strong β-Ga₂O₃($\bar{4}$02) peak and a weak β-Ga₂O₃($\bar{3}$10) peak were observed, which indicate that a highly ($\bar{2}$01)-oriented β-Ga₂O₃ layer was grown on the c-plane sapphire substrate by the MOVPE method.

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