Oxidation of GaN: An ab initio thermodynamic approach

GaN is a wide-band-gap semiconductor used in high-efficiency light-emitting diodes and solar cells. The solid is produced industrially at high chemical purities by deposition from a vapor phase, and oxygen may be included at this stage. Oxidation represents a potential path for tuning its properties without introducing more exotic elements or extreme processing conditions. In this work, ab initio computational methods are used to examine the energy potentials and electronic properties of different extents of oxidation in GaN. Solid-state vibrational properties of Ga, GaN, Ga${}_2$O${}_3$, and a single substitutional oxygen defect have been studied using the harmonic approximation with supercells. A thermodynamic model is outlined which combines the results of ab initio calculations with data from experimental literature. This model allows free energies to be predicted for arbitrary reaction conditions within a wide process envelope. It is shown that complete oxidation is favorable for all industrially relevant conditions, while the formation of defects can be opposed by the use of high temperatures and a high N${}_2$:O${}_2$ ratio.

Figure 1

Unit cell with bounding box for (a) GaN and (b) $\beta$-Ga${}_2$O${}_3$: dark spheres represent Ga atoms and lighter spheres show the position of N (a) and O (b) atoms.

Figure 2

Phonon band structure and density of states for GaN.

Figure 3

Phonon band structure and density of states for Ga${}_{36}$N${}_{35}$O.

Figure 4

Phonon band structure and density of states for Ga.

Figure 5

Phonon band structure and density of states for Ga${}_2$O${}_3$.

Figure 6

Solid-state vibrational entropies from phonon calculations.

Figure 7

Solid-state heat capacities from phonon calculations.

Figure 8

Heat capacity for GaN: (–) PBEsol or harmonic approximation; (- -) Debye–Einstein fit to adiabatic calorimetry measurements, Danilchenko et al.[44]; ($\cdots$) DSC measurements and empirical fit by Jacob et al.[45]; (- $·$ -) fit by Leitner et al., incorporating data from Calvet calorimetry and other literature.[46]

Figure 9

Heat capacity for Ga${}_2$O${}_3$: (–) PBEsol with harmonic approximation; (- -) low temperature calorimetry data from Adams[47]; ($\cdots$) high-temperature calorimetry from Mills.[48]

Figure 10

Difference in heat capacity between pure GaN and a 72-atom supercell with single oxygen substitution: $\Delta C_v=C_{v,{\mathrm{Ga}}_{36}{\mathrm{N}}_{35}\mathrm{O}}-C_{v,36\mathrm{GaN}}$.

Figure 11

Contribution of energy terms to overall ab initio formation enthalpy of GaN ($\Delta H_{f,\mathrm{GaN}}^{\theta }$) compared to experimental values $\Delta H_{f,\mathrm{GaN}}^{\theta ,\mathrm{CRC}}$ and $\Delta H_{f,\mathrm{GaN}}^{\theta ,2009}$, from the CRC Handbook and Jacob and Rajita, respectively.[32, 57]

Figure 12

Contribution of energy terms to overall ab initio formation enthalpy of Ga${}_2$O${}_3$ ($\Delta H_{f,{\mathrm{Ga}}_2{\mathrm{O}}_3}^{\theta }$) compared to the experimental value $\Delta H_{f,{\mathrm{Ga}}_2{\mathrm{O}}_3}^{\theta ,\mathrm{expt}}$.[32]

Figure 13

Modeled Gibbs free energy of complete oxidation from GaN to Ga${}_2$O${}_3$. For each line the corresponding partial pressures, $[p{\mathrm{N}}_2,p{\mathrm{O}}_2]$, are given in Pa.

Figure 14

Modeled Gibbs free energy of complete oxidation from GaN to Ga${}_2$O${}_3$ at 1000 K. Absolute pressure is varied for an atmosphere containing 20%${}_{\mathrm{vol}}$ O${}_2$, 80%${}_{\mathrm{vol}}$ N${}_2$.

Figure 15

$\circ$: Enthalpy change (298.15 K, 0.2 bar O${}_2$, 0.8 bar N${}_2$) associated with partial oxidation (single oxygen substitution for GaN supercells); $*$: enthalpy change including band-filling correction (extrapolation to dilute limit).

Figure 16

Modeled Gibbs free energy of partial oxidation from GaN to Ga${}_{36}$N${}_{35}$O. For each line the corresponding partial pressures, $[p_{{\mathrm{N}}_2},p_{{\mathrm{O}}_2}]$, are given in Pa.

Figure 17

Gibbs free-energy surface of oxygen defect formation in a 72-atom GaN supercell. Contours are labeled with Gibbs free-energy change ($\Delta G$ in kJ mol${}^{-1}$); values above zero (i.e., unfavorable) are shaded.

Figure 18

Gibbs free-energy surface of oxygen defect formation in a 128-atom GaN supercell. Contours are labeled with Gibbs free-energy change ($\Delta G$ in kJ mol${}^{-1}$); values above zero (i.e., unfavorable) are shaded.