Clarifying the atomic origin of electron killers inβ-Ga2O3 from the first-principles study of electron capture rates

Zhaojun Suo; Linwang Wang; Shushen Li; Junwei Luo

doi:10.1088/1674-4926/43/11/112801

Journal of Semiconductors, Volume. 43, Issue 11, 112801(2022)

Clarifying the atomic origin of electron killers inβ-Ga₂O₃ from the first-principles study of electron capture rates

Zhaojun Suo^1,2, Linwang Wang^1、*, Shushen Li^1,2, and Junwei Luo^1,2、**

¹State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

²Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

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Fig. 1. (Color online) The partial charge density of the defect states of (a) Ti_GaI (substitute on the tetrahedral site) and (b) Ti_GaII (substitute on the octahedral site) defects in $β$ -Ga₂O₃.

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Fig. 2. (Color online) The defect transition levels of Ti_Ga and Fe_Ga in $β$ -Ga₂O₃ predicted by the first-principles calculations compared with the defect signaturesE₁,E₂,E₃ observed in DLTS measurements^[4]. All energy levels are referenced to the CBM, which is 4.9 eV above the VBM and gives rise to $β$ -Ga₂O₃ a bandgap of 4.9 eV.

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Fig. 3. (Color online) First-principles-calculatedσ_n as a function of the transition levelε_i/f for TiGa and FeGa at 300 K. The vertical arrows pointed out theσ_n using the calculated transition levelsε_i/f inTable 3. The energy is referenced to the CBM which is 0 eV.

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Fig. 4. (Color online) Items in |V_C|² for Ti_Ga and Fe_Gadefects. Ph-DOS as a function of phonon frequency for the supercell containing (a) Ti_Ga and (b) Fe_Ga. The coupling constant |V_C|² as a function of phonon frequency in the electron-phonon coupling with (c) Ti_GaI, (d) Ti_GaII, (e) Fe_GaI, and (f) Fe_GaII.

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Fig. 5. (Color online) The formation energy of Ti_Ga and Fe_Ga defects as a function of Fermi level under (a) O-poor conditions and (b) O-rich conditions. The Fermi energy is referenced to CBM which is set to 0 eV.

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Fig. 6. (Color online) Schematic diagram forσ_n(ε_i/f) ofE₂ candidates with proper reorganization energyλ.ε_i/f is referenced to CBM which is 0 eV at the right of the horizontal axis. The experimental defect level ofE₂ is 0.74 eV^[4] below the CBM, shown as the vertical dotted line. The horizontal dotted lines indicate the minimum and maximum experimentalσ_n((0.3–3) × 10^–15 cm²^[4]) ofE₂. For the candidates, the downward “parabola” is intrinsic and the maximumσ_n remains still (see the black curve which is for Fe_GaII fromFig. 3), while the reorganization energy can be adjusted through shifting the “parabola” curve left (increasingλ) and right (decreasingλ). Meanwhile,σ_n of the blue and red curves at 0.74 eV should be within the experimental range,σ_n ofE₂, to give the reorganization energy at ~1.4 eV (left shifting) and ~0.1 eV (right shifting), respectively.

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Table 0. First-principles calculated results of Ti_Ga and Fe_Ga defects in $β$ -Ga₂O₃. The transition levels $ε_{i / f}$ and the configuration difference $Δ Q$ are in comparison with those reported in the literature. Reorganization energies $λ$ , electron-phonon coupling constants ${| V_{C} |}^{2}$ , and electron capture cross-sections $σ_{n}$ of Ti_Ga and Fe_Ga are included.

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Table 0. First-principles calculated results of Ti_Ga and Fe_Ga defects in $β$ -Ga₂O₃. The transition levels $ε_{i / f}$ and the configuration difference $Δ Q$ are in comparison with those reported in the literature. Reorganization energies $λ$ , electron-phonon coupling constants ${| V_{C} |}^{2}$ , and electron capture cross-sections $σ_{n}$ of Ti_Ga and Fe_Ga are included.

Parameter	Defect	Ti_GaI	Ti_GaII	Fe_GaI	Fe_GaII
$ε_{i / f}$ (eV)	Cal.	(+/0) 0.59	(+/0) 1.08	(0/–) 0.61	(0/–) 0.74
$ε_{i / f}$ (eV)	Refs. [10,11]	0.60	1.13	0.62	0.72
$Δ Q$ (amu^1/2/Å)	Cal.	2.06	1.42	1.61	1.32
$Δ Q$ (amu^1/2/Å)	Refs. [10,11]	~2.0	1.35	1.63	1.22
$λ$ (eV)	$E_{j i} - E_{i i}$	1.06	0.81	0.76	0.70
${\| V_{C} \|}^{2}$ (eV²)	Cal. 300 K	0.58	0.56	0.43	0.48
$σ_{n}$ (cm²)	Cal. 300 K	8.56 × 10^–14	2.97 × 10^–13	4.23 × 10^–13	6.42 × 10^–13

Table 0. Lattice parameters ( $a$ , b, c, and $β$ ), bandgap $E_{gap}$ , and formation energy $Δ H_{f}$ of $β$ -Ga₂O₃ obtained from our calculations, HSE06 results reported in the literature, and experimental measurements (Expt.).

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Table 0. Lattice parameters ( $a$ , b, c, and $β$ ), bandgap $E_{gap}$ , and formation energy $Δ H_{f}$ of $β$ -Ga₂O₃ obtained from our calculations, HSE06 results reported in the literature, and experimental measurements (Expt.).

Parameter	This work	HSE06	Expt.
^a Ref. [21];^b Ref. [22];^c Ref. [23] ;^d Ref. [24] ;^e Ref. [25];^f Ref. [26].
$a$ (Å)	12.20	12.23^a	12.214^d
$b$ (Å)	3.03	3.03^a	3.037^d
$c$ (Å)	5.78	5.79^a	5.798^d
$β$ (deg)	103.8	103.9^b	103.8^d
$E_{gap}$ (eV)	4.9	4.9^a	4.9^e
$Δ H_{f} (β$ - ${Ga}_{2} O_{3})$ (eV)	–12.7	–10.3^c	–11.3^f

Table 0. Compilation of energy levels (below the CBM and unit in eV) and electron capture cross-sections of three significant defect traps in $β$ -Ga₂O₃ obtained from different DLTS measurements.

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Table 0. Compilation of energy levels (below the CBM and unit in eV) and electron capture cross-sections of three significant defect traps in $β$ -Ga₂O₃ obtained from different DLTS measurements.

Signature	E₁	E₂	E₃	Reference
Level (eV)	0.55	0.74	1.04	Ref. [4]
	0.63	0.81	1.03	Ref. [5]
	–	0.80	1.10	Ref. [6]
$σ_{n}$ (cm²)	(0.3–3) × 10^–14	(0.3–3) × 10^–15	(0.6–6) × 10^–13	Ref. [4]
	(0.3–5) × 10^–13	(0.2–1.2) × 10^–15	2 × 10^–14–1 × 10^–12	Ref. [7]
	2.7 × 10^–13	6 × 10^–15	1 × 10^–13	Ref. [5]

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Zhaojun Suo, Linwang Wang, Shushen Li, Junwei Luo. Clarifying the atomic origin of electron killers inβ-Ga₂O₃ from the first-principles study of electron capture rates[J]. Journal of Semiconductors, 2022, 43(11): 112801

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Paper Information

Category: Articles

Received: Apr. 27, 2022

Accepted: --

Published Online: Nov. 18, 2022

The Author Email: Wang Linwang (lwwang@semi.ac.cn), Luo Junwei (jwluo@semi.ac.cn)

DOI:10.1088/1674-4926/43/11/112801

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Table 0. Lattice parameters ( a, b, c, and β), bandgap Egap, and formation energy ΔHf of β-Ga2O3 obtained from our calculations, HSE06 results reported in the literature, and experimental measurements (Expt.).

Table 0. Lattice parameters ( a, b, c, and β), bandgap Egap, and formation energy ΔHf of β-Ga2O3 obtained from our calculations, HSE06 results reported in the literature, and experimental measurements (Expt.).

Table 0. Compilation of energy levels (below the CBM and unit in eV) and electron capture cross-sections of three significant defect traps in β-Ga2O3 obtained from different DLTS measurements.

Table 0. Compilation of energy levels (below the CBM and unit in eV) and electron capture cross-sections of three significant defect traps in β-Ga2O3 obtained from different DLTS measurements.

Table 0. Lattice parameters ( $a$ , b, c, and $β$ ), bandgap $E_{gap}$ , and formation energy $Δ H_{f}$ of $β$ -Ga₂O₃ obtained from our calculations, HSE06 results reported in the literature, and experimental measurements (Expt.).

Table 0. Lattice parameters ( $a$ , b, c, and $β$ ), bandgap $E_{gap}$ , and formation energy $Δ H_{f}$ of $β$ -Ga₂O₃ obtained from our calculations, HSE06 results reported in the literature, and experimental measurements (Expt.).

Table 0. Compilation of energy levels (below the CBM and unit in eV) and electron capture cross-sections of three significant defect traps in $β$ -Ga₂O₃ obtained from different DLTS measurements.

Table 0. Compilation of energy levels (below the CBM and unit in eV) and electron capture cross-sections of three significant defect traps in $β$ -Ga₂O₃ obtained from different DLTS measurements.