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

Journals >Journal of Semiconductors >Volume 43 >Issue 11 >Page 112801 > Article

Journal of Semiconductors
Vol. 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、**

Author Affiliations

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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DOI: 10.1088/1674-4926/43/11/112801 Cite this Article

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 Copy Citation Text

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(Color online) The partial charge density of the defect states of (a) TiGaI (substitute on the tetrahedral site) and (b) TiGaII (substitute on the octahedral site) defects inβ-Ga2O3.

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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(Color online) The defect transition levels of TiGa and FeGa inβ-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 toβ-Ga2O3 a bandgap of 4.9 eV.

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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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. 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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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. Lattice parameters (

a

, b, c, and

β

), bandgap

E_{gap}

, and formation energy

Δ H_{f}

β

-Ga₂O₃ obtained from our calculations, HSE06 results reported in the literature, and experimental measurements (Expt.).

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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]