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Abstract

Using first-principles calculations, we investigate the stability and electronic properties of five isomers of two-dimensional (2D) GeSe monolayer under in-plane strain. Our calculated results show that the five isomers of GeSe monolayer are all stable. It is found that the α-GeSe has a direct band gap, while each of the β-GeSe, γ-GeSe, δ-GeSe and ε-GeSe possesses an indirect band gap. By applying compressive or tensile uniaxial and biaxial strain to the five GeSe isomers, the indirect-to-direct transition in band gap is found. In the α-GeSe, the changes from indirect-to-direct and semiconducting-to-metallic are both found under an applied strain. In the 2D β-GeSe and γ-GeSe, an adjustable range of indirect band gap under strain is found. Moreover, a direct band gap in the δ-GeSe is found separately under the biaxial compression strain of σ _xy= –2% and σ _xy= –4%. By applying a tensile strain of 10% along the armchair direction in ε-GeSe, a transition from an indirect to direct band gap occurs. When the tensile strain is continuously increased to 20%, the band structure of ε-GeSe maintains direct character. This direct band gap can be tuned from 1.21 eV to 1.44 eV. When 10% tensile strain is applied along the biaxial direction, the transition in band gap from indirect-to-direct also occurs. Our results indicate that the direct band gap can be tuned from 0.61 eV to 1.19 eV when the tensile strain is increased from 10% to 19% in ε-GeSe.

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Authors and contacts

Corresponding author:Yuan Jian-Mei,yuanjm@xtu.edu.cn; Mao Yu-Liang,ylmao@xtu.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 11471280), the Research Foundation of Education Bureau of Hunan Province, China (Grant No. 17A207), and the Natural Science Foundation of Hunan Province, China (Grant No. 2018JJ2130).

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	α-GeSe	β-GeSe	γ-GeSe	δ-GeSe	ε-GeSe
E₀	73.88	39.55	77.92	151.22	179.68
E_f/i/meV	0.037	0.016	0.041	0.077	0.664
E_f/i/E₀	0.05%	0.04%	0.05%	0.05%	0.03%

DownLoad: CSV

	α-GeSe	β-GeSe	γ-GeSe	δ-GeSe	ε-GeSe
a/Å	4.27	3.68	3.67	5.80	6.85
b/Å	3.98	3.68	5.89	5.84	6.43
h/Å	2.52	1.45	1.76	2.52	1.72
\|E_b\|/eV·atom^–1	4.14	4.12	4.11	4.13	4.08
E_g/eV	1.14	2.30	1.77	1.58	1.78

DownLoad: CSV

Strain/%		d₁/Å	d₂/Å	d₃/Å	θ₁	θ₂	E_g/eV
	σ_x	2.68	2.51	2.60	85.6	86.7	1.56 (ind.)
–10	σ_y	2.60	2.58	2.56	98.2	85.1	1.41 (ind.)
	σ_xy	2.60	2.52	2.52	89.6	77.8	0.85 (ind.)
	σ_x	2.67	2.51	2.60	87.4	87.2	1.61 (ind.)
–8	σ_y	2.61	2.57	2.57	97.1	85.8	1.55 (ind.)
	σ_xy	2.60	2.52	2.54	90.2	80.3	1.32 (ind.)
	σ_x	2.67	2.52	2.60	89.1	87.8	1.66 (ind.)
–6	σ_y	2.61	2.56	2.58	96.3	86.6	1.67 (ind.)
	σ_xy	2.61	2.52	2.56	90.8	82.8	1.71 (ind.)
	σ_x	2.66	2.52	2.60	90.9	88.3	1.72 (ind.)
–4	σ_y	2.62	2.55	2.59	95.5	87.5	1.77 (ind.)
	σ_xy	2.62	2.53	2.57	91.7	85.5	1.90 (ind.)
	σ_x	2.65	2.53	2.60	92.4	88.8	1.75 (ind.)
–2	σ_y	2.63	2.55	2.59	94.8	88.4	1.84 (ind.)
	σ_xy	2.64	2.53	2.59	92.7	87.4	1.89 (ind.)
0		2.65	2.54	2.60	94.1	89.3	1.78 (ind.)
	σ_x	2.65	2.55	2.60	95.8	89.7	1.75 (ind.)
2	σ_y	2.67	2.54	2.60	93.3	90.5	1.62 (ind.)
	σ_xy	2.67	2.55	2.60	95.8	91.3	1.62 (ind.)
	σ_x	2.64	2.56	2.60	97.2	90.2	1.66 (ind.)
4	σ_y	2.69	2.54	2.60	93.2	91.6	1.48 (ind.)
	σ_xy	2.68	2.56	2.60	98.0	92.6	1.50 (ind.)
	σ_x	2.63	2.57	2.61	99.0	90.2	1.60 (ind.)
6	σ_y	2.71	2.54	2.60	92.8	92.8	1.35 (ind.)
	σ_xy	2.70	2.57	2.60	100.2	93.7	1.40 (ind.)
	σ_x	2.63	2.59	2.61	100.8	90.4	1.51 (ind.)
8	σ_y	2.74	2.54	2.60	92.8	94.1	1.24 (ind.)
	σ_xy	2.71	2.59	2.60	102.6	94.9	1.30 (ind.)
	σ_x	2.62	2.60	2.61	103.5	89.9	1.44 (dir.)
10	σ_y	2.77	2.54	2.59	93.0	95.5	1.16 (ind.)
	σ_xy	2.73	2.60	2.60	105.1	96.1	1.19 (dir.)
	σ_x	2.62	2.61	2.62	105.5	90.0	1.37 (dir.)
12	σ_y	2.80	2.54	2.59	92.9	96.8	1.09 (ind.)
	σ_xy	2.75	2.61	2.59	107.7	97.6	1.00 (dir.)
	σ_x	2.61	2.62	2.62	108.2	89.4	1.32 (dir.)
14	σ_y	2.84	2.53	2.58	93.2	98.3	1.05 (ind.)
	σ_xy	2.77	2.62	2.58	110.3	99.4	0.84 (dir.)
	σ_x	2.60	2.63	2.63	110.8	89.0	1.28 (dir.)
16	σ_y	2.87	2.53	2.57	93.4	100.0	1.03 (ind.)
	σ_xy	2.78	2.64	2.57	112.6	101.7	0.67 (dir.)
	σ_x	2.60	2.63	2.63	113.1	88.8	1.24 (dir.)
18	σ_y	2.92	2.52	2.56	93.5	102.0	0.98 (ind.)
	σ_xy	2.79	2.65	2.55	115.2	103.7	0.63 (dir.)
	σ_x	2.59	2.64	2.64	115.6	88.3	1.21 (dir.)
20	σ_y	2.96	2.51	2.54	94.1	103.8	0.94 (ind.)
	σ_xy	2.72	2.70	2.54	123.7	108.1	0.99 (ind.)

DownLoad: CSV

	σ_x= 20%	σ_y= 20%	σ_xy= 20%
E₀/meV	165.49	156.07	132.56
E_f/i/meV	2.650	0.030	0.005
E_f/i/E₀	1.60%	0.02%	0.03%

DownLoad: CSV

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Vol. 68, Issue 11 - 2019-06-05

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