A family of flexible two-dimensional semiconductors: MgMX<sub>2</sub>Y<sub>6 </sub>(M = Ti/Zr/Hf; X = Si/Ge; Y = S/Se/Te)

Fig. 5. (Color online) Tensile stress σ, as a function of uniaxial strain, ε, along the (a) x- and (b) y-directions and (c) of biaxial strain, respectively, for ML MgMX₂Y₆ and In₂X₂Y₆.

Download full size

View in Article

Fig. 6. (Color online) Projected electronic band structures of MgMX₂Y₆ MLs based on HSE06+SOC calculation.

Download full size

View in Article

Fig. 7. (Color online) Projected electronic band structures of In₂X₂Y₆ MLs based on HSE06+SOC calculation.

Download full size

View in Article

Fig. 8. (Color online) The band edges of MgMX₂Y₆ and In₂X₂Y₆ MLs. The vacuum level is set to zero. The work functions of Ag, Ti, Cu, Au and Pt have been marked in the figure.

Download full size

View in Article

Fig. 9. (Color online) Optical absorption coefficient of MgMX₂Y₆ and In₂X₂Y₆ MLs based on HSE06+SOC calculations.

Download full size

View in Article

Table 0. Calculated elastic constant C₁₁/C₂₂/C₁₂/C₆₆ (N/m), axial Young’s modulus Y₁₁/Y₂₂ (N/m), Poisson’s ratio v₁₁/v₂₂, ultimate strength σ* (N/m), ultimate strain ε*, corresponding to the ultimate strength for x, y, and biaxial tensions of MgMX₂Y₆ and In₂X₂Y₆ MLs.

View table

View in Article

Table 0. Calculated elastic constant C₁₁/C₂₂/C₁₂/C₆₆ (N/m), axial Young’s modulus Y₁₁/Y₂₂ (N/m), Poisson’s ratio v₁₁/v₂₂, ultimate strength σ* (N/m), ultimate strain ε*, corresponding to the ultimate strength for x, y, and biaxial tensions of MgMX₂Y₆ and In₂X₂Y₆ MLs.

Material	C₁₁/C₂₂	C₁₂	C₆₆	$C_{11}^{2} - C_{12}^{2}$	Y₁₁/Y₂₂	v₁₁/v₂₂	x		y		Biaxial
Material	C₁₁/C₂₂	C₁₂	C₆₆	$C_{11}^{2} - C_{12}^{2}$	Y₁₁/Y₂₂	v₁₁/v₂₂	σ^*	ε^*	σ^*	ε^*	σ^*	ε^*
MgTiSi₂S₆	71.88	20.35	25.76	4752.31	66.12	0.28	5.67	0.14	4.77	0.11	8.95	0.17
MgTiSi₂Se₆	59.69	17.27	21.21	3264.25	54.69	0.29	4.93	0.16	3.70	0.10	6.23	0.12
MgTiSi₂Te₆	45.56	13.51	16.03	1893.41	41.56	0.30	4.16	0.20	2.53	0.08	4.83	0.12
MgTiGe₂S₆	66.55	19.82	23.36	4036.08	60.65	0.30	5.46	0.15	3.85	0.08	6.92	0.12
MgTiGe₂Se₆	55.27	16.54	19.37	2781.04	50.32	0.30	4.63	0.18	3.32	0.10	6.07	0.14
MgTiGe₂Te₆	41.09	11.18	14.95	1563.48	38.05	0.27	3.78	0.22	2.29	0.08	4.51	0.14
MgZrSi₂S₆	65.28	18.17	23.56	3932.06	60.23	0.28	5.83	0.17	3.76	0.10	6.90	0.12
MgZrSi₂Se₆	55.89	15.63	20.13	2879.43	51.52	0.28	5.08	0.19	3.13	0.09	5.70	0.11
MgZrSi₂Te₆	43.58	12.34	15.62	1746.97	40.09	0.28	4.23	0.23	2.33	0.08	4.38	0.11
MgZrGe₂S₆	60.66	17.36	21.65	3378.06	55.69	0.29	5.50	0.17	6.53	0.12	6.53	0.12
MgZrGe₂Se₆	51.80	14.83	18.49	2463.40	47.56	0.29	4.74	0.20	2.90	0.09	5.38	0.12
MgZrGe₂Te₆	40.76	11.50	14.63	1529.26	37.52	0.28	3.87	0.25	2.14	0.08	4.44	0.15
MgHfSi₂S₆	73.04	20.68	26.18	4907.98	67.19	0.28	6.42	0.17	4.47	0.12	7.53	0.11
MgHfSi₂Se₆	60.66	17.55	21.55	3371.17	55.58	0.29	5.98	0.11	3.63	0.10	5.54	0.19
MgHfSi₂Te₆	45.56	13.51	16.03	1893.41	41.56	0.30	4.56	0.22	2.52	0.09	4.63	0.11
MgHfGe₂S₆	60.66	17.36	21.65	3378.06	55.69	0.29	6.04	0.18	4.09	0.10	6.07	0.10
MgHfGe₂Se₆	51.80	14.83	18.49	2463.40	47.56	0.29	5.14	0.20	3.27	0.09	5.66	0.12
MgHfGe₂Te₆	40.76	11.50	14.63	1529.26	37.52	0.28	4.13	0.23	2.34	0.08	4.49	0.13
In₂Si₂S₆	73.27	22.19	25.54	4876.27	66.55	0.30	4.35	0.11	4.17	0.11	6.89	0.14
In₂Si₂Se₆	62.45	19.03	21.71	3537.50	56.65	0.30	3.78	0.11	3.28	0.11	5.81	0.14
In₂Si₂Te	50.16	14.99	17.59	2291.59	45.69	0.30	3.05	0.11	2.20	0.09	4.63	0.13
In₂Ge₂S₆	68.56	21.01	23.77	4258.46	62.11	0.31	4.22	0.10	4.02	0.12	6.97	0.15
In₂Ge₂Se₆	58.56	18.09	20.23	3101.50	52.96	0.31	3.70	0.11	3.17	0.11	6.04	0.15
In₂Ge₂Te₆	47.12	14.28	16.42	2016.88	42.80	0.30	3.03	0.12	2.10	0.09	4.61	0.14

Table 0. Bader charge analysis of MgMX₂Y₆ and In₂X₂Y₆ MLs.

View table

View in Article

Table 0. Bader charge analysis of MgMX₂Y₆ and In₂X₂Y₆ MLs.

Material	Mg/In	Ti/Zr/Hf	Si/Ge	S/Se/Te	Material	Mg/In	Ti/Zr/Hf	Si/Ge	S/Se/Te
MgTiSi₂S₆	+2	+1.96	+3.00	−1.66	MgHfSi₂S₆	+2	+3.98	+2.98	−1.99
MgTiSi₂Se₆	+2	+2.04	+2.96	−1.66	MgHfSi₂Se₆	+2	+3.76	+2.94	−1.94
MgTiSi₂Te₆	+2	+1.98	+0.65	−0.88	MgHfSi₂Te₆	+2	+2.88	+0.74	−1.06
MgTiGe₂S₆	+2	+1.98	+3.02	−1.67	MgHfGe₂S₆	+2	+3.98	+2.98	−1.99
MgTiGe₂Se₆	+2	+1.72	+2.97	−1.61	MgHfGe₂Se₆	+2	+3.96	+2.96	−1.98
MgTiGe₂Te₆	+2	+1.58	+0.46	−0.75	MgHfGe₂Te₆	+2	+2.88	+0.50	−0.98
MgZrSi₂S₆	+2	+2.24	+2.98	−1.70	In₂Si₂S₆	+3	−	+3.00	−2.00
MgZrSi₂Se₆	+2	+2.06	+2.95	−1.66	In₂Si₂Se₆	+3	−	+2.97	−1.99
MgZrSi₂Te₆	+2	+1.78	+0.75	−0.88	In₂Si₂Te₆	+3	−	+0.54	−1.18
MgZrGe₂S₆	+2	+2.24	+2.98	−1.70	In₂Ge₂S₆	+3	−	+2.97	−1.99
MgZrGe₂Se₆	+2	+2.06	+2.95	−1.66	In₂Ge₂Se₆	+3	−	+2.97	−1.99
MgZrGe₂Te₆	+2	+1.84	+0.51	−0.81	In₂Ge₂Te₆	+3	−	+0.48	−1.16

Table 0. Calculated lattice constant a/b (Å), bond length Mg (In)-Y/M-Y/X-X/X-Y (Å), buckling height d (Å), band gaps at HSE06+SOC ( $E_{g}^{HSE + SOC}$ , eV) levels, the valence band maximum (VBM, eV) and conduce band minimum (CBM, eV) at HSE06+SOC level.

View table

View in Article

Table 0. Calculated lattice constant a/b (Å), bond length Mg (In)-Y/M-Y/X-X/X-Y (Å), buckling height d (Å), band gaps at HSE06+SOC ( $E_{g}^{HSE + SOC}$ , eV) levels, the valence band maximum (VBM, eV) and conduce band minimum (CBM, eV) at HSE06+SOC level.

Material	a/b	Mg/In-Y	M-Y	X-X	X-Y	d	VBM	CBM	$E_{g}^{HSE + SOC}$
MgTiSi₂S₆	6.147	2.654	2.490	2.231	2.144	3.16	−6.74	−4.96	1.783
MgTiSi₂Se₆	6.461	2.798	2.619	2.254	2.299	3.37	−6.51	−4.82	1.691
MgTiSi₂Te₆	7.015	3.026	2.825	2.295	2.530	3.63	−5.56	−4.55	1.011
MgTiGe₂S₆	6.269	2.653	2.487	2.355	2.257	3.15	−6.61	−4.96	1.654
MgTiGe₂Se₆	6.572	2.798	2.620	2.385	2.401	3.37	−6.36	−4.84	1.517
MgTiGe₂Te₆	7.107	3.026	2.825	2.435	2.617	3.64	−5.47	−4.60	0.870
MgZrSi₂S₆	6.250	2.681	2.607	2.233	2.149	3.26	−6.83	−4.53	2.307
MgZrSi₂Se₆	6.556	2.820	2.739	2.261	2.302	3.48	−6.71	−4.49	2.225
MgZrSi₂Te₆	7.102	3.045	2.947	2.303	2.530	3.74	−5.69	−4.38	1.314
MgZrGe₂S₆	6.372	2.678	2.608	2.354	2.261	3.26	−6.78	−4.69	2.084
MgZrGe₂Se₆	6.662	2.818	2.740	2.388	2.402	3.49	−6.48	−4.58	1.905
MgZrGe₂Te₆	7.187	3.042	2.946	2.440	2.616	3.76	−5.52	−4.44	1.074
MgHfSi₂S₆	6.218	2.675	2.580	2.228	2.151	3.25	−6.92	−4.42	2.500
MgHfSi₂Se₆	6.530	2.815	2.711	2.256	2.303	3.46	−6.69	−4.30	2.398
MgHfSi₂Te₆	7.084	3.041	2.919	2.300	2.532	3.72	−5.64	−4.18	1.456
MgHfGe₂S₆	6.341	2.674	2.580	2.348	2.262	3.25	−6.83	−4.60	2.232
MgHfGe₂Se₆	6.638	2.815	2.711	2.383	2.404	3.46	−6.47	−4.43	2.045
MgHfGe₂Te₆	7.172	3.041	2.917	2.436	2.618	3.73	−5.58	−4.39	1.189
In₂Si₂S₆	6.278	2.706	−	2.270	2.150	3.41	−6.92	−4.21	2.704
In₂Si₂Se₆	6.600	2.835	−	2.294	2.303	3.59	−6.44	−4.25	2.185
In₂Si₂Te₆	7.153	3.044	−	2.329	2.533	3.83	−5.54	−4.28	1.261
In₂Ge₂S₆	6.385	2.708	−	2.375	2.259	3.43	−6.93	−4.47	2.459
In₂Ge₂Se₆	6.696	2.836	−	2.409	2.401	3.61	−6.44	−4.49	1.952
In₂Ge₂Te₆	7.234	3.043	−	2.457	2.616	3.85	−5.48	−4.26	1.220

Tools

Get Citation

Copy Citation Text

Junhui Yuan, Kanhao Xue, Xiangshui Miao, Lei Ye. A family of flexible two-dimensional semiconductors: MgMX₂Y₆(M = Ti/Zr/Hf; X = Si/Ge; Y = S/Se/Te)[J]. Journal of Semiconductors, 2023, 44(4): 042101

Download Citation

EndNote(RIS)BibTex Plain Text

Set citation alerts for article

Save article for my favorites

Paper Information

Category: Articles

Received: Nov. 1, 2022

Accepted: --

Published Online: Apr. 24, 2023

The Author Email: Xue Kanhao (xkh@hust.edu.cn), Ye Lei (leiye@hust.edu.cn)

DOI:10.1088/1674-4926/44/4/042101

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 0. Calculated elastic constant C11/C22/C12/C66 (N/m), axial Young’s modulus Y11/Y22 (N/m), Poisson’s ratio v11/v22, ultimate strength σ* (N/m), ultimate strain ε*, corresponding to the ultimate strength for x, y, and biaxial tensions of MgMX2Y6 and In2X2Y6 MLs.

Table 0. Calculated elastic constant C11/C22/C12/C66 (N/m), axial Young’s modulus Y11/Y22 (N/m), Poisson’s ratio v11/v22, ultimate strength σ* (N/m), ultimate strain ε*, corresponding to the ultimate strength for x, y, and biaxial tensions of MgMX2Y6 and In2X2Y6 MLs.

Table 0. Bader charge analysis of MgMX2Y6 and In2X2Y6 MLs.

Table 0. Bader charge analysis of MgMX2Y6 and In2X2Y6 MLs.

Table 0. Calculated lattice constant a/b (Å), bond length Mg (In)-Y/M-Y/X-X/X-Y (Å), buckling height d (Å), band gaps at HSE06+SOC ( EgHSE+SOC , eV) levels, the valence band maximum (VBM, eV) and conduce band minimum (CBM, eV) at HSE06+SOC level.

Table 0. Calculated lattice constant a/b (Å), bond length Mg (In)-Y/M-Y/X-X/X-Y (Å), buckling height d (Å), band gaps at HSE06+SOC ( EgHSE+SOC , eV) levels, the valence band maximum (VBM, eV) and conduce band minimum (CBM, eV) at HSE06+SOC level.

Table 0. Bader charge analysis of MgMX₂Y₆ and In₂X₂Y₆ MLs.

Table 0. Bader charge analysis of MgMX₂Y₆ and In₂X₂Y₆ MLs.

Table 0. Calculated lattice constant a/b (Å), bond length Mg (In)-Y/M-Y/X-X/X-Y (Å), buckling height d (Å), band gaps at HSE06+SOC ( $E_{g}^{HSE + SOC}$ , eV) levels, the valence band maximum (VBM, eV) and conduce band minimum (CBM, eV) at HSE06+SOC level.

Table 0. Calculated lattice constant a/b (Å), bond length Mg (In)-Y/M-Y/X-X/X-Y (Å), buckling height d (Å), band gaps at HSE06+SOC ( $E_{g}^{HSE + SOC}$ , eV) levels, the valence band maximum (VBM, eV) and conduce band minimum (CBM, eV) at HSE06+SOC level.