Calculation of Conduction Band Structure Tensile Strained Ge1-xSnx Alloys for Achieving Direct Band Gap Materials

Qinqin Sun; Shihao Huang

doi:10.3788/LOP57.091602

Laser & Optoelectronics Progress, Volume. 57, Issue 9, 091602(2020)

Calculation of Conduction Band Structure Tensile Strained Ge_1-_xSn_x Alloys for Achieving Direct Band Gap Materials

Qinqin Sun¹ and Shihao Huang^2,3、*

Author Affiliations

¹School of Applied Technology, Fujian University of Technology, Fuzhou, Fujian 350118, China

²School of Information Science and Engineering, Fujian University of Technology, Fuzhou, Fujian 350118, China

³Research Center for Microelectronics Technology, Fujian University of Technology, Fuzhou, Fujian 350118, China

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Figures & Tables(7)

Fig. 1. Various strain components as a function of in-plane strain. (a) Biaxial tensile strain paralleled to the (001) plane; (b) biaxial tensile strain paralleled to the (110) plane; (c) biaxial tensile strain paralleled to the (111) plane; (d) uniaxial tensile strain paralleled to the [001] direction; (e) uniaxial tensile strain paralleled to the [110] direction; (f) uniaxial tensile strain paralleled to the [111] direction

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Fig. 2. Changes in the bandgaps of Ge_0.97Sn_0.03 with various type of strains. (a) Biaxial tensile strain paralleled to the (001) plane; (b) biaxial tensile strain paralleled to the (110) plane; (c) biaxial tensile strain paralleled to the (111) plane

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Fig. 3. Energy separation between the direct and indirect conduction band minima in Ge_1-_xSn_x as a function of strain and Sn composition with various type of strains. (a) Biaxial tensile strain paralleled to the (001) plane; (b) biaxial tensile strain paralleled to the (110) plane; (c) biaxial tensile strain paralleled to the (111) plane

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Fig. 4. Changes in the bandgaps of Ge_0.97Sn_0.03 with various type of strains. (a) Uniaxial tensile strain paralleled to the [001] direction; (b) uniaxial tensile strain paralleled to the [110] direction; (c) uniaxial tensile strain paralleled to the [111] direction

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Fig. 5. Energy separation between the direct and indirect conduction band minima in Ge_1-_xSn_x as a function of strain and Sn composition with various type of strains. (a) Uniaxial tensile strain paralleled to the [001] direction; (b) uniaxial tensile strain paralleled to the [110] direction; (c) uniaxial tensile strain paralleled to the [111] direction

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Table 1. Parameters for Ge and Sn^[10,13,15]
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Table 1. Parameters for Ge and Sn^[10,13,15]
Element C₁₁ /GPa C₁₂ /GPa C₄₄ /GPa $\begin{matrix} Ξ_{d}^{Γ} \end{matrix}$ /eV $\begin{matrix} Ξ_{d}^{L} \end{matrix}$ /eV $\begin{matrix} Ξ_{u}^{L} \end{matrix}$ /eV
Ge 115.06 44.50 59.18 -10 -2.27 15.23
Sn 57.72 25.82 34.20 -7.21 -2.25 -2.2

Table 2. Critical strains for Ge under biaxial and uniaxial tension strain where the indirect-to-direct band-gap transition occurs

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Table 2. Critical strains for Ge under biaxial and uniaxial tension strain where the indirect-to-direct band-gap transition occurs

Method	Biaxial tensile strain			Uniaxial tensile strain			Ref.
Method	(001)		(110)	(111)	[001]	[110]	[111]
Deformation potential theory	1.57%	3.34%	Unreached	4.35%	Unreached	Unreached	This work
Hybrid density-functional theory	1.50%	2.30%	Unreached	4.20%	Unreached	3.70%	[24]
Generalized gradient approximation	1.70%	3.50%	Unreached	3.05%	1.71%	1.05%	[23]
Generalized gradient approximation plus U	2.91%	3.50%	Unreached	8.56%	Unreached	5.69%	[25]

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Qinqin Sun, Shihao Huang. Calculation of Conduction Band Structure Tensile Strained Ge_1-_xSn_x Alloys for Achieving Direct Band Gap Materials[J]. Laser & Optoelectronics Progress, 2020, 57(9): 091602

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