Electronic Structures and Optical Properties of Cu-based Semiconductors with Chalcopyrite-type Structure†

doi:10.7503/cjcu20180550

Abstract

Abstract:

The density functional theory(DFT) based on the pseudo-potential plane wave basis was employed to investigate the geometries, electronic structures, linear and second-order nonlinear optical properties of the CuXY₂(X=Ga, In; Y=S, Se, Te) crystals with chalcopyrite structure. The results indicate that these compounds are semiconductors with a direct gap and have similar band structures. The static dielectric constants, the refractive indices and the second harmonic generation(SHG) coefficients(d₃₆) of these compounds increase in the sequence of S→Se→Te for the same X atom. Among the occupied bands, those states near the top of the valence band contribute mostly to the SHG effect, which are dominated by the components of C $u 3 d$ orbitals and the valence p orbitals of Y atom. While for the unoccupied bands, the bands mainly derived from valence p orbitals of X atoms have obvious influences on the SHG coefficient. Among these six crystals, CuInSe₂ has high photoconductivity and better absorption of sunlight. In addition, CuGaS₂ and CuGaSe₂ crystal have potential applications in the second-order nonlinear optical fields based on their birefringences and SHG strengths.

Key words: Density functional theory(DFT), Electronic structure, Optical property, Second harmonic generation, Chalcopyrite

CLC Number:

O641

TrendMD:

ZHOU Hegen,JIN Hua,GUO Huirui,LIN Jing,ZHANG Yongfan. Electronic Structures and Optical Properties of Cu-based Semiconductors with Chalcopyrite-type Structure^†[J]. Chem. J. Chinese Universities, 2019, 40(3): 518.

Figures/Tables 15

Fig.1 Unit cell of CuXY2 crystal with chalcopyrite structure

Table 1 Experimental and theoretical results of cell parameters and band gaps of CuXY2 crystals

Crystal	a/nm		c/nm		Volume/nm³		E_g/eV		Ref.	Scissor/eV
Crystal	Exp.	Cal.	Exp.	Cal.	Exp.	Cal.	Exp.	Cal.	Ref.	Scissor/eV
CuGaS₂	0.5360	0.5368	1.0491	1.0561	0.2995	0.3069	2.43	0.669	[14]	1.761
CuGaSe₂	0.5614	0.5667	1.1022	1.1258	0.3474	0.3615	1.68	0.053	[31]	1.627
CuGaTe₂	0.6024	0.6083	1.1940	1.2156	0.4332	0.4498	1.24	0.225	[32]	1.015
CuInS₂	0.5523	0.5592	1.1122	1.1243	0.3392	0.3516	1.53	0.022	[33]	1.508
CuInSe₂	0.5782	0.5874	1.1617	1.1786	0.3884	0.4067	1.04	0.015	[34]	1.025
CuInTe₂	0.6194	0.6283	1.2416	1.2621	0.4764	0.4982	1.06	0.001	[35]	1.059

Fig.2 Band structures of CuGaTe2(A) and CuInTe2(B) crystals The Fermi level(EF) is set to the top of valence bands.

Fig.3 Total and partial density of states(DOSs) of CuGaTe2(A1—A4) and CuInTe2(B1—B4) crystals (A1, B1) Total; (A2, B2) Cu; (A3) Ga; (B3) In; (A4, B4) Te. The zero energy is set to Fermi level(EF).

Fig.4 Variations of the real part(A)—(F) and imaginary part(G)—(L) of dielectric function of CuXY2 crystals(A, G) CuGaS2; (B, H) CuGaSe2; (C, I) CuGaTe2; (D, J) CuInS2; (E, K) CuInSe2; (F, L) CuInTe2.

Fig.5 Variations of the refractive index and birefringence of CuGaS2(A),CuGaSe2(B) and CuGaTe2(C) crystals

Fig.6 Variations of reflectivity of CuGaS2(A), CuGaSe2(B) and CuGaTe2(C) crystals Rx and Rz are the reflectivity along x and z directions, respectively.

Fig.7 Variations of real part of photoconductivity of CuGaS2(A), CuGaSe2(B), CuGaTe2(C), CuInS2(D), CuInSe2(E) and CuInTe2(F) crystalsσx and σz are the photoconductivity along x and z directions, respectively.

Table 2 Experimental and theoretical values of refractive index and d36 of CuXY2 crystals

Crystal	Refractive index at zero frequency			d₃₆/(pm·V^-1) at wavelength of 10.6 μm
Crystal	This work	Other works	Exp.	This work	Other works	Exp.
CuGaS₂	2.70	2.77^[16]	2.5—3.05^[38]	13.06	11.35^[15]	14.5±15%^[40]
		2.62^[36]	2.2—2.9^[39]
CuGaSe₂	2.93	3.69^[16]	2.34—3.38^[38]	28.74	27.75^[15]	30.0±10%^[40]
		2.82^[36]
CuGaTe₂	3.35	4.99^[16]		114.87	70.00^[15]
CuInS₂	2.98	3.22^[16]	2.38—2.82^[38]	17.87	15.85^[15]	10.6±15%^[40]
		2.76^[36]	1.6—3^[39]
CuInSe₂	3.32	3.54^[16]	2.04—3.12^[38]	60.16	36.25^[15]
		3.10^[36]
CuInTe₂	3.76	4.98^[16]		82.02	63.00^[15]
		3.05^[37]

Fig.8 Variations of d36 coefficient as a function of the numbers of occupied bands of CuGaS2(a) and CuInS2(b)(A), CuGaSe2(a) and CuInSe2(b)(B), CuGaTe2(a) and CuInTe2(b)(C) crystalsThe index of HOCO is 26, and the d36 magnitude is obtained by considering a total of 34 unoccupied energy bands.

Fig.9 Variations of HOCO band component of CuXY2 at the k point of [0.4,0.2,0] (A) Cu; (B) X; (C) Y.

Fig.10 Correlations between d36 coefficients and the occupied(A1—A4)/ unoccupied(B1—B4) DOSs of CuGaS2 crystals(A1, B1) Cu; (A2, B2) Ga; (A3, B3) S; (A4, B4) d36. The zero energy is set to EF, and the d36 magnitude at a certain energy level(E) is obtained by considering all the occupied/unoccupied bands distributed in the region between E and EF.

Fig.11 Variations of d36 coefficient as a function of the numbers of unoccupied bands of CuXY2The index of the LUCO is 27, and the d36 magnitude is obtained by considering a total of 26 occupied energy bands.

Fig.12 3D charge density maps of unoccupied bands from the 32nd to 36th of CuGaY2(A) CuGaS2; (B) CuGaSe2; (C) CuGaTe2. The corresponding isovalue is 6.0 e/nm3.

Fig.13 Frequency-dependent variations of the d36 coefficients of CuGaY2(A) and CuInY2(B) crystals (A) a. CuGaS2; b. CuGaSe2; c. CuGaTe2. (B) a. CuInS2; b. CuInSe2; c. CuInTe2.

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