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热电材料是通过载流子作用实现热能和电能直接转换的功能材料，在能源、环境、国防等领域具有重要应用. 如何提高材料的转换效率是目前热电材料研究的关键. 最近发现，三元黄铜矿I-III-IV2（I=Ag，Cu；III=Al，Ga，In；IV=S，Se，Te）是一类潜在的高性能热电材料，其结构独特，可通过多种途径优化其性能. 本文采用基于密度泛函理论的第一性原理方法系统地研究CuGaTe2和CuInTe2的电子特性，为提高其热电效率提供新思路. 研究发现改进的Becke Johnson-广义梯度近似比广义梯度近似交换关联近似计算的能隙值更接近实验值. 基于玻尔兹曼理论研究了体系热电性质，发现通过优化载流子的浓度可以改善体系的热电性. 通过拟合计算的晶格热导率发现，在300-800 K，CuGaTe2和CuInTe2的晶格热导率和温度成反比，表明其晶格热导率主要来源于声子散射，并且声子散射又是以Umklapp散射为主. CuGaTe2在700 K的热电优值ZT 可以达到0.63，远大于其他Te类材料的ZT值.The thermoelectric material is a kind of new functional material, which can convert industrial waste heat and automobile exhaust into the available electric energy by the interaction of carriers. It is widely used in energy, environment, national defense and other fields. For the research of thermoelectric materials, it is the most important to improve the conversion efficiency now. Due to their unique structural properties, the ternary chalcopyrite semiconductors I-III-IV2 (I=Ag, Cu; III=Al, Ga, In; IV=S, Se, Te) display the better thermoelectric performances at high temperature. Many studies show that there are many ways to improve their performances. In order to optimize their thermoelectric efficiencies the structural, elastic and thermoelectric properties of CuGaTe2 and CuInTe2 are studied by employing the density function theory and semi-classical Boltzmann transport theory within the constant time approximation. The electronic band structures are calculated using the Tran-Blaha modified Becke-Johnson potential (MBJ-GGA) and the generalized gradient approximation (GGA). The calculated band gaps with MBJ-GGA of CuGaTe2and CuInTe2 are 0.86 and 0.56 eV, which are more accurate than the calculated values with GGA. The shear modulus, and Young's modulus and sound velocities are determined from the obtained elastic constants. The constant-volume heat capacity is estimated based on the quasi-harmonic Debye model. The calculated temperature dependence of heat capacity agrees very well with the experimental result. Below room temperature, the heat capacity increases quickly with the increasing of temperature. Above room temperature, the heat capacity approaches to the Dulong-Petit limit. In paper, we assume that the lattice thermal conductivities of CuGaTe2 and CuInTe2 are mainly from the phonon scattering. And the phonon scattering is dominated by Umklapp scattering. The calculated lattice thermal conductivities can fit the form kl = A/T-Bin the temperature range of 300-800 K. For CuGaTe2, A = 2869.96 and B = 2.86. The fitting result well approaches to the experimental values and other theoretical results. Based on the calculated band structures with mBJ-GGA potential, the transport properties of CuGaTe2 and CuInTe2 each as a function of chemical potential at various temperatures are investigated. The values of Seebeck coefficient S first increase and then decrease for n-type and p-type doping at low carrier concentrations, which are consistent with the previous results. Electrical conductivity divided by scattering time, i.e. / increases monotonically with chemical potential increasing. The power factor divided by scattering time, i.e. S2/ first increases and then decreases with chemical potential increasing. The magnitude of S2/ increases with temperature increasing. Besides, it is found that the value of S2/ for p-type doping is larger than that for n-type doping. These results show that optimizing the carrier concentration can improve their thermoelectric performances. In order to calculate the electrical conductivity, in this paper we estimate the scattering time from the experiments of Ref.[3]. The CuGaTe2 at 700 K possesses a figure of merit 0.63. These calculated results show that CuGaTe2 and CuInTe2 both are good thermoelectric materials with p-type doping.
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Keywords:
- chalcopyrite semiconductors /
- thermoelectric materials /
- Boltzmann theory /
- first-principle
[1] Charoenphakdee A, Kurosaki K, Muta H, Uno M, Yamanaka S 2009 Mater. Trans. 50 1603
[2] Yusufu A, Kurosaki K, Kosuga A, Sugahara T, Ohishi Y, Muta H, Yamanaka S 2011 Appl. Phys. Lett. 99 061902
[3] Plirdpring T, Kurosaki K, Kosuga A, Day T, Firdosy S, Ravi V, Muta H 2012 Adv. Mater. 24 3622
[4] Liu R, Xi L, Liu H, Shi X, Zhang W, Chen L 2012 Chem. Commun. 48 3818
[5] Zhu Y, Zhang X Y, Zhang S H, Ma M Z, Liu R P, Tian H Y 2015 Acta Phys. Sin. 64 77103 (in Chinese) [朱岩, 张新宇, 张素红, 马明臻, 刘日平, 田宏燕 2015 64 77103]
[6] Sun Z, Chen S P, Yang J F, Meng Q S, Cui J L 2014 Acta Phys. Sin. 63 057201 (in Chinese) [孙政, 陈少平, 杨江锋, 孟庆森, 崔教林 2014 63 057201]
[7] Xue L, Xu B, Yi L 2014 Chin. Phys. B 23 037103
[8] Blaha P Schwarz K, Madsen G K H Kvasnicka D, Luitz J 2001 WIEN2K, An Augmented Plane Wave+Local Orbitals Pro-gram for Calculating Crystal Properties (Wien, Austria: K Schwarz, Tech. Univ.)
[9] Madsen G K H, Singh D J 2006 Comput. Phys. Commun. 175 67
[10] Bodnar I V, Orlova N S {1986 Cryst. Res. Technol 21 109
[11] Avon J E Yoodee K, Woolley J C 1984 J. Appl. Phys. 55 524
[12] Johnson E R, Becke A D 2006 J. Chem. Phys. 124 174104
[13] Zhang X Z, Shen K S, Jiao Z Y, Huang X F 2013 Comput. Theor. Chem. 1010 67
[14] Jaffe J E, Zunger A 1983 Phys. Rev. B 28 5822
[15] Singh D J, Mazin I I 1997 Phys. Rev. B 56 R1650
[16] Tao X, Jund P, Colinet C, Tedenac J C 2009 Phys. Rev. B 80 104103
[17] Verma A S, Sharma S, Bhandari R, Sarkar B K, Jindal V K 2012 Mater. Chem. Phys. 132 416
[18] Bachmann K J, Hsu F S L, Thiel F A, Kasper H M 1977 J. Electron. Mater. 6 431
[19] Kumar V, Tripathy S K 2014 J. Alloys Compd. 582 101
[20] Shao D Y, Hui Q, Li X, Chen J J, Li C M, Cheng N P {2015 Acta Phys. Sin. 64 207102 (in Chinese) [邵栋元, 惠群, 李孝, 陈晶晶, 李春梅,程南璞 2015 64 207102]
[21] Ouahrani T, Otero-de-la-Roza A, Reshak A H, Khenata R, Faraoun H I, Amrani B, Luaa V 2010 Physica B 405 3658
[22] Verma A S, Bhardwaj S R 2006 Phys. Stat. Sol. 243 4025
[23] Schreiber E, Orson L 1974 Elastic Constants and their Measurement(Mishawaka: Better World Books)
[24] Huang K, Han L Q 1998 Solid-state Physics (Beijing: Higher Education Press) p125 (in Chinese) [黄昆, 韩汝琦 1988 固体物理学 (北京: 高等教育出版) 第 125页]
[25] Zou D F Xie S H, Liu Y Y, Lin J G, Li J Y 2013 J. Alloys Compd. 570 150
[26] Leibfried G, Schlomann E {1954 Nachr. Akad. Wiss. Gottingen Math-physik Kl. 2a 4 71
[27] Tang X F, Xie W J, Li H, Zhao W Y, Zhang Q J 2007 Appl. Phys. Lett. 90 12102
[28] LaLonde A D, Pei Y, Wang H, Snyder G J 2011 Mater. Today 14 526
[29] Ong K P, Singh D J Wu P 2011 Phys. Rev. B 83 115110
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[1] Charoenphakdee A, Kurosaki K, Muta H, Uno M, Yamanaka S 2009 Mater. Trans. 50 1603
[2] Yusufu A, Kurosaki K, Kosuga A, Sugahara T, Ohishi Y, Muta H, Yamanaka S 2011 Appl. Phys. Lett. 99 061902
[3] Plirdpring T, Kurosaki K, Kosuga A, Day T, Firdosy S, Ravi V, Muta H 2012 Adv. Mater. 24 3622
[4] Liu R, Xi L, Liu H, Shi X, Zhang W, Chen L 2012 Chem. Commun. 48 3818
[5] Zhu Y, Zhang X Y, Zhang S H, Ma M Z, Liu R P, Tian H Y 2015 Acta Phys. Sin. 64 77103 (in Chinese) [朱岩, 张新宇, 张素红, 马明臻, 刘日平, 田宏燕 2015 64 77103]
[6] Sun Z, Chen S P, Yang J F, Meng Q S, Cui J L 2014 Acta Phys. Sin. 63 057201 (in Chinese) [孙政, 陈少平, 杨江锋, 孟庆森, 崔教林 2014 63 057201]
[7] Xue L, Xu B, Yi L 2014 Chin. Phys. B 23 037103
[8] Blaha P Schwarz K, Madsen G K H Kvasnicka D, Luitz J 2001 WIEN2K, An Augmented Plane Wave+Local Orbitals Pro-gram for Calculating Crystal Properties (Wien, Austria: K Schwarz, Tech. Univ.)
[9] Madsen G K H, Singh D J 2006 Comput. Phys. Commun. 175 67
[10] Bodnar I V, Orlova N S {1986 Cryst. Res. Technol 21 109
[11] Avon J E Yoodee K, Woolley J C 1984 J. Appl. Phys. 55 524
[12] Johnson E R, Becke A D 2006 J. Chem. Phys. 124 174104
[13] Zhang X Z, Shen K S, Jiao Z Y, Huang X F 2013 Comput. Theor. Chem. 1010 67
[14] Jaffe J E, Zunger A 1983 Phys. Rev. B 28 5822
[15] Singh D J, Mazin I I 1997 Phys. Rev. B 56 R1650
[16] Tao X, Jund P, Colinet C, Tedenac J C 2009 Phys. Rev. B 80 104103
[17] Verma A S, Sharma S, Bhandari R, Sarkar B K, Jindal V K 2012 Mater. Chem. Phys. 132 416
[18] Bachmann K J, Hsu F S L, Thiel F A, Kasper H M 1977 J. Electron. Mater. 6 431
[19] Kumar V, Tripathy S K 2014 J. Alloys Compd. 582 101
[20] Shao D Y, Hui Q, Li X, Chen J J, Li C M, Cheng N P {2015 Acta Phys. Sin. 64 207102 (in Chinese) [邵栋元, 惠群, 李孝, 陈晶晶, 李春梅,程南璞 2015 64 207102]
[21] Ouahrani T, Otero-de-la-Roza A, Reshak A H, Khenata R, Faraoun H I, Amrani B, Luaa V 2010 Physica B 405 3658
[22] Verma A S, Bhardwaj S R 2006 Phys. Stat. Sol. 243 4025
[23] Schreiber E, Orson L 1974 Elastic Constants and their Measurement(Mishawaka: Better World Books)
[24] Huang K, Han L Q 1998 Solid-state Physics (Beijing: Higher Education Press) p125 (in Chinese) [黄昆, 韩汝琦 1988 固体物理学 (北京: 高等教育出版) 第 125页]
[25] Zou D F Xie S H, Liu Y Y, Lin J G, Li J Y 2013 J. Alloys Compd. 570 150
[26] Leibfried G, Schlomann E {1954 Nachr. Akad. Wiss. Gottingen Math-physik Kl. 2a 4 71
[27] Tang X F, Xie W J, Li H, Zhao W Y, Zhang Q J 2007 Appl. Phys. Lett. 90 12102
[28] LaLonde A D, Pei Y, Wang H, Snyder G J 2011 Mater. Today 14 526
[29] Ong K P, Singh D J Wu P 2011 Phys. Rev. B 83 115110
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