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能带工程通过改变材料的能带结构可以显著提升其电学和光学性质，已广泛应用于半导体材料的改性研究.双轴张应力和Sn组分共同作用下的Ge1-xSnx合金，不仅可以解决直接带隙转变所需高Sn组分带来的工艺难题，而且载流子迁移率会显著提升，在单片光电集成领域有很好的应用前景.根据形变势理论，分析了（001）面双轴张应变Ge1-xSnx的带隙转变条件，并给出了在带隙转变临界点Sn组分和双轴张应力的关系；采用8kp方法，得到了临界带隙双轴张应变Ge1-xSnx在布里渊区中心点附近的能带结构，进而计算得到电子与空穴有效质量；基于载流子散射模型，计算了电子与空穴迁移率.计算结果表明：较低Sn组分和双轴张应力的组合即可得到直接带隙Ge1-xSnx合金，且直接带隙宽度随着应力的增大而减小；临界带隙双轴张应变Ge1-xSnx具有极高的电子迁移率，空穴迁移率在较小应力作用下即可显著提升.考虑工艺实现难度和材料性能两个方面，可以选择4% Sn组分与1.2 GPa双轴张应力或3% Sn组分与1.5 GPa双轴张应力的组合用于高速器件和光电器件的设计.
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关键词:
- 双轴张应变Ge1-xSnx /
- kp方法 /
- 能带结构 /
- 迁移率
Optoelectronic integration technology which utilizes CMOS process to achieve the integration of photonic devices has the advantages of high integration, high speed and low power consumption. The Ge1-xSnx alloys have been widely used in photodetectors, light-emitting diodes, lasers and other optoelectronic integration areas because they can be converted into direct bandgap semiconductors as the Sn component increases. However, the solid solubility of Sn in Ge as well as the large lattice mismatch between Ge and Sn resulting from the Sn composition cannot be increased arbitrarily:it is limited, thereby bringing a lot of challenges to the preparation and application of direct bandgap Ge1-xSnx. Strain engineering can also modulate the band structure to convert Ge from an indirect bandgap into a direct bandgap, where the required stress is minimal under biaxial tensile strain on the (001) plane. Moreover, the carrier mobility, especially the hole mobility, is significantly enhanced. Therefore, considering the combined effect of alloying and biaxial strain on Ge, it is possible not only to reduce the required Sn composition or stress for direct bandgap transition, but also to further enhance the optical and electrical properties of Ge1-xSnx alloys. The energy band structure is the theoretical basis for studying the optical and electrical properties of strained Ge1-xSnx alloys. In this paper, according to the theory of deformation potential, the relationship between Sn component and stress at the critical point of bandgap transition is given by analyzing the bandgap transition condition of biaxial tensile strained Ge1-xSnx on the (001) plane. The energy band structure of strained Ge1-xSnx with direct bandgap at the critical state is obtained through diagonalizing an 8-level kp Hamiltonian matrix which includes the spin-orbit coupling interaction and strain effect. According to the energy band structure and scattering model, the effective mass and mobility of carriers are quantitatively calculated. The calculation results indicate that the combination of lower Sn component and stress can also obtain the direct bandgap Ge1-xSnx, and its bandgap width decreases with the increase of stress. The strained Ge1-xSnx with direct bandgap has a very high electron mobility due to the small electron effective mass, and the hole mobility is significantly improved under the effect of stress. Considering both the process realization and the material properties, a combination of 4% Sn component and 1.2 GPa stress or 3% Sn component and 1.5 GPa stress can be selected for designing the high speed devices and optoelectronic devices.-
Keywords:
- biaxial tensile strained Ge1-xSnx /
- kp method /
- energy band structure /
- mobility
[1] Morea M, Brendel C E, Zang K, Suh J, Fenrich C S, Huang Y C, Chung H, Huo Y, Kamins T I, Saraswat K C, Harris J S 2017 Appl. Phys. Lett. 110 091109
[2] Senaratne C L, Wallace P M, Gallagher J D, Sims P E, Kouvetakis J, Menndez J 2016 J. Appl. Phys. 120 025701
[3] Hart J, Adam T, Kim Y, Huang Y C, Reznicek A, Hazbun R, Gupta J, Kolodzey J 2016 J. Appl. Phys. 119 093105
[4] Zhou Y, Dou W, Du W, Pham T, Ghetmiri S A, Al-Kabi S, Mosleh A, Alher M, Margetis J, Tolle J, Sun G, Soref R, Li B, Mortazavi M, Naseem H, Yu S Q 2016 J. Appl. Phys. 120 023102
[5] Wirths S, Geiger R, Driesch N V D, Mussler G, Stoica T, Mantl S, Ikonic Z, Luysberg M, Chiussi S, Hartmann J M, Sigg H, Faist J, Buca D, Grtzmacher D 2015 Nat. Photonics 9 88
[6] Liu Y, Yan J, Wang H, Cheng B, Han G 2015 Int. J. Thermophys. 36 980
[7] Taoka N, Capellini G, Schlykow V, Montanari M, Zaumseil P, Nakatsuka O, Zaima S, Schroeder T 2017 Mater. Sci. Semicond. Process. 57 48
[8] Huang Y S, Tsou Y J, Huang C H, Huang C H, Lan H S, Liu C W, Huang Y C, Chung H, Chang C P, Chu S S, Kuppurao S 2017 IEEE Trans. Electron Dev. 64 2498
[9] Margetis J, Mosleh A, Al-Kabi S, Ghetmiri S A, Du W, Dou W, Benamara M, Li B, Mortazavi M, Naseem H A, Yu S Q, Tolle J 2017 J. Cryst. Growth 463 128
[10] Mosleh A, Alher M A, Cousar L C, Du W, Ghetmiri S A, Pham T, Grant J M, Sun G, Soref R A, Li B, Naseem H A, Yu S Q 2015 Front. Mater. 2 30
[11] Kurdi M E, Fishman G, Sauvage S, Boucaud P 2010 J. Appl. Phys. 107 013710
[12] Liu L, Zhang M, Hu L, Di Z, Zhao S J 2014 J. Appl. Phys. 116 113105
[13] Bai M, Xuan R X, Song J J, Zhang H M, Hu H Y, Shu B 2015 Acta Phys. Sin. 64 038501 (in Chinese)[白敏, 宣荣喜, 宋建军, 张鹤鸣, 胡辉勇, 舒斌 2015 物理学报 64 038501]
[14] D'Costa V R, Cook C S, Birdwell A G, Littler C L, Canonico M, Zollner S, Kouvetakis J, Menndez J 2006 Phys. Rev. B 73 125207
[15] Madelung O, Rssler U, Schulz M 2002 SemiconductorsGroup IV Elements, IV-IV and Ⅲ- V Compounds. Part b-Electronic, Transport, Optical and Other Properties (Berlin: Springer) p2801, p3106
[16] Bahder T B 1990 Phys. Rev. B 41 11992
[17] Pryor C 1998 Phys. Rev. B 57 7190
[18] Zhu Y H, Xu Q, Fan W J, Wang J W 2010 J. Appl. Phys. 107 073108
[19] Ye L X 1997 Monte Carlo Simulation of the Small-Scale Semiconductor Devices (Beijing: Science Press) p318, 384 (in Chinese)[叶良修 1997 小尺寸半导体器件的蒙特卡罗模拟 (北京: 科学出版社) 第318页, 第384页]
[20] Ye L X 2007 Semiconductor Physics (2nd Ed.) Part One (Beijing: Higher Education Press) p203 (in Chinese)[叶良修 2007 半导体物理学(第二版)上册 (北京: 高等教育出版社)第 203 页]
[21] Sun Y, Thompson S E, Nishida T 2010 Strain Effect in Semiconductors: Theory and Device Applications (New York: Springer) pp193-201
[22] Wang X Y, Zhang H M, Song J J, Ma J L, Wang G Y, An J H 2011 Acta Phys. Sin. 60 077205 (in Chinese)[王晓艳, 张鹤鸣, 宋建军, 马建立, 王冠宇, 安久华 2011 物理学报 60 077205]
[23] Song J J, Zhang H M, Hu H Y, Wang X Y, Wang G Y 2012 Acta Phys. Sin. 61 057304 (in Chinese)[宋建军, 张鹤鸣, 胡辉勇, 王晓艳, 王冠宇 2012 物理学报 61 057304]
[24] Nguyen P H, Hofmann K R 2003 J. Appl. Phys. 94 375
[25] Fischetti M V, Laux S E 1996 J. Appl. Phys. 80 2234
[26] Song P, Cai L C, Tao T J, Yuan S, Chen H, Huang J, Zhao X W, Wang X J 2016 J. Appl. Phys. 120 195101
[27] Myers V W 1967 J. Phys. Chem. Solids 28 2207
[28] Adachi S 2009 Properties of Semiconductor Alloys: Group-IV, Ⅲ- V and Ⅱ- VI Semiconductors (Chichester: John Wiley Sons Ltd.) p18
[29] Chen R, Lin H, Huo Y, Hitzman C, Kamins T I, Harris J S 2011 Appl. Phys. Lett. 99 181125
[30] Dai X Y, Yang C, Song J J, Zhang H M, Hao Y, Zheng R C 2012 Acta Phys. Sin. 61 237102 (in Chinese)[戴显英, 杨程, 宋建军, 张鹤鸣, 郝跃, 郑若川 2012 物理学报 61 237102]
[31] Lin H, Chen R, Huo Y, Kamins T I, Harris J S 2011 Appl. Phys. Lett. 98 261917
[32] Lin H, Chen R, Lu W, Huo Y, Kamins T I, Harris J S 2012 Appl. Phys. Lett. 100 102109
[33] Gassenq A, Milord L, Aubin J, Guilloy K, Tardif S, Pauc N, Rothman J, Chelnokov A, Hartmann J M, Reboud V, Calvo V 2016 Appl. Phys. Lett. 109 242107
[34] Lieten R R, Seo J W, Decoster S, Vantomme A, Peters S, Bustillo K C, Haller E E, Menghini M, Locquet J P 2013 Appl. Phys. Lett. 102 052106
[35] Wirths S, Stange D, Pampilln M A, Tiedemann A T, Mussler G, Fox A, Breuer U, Baert B, Andrs E S, Nguyen N D, Hartmann J M, Ikonic Z, Mantl S, Buca D 2015 ACS Appl. Mater. Interfaces 7 62
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[1] Morea M, Brendel C E, Zang K, Suh J, Fenrich C S, Huang Y C, Chung H, Huo Y, Kamins T I, Saraswat K C, Harris J S 2017 Appl. Phys. Lett. 110 091109
[2] Senaratne C L, Wallace P M, Gallagher J D, Sims P E, Kouvetakis J, Menndez J 2016 J. Appl. Phys. 120 025701
[3] Hart J, Adam T, Kim Y, Huang Y C, Reznicek A, Hazbun R, Gupta J, Kolodzey J 2016 J. Appl. Phys. 119 093105
[4] Zhou Y, Dou W, Du W, Pham T, Ghetmiri S A, Al-Kabi S, Mosleh A, Alher M, Margetis J, Tolle J, Sun G, Soref R, Li B, Mortazavi M, Naseem H, Yu S Q 2016 J. Appl. Phys. 120 023102
[5] Wirths S, Geiger R, Driesch N V D, Mussler G, Stoica T, Mantl S, Ikonic Z, Luysberg M, Chiussi S, Hartmann J M, Sigg H, Faist J, Buca D, Grtzmacher D 2015 Nat. Photonics 9 88
[6] Liu Y, Yan J, Wang H, Cheng B, Han G 2015 Int. J. Thermophys. 36 980
[7] Taoka N, Capellini G, Schlykow V, Montanari M, Zaumseil P, Nakatsuka O, Zaima S, Schroeder T 2017 Mater. Sci. Semicond. Process. 57 48
[8] Huang Y S, Tsou Y J, Huang C H, Huang C H, Lan H S, Liu C W, Huang Y C, Chung H, Chang C P, Chu S S, Kuppurao S 2017 IEEE Trans. Electron Dev. 64 2498
[9] Margetis J, Mosleh A, Al-Kabi S, Ghetmiri S A, Du W, Dou W, Benamara M, Li B, Mortazavi M, Naseem H A, Yu S Q, Tolle J 2017 J. Cryst. Growth 463 128
[10] Mosleh A, Alher M A, Cousar L C, Du W, Ghetmiri S A, Pham T, Grant J M, Sun G, Soref R A, Li B, Naseem H A, Yu S Q 2015 Front. Mater. 2 30
[11] Kurdi M E, Fishman G, Sauvage S, Boucaud P 2010 J. Appl. Phys. 107 013710
[12] Liu L, Zhang M, Hu L, Di Z, Zhao S J 2014 J. Appl. Phys. 116 113105
[13] Bai M, Xuan R X, Song J J, Zhang H M, Hu H Y, Shu B 2015 Acta Phys. Sin. 64 038501 (in Chinese)[白敏, 宣荣喜, 宋建军, 张鹤鸣, 胡辉勇, 舒斌 2015 物理学报 64 038501]
[14] D'Costa V R, Cook C S, Birdwell A G, Littler C L, Canonico M, Zollner S, Kouvetakis J, Menndez J 2006 Phys. Rev. B 73 125207
[15] Madelung O, Rssler U, Schulz M 2002 SemiconductorsGroup IV Elements, IV-IV and Ⅲ- V Compounds. Part b-Electronic, Transport, Optical and Other Properties (Berlin: Springer) p2801, p3106
[16] Bahder T B 1990 Phys. Rev. B 41 11992
[17] Pryor C 1998 Phys. Rev. B 57 7190
[18] Zhu Y H, Xu Q, Fan W J, Wang J W 2010 J. Appl. Phys. 107 073108
[19] Ye L X 1997 Monte Carlo Simulation of the Small-Scale Semiconductor Devices (Beijing: Science Press) p318, 384 (in Chinese)[叶良修 1997 小尺寸半导体器件的蒙特卡罗模拟 (北京: 科学出版社) 第318页, 第384页]
[20] Ye L X 2007 Semiconductor Physics (2nd Ed.) Part One (Beijing: Higher Education Press) p203 (in Chinese)[叶良修 2007 半导体物理学(第二版)上册 (北京: 高等教育出版社)第 203 页]
[21] Sun Y, Thompson S E, Nishida T 2010 Strain Effect in Semiconductors: Theory and Device Applications (New York: Springer) pp193-201
[22] Wang X Y, Zhang H M, Song J J, Ma J L, Wang G Y, An J H 2011 Acta Phys. Sin. 60 077205 (in Chinese)[王晓艳, 张鹤鸣, 宋建军, 马建立, 王冠宇, 安久华 2011 物理学报 60 077205]
[23] Song J J, Zhang H M, Hu H Y, Wang X Y, Wang G Y 2012 Acta Phys. Sin. 61 057304 (in Chinese)[宋建军, 张鹤鸣, 胡辉勇, 王晓艳, 王冠宇 2012 物理学报 61 057304]
[24] Nguyen P H, Hofmann K R 2003 J. Appl. Phys. 94 375
[25] Fischetti M V, Laux S E 1996 J. Appl. Phys. 80 2234
[26] Song P, Cai L C, Tao T J, Yuan S, Chen H, Huang J, Zhao X W, Wang X J 2016 J. Appl. Phys. 120 195101
[27] Myers V W 1967 J. Phys. Chem. Solids 28 2207
[28] Adachi S 2009 Properties of Semiconductor Alloys: Group-IV, Ⅲ- V and Ⅱ- VI Semiconductors (Chichester: John Wiley Sons Ltd.) p18
[29] Chen R, Lin H, Huo Y, Hitzman C, Kamins T I, Harris J S 2011 Appl. Phys. Lett. 99 181125
[30] Dai X Y, Yang C, Song J J, Zhang H M, Hao Y, Zheng R C 2012 Acta Phys. Sin. 61 237102 (in Chinese)[戴显英, 杨程, 宋建军, 张鹤鸣, 郝跃, 郑若川 2012 物理学报 61 237102]
[31] Lin H, Chen R, Huo Y, Kamins T I, Harris J S 2011 Appl. Phys. Lett. 98 261917
[32] Lin H, Chen R, Lu W, Huo Y, Kamins T I, Harris J S 2012 Appl. Phys. Lett. 100 102109
[33] Gassenq A, Milord L, Aubin J, Guilloy K, Tardif S, Pauc N, Rothman J, Chelnokov A, Hartmann J M, Reboud V, Calvo V 2016 Appl. Phys. Lett. 109 242107
[34] Lieten R R, Seo J W, Decoster S, Vantomme A, Peters S, Bustillo K C, Haller E E, Menghini M, Locquet J P 2013 Appl. Phys. Lett. 102 052106
[35] Wirths S, Stange D, Pampilln M A, Tiedemann A T, Mussler G, Fox A, Breuer U, Baert B, Andrs E S, Nguyen N D, Hartmann J M, Ikonic Z, Mantl S, Buca D 2015 ACS Appl. Mater. Interfaces 7 62
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