Calculations of energy band structure and mobility in critical bandgap strained Ge1-xSnx based on Sn component and biaxial tensile stress modulation

Di Lin-Jia; Dai Xian-Ying; Song Jian-Jun; Miao Dong-Ming; Zhao Tian-Long; Wu Shu-Jing; Hao Yue

doi:10.7498/aps.67.20171969

Abstract

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:

Authors and contacts

1.
State Key Discipline Laboratory of Wide Bandgap Semiconductor Technologies, School of Microelectronics, Xidian University, Xi'an 710071, China

Corresponding author: Dai Xian-Ying, xydai@xidian.edu.cn;jianjun_79_81@xidian.edu.cn;miaodongmingi@126.com ; Song Jian-Jun, xydai@xidian.edu.cn;jianjun_79_81@xidian.edu.cn;miaodongmingi@126.com ; Miao Dong-Ming, xydai@xidian.edu.cn;jianjun_79_81@xidian.edu.cn;miaodongmingi@126.com ;

Funds: Project supported by the Advance Research Foundation of China (Grant No. 9140A08020115DZ01024) and the China Postdoctoral Science Foundation (Grant No. 2017M613061).

References

[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

Cited By

[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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