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Chin. Phys. B, 2021, Vol. 30(8): 087201    DOI: 10.1088/1674-1056/ac0133

Group velocity matters for accurate prediction of phonon-limited carrier mobility

Qiao-Lin Yang(杨巧林)1,2, Hui-Xiong Deng(邓惠雄)1,2, Su-Huai Wei(魏苏淮)3, and Jun-Wei Luo(骆军委)1,2,4,†
1 State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China;
2 Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China;
3 Beijing Computational Science Research Center, Beijing 100193, China;
4 Beijing Academy of Quantum Information Sciences, Beijing 100193, China
Abstract  First-principles approaches have recently been developed to replace the phenomenological modeling approaches with adjustable parameters for calculating carrier mobilities in semiconductors. However, in addition to the high computational cost, it is still a challenge to obtain accurate mobility for carriers with a complex band structure, e.g., hole mobility in common semiconductors. Here, we present a computationally efficient approach using isotropic and parabolic bands to approximate the anisotropy valence bands for evaluating group velocities in the first-principles calculations. This treatment greatly reduces the computational cost in two ways: relieves the requirement of an extremely dense κ mesh to obtain a smooth change in group velocity, and reduces the 5-dimensional integral to 3-dimensional integral. Taking Si and SiC as two examples, we find that this simplified approach reproduces the full first-principles calculation for mobility. If we use experimental effective masses to evaluate the group velocity, we can obtain hole mobility in excellent agreement with experimental data over a wide temperature range. These findings shed light on how to improve the first-principles calculations towards predictive carrier mobility in high accuracy.
Keywords:  electron-phonon interaction      phonon-limited hole mobility      Boltzmann transport equation  
Received:  23 April 2021      Revised:  12 May 2021      Accepted manuscript online:  14 May 2021
PACS:  72.10.-d (Theory of electronic transport; scattering mechanisms)  
  72.10.Bg (General formulation of transport theory)  
  72.20.Fr (Low-field transport and mobility; piezoresistance)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11925407 and 61927901) and the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. ZDBS-LY-JSC019).
Corresponding Authors:  Jun-Wei Luo     E-mail:

Cite this article: 

Qiao-Lin Yang(杨巧林), Hui-Xiong Deng(邓惠雄), Su-Huai Wei(魏苏淮), and Jun-Wei Luo(骆军委) Group velocity matters for accurate prediction of phonon-limited carrier mobility 2021 Chin. Phys. B 30 087201

[1] Di L J, Dai X Y, et al. 2018 Acta Phys. Sin. 67027101(in Chinese)
[2] Deng H X, Luo J W and Wei S H 2018 Chin. Phys. B 27117104
[3] Lundstrom M 2000 Fundamentals of carrier transport, 2nd ed edn. (Cambridge:Cambridge University Press)
[4] Yu P Y and Cardona M 2010 Fundamentals of semiconductors:physics and materials properties 4th edn. (Berlin:Springer)
[5] Ponce S, Margine E R and Giustino F 2018 Phys. Rev. B 97121201
[6] Giustino F 2017 Rev. Mod. Phys. 89015003
[7] Shockley W and Bardeen J 1950 Phys. Rev. 77407
[8] Herring C and Vogt E 1956 Phys. Rev. 101944
[9] Tiersten M 1961 IBM J. Res. Dev. 5122
[10] Lawaetz P 1968 Phys. Rev. 174867
[11] Hamaguchi C 2010 Basic semiconductor physics 2nd ed edn. (Berlin:Springer-Verlag)
[12] Bir G L and Pikus G E 1974 Symmetry and strain-induced effects in semiconductors (New York:Wiley)
[13] Frohlich H 1954 Adv. Phys. 3325
[14] Meijer H and Polder D 1953 Physica 19255
[15] Kranzer D 1974 Phys. Status Solidi A 2611
[16] Wiley J D 1971 Phys. Rev. B 42485
[17] Wiley J D and DiDomenico M 1970 Phys. Rev. B 2427
[18] Li W 2015 Phys. Rev. B 92075405
[19] Liu T H, Zhou J, Liao B, Singh D J and Chen G 2017 Phys. Rev. B 95075206
[20] Ma J, Nissimagoudar A and Li W 2018 Phys. Rev. B 97045201
[21] Deng T, et al. 2020 npj Comput. Mater. 61
[22] Ponce S, Margine E R, Verdi C and Giustino F 2016 Comput. Phys. Communs. 209116
[23] Giannozzi P, et al. 2017 J. Phys.:Condens. Matter 29465901
[24] Mostofi A A, et al. 2014 Comput. Phys. Commun. 1852309
[25] Hamann D R 2013 Phys. Rev. B 88085117
[26] Schlipf M and Gygi F 2015 Comput. Phys. Commun. 19636
[27] Scherpelz P, Govoni M, Hamada I and Galli G 2016 J. Chem. Theory Comput. 123523
[28] Ponce S, Jena D and Giustino F 2019 Phys. Rev. B 100085204
[29] Liu T H, et al. 2018 Phys. Rev. B 98081203
[32] Sze S M and Ng K K 2007 Physics of semiconductor devices 3rd edn. (Hoboken:Wiley-Interscience)
[33] Dresselhaus G, Kip A F and Kittel C 1955 Phys. Rev. 98368
[34] Bimberg D, et al. 1982 Physics of Group IV Elements and III-V Compounds/Physik der Elemente der IV. Gruppe und der III-V Verbindungen, Condensed Matter (Berlin:Springer-Verlag)
[35] Morin F J and Maita J P 1954 Phys. Rev. 9628
[36] Logan R A and Peters A J 1960 J. Appl. Phys. 31122
[37] Ludwig G W and Watters R L 1956 Phys. Rev. 1011699
[38] Jacoboni C, Canali C, Ottaviani G and Alberigi Quaranta A 1977 SolidState Electron. 2077
[39] Yamanaka M, Daimon H, Sakuma E, Misawa S and Yoshida S 1987J. Appl. Phys. 61599
[40] Nishino S, Powell J A and Will H A 1983 Appl. Phys. Lett. 42460
[41] Lebedev A A, et al. 2008 Semicond. Sci. Technol.23075004
[42] Meng F, Ma J, He J and Li W 2019 Phys. Rev. B 99045201
[43] Kim Y S, Marsman M, Kresse G, Tran F and Blaha P 2010 Phys. Rev. B 82205212
[44] Wang L and Zunger A 1994 J. Chem. Phys. 1002394
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[1] Ding Xiu-xiang, Liang Jiu-qing. LARMOR PRECESSION AND THE BARRIER INTERACTION TIME[J]. Chin. Phys. B, 1999, 8(6): 409 -415 .
[2] Xue Qi-zhen, Xue Qi-kun, S. Kuwano, K. Nakayama, T. Sakurai. GROWTH MODE AND SURFACE RECONSTRUCTION OF GaN(000$\bar{1}$) THIN FILMS ON 6H-SiC(000$\bar{1}$)[J]. Chin. Phys. B, 2001, 10(13): 157 -162 .
[4] Wu Xiang-Yao, Yin Xin-Guo, Guo Yi-Qing. Non-factorizable contributions in D0→$\pi^+\pi^-$ decay[J]. Chin. Phys. B, 2004, 13(4): 469 -472 .
[5] Wu Hui-Bin. Potential method of integration for solving the equations of mechanical systems[J]. Chin. Phys., 2006, 15(5): 899 -902 .
[6] Liu Xiao-Juan(刘小娟), Zhou Bing-Ju(周并举), Liu Ming-Wei (刘明伟), and Li Shou-Cun(李寿存). Preparation and control of entangled states in the two-mode coherent fields interacting with a moving atom via two-photon process[J]. Chin. Phys., 2007, 16(12): 3685 -3691 .
[7] Liu Yang-Zheng(刘扬正), Jiang Chang-Sheng(姜长生), Lin Chang-Sheng(林长圣), and Jiang Yao-Mei(蒋耀妹). Chaos synchronization between two different 4D hyperchaotic Chen systems[J]. Chin. Phys., 2007, 16(3): 660 -665 .
[8] Wang Hong-Yan(王红艳), Li Xi-Bo(李喜波), Tang Yong-Jian(唐永建), R. Bruce King, and Henry F. Schaefer III. Structures and electronic properties of Aun-1Cu and Aun (n≤9) clusters[J]. Chin. Phys., 2007, 16(6): 1660 -1664 .
[9] Wang Ji-Suo(王继锁) and Meng Xiang-Guo(孟祥国). The nonlinear squeezed one-photon states and their nonclassical properties[J]. Chin. Phys., 2007, 16(8): 2422 -2427 .
[10] Liu Li(刘立), Zhang Liang-Ying(张良英), and Cao Li(曹力). Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator[J]. Chin. Phys. B, 2009, 18(10): 4182 -4186 .