Profiling Electronic and Phononic Band Structures of Semiconductors at Finite Temperatures: Methods and Applications

doi:10.1088/0256-307X/41/2/026301

Chin. Phys. Lett.

2024, Vol. 41

Issue (2): 026301 DOI: 10.1088/0256-307X/41/2/026301

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES

Profiling Electronic and Phononic Band Structures of Semiconductors at Finite Temperatures: Methods and Applications

Xie Zhang^1*, Jun Kang^2*, and Su-Huai Wei^2*

¹School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, China
²Beijing Computational Science Research Center, Beijing 100193, China

Cite this article:

Xie Zhang, Jun Kang, and Su-Huai Wei 2024 Chin. Phys. Lett. 41 026301

Download: PDF(29301KB) PDF(mobile)(29337KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract Semiconductor devices are often operated at elevated temperatures that are well above zero Kelvin, which is the temperature in most first-principles density functional calculations. Computational approaches to computing and understanding the properties of semiconductors at finite temperatures are thus in critical demand. In this review, we discuss the recent progress in computationally assessing the electronic and phononic band structures of semiconductors at finite temperatures. As an emerging semiconductor with particularly strong temperature-induced renormalization of the electronic and phononic band structures, halide perovskites are used as a representative example to demonstrate how computational advances may help to understand the band structures at elevated temperatures. Finally, we briefly illustrate the remaining computational challenges and outlook promising research directions that may help to guide future research in this field.

Received: 18 November 2023 Review Published: 01 February 2024

PACS:	61.82.Fk	(Semiconductors)
	31.15.es	(Applications of density-functional theory (e.g., to electronic structure and stability; defect formation; dielectric properties, susceptibilities; viscoelastic coefficients; Rydberg transition frequencies))
	63.20.dk	(First-principles theory)
	63.20.D-	(Phonon states and bands, normal modes, and phonon dispersion)

TRENDMD:

URL:

https://cpl.iphy.ac.cn/10.1088/0256-307X/41/2/026301 OR https://cpl.iphy.ac.cn/Y2024/V41/I2/026301

Service
	E-mail this article
	E-mail Alert
	RSS
Articles by authors
	Xie Zhang
	Jun Kang
	and Su-Huai Wei

[1]	Zhang L X, Pan X Y, Liu L, and Ding L M 2022 J. Semicond. 43 030203
[2]	Zhang X, Turiansky M E, and van de Walle C G 2021 Nat. Mater. 20 971
[3]	DelRio F W, Grutzik S J, Mook W M, Dickens S M, Kotula P G, Stauffer D D, and Boyce B L 2022 Mater. Res. Lett. 10 728
[4]	Du L, Gao X Y, Yang C C, and Jiang Q 2023 Mater. Res. Lett. 11 159
[5]	Fang S X, Li Q J, Li Z L, Dong Q, Jing X L, Li C Y, Li H Y, Liu R, and Liu B B 2023 Mater. Res. Lett. 11 134
[6]	Jiang Y Y, Lu Y Y, Zhang Z F, Chang L G, Li J H, Han X, Gan L, Sui M L, and Yan P F 2023 Mater. Res. Lett. 11 471
[7]	Wang Q, Tang Y P, Horita Z, and Iikubo S 2022 Mater. Res. Lett. 10 521
[8]	Zhang X, Shen J X, and van de Walle C G 2020 Phys. Rev. Lett. 125 037401
[9]	Dou B Y, Falletta S, Neugebauer J, Zhang X, and Wei S H 2023 Phys. Rev. Appl. 19 054054
[10]	Wang Z H, Zhang X, and Wei S H 2022 J. Phys. Chem. Lett. 13 11438
[11]	Zhang Y Y, Chen S, Xu P, Xiang H, Walsh A, and Wei S H 2018 Chin. Phys. Lett. 35 036104
[12]	Zhang X, Shen J X, and Van de Walle C G 2020 Adv. Energy Mater. 10 1902830
[13]	Yan X L, Li P, Wei S H, and Huang B 2021 Chin. Phys. Lett. 38 087103
[14]	Kang J, Zhang X, and Wei S H 2022 Chin. Phys. B 31 107105
[15]	Zhang X, Kang J, and Wei S H 2023 Nat. Comput. Sci. 3 210
[16]	Wang H C, Wang Z H, Chen X Y, Zhu W, and Zhang X 2023 Chin. Phys. Lett. 40 047701
[17]	Shao B, Jiang X, Meng S, and Huang B 2023 Chin. Phys. Lett. 40 087303
[18]	Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169
[19]	Soler J M, Artacho E, Gale J D, García A, Ordejón P, and Sánchez-Portal D 2002 J. Phys.: Condens. Matter 14 2745
[20]	Clark S J, Segall M D, Pickard C J, Hasnip P J, Refson K, and Payne M C 2005 Z. Kristallogr. - Cryst. Mater. 220 567
[21]	Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti G L, Cococcioni M, Dabo I, Dal C A, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen A P, Umari P, and Wentzcovitch R M 2009 J. Phys.: Condens. Matter 21 395502
[22]	Weinert M, Podloucky R, and Redinger J 2009 J. Phys.: Condens. Matter 21 084201
[23]	Boeck S, Freysoldt C, Ismer L, and Neugebauer J 2011 Comput. Phys. Commun. 182 543
[24]	Blaha P, Schwarz K, Tran F, Madsen G K H, and Marks L D 2020 J. Chem. Phys. 152 074101
[25]	Gonze X, Amadon B, Antonius G, Arnardi F, Baguet L, Beuken J M, Bieder J, Bottin F, Bouchet J, Bousquet E, Brouwer N, Bruneval F, Brunin G, Cavignac T, Charraud J B, Chen W, Côté M, Cottenier S, Denier J, Geneste G, Ghosez P, Giantomassi M, Gillet Y, Gingras O, Hamann D R, Hautier G, He X, Helbig N, Holzwarth N, Jia Y, Jollet F, Lafargue-Dit-Hauret W, Lejaeghere K, Marques M A L, Martin A, Martins C, Miranda H P C, Naccarato F, Persson K, Petretto G, Planes V, Pouillon Y, Prokhorenko S, Ricci F, Rignanese G M, Romero A H, Schmitt M M, Torrent M, Van Setten M J, Van Troeye B, Zérah G, and Zwanziger J W 2020 Comput. Phys. Commun. 248 107042
[26]	Kresse G, Furthmüller J, and Hafner J 1995 Europhys. Lett. 32 729
[27]	Parlinski K, Li Z Q, and Kawazoe Y 1997 Phys. Rev. Lett. 78 4063
[28]	Giannozzi P, Pavone P, and Baroni S 1991 Phys. Rev. B 43 7231
[29]	Gonze X and Lee C 1997 Phys. Rev. B 55 10355
[30]	Togo A and Tanaka I 2015 Scr. Mater. 108 1
[31]	Hellmann H 1933 Z. Phys. 85 180
[32]	Feynman R P 1939 Phys. Rev. 56 340
[33]	Hickel T, Körmann F, and Neugebauer J 2012 J. Phys.: Condens. Matter 24 053202
[34]	Körmann F, Dick A, Grabowski B, Hallstedt B, Hickel T, and Neugebauer J 2008 Phys. Rev. B 78 033102
[35]	Glensk A, Hickel T, and Neugebauer J 2014 Phys. Rev. X 4 011018
[36]	Körmann F, Grabowski B, Dutta B, Hickel T, Fultz B, and Neugebauer J 2014 Phys. Rev. Lett. 113 165503
[37]	Grabowski B, Ikeda Y, Srinivasan P, Körmann F, Freysoldt C, Shapeev A, and Neugebauer J 2019 npj Comput. Mater. 5 80
[38]	Iftimie R, Minary P, and Tuckerman M E 2005 Proc. Natl. Acad. Sci. USA 102 6654
[39]	Wei S H, Bernard J E, and Zunger A 1990 Phys. Rev. B 42 9622
[40]	Zunger A, Ferreira L G, and Bernard J E 1990 Phys. Rev. Lett. 65 353
[41]	Elvira V and Martino L 2021 Advances in Importance Sampling. In: Balakrishnan N, Colton T, Everitt B, Ruggeri F and Teugels J L (eds) Wiley StatsRef: Statistics Reference Online (New York: Wiley) pp 1–14
[42]	Behler J and Csányi G 2021 Eur. Phys. J. B 94 142
[43]	Williams F E 1951 Phys. Rev. 82 281
[44]	Lax M 1952 J. Chem. Phys. 20 1752
[45]	Zacharias M, Patrick C E, and Giustino F 2015 Phys. Rev. Lett. 115 177401
[46]	Monserrat B, Dreyer C E, and Rabe K M 2018 Phys. Rev. B 97 104310
[47]	Bravić I and Monserrat B 2019 Phys. Rev. Mater. 3 065402
[48]	West D and Estreicher S K 2006 Phys. Rev. Lett. 96 115504
[49]	Monserrat B, Drummond N D, and Needs R J 2013 Phys. Rev. B 87 144302
[50]	Monserrat B 2016 Phys. Rev. B 93 014302
[51]	Monserrat B 2018 J. Phys.: Condens. Matter 30 083001
[52]	Zacharias M and Giustino F 2016 Phys. Rev. B 94 075125
[53]	Zacharias M and Giustino F 2020 Phys. Rev. Res. 2 013357
[54]	Fan H Y 1951 Phys. Rev. 82 900
[55]	Giustino F, Louie S G, and Cohen M L 2010 Phys. Rev. Lett. 105 265501
[56]	Allen P B and Heine V 1976 J. Phys. C 9 2305
[57]	Allen P B and Cardona M 1981 Phys. Rev. B 23 1495
[58]	Allen P B and Cardona M 1983 Phys. Rev. B 27 4760
[59]	Popescu V and Zunger A 2012 Phys. Rev. B 85 085201
[60]	Medeiros P V C, Stafström S, and Björk J 2014 Phys. Rev. B 89 041407
[61]	Karki B B, De Gironcoli S, and Baroni S 2000 Phys. Rev. B 61 8793
[62]	Hellman O, Abrikosov I A, and Simak S I 2011 Phys. Rev. B 84 180301
[63]	Hellman O, Abrikosov I A, and Simak S I 2013 Phys. Rev. B 87 104111
[64]	Werthamer N R 1970 Phys. Rev. B 1 572
[65]	Souvatzis P, Katsnelson M, and Rudin S 2008 Phys. Rev. Lett. 100 095901
[66]	Errea I, Calandra M, and Mauri F 2014 Phys. Rev. B 89 064302
[67]	Tadano T and Tsuneyuki S 2015 Phys. Rev. B 92 054301
[68]	Kojima A, Shirai Y, and Miyasaka T 2009 J. Am. Chem. Soc. 131 6050
[69]	Zhao Y, Ma F, Qu Z, Yu S, Shen T, Deng H X, Chu X, Peng X, Zhang X, and You J 2022 Science 377 531
[70]	Park J, Kim J, Yun H S, Paik M J, Noh E, Mun H J, Shin T J, and Seok S I 2023 Nature 616 724
[71]	Huang Z J, Bai Y, Huang X D, Li J T, Wu Y T, Chen Y H, Li K L, Niu X X, Li N X, Liu G L, Zhang Y, Zai H, Chen Q, Wang L, and Zhou H 2023 Nature 623 531
[72]	Ma D X, Lin K B, Dong Y T, Choubisa H, Proppe A H, Wu D, Wang Y K, Chen B, Li P, Fan J Z, Yuan F, Johnston A, Liu Y, Kang Y, Wei Z, and Sargent E H 2021 Nature 599 594
[73]	Zhang Q, Ha S T, Liu X F, Sum T C, and Xiong Q H 2014 Nano Lett. 14 5995
[74]	Luo J H, Im J H, Mayer M T, Schreier M, Nazeeruddin M K, Park N G, Fan H J, and Gratzel M 2014 Science 345 1593
[75]	Chen B, Li T, Dong Q F, Mosconi E, Song J, Chen Z, Deng Y, Liu Y, Ducharme S, Angelis F D, and Huang J 2018 Nat. Mater. 17 1020
[76]	Chen Q S, Wu J, Ou X Y, Huang B L, Almutlaq J, Zhumekenov A A, Guan X, Han S, Liang L, Yi Z, Li J, Xie X, Wang Y, Li Y, Fan D, Teh D B L, All A H, Mohammed O F, Bakr O M, Wu T, Bettinelli M, Huang W, and Liu X 2018 Nature 561 88
[77]	Poglitsch A and Weber D 1987 J. Chem. Phys. 87 6373
[78]	Stoumpos C C, Malliakas C D, Peters J A, Liu Z, Sebastian M, Im J, Chasapis T C, Wibowo A C, Chung D Y, Wessels B W, and Kanatzidis M G 2013 Cryst. Growth & Des. 13 2722
[79]	Bakulin A A, Selig O, Bakker H J, Rezus Y L A, Müller C, Glaser T, Lovrincic R, Sun Z, Chen Z, Frost J M, and Jansen T L C 2015 J. Phys. Chem. Lett. 6 3663
[80]	Lahnsteiner J, Kresse G, Kumar A, Franchini C, and Bokdam M 2016 Phys. Rev. B 94 214114
[81]	Yang R X, Skelton J M, Frost J M, and Walsh A 2017 J. Phys. Chem. Lett. 8 4720
[82]	Straus D B, Abeykoon A M, and Cava R J 2020 Adv. Mater. 32 2001069
[83]	Lanigan-Atkins T, He X, Krogstad M J, Pajerowski D M, Abernathy D L, Xu G N M N, Xu Z, Chung D Y, Kanatzidis M G, Osborn R, and Delaire O 2021 Nat. Mater. 20 977
[84]	Gehrmann C, Zhu X, and Egger D A 2022 Adv. Sci. 9 2200706
[85]	Zhu X Z, Caicedo-Dávila S, Gehrmann C, and Egger D A 2022 ACS Appl. Mater. & Interfaces 14 22973
[86]	Wu X W, Ming C, Shi J, Wang H, West D, Zhang S B, and Sun Y Y 2022 Chin. Phys. Lett. 39 046101
[87]	Zhang X, Wang W, and Van de Walle C G 2018 ACS Energy Lett. 3 2329
[88]	Fabini D H, Siaw T A, Stoumpos C C, Laurita G, Olds D, Page K, Hu J G, Han S, and Seshadri R 2017 J. Am. Chem. Soc. 139 16875
[89]	Chen T R, Foley B J, Ipek B, Tyagi M, Copley J R D, Choi J J, and Lee S H 2015 Phys. Chem. Chem. Phys. 17 31278
[90]	Mattoni A, Saba M I, and Delugas P 2015 J. Phys. Chem. C 119 17421
[91]	Kang J and Wang L W 2017 J. Phys. Chem. Lett. 8 3875
[92]	Saleh G, Biffi G, Di Stasio F, Martín-García B, Abdelhady A L, Krahne R, and Artyukhin S 2021 Chem. Mater. 33 8524
[93]	Svane K L, Forse A C, Grey C P, Kieslich G, Walsh A, and Butler K T 2017 J. Phys. Chem. Lett. 8 6154
[94]	Yin W J, Yang J H, Yan Y, and Wei S H 2015 J. Mater. Chem. A 3 8926
[95]	Kang J, Li J, and Wei S H 2021 Appl. Phys. Rev. 8 031302
[96]	Wang S S, Huang M L, Wu Y M, and Chen S Y 2021 Adv. Theory Simul. 4 2100060
[97]	Gao Q, Kang J, and Wei S H 2021 Phys. Rev. B 104 064204
[98]	Zhao B Q, Li Y L, Chen X Y, Han Y Y, Wei S H, Wu K F, and Zhang X 2023 Adv. Sci. 2300386
[99]	Kang Y G and Han S 2018 Phys. Rev. Appl. 10 044013
[100]	Foley B J, Marlowe D L, Sun K, Saidi W A, Gupta M C, and Choi J J 2015 Appl. Phys. Lett. 106 243904
[101]	Wang H Y, Tal A, Bischoff T, Gono P, and Pasquarello A 2022 npj Comput. Mater. 8 237
[102]	Perdew J P, Burke K, and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[103]	Milot R L, Eperon G E, Johnston M B, and Herz L M 2015 Adv. Funct. Mater. 25 6218
[104]	Saidi W A, Poncé S, and Monserrat B 2016 J. Phys. Chem. Lett. 7 5247
[105]	Richter J M, Chen K, Sadhanala A, Butkus J, Rivett J P H, Friend R H, Hodgkiss J M, and Deschler F 2018 Adv. Mater. 30 1803379
[106]	Xu Q L, Stroppa A, Lv J, Zhao X G, Yang D W, Biswas K, and Zhang L J 2019 Phys. Rev. Mater

Related articles from Frontiers Journals

[1]	Wenkai Zhu, Shihong Xie, Hailong Lin, Gaojie Zhang, Hao Wu, Tiangui Hu, Ziao Wang, Xiaomin Zhang, Jiahan Xu, Yujing Wang, Yuanhui Zheng, Faguang Yan, Jing Zhang, Lixia Zhao, Amalia Patanè, Jia Zhang, Haixin Chang, and Kaiyou Wang. Large Room-Temperature Magnetoresistance in van der Waals Ferromagnet/Semiconductor Junctions[J]. Chin. Phys. Lett., 2022, 39(12): 026301
[2]	Yanling Zhang , Xiaozhu Hao , Yanping Huang , Fubo Tian, Da Li , Youchun Wang , Hao Song , and Defang Duan . Structural and Electrical Properties of Be$_{x}$Zn$_{1-x}$O Alloys under High Pressure[J]. Chin. Phys. Lett., 2021, 38(2): 026301
[3]	Qing Liao, Long Kang, Tong-Min Zhang, Hui-Ping Liu, Tao Wang, Xiao-Gang Li, Jin-Yu Li, Zhen Yang, and Bing-Sheng Li. Comparison of Cavities Formed in Single Crystalline and Polycrystalline $\alpha$-SiC after H Implantation[J]. Chin. Phys. Lett., 2020, 37(7): 026301
[4]	Hui-Ping Liu, Jin-Yu Li, Bing-Sheng Li. Microstructure of Hydrogen-Implanted Polycrystalline $\alpha$-SiC after Annealing[J]. Chin. Phys. Lett., 2018, 35(9): 026301
[5]	Li-Hua Dai, Da-Wei Bi, Zheng-Xuan Zhang, Xin Xie, Zhi-Yuan Hu, Hui-Xiang Huang, Shi-Chang Zou. Metastable Electron Traps in Modified Silicon-on-Insulator Wafer[J]. Chin. Phys. Lett., 2018, 35(5): 026301
[6]	Rui Wu, Jun-Ling Wang, Gang Yan, Rong Wang. Photoluminescence Analysis of Electron Damage for Minority Carrier Diffusion Length in GaInP/GaAs/Ge Triple-Junction Solar Cells[J]. Chin. Phys. Lett., 2018, 35(4): 026301
[7]	Jun-Ling Wang, Tian-Cheng Yi, Yong Zheng, Rui Wu, Rong Wang. Temperature-Dependent Photoluminescence Analysis of 1.0MeV Electron Irradiation-Induced Nonradiative Recombination Centers in n$^{+}$–p GaAs Middle Cell of GaInP/GaAs/Ge Triple-Junction Solar Cells[J]. Chin. Phys. Lett., 2017, 34(7): 026301
[8]	Yu-Zhu Liu, Bing-Sheng Li, Hua Lin, Li Zhang. Recrystallization Phase in He-Implanted 6H-SiC[J]. Chin. Phys. Lett., 2017, 34(7): 026301
[9]	Yu-Zhu Liu, Bing-Sheng Li, Li Zhang. High-Temperature Annealing Induced He Bubble Evolution in Low Energy He Ion Implanted 6H-SiC[J]. Chin. Phys. Lett., 2017, 34(5): 026301
[10]	Yong Zheng, Tian-Cheng Yi, Jun-Ling Wang, Peng-Fei Xiao, Rong Wang. Radiation Damage Analysis of Individual Subcells for GaInP/GaAs/Ge Solar Cells Using Photoluminescence Measurements[J]. Chin. Phys. Lett., 2017, 34(2): 026301
[11]	Xiao-Nian Liu, Li-Hua Dai, Bing-Xu Ning, Shi-Chang Zou. Total-Ionizing-Dose-Induced Body Current Lowering in the 130nm PDSOI I/O NMOSFETs[J]. Chin. Phys. Lett., 2017, 34(1): 026301
[12]	Yi Han, Bing-Sheng Li, Zhi-Guang Wang, Jin-Xin Peng, Jian-Rong Sun, Kong-Fang Wei, Cun-Feng Yao, Ning Gao, Xing Gao, Li-Long Pang, Ya-Bin Zhu, Tie-Long Shen, Hai-Long Chang, Ming-Huan Cui, Peng Luo, Yan-Bin Sheng, Hong-Peng Zhang, Xue-Song Fang, Si-Xiang Zhao, Jin Jin, Yu-Xuan Huang, Chao Liu, Dong Wang, Wen-Hao He, Tian-Yu Deng, Peng-Fei Tai, Zhi-Wei Ma. H-ion Irradiation-induced Annealing in He-ion Implanted 4H-SiC[J]. Chin. Phys. Lett., 2017, 34(1): 026301
[13]	Xin Wang, Wu Lu, Wu-Ying Ma, Qi Guo, Zhi-Kuan Wang, Cheng-Fa He, Mo-Han Liu, Xiao-Long Li, Jin-Cheng Jia. Radiation Resistance of Fluorine-Implanted PNP Using Gated-Controlled Lateral PNP Transistor Structure[J]. Chin. Phys. Lett., 2016, 33(08): 026301
[14]	Yi-Ming Li, Li-Xia Qiu, Zhan-Hui Ding, Yong-Feng Li, Bin Yao, Zhen-Yu Xiao, Pin-Wen Zhu. High-Pressure Preparation of High-Density Cu$_{2}$ZnSnS$_{4}$ Materials[J]. Chin. Phys. Lett., 2016, 33(07): 026301
[15]	R. Perumal, Z. Hassan, R.Saravanan. Structural, Morphological and Electrical Properties of In-Doped Zinc Oxide Nanostructure Thin Films Grown on p-Type Gallium Nitride by Simultaneous Radio-Frequency Direct-Current Magnetron Co-Sputtering[J]. Chin. Phys. Lett., 2016, 33(06): 026301

Viewed

Full text

Abstract