Thermal transport in semiconductor nanostructures, graphene, and related two-dimensional materials

doi:10.1088/1674-1056/27/5/056301

摘要/Abstract

摘要： We review experimental and theoretical results on thermal transport in semiconductor nanostructures (multilayer thin films, core/shell and segmented nanowires), single-and few-layer graphene, hexagonal boron nitride, molybdenum disulfide, and black phosphorus. Different possibilities of phonon engineering for optimization of electrical and heat conductions are discussed. The role of the phonon energy spectra modification on the thermal conductivity in semiconductor nanostructures is revealed. The dependence of thermal conductivity in graphene and related two-dimensional (2D) materials on temperature, flake size, defect concentration, edge roughness, and strain is analyzed.

关键词: phonons, thermal conductivity, nanowire, graphene, two-dimensional (2D) materials

Abstract: We review experimental and theoretical results on thermal transport in semiconductor nanostructures (multilayer thin films, core/shell and segmented nanowires), single-and few-layer graphene, hexagonal boron nitride, molybdenum disulfide, and black phosphorus. Different possibilities of phonon engineering for optimization of electrical and heat conductions are discussed. The role of the phonon energy spectra modification on the thermal conductivity in semiconductor nanostructures is revealed. The dependence of thermal conductivity in graphene and related two-dimensional (2D) materials on temperature, flake size, defect concentration, edge roughness, and strain is analyzed.

Key words: phonons, thermal conductivity, nanowire, graphene, two-dimensional (2D) materials

中图分类号: (Phonons in graphene)

63.22.Rc

63.22.-m (Phonons or vibrational states in low-dimensional structures and nanoscale materials) 65.80.Ck (Thermal properties of graphene) 65.80.-g (Thermal properties of small particles, nanocrystals, nanotubes, and other related systems)

Alexandr I. Cocemasov, Calina I. Isacova, Denis L. Nika. Thermal transport in semiconductor nanostructures, graphene, and related two-dimensional materials[J]. 中国物理B, 2018, 27(5): 56301-056301.

Alexandr I. Cocemasov, Calina I. Isacova, Denis L. Nika. Thermal transport in semiconductor nanostructures, graphene, and related two-dimensional materials[J]. Chin. Phys. B, 2018, 27(5): 56301-056301.

参考文献 143

[77]	Ma F, Zheng H B, Sun Y J, Yang D, Xu K W and Chu P K 2012 Appl. Phys. Lett. 101 111904
[12]	Mingo N and Yang L 2003 Phys. Rev. B 68 245406
[1]	Balandin A A 2005 J. Nanosci. Nanotechnol. 5 1015
[13]	Zincenco N D, Nika D L, Pokatilov E P and A. A 2007 J. Phys.:Conf. Ser. 92 012086
[78]	Fthenakis Z G, Zhu Z and Tomanek D 2014 Phys. Rev. B 89 125421
[2]	Balandin A A and Nika D L 2012 Materials Today 15 266
[14]	Aksamija Z and Knezevic I 2010 Phys. Rev. B 82 045319
[79]	Pereira L F C and Donadio D 2013 Phys. Rev. B 87 125424
[3]	Balandin A A, Pokatilov E P and Nika D L 2007 J. Nanoel. Optoel. 2 140
[80]	Malekpour H, Ramnani P, Srinivasan S, Balasubramanian G, Nika D L, Mulchandani A, Lake R K and Balandin A A 2016 Nanoscale 8 14608
[15]	Cocemasov A I and Nika D L 2012 J. Nanoel. Optoel. 7 370
[4]	Bannov N, Mitin V and Stroscio M 1994 Phys. Stat. Sol. (b) 183 131
[16]	Crismari D V and Nika D L 2012 J. Nanoel. Optoel. 7 701
[81]	Shen Y, Xie G, Wei X, Zhang K, Tang M, Zhong J, Zhang G and Zhang Y W 2014 J. Appl. Phys. 115 063507
[5]	Bannov N, Aristov V, Mitin V and Stroscio M A 1995 Phys. Rev. B 51 9930
[82]	Feng T and Ruan X 2018 Phys. Rev. B 97 045202
[17]	Cocemasov A I, Nika D L, Fomin V M, Grimm D and Schmidt O G 2015 Appl. Phys. Lett. 107 011904
[6]	Nishiguchi N, Ando Y and Wybourne M 1997 J. Phys.:Condens. Matter 9 5751
[18]	Li D, Wu Y, Kim P, Shi L, Yang P and Majumdar A 2003 Appl. Phys. Lett. 83 2934
[83]	Jang W, Chen Z, Bao W, Lau C N and Dames C 2010 Nano Lett. 10 3909
[7]	Balandin A A and Wang K L 1998 Phys. Rev. B 58 1544
[19]	Liu W and Ashegi M 2006 J. Heat Transfer 128 75
[84]	Nika D L and Balandin A A 2012 J. Phys.:Condens. Matter 24 233203
[8]	Balandin A A and Wang K L 1998 J. Appl. Phys. 84 6149
[85]	Shahil K M F and Balandin A A 2012 Nano Lett. 12 861
[20]	Boukai A I, Bunimovich Y, Tahir-Kheli J, Yu J K, Goddard Ⅲ W A and Heath J R 2008 Nature 451 168
[9]	Khitun A, Balandin A A and Wang K L 1999 Superlattices Microstruct. 26 181
[86]	Pop E, Varshney V and Roy A K 2012 MRS Bull. 37 1273
[21]	Hochbaum A I, Chen K, Delgado R D, Liang W, Garnett E C, Najarian M, Majumdar A and Yang P 2008 Nature 451 163
[10]	Zou J and Balandin A A 2001 J. Appl. Phys. 89 2932
[87]	Sadeghi M, Pettes M T and Shi L 2012 Solid State Commun. 152 1321
[22]	Wingert M C, Kwon S, Hu M, Poulikakos D, Xiang J and Chen R 2015 Nano Lett. 15 2605
[11]	Mingo N 2003 Phys. Rev. B 68 113308
[23]	Zhao Y, Yang L, Kong L, Nai M H, Liu D, Wu J, Liu Y, Chiam S Y, Chim W K, Lim C T, Li B, Thong J T L and Hippalgaonkar K 2017 Adv. Funct. Mater. 27 1702824
[88]	Wermhoff A P 2012 Int. J. Transp. Phenom. 13 121
[12]	Mingo N and Yang L 2003 Phys. Rev. B 68 245406
[89]	Renteria J D, Nika D L and Balandin A A 2014 Appl. Sci. 4 525
[24]	Pokatilov E P, Nika D L and Balandin A A 2003 Superlattices Microstruct. 33 155
[13]	Zincenco N D, Nika D L, Pokatilov E P and A. A 2007 J. Phys.:Conf. Ser. 92 012086
[90]	Malekpour H and Balandin A A 2018 J. Raman Spectrosc. 49 106
[25]	Pokatilov E P, Nika D L and Balandin A A 2004 Appl. Phys. Lett. 85 825
[14]	Aksamija Z and Knezevic I 2010 Phys. Rev. B 82 045319
[91]	Ghosh S, Bao W, Nika D L, Subrina S, Pokatilov E P, Lau C N and Balandin A A 2010 Nat. Mater. 9 555
[26]	Pokatilov E P, Nika D L and Balandin A A 2005 Phys. Rev. B 72 113311
[15]	Cocemasov A I and Nika D L 2012 J. Nanoel. Optoel. 7 370
[92]	Ghosh S, Nika D L, Pokatilov E P and Balandin A A 2009 New J. Phys. 11 095012
[27]	Nika D L, Pokatilov E P and Balandin A A 2008 Appl. Phys. Lett. 93 173111
[16]	Crismari D V and Nika D L 2012 J. Nanoel. Optoel. 7 701
[93]	Judek J, Gertych A P, Świniarski M, Łapinska A, Dużyńska A and Zdrojek M 2015 Sci. Rep. 5 12422
[28]	Nika D L, Zincenco N D and P. E 2009 J. Nanoel. Optoel. 4 180
[17]	Cocemasov A I, Nika D L, Fomin V M, Grimm D and Schmidt O G 2015 Appl. Phys. Lett. 107 011904
[94]	Vallabhaneni A K, Singh D, Bao H, Murthy J and Ruan X 2016 Phys. Rev. B 93 125432
[29]	Nika D L, Pokatilov E P, Balandin A A, Fomin V M, Rastelli A and Schmidt O G 2011 Phys. Rev. B 84 165415
[18]	Li D, Wu Y, Kim P, Shi L, Yang P and Majumdar A 2003 Appl. Phys. Lett. 83 2934
[30]	Hu M, Giapis K P, Goicochea J V, Zhang X and Poulikakos D 2011 Nano Lett. 11 618
[95]	Li Q Y, Xia K, Zhang J, Zhang Y, Li Q, Takashi K and Zhang X 2017 Nanoscale 9 10784
[19]	Liu W and Ashegi M 2006 J. Heat Transfer 128 75
[96]	Jo I, Pettes M T, Lindsay L, Ou E, Weathers A, Moore A L and Shi L 2015 AIP Advances 5 053206
[31]	Wingert M C, Chen Z C Y, Dechaumphai E, Moon J, Kim J H, Xiang J and Chen R 2011 Nano Lett. 11 5507
[20]	Boukai A I, Bunimovich Y, Tahir-Kheli J, Yu J K, Goddard Ⅲ W A and Heath J R 2008 Nature 451 168
[97]	Jeong J Y, Lee K M, Shrestha R, Horne K, Das S, Choi W, Kim M and Choi T Y 2016 Mater. Res. Express 3 055004
[32]	Nika D L, Cocemasov A I, Isacova C I, Balandin A A, Fomin V M and Schmidt O G 2012 Phys. Rev. B 85 205439
[21]	Hochbaum A I, Chen K, Delgado R D, Liang W, Garnett E C, Najarian M, Majumdar A and Yang P 2008 Nature 451 163
[98]	Liu J, Wang T, Xu S, Yuan P, Xu X and Wang X 2016 Nanoscale 8 10298
[33]	Bi K, Wang J, Wang Y, Sha J, Wang Z, Chen M and Chen Y 2012 Phys. Lett. A 376 2668
[22]	Wingert M C, Kwon S, Hu M, Poulikakos D, Xiang J and Chen R 2015 Nano Lett. 15 2605
[99]	Pettes M T, Jo I, Yao Z and Shi L 2011 Nano Lett. 11 1195
[34]	Hu M and Poulikakos D 2012 Nano Lett. 12 5487
[23]	Zhao Y, Yang L, Kong L, Nai M H, Liu D, Wu J, Liu Y, Chiam S Y, Chim W K, Lim C T, Li B, Thong J T L and Hippalgaonkar K 2017 Adv. Funct. Mater. 27 1702824
[100]	Jang W, Bao W, Ling L, Lau C N and Dames C 2013 Appl. Phys. Lett. 103 133102
[35]	Nika D L, Cocemasov A I, Crismari D V and Balandin A A 2013 Appl. Phys. Lett. 102 213109
[24]	Pokatilov E P, Nika D L and Balandin A A 2003 Superlattices Microstruct. 33 155
[101]	Wang Z, Xie R, Bui C T, Liu D, Ni X, Li B and Thong J T L 2011 Nano Lett. 11 113
[36]	Benisty H, SotomayorTorrés C M and Weisbuch C 1991 Phys Rev B 44 10945
[25]	Pokatilov E P, Nika D L and Balandin A A 2004 Appl. Phys. Lett. 85 825
[102]	Cocemasov A I, Nika D L and Balandin A A 2013 Phys. Rev. B 88 035428
[37]	Murdin B N, Heiss W, Langerak C J G M, Lee S C, Galbraith I, Strasser G, Gornik E, Helm M and Pidgeon C R 1997 Phys. Rev. B 55 5171
[26]	Pokatilov E P, Nika D L and Balandin A A 2005 Phys. Rev. B 72 113311
[103]	Nika D L, Cocemasov A and Balandin A A 2014 Appl. Phys. Lett. 105 031904
[38]	Heitz R, Born H, Guffarth F, Stier O, Schliwa A, Hoffmann A and Bimberg D 2001 Phys. Rev. B 64 241305
[27]	Nika D L, Pokatilov E P and Balandin A A 2008 Appl. Phys. Lett. 93 173111
[104]	Cocemasov A I, Nika D L and Balandin A A 2015 Nanoscale 7 12851
[39]	Inoue K and Matsuno T 1993 Phys. Rev. B 47 3771
[28]	Nika D L, Zincenco N D and P. E 2009 J. Nanoel. Optoel. 4 180
[105]	Limbu T B, Hahn K R, Mendoza F, Sahoo S, Razink J J, Katiyar R S and Morell G 2017 Carbon 117 367
[40]	Tsuchiya T and Ando T 1993 Phys. Rev. B 48 4599
[29]	Nika D L, Pokatilov E P, Balandin A A, Fomin V M, Rastelli A and Schmidt O G 2011 Phys. Rev. B 84 165415
[106]	Kuang Y, Lindsay L and Huang B 2015 Nano Lett. 15 6121
[41]	Zianni X, Simserides C and Triberis G 1997 Phys. Rev. B 55 16324
[30]	Hu M, Giapis K P, Goicochea J V, Zhang X and Poulikakos D 2011 Nano Lett. 11 618
[107]	Zhan H, Zhang Y, Bell J M and Gu Y 2015 J. Phys. Chem. C 119 1748
[42]	Pokatilov E P, Nika D L, Askerov A S and Balandin A A 2007 J. App. Phys. 102 054304
[31]	Wingert M C, Chen Z C Y, Dechaumphai E, Moon J, Kim J H, Xiang J and Chen R 2011 Nano Lett. 11 5507
[108]	Shen X, Wang Z, Wu Y, Liu X, He Y B and Kim J K 2016 Nano Lett. 16 3585
[43]	Pokatilov E P, Nika D L and Balandin A A 2004 J. Appl. Phys. 95 5626
[32]	Nika D L, Cocemasov A I, Isacova C I, Balandin A A, Fomin V M and Schmidt O G 2012 Phys. Rev. B 85 205439
[109]	Si C, Lu G, Cao B Y, Wang X D, Fan Z and Feng Z H 2017 J. Appl. Phys. 121 205102
[33]	Bi K, Wang J, Wang Y, Sha J, Wang Z, Chen M and Chen Y 2012 Phys. Lett. A 376 2668
[44]	Pokatilov E P, Nika D L and Balandin A A 2006 Appl. Phys. Lett. 89 113508
[110]	D'Souza R and Mukherjee S 2017 Phys. Rev. B 95 085435
[34]	Hu M and Poulikakos D 2012 Nano Lett. 12 5487
[45]	Fonoberov V A and Balandin A A 2006 Nano Lett. 6 2442
[111]	Li L H and Chen Y 2016 Adv. Funct. Mater. 26 2594
[35]	Nika D L, Cocemasov A I, Crismari D V and Balandin A A 2013 Appl. Phys. Lett. 102 213109
[46]	Kargar F, Debnath B, Kakko J P, Sainatjoki A, Lipsanen H, Nika D L, Lake R K and Balandin A A 2016 Nat. Comm. 7 13400
[112]	Jo I, Pettes M T, Kim J, Watanabe K, Taniguchi T, Yao Z and Shi L 2013 Nano Lett. 13 550
[47]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666
[36]	Benisty H, SotomayorTorrés C M and Weisbuch C 1991 Phys Rev B 44 10945
[113]	Zhou H, Zhu J, Liu Z, Yan Z, Fan X, Lin J and Tour J M 2014 Nano Res. 7 1232
[37]	Murdin B N, Heiss W, Langerak C J G M, Lee S C, Galbraith I, Strasser G, Gornik E, Helm M and Pidgeon C R 1997 Phys. Rev. B 55 5171
[48]	Zhang Y, Tan Y W, Stormer H L and Kim P 2005 Nature 438 201
[114]	Wang C, Guo J, Dong L, Aiyiti A, Xu X and Li B 2016 Sci. Rep. 6 25334
[49]	Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M R and Geim A K 2008 Science 320 1308
[38]	Heitz R, Born H, Guffarth F, Stier O, Schliwa A, Hoffmann A and Bimberg D 2001 Phys. Rev. B 64 241305
[115]	Sichel E K, Miller R E, Abrahams M S and Buiocchi C J 1976 Phys. Rev. B 13 4607
[50]	Mak K F, Shan J and Heinz T F 2011 Phys. Rev. Lett. 106 046401
[39]	Inoue K and Matsuno T 1993 Phys. Rev. B 47 3771
[116]	Lindsay L and Broido D A 2011 Phys. Rev. B 84 155421
[51]	Balandin A A, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F and Lau C 2008 Nano Lett. 8 902
[40]	Tsuchiya T and Ando T 1993 Phys. Rev. B 48 4599
[117]	Mak K F, Lee C, Hone J., Shan J and F. T 2010 Phys. Rev. Lett. 105 136805
[52]	Balandin A A 2011 Nat. Mat. 10 569
[41]	Zianni X, Simserides C and Triberis G 1997 Phys. Rev. B 55 16324
[118]	Radisavljevic B, Radenovic A, Brivio J, Giacometti I V and Kis A 2011 Nat. Nanotechnol. 6 147
[53]	Nika D L and Balandin A A 2017 Rep. Prog. Phys. 80 36502
[42]	Pokatilov E P, Nika D L, Askerov A S and Balandin A A 2007 J. App. Phys. 102 054304
[119]	Yan R, Simpson J R, Bertolazzi S, Brivio J, Watson M, Wu X and Xing H G 2014 ACS Nano 8 986
[54]	Ghosh S, Calizo I, Teweldebrhan D, Pokatilov E P, Nika D L, Balandin A A, Bao W, Miao F and Lau C N 2008 Appl. Phys. Lett. 92 151911.
[43]	Pokatilov E P, Nika D L and Balandin A A 2004 J. Appl. Phys. 95 5626
[120]	Jo I, Pettes M T, Ou E, Wu W and Shi L 2014 Appl. Phys. Lett. 104 201902
[55]	Bolotin K I, Sikes K J, Jiang Z, Klima M, Fudenberg G, Hone J, Kim P and Stormer H L 2008 Solid State Commun. 146 351
[44]	Pokatilov E P, Nika D L and Balandin A A 2006 Appl. Phys. Lett. 89 113508
[121]	Taube A, Judek J, Lapiníska A and Zdrojek M 2015 ACS Appl. Mater. Interfaces 7 5061
[56]	Hong X, Posadas A, Zou K, Ahn C H and Zhu J 2009 Phys. Rev. Lett. 102 136808
[45]	Fonoberov V A and Balandin A A 2006 Nano Lett. 6 2442
[122]	Cai Y, Lan J, Zhang G and Zhang Y W 2014 Phys. Rev. B 89 035438
[57]	Cai W, Moore A L, Zhu Y, Li X, Chen S, Sh L and Ruoff R S 2010 Nano Lett. 10 1645
[46]	Kargar F, Debnath B, Kakko J P, Sainatjoki A, Lipsanen H, Nika D L, Lake R K and Balandin A A 2016 Nat. Comm. 7 13400
[123]	Ding Z, Jiang J W, Pei Q X and Zhang Y 2015 Nanotechnology 26 065703
[58]	Jauregui L A, Yue Y, Sidorov A N, Hu J, Yu Q, Lopez G, Jalilian R, Benjamin D K, Delk D A, Wu W, Liu Z, Wang X, Jiang Z, Ruan X, Bao J, Pei S S and Chen Y P 2010 ECS Trans. 28 73
[47]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666
[124]	Ding Z, Pei Q X, Jiang J W and Zhang Y W 2015 J. Phys. Chem. C 119 16358
[59]	Chen S, Wu Q, Mishra C, Kang J, Zhang H, Cho K, Cai W, Balandin A A and Ruoff R S 2012 Nat. Mater. 11 203
[48]	Zhang Y, Tan Y W, Stormer H L and Kim P 2005 Nature 438 201
[125]	Gu X, Li B and Yang R 2016 J. Appl. Phys. 119 085106
[60]	Li H, Ying H, Chen X, Nika D L, Cocemasov A I, Cai W, Balandin A A and Chen S 2014 Nanoscale 6 13402
[49]	Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M R and Geim A K 2008 Science 320 1308
[126]	Liu J, Choi G M and Cahill D G 2014 J. Appl. Phys. 116 233107
[61]	Dorgan V E, Behnam A, Conley H J, Bolotin K I and Pop E 2013 Nano Lett. 13 4581
[50]	Mak K F, Shan J and Heinz T F 2011 Phys. Rev. Lett. 106 046401
[127]	Li L, Yu Y, Ye G J, Ge Q, Ou X, Wu H and Zhang Y 2014 Nat. Nanotechnol. 9 372
[62]	Seol J H, Jo I, Moore A L, Lindsay L, Aitken Z H, Pettes M T, Li X, Yao Z, Huang R, Broido D, Mingo N, Ruoff R S and Shi L 2010 Science 328 213
[51]	Balandin A A, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F and Lau C 2008 Nano Lett. 8 902
[128]	Xia F, Wang H and Jia Y 2014 Nat. Commun. 5 4458
[63]	Nika D L, Pokatilov E P, Askerov A S and Balandin A A 2009 Phys. Rev. B 79 155413
[52]	Balandin A A 2011 Nat. Mat. 10 569
[129]	Koenig S P, Doganov R A, Schmidt H, Castro Neto A H and Özyilmaz B 2014 Appl. Phys. Lett. 104 103106
[64]	Lindsay L, Broido D and Mingo N 2010 Phys. Rev. B 82 115427
[53]	Nika D L and Balandin A A 2017 Rep. Prog. Phys. 80 36502
[130]	Ong Z Y, Cai Y, Zhang G and Zhang Y W 2014 J. Phys. Chem. C 118 25272
[65]	Lindsay L, Li W, Carrete J, Mingo N, Broido D A and Reinecke T L 2014 Phys. Rev. B 89 155426
[54]	Ghosh S, Calizo I, Teweldebrhan D, Pokatilov E P, Nika D L, Balandin A A, Bao W, Miao F and Lau C N 2008 Appl. Phys. Lett. 92 151911.
[131]	Zhu L, Zhang G and Li B 2014 Phys. Rev. B 90 214302
[66]	Klemens P G 2000 J. Wide Bandgap Mater. 7 332
[55]	Bolotin K I, Sikes K J, Jiang Z, Klima M, Fudenberg G, Hone J, Kim P and Stormer H L 2008 Solid State Commun. 146 351
[132]	Xu W, Zhu L, Cai Y, Zhang G and Li B 2015 J. Appl. Phys. 117 214308
[67]	Klemens P G 2001 Int. J. Thermophys. 22 265
[56]	Hong X, Posadas A, Zou K, Ahn C H and Zhu J 2009 Phys. Rev. Lett. 102 136808
[133]	Luo Z, Maassen J, Deng Y, Du Y, Garrelts R P, Lundstrom M S and Xu X 2015 Nat. Commun. 6 8572
[68]	Nika D L, Ghosh S, Pokatilov E P and Balandin A A 2009 Appl. Phys. Lett. 94 203103
[57]	Cai W, Moore A L, Zhu Y, Li X, Chen S, Sh L and Ruoff R S 2010 Nano Lett. 10 1645
[134]	Hong Y, Zhang J, Huang X and Zeng X C 2015 Nanoscale 7 18716
[69]	Nika D L, Askerov A S and Balandin A A 2012 Nano Lett. 12 3238
[58]	Jauregui L A, Yue Y, Sidorov A N, Hu J, Yu Q, Lopez G, Jalilian R, Benjamin D K, Delk D A, Wu W, Liu Z, Wang X, Jiang Z, Ruan X, Bao J, Pei S S and Chen Y P 2010 ECS Trans. 28 73
[135]	Liu T H and Chang C C 2015 Nanoscale 7 10648.
[70]	Fugallo G, Cepellotti A, Paulato L, Lazzeri N, Marzari N and Mauri F 2014 Nano Lett. 14 6109
[59]	Chen S, Wu Q, Mishra C, Kang J, Zhang H, Cho K, Cai W, Balandin A A and Ruoff R S 2012 Nat. Mater. 11 203
[136]	Qin G, Yan Q B, Qin Z, Yue S Y, Hu M and Su G 2015 Phys. Chem. Chem. Phys. 17 4854
[71]	Munoz E, Lu J and Yakobson B I 2010 Nano Lett. 10 1652
[60]	Li H, Ying H, Chen X, Nika D L, Cocemasov A I, Cai W, Balandin A A and Chen S 2014 Nanoscale 6 13402
[137]	Jain A and McGaughey A J 2015 Sci. Rep. 5 8501
[72]	Jiang J W, Wang J S and Li B 2009 Phys. Rev. B 79 205418
[61]	Dorgan V E, Behnam A, Conley H J, Bolotin K I and Pop E 2013 Nano Lett. 13 4581
[138]	Zhang Y Y, Pei Q X, Jiang J W, Wei N and Zhang Y W 2016 Nanoscale 8 483
[73]	Jang Y Y, Cheng Y, Pei Q X, Wang C W and Xiang Y 2012 Phys. Lett. A 376 3668
[62]	Seol J H, Jo I, Moore A L, Lindsay L, Aitken Z H, Pettes M T, Li X, Yao Z, Huang R, Broido D, Mingo N, Ruoff R S and Shi L 2010 Science 328 213
[139]	Liu X, Gao J, Zhang G and Zhang YW 2017 Adv. Funct. Mater. 27 1702776
[74]	Park M, Lee S C and Kim Y S 2013 J. Appl. Phys. 114 053506
[63]	Nika D L, Pokatilov E P, Askerov A S and Balandin A A 2009 Phys. Rev. B 79 155413
[140]	Jang H, Wood J D, Ryder C R, Hersam M C and Cahill D G 2015 Adv. Mater. 27 8017
[75]	Alofi A and Srivastava G P 2012 J. Appl. Phys. 112 013517
[64]	Lindsay L, Broido D and Mingo N 2010 Phys. Rev. B 82 115427
[141]	Kang J S, Ke M and Hu Y 2017 Nano Lett. 17 1431
[76]	Alofi A and Srivastava G P 2013 Phys. Rev. B 87 115421
[65]	Lindsay L, Li W, Carrete J, Mingo N, Broido D A and Reinecke T L 2014 Phys. Rev. B 89 155426
[142]	Lee S, Yang F, Suh J, Yang S, Lee Y, Li G and Park J 2015 Nat. Commun. 6 8573
[77]	Ma F, Zheng H B, Sun Y J, Yang D, Xu K W and Chu P K 2012 Appl. Phys. Lett. 101 111904
[66]	Klemens P G 2000 J. Wide Bandgap Mater. 7 332
[143]	Smith B, Vermeersch B, Carrete J, Ou E, Kim J, Mingo N, Akinwande D and Shi L 2017 Adv. Mater. 29 1603756
[78]	Fthenakis Z G, Zhu Z and Tomanek D 2014 Phys. Rev. B 89 125421
[67]	Klemens P G 2001 Int. J. Thermophys. 22 265
[79]	Pereira L F C and Donadio D 2013 Phys. Rev. B 87 125424
[68]	Nika D L, Ghosh S, Pokatilov E P and Balandin A A 2009 Appl. Phys. Lett. 94 203103
[80]	Malekpour H, Ramnani P, Srinivasan S, Balasubramanian G, Nika D L, Mulchandani A, Lake R K and Balandin A A 2016 Nanoscale 8 14608
[69]	Nika D L, Askerov A S and Balandin A A 2012 Nano Lett. 12 3238
[81]	Shen Y, Xie G, Wei X, Zhang K, Tang M, Zhong J, Zhang G and Zhang Y W 2014 J. Appl. Phys. 115 063507
[70]	Fugallo G, Cepellotti A, Paulato L, Lazzeri N, Marzari N and Mauri F 2014 Nano Lett. 14 6109
[82]	Feng T and Ruan X 2018 Phys. Rev. B 97 045202
[71]	Munoz E, Lu J and Yakobson B I 2010 Nano Lett. 10 1652
[83]	Jang W, Chen Z, Bao W, Lau C N and Dames C 2010 Nano Lett. 10 3909
[72]	Jiang J W, Wang J S and Li B 2009 Phys. Rev. B 79 205418
[84]	Nika D L and Balandin A A 2012 J. Phys.:Condens. Matter 24 233203
[73]	Jang Y Y, Cheng Y, Pei Q X, Wang C W and Xiang Y 2012 Phys. Lett. A 376 3668
[85]	Shahil K M F and Balandin A A 2012 Nano Lett. 12 861
[74]	Park M, Lee S C and Kim Y S 2013 J. Appl. Phys. 114 053506
[86]	Pop E, Varshney V and Roy A K 2012 MRS Bull. 37 1273
[75]	Alofi A and Srivastava G P 2012 J. Appl. Phys. 112 013517
[87]	Sadeghi M, Pettes M T and Shi L 2012 Solid State Commun. 152 1321
[76]	Alofi A and Srivastava G P 2013 Phys. Rev. B 87 115421
[88]	Wermhoff A P 2012 Int. J. Transp. Phenom. 13 121
[77]	Ma F, Zheng H B, Sun Y J, Yang D, Xu K W and Chu P K 2012 Appl. Phys. Lett. 101 111904
[89]	Renteria J D, Nika D L and Balandin A A 2014 Appl. Sci. 4 525
[78]	Fthenakis Z G, Zhu Z and Tomanek D 2014 Phys. Rev. B 89 125421
[90]	Malekpour H and Balandin A A 2018 J. Raman Spectrosc. 49 106
[79]	Pereira L F C and Donadio D 2013 Phys. Rev. B 87 125424
[91]	Ghosh S, Bao W, Nika D L, Subrina S, Pokatilov E P, Lau C N and Balandin A A 2010 Nat. Mater. 9 555
[80]	Malekpour H, Ramnani P, Srinivasan S, Balasubramanian G, Nika D L, Mulchandani A, Lake R K and Balandin A A 2016 Nanoscale 8 14608
[92]	Ghosh S, Nika D L, Pokatilov E P and Balandin A A 2009 New J. Phys. 11 095012
[81]	Shen Y, Xie G, Wei X, Zhang K, Tang M, Zhong J, Zhang G and Zhang Y W 2014 J. Appl. Phys. 115 063507
[93]	Judek J, Gertych A P, Świniarski M, Łapinska A, Dużyńska A and Zdrojek M 2015 Sci. Rep. 5 12422
[82]	Feng T and Ruan X 2018 Phys. Rev. B 97 045202
[94]	Vallabhaneni A K, Singh D, Bao H, Murthy J and Ruan X 2016 Phys. Rev. B 93 125432
[83]	Jang W, Chen Z, Bao W, Lau C N and Dames C 2010 Nano Lett. 10 3909
[95]	Li Q Y, Xia K, Zhang J, Zhang Y, Li Q, Takashi K and Zhang X 2017 Nanoscale 9 10784
[84]	Nika D L and Balandin A A 2012 J. Phys.:Condens. Matter 24 233203
[96]	Jo I, Pettes M T, Lindsay L, Ou E, Weathers A, Moore A L and Shi L 2015 AIP Advances 5 053206
[85]	Shahil K M F and Balandin A A 2012 Nano Lett. 12 861
[97]	Jeong J Y, Lee K M, Shrestha R, Horne K, Das S, Choi W, Kim M and Choi T Y 2016 Mater. Res. Express 3 055004
[86]	Pop E, Varshney V and Roy A K 2012 MRS Bull. 37 1273
[98]	Liu J, Wang T, Xu S, Yuan P, Xu X and Wang X 2016 Nanoscale 8 10298
[87]	Sadeghi M, Pettes M T and Shi L 2012 Solid State Commun. 152 1321
[99]	Pettes M T, Jo I, Yao Z and Shi L 2011 Nano Lett. 11 1195
[88]	Wermhoff A P 2012 Int. J. Transp. Phenom. 13 121
[100]	Jang W, Bao W, Ling L, Lau C N and Dames C 2013 Appl. Phys. Lett. 103 133102
[89]	Renteria J D, Nika D L and Balandin A A 2014 Appl. Sci. 4 525
[101]	Wang Z, Xie R, Bui C T, Liu D, Ni X, Li B and Thong J T L 2011 Nano Lett. 11 113
[90]	Malekpour H and Balandin A A 2018 J. Raman Spectrosc. 49 106
[102]	Cocemasov A I, Nika D L and Balandin A A 2013 Phys. Rev. B 88 035428
[91]	Ghosh S, Bao W, Nika D L, Subrina S, Pokatilov E P, Lau C N and Balandin A A 2010 Nat. Mater. 9 555
[103]	Nika D L, Cocemasov A and Balandin A A 2014 Appl. Phys. Lett. 105 031904
[92]	Ghosh S, Nika D L, Pokatilov E P and Balandin A A 2009 New J. Phys. 11 095012
[104]	Cocemasov A I, Nika D L and Balandin A A 2015 Nanoscale 7 12851
[93]	Judek J, Gertych A P, Świniarski M, Łapinska A, Dużyńska A and Zdrojek M 2015 Sci. Rep. 5 12422
[105]	Limbu T B, Hahn K R, Mendoza F, Sahoo S, Razink J J, Katiyar R S and Morell G 2017 Carbon 117 367
[94]	Vallabhaneni A K, Singh D, Bao H, Murthy J and Ruan X 2016 Phys. Rev. B 93 125432
[106]	Kuang Y, Lindsay L and Huang B 2015 Nano Lett. 15 6121
[95]	Li Q Y, Xia K, Zhang J, Zhang Y, Li Q, Takashi K and Zhang X 2017 Nanoscale 9 10784
[107]	Zhan H, Zhang Y, Bell J M and Gu Y 2015 J. Phys. Chem. C 119 1748
[96]	Jo I, Pettes M T, Lindsay L, Ou E, Weathers A, Moore A L and Shi L 2015 AIP Advances 5 053206
[108]	Shen X, Wang Z, Wu Y, Liu X, He Y B and Kim J K 2016 Nano Lett. 16 3585
[97]	Jeong J Y, Lee K M, Shrestha R, Horne K, Das S, Choi W, Kim M and Choi T Y 2016 Mater. Res. Express 3 055004
[109]	Si C, Lu G, Cao B Y, Wang X D, Fan Z and Feng Z H 2017 J. Appl. Phys. 121 205102
[98]	Liu J, Wang T, Xu S, Yuan P, Xu X and Wang X 2016 Nanoscale 8 10298
[110]	D'Souza R and Mukherjee S 2017 Phys. Rev. B 95 085435
[99]	Pettes M T, Jo I, Yao Z and Shi L 2011 Nano Lett. 11 1195
[111]	Li L H and Chen Y 2016 Adv. Funct. Mater. 26 2594
[100]	Jang W, Bao W, Ling L, Lau C N and Dames C 2013 Appl. Phys. Lett. 103 133102
[112]	Jo I, Pettes M T, Kim J, Watanabe K, Taniguchi T, Yao Z and Shi L 2013 Nano Lett. 13 550
[101]	Wang Z, Xie R, Bui C T, Liu D, Ni X, Li B and Thong J T L 2011 Nano Lett. 11 113
[113]	Zhou H, Zhu J, Liu Z, Yan Z, Fan X, Lin J and Tour J M 2014 Nano Res. 7 1232
[102]	Cocemasov A I, Nika D L and Balandin A A 2013 Phys. Rev. B 88 035428
[114]	Wang C, Guo J, Dong L, Aiyiti A, Xu X and Li B 2016 Sci. Rep. 6 25334
[103]	Nika D L, Cocemasov A and Balandin A A 2014 Appl. Phys. Lett. 105 031904
[115]	Sichel E K, Miller R E, Abrahams M S and Buiocchi C J 1976 Phys. Rev. B 13 4607
[104]	Cocemasov A I, Nika D L and Balandin A A 2015 Nanoscale 7 12851
[116]	Lindsay L and Broido D A 2011 Phys. Rev. B 84 155421
[105]	Limbu T B, Hahn K R, Mendoza F, Sahoo S, Razink J J, Katiyar R S and Morell G 2017 Carbon 117 367
[117]	Mak K F, Lee C, Hone J., Shan J and F. T 2010 Phys. Rev. Lett. 105 136805
[106]	Kuang Y, Lindsay L and Huang B 2015 Nano Lett. 15 6121
[118]	Radisavljevic B, Radenovic A, Brivio J, Giacometti I V and Kis A 2011 Nat. Nanotechnol. 6 147
[107]	Zhan H, Zhang Y, Bell J M and Gu Y 2015 J. Phys. Chem. C 119 1748
[119]	Yan R, Simpson J R, Bertolazzi S, Brivio J, Watson M, Wu X and Xing H G 2014 ACS Nano 8 986
[108]	Shen X, Wang Z, Wu Y, Liu X, He Y B and Kim J K 2016 Nano Lett. 16 3585
[120]	Jo I, Pettes M T, Ou E, Wu W and Shi L 2014 Appl. Phys. Lett. 104 201902
[109]	Si C, Lu G, Cao B Y, Wang X D, Fan Z and Feng Z H 2017 J. Appl. Phys. 121 205102
[121]	Taube A, Judek J, Lapiníska A and Zdrojek M 2015 ACS Appl. Mater. Interfaces 7 5061
[110]	D'Souza R and Mukherjee S 2017 Phys. Rev. B 95 085435
[122]	Cai Y, Lan J, Zhang G and Zhang Y W 2014 Phys. Rev. B 89 035438
[111]	Li L H and Chen Y 2016 Adv. Funct. Mater. 26 2594
[123]	Ding Z, Jiang J W, Pei Q X and Zhang Y 2015 Nanotechnology 26 065703
[112]	Jo I, Pettes M T, Kim J, Watanabe K, Taniguchi T, Yao Z and Shi L 2013 Nano Lett. 13 550
[124]	Ding Z, Pei Q X, Jiang J W and Zhang Y W 2015 J. Phys. Chem. C 119 16358
[113]	Zhou H, Zhu J, Liu Z, Yan Z, Fan X, Lin J and Tour J M 2014 Nano Res. 7 1232
[125]	Gu X, Li B and Yang R 2016 J. Appl. Phys. 119 085106
[114]	Wang C, Guo J, Dong L, Aiyiti A, Xu X and Li B 2016 Sci. Rep. 6 25334
[126]	Liu J, Choi G M and Cahill D G 2014 J. Appl. Phys. 116 233107
[115]	Sichel E K, Miller R E, Abrahams M S and Buiocchi C J 1976 Phys. Rev. B 13 4607
[127]	Li L, Yu Y, Ye G J, Ge Q, Ou X, Wu H and Zhang Y 2014 Nat. Nanotechnol. 9 372
[116]	Lindsay L and Broido D A 2011 Phys. Rev. B 84 155421
[128]	Xia F, Wang H and Jia Y 2014 Nat. Commun. 5 4458
[117]	Mak K F, Lee C, Hone J., Shan J and F. T 2010 Phys. Rev. Lett. 105 136805
[129]	Koenig S P, Doganov R A, Schmidt H, Castro Neto A H and Özyilmaz B 2014 Appl. Phys. Lett. 104 103106
[118]	Radisavljevic B, Radenovic A, Brivio J, Giacometti I V and Kis A 2011 Nat. Nanotechnol. 6 147
[130]	Ong Z Y, Cai Y, Zhang G and Zhang Y W 2014 J. Phys. Chem. C 118 25272
[119]	Yan R, Simpson J R, Bertolazzi S, Brivio J, Watson M, Wu X and Xing H G 2014 ACS Nano 8 986
[131]	Zhu L, Zhang G and Li B 2014 Phys. Rev. B 90 214302
[120]	Jo I, Pettes M T, Ou E, Wu W and Shi L 2014 Appl. Phys. Lett. 104 201902
[132]	Xu W, Zhu L, Cai Y, Zhang G and Li B 2015 J. Appl. Phys. 117 214308
[121]	Taube A, Judek J, Lapiníska A and Zdrojek M 2015 ACS Appl. Mater. Interfaces 7 5061
[133]	Luo Z, Maassen J, Deng Y, Du Y, Garrelts R P, Lundstrom M S and Xu X 2015 Nat. Commun. 6 8572
[122]	Cai Y, Lan J, Zhang G and Zhang Y W 2014 Phys. Rev. B 89 035438
[134]	Hong Y, Zhang J, Huang X and Zeng X C 2015 Nanoscale 7 18716
[123]	Ding Z, Jiang J W, Pei Q X and Zhang Y 2015 Nanotechnology 26 065703
[135]	Liu T H and Chang C C 2015 Nanoscale 7 10648.
[124]	Ding Z, Pei Q X, Jiang J W and Zhang Y W 2015 J. Phys. Chem. C 119 16358
[136]	Qin G, Yan Q B, Qin Z, Yue S Y, Hu M and Su G 2015 Phys. Chem. Chem. Phys. 17 4854
[125]	Gu X, Li B and Yang R 2016 J. Appl. Phys. 119 085106
[137]	Jain A and McGaughey A J 2015 Sci. Rep. 5 8501
[126]	Liu J, Choi G M and Cahill D G 2014 J. Appl. Phys. 116 233107
[127]	Li L, Yu Y, Ye G J, Ge Q, Ou X, Wu H and Zhang Y 2014 Nat. Nanotechnol. 9 372
[138]	Zhang Y Y, Pei Q X, Jiang J W, Wei N and Zhang Y W 2016 Nanoscale 8 483
[128]	Xia F, Wang H and Jia Y 2014 Nat. Commun. 5 4458
[139]	Liu X, Gao J, Zhang G and Zhang YW 2017 Adv. Funct. Mater. 27 1702776
[129]	Koenig S P, Doganov R A, Schmidt H, Castro Neto A H and Özyilmaz B 2014 Appl. Phys. Lett. 104 103106
[140]	Jang H, Wood J D, Ryder C R, Hersam M C and Cahill D G 2015 Adv. Mater. 27 8017
[130]	Ong Z Y, Cai Y, Zhang G and Zhang Y W 2014 J. Phys. Chem. C 118 25272
[141]	Kang J S, Ke M and Hu Y 2017 Nano Lett. 17 1431
[131]	Zhu L, Zhang G and Li B 2014 Phys. Rev. B 90 214302
[142]	Lee S, Yang F, Suh J, Yang S, Lee Y, Li G and Park J 2015 Nat. Commun. 6 8573
[132]	Xu W, Zhu L, Cai Y, Zhang G and Li B 2015 J. Appl. Phys. 117 214308
[143]	Smith B, Vermeersch B, Carrete J, Ou E, Kim J, Mingo N, Akinwande D and Shi L 2017 Adv. Mater. 29 1603756
[133]	Luo Z, Maassen J, Deng Y, Du Y, Garrelts R P, Lundstrom M S and Xu X 2015 Nat. Commun. 6 8572
[134]	Hong Y, Zhang J, Huang X and Zeng X C 2015 Nanoscale 7 18716
[135]	Liu T H and Chang C C 2015 Nanoscale 7 10648.
[136]	Qin G, Yan Q B, Qin Z, Yue S Y, Hu M and Su G 2015 Phys. Chem. Chem. Phys. 17 4854
[137]	Jain A and McGaughey A J 2015 Sci. Rep. 5 8501
[138]	Zhang Y Y, Pei Q X, Jiang J W, Wei N and Zhang Y W 2016 Nanoscale 8 483
[139]	Liu X, Gao J, Zhang G and Zhang YW 2017 Adv. Funct. Mater. 27 1702776
[140]	Jang H, Wood J D, Ryder C R, Hersam M C and Cahill D G 2015 Adv. Mater. 27 8017
[141]	Kang J S, Ke M and Hu Y 2017 Nano Lett. 17 1431
[142]	Lee S, Yang F, Suh J, Yang S, Lee Y, Li G and Park J 2015 Nat. Commun. 6 8573
[143]	Smith B, Vermeersch B, Carrete J, Ou E, Kim J, Mingo N, Akinwande D and Shi L 2017 Adv. Mater. 29 1603756