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β-Ga2O3具有禁带宽度大、击穿电场强的优点, 在射频及功率器件领域具有广阔的应用前景. β-Ga2O3 (
$ \bar 201 $ )晶面和AlN (0002)晶面较小的晶格失配和较大的导带阶表明二者具有结合为异质结并形成二维电子气(two-dimensional electron gas, 2DEG)的理论基础, 引起了众多研究者关注. 本文利用AlN的表面态假设, 通过求解薛定谔-泊松方程组计算了AlN/β-Ga2O3异质结导带形状和2DEG面密度, 并将结果应用于玻尔兹曼输运理论, 计算了离化杂质散射、界面粗糙散射、声学形变势散射、极性光学声子散射等主要散射机制限制的迁移率, 评估了不同散射机制的相对重要性. 结果表明, 2DEG面密度随AlN厚度的增加而增加, 当AlN厚度为6 nm, 2DEG面密度可达1.0×1013 cm–2, 室温迁移率为368.6 cm2/(V·s). 在T < 184 K的中低温区域, 界面粗糙散射是限制2DEG迁移率的主导散射机制, T > 184 K的温度区间, 极性光学声子散射是限制2DEG迁移率的主导散射机制.-
关键词:
- AlN/β-Ga2O3异质结 /
- 二维电子气 /
- 电子输运 /
- 迁移率
The β-Ga2O3 has received much attention in the field of power and radio frequency electronics, due to an ultrawide bandgap energy of ~4.9 eV and a high breakdown field strength of ~8 MV/cm (Poncé et al.2020 Phys. Rev. Res. 2 033102 ). The in-plane lattice mismatch of 2.4% between the ($ \bar 201 $ ) plane of β-Ga2O3 and the (0002) plane of wurtzite AlN is beneficial to the formation of an AlN/β-Ga2O3 heterostructure (Sun et al.2017 Appl. Phys. Lett. 111 162105 ), which is a potential candidate for β-Ga2O3-based high electron mobility transistors (HEMTs). In this study, the Schrödinger-Poisson equations are solved to calculate the AlN/β-Ga2O3 conduction band profile and the two-dimensional electron gas(2DEG) sheet density, based on the supposition that the 2DEG originates from door-like surface states distributed evenly below the AlN conduction band. The main scattering mechanisms in AlN/β-Ga2O3 heterostructures, i.e. the ionized impurity scattering, interface roughness scattering, acoustic deformation-potential scattering, and polar optical phonon scattering, are investigated by using the Boltzmann transport theory. Besides, the relative importance of different scattering mechanisms is evaluated. The results show that at room temperature, the 2DEG sheet density increases with the augment of AlN thickness, and reaches 1.0×1013 cm–2 at an AlN thickness of 6 nm. With the increase of the 2DEG sheet density, the ionized impurity scattering limited mobility increases, but other scattering mechanisms limited mobilities decrease. The interface roughness scattering dominates the mobility at low temperature and moderate temperature (T < 148 K), and the polar optical phonon scattering dominates the mobility at temperatures above 148 K. The room-temperature mobility is 368.6 cm2/(V·s) for the AlN/β-Ga2O3 heterostructure with an AlN thickness of 6 nm.-
Keywords:
- AlN/β-Ga2O3 heterostructures /
- two-dimensional electron gas /
- electron transport /
- mobility
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图 1 (a) β-Ga2O3 (
$\bar 201 $ )晶面和(b)AlN (0002)晶面的原子排列Fig. 1. The atomic arrangement in (a) (
$\bar 201 $ ) plane of β-Ga2O3 and (b) (0002) plane of AlN.
图 2 AlN/β-Ga2O3异质结表面态能级分布示意图
Fig. 2. Schematic drawing of energy distribution of surface states in an AlN/β-Ga2O3 heterostructure.
图 3 AlN/β-Ga2O3异质结导带形状和2DEG浓度分布, AlN厚度
$ d=6 $ nmFig. 3. The conduction band profile and spatially distributed density of the 2DEG in an AlN/β-Ga2O3 heterostructure with an AlN thickness of 6 nm.
图 4 2DEG面密度对AlN厚度的依赖关系
Fig. 4. Dependence of the 2DEG sheet density on the AlN thickness.
图 5 IRS限制的迁移率对相关长度
$ \varLambda $ 的依赖关系Fig. 5. Dependence of the mobility limited by IRS on correlation length
$ \varLambda $ for different roughness heights.
图 6 300 K时离化杂质散射限制的动量弛豫时间(
$ {\tau }_{\rm{I}\rm{I}\rm{S}} $ )、界面粗糙散射限制的动量弛豫时间($ {\tau }_{\rm{D}\rm{P}} $ )、声学形变势散射限制的动量弛豫时间($ {\tau }_{\rm{D}\rm{P}} $ )对电子能量的依赖关系Fig. 6. Dependence of the momentum relaxation time limited by ionized impurity scattering (
$ {\tau }_{\rm{I}\rm{I}\rm{S}} $ ), interface roughness scattering ($ {\tau }_{\rm{I}\rm{R}\rm{S}} $ ) and acoustic DP scattering ($ {\tau }_{\rm{D}\rm{P}} $ ) on the electron energy.
图 7 动量弛豫时间对电子能量的依赖关系
Fig. 7. Dependence of the momentum relaxation time on the electron energy.
图 8 300 K时离化杂质散射限制的迁移率(
$ {\mu }_{\rm{I}\rm{I}\rm{S}} $ )、界面粗糙散射限制的迁移率($ {\mu }_{\rm{I}\rm{R}\rm{S}} $ )、声学形变势散射限制的迁移率($ {\mu }_{\rm{D}\rm{P}} $ )、极性光学声子散射限制的迁移率($ {\mu }_{\rm{P}\rm{O}} $ )对2DEG面密度的依赖Fig. 8. Dependence of the mobility limited by ionized impurity scattering (
$ {\mu }_{\rm{I}\rm{I}\rm{S}} $ ), interface roughness scattering ($ {\mu }_{\rm{I}\rm{R}\rm{S}} $ ), acoustic DP scattering ($ {\mu }_{\rm{D}\rm{P}} $ ) and PO phonon scattering ($ {\mu }_{\rm{P}\rm{O}} $ ) on the 2DEG sheet density at 300 K.
图 9
$ {\mu }_{\rm{D}\rm{P}} $ ,$ {\mu }_{\rm{I}\rm{I}\rm{S}} $ ,$ {\mu }_{\rm{I}\rm{R}\rm{S}} $ ,$ {\mu }_{\rm{P}\rm{O}} $ 以及总的迁移率($ {\mu }_{\rm{T}\rm{O}\rm{T}} $ )对温度的依赖关系, 相关长度$ \varLambda =5\;\rm{n}\rm{m} $ , 粗糙高度$\varDelta =1\;\rm{n}\rm{m}$ Fig. 9. Temperature dependence of the
$ {\mu }_{\rm{D}\rm{P}} $ ,$ {\mu }_{\rm{I}\rm{I}\rm{S}} $ ,$ {\mu }_{\rm{I}\rm{R}\rm{S}} $ ,$ {\mu }_{\rm{P}\rm{O}} $ , and the total mobility$ {\mu }_{\rm{T}\rm{O}\rm{T}} $ , the correlation length$ \varLambda =5 $ nm and roughness height$\varDelta =1$ nm.表 1 计算过程中用到的AlN/β-Ga2O3异质结参数(
$ {m}_{0} $ 为自由电子质量)Table 1. Parameters of AlN/β-Ga2O3 heterostructure employed in calculations (
$ {m}_{0} $ is the free electron mass).物理量 符号/单位 参数值 AlN晶格常数 aAlN/Å 3.112[26] AlN压电常数 e31/(C·m−2) –0.60[26] e33/(C·m−2) 1.55[26] AlN弹性系数 c13/GPa 9.0[26] c33/GPa 10.7[26] β-Ga2O3晶格常数 $ b_{\rm Ga_2O_3} $/Å 3.037[14] β-Ga2O3质量密度 ρ/(g·cm–3) 5.88[38] β-Ga2O3声学形变势 D/eV 6.9[39] β-Ga2O3纵声学模速度 ul/(m·s–1) 6.8×103[39] β-Ga2O3电子有效质量 m* 0.28m0[40] β-Ga2O3高频介电常数 $ {\varepsilon }_{\infty } $ 3.57[41–43] β-Ga2O3低频介电常数 $ {\varepsilon }_{\rm{s}} $ 10.2[41–43] β-Ga2O3极性光学声子能量 $ \hslash {\omega }_{\rm{P}\rm{O}}/\rm{m}\rm{e}\rm{V} $ 94 [44,45] 
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[1] Green A J, Speck J, Xing G, et al. 2022 APL Mater. 10 029201
Google Scholar
[2] Ranga P, Bhattacharyya A, Chmielewski A, Roy S, Sun R, Scarpulla M A, Alem N, Krishnamoorthy S 2021 Appl. Phys. Express 14 025501
Google Scholar
[3] Wong M H, Bierwagen O, Kaplar R J, Umezawa H 2021 J. Mater. Res. 36 4601
Google Scholar
[4] 郭道友, 李培刚, 陈政委, 吴真平, 唐为华 2019 物理学报 68 078501
Google Scholar
Guo D Y, Li P G, Chen Z W, Wu Z P, Tang W H 2019 Acta Phys. Sin. 68 078501
Google Scholar
[5] Poncé S, Giustino F 2020 Phys. Rev. Res. 2 033102
Google Scholar
[6] Ghosh K, Singisetti U 2017 J. Appl. Phys. 122 035702
Google Scholar
[7] Nehate S, Saikumar A K, Sundaram K 2021 Crit. Rev. Solid State 47 538
Google Scholar
[8] Wang D P, Li J N, Jiao A N, Zhang X C, Lu X l, Ma X H, Hao Y 2021 J. Alloys Compd. 855 157296
Google Scholar
[9] Ranga P, Bhattacharyya A, Rishinaramangalam A, Ooi Y K, Scarpulla M A, Feezell D, Krishnamoorthy S 2020 Appl. Phys. Express 13 045501
Google Scholar
[10] Tadjer M J, Sasaki K, Wakimoto D, Anderson T J, Mastro M A, Gallagher J C, Jacobs A G, Mock A L, Koehler A D, Ebrish M, Hobart K D, Kuramata A 2021 J. Vac. Sci. Technol. 39 033402
Google Scholar
[11] Krishnamoorthy S, Xia Z, Joishi C, Zhang Y, McGlone J, Johnson J, Brenner M, Arehart A R, Hwang J, Lodha S, Rajan S 2017 Appl. Phys. Lett. 111 023502
Google Scholar
[12] Kalarickal N K, Xia Z B, McGlone J F, Liu Y M, Moore W, Arehart A R, Ringel S A, Rajan S 2020 J. Appl. Phys. 127 215706
Google Scholar
[13] Zhang Y W, Neal A, Xia Z B, Joishi C, Johnson J M, Zheng Y H, Bajaj S, Brenner M, Dorsey D, Chabak K, Jessen G, Hwang J, Mou S, Heremans J P, Rajan S 2018 Appl. Phys. Lett. 112 173502
Google Scholar
[14] Sun H D, Torres Castanedo C G, Liu K K, Li K H, Guo W Z, Lin R H, Liu X W, Li J T, Li X H 2017 Appl. Phys. Lett. 111 162105
Google Scholar
[15] Ho S T 2020 M. S. Dessertation (New York: Cornell University)
[16] Yan P R, Zhang Z, Xu Y, Chen H, Chen D Z, Feng Q, Xu S R, Zhang Y C, Zhang J C, Zhang C F, Hao Y 2022 Vacuum 204 111381
Google Scholar
[17] Singh R, Lenka T R, Velpula R T, Jain B, Bui H Q T, Nguyen H P T 2021 Int. J. Numer. Model. El. 34 e2794
Google Scholar
[18] Song K, Zhang H C, Fu H Q, Yang C, Singh R, Zhao Y J, Sun H D, Long S B 2020 J. Phys. D Appl. Phys. 53 345107
Google Scholar
[19] Jiao W Y, Kong W, Li J C, Collar K, Kim T H, Losurdo M, Brown A S 2016 Appl. Phys. Lett. 109 082103
Google Scholar
[20] Yu C, Debdeep J 2007 Appl. Phys. Lett. 90 182112
Google Scholar
[21] Singh R, Lenka T R, Velpula R T, Jain B, Bui H Q T, Nguyen H P T 2020 J. Semicond. 41 102802
Google Scholar
[22] Gordon L, Miao M-S, Chowdhury S, Higashiwaki M, Mishra U K, van de Walle C G 2010 J. Phys. D: Appl. Phys. 43 505501
Google Scholar
[23] Goyal N, Iniguez B, Fjeldly T A 2013 AIP Conf. Proc. 1566 393
Google Scholar
[24] Goyal N, Fjeldly T A 2016 IEEE T. Electron Dev. 63 881
Google Scholar
[25] 陈谦, 李群, 杨莺 2019 物理学报 68 017301
Google Scholar
Chen Q, Li Q, Yang Y 2019 Acta Phys. Sin. 68 017301
Google Scholar
[26] Ambacher O, Smart J, Shealy J R, Weimann N G, Chu K, Murphy M, Schaff W J, Eastman L F, Dimitrov R, Wittmer L, Stutzmann M, Rieger W, Hilsenbeck J 1999 J. Appl. Phys. 85 3222
Google Scholar
[27] 李群, 陈谦, 种景 2018 物理学报 67 027303
Google Scholar
Li Q, Chen Q, Chong J 2018 Acta Phys. Sin. 67 027303
Google Scholar
[28] 张阳, 顾书林, 叶建东, 黄时敏, 顾然, 陈斌, 朱顺明, 郑有炓 2013 物理学报 62 150202
Google Scholar
Zhang Y, Gu S L, Ye J D, Huang S M, Gu R, Chen B, Zhu S M, Zhen Y D 2013 Acta Phys. Sin. 62 150202
Google Scholar
[29] Li Q, Zhang J W, Meng L, Hou X 2014 Phys. Status Solidi B 251 755
Google Scholar
[30] Li Q, Zhang J W, Zhang Z Y, Li F N, Hou X 2014 Semicond. Sci. Technol. 29 115001
Google Scholar
[31] Li Q, Zhang J W, Chong J, Hou X 2013 Appl. Phys. Express 6 121102
Google Scholar
[32] Kawamura T, Das Sarma S 1992 Phys. Rev., B: Condens. Matter. 45 3612
Google Scholar
[33] Goodnick S M, Ferry D K, Wilmsen C W 1985 Phys. Rev. B 32 8171
Google Scholar
[34] Gurusinghe M N, Davidsson S K, Andersson T G 2005 Phys. Rev. B 72 45316
Google Scholar
[35] Ishibashi A, Takeishi H, Mannoh M, Yabuuchi Y, Ban Y 1996 J. Electron. Mater. 25 799
Google Scholar
[36] Li J M, Wu J J, Han X X, Lu Y W, Liu X L, Zhu Q S, Wang Z G 2005 Semicond. Sci. Technol. 20 1207
Google Scholar
[37] Anderson D, Zakhleniuk N, Babiker M, Ridley B, Bennett C 2001 Phys. Rev. B 63 245313
Google Scholar
[38] Parisini, Antonella, Fornari, Roberto 2016 Semicond. Sci. Technol. 31 35023.1
Google Scholar
[39] Zhi G, Verma A, Wu X, Sun F, Hickman A, Masui T, Kuramata A, Higashiwaki M, Jena D, Luo T 2015 Appl. Phys. Lett. 106 591
[40] Varley J B, Weber J R, Janotti A, Van d W, C. G. 2010 Appl. Phys. Lett. 108 142106
Google Scholar
[41] Passlack M, Hunt N, Schubert E F, Zydzik G J, Hong M, Mannaerts J P, Opila R L, Fischer R J 1994 Appl. Phys. Lett. 64 2715
Google Scholar
[42] Passlack M, Hong M, Schubert E F, Kwo J R, Mannaerts J P, Chu S, Moriya N, Thiel F A 1995 Appl. Phys. Lett. 66 625
Google Scholar
[43] Rebien M, Henrion W, Hong M, Mannaerts J P, Fleischer M 2002 Appl. Phys. Lett. 81 250
Google Scholar
[44] Rode D L 1970 Phys. Rev. B 2 1012
Google Scholar
[45] Liu B, Gu M, Liu X 2007 Appl. Phys. Lett. 91 172102
Google Scholar
[46] Fischer A, Kühne H, Richter H 1994 Phys. Rev. Lett. 73 2712
Google Scholar
[47] Sanchez A M, Pacheco F J, Molina S I, Stemmer J, Aderhold J, Graul J 2001 J. Electron. Mater. 30 L17
Google Scholar
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