不同晶面应变纤锌矿GaN/AlN量子阱的价带结构理论研究

doi:10.12052/gdutxb.220158

摘要/Abstract

摘要： 为深刻理解应变异质结量子阱结构的物理性质，帮助改进基于宽禁带氮化物半导体器件的设计，本文基于六带应力相关的k·p哈密顿量与自洽薛定谔−泊松方程建立了在场约束效应下极性 (0001)、半极性 ($10\bar 12 $) 及非极性 ($10\bar 10 $) 晶面的纤锌矿GaN/AlN量子阱价带子带模型，并给出了不同晶面GaN/AlN量子阱在双轴和单轴应力作用下的子带能量色散关系。根据应力对量子阱价带结构的影响，对应力与空穴有效质量之间的微观物理关系进行了综合研究。结果表明，价带结构对晶体取向的改变有很大的依赖性。双轴应力对有效质量的改善效果不大，然而单轴压缩应力通过降低垂直沟道方向的能量使低有效质量区域获得更多的空穴，从而有效降低空穴有效质量，且在不同晶面的结构中都减少了约90%。

关键词: 价带结构, 应力, GaN/AlN量子阱, 晶面, k·p方法

Abstract: In order to deeply understand the physical properties of strained heterojunction quantum well structures and improve the design of wide-bandgap nitride semiconductor devices, in this paper, based on the six-band stress-dependent k·p Hamiltonian and the self-consistent Schrodinger-Poisson equation, the valence subband model of wurtzite GaN/AlN quantum well with polar (0001) , semi-polar ($10\bar 12 $) and non-polar ($10\bar 10 $) orientations under field confinement was established. The subband energy dispersion relations between GaN/AlN quantum well with different crystal orientations under biaxial and uniaxial stresses were also given. According to the influence of stress on the valence band structure of quantum well, the microcosmic physical relationship between stress and hole effective mass was studied comprehensively. The results show that the valence band structure heavily depends on the modification in crystal orientation. The biaxial stress has little effect on the improvement of effective mass. However, uniaxial compressive stress can obtain more holes in the region of low effective mass by reducing the energy in the vertical channel direction, such that the hole effective mass can be effectively reduced. And it is reduced by about 90% in the structure of different crystal orientations.

Key words: valence band structure, stress, GaN/AlN quantum well, crystal orientations, k·p method

中图分类号:

TN301

刘亚群, 李希越, 章国豪. 不同晶面应变纤锌矿GaN/AlN量子阱的价带结构理论研究[J]. 广东工业大学学报, 2024, 41(01): 119-126.

Liu Ya-qun, Li Xi-yue, Zhang Gary. Theoretical Study on Valence Band Structure of Strained Wurtzite GaN/AlN Quantum Well with Different Crystal Orientations[J]. Journal of Guangdong University of Technology, 2024, 41(01): 119-126.

参考文献

[1] IKEDA N, NIIYAMA Y, KAMABAYASHI H, et al. GaN power transistors on Si substrates for switching [J]. Proceedings of the IEEE, 2010, 98(7): 1151-1161.
[2] FLACK T J, PUSHPAKARAN B N, BAYNE S B. GaN technology for power electronic applications: a review [J]. Journal of Electronic Materials, 2016, 45(6): 2673-2682.
[3] ZHENG Z Y, ZHANG L, SONG W J, et al. Gallium nitride-based complementary logic integrated circuits [J]. Nature Electronics, 2021, 4: 595-603.
[4] SIRENKO Y M, JEON J B, KIM W K, et al. Envelope-function formalism for valence bands in wurtzite quantum wells [J]. Physical Review B, 1996, 53(4): 1997-2009.
[5] CHUANG S L, CHAO C S. Effective mass Hamiltonian for strained wurtzite GaN and analytical solutions [J]. Applied Physicas Letters, 1996, 68(12): 1657-1659.
[6] FRITSCH D, SCHMIDT H, GRUNDMANN M. Band-structure pseudopotential calculation of zinc-blende and wurtzite AlN, GaN, and InN [J]. Physical Review B, 2003, 67(23): 235205.
[7] AMBACHER O, SMART J, SHEALY J R, et al. Two-dimensional electron gases induced by spontaneous and piezoelectric polarization charges in N- and Ga-face AlGaN/GaN heterostructures [J]. Journal of Applied Physics, 1999, 85(6): 3222-3233.
[8] NOMOTO K, CHAUDHURI R, BADER S J, et al. GaN/AlN p-channel HEFTs with I_mas>420 mA/mm and ~20 GHz f_T/f_MAX[C]//2020 IEEE International Electron Devices Meeting (IEDM) . San Francisco, CA, USA: IEEE, 2020.
[9] 聂玉虎. GaN材料应变沿表面法线分布信息的XRD测量方法研究[D]. 西安: 西安电子科技大学, 2014.
[10] SONG H, SUH J, KIM E K, et al. Growth of high quality a-plane GaN epi-layer on r-plane sapphire substrates with optimization of multi-buffer layer [J]. Journal of Crystal Growth, 2010, 312(21): 3122-3126.
[11] JUNG C, JANG J, HWANG J, et al. Defect reduction in (11-22) semipolar GaN with embedded InN islands on m-plane sapphire [J]. Journal of Crystal Growth, 2013, 370(5): 26-29.
[12] PONCE S, JENA D, GIUSTINO F. Route to high hole mobility in GaN via reversal of crystal-field splitting [J]. Physical Review Letters, 2019, 123(9): 096602.
[13] GUPTA C, TSUKADA Y, ROMANCZYK B, et al. First demonstration of improvement in hole conductivity in c-plane III-nitrides through application of uniaxial strain [J]. Japanese Journal of Applied Physics, 2019, 58(3): 030908.
[14] BADER S J, CHAUDHURI R, SCHUBERT M, et al. Wurtzite phonons and the mobility of a GaN/AlN 2D hole gas [J]. Applied Physics Letters, 2019, 114(25): 253501.
[15] CHUANG S L, CHANG C S. K·P method for strained wurtzite semiconductors [J]. Physical Review B, 1996, 54(4): 2491-2504.
[16] KANE E O. Band structure of indium antimonide [J]. Journal of Physics and Chemistry of Solids, 1957, 1(4): 249-261.
[17] BYKHOVSKI A, GELMONT B L, SHUR M S. Strain and charge distribution in GaN-AlN-GaN semiconductor-insulator-semiconductor structure for arbitrary growth orientation [J]. Applied Physics Letters, 1993, 63(16): 2243-2245.
[18] CALIN G. K·P theory of semiconductor nanostructures[D]. Worcester: Worcester Polytechnic Institute, 2005.
[19] BYKHOVSKI A, GELMONT B, SHUR M S, et al. Current-voltage characteristics of strained piezoelectric structures [J]. Journal of Applied Physics, 1995, 77(4): 1616-1620.
[20] CHAUDHURI R, BADER S J, CHEN Z, et al. A polarization-induced 2D hole gas in undoped gallium nitride quantum wells [J]. Science, 2019, 365(6460): 1454-1457.
[21] SMITH D L, MAILHIOT C. Piezoelectric effects in strained-layer superlattices [J]. Journal of Applied Physics, 1988, 63(8): 2717-2719.
[22] BASTARD G, MENDEZ E E, CHANG L L, et al. Variational calculations on a quantum well in an electric field [J]. Physical Review B, 1983, 28(6): 3241-3245.
[23] LIU Y, LI X, ZHANG G, et al. The calculation for quantized valence subband structure of zinc-blende GaN heterojunction quantum well based on k·p method [J]. Semiconductor Science and Technology, 2021, 36(12): 1-9.
[24] BREY L, DEMPSEY J, JOHNSON N F, et al. Infrared optical absorption in imperfect parabolic quantum wells [J]. Physical Review B, 1990, 42(2): 1240-1247.
[25] VURGAFTMAN I, MEYER J R, RAM-MOHAN L R. Band parameters for III-V compound semiconductors and their alloys [J]. Journal of Applied Physics, 2001, 89(11): 5815-5875.
[26] BYKHOVSKI A D, KAMINSKI V V, SHUR M S, et al. Piezoresistive effect in wurtzite n-type GaN [J]. Applied Physics Letters, 1996, 68(6): 818-819.
[27] SUZUKI M, UENOYAMA T, YANASE A. First-principles calculations of effective-mass parameters of AlN and GaN [J]. Physical Review B Condens Matter, 1995, 52(11): 8132-8139.
[28] WEBER O, IRISAWA T, NUMATA T, et al. Examination of additive mobility enhancements for uniaxial stress combined with biaxially strained Si, biaxially strained SiGe and Ge channel MOSFETs[C]//IEEE International Electron Devices Meeting. Washington, DC: IEEE, 2007.
[29] ADACHI S. Properties of group-IV, III-V and II-VI semiconductors[M]. New York: John Wiley & Sons Inc. , 2005: 114-115.
[30] SIRENKO Y M, JEON J B, KIM K W, et al. Strain effects on valence band structure in würtzite GaN quantum wells [J]. Applied Physics Letters, 1996, 69(17): 2504-2506.
[31] PARK S H. Many-body optical gain of ( $10 \bar{1}0 $ ) wurtzite GaN/AlGaN quantum-well lasers [J]. Applied Physics Letters, 2000, 77(25): 4095-4097.
[32] NIWA A, OHTOSHI T, KURODA T. Valence subband structures of ( $10 \bar{1} 0$ ) -GaN/AlGaN strained quantum wells calculated by the tight-binding method [J]. Applied Physics Letters, 1997, 70(16): 2159-2161.

相关文章 15

[1]	王晓锋, 何小琦, 尧彬. PBGA封装回流焊翘曲变形仿真与验证[J]. 广东工业大学学报, 2020, 37(02): 94-101.
[2]	周若洋, 杨雪强, 刘攀, 郑丽婷, 陈涛. 不同加荷方向下横观各向同性饱和粗砂的真三轴试验研究[J]. 广东工业大学学报, 2020, 37(01): 58-64.
[3]	禹智涛, 潘浩, 贺绍华. 预应力轴压比对节段拼装桥墩力学性能影响分析[J]. 广东工业大学学报, 2019, 36(04): 85-91.
[4]	王亚文, 谷爱昱, 严柏平, 雒浪. 步行能量采集器中磁致伸缩材料的机-磁耦合特性研究[J]. 广东工业大学学报, 2018, 35(04): 25-31.
[5]	马平, 廖明易, 王志勇. 起重机械用绳排索具力学与疲劳特性研究[J]. 广东工业大学学报, 2016, 33(05): 65-68.
[6]	杨雪强, 刘勇健, 吉小明. 考虑土体自重应力场的拱效计算方法[J]. 广东工业大学学报, 2016, 33(03): 76-80.
[7]	傅胤荣, 胡义华, 金亚洪. 应力发光材料BaZrSi₃O₉的制备与发光特性研究[J]. 广东工业大学学报, 2015, 32(04): 17-20.
[8]	刘昆，彭美春，林怡青，王海龙. 基于ANSYS Workbench鼓式制动器冲焊蹄的有限元分析[J]. 广东工业大学学报, 2013, 30(1): 92-96.
[9]	路浩东 , 袁鸽成 , 冷文兵 , 李仲华 , 朱振华. 极化电位对5083铝合金型材应力腐蚀行为的影响[J]. 广东工业大学学报, 2010, 27(2): 43-46.
[10]	冷文兵; 袁鸽成; 倪学明; 路浩东;. 5083铝合金在3.5%NaCl溶液中的应力腐蚀行为[J]. 广东工业大学学报, 2009, 26(1): 7-.
[11]	任凤鸣；袁兵；. 垫层对工作井应力与变形影响的分析[J]. 广东工业大学学报, 2007, 24(1): 56-60.
[12]	杨雪强；宫全美；李彰明； . 对三种强度破坏准则的物理解释[J]. 广东工业大学学报, 2007, 24(03): 76-83.
[13]	史宏彦；白琳； . 平面应变条件下土的非共轴变形特性[J]. 广东工业大学学报, 2007, 24(03): 84-87.
[14]	谭德盼；姜海波；何柏青；吕艳； . 斜腿刚架拱桥微弯板的病害原因分析[J]. 广东工业大学学报, 2007, 24(03): 88-91.
[15]	罗志强； . 沥青加铺层构建应力吸收层的特性分析[J]. 广东工业大学学报, 2007, 24(03): 92-95.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed