搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

InAlN/GaN异质结二维电子气波函数的变分法研究

李群 陈谦 种景

引用本文:
Citation:

InAlN/GaN异质结二维电子气波函数的变分法研究

李群, 陈谦, 种景

Variational study of the 2DEG wave function in InAlN/GaN heterostructures

Li Qun, Chen Qian, Chong Jing
PDF
导出引用
  • 使用变分法推导了InAlN/GaN异质结二维电子气波函数和基态能级的解析表达式,并讨论了InAlN/GaN异质结结构参数对二维电子气电学特性的影响.在假设二维电子气来源于表面态的前提下,使用了一个包含两个变分参数的尝试波函数推导电子总能量期望值,并通过寻找能量期望极小值确定变分参数.计算结果显示,二维电子气面密度随InAlN厚度的增大而增大,且理论结果与实验结果一致.二维电子气面密度增大抬高了基态能级与费米能级,并保持二者之差增大以容纳更多电子.InAlN/GaN界面处的极化强度失配随着In组分增大而减弱,二维电子气面密度随之减小,并导致基态能级与费米能级减小.所建立的模型能够解释InAlN/GaN异质结二维电子气的部分电学行为,并为电子输运与光学跃迁的研究提供了解析表达式.
    The variational method has been widely used to study the electronic structures of heterostructure materials in spite of this method being less accurate than the numerical method, because analytical formulas for some electrical parameters can be derived using this method. However, effects of surface states on the two-dimensional electron gas (2DEG) have not been taken into account in the variational studies of GaN-based heterostructures. In the present study, analytical formulas for the electron wave function and ground state energy level of the 2DEG in InAlN/GaN heterostructures are derived using the variational method, and the influences of structural parameters of InAlN/GaN heterostructures on the electrical properties are discussed. In the theoretical model, evenly distributed surface states below the conduction band are assumed to be the origin of the 2DEG, and the polarization charges at the InAlN surface and the InAlN/GaN interface due to spontaneous and piezoelectric polarization effects in InAlN/GaN heterostructures are taken into account. A trial envelope wave function with two variational parameters is used to derive the expectation value of the total energy per electron. The variational parameters are determined by minimizing the expectation value. The model predicts a linear conduction band profile in InAlN barrier layer and an approximately triangular-shaped potential well on the GaN side of the InAlN/GaN interface. Electrons released from the surface states are confined in the potential well, forming the 2DEG. The 2DEG sheet density for the lattice-matched InAlN/GaN heterostructure with a 15 nm InAlN layer is 1.961013 cm-2, and the average distance from the InAlN/GaN interface of electrons is 2.23 nm. The 2DEG sheet density increases rapidly with InAlN thickness increasing when the InAlN layer exceeds the critical thickness, and starts to be saturated above 15 nm. The dependence of the calculated 2DEG sheet density on the InAlN thickness quantitatively agrees with recently reported experimental data. The increasing 2DEG sheet density results in increasing the ground state energy level and Fermi energy, and the energy spacing between the two also increases for containing more electrons. The polarization discontinuity at the InAlN/GaN interface decreases with increasing In mole fraction, causing the 2DEG sheet density to decrease, and thus the ground state energy level and the Fermi energy to decrease. This model is conducive to understanding the electrical behaviors of InAlN/GaN heterostructures and providing readily applicable formulas for studying the electron transport and optical transitions.
      通信作者: 李群, liqun@xaut.edu.cn
    • 基金项目: 国家自然科学基金(批准号:11647053)和陕西省教育厅科学研究计划项目(批准号:17JK0552)资助的课题.
      Corresponding author: Li Qun, liqun@xaut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11647053) and the Scientific Research Program Funded by Shaanxi Provincial Education Department, China (Grant No. 17JK0552).
    [1]

    Li Q, Zhang J W, Meng L, Hou X 2014 Phys. Status Solidi B 251 755

    [2]

    Zhang Y, Gu S L, Ye J D, Huang S M, Gu R, Chen B, Zhu S M, Zheng Y D 2013 Acta Phys. Sin. 62 150202 (in Chinese)[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]

    [3]

    Tien N T, Thao D N, Thao P T B, Quang D N 2015 Physica B 479 62

    [4]

    Manouchehri F, Valizadeh P, Kabir M Z 2014 J. Vac. Sci. Technol. A 32 021104

    [5]

    Stern F 1972 Phys. Rev. B 5 4891

    [6]

    Fouillant C, Alibert C 1994 Am. J. Phys. 62 564

    [7]

    Hao Y, Zhang J F, Zhang J C, Ma X H, Zheng X F 2015 Chin. Sci. Bull. 60 874 (in Chinese)[郝跃, 张金风, 张进成, 马晓华, 郑雪峰 2015 科学通报 60 874]

    [8]

    Fang Y L, Feng Z H, Yin J Y, Zhang Z R, Lv Y J, Dun S B, Liu B, Li C M, Cai S J 2015 Phys. Status Solidi B 252 1006

    [9]

    Arulkumaran S, Ng G I, Ranjan K, Kumar C M M, Foo S C, Ang K S, Vicknesh S, Dolmanan S B, Bhat T, Tripathy S 2015 Jpn. J. Appl. Phys. 54 04DF12

    [10]

    Goyal N, Fjeldly T A 2016 IEEE Trans. Electron Dev. 63 881

    [11]

    Jiao W, Kong W, Li J, Collar K, Kim T H, Losurdo M, Brown A S 2016 Appl. Phys. Lett. 109 082103

    [12]

    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

    [13]

    Quang D N, Tung N H, Tuoc V N, Minh N V, Huy H A, Hien D T 2006 Phys. Rev. B 74 205312

    [14]

    Ando T 1982 J. Phys. Soc. Jpn. 51 3900

    [15]

    Yang P, L Y W, Wang X B 2015 Acta Phys. Sin. 64 197303 (in Chinese)[杨鹏, 吕燕伍, 王鑫波 2015 物理学报 64 197303]

    [16]

    Cao Y, Jena D 2007 Appl. Phys. Lett. 90 182112

    [17]

    Kaun S W, Ahmadi E, Mazumder B, Wu F, Kyle E C H, Burke P G, Mishra U K, Speck J S 2014 Semicond. Sci. Technol. 29 045011

    [18]

    Dong X, Li Z H, Li Z Y, Zhou J J, Li L, Li Y, Zhang L, Xu X J, Xu X, Han C L 2010 Chin. Phys. Lett. 27 037102

    [19]

    Zhang J F, Wang P Y, Xue J S, Zhou Y B, Zhang J C, Hao Y 2011 Acta Phys. Sin. 60 117305 (in Chinese)[张金风, 王平亚, 薛军帅, 周勇波, 张进成, 郝跃 2011 物理学报 60 117305]

    [20]

    Xue J S, Zhang J C, Zhang W, Li L, Meng F N, Lu M, Jing N, Hao Y 2012 J. Cryst. Growth 343 110

    [21]

    Čičo K, Gregu෌ov D, Gaži, oltys J, Kuzmk J, Carlin J F, Grandjean N, Pogany D, Frhlich K 2010 Phys. Status Solidi C 7 108

  • [1]

    Li Q, Zhang J W, Meng L, Hou X 2014 Phys. Status Solidi B 251 755

    [2]

    Zhang Y, Gu S L, Ye J D, Huang S M, Gu R, Chen B, Zhu S M, Zheng Y D 2013 Acta Phys. Sin. 62 150202 (in Chinese)[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]

    [3]

    Tien N T, Thao D N, Thao P T B, Quang D N 2015 Physica B 479 62

    [4]

    Manouchehri F, Valizadeh P, Kabir M Z 2014 J. Vac. Sci. Technol. A 32 021104

    [5]

    Stern F 1972 Phys. Rev. B 5 4891

    [6]

    Fouillant C, Alibert C 1994 Am. J. Phys. 62 564

    [7]

    Hao Y, Zhang J F, Zhang J C, Ma X H, Zheng X F 2015 Chin. Sci. Bull. 60 874 (in Chinese)[郝跃, 张金风, 张进成, 马晓华, 郑雪峰 2015 科学通报 60 874]

    [8]

    Fang Y L, Feng Z H, Yin J Y, Zhang Z R, Lv Y J, Dun S B, Liu B, Li C M, Cai S J 2015 Phys. Status Solidi B 252 1006

    [9]

    Arulkumaran S, Ng G I, Ranjan K, Kumar C M M, Foo S C, Ang K S, Vicknesh S, Dolmanan S B, Bhat T, Tripathy S 2015 Jpn. J. Appl. Phys. 54 04DF12

    [10]

    Goyal N, Fjeldly T A 2016 IEEE Trans. Electron Dev. 63 881

    [11]

    Jiao W, Kong W, Li J, Collar K, Kim T H, Losurdo M, Brown A S 2016 Appl. Phys. Lett. 109 082103

    [12]

    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

    [13]

    Quang D N, Tung N H, Tuoc V N, Minh N V, Huy H A, Hien D T 2006 Phys. Rev. B 74 205312

    [14]

    Ando T 1982 J. Phys. Soc. Jpn. 51 3900

    [15]

    Yang P, L Y W, Wang X B 2015 Acta Phys. Sin. 64 197303 (in Chinese)[杨鹏, 吕燕伍, 王鑫波 2015 物理学报 64 197303]

    [16]

    Cao Y, Jena D 2007 Appl. Phys. Lett. 90 182112

    [17]

    Kaun S W, Ahmadi E, Mazumder B, Wu F, Kyle E C H, Burke P G, Mishra U K, Speck J S 2014 Semicond. Sci. Technol. 29 045011

    [18]

    Dong X, Li Z H, Li Z Y, Zhou J J, Li L, Li Y, Zhang L, Xu X J, Xu X, Han C L 2010 Chin. Phys. Lett. 27 037102

    [19]

    Zhang J F, Wang P Y, Xue J S, Zhou Y B, Zhang J C, Hao Y 2011 Acta Phys. Sin. 60 117305 (in Chinese)[张金风, 王平亚, 薛军帅, 周勇波, 张进成, 郝跃 2011 物理学报 60 117305]

    [20]

    Xue J S, Zhang J C, Zhang W, Li L, Meng F N, Lu M, Jing N, Hao Y 2012 J. Cryst. Growth 343 110

    [21]

    Čičo K, Gregu෌ov D, Gaži, oltys J, Kuzmk J, Carlin J F, Grandjean N, Pogany D, Frhlich K 2010 Phys. Status Solidi C 7 108

  • [1] 周展辉, 李群, 贺小敏. AlN/β-Ga2O3异质结电子输运机制. 物理学报, 2023, 72(2): 028501. doi: 10.7498/aps.72.20221545
    [2] 冉峰, 梁艳, 张坚地. 氧化物异质界面上的准二维超导. 物理学报, 2023, 72(9): 097401. doi: 10.7498/aps.72.20230044
    [3] 王健, 吴重庆. 低差分模式群时延少模光纤的变分法分析及优化. 物理学报, 2022, 71(9): 094206. doi: 10.7498/aps.71.20212198
    [4] 张雪冰, 刘乃漳, 姚若河. AlGaN/GaN高电子迁移率晶体管中二维电子气的极化光学声子散射. 物理学报, 2020, 69(15): 157303. doi: 10.7498/aps.69.20200250
    [5] 马嵩松, 舒天宇, 朱家旗, 李锴, 吴惠桢. Ⅳ-Ⅵ族化合物半导体异质结二维电子气研究进展. 物理学报, 2019, 68(16): 166801. doi: 10.7498/aps.68.20191074
    [6] 郭海君, 段宝兴, 袁嵩, 谢慎隆, 杨银堂. 具有部分本征GaN帽层新型AlGaN/GaN高电子迁移率晶体管特性分析. 物理学报, 2017, 66(16): 167301. doi: 10.7498/aps.66.167301
    [7] 周洁, 杨双波. 周期受击陀螺系统波函数的分形. 物理学报, 2014, 63(22): 220507. doi: 10.7498/aps.63.220507
    [8] 李加东, 程珺洁, 苗斌, 魏晓玮, 张志强, 黎海文, 吴东岷. 生物分子膜门电极AlGaN/GaN高电子迁移率晶体管(HEMT)生物传感器研究. 物理学报, 2014, 63(7): 070204. doi: 10.7498/aps.63.070204
    [9] 王现彬, 赵正平, 冯志红. N极性GaN/AlGaN异质结二维电子气模拟. 物理学报, 2014, 63(8): 080202. doi: 10.7498/aps.63.080202
    [10] 熊庄, 汪振新, Naoum C. Bacalis. 基于改进变分法对原子激发态精确波函数的研究. 物理学报, 2014, 63(5): 053104. doi: 10.7498/aps.63.053104
    [11] 张阳, 顾书林, 叶建东, 黄时敏, 顾然, 陈斌, 朱顺明, 郑有炓. ZnMgO/ZnO异质结构中二维电子气的研究. 物理学报, 2013, 62(15): 150202. doi: 10.7498/aps.62.150202
    [12] 王威, 周文政, 韦尚江, 李小娟, 常志刚, 林铁, 商丽燕, 韩奎, 段俊熙, 唐宁, 沈波, 褚君浩. GaN/AlxGa1-xN异质结二维电子气的磁电阻研究. 物理学报, 2012, 61(23): 237302. doi: 10.7498/aps.61.237302
    [13] 张金风, 王平亚, 薛军帅, 周勇波, 张进成, 郝跃. 高电子迁移率晶格匹配InAlN/GaN材料研究. 物理学报, 2011, 60(11): 117305. doi: 10.7498/aps.60.117305
    [14] 王平亚, 张金风, 薛军帅, 周勇波, 张进成, 郝跃. 晶格匹配InAlN/GaN和InAlN/AlN/GaN材料二维电子气输运特性研究. 物理学报, 2011, 60(11): 117304. doi: 10.7498/aps.60.117304
    [15] 熊涛, 张杰, 陈祥磊, 叶邦角, 杜淮江, 翁惠民. 单晶固体中正电子波函数的计算. 物理学报, 2010, 59(10): 7374-7377. doi: 10.7498/aps.59.7374
    [16] 徐志君, 聂青苗, 李鹏华. 用遗传算法研究一维光晶格中玻色凝聚气体基态波函数. 物理学报, 2009, 58(5): 2878-2883. doi: 10.7498/aps.58.2878
    [17] 周忠堂, 郭丽伟, 邢志刚, 丁国建, 谭长林, 吕 力, 刘 建, 刘新宇, 贾海强, 陈 弘, 周均铭. AlGaN/AlN/GaN结构中二维电子气的输运特性. 物理学报, 2007, 56(10): 6013-6018. doi: 10.7498/aps.56.6013
    [18] 朱 博, 桂永胜, 周文政, 商丽燕, 郭少令, 褚君浩, 吕 捷, 唐 宁, 沈 波, 张福甲. Al0.22Ga0.78N/GaN二维电子气中的弱局域和反弱局域效应. 物理学报, 2006, 55(5): 2498-2503. doi: 10.7498/aps.55.2498
    [19] 孔月婵, 郑有炓, 周春红, 邓永桢, 顾书林, 沈 波, 张 荣, 韩 平, 江若琏, 施 毅. AlGaN/GaN异质结构中极化与势垒层掺杂对二维电子气的影响. 物理学报, 2004, 53(7): 2320-2324. doi: 10.7498/aps.53.2320
    [20] 孔月婵, 郑有炓, 储荣明, 顾书林. AlxGa1-xN/GaN异质结构中Al组分对二维电子气性质的影响. 物理学报, 2003, 52(7): 1756-1760. doi: 10.7498/aps.52.1756
计量
  • 文章访问数:  5765
  • PDF下载量:  141
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-08-13
  • 修回日期:  2017-10-02
  • 刊出日期:  2019-01-20

/

返回文章
返回