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在纤锌矿结构Zn1-xMgxO/ZnO异质结构中发现了高迁移率的二维电子气(2DEG), 2DEG 的产生很可能是由于界面上存在不连续极化, 而且2DEG通常也被认为是由极化电荷产生的结果. 为了探索2DEG的形成机理及其产生的根源, 研究Zn1-xMgxO合金的极化特性与ZnO/Zn1-xMgxO超晶格的能带排列是非常必要的. 基于第一性原理广义梯度近似+U方法研究了Zn1-xMgxO合金的自发极化随Mg组分x的变化关系, 其中极化特性的计算采用Berry-phase方法. 由于ZnO与Zn1-xMgxO 面内晶格参数大小相当, ZnO 与Zn1-xMgxO 的界面匹配度优良, 所以ZnO/Zn1-xMgxO 超晶格模型较容易建立. 计算了Mg0.25Zn0.75O/ZnO超晶格静电势的面内平均及其沿着Z(0001)方向上的宏观平均. (5+3)Mg0.25Zn0.75O/ZnO超晶格拥有较大的尺寸, 确保远离界面的Mg0.25Zn0.75O与ZnO区域与块体计算情况一致. 除此之外, 基于宏观平均为能量参考, 计算得到Mg0.25Zn0.75O/ZnO超晶格界面处价带偏差为0.26 eV, 并且导带偏差与价带偏差的比值处于合理区间, 这与近来实验上报道的结果相符. 除了ZnO在[0001]方向上产生自发极化外, 由于在ZnO中引入Mg杂质会产生应变应力, 导致MgxZn1-xO层产生额外的极化值. 这样必然会在Mg0.25Zn0.75O/Zn界面处产生非连续极化现象, 促使单极性电荷在界面处积累, 从而在Mg0.25Zn0.75O/Zn超晶格中产生内在电场. 此外, 计算了Mg0.25Zn0.75O/ZnO超晶格的能带排列, 由于价带偏差 EV=0.26 eV与导带偏差EC=0.33 eV, 表明能带遵循I型排列. Mg0.25Zn0.75O/ZnO 的这种能带排列方式足以让电子与空穴在势阱中产生禁闭作用. 2DEG在电子学与光电子学领域都有重要应用, 本文的研究结果将对Mg0.25Zn0.75O/ZnO 界面2DEG的设计与优化中起到重要作用, 并且可以作为研究其他Mg组分的MgxZn1-xO/ZnO超晶格界面电子气特性的参考依据.Two-dimensional (2D) electron gas with high-mobility is found in wurtzite ZnO/Zn(Mg)O heterostructure, which probably arises from the polarization discontinuity at the ZnO/Zn(Mg)O interface, and the 2D electron gas in the heterostructure is usually also regarded as resulting from polarization-induced charge. In order to explore both the formation mechanism and the origin of the 2D electron gas in ZnMgO/ZnO heterostructure, it is necessary to study the polarization properties of Zn1-xMgxO alloy and energy band alignment of ZnO/Zn1-xMgxO super-lattice. In this paper, we study the polarization properties of Zn1-xMgxO alloy with different Mg compositions by using first-principles calculations with GGA+U method, and the polarization properties are calculated according to Berry-phase method. Owing to the excellent match between the in-plane lattice constants of ZnO and Zn1-xMgxO, the lattice constants of the ZnO and Zn1-xMgxO interface are similar, ZnO/Zn1-xMgxO super-lattice could be constructed easily. The planar-averaged electrostatic potential for the Mg0.25Zn0.75O/ZnO super-lattice and the macroscopically averaged potential along Z(0001) direction are calculated. The large size of (5+3) Mg0.25Zn0.75O/ZnO super-lattice ensures the convergence of potential to its bulk value in the region of the ZnO layer and Mg0.25Zn0.75O layer far from ZnO/Zn1-xMgxO interface. Besides, the valence band offset at the Mg0.25Zn0.75O/ZnO interface is calculated to be 0.26~eV based on the macroscopically averaged potential mentioned above, and the ratio of conduction band offset (EC) to valence band offset (EV) is in a reasonable range, and this is in substantial agreement with the values reported in recent experimental results. Because strain induces additional piezoelectric polarization in MgxZn1-xO, which is introduced by Mg dopant, the lack of inversion symmetry and the bulk ZnO induce its spontaneous polarization in the [0001] direction. The polarization discontinuity at the Mg0.25Zn0.75O/ZnO interface leads to the charge accumulation in the form of interface monopoles, giving rise to built-in electric fields in the super-lattice. In addition, energy alignment determination of the Mg0.25Zn0.75O/ZnO super-lattice is performed, which shows a type-I band alignment with EV=0.26 eV and EC=0.33 eV. The determination of the band alignment indicates that the Mg0.25Zn0.75O/ZnO super-lattice is competent to the confining of both electron and hole. These findings will be useful for designing and optimizing the 2D electron gas at Mg0.25Zn0.75O/ZnO interface, which can be regarded as an important reference for studying the 2D electron gas at MgxZn1-xO/ZnO super-lattices for electronics and optoelectronics applications.
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Keywords:
- MgZnO /
- spontaneous polarization /
- electrostatic potential average /
- band offset
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[21] Rao G, Sauberlich F, Klein A 2005 Appl. Phys. Lett. 87 032101
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[23] Ohtomo A, Kawasaki M, Ohkubo I, Koinuma H, Yasuda T, Segawa Y 1999 Appl. Phys. Lett. 75 980
[24] Janotti A, van de Walle C G 2007 Phys. Rev. B 75 121201
[25] Coli G, Bajaj K 2001 Appl. Phys. Lett. 78 2861
[26] Su S C, Lu Y M, Zhang Z Z, Shan C X, Li B H, Shen D Z, Yao B, Zhang J Y, Zhao D X, Fan X W 2008 Appl. Phys. Lett. 93 082108
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[29] Morhain C, Bretagnon T, Lefebvre P, Tang X, Valvin P, Guillet T, Gil B, Taliercio T, Teisseire D M, Vinter B, Deparis C 2005 Phys. Rev. B 72 241305
[30] van de Valle C G, Martin R M 1987 Phys. Rev. B 35 8154
[31] Ohtomo A, Kawasaki M, Koida T, Masubuchi K, Koinuma H, Sakurai Y, Yoshida Y, Yasuda T, Segawa Y 1998 Appl. Phys. Lett. 72 2466
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[1] Chakhalian J, Millis A J, Rondinelli J 2012 Nat. Mater. 11 92
[2] Hwang H Y, Iwasa Y, Kawasaki M, Keimer B, Nagaosa N, Tokura Y 2012 Nat. Mater. 11 103
[3] Ji X, Zhu Y, Chen M M, Su L X, Chen A Q, Gui X C, Xiang R, Tang Z K 2014 Sci. Rep. 4 4185
[4] Tsukazaki A, Ohtomo A, Kita T, Ohno Y, Ohno H, Kawasaki M 2007 Science 315 1388
[5] Tsukazaki A, Akasaka S, Nakahara K, Ohno Y, Ohno H, Maryenko D, Ohtomo A, Kawasaki M 2010 Nat. Mater. 9 889
[6] Han K, Tang N, Ye J D, Duan J X, Liu Y C, Teo K L, Shen B 2012 Appl. Phys. Lett. 100 192105
[7] Chen H, Gu S L, Liu J G, Ye J D, Tang K, Zhu S M, Zheng Y D 2011 Appl. Phys. Lett. 99 211906
[8] Ye J D, Lim S T, Bosman M, Gu S L, Zheng Y D, Tan H H, Jagadish C, Sun X W, Teo K L 2012 Sci. Rep. 2 533
[9] Monroy E, Omnes F, Calle F 2003 Semicond. Sci. Technol. 18 R33
[10] Fan M M, Liu K W, Chen X, Zhang Z Z, Li B H, Zhao H F, Shen D Z 2015 J. Mater. Chem. C 3 313
[11] Zhu Y Z, Chen G D, Ye H, Walsh A, Moon C Y, Wei S H 2008 Phys. Rev. B 77 245209
[12] Wu K P, Jiang J H, Tang K, Gu S L, Ye J D, Zhu S M, Lu K L, Zhou M R, Xu M X, Zhang R, Zheng Y D 2014 J. Magn. Magn. Mater. 355 51
[13] Zhang W, Xue J S, Zhou X W, Zhang Y, Liu Z Y, Zhang J C, Hao Y 2012 Chin. Phys. B 21 077103
[14] Liu N Y, Liu L, Wang L, Yang W, Li D, Li L, Cao W Y, Lu C M, Wan C H, Chen W H, Hu X D 2012 Chin. Phys. B 21 017806
[15] Rao X, Wang R Z, Gao J X, Yan H 2015 Acta Phys. Sin. 64 107303(in Chinese) [饶雪, 王如志, 曹觉先, 严辉 2015 物理学报 64 107303]
[16] Niranjan M K, Wang Y, Jaswal S S, Tsymbal E Y 2009 Phys. Rev. Lett. 103 016804
[17] Wang Y, Niranjan M K, Janicka K, Velev J P, Zhuravlev M Y, Jaswal S S, Tsymbal E Y 2010 Phys. Rev. B 82 094114
[18] Wei S, Zunger A 1998 Appl. Phys. Lett. 72 2011
[19] Gruber T, Kirchner C, Kling R, Reuss F, Waag A 2004 Appl. Phys. Lett. 84 5359
[20] Park S, Ahn D 2005 Appl. Phys. Lett. 87 253509
[21] Rao G, Sauberlich F, Klein A 2005 Appl. Phys. Lett. 87 032101
[22] Olson D C, Shaheen S E, White M S, Mitchell W J, van Hest M F A M, Collins R T, Ginley D S 2007 Adv. Funct. Mater. 17 264
[23] Ohtomo A, Kawasaki M, Ohkubo I, Koinuma H, Yasuda T, Segawa Y 1999 Appl. Phys. Lett. 75 980
[24] Janotti A, van de Walle C G 2007 Phys. Rev. B 75 121201
[25] Coli G, Bajaj K 2001 Appl. Phys. Lett. 78 2861
[26] Su S C, Lu Y M, Zhang Z Z, Shan C X, Li B H, Shen D Z, Yao B, Zhang J Y, Zhao D X, Fan X W 2008 Appl. Phys. Lett. 93 082108
[27] Wu X, Vanderbilt D, Hamann D R 2005 Phys. Rev. B 72 035105
[28] Bretagnon T, Lefebvre P, Guillet T, Taliercio T, Gil B, Morhain C 2007 Appl. Phys. Lett. 90 201912
[29] Morhain C, Bretagnon T, Lefebvre P, Tang X, Valvin P, Guillet T, Gil B, Taliercio T, Teisseire D M, Vinter B, Deparis C 2005 Phys. Rev. B 72 241305
[30] van de Valle C G, Martin R M 1987 Phys. Rev. B 35 8154
[31] Ohtomo A, Kawasaki M, Koida T, Masubuchi K, Koinuma H, Sakurai Y, Yoshida Y, Yasuda T, Segawa Y 1998 Appl. Phys. Lett. 72 2466
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