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 av-eraged 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 intro-duced 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 de-termination 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.%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Mg0.25 Zn0.75 O/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.
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