中文摘要：

第一性原理计算方法在解释实验现象和预测新材料结构及其性质上有着重要作用.因此,通过基于密度泛函理论的第一性原理的方法,本文系统地研究了Mg和Si掺杂闪锌矿和纤锌矿两种晶体结构的GaN/AlN超晶格体系中的能量稳定性以及电学性质.结果表明：在势阱层（GaN层）中,掺杂原子在体系中的掺杂形成能不随掺杂位置的变化而发生变化,在势垒层（Al N层）中也是类似的情况,这表明对于掺杂原子来说,替代势垒层（或势阱层）中的任意阳离子都是等同的;然而,相比势阱层和势垒层的掺杂形成能却有很大的不同,并且势阱层的掺杂形成能远低于势垒层的掺杂形成能,即掺杂元素（MgGa,MgAl,SiGa和SiAl）在势阱区域的形成能更低,这表明杂质原子更易掺杂于结构的势阱层中.此外,闪锌矿更低的形成能表明：闪锌矿结构的超晶格体系比纤锌矿结构的超晶格体系更易于实现掺杂;其中,闪锌矿结构中,负的形成能表明：当Mg原子掺入闪锌矿结构的势阱层中会自发引起缺陷.由此,制备以闪锌矿结构超晶格体系为基底的p型半导体超晶格比制备n型半导体超晶格需要的能量更低并且更为容易制备.对于纤锌矿体系来说,制备p型和n型半导体的难易程度基本相同.电子态密度对掺杂体系的稳定性和电学性质进一步分析发现,掺杂均使得体系的带隙减小,掺杂前后仍然为第一类半导体.综上所述,本文内容为当前实验中关于纤锌矿结构难以实现p型掺杂问题提供了一种新的技术思路,即可通过调控相结构实现其p型掺杂.

英文摘要：

First-principles calculation is a quite powerful tool for explaining experimental phenomena and predicting the properties of new materials. Based on the first-principles calculation within the density functional theory, the energetic stabilities and electronic properties of Mg and Si doped GaN/A1N superlattices with wurtzite and zinc-blende structures are investigated. The results show that there is no variation in formation energy if the doping position is changed when the impurities are doped in the well （GaN） region, and the same situation also happens in the barriers （A1N） region. Thus it is equivalent for dopants to replace Ga atoms in the cation site of wells or A1 atoms in the cation site of barrers. However, the formation energies of these dopants in the well region and the barrier region are different. Compared with the formation energy in the barrier region, it is much lower in the well region. That is to say, the impurities in the cation site （MgGa, MgA1, SiGa and SiAl） present lower formation energies in the wells of GaN/A1N SLs with wurtzite and zinc-blende structures. In addition, the impurities in zinc-blende GaN/A1N superlattices present lower formation energy than in the wurtzite structure. The negative formation energy illustrates that the defects are spontaneously formed if Mg-atom is mixed into the wells of the zinc-blende structure. Therefore, in experiment, for the zinc-blende superlattice structure, preparing p-type semiconductor needs less energy than preparing n-type semiconductor. And for the wurtzite superlattice structure, preparing p-type semiconductor needs the same energy as preparing n-type semiconductor. Furthermore, the relationships between the distribution of the electronic states and their structures are analyzed. It is found that the different kinds of dopants lead to different band bendings, owing to the modified polarization fields. The spatial distributions of electrons and holes, plotted by the partial charge densities, reveal that electrons and holes experien