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In SrTiO3-based oxide heterostructures, the mobility of the two-dimensional electron gas (2DEG) at the interface is relatively low at room temperature due to the influence of Ti 3d orbitals, which limits their applications in semiconductor devices. In contrast, the conduction band bottom of SnO2 is composed of Sn 5s orbitals, and it has been demonstrated that bulk SnO2 exhibits high carrier mobility at room temperature. Therefore, SnO2-based heterostructure interfaces have the potential to form 2DEG with high mobility at room temperature. In this paper, we construct a heterostructure (HfO2)7/(SnO2)13 with $2 \times 1$ supercell in (001) plane and systematically investigate the electronic structure of the heterostructure by using first-principles calculations. The calculation results show that the defect-free (HfO2)7/(SnO2)13 heterostructure has a band structure similar to that of a semiconductor, and there is no 2DEG near the interface of the heterostructure. However, the conduction band bottom is mainly contributed by non-degenerate Sn 5s orbitals in this situation. In the in-plane $2 \times 1$ supercell of the (HfO2)7/(SnO2)13 heterostructure, each layer contains 8 oxygen atoms (the thickness of 1 unit cell is defined as a layer). When an oxygen atom in a layer on the SnO2 side near the interface of the heterostructure is removed, the presence of the oxygen vacancy leads to the formation of a defect band below the conduction band. This will lead to hopping conductivity in the heterostructure. However, 2DEG still does not appear near the heterostructure interface. When the oxygen vacancy is located in the surface layer of the HfO2 in the supercell structure, the presence of the oxygen vacancy leads to the formation of a defect state in the surface. The electrons in the defect state are localized and do not contribute to conductivity. However, the defect band overlaps with the conduction band at the interface, causing the electrons on the surface of HfO2 to tunnel towards the interface. In this scenario, the 2DEG emerges in the vicinity of the heterostructure interface. In addition, for HfO2/SnO2 heterostructures with thinner HfO2 layers, such as HfO2 layer with a thickness of 7 unit cells (about 2.37 nm), the H atoms adsorbed on the HfO2 surface provide electrons for the heterostructure. Some of these electrons transfer to the conduction band near the interface, leading to the formation of a 2DEG in that region. Meanwhile, the remaining electrons stay on the surface, forming a conductive layer with a thickness of approximately 2 unit cells. As the thickness of the HfO2 layer increases, the probability of electrons transferring from the surface to the interface gradually decreases, resulting in a gradual decrease in the electron density at the interface.
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图 1 SnO2和HfO2块体的能带结构图(费米能级设为零点) (a), (b)采用GGA+U所得(a) SnO2和(b)HfO2的能带结构; (c), (d)采用$U_{\text{O}}^{{\text{2p}}}$ = 8 eV的GGA+U所得(c) SnO2和(d) HfO2的能带结构; (e), (f)采用HSE杂化泛函所得(e) SnO2和(f)HfO2的能带结构; (g), (h)采用$U_{\text{O}}^{{\text{2p}}}$ = 14 eV的GGA+U所得(g)SnO2和(h)HfO2的能带结构
Figure 1. Band structure of bulk SnO2 and HfO2. The band structures of (a) SnO2 and (b) HfO2 obtained by GGA+U; (c) SnO2 and (d) HfO2 obtained by GGA+U with $U_{\text{O}}^{{\text{2p}}}$ = 8 eV; The band structures of (e) SnO2 and (f) HfO2 obtained by HSE hybrid functional; The band structures of (g) SnO2 and (h) HfO2 obtained by GGA+U with $U_{\text{O}}^{{\text{2p}}}$ = 14 eV. The Fermi level is set as zero.
图 2 面内2×1 (HfO2)7/(SnO2)13异质结构示意图
Figure 2. Schematic structure of the in-plane 2×1 (HfO2)7/(SnO2)13 heterostructure.
图 3 (HfO2)7/(SnO2)13异质结构的电子结构(费米能级设为零点) (a)能带结构图, 方形点线标记能带来源于异质结表面L7层不饱和悬键的畸变; (b)原子层分解态密度图; (c)平面平均电荷密度差, 其中负值和正值分别表示电子的耗尽和积累, L表示沿异质结构的距离, 点划线给出了异质结界面的位置; (d) Sn, Hf, O原子轨道投影态密度
Figure 3. Electronic structure of (HfO2)7/(SnO2)13 heterostructure. (a) The energy band structure. The band marked by the square dots originates from the distortion of the unsaturated dangling bonds of the L7 layer near the heterojunction surface. (b) The partial density of states projected onto atomic planes. (c) The plane-averaged charge density difference. The negative and positive values represent the depletion and accumulation of electrons, respectively. L is noted as the distance along direction of the heterostructure, and the dashed line gives the location of the interface. (d) Projection density of states for Sn, Hf, and O atomic orbitals, where the Fermi level is set as zero.
图 4 (HfO2)7/(SnO2)13异质结表面和界面附近不同原子层的氧空位形成能, 其中点划线给出了异质结界面的位置, 圆圈标记为SnO2侧和HfO2侧的氧空位形成能最低的位置
Figure 4. Formation energies of oxygen vacancies in different atomic layers near the surface and interface of (HfO2)7/(SnO2)13 heterostructure. The dashed line gives the position of the heterojunction interface, and the circles mark the lowest oxygen vacancy formation energy on the SnO2 side and the HfO2 side.
图 5 存在氧空位时(HfO2)7/(SnO2)13异质结的能带结构图和原子层分解态密度图 (a), (b)氧空位位于L$\overline {2} $原子层的情况; (c), (d)氧空位位于L7原子层的情况; 粗线标记能带为氧空位的缺陷能级, 计算结果基于$U_{\text{O}}^{2{\text{p}}}$ = 14 eV的GGA+U方法, 费米能级设为零点
Figure 5. Energy band structure and partial density of states projected onto atomic planes of (HfO2)7/(SnO2)13 heterostructure with oxygen vacancy: (a), (b) The cases for oxygen vacancy on the L$\overline {2} $ layer; (c), (d) the cases for oxygen vacancy on the L7 layer. The band marked by bold line are the defective energy levels of the oxygen vacancy. The calculation results are based on the GGA+U method of $U_{\text{O}}^{{\text{2p}}}$ = 14 eV, and the Fermi level is set as zero.
图 6 表面吸附H原子的(HfO2)7/(SnO2)13异质结的电子结构(费米能级设为零点) (a)能带结构图, 方形点线标记能带来源于表面处电子, 圆圈标记能带来自界面处电子; (b)原子层分解态密度图
Figure 6. Electronic structure of (HfO2)7/(SnO2)13 heterostructure adsorbed H atoms on the surface. (a) The energy band structure. The band marked by the square dots originates from the surface electrons, and the band marked by the circles comes from electrons at interface. (b) The partial density of states projected onto atomic planes. The Fermi level is set as zero.
图 7 表面吸附H原子 $ {\left( {{\text{Hf}}{{\text{O}}_2}} \right)_l}/{\left( {{\text{Sn}}{{\text{O}}_2}} \right)_{13}} $(l = 7, 8, 9, 10)异质结界面附近的电子浓度
Figure 7. Electron density near the interface of $ {\left( {{\text{Hf}}{{\text{O}}_2}} \right)_l}/{\left( {{\text{Sn}}{{\text{O}}_2}} \right)_{13}} $ (l = 7, 8, 9, 10) heterostructures adsorbed H atoms on the HfO2 surface.
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