摘要
氧化锌(ZnO)具有如下三大优点:首先,它是半导体材料,具有较宽的带隙(3.37 eV)和较大的激子结合能(60 meV),它是一种重要的功能氧化物,具有良好的近紫外散射和透明传导性能;其次,ZnO因其非中心对称的晶体结构而具有压电性,这是其用于机电耦合的传感器和转换器中应具备的关键特性;最后,ZnO具有良好的生物适应性,可以直接应用于生物医学领域而无需被覆。正因为这三大特点,ZnO很有可能在将来的研究和应用中成为最重要的纳米材料之一。本文应用基于第一原理的密度泛函理论,对ZnO尤其是其低维纳米结构的压电性能、弹性性能、结构特性、能量特性等基态性能进行了系统地计算分析,主要包括以下内容:
(1)二维ZnO纳米薄膜的压电性能研究。通过基于密度泛函理论的Berry相极化计算方法,对ZnO纳米薄膜的压电性能的尺寸效应进行了计算和分析。研究发现,对于二维ZnO纳米薄膜,随着厚度的增加,其等效压电系数单调地增加。当其厚度达到10个Zn-O双层(约2.4 nm)时,其等效压电系数已开始超过体块值3%左右。当薄膜的厚度继续增加至12个Zn-O双层(约2.9 nm)时,其等效压电系数可超过体块值11%以上。这是因为在低维纳米结构中,量子受限效应凸显作用,对于本文研究的最大厚度仅有几个纳米的薄膜来说,电子被强烈地限制在薄膜以内。这时,随着厚度的增加,存在于Zn-O双层间的自发极化将不断地累加,从而导致结构达到一定厚度时,其极化变化率(即压电系数)超过了体块的值。然而随着厚度继续增加,量子受限效应逐渐减弱,此时,纳米薄膜的等效压电系数将随着表面效应的减弱逐渐趋向体块的值。此外,我们的理论结果与实验中发现的ZnO纳米带沿同一方向的压电系数超出体块值的结果相吻合。
(2)一维ZnO纳米线的压电性能研究。通过密度泛函理论计算对不同直径(0.4 nm～3.0 nm)的沿[0001]方向生长的一维ZnO纳米线的压电性能进行了研究。研究发现,ZnO纳米线的等效压电系数随着直径的增加而增大,但至少在本文计算能力所能达到的范围内数值上要远低于相应的体块值。分析表明,ZnO纳米线内部的结构重构以及不可避免的量子受限效应是这种尺寸效应存在的主要原因。电子结构计算得到ZnO纳米线的能带隙随着直径的增加从2.8下降到1.1 eV。
(3)二维ZnO纳米薄膜和一维ZnO纳米线的弹性系数计算。通过计算分析ZnO二维纳米薄膜和一维纳米线的等效弹性系数,发现它们在有限尺寸范围内均具有明显的尺寸效应。对于厚度小于6个Zn-O双层的ZnO纳米薄膜,其等效弹性系数远小于相应的体块值,而当薄膜厚度继续增大,其等效弹性系数逐渐趋近于体块值,且基本不再变化。对于沿[0001]方向生长的ZnO纳米线,其相应的等效弹性系数在直径非常小时也远低于体块值,而随着纳米线的直径逐渐增大,其等效弹性系数基本呈线性地接近体块值。由于计算量太大,我们研究的最大直径的ZnO纳米线直径仅为约2.4 nm,其等效弹性系数达到体块值的88%。低维纳米结构中大的表面/体积比率值是造成这种尺寸效应的主要原因。在论文成文时这部分工作仍在继续中。
(4)零维ZnO纳米团簇的结构和特殊物性研究。通过对六棱柱形ZnO零维纳米团簇的结构优化和能级分析,发现结构弛豫使Zn原子朝团簇中心运动,而O原子则朝相反的方向移动,这对确定实验中何时施加使结构中悬键钝化的表面活性剂是十分重要的,因为往往它们会与O原子优先成键。此外,我们还发现一种由48个原子构成的ZnO团簇在结构优化后发生了由四配位的纤维锌矿结构到六配位的岩盐结构的相变,这表明为保证直接从体块结构中分割出的团簇结构的稳定性,应使其含有尽可能少的悬键。
(5)II-VI族半导体材料的电光张量计算。应用密度泛函微扰理论对具有纤维锌矿和闪锌矿结构的II-VI族半导体化合物分别进行了电光系数的计算。并得到了ZnO在不同应变下的电光张量和非线性光学系数。结果表明,在具有纤维锌矿的II-VI族化合物中,ZnO明显具有最高的弹性系数和压电系数,以及最大的电光系数。具有闪锌矿结构的II-VI族化合物的压电系数明显低于纤维锌矿结构约一个数量级。ZnO的电光系数和非线性光学系数的绝对值均随着应变的增加而几乎线性地减小,应变由-1%增加到1%,其电光系数减小了约9.5%,非线性光学系数相应的减小幅度约为8.2%。
Zinc oxide (ZnO) has three key advantages. First, it is a semiconductor, with a direct wide band gap of 3.37 eV and a large exciton binding energy (60 meV). It is an important functional oxide, exhibiting near-ultraviolet emission and transparent conductivity. Secondly, because of its noncentral symmetry, ZnO is piezoelectric, which is a key property in building electromechanical coupled sensors and transducers. Finally, ZnO is bio-safe and biocompatible, and can be used for biomedical applications without coating. With these three unique characteristics, ZnO could be one of the most important nanomaterials in future research and applications. In this thesis, first-principles density-functional theory (DFT) calculations are systematically performed to study the various ground-state properties, such as piezoelectric properties, elastic properties, structural features, energy properties, etc., of ZnO and especially its nanostructures. The main contents are listed below:
(1) Study on Piezoelectricity of two-dimensional ZnO nanofilms. Size-dependent piezoelectricity of ZnO nanofilms is calculated and analyzed by using DFT based Berry phase polarization computational method. It is found that the effective piezoelectric constant of the ZnO nanofilms increases with increasing thickness, and becomes higher than that of bulk ZnO when the number of Zn-O double layers increases to 10 (2.4 nm in thickness). And the piezoelectric response can be 11% higher than the bulk value when the number of the Zn-O double layers is increased to 12. Because the quantum confinement effect is raised in the low-dimensional nanostructures, for the nanofilms of several nanometers in thickness, the electrons are strongly confined within the slab. The spontaneous polarizations existing between the Zn-O double layers will be accumulated with the increasing film thickness, which may result in higher change rates of polarizations for very thin nanofilms. However, with the film thickness continually increasing, after a possible critical point, the accumulation will not dominate the piezoelectric property. Then the surface effect will trail off, and the piezoelectric constant will approach to the bulk value. In addition, our result coincides with the experimental result that the effective piezoelectric coefficient of ZnO nanobelt with the (0001) top surface could be higher than that of the bulk ZnO.
(2) Study on Piezoelectricity of one-dimensional ZnO nanowires. Size-dependent piezoelectricity in [0001]-oriented ZnO nanowires (0.4~3.0 nm in diameter) is investigated using DFT calculations. The effective piezoelectric constant of ZnO nanowires is found to increase with increasing diameter, but the values are much smaller than that of bulk ZnO, at least in the limited size studied in the present calculations. Both the structure reconstruction and quantum confinement in ZnO nanowire are considered to be the main contributions to this size effect. Energy bands calculations show that with increasing diameter, the band gap of the ZnO nanowires decreases from 2.8 to 1.1 eV.
(3) Calculations on the elastic constants of 2D ZnO nanofilms and 1D ZnO nanowires. The effective elastic constants of ZnO nanofilms and nanowires are calculated and analyzed. Obvious size effects are also found in the limited sizes for both the two cases. For the nanofilms with less than 6 Zn-O double layers, their effective elastic constants are much lower than the corresponding bulk value. While the film thickness continues increasing, the obtained result becomes almost invariable and approaches to the bulk value. For the [0001]-oriented ZnO nanowires, their corresponding effective elastic constants are also much lower than the bulk value when the diameter is very small. However, with increasing diameter, the elastic constant increases almost linearly to approach the bulk value. In our limited computational scale, the obtained effective elastic constant of the nanowires increases to around 88% of the corresponding bulk value when the diameter is about 2.4 nm. This size effect is mainly due to the increased surface/volume ratio in nanoscale. This work is still ongoing when completing the present thesis.
(4) Study on the structures and properties of zero-dimensional ZnO nanoclusters. Through structural optimizations and energy levels analysis on zero-dimensional ZnO nanoclusters with hexagonal prism configurations, we found that the structural relaxations led to zinc atoms moving toward the center of the cluster, whereas oxygen atoms moving outward. This is important to know when attempting to passivate dangling bonds at the surfaces with surfactants, since they will then be bonded first of all to oxygen atoms. In addition, the shape-driven phase transition from the four-coordinate wurtzite to the six-coordinate rocksalt structure is found in a ZnO cluster with 48 atoms, which implies that cutting out a stoichiometric cluster with more favorable structure, the dangling bonds should be as few as possible.
(5) Calculations on electro-optic tensors of II-VI semiconducting materials. The electro-optic coefficients of the II-VI semiconducting compounds with wurtzite and zinc-blende structures are calculated by using DFT perturbation theory. Especially, the electro-optic tensors and the nonlinear optical constants of ZnO with different strains are also obtained. It is shown that among the II-VI compounds ZnO has the highest elastic constant, piezoelectric constant, and electro-optic coefficient. The piezoelectric constants of the II-VI compounds with zinc-blende structure are almost one order smaller than that of the materials with wurtzite structure. With increasing strains from -1% to 1%, both the electro-optic coefficient and the absolute value of the nonlinear optical constant of ZnO decrease almost linearly by 9.5% and 8.2%, respectively.
引文
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