量子点结构与微波烧结粉体ZnO的数值模拟研究
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摘要
这篇论文“量子点结构与微波烧结粉体ZnO的数值模拟研究”,主要是利用Matlab数值软件编程实现了量子点电子结构的数值求解,模拟结果与相关文献进行对比分析,论证了模型与程序的合理有效性,并结合与量子点性质相关的公式推导进一步给出了应用实例,这里涉及讨论的模型包含金字塔型单量子点结构,垂直对准和水平耦合双量子点系统,引入浸润层,周期型量子阱中点结构等,同时对一些算法也提出了改进与推广。另外,论文还涉及研究了微波烧结主题,通过使用Comsol软件的微波加热模块,实现了三维模拟研究微波炉烧结粉体ZnO过程,并计入保温层的热交互作用,分析讨论了ZnO的电磁场及温场在烧结过程中变化。全文主要由五个部分组成,对应的研究内容以及结论如下：
1、由于半导体导带具有非抛物性,导致导带电子有效质量与势能相关,通过有限差分格式离散的薛定谔方程并使用通分数值运算,获得了五阶多项式矩阵,为了求解多项式矩阵,我们提出了一个简单的本征能扫描技术,通过数学理论推导以及数值运算验证了该技术的有效性和实用性,同时说明其可扩展应用到求解任意阶多项式矩阵的本征值,利用该方法我们拟在能带非抛物性框架下研究孤立量子点以及垂直对准双量子点系统,通过改变量子点的体积以及双量子点系统的耦合距离等条件,获得了丰富的电子态信息。
2、利用有限差分法离散求解导带电子的薛定谔方程并证明可有效用于研究真实三维量子阱中点结构,通过有限元格式来自动集成跳跃的界面条件而不是显式强迫赋值,并通过改变边界条件的方法,分别实现了模拟孤立型以及周期阵列型的量子点结构,结合光学跃迁分析讨论了获得的相关本征能谱。
3、由于量子点生长技术的不断成熟,当前工业以及实验室已经能设计并生长出如将量子点嵌入量子阱中,双量子点耦合等多种量子点结构,我们以金字塔型量子点为基准并计入浸润层来模拟并讨论相关量子点系统的电子能态信息,处于实空间有效的常数单带电子包络函数法被应用,其优势不仅在于可模拟任意形状与结构的量子点,而且通过简单的三角积分,我们可以获得近似解析结果,从而在适中的运算成本下保证了运算结果的精确度。
4、利用倒易空间的电子包络函数平面波展开法来求解薛定谔方程,模拟并对比了周期势场中嵌入量子阱中不同形状的量子点的电子本征能谱,计算了对应结构的应变情况,并通过假定均匀扩散以及应力平均分布,在傅立叶空间中引入的菲克定律,以减弱因子形式集成到运算中来模拟退火后处理技术导致的互扩散影响,计算了处于不同电场下的导带电子能级变化,讨论了阱中点结构的压电势,初步推导了局域场作用公式,最后分析计算不同掺杂浓度和铟组分对该系统的光学吸收谱的影响。
5、以ZnO粉体材料为基础,利用Comsol软件根据微波加热初始电场分布确定了ZnO粉体以及波导入口的位置等相关参数值,数值模拟了微波烧结粉体过程中模拟区域的温场变化,通过对比单源与双源微波加热情况,说明了相同功率下应用双源加热更有效,首次模拟了在多孔氧化铝保温层条件下双源微波加热ZnO粉体过程,对比分析了保温层存在与否粉体的相关区域中心同边界点的升温特点,并呈现了微波加热过程保温层的影响。
The dissertation "Numerical simulation of quantum dots'structures and microwave sintering ZnO powder", mainly achieving the numerical solving the electronic structures of quangtum dots by programming with the help of Matlab software. Based on comparing and analyzing the results obtained with other literatures, both the programs and models are reasonable and effective, then combining with the formulas derived which corresponding to the properties of quantum dots, some application examples are shown. These models above include pyramidal pure quantum dot, vertically aligned or/and horizontal coupling quantum dots, the introduced wetting layer, periodical quantum dots-in-a-well and so on. Some algorithms are improved and developed. In addition, the theme of microwave sintering is also studied in this paper, using the Comsol software, realizing the3D simulation of the process of microwave sintering the powder ZnO in furnace, taking the heating exchanging effect from the insulation layer and sintering atmosphere into account, we analyze and discuss the changes of electromagnetic and temperature field during the sintering period. The full text mainly consists of five parts, the corresponding research contents and conclusions are as follows:
1, As the result of the conduction band non-parabolicity of the semiconductor, the conduction band electronic effective mass is related to the potential energy, discretizing the Schrodinger equation in the finite difference scheme, numerical computation using the common denominator, a fifth-order polynomial matrix is obtained. In order to solve the polynomial matrix, we propose a simple eigen energy scanning technology, based on the mathematics analysis and numerical computing, the effectiveness and practicality of the method is proven, and it can be extended to get the eigenvalues of the arbitrary polynomial matrix. Using this method, under the framework of band non-parabolicity, the isolated dot and the vertical aligned quantum dots system are studied, by changing the size of the quantum dot or/and the coupling distance in the quantum dots system and other conditions, access to a wealth of information on electronic states.
2, Using the finite difference method, the Schrodinger equation of the electronic conduction band is solved, and it is demonstrated effective for studying the true3D quantum dots-in-a-well structure, based on the finite difference methods having a wide range industrial application of simulation and its finite element format which can be automatically integrated the jump interface condition without the need to explicitly adding to, by changing the boundary conditions, we can calculate isolated and periodic arrayed quantum dots structure, respectively, due to the optical transition, the corresponding eigen-energy spectrum is discussed.
3, Thanks to the mature technology of the growth of quantum dots, the current industrial and laboratory has been able to design and grow out of such as quantum dots embedded quantum wells, the coupled double quantum dots'structure and so on. Based on the pyramidal quantum dots and taking the wetting layer into account, we simulate and analyze the electronic information of the corresponding quantum dots' system. A constant single-band electronic envelope function method is applied, its advantage lies not only can simulate arbitrary shape and structure of quantum dots, but also can obtain analysis results by a simple triangular integration, then at a moderate cost to guarantee the accuracy of the calculating results.
4, The electronic envelope function plane wave expansion method is applied to solve the Schrodinger equation in the reciprocal space, simulating and comparing the electronic eigen spectrum from the quantum dots with different shapes (which embedded in quantum well under the periodic potential field, then the distribution of strain in the quantum structure is calculated diffusion. If assuming evenly distributing stress and uniform diffusion, by introducing Fick's law in the Fourier space, in order to weaken the form factor integrated into the computations of simulating annealing post-processing which resulting in the interdiffusion, the electric field effect on electronic energy levels is studied in different electric field and the piezoelectric potential of the quantum dots is discussed, the local field effect formula is preliminarily derived, then analyzing the impact of different doping density and In concentration on the optical obsorption.
5, We simulates the changes of temperature field (TF) in ZnO powder during the process of microwave sintering. According to the distribution of the electric field (EF) at the initial microwave heating, some parameters of the locations of ZnO powder and the ports of waveguides are fixed. By comparing with the single-source (SS) heating, the application of dual-source (DS) heating with the same power is demonstrated more effective. For the first time to simulate the process of DS microwave heating ZnO powder with the porous alumina insulation layer, and by the way of the comparative analysis of the heating characteristics of the powder's center and boundary points with and without the insulation layer, the effect of the insulation is shown.
1、由于半导体导带具有非抛物性,导致导带电子有效质量与势能相关,通过有限差分格式离散的薛定谔方程并使用通分数值运算,获得了五阶多项式矩阵,为了求解多项式矩阵,我们提出了一个简单的本征能扫描技术,通过数学理论推导以及数值运算验证了该技术的有效性和实用性,同时说明其可扩展应用到求解任意阶多项式矩阵的本征值,利用该方法我们拟在能带非抛物性框架下研究孤立量子点以及垂直对准双量子点系统,通过改变量子点的体积以及双量子点系统的耦合距离等条件,获得了丰富的电子态信息。
2、利用有限差分法离散求解导带电子的薛定谔方程并证明可有效用于研究真实三维量子阱中点结构,通过有限元格式来自动集成跳跃的界面条件而不是显式强迫赋值,并通过改变边界条件的方法,分别实现了模拟孤立型以及周期阵列型的量子点结构,结合光学跃迁分析讨论了获得的相关本征能谱。
3、由于量子点生长技术的不断成熟,当前工业以及实验室已经能设计并生长出如将量子点嵌入量子阱中,双量子点耦合等多种量子点结构,我们以金字塔型量子点为基准并计入浸润层来模拟并讨论相关量子点系统的电子能态信息,处于实空间有效的常数单带电子包络函数法被应用,其优势不仅在于可模拟任意形状与结构的量子点,而且通过简单的三角积分,我们可以获得近似解析结果,从而在适中的运算成本下保证了运算结果的精确度。
4、利用倒易空间的电子包络函数平面波展开法来求解薛定谔方程,模拟并对比了周期势场中嵌入量子阱中不同形状的量子点的电子本征能谱,计算了对应结构的应变情况,并通过假定均匀扩散以及应力平均分布,在傅立叶空间中引入的菲克定律,以减弱因子形式集成到运算中来模拟退火后处理技术导致的互扩散影响,计算了处于不同电场下的导带电子能级变化,讨论了阱中点结构的压电势,初步推导了局域场作用公式,最后分析计算不同掺杂浓度和铟组分对该系统的光学吸收谱的影响。
5、以ZnO粉体材料为基础,利用Comsol软件根据微波加热初始电场分布确定了ZnO粉体以及波导入口的位置等相关参数值,数值模拟了微波烧结粉体过程中模拟区域的温场变化,通过对比单源与双源微波加热情况,说明了相同功率下应用双源加热更有效,首次模拟了在多孔氧化铝保温层条件下双源微波加热ZnO粉体过程,对比分析了保温层存在与否粉体的相关区域中心同边界点的升温特点,并呈现了微波加热过程保温层的影响。
The dissertation "Numerical simulation of quantum dots'structures and microwave sintering ZnO powder", mainly achieving the numerical solving the electronic structures of quangtum dots by programming with the help of Matlab software. Based on comparing and analyzing the results obtained with other literatures, both the programs and models are reasonable and effective, then combining with the formulas derived which corresponding to the properties of quantum dots, some application examples are shown. These models above include pyramidal pure quantum dot, vertically aligned or/and horizontal coupling quantum dots, the introduced wetting layer, periodical quantum dots-in-a-well and so on. Some algorithms are improved and developed. In addition, the theme of microwave sintering is also studied in this paper, using the Comsol software, realizing the3D simulation of the process of microwave sintering the powder ZnO in furnace, taking the heating exchanging effect from the insulation layer and sintering atmosphere into account, we analyze and discuss the changes of electromagnetic and temperature field during the sintering period. The full text mainly consists of five parts, the corresponding research contents and conclusions are as follows:
1, As the result of the conduction band non-parabolicity of the semiconductor, the conduction band electronic effective mass is related to the potential energy, discretizing the Schrodinger equation in the finite difference scheme, numerical computation using the common denominator, a fifth-order polynomial matrix is obtained. In order to solve the polynomial matrix, we propose a simple eigen energy scanning technology, based on the mathematics analysis and numerical computing, the effectiveness and practicality of the method is proven, and it can be extended to get the eigenvalues of the arbitrary polynomial matrix. Using this method, under the framework of band non-parabolicity, the isolated dot and the vertical aligned quantum dots system are studied, by changing the size of the quantum dot or/and the coupling distance in the quantum dots system and other conditions, access to a wealth of information on electronic states.
2, Using the finite difference method, the Schrodinger equation of the electronic conduction band is solved, and it is demonstrated effective for studying the true3D quantum dots-in-a-well structure, based on the finite difference methods having a wide range industrial application of simulation and its finite element format which can be automatically integrated the jump interface condition without the need to explicitly adding to, by changing the boundary conditions, we can calculate isolated and periodic arrayed quantum dots structure, respectively, due to the optical transition, the corresponding eigen-energy spectrum is discussed.
3, Thanks to the mature technology of the growth of quantum dots, the current industrial and laboratory has been able to design and grow out of such as quantum dots embedded quantum wells, the coupled double quantum dots'structure and so on. Based on the pyramidal quantum dots and taking the wetting layer into account, we simulate and analyze the electronic information of the corresponding quantum dots' system. A constant single-band electronic envelope function method is applied, its advantage lies not only can simulate arbitrary shape and structure of quantum dots, but also can obtain analysis results by a simple triangular integration, then at a moderate cost to guarantee the accuracy of the calculating results.
4, The electronic envelope function plane wave expansion method is applied to solve the Schrodinger equation in the reciprocal space, simulating and comparing the electronic eigen spectrum from the quantum dots with different shapes (which embedded in quantum well under the periodic potential field, then the distribution of strain in the quantum structure is calculated diffusion. If assuming evenly distributing stress and uniform diffusion, by introducing Fick's law in the Fourier space, in order to weaken the form factor integrated into the computations of simulating annealing post-processing which resulting in the interdiffusion, the electric field effect on electronic energy levels is studied in different electric field and the piezoelectric potential of the quantum dots is discussed, the local field effect formula is preliminarily derived, then analyzing the impact of different doping density and In concentration on the optical obsorption.
5, We simulates the changes of temperature field (TF) in ZnO powder during the process of microwave sintering. According to the distribution of the electric field (EF) at the initial microwave heating, some parameters of the locations of ZnO powder and the ports of waveguides are fixed. By comparing with the single-source (SS) heating, the application of dual-source (DS) heating with the same power is demonstrated more effective. For the first time to simulate the process of DS microwave heating ZnO powder with the porous alumina insulation layer, and by the way of the comparative analysis of the heating characteristics of the powder's center and boundary points with and without the insulation layer, the effect of the insulation is shown.
引文
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