低维半导体量子结构中氢施主杂质电子态的研究
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摘要
随着半导体纳米技术的发展，人们可以制备出各种类型和形状的二维量子阱、一维量子线、零维量子点等低维量子结构。由于低维纳米结构材料与块体材料相比因其独特的光、电特性，使得低维半导体器件和功能材料在光通信等诸多领域都具有潜在的应用前景。
本文在有效质量包络函数近似下采用变分法研究了低维半导体纳米结构中的电子态，主要研究内容如下：
1.简单地介绍了低维半导体材料的有关概念和低维半导体的主要类型,给出了几种具体的低维半导体材料的外延生长方法，列举了几种可应用于光通信中的半导体器件。
2.在有效质量包络函数近似下，我们用变分法研究了对称双量子阱GaN/Al x Ga1-xN异质结构中氢施主杂质的基态束缚能，计算结果表明，当双量子阱中间势垒宽度一定时，随着阱宽的增大束缚能先是逐渐增大直到达到一个极大值，然后开始逐渐减小。在量子阱宽度一定时，随着中间垒宽度的增加束缚能逐渐减小，并在中间势垒宽度增加到一定宽度时双量子阱情况与单量子阱情况相似，束缚能不再发生明显变化。与此同时，我们研究了加入电场后异质结构的电子态。加入电场后异质结构导带势能发生了明显的倾斜。由于导带势能的变化从而影响了异质结构其他性质的变化。
3.研究了有无外加电场时对称双量子线异质结构中Gax In1xAs/Ga0.20In0.80As0.44P0.56氢施主杂质的电子态。结果表明，加入电场后双量子线导带势能发生了明显的变化。为了更好地了解该异质结构的性质，分别计算了加入电场和未加电场两种情况下束缚能和波函数随施主位置变化的关系，同时还研究了量子线中间势垒层宽度一定时束缚能随量子线直径变化关系以及量子线直径一定时束缚能随量子线势垒宽度的变化关系。当量子线直径为定值其势垒宽度达到一定值时，束缚能发生明显的变化，这是因为当量子线势垒宽度足够大时，双量子线之间的耦合作用较小，从而其性质类似于单个量子线。最后，研究了在量子结构一定时加入不同电场强度时施主杂质分别在左量子线中心、中间势垒中心、右量子线中心时束缚能的变化。
4.我们在有效质量包络函数近似下用变分法研究了Gax In1xAs/Ga0.20In0.80As0.44P0.56量子点中类氢施主杂质的电子态。随着施主位置的变化束缚能关于异质结构中心对称，先增大并在达到一个峰值时开始减小。计算出了杂质的基态束缚能以及杂质的前四个能级，发现杂质的能级随着量子点直径的增加而减小。类氢施主杂质的位置和量子点尺寸对束缚能都有较为明显的影响。其中，氢施主杂质的束缚能不是量子点直径的单调函数，而是先增加至一最大值后开始逐渐减小。
With the development of the semi-conductive nano-technology, it is possible to fabricatevarious kinds of two-dimensional quantum well (QW), one-dimensional quantum well wire(QWW), zero-dimensional quantum dot (QD). Low-dimensional semiconductor materials havesparked a worldwide interest due to their unique optical, electronical properties and theirpotential applications in optical communication, semiconductor device and functional materials.
In this paper, under the effectives-mass envelope-function theory, the electron states ofhydrogenic donor impurity in low-dimension semiconductor structures are studied using thevariational method. The main contents are presented as following:
1. The concept and the main kinds of the low-dimension semiconductor are given briefly. Theepitaxy growth methods of low-dimension materials are introduced systematically. The specificsemiconductor device which is applied in optical communication is discussed.
2. Under the effectives-mass envelope-function theory, the binding energy of the system inGaN/Alx Ga1xNsymmetric double quantum wells are theoretically calculated using thevariational method. The calculation results indicate that with the fixed the middle barrier ofdouble quantum wells, the binding energy increases until it reaches a maximum value, and thendecreases as the well width increases. When the well width of the system is a fixed value, thebinding energy decreases gradually with the width of the middle barrier increasing, and theproperties of the double quantum well is similar to the single quantum well when the width ofmiddle barrier reaches to a fixed value, the biding energy changes not significantly. Meanwhile,we study the electron state of the heterostructure which is applied in external electric field. Thepotential energy of conduct band changes obviously when the heterostructure is applied inexternal electric field. And then the properties of the heterostructure change significantly also.
3. The influence of applied external electric fields on the hydrogenic donor impurity inGax In1xAs/Ga0.20In0.80As0.44P0.56quantum wire structures is studied. The results indicate thatthe potential energy of conduct band changes significantly with applied external electric filed. Inorder to know more about the properties of the heterostructure, the binding energy and the wavefunctions with the donor in the different position are presented without and with external electricfield. The binding energy increases until it reaches a maximum value, and then decreases as theradius of quantum wire increases. Variations of donor binding energy with the quantum wire ofcentre barrier width are also calculated. When the donor is in the central of the second quantumwire with the width of quantum wire barrier reaches to a fixed value, we find the binding energy changes obviously. This is because the properties of the double quantum wires is similar to asingle quantum wire when the width of the middle quantum wire barrier is wide enough. Lastly,we study the binding energy with applied different external electric field and the donor indifferent position.
4. With the same method, we study the hydrogenic donor impurity electric state in quantumdot. We calculated the binding energy and the first four energy levels. We found that the bindingenergy is symmetric for the heterostructure. It increases until reaches to a maximum value withthe donor position, and then decreases. The binding energy of each four energy level is decreasewith the quantum dot diameter increasing. The donor position and the quantum dot dimensioncan affect the binding energy. And the binding energy is non-monotonic function of the donorposition. The binding energy is increasing until it reaches a maximum value and then decreasing.
本文在有效质量包络函数近似下采用变分法研究了低维半导体纳米结构中的电子态，主要研究内容如下：
1.简单地介绍了低维半导体材料的有关概念和低维半导体的主要类型,给出了几种具体的低维半导体材料的外延生长方法，列举了几种可应用于光通信中的半导体器件。
2.在有效质量包络函数近似下，我们用变分法研究了对称双量子阱GaN/Al x Ga1-xN异质结构中氢施主杂质的基态束缚能，计算结果表明，当双量子阱中间势垒宽度一定时，随着阱宽的增大束缚能先是逐渐增大直到达到一个极大值，然后开始逐渐减小。在量子阱宽度一定时，随着中间垒宽度的增加束缚能逐渐减小，并在中间势垒宽度增加到一定宽度时双量子阱情况与单量子阱情况相似，束缚能不再发生明显变化。与此同时，我们研究了加入电场后异质结构的电子态。加入电场后异质结构导带势能发生了明显的倾斜。由于导带势能的变化从而影响了异质结构其他性质的变化。
3.研究了有无外加电场时对称双量子线异质结构中Gax In1xAs/Ga0.20In0.80As0.44P0.56氢施主杂质的电子态。结果表明，加入电场后双量子线导带势能发生了明显的变化。为了更好地了解该异质结构的性质，分别计算了加入电场和未加电场两种情况下束缚能和波函数随施主位置变化的关系，同时还研究了量子线中间势垒层宽度一定时束缚能随量子线直径变化关系以及量子线直径一定时束缚能随量子线势垒宽度的变化关系。当量子线直径为定值其势垒宽度达到一定值时，束缚能发生明显的变化，这是因为当量子线势垒宽度足够大时，双量子线之间的耦合作用较小，从而其性质类似于单个量子线。最后，研究了在量子结构一定时加入不同电场强度时施主杂质分别在左量子线中心、中间势垒中心、右量子线中心时束缚能的变化。
4.我们在有效质量包络函数近似下用变分法研究了Gax In1xAs/Ga0.20In0.80As0.44P0.56量子点中类氢施主杂质的电子态。随着施主位置的变化束缚能关于异质结构中心对称，先增大并在达到一个峰值时开始减小。计算出了杂质的基态束缚能以及杂质的前四个能级，发现杂质的能级随着量子点直径的增加而减小。类氢施主杂质的位置和量子点尺寸对束缚能都有较为明显的影响。其中，氢施主杂质的束缚能不是量子点直径的单调函数，而是先增加至一最大值后开始逐渐减小。
With the development of the semi-conductive nano-technology, it is possible to fabricatevarious kinds of two-dimensional quantum well (QW), one-dimensional quantum well wire(QWW), zero-dimensional quantum dot (QD). Low-dimensional semiconductor materials havesparked a worldwide interest due to their unique optical, electronical properties and theirpotential applications in optical communication, semiconductor device and functional materials.
In this paper, under the effectives-mass envelope-function theory, the electron states ofhydrogenic donor impurity in low-dimension semiconductor structures are studied using thevariational method. The main contents are presented as following:
1. The concept and the main kinds of the low-dimension semiconductor are given briefly. Theepitaxy growth methods of low-dimension materials are introduced systematically. The specificsemiconductor device which is applied in optical communication is discussed.
2. Under the effectives-mass envelope-function theory, the binding energy of the system inGaN/Alx Ga1xNsymmetric double quantum wells are theoretically calculated using thevariational method. The calculation results indicate that with the fixed the middle barrier ofdouble quantum wells, the binding energy increases until it reaches a maximum value, and thendecreases as the well width increases. When the well width of the system is a fixed value, thebinding energy decreases gradually with the width of the middle barrier increasing, and theproperties of the double quantum well is similar to the single quantum well when the width ofmiddle barrier reaches to a fixed value, the biding energy changes not significantly. Meanwhile,we study the electron state of the heterostructure which is applied in external electric field. Thepotential energy of conduct band changes obviously when the heterostructure is applied inexternal electric field. And then the properties of the heterostructure change significantly also.
3. The influence of applied external electric fields on the hydrogenic donor impurity inGax In1xAs/Ga0.20In0.80As0.44P0.56quantum wire structures is studied. The results indicate thatthe potential energy of conduct band changes significantly with applied external electric filed. Inorder to know more about the properties of the heterostructure, the binding energy and the wavefunctions with the donor in the different position are presented without and with external electricfield. The binding energy increases until it reaches a maximum value, and then decreases as theradius of quantum wire increases. Variations of donor binding energy with the quantum wire ofcentre barrier width are also calculated. When the donor is in the central of the second quantumwire with the width of quantum wire barrier reaches to a fixed value, we find the binding energy changes obviously. This is because the properties of the double quantum wires is similar to asingle quantum wire when the width of the middle quantum wire barrier is wide enough. Lastly,we study the binding energy with applied different external electric field and the donor indifferent position.
4. With the same method, we study the hydrogenic donor impurity electric state in quantumdot. We calculated the binding energy and the first four energy levels. We found that the bindingenergy is symmetric for the heterostructure. It increases until reaches to a maximum value withthe donor position, and then decreases. The binding energy of each four energy level is decreasewith the quantum dot diameter increasing. The donor position and the quantum dot dimensioncan affect the binding energy. And the binding energy is non-monotonic function of the donorposition. The binding energy is increasing until it reaches a maximum value and then decreasing.
引文
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[2]蔡开清.用于光纤通信的半导体发光二极管的结构及其性能[J].半导体光电，1985,02:33-34.
[3] A. R. Goodwin等.用于单模光纤通信线路中的高可靠性半导体激光器的设计与制造[J].纳米电子技术,1989,04:47-55.
[4]张瑞华.光纤通信用长波长半导体激光器的研究与进展[J].微纳电子技术,1983,04:14-24.
[5] KLAUS PETERMAN, GUNTHER ARNOLD,何兴仁,蒋涛.光纤通信系统中半导体激光器的噪声与失真特性[J].半导体光电,1982,04：44-56.
[6]张建立.光通信中基于半导体工艺的硅基光波导技术的研究[D].浙江：浙江大学信息学院,2005.
[7]卜晓兵.单个量子点的荧光光谱成像和散射成像[D].湖南:湖南大学,2009.
[8]冯华君,李晓彤.编著浙江大学出版社,2001,1月《信息物理基础》103页.
[9]薛华.间接带隙纳米半导体材料的量子限制理论[J].西北民族学院学报（自然科学版）,1998,19(1):403-106.
[10] T. P. Pearsall. GaInAsP Alloy Semiconductors[M]. New York: JOHN WILEY&SONS,1982.
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