无机纳米管的电、热学性能及掺杂效应
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摘要
为了更为深入地了解碳、氮化硼等无机纳米管的物理性能,我们研究了无机纳米管的电、热学性质以及掺杂效应,得到了一些有意义的结果。本论文首先对于无机纳米管的研究现状,包括结构形态、发现和制备、物理性能与应用前景进行了系统的评述。在此基础上,通过构建结构模型并选用合适的研究方法,如密度泛函理论、晶格动力学理论等研究了无机纳米管的电、声子结构、热学性质以及掺杂对物性的影响,探讨了单壁、多壁碳纳米管以及具有复合结构的双壁纳米管的掺杂效应,考察了物理性能与结构参数之间的关联特征,并研究了物理机理。本文的安排如下:
(1)第一章,阐述了无机纳米管的研究背景和历史,以及无机纳米管的典型结构,并对其物理性能和应用前景做了一个简要介绍。
(2)第二章,介绍了已广泛应用于计算碳纳米管的电子结构和声子结构的紧束缚方法和力常数模型。通过数值计算,给出了采用紧束缚方法计算的单壁碳纳米管的电子结构的主要特征。另外,简要介绍了我们发展的用于获得碳纳米管上两个原子之间的力常数矩阵的五步旋转方法,并给出了扶手椅型和锯齿型碳纳米管的声子结构以及振动模式密度。
(3)第三章,由于碳纳米管的卷曲效应,传统的紧束缚模型和力常数模型已经不能够直接用于小管径碳纳米管的电、声子结构的计算。对于电子结构,我们采用密度泛函理论计算了单壁碳纳米管的电子结构,重点探讨了卷曲效应对于电子结构的影响。结果表明,在大管径碳纳米管中卷曲效应对于电子结构的影响并不明显,紧束缚理论能够用来描述其电子特征。但是对于小管径碳纳米管,强的卷曲效应使得紧束缚理论的预测失效。此外,卷曲效应对于双壁碳纳米管的电子结构有较大影响,由于内管和外管之间的结构卷曲程度不同,费米面附近的电子态发生明显移动,导致半导体-半导体型双壁碳纳米管的能隙显著降低。此外,从单壁碳纳米管的卷曲能出发,推导了单壁碳纳米管原子间的径向力常数与石墨片的力常数以及卷曲程度之间的解析表达式,该表达式表明:当石墨片卷曲成单壁碳纳米管时,由于体系总能量和原子键长的改变,力常数将会发生改变。考虑卷曲效应,计算了管径为4?的单壁碳纳米管的径向呼吸模式,并与他人的计算结果做了比较,与实验结果符合较好。
(4)第四章,采用力常数模型,计算了氮化硼纳米管的声子结构。根据氮化硼纳米管的结构对称性,指认了Raman模式并研究了Raman模式的频率与管径之间的关系。计算了氮化硼纳米管的比热,提出了比热与管径和螺旋度之间的经验公式。基于Landauer理论,计算了单壁氮化硼纳米管的弹道热导系数,结果表明低温热输运呈现量子特征,热导系数随着管径的增加而升高。另外,通过计算多壁碳纳米管和单晶氮化镓纳米管的比热,分析了表面效应和量子尺寸效应对于比热的影响,在这两类纳米管中,量子尺寸效应和表面效应分别在各自的比热的尺寸变化中起着主导作用。基于三声子散射的微扰理论,计算了多壁碳纳米管和单壁碳纳米管管束的热导率,计算结果表明,单壁碳纳米管的热导率在相同管径下,螺旋型碳纳米管的热导率最低。另外,在强、弱耦合情况下,单壁碳纳米管管束和多壁碳纳米管的热导率明显不同于单根单壁碳纳米管,强的管间耦合作用能够极大地抑制了碳纳米管的热传导性能。
(5)第五章,选取适当的原子间相互作用势,计算了碱金属掺杂的单壁碳纳米管管束的声子结构和比热,探讨了高频模式频率随着掺杂浓度的变化关系,并发现由于钾原子振动模式在低频占主导地位引起低温比热偏离正常的变化关系。
(6)第六章,为了检验双壁纳米管是否具有类似于经典圆柱形电容器的电荷屏蔽行为,我们计算了钾掺杂双壁碳纳米管和碳-氮化硼纳米管的电子结构和电荷分布。对于大管径的双壁碳纳米管,电荷分布与经典的圆柱形电容器类似,电荷尽可能分布在外管。由于卷曲效应,在半导体-半导体和金属性-半导体性双壁碳纳米管中,钾掺杂使得小管径的内管带上了较多的电荷。如果外管是绝缘性的氮化硼纳米管,由于费米面附近的电子态主要属于碳纳米管,电荷将优先分布在内管。我们也探讨了钾、溴共掺杂对于单壁和双壁碳纳米管的性能的影响,在双壁碳纳米管中,共掺杂使得外管和内管带上正、负不同的电荷,使其可能在p-n结中得到应用。
(7)第七章,本论文的总结以及对于未来工作的展望。
In order to provide considerable insight into physical properties of inorganic nanotubes, such as carbon and boron nitride nanotubes, we studied electronic and thermal properties of inorganic nanotubes. A number of interesting results are obtained. In this dissertation, we first comment current situation of investigations for inorganic nanotubes, including their structures, discovery and synthesis, properties and application perspective. By virtue of suitable theoretical methods, such as density functional theory and lattice dynamics theory, we investigated phonon, electronic structures, thermal properties and the effect of doping on electronic structures. The single-walled, multi-walled carbon nanotubes and double-walled nanotube with different species were also studied. Especially, we discussed the structural dependence of physical properties and potential mechanism. My dissertation is organized as follows:
In Chapter 1, The history, background, structures, properties and application perspective were introduced.
Chapter 2 is devoted to the well-known tight-binding and force constant methods, which have been widely used in previous calculations. We calculated the electronic and phonon structures of single-walled carbon nanotubes. Moreover, we developed the five-step-rotation method, which can be used to derive the force constant matrix between two atoms in carbon nanotubes.
Chapter 3, Due to the curvature effect, the tight-binding and force constant methods mentioned above can not be directly used to calculate electronic and phonon structure of small diameter carbon nanotubes. Based on density functional theory, we perform systematic calculations of electronic structures of single-walled carbon nanotubes and discuss the effect of strong curvature on electronic structures. The results show that the variation of electronic structure due to curvature effect is small in large diameter nanotubes. However, strong curvature can invalidate the prediction of tight-binding theory. Because of the difference of structural curvature between inner and outer tubes, the shift of electronic states near the Fermi level occurs, leading to the pronounced decrease of band gap of semiconducting@semiconducting double-walled carbon nanotubes. Based on the curvature energy, we derived an analytical expression, which relates the radial force constant of nanotube to that of graphene and structural curvature. According to this expression, the nanotube force constants would be changed when the graphite sheet is rolled into carbon nanotube. This is due to the variation of total energy and bond length. Using the revised force constants, we calculated the radial breathing mode of 4? diameter carbon nanotubes. Our results are in good agreement with experimental observation and other theoretical calculations.
Chapter 4, Based on the force constant model, the phonon structures of boron nitride nanotubes and diameter dependence of Raman mode frequency are obtained. We calculate the specific heat of boron nitride nanotubes and present the fitting formulas for diameter and chirality dependence of specific heat. Using Landauer theory, we calculate thermal conductance of single-walled boron nitride nanotube. The results show that thermal conductance at low temperature is quantized and increases with the increasing diameter. We calculate specific heat of multi-walled carbon nanotubes and single-crystal GaN nanotube and find that the specific heat is dominated by quantized size effect and surface effect. From the perturbation theory of three-phonon scattering process, we calculate thermal conductivity of single-walled and multi-walled carbon nanotubes. Thermal conductivity of chiral nanotubes is smaller than that of achiral nanotubes when both have the same diameter. Thermal transport of carbon nanotube can be suppressed by strong intertube coupling, which may be arisen from the structural defects of samples.
Chapter 5, Using suitable interatomic interaction potential, we calculate the phonon structures and specific heat of single-walled carbon nanotube bundles doped with potassium. The frequency of high-frequency modes decreases linearly with the doping concentration. The low temperature specific heat deviates from the usual variation since the phonon modes of potassium dominate the low frequency phonon structures.
Chapter 6, We calculate the electronic structures and radial charge distribution of potassium doped double-walled carbon nanotubes and carbon-boron nitride nanotubes. For large diameter double-walled carbon nanotubes, most of transferred charges reside on the outer tube. Due to curvature effect, a part of transferred charges are distributed on inner tube of semiconducting-semiconducting and metal-semiconducting nanotubes. If the outer tube is boron nitride nanotube, the transferred charges prefer residing on the inner tube owing to the predominance of electronic bands of inner tubes. Moreover, we discuss the effect of co-doping on electronic properties in potassium and bromine doped double-walled carbon nanotubes.
Chapter 7, The summary and prospect are given in this chapter.
(1)第一章,阐述了无机纳米管的研究背景和历史,以及无机纳米管的典型结构,并对其物理性能和应用前景做了一个简要介绍。
(2)第二章,介绍了已广泛应用于计算碳纳米管的电子结构和声子结构的紧束缚方法和力常数模型。通过数值计算,给出了采用紧束缚方法计算的单壁碳纳米管的电子结构的主要特征。另外,简要介绍了我们发展的用于获得碳纳米管上两个原子之间的力常数矩阵的五步旋转方法,并给出了扶手椅型和锯齿型碳纳米管的声子结构以及振动模式密度。
(3)第三章,由于碳纳米管的卷曲效应,传统的紧束缚模型和力常数模型已经不能够直接用于小管径碳纳米管的电、声子结构的计算。对于电子结构,我们采用密度泛函理论计算了单壁碳纳米管的电子结构,重点探讨了卷曲效应对于电子结构的影响。结果表明,在大管径碳纳米管中卷曲效应对于电子结构的影响并不明显,紧束缚理论能够用来描述其电子特征。但是对于小管径碳纳米管,强的卷曲效应使得紧束缚理论的预测失效。此外,卷曲效应对于双壁碳纳米管的电子结构有较大影响,由于内管和外管之间的结构卷曲程度不同,费米面附近的电子态发生明显移动,导致半导体-半导体型双壁碳纳米管的能隙显著降低。此外,从单壁碳纳米管的卷曲能出发,推导了单壁碳纳米管原子间的径向力常数与石墨片的力常数以及卷曲程度之间的解析表达式,该表达式表明:当石墨片卷曲成单壁碳纳米管时,由于体系总能量和原子键长的改变,力常数将会发生改变。考虑卷曲效应,计算了管径为4?的单壁碳纳米管的径向呼吸模式,并与他人的计算结果做了比较,与实验结果符合较好。
(4)第四章,采用力常数模型,计算了氮化硼纳米管的声子结构。根据氮化硼纳米管的结构对称性,指认了Raman模式并研究了Raman模式的频率与管径之间的关系。计算了氮化硼纳米管的比热,提出了比热与管径和螺旋度之间的经验公式。基于Landauer理论,计算了单壁氮化硼纳米管的弹道热导系数,结果表明低温热输运呈现量子特征,热导系数随着管径的增加而升高。另外,通过计算多壁碳纳米管和单晶氮化镓纳米管的比热,分析了表面效应和量子尺寸效应对于比热的影响,在这两类纳米管中,量子尺寸效应和表面效应分别在各自的比热的尺寸变化中起着主导作用。基于三声子散射的微扰理论,计算了多壁碳纳米管和单壁碳纳米管管束的热导率,计算结果表明,单壁碳纳米管的热导率在相同管径下,螺旋型碳纳米管的热导率最低。另外,在强、弱耦合情况下,单壁碳纳米管管束和多壁碳纳米管的热导率明显不同于单根单壁碳纳米管,强的管间耦合作用能够极大地抑制了碳纳米管的热传导性能。
(5)第五章,选取适当的原子间相互作用势,计算了碱金属掺杂的单壁碳纳米管管束的声子结构和比热,探讨了高频模式频率随着掺杂浓度的变化关系,并发现由于钾原子振动模式在低频占主导地位引起低温比热偏离正常的变化关系。
(6)第六章,为了检验双壁纳米管是否具有类似于经典圆柱形电容器的电荷屏蔽行为,我们计算了钾掺杂双壁碳纳米管和碳-氮化硼纳米管的电子结构和电荷分布。对于大管径的双壁碳纳米管,电荷分布与经典的圆柱形电容器类似,电荷尽可能分布在外管。由于卷曲效应,在半导体-半导体和金属性-半导体性双壁碳纳米管中,钾掺杂使得小管径的内管带上了较多的电荷。如果外管是绝缘性的氮化硼纳米管,由于费米面附近的电子态主要属于碳纳米管,电荷将优先分布在内管。我们也探讨了钾、溴共掺杂对于单壁和双壁碳纳米管的性能的影响,在双壁碳纳米管中,共掺杂使得外管和内管带上正、负不同的电荷,使其可能在p-n结中得到应用。
(7)第七章,本论文的总结以及对于未来工作的展望。
In order to provide considerable insight into physical properties of inorganic nanotubes, such as carbon and boron nitride nanotubes, we studied electronic and thermal properties of inorganic nanotubes. A number of interesting results are obtained. In this dissertation, we first comment current situation of investigations for inorganic nanotubes, including their structures, discovery and synthesis, properties and application perspective. By virtue of suitable theoretical methods, such as density functional theory and lattice dynamics theory, we investigated phonon, electronic structures, thermal properties and the effect of doping on electronic structures. The single-walled, multi-walled carbon nanotubes and double-walled nanotube with different species were also studied. Especially, we discussed the structural dependence of physical properties and potential mechanism. My dissertation is organized as follows:
In Chapter 1, The history, background, structures, properties and application perspective were introduced.
Chapter 2 is devoted to the well-known tight-binding and force constant methods, which have been widely used in previous calculations. We calculated the electronic and phonon structures of single-walled carbon nanotubes. Moreover, we developed the five-step-rotation method, which can be used to derive the force constant matrix between two atoms in carbon nanotubes.
Chapter 3, Due to the curvature effect, the tight-binding and force constant methods mentioned above can not be directly used to calculate electronic and phonon structure of small diameter carbon nanotubes. Based on density functional theory, we perform systematic calculations of electronic structures of single-walled carbon nanotubes and discuss the effect of strong curvature on electronic structures. The results show that the variation of electronic structure due to curvature effect is small in large diameter nanotubes. However, strong curvature can invalidate the prediction of tight-binding theory. Because of the difference of structural curvature between inner and outer tubes, the shift of electronic states near the Fermi level occurs, leading to the pronounced decrease of band gap of semiconducting@semiconducting double-walled carbon nanotubes. Based on the curvature energy, we derived an analytical expression, which relates the radial force constant of nanotube to that of graphene and structural curvature. According to this expression, the nanotube force constants would be changed when the graphite sheet is rolled into carbon nanotube. This is due to the variation of total energy and bond length. Using the revised force constants, we calculated the radial breathing mode of 4? diameter carbon nanotubes. Our results are in good agreement with experimental observation and other theoretical calculations.
Chapter 4, Based on the force constant model, the phonon structures of boron nitride nanotubes and diameter dependence of Raman mode frequency are obtained. We calculate the specific heat of boron nitride nanotubes and present the fitting formulas for diameter and chirality dependence of specific heat. Using Landauer theory, we calculate thermal conductance of single-walled boron nitride nanotube. The results show that thermal conductance at low temperature is quantized and increases with the increasing diameter. We calculate specific heat of multi-walled carbon nanotubes and single-crystal GaN nanotube and find that the specific heat is dominated by quantized size effect and surface effect. From the perturbation theory of three-phonon scattering process, we calculate thermal conductivity of single-walled and multi-walled carbon nanotubes. Thermal conductivity of chiral nanotubes is smaller than that of achiral nanotubes when both have the same diameter. Thermal transport of carbon nanotube can be suppressed by strong intertube coupling, which may be arisen from the structural defects of samples.
Chapter 5, Using suitable interatomic interaction potential, we calculate the phonon structures and specific heat of single-walled carbon nanotube bundles doped with potassium. The frequency of high-frequency modes decreases linearly with the doping concentration. The low temperature specific heat deviates from the usual variation since the phonon modes of potassium dominate the low frequency phonon structures.
Chapter 6, We calculate the electronic structures and radial charge distribution of potassium doped double-walled carbon nanotubes and carbon-boron nitride nanotubes. For large diameter double-walled carbon nanotubes, most of transferred charges reside on the outer tube. Due to curvature effect, a part of transferred charges are distributed on inner tube of semiconducting-semiconducting and metal-semiconducting nanotubes. If the outer tube is boron nitride nanotube, the transferred charges prefer residing on the inner tube owing to the predominance of electronic bands of inner tubes. Moreover, we discuss the effect of co-doping on electronic properties in potassium and bromine doped double-walled carbon nanotubes.
Chapter 7, The summary and prospect are given in this chapter.
引文
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