黑磷的电输运和光电特性研究以及电子气系统磁光电导率公式的推广

发布时间：2018-05-31 21:43

本文选题：黑磷 + 电子迁移率　；参考：《中国科学技术大学》2017年博士论文

【摘要】：在凝聚态物理和微纳电子学领域,自从石墨烯被发现以来,具有原子层厚度的二维材料成为了人们研究的热点。这些二维材料因为具有独特的电学、光学、机械和热学等性质,被人们认为是研发新一代电子器件的后备原材料。黑磷是最近两年来研究比较火的新颖二维材料,由于具有独特的电子结构得到了人们普遍关注。黑磷各向异性的能带结构使其具有与其他二维材料不一样的物理性质,在电子、光学和光电器件方面具有潜在的应用价值。黑磷已经成功地应用于制备场效应晶体管。我们都知道开关比和载流子迁移率是决定场效应晶体管性能的主要物理参数,开关比和载流子迁移率的大小直接影响了场效应晶体管的实际应用价值。载流子迁移率的大小受到很多散射机制的影响,比如电子(空穴)-杂质散射和电子(空穴)-声子散射等。目前,关于黑磷载流子迁移率的实验工作比较多,但是关于n型黑磷电子迁移率的理论研究尚不完善,黑磷电子迁移率受杂质散射等因素的影响尚不清晰,黑磷电子迁移率的研究将为黑磷用于实际器件中提供理论参考具有重要的意义。加之黑磷是直接带隙半导体,而且带隙大小随黑磷厚度可调,带隙能量对应的波长在可见光到红外波段,使得黑磷在光学和光电器件方面具有较好的应用前景。而且黑磷具有各向异性的能带结构,其光学和光电性质在不同方向表现出差异性,然而单层黑磷的光电导和光透射性质还没有得到充分的研究。在一些合金材料和由纳米结构材料构成的薄膜里,光电导率往往会偏离Drude模型。2001年Smith提出了 Drude-Smith模型,引入了电子背散射效应成功地解释了这种光电导率偏离Drude模型的行为。随后Drude-Smith光电导率公式被广泛用于研究材料的电子局域化效应和金属-绝缘体转变过程。然而,有磁场的Drude-Smith公式一直没有得到发展。所以在磁场作用下,具有金属-绝缘体转变性质和非Drude行为材料的磁光电导率特性、电子背散射效应(或电子局域化)尚未得到研究。基于上述讨论,在本文中我们系统研究了黑磷的电输运和光电特性,并发展了用于研究电子气系统磁光电特性的Drude-Smith模型。该论文主要的研究工作有:(1)理论研究了低温下n型单层黑磷的电子结构和电输运性质。我们首先利用k · p理论得到了单层黑磷中自由电子的能量色散关系,并把严格的能量色散关系和长波近似条件的能量色散关系分别定义为Model Ⅰ和Model Ⅱ。我们利用这两个能量色散关系分别计算了电子态密度、系统的化学势(低温下为费米能级)和电子屏蔽长度。利用费米黄金定则计算了电子-杂质散射为主要散射机制的电子跃迁几率,并考虑了电子屏蔽效应。利用玻尔兹曼方程来研究系统对外场的响应过程。在求解玻尔兹曼方程时利用了动量平衡方程。理论计算结果表明,通过Model Ⅱ计算得到的电子态密度是一个单位阶梯函数,这和具有抛物线型能量色散关系的半导体基二维电子气的态密度是一样的。而Model Ⅰ的电子态密度比Model Ⅱ大一些,这是因为Model Ⅰ的能量色散关系是非抛物线型。对于费米能级,Model Ⅰ和Ⅱ的计算结果差别极小。通过Model Ⅰ计算得到的电子屏蔽长度随电子浓度的增加而增大,而Model Ⅱ的电子屏蔽长度是一个常数,即不随电子浓度改变而改变。利用这两种能量色散关系计算得到的黑磷电子迁移率都能与实验符合很好。通过计算我们还发现电子迁移率具有较大的各向异性,在杂质浓度一定的情况下x方向(armchiar)的电子迁移率始终大于y方向(zigzag)的电子迁移率。这是因为x方向的电子有效质量比y方向的小。我们还计算了不同杂质浓度下的电子迁移率,发现黑磷电子迁移率随杂质浓度的增加而减小,同时也发现了电子迁移率的各向异性不随杂质浓度的变化而改变。(2)研究了单层黑磷光电导和光透射性质及其各向异性的特点。利用k·p理论得到了单层黑磷中自由电子的哈密顿量,并在哈密顿量里考虑了外部光场的作用,考虑线偏振光沿不同方向加载到黑磷上时得到了不同方向的电子-光子相互作用矩阵。将外部光场视为微扰场,利用费米黄金定则得到了电子受光激发的带间跃迁几率。我们利用玻尔兹曼方程研究了黑磷系统对外部光场的响应过程,并结合能量平衡方程计算了导带电子的能量转移率,进而计算了单层黑磷的光电导和光透射系数。理论计算表明,单层黑磷的光电导和光透射系数存在较大的各向异性,表现为x方向的光电导(光透射系数)要比y方向大(小)。还研究了电子浓度对单层黑磷光电导和光透射的影响,计算结果表明随着电子浓度的增大光电导的阈值边发生蓝移。在相同光子能量情况下,单层黑磷的光电导随着电子浓度的增大而下降。(3)发展了在磁场和光场共同作用下的用于研究材料的金属-绝缘体转变和非Drude行为的磁光电物理特性的Drude-Smith公式。在Drude-Smith模型的基础上,我们建立了有磁场的纵向和横向电流响应函数,经过傅里叶变换得到了纵向和横向磁光电导率。在该公式里引入了可以用于描述电子背散射或电子局域化效应的参数a。我们研究了在不同电子背散射强度下的电流响应函数随时间的演化过程和纵、横磁光电导率随外部光场频率的变化行为。为了描述上的便利,在计算过程中有效质量取为m*= 0.065me,电子的弛豫时间为τ = 0.5ps(皮秒)。计算结果表明,在不考虑磁场情况下,纵向电流响应函数为正值且随时间按照指数形式衰减,横向电流响应函数为零。当考虑磁场作用之后,纵、横电流响应函数会以回旋频率ωc进行振荡并随着时间按照指数形式衰减。随着参数a的减小,即电子背散射效应增强,纵、横电流响应函数的振荡幅值发生了改变。当ωcτ～1被满足时候,通过纵向光电导率σxx(ω)和横向光电导率σxy(ω)可以观察到回旋共振效应。对于纵向光电导率实部Reσxx(ω),当考虑电子背散射效应之后,回旋共振峰变成了波谷,并在波谷两侧形成了两个新波峰,说明了电子背散射效应改变了系统的能量耗散过程。随着参数a的减小,新形成的波谷变得越来越深。而对于横向光电导率的实部Reσxy(ω),a的减小没有改变其形状特征,只是加强了原来的变化趋势使得波谷更深波峰更高。研究还发现电子背散射效应改变了纵向光电导率虚部Imσxx(ω)在回旋共振频率附近对频率的依赖关系,但是没有改变横向光电导率虚部Imσxy(ω)的形状特点,具体表现为参数a的减小只是使得Imσxy(ω)在回旋共振频率ω～ωc处的波谷更深了。最后,我们利用磁光电导率Drude-Smith公式还研究了 VO_2薄膜材料在THz频段的介电函数的性质。我们发现电子背散射效应会导致VO_2薄膜材料的介电函数发生变号行为而且也改变了介电函数随外场频率变化的趋势。
[Abstract]:In the field of condensed matter physics and microelectronics, since the discovery of graphene, the two-dimensional material with the thickness of the atomic layer has become a hot spot of research. These two dimensional materials have been considered to be a backup material for the development of a new generation of electronic devices because of their unique electrical, optical, mechanical and thermal properties. New two dimensional materials have been widely studied for two years. Because of their unique electronic structure, the energy band structure of the anisotropic black phosphorus has a potential application value in electronic, optical and optoelectronic devices. Field effect transistors. We all know that the switching ratio and carrier mobility are the main physical parameters determining the performance of field effect transistors. The size of the switching ratio and carrier mobility directly affects the practical application value of the field effect transistor. The size of the carrier mobility is influenced by many scattering mechanisms, such as electron (hole) - heterozygosity. Mass scattering and electron (hole) - phonon scattering, and so on. At present, there are many experiments on the mobility of black phosphorus carrier, but the theoretical research on electron mobility of N type black phosphorus is not perfect. The influence of impurity scattering on the electron mobility of black phosphorus is not clear. The study of the electronic mobility of black phosphorus will be used for practical devices. It is of great significance to provide theoretical reference. In addition, the black phosphorus is a direct band gap semiconductor, and the band gap is adjustable with the thickness of black phosphorus. The band gap energy corresponds to the wavelength in the visible to infrared band, making the black phosphorus have a good application prospect in the optical and photoelectric devices. And the black phosphorus has an anisotropic band structure, and its light has an anisotropic energy band structure. The photoconductivity and optical transmission properties of the single layer black phosphorus have not been fully studied. In some alloy materials and films made of nanostructured materials, the photoconductivity tends to deviate from the Drude model.2001 Smith and bring out the Drude-Smith model and introduce the electronic backscattering. The effect successfully explains the behavior of this photoconductivity deviating from the Drude model. Subsequently, the Drude-Smith photoconductivity formula is widely used to study the electronic localization effect and the metal insulator transition process. However, the Drude-Smith formula with a magnetic field has not been developed. The magneto-optical conductivity properties of denatured and non Drude behavior materials, electronic backscattering effects (or electronic localization) have not been studied. Based on the above discussion, we have systematically studied the electrical transport and photoelectrical properties of black phosphorus, and developed a Drude-Smith model for the study of the magneto to optoelectronic properties of the electronic gas system. The study is as follows: (1) the electronic structure and electrical transport properties of N type single layer black phosphorus at low temperature are studied theoretically. First, we use the k p theory to obtain the energy dispersion relation of free electrons in single layer black phosphorus, and the strict energy dispersion relation and the energy dispersion relation of the long wave approximation conditions are defined as Model I and Model II. The electron state density, the chemical potential of the system (the Fermi level at low temperature) and the electron shielding length are calculated by the two energy dispersion relations. The electron transition probability of the electron impurity scattering as the main scattering mechanism is calculated by the Fermi gold rule, and the electron shielding effect is considered. The momentum equilibrium equation is used in solving the Boltzmann equation. The theoretical calculation shows that the electronic density of states obtained by Model II is a unit ladder function, which is the same as the density of states of the two-dimensional electron gas with parabolic energy dispersion relation. And the electron density of Model I is the same. This is because the energy dispersion relation of Model I is a non parabolic type. For the Fermi level, the difference between the calculation results of Model I and II is very small. The electron shielding length obtained by the Model I calculation increases with the increase of the electron concentration, and the electronic screen length of Model II is a constant, that is, it does not follow the electron concentration. The electron mobility of black phosphorus obtained by these two energy dispersion relations can be in good agreement with the experiment. By calculation we also found that the electron mobility has a larger anisotropy, and the electron migration rate of the X direction (armchiar) is always greater than that of the Y direction (zigzag) in the case of a certain impurity concentration. This is because the electron effective mass of the X direction is smaller than that in the Y direction. We also calculate the electron mobility under different impurity concentrations. It is found that the electron mobility of the black phosphorus decreases with the increase of the impurity concentration. At the same time, the anisotropy of the electron mobility is found not to change with the variation of the impurity concentration. (2) the single layer black phosphorescence conductance is studied. The property of light transmission and its anisotropy. The Hamiltonian of free electrons in single layer black phosphorus is obtained by using K. P theory. The effect of the external light field is considered in the Hamiltonian. The electron beam interaction matrix in different directions is obtained when the linear polarized light is loaded on the black phosphorus along different directions. The external light field is considered as a micro field. The interband transition probability of electrons stimulated by light is obtained by the Fermi gold rule. We use the Boltzmann equation to study the response process of the external light field in the black phosphorus system, and calculate the energy transfer rate of the conduction band electron with the energy balance equation. The theoretical calculation of the photoconductivity and the light transmission coefficient of the single layer black phosphorus is calculated. It is shown that the photoconductivity and light transmission coefficient of single layer black phosphorus has a larger anisotropy, which shows that the photoconductivity (light transmission coefficient) in the direction of X is larger than that in the Y direction. The effect of the electron concentration on the single layer black phosphorescence conductance and light transmission is also studied. Under the same photon energy, the photoconductivity of the monolayer black phosphorus decreases with the increase of the electron concentration. (3) the Drude-Smith formula for the magneto optoelectronic physical properties of the metal insulator transition and non Drude behavior used to study the material under the joint action of magnetic field and light field is developed. On the basis of the Drude-Smith model, we have established a magnetic field. Longitudinal and transverse current response function, the longitudinal and transverse magneto-optical conductivity is obtained by Fourier transform. In this formula, we introduce a parameter A. that can be used to describe the electron backscattering or electron localization effect. We studied the evolution and longitudinal, transverse magnetic optoelectronic response function of the current response function at different electron backscattering intensity. In order to describe the convenience, the effective mass is m*= 0.065me in the calculation process, the relaxation time of the electron is tau = 0.5ps (picosecond). The calculation results show that the longitudinal current response function is positive and attenuates exponentially with time without the magnetic field, and the transverse current response function The number is zero. When the magnetic field is considered, the transverse current response function oscillates at the cyclotron frequency omega C and attenuates exponentially with time. As the parameter a decreases, the electron backscattering effect is enhanced and the amplitude of the transverse current response function changes. When the Omega C tau 1 is satisfied, the longitudinal photoconductivity is passed. Sigma XX (omega) and transverse photoconductivity (o) XY (omega) can observe the cyclotron resonance effect. For the longitudinal photoconductivity Re sigma XX (omega), when the electron backscattering effect is taken into consideration, the cyclotron resonance peak becomes the trough, and two new peaks are formed on both sides of the trough, indicating that the electric back scattering effect changes the energy dissipation process of the system. With the reference, the energy dissipation process is changed. As the number of a decreases, the newly formed trough becomes deeper and deeper. For the real Re sigma XY (omega) of the transverse photoconductivity, the decrease of a does not change its shape characteristics, but it only strengthens the original trend to make the trough deeper wave peak higher. The study also shows that the electron backscattering effect changes the imaginary part of the imaginary part of the longitudinal photoconductivity, Im sigma XX (omega) in cyclotron resonance The dependence of frequency on the frequency is not changed, but it does not change the shape characteristics of the imaginary part Im sigma XY (omega) of the transverse photoconductivity. It is shown that the decrease of the parameter a is only making the Im sigma XY (omega) deeper in the roughing valley of the cyclotron resonance frequency Omega C. Finally, we also use the Drude-Smith formula of magnetic conductivity to study the THz frequency of the VO_2 film material in the THz frequency. It is found that the electron backscattering effect will lead to the change of the dielectric function of the VO_2 film material and the change of the dielectric function with the change of the field frequency.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O469

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