本文選題：黑磷 + 電子遷移率　； 參考：《中國(guó)科學(xué)技術(shù)大學(xué)》2017年博士論文

【摘要】：在凝聚態(tài)物理和微納電子學(xué)領(lǐng)域,自從石墨烯被發(fā)現(xiàn)以來,具有原子層厚度的二維材料成為了人們研究的熱點(diǎn)。這些二維材料因?yàn)榫哂歇?dú)特的電學(xué)、光學(xué)、機(jī)械和熱學(xué)等性質(zhì),被人們認(rèn)為是研發(fā)新一代電子器件的后備原材料。黑磷是最近兩年來研究比較火的新穎二維材料,由于具有獨(dú)特的電子結(jié)構(gòu)得到了人們普遍關(guān)注。黑磷各向異性的能帶結(jié)構(gòu)使其具有與其他二維材料不一樣的物理性質(zhì),在電子、光學(xué)和光電器件方面具有潛在的應(yīng)用價(jià)值。黑磷已經(jīng)成功地應(yīng)用于制備場(chǎng)效應(yīng)晶體管。我們都知道開關(guān)比和載流子遷移率是決定場(chǎng)效應(yīng)晶體管性能的主要物理參數(shù),開關(guān)比和載流子遷移率的大小直接影響了場(chǎng)效應(yīng)晶體管的實(shí)際應(yīng)用價(jià)值。載流子遷移率的大小受到很多散射機(jī)制的影響,比如電子(空穴)-雜質(zhì)散射和電子(空穴)-聲子散射等。目前,關(guān)于黑磷載流子遷移率的實(shí)驗(yàn)工作比較多,但是關(guān)于n型黑磷電子遷移率的理論研究尚不完善,黑磷電子遷移率受雜質(zhì)散射等因素的影響尚不清晰,黑磷電子遷移率的研究將為黑磷用于實(shí)際器件中提供理論參考具有重要的意義。加之黑磷是直接帶隙半導(dǎo)體,而且?guī)洞笮‰S黑磷厚度可調(diào),帶隙能量對(duì)應(yīng)的波長(zhǎng)在可見光到紅外波段,使得黑磷在光學(xué)和光電器件方面具有較好的應(yīng)用前景。而且黑磷具有各向異性的能帶結(jié)構(gòu),其光學(xué)和光電性質(zhì)在不同方向表現(xiàn)出差異性,然而單層黑磷的光電導(dǎo)和光透射性質(zhì)還沒有得到充分的研究。在一些合金材料和由納米結(jié)構(gòu)材料構(gòu)成的薄膜里,光電導(dǎo)率往往會(huì)偏離Drude模型。2001年Smith提出了 Drude-Smith模型,引入了電子背散射效應(yīng)成功地解釋了這種光電導(dǎo)率偏離Drude模型的行為。隨后Drude-Smith光電導(dǎo)率公式被廣泛用于研究材料的電子局域化效應(yīng)和金屬-絕緣體轉(zhuǎn)變過程。然而,有磁場(chǎng)的Drude-Smith公式一直沒有得到發(fā)展。所以在磁場(chǎng)作用下,具有金屬-絕緣體轉(zhuǎn)變性質(zhì)和非Drude行為材料的磁光電導(dǎo)率特性、電子背散射效應(yīng)(或電子局域化)尚未得到研究。基于上述討論,在本文中我們系統(tǒng)研究了黑磷的電輸運(yùn)和光電特性,并發(fā)展了用于研究電子氣系統(tǒng)磁光電特性的Drude-Smith模型。該論文主要的研究工作有:(1)理論研究了低溫下n型單層黑磷的電子結(jié)構(gòu)和電輸運(yùn)性質(zhì)。我們首先利用k · p理論得到了單層黑磷中自由電子的能量色散關(guān)系,并把嚴(yán)格的能量色散關(guān)系和長(zhǎng)波近似條件的能量色散關(guān)系分別定義為Model Ⅰ和Model Ⅱ。我們利用這兩個(gè)能量色散關(guān)系分別計(jì)算了電子態(tài)密度、系統(tǒng)的化學(xué)勢(shì)(低溫下為費(fèi)米能級(jí))和電子屏蔽長(zhǎng)度。利用費(fèi)米黃金定則計(jì)算了電子-雜質(zhì)散射為主要散射機(jī)制的電子躍遷幾率,并考慮了電子屏蔽效應(yīng)。利用玻爾茲曼方程來研究系統(tǒng)對(duì)外場(chǎng)的響應(yīng)過程。在求解玻爾茲曼方程時(shí)利用了動(dòng)量平衡方程。理論計(jì)算結(jié)果表明,通過Model Ⅱ計(jì)算得到的電子態(tài)密度是一個(gè)單位階梯函數(shù),這和具有拋物線型能量色散關(guān)系的半導(dǎo)體基二維電子氣的態(tài)密度是一樣的。而Model Ⅰ的電子態(tài)密度比Model Ⅱ大一些,這是因?yàn)镸odel Ⅰ的能量色散關(guān)系是非拋物線型。對(duì)于費(fèi)米能級(jí),Model Ⅰ和Ⅱ的計(jì)算結(jié)果差別極小。通過Model Ⅰ計(jì)算得到的電子屏蔽長(zhǎng)度隨電子濃度的增加而增大,而Model Ⅱ的電子屏蔽長(zhǎng)度是一個(gè)常數(shù),即不隨電子濃度改變而改變。利用這兩種能量色散關(guān)系計(jì)算得到的黑磷電子遷移率都能與實(shí)驗(yàn)符合很好。通過計(jì)算我們還發(fā)現(xiàn)電子遷移率具有較大的各向異性,在雜質(zhì)濃度一定的情況下x方向(armchiar)的電子遷移率始終大于y方向(zigzag)的電子遷移率。這是因?yàn)閤方向的電子有效質(zhì)量比y方向的小。我們還計(jì)算了不同雜質(zhì)濃度下的電子遷移率,發(fā)現(xiàn)黑磷電子遷移率隨雜質(zhì)濃度的增加而減小,同時(shí)也發(fā)現(xiàn)了電子遷移率的各向異性不隨雜質(zhì)濃度的變化而改變。(2)研究了單層黑磷光電導(dǎo)和光透射性質(zhì)及其各向異性的特點(diǎn)。利用k·p理論得到了單層黑磷中自由電子的哈密頓量,并在哈密頓量里考慮了外部光場(chǎng)的作用,考慮線偏振光沿不同方向加載到黑磷上時(shí)得到了不同方向的電子-光子相互作用矩陣。將外部光場(chǎng)視為微擾場(chǎng),利用費(fèi)米黃金定則得到了電子受光激發(fā)的帶間躍遷幾率。我們利用玻爾茲曼方程研究了黑磷系統(tǒng)對(duì)外部光場(chǎng)的響應(yīng)過程,并結(jié)合能量平衡方程計(jì)算了導(dǎo)帶電子的能量轉(zhuǎn)移率,進(jìn)而計(jì)算了單層黑磷的光電導(dǎo)和光透射系數(shù)。理論計(jì)算表明,單層黑磷的光電導(dǎo)和光透射系數(shù)存在較大的各向異性,表現(xiàn)為x方向的光電導(dǎo)(光透射系數(shù))要比y方向大(小)。還研究了電子濃度對(duì)單層黑磷光電導(dǎo)和光透射的影響,計(jì)算結(jié)果表明隨著電子濃度的增大光電導(dǎo)的閾值邊發(fā)生藍(lán)移。在相同光子能量情況下,單層黑磷的光電導(dǎo)隨著電子濃度的增大而下降。(3)發(fā)展了在磁場(chǎng)和光場(chǎng)共同作用下的用于研究材料的金屬-絕緣體轉(zhuǎn)變和非Drude行為的磁光電物理特性的Drude-Smith公式。在Drude-Smith模型的基礎(chǔ)上,我們建立了有磁場(chǎng)的縱向和橫向電流響應(yīng)函數(shù),經(jīng)過傅里葉變換得到了縱向和橫向磁光電導(dǎo)率。在該公式里引入了可以用于描述電子背散射或電子局域化效應(yīng)的參數(shù)a。我們研究了在不同電子背散射強(qiáng)度下的電流響應(yīng)函數(shù)隨時(shí)間的演化過程和縱、橫磁光電導(dǎo)率隨外部光場(chǎng)頻率的變化行為。為了描述上的便利,在計(jì)算過程中有效質(zhì)量取為m*= 0.065me,電子的弛豫時(shí)間為τ = 0.5ps(皮秒)。計(jì)算結(jié)果表明,在不考慮磁場(chǎng)情況下,縱向電流響應(yīng)函數(shù)為正值且隨時(shí)間按照指數(shù)形式衰減,橫向電流響應(yīng)函數(shù)為零。當(dāng)考慮磁場(chǎng)作用之后,縱、橫電流響應(yīng)函數(shù)會(huì)以回旋頻率ωc進(jìn)行振蕩并隨著時(shí)間按照指數(shù)形式衰減。隨著參數(shù)a的減小,即電子背散射效應(yīng)增強(qiáng),縱、橫電流響應(yīng)函數(shù)的振蕩幅值發(fā)生了改變。當(dāng)ωcτ～1被滿足時(shí)候,通過縱向光電導(dǎo)率σxx(ω)和橫向光電導(dǎo)率σxy(ω)可以觀察到回旋共振效應(yīng)。對(duì)于縱向光電導(dǎo)率實(shí)部Reσxx(ω),當(dāng)考慮電子背散射效應(yīng)之后,回旋共振峰變成了波谷,并在波谷兩側(cè)形成了兩個(gè)新波峰,說明了電子背散射效應(yīng)改變了系統(tǒng)的能量耗散過程。隨著參數(shù)a的減小,新形成的波谷變得越來越深。而對(duì)于橫向光電導(dǎo)率的實(shí)部Reσxy(ω),a的減小沒有改變其形狀特征,只是加強(qiáng)了原來的變化趨勢(shì)使得波谷更深波峰更高。研究還發(fā)現(xiàn)電子背散射效應(yīng)改變了縱向光電導(dǎo)率虛部Imσxx(ω)在回旋共振頻率附近對(duì)頻率的依賴關(guān)系,但是沒有改變橫向光電導(dǎo)率虛部Imσxy(ω)的形狀特點(diǎn),具體表現(xiàn)為參數(shù)a的減小只是使得Imσxy(ω)在回旋共振頻率ω～ωc處的波谷更深了。最后,我們利用磁光電導(dǎo)率Drude-Smith公式還研究了 VO_2薄膜材料在THz頻段的介電函數(shù)的性質(zhì)。我們發(fā)現(xiàn)電子背散射效應(yīng)會(huì)導(dǎo)致VO_2薄膜材料的介電函數(shù)發(fā)生變號(hào)行為而且也改變了介電函數(shù)隨外場(chǎng)頻率變化的趨勢(shì)。
[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.
【學(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：O469

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