太赫兹场和磁场作用下超晶格非线性动力学研究
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摘要
太赫兹场和磁场与低维半导体的相互作用是当前理论和实验研究的热点。外场会强烈影响半导体系统的电学和光学特性，并表现出许多有趣的物理现象和丰富的物理内涵。本论文主要研究了电场和磁场共同作用下半导体超晶格中电子的动力学特性，研究内容和主要结论包括以下几个方面：
1．利用离散的漂移扩散模型研究了电场和磁场共同作用下共振隧穿超晶格中电子的输运特性。通过考虑磁场对电子运动的操控，计算得到不同磁场下超晶格中电子的漂移速度-电场关系，利用漂移扩散方程计算了超晶格中电场的时空分布和电流随时间的演化关系。研究表明，随着磁场的变化，超晶格中周期性运动的动态电场畴可以转化为静态电场畴。
2．研究了共振隧穿超晶格在电场和磁场作用下的混沌动力学特性。当外加一个小信号交流电场到自振荡的超晶格系统时，由于系统内部的自振荡与外加交流场的振荡相互竞争，超晶格表现出非常复杂的电流振荡特性，并且当外加电场的振荡频率与超晶格自振荡频率之比处于黄金分割率时，电流振荡最为复杂。利用庞加莱分形图、相图、第一返回图和付立叶变换谱等不同的混沌探测方法研究了周期、准周期和混沌状态的鉴别。
3．利用平衡方程方法研究了太赫兹场作用下微带超晶格的电流响应特性。通过计算谐波随外加直流电场的变化关系，发现谐波电流在Bloch频率ω_B为外加电场频率ω的整数倍时出现共振峰。此外，还研究了超晶格对外加电场的直流-交流转换效率以及最大转换效率与外加电场的关系。
4．研究了磁场垂直于超晶格生长方向时超晶格微带中的电子在周期性电场作用下的混沌动力学特性。结果表明，由于在微带中运动的电子与自洽电场耦合产生了协同非线性振荡模式，而外加电场引起的电子Bloch振荡以及磁场引起的电子回旋振荡与这一模式产生相互作用引起了周期、准周期以及混沌现象的产生。
Interaction between terahertz (THz) radiation and semiconductor nanostructures has been the subject of growing interest both theoretically and experimentally. When a magnetic field is applied to the system, the electronic and optical properties will be strongly modified and many interesting phenomena will show up. In this thesis, we study the nonlinear dynamics of electrons in superlattices (SLs) under THz electric field and magnetic field. The contents and main conclusions are listed as follows:
1. Electron transport in resonant tunnelling SLs driven by crossed electric and magnetic fields has been studied using discrete drift diffusion model. By considering the effect of magnetic field on electron transport, we calculated the velocity-field characteristic under different magnetic fields. Spatiotemporal evolution of electric field domain and time-dependent current oscillation have been obtained by solving the drift diffusion equations. It is found that dynamic electric field domain can be converted to the stationary one by increasing the magnetic field.
2. Chaotic dynamics in resonant tunnelling SLs driven by electric and magnetic fields has been studied. When a small ac signal is superimposed on the self-oscillating system, a typical nonlinear dynamic system is constructed and different current oscillation modes show up, which is attributed to the nonlinear interaction between the internally generated periodic motion of the accumulated charge wave and the external ac signal. Several kinds of chaos-detecting methods, including Poincare bifurcation diagram, phase plot, first return map, and Fourier spectra, were used to distinguish periodic, quasiperiodic, and chaotic states.
3. We have numerically calculated the current characteristic of miniband SLs under THz electric field. It is found that harmonic current exhibits resonant peaks whenω_b = mω, whereω_B andωare frequencies of Bloch oscillation and external THz field, respectively. In addition, we have studied the dc-to-rf conversion efficiency and relation between maximum efficiency and dc electric field of the SL system.
4. Chaotic dynamics in miniband SLs under crossed electric and magnetic fields has been investigated. It is shown that the coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field, the intrinsic Bloch-type oscillatory mode, and cyclotron oscillatory mode, leads to the appearance of complicated dynamics, including chaos.
1．利用离散的漂移扩散模型研究了电场和磁场共同作用下共振隧穿超晶格中电子的输运特性。通过考虑磁场对电子运动的操控，计算得到不同磁场下超晶格中电子的漂移速度-电场关系，利用漂移扩散方程计算了超晶格中电场的时空分布和电流随时间的演化关系。研究表明，随着磁场的变化，超晶格中周期性运动的动态电场畴可以转化为静态电场畴。
2．研究了共振隧穿超晶格在电场和磁场作用下的混沌动力学特性。当外加一个小信号交流电场到自振荡的超晶格系统时，由于系统内部的自振荡与外加交流场的振荡相互竞争，超晶格表现出非常复杂的电流振荡特性，并且当外加电场的振荡频率与超晶格自振荡频率之比处于黄金分割率时，电流振荡最为复杂。利用庞加莱分形图、相图、第一返回图和付立叶变换谱等不同的混沌探测方法研究了周期、准周期和混沌状态的鉴别。
3．利用平衡方程方法研究了太赫兹场作用下微带超晶格的电流响应特性。通过计算谐波随外加直流电场的变化关系，发现谐波电流在Bloch频率ω_B为外加电场频率ω的整数倍时出现共振峰。此外，还研究了超晶格对外加电场的直流-交流转换效率以及最大转换效率与外加电场的关系。
4．研究了磁场垂直于超晶格生长方向时超晶格微带中的电子在周期性电场作用下的混沌动力学特性。结果表明，由于在微带中运动的电子与自洽电场耦合产生了协同非线性振荡模式，而外加电场引起的电子Bloch振荡以及磁场引起的电子回旋振荡与这一模式产生相互作用引起了周期、准周期以及混沌现象的产生。
Interaction between terahertz (THz) radiation and semiconductor nanostructures has been the subject of growing interest both theoretically and experimentally. When a magnetic field is applied to the system, the electronic and optical properties will be strongly modified and many interesting phenomena will show up. In this thesis, we study the nonlinear dynamics of electrons in superlattices (SLs) under THz electric field and magnetic field. The contents and main conclusions are listed as follows:
1. Electron transport in resonant tunnelling SLs driven by crossed electric and magnetic fields has been studied using discrete drift diffusion model. By considering the effect of magnetic field on electron transport, we calculated the velocity-field characteristic under different magnetic fields. Spatiotemporal evolution of electric field domain and time-dependent current oscillation have been obtained by solving the drift diffusion equations. It is found that dynamic electric field domain can be converted to the stationary one by increasing the magnetic field.
2. Chaotic dynamics in resonant tunnelling SLs driven by electric and magnetic fields has been studied. When a small ac signal is superimposed on the self-oscillating system, a typical nonlinear dynamic system is constructed and different current oscillation modes show up, which is attributed to the nonlinear interaction between the internally generated periodic motion of the accumulated charge wave and the external ac signal. Several kinds of chaos-detecting methods, including Poincare bifurcation diagram, phase plot, first return map, and Fourier spectra, were used to distinguish periodic, quasiperiodic, and chaotic states.
3. We have numerically calculated the current characteristic of miniband SLs under THz electric field. It is found that harmonic current exhibits resonant peaks whenω_b = mω, whereω_B andωare frequencies of Bloch oscillation and external THz field, respectively. In addition, we have studied the dc-to-rf conversion efficiency and relation between maximum efficiency and dc electric field of the SL system.
4. Chaotic dynamics in miniband SLs under crossed electric and magnetic fields has been investigated. It is shown that the coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field, the intrinsic Bloch-type oscillatory mode, and cyclotron oscillatory mode, leads to the appearance of complicated dynamics, including chaos.
引文
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