外场下半导体异质结的非线性动力学行为研究
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摘要
随着半导体器件的发展,半导体中载流子的输运引起了广泛的关注。本论文基于实空间电荷转移模型和分立漂移理论模型研究了外场下半导体异质结的非线性动力学行为。主要结论有:
(1)对空间分布均匀的GaAs/AlGaAs异质结,系统中出现呈倒S形的负微分电导。随外加磁场强度和微波辐照体系特征为:(ⅰ)选取直流偏置位于负微分电导区域,在低磁场强度时,系统表现出自维持振荡,相应动态伏安特性曲线呈回滞现象,系统中有两吸引子(极限环和稳定的焦点)共存。当磁场强度增加到一定程度时,系统的稳定性发生改变,自维持振荡逐渐消失。伏安曲线上的回滞更加明显,回滞区域变宽;(ⅱ)考虑微波辐照和磁场共同作用时,由于系统自维持振荡和外部交流信号之间的耦合,系统表现出多种振荡模式如周期、准周期和锁频。随外加微波振幅的变化,系统经倍周期分叉通向混沌,这同实验中的现象是一致的。在磁场强度较大时,微波辐照下,系统在两个稳恒的态之间转变,相应纵向电阻受微波辐照频率的变化而呈现周期振荡,对理解最新的“零电阻”实验现象有所帮助。(ⅲ)结合系统的混沌行为,采用延迟反馈法对其控制。分析了系统动力学行为随外加反馈控制参数的分叉。研究表明,变化延迟时间和反馈权重,系统将在不同的态之间来回转变,当延迟时间恰好等于镶嵌在混沌吸引子中的不稳定轨道的周期时,该不稳定周期可以被稳定住,延迟反馈信号趋于零。
(2)对于空间分布不均匀的GaAs/AlGaAs异质结,我们建立了描述其随空间和时间变化的偏微分方程。在直流偏置情况下,系统中有电场畴形成,其周期移动引起了自维持振荡。随后,分析了磁场对系统中出现的电场畴的影响,发现随磁场增加电场畴的宽度逐渐变窄,自维持振荡的振幅也有所减少。在周期信号的驱动下,随驱动信号的振幅的变化,系统展现出和空间均匀的GaAs/AlGaAs异质结相似的动力学行为,不同的是其通向混沌的道路为阵发通向时空混沌,并给出了其相应的电场畴的分布图。
(3)对于弱耦合的GaAs/AlAs超晶格,其垂直输运的主要模式为顺序共振隧穿。电子漂移速度随外加电场变化可以出现负微分电导区域,同时也在系统中形成了电荷积累层构成的单极电场畴。选取合适的掺杂浓度和直流偏压系统可以促使电场畴在超晶格中周期移动,从而引起电流的振荡。受磁场的作用,稳定的电场畴易于形成,因此,系统中能产生自维持振荡的区域将有所减少。另外,对应不同的掺杂浓度,电场随空间分布也有所不同。考虑到周期驱动时,系统也表现出上述类似的复杂动力学行为。
The carrier transport in semiconductors has a considerable attention with the development of semiconductor devices. Based on the real-space electron transfer model and the discrete drift model, we investigate theoretically the nonlinear dynamics of the semiconductor heterostructures under external fields. Main results are summarized as follows:
(1) In the case for homogeneous GaAs/AlGaAs heterostructure, the static current-voltage characteristic curve exhibits an inverted S-shaped negative differential conductivity (NDC). Thus, the system shows complex dynamic behaviors under the magnetic field and the microwave irradiation. (i)As the dc bias is set within the NDC region, the current self-sustained oscillations can be found when a relatively small magnetic field is applied. Then, the hysteresis in the dynamic current-voltage curves can be found and two stable attractors coexist in the system. With further increasing the magnetic field, the stability of the system will be changed and the selfe-sustained oscillations disappear. However, the hysteresis phenomenon is more clearly and the width of the hysteresis is broader, (ii) Considering the action of the microwave irradiation and the magnetic fields, the system shows different oscillation modes like period、quasiperiodicity and frequency-locking due to the coupling between the internal and the external signal. The routes from period-doubling to chaos can be found with changes of the irradiation amplitude which is agreement with the experiment. Under a large magnetic field, the system will be transferred between two time-independent steady states; and the sustem longitudinal resistance shows an interesting oscillation with period tuned by the ratio of microwave radiation frequency. This provides a help to understand the "zero-resistance" experiment, (iii) The time-delayed feedback method is applied to control the chaotic dynamics in the system. The bifurcation about the dynamics with the control parameters is given. The results show that the system will be changed between different states with varying delayed time and feedback strength. As for the delayed time is equal to the period of the unstable period orbit embedded in the chaotic attractors, this orbit is stabilized and the feedback signal is close to zero.
(2) In the case for inhomogeneous GaAs/AlGaAs heterostructure, the properties of the dynamics can be described by a set of partial differential equations. For pure dc bias at a fixed magnetic field, the self-sustained oscillations are observed due to the travelling high electric field domain in the system. Varying the magnetic field, the width of the domain and the oscillational amplitude will be changed. Driven by an periodic signal, the system shows similar results with the homogeneous GaAs/AlGaAs heterostructure except that the routes from intermittent to chaos.
(3) In the case for weakly coupled GaAs/AlAs superlattices, the main electron vertical transport mechanism is sequential resonant tunneling. The drift velocity as a function of the applied electric field can result in the NDC and a monopole domain formed by charge accumulation layer appears in superlattices. Under the appropriate doping densities and applied dc voltages, the current oscillations occur due to the motion of the charge domain over a few periods of the SL. The magnetic field B seems to be favorite for the formation of the static electric field domains and to depress the current oscillation. Thus, the oscillation regime will be narrowed as the magnetic field strength increases. For different doping densities, the distribution of the electric field in superlattices is different. Driven by a periodic signal, the system shows interesting nonlinear behaviors like quasiperiodicity, frequency-locking, and period.
(1)对空间分布均匀的GaAs/AlGaAs异质结,系统中出现呈倒S形的负微分电导。随外加磁场强度和微波辐照体系特征为:(ⅰ)选取直流偏置位于负微分电导区域,在低磁场强度时,系统表现出自维持振荡,相应动态伏安特性曲线呈回滞现象,系统中有两吸引子(极限环和稳定的焦点)共存。当磁场强度增加到一定程度时,系统的稳定性发生改变,自维持振荡逐渐消失。伏安曲线上的回滞更加明显,回滞区域变宽;(ⅱ)考虑微波辐照和磁场共同作用时,由于系统自维持振荡和外部交流信号之间的耦合,系统表现出多种振荡模式如周期、准周期和锁频。随外加微波振幅的变化,系统经倍周期分叉通向混沌,这同实验中的现象是一致的。在磁场强度较大时,微波辐照下,系统在两个稳恒的态之间转变,相应纵向电阻受微波辐照频率的变化而呈现周期振荡,对理解最新的“零电阻”实验现象有所帮助。(ⅲ)结合系统的混沌行为,采用延迟反馈法对其控制。分析了系统动力学行为随外加反馈控制参数的分叉。研究表明,变化延迟时间和反馈权重,系统将在不同的态之间来回转变,当延迟时间恰好等于镶嵌在混沌吸引子中的不稳定轨道的周期时,该不稳定周期可以被稳定住,延迟反馈信号趋于零。
(2)对于空间分布不均匀的GaAs/AlGaAs异质结,我们建立了描述其随空间和时间变化的偏微分方程。在直流偏置情况下,系统中有电场畴形成,其周期移动引起了自维持振荡。随后,分析了磁场对系统中出现的电场畴的影响,发现随磁场增加电场畴的宽度逐渐变窄,自维持振荡的振幅也有所减少。在周期信号的驱动下,随驱动信号的振幅的变化,系统展现出和空间均匀的GaAs/AlGaAs异质结相似的动力学行为,不同的是其通向混沌的道路为阵发通向时空混沌,并给出了其相应的电场畴的分布图。
(3)对于弱耦合的GaAs/AlAs超晶格,其垂直输运的主要模式为顺序共振隧穿。电子漂移速度随外加电场变化可以出现负微分电导区域,同时也在系统中形成了电荷积累层构成的单极电场畴。选取合适的掺杂浓度和直流偏压系统可以促使电场畴在超晶格中周期移动,从而引起电流的振荡。受磁场的作用,稳定的电场畴易于形成,因此,系统中能产生自维持振荡的区域将有所减少。另外,对应不同的掺杂浓度,电场随空间分布也有所不同。考虑到周期驱动时,系统也表现出上述类似的复杂动力学行为。
The carrier transport in semiconductors has a considerable attention with the development of semiconductor devices. Based on the real-space electron transfer model and the discrete drift model, we investigate theoretically the nonlinear dynamics of the semiconductor heterostructures under external fields. Main results are summarized as follows:
(1) In the case for homogeneous GaAs/AlGaAs heterostructure, the static current-voltage characteristic curve exhibits an inverted S-shaped negative differential conductivity (NDC). Thus, the system shows complex dynamic behaviors under the magnetic field and the microwave irradiation. (i)As the dc bias is set within the NDC region, the current self-sustained oscillations can be found when a relatively small magnetic field is applied. Then, the hysteresis in the dynamic current-voltage curves can be found and two stable attractors coexist in the system. With further increasing the magnetic field, the stability of the system will be changed and the selfe-sustained oscillations disappear. However, the hysteresis phenomenon is more clearly and the width of the hysteresis is broader, (ii) Considering the action of the microwave irradiation and the magnetic fields, the system shows different oscillation modes like period、quasiperiodicity and frequency-locking due to the coupling between the internal and the external signal. The routes from period-doubling to chaos can be found with changes of the irradiation amplitude which is agreement with the experiment. Under a large magnetic field, the system will be transferred between two time-independent steady states; and the sustem longitudinal resistance shows an interesting oscillation with period tuned by the ratio of microwave radiation frequency. This provides a help to understand the "zero-resistance" experiment, (iii) The time-delayed feedback method is applied to control the chaotic dynamics in the system. The bifurcation about the dynamics with the control parameters is given. The results show that the system will be changed between different states with varying delayed time and feedback strength. As for the delayed time is equal to the period of the unstable period orbit embedded in the chaotic attractors, this orbit is stabilized and the feedback signal is close to zero.
(2) In the case for inhomogeneous GaAs/AlGaAs heterostructure, the properties of the dynamics can be described by a set of partial differential equations. For pure dc bias at a fixed magnetic field, the self-sustained oscillations are observed due to the travelling high electric field domain in the system. Varying the magnetic field, the width of the domain and the oscillational amplitude will be changed. Driven by an periodic signal, the system shows similar results with the homogeneous GaAs/AlGaAs heterostructure except that the routes from intermittent to chaos.
(3) In the case for weakly coupled GaAs/AlAs superlattices, the main electron vertical transport mechanism is sequential resonant tunneling. The drift velocity as a function of the applied electric field can result in the NDC and a monopole domain formed by charge accumulation layer appears in superlattices. Under the appropriate doping densities and applied dc voltages, the current oscillations occur due to the motion of the charge domain over a few periods of the SL. The magnetic field B seems to be favorite for the formation of the static electric field domains and to depress the current oscillation. Thus, the oscillation regime will be narrowed as the magnetic field strength increases. For different doping densities, the distribution of the electric field in superlattices is different. Driven by a periodic signal, the system shows interesting nonlinear behaviors like quasiperiodicity, frequency-locking, and period.
引文
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