Generalization of the two-dimensional Child–Langmuir law for non-zero injection velocities in a planar diode

2009 ◽  
Vol 75 (1) ◽  
pp. 85-90 ◽  
Author(s):  
YA-MIN QUAN ◽  
YAO-GEN DING
Keyword(s):  
Potential Energy ◽  
Initial Energy ◽  
Injection Velocity ◽  
Two Dimensional ◽  
Planar Diode ◽  
Simple Analytic Expression ◽  
Calculation Results ◽  
Analytic Expression

AbstractA simple analytic expression of the two-dimensional Child–Langmuir law is derived for non-zero injection velocities and Lau's result is obtained in our model by setting the injection velocity equal to zero. The calculation results show that the modify term in our model is larger than Lau's with a non-zero electronic initial energy, and it is twice as large as Lau's when the electronic initial energy is much greater than the potential energy of the gap.

scholarly journals On the 3D → 2D Isomerization of Hexaborane(12)

Chemistry ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 28-38
Author(s):  
Josep M. Oliva-Enrich ◽  
Ibon Alkorta ◽  
José Elguero ◽  
Maxime Ferrer ◽  
José I. Burgos
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Transition States ◽  
Three Dimensional ◽  
Reaction Coordinate ◽  
Intrinsic Reaction Coordinate ◽  
Limiting Factor ◽  
Two Dimensional ◽  
Axis Of Rotation

By following the intrinsic reaction coordinate connecting transition states with energy minima on the potential energy surface, we have determined the reaction steps connecting three-dimensional hexaborane(12) with unknown planar two-dimensional hexaborane(12). In an effort to predict the potential synthesis of finite planar borane molecules, we found that the reaction limiting factor stems from the breaking of the central boron-boron bond perpendicular to the C2 axis of rotation in three-dimensional hexaborane(12).

CALCULATION OF THE INTENSITY-DEPENDENT ABSORPTION SPECTRUM IN TWO-DIMENSIONAL ELECTRON SYSTEMS

2011 ◽  
Vol 25 (11) ◽  
pp. 863-872
Author(s):  
TRAN CONG PHONG ◽  
VO THANH LAM ◽  
LUONG VAN TUNG
Keyword(s):  
Phonon Scattering ◽  
Two Dimensional ◽  
Electron Systems ◽  
Quantum Kinetic Equation ◽  
Dimensional Electron ◽  
Semiconductor Superlattice ◽  
Optical Phonon Scattering ◽  
Dependent Absorption ◽  
Analytic Expression ◽  
Two Dimensional Electron Systems

General analytic expression for the intensity-dependent absorption coefficient (IDAC) of an intense electromagnetic wave (IEMW) in two-dimensional electron systems (2DES) is obtained by using the quantum kinetic equation (QKE) for electrons in the case of electron–optical phonon scattering in a doped semiconductor superlattice (DSSL). The dependence of IDAC on the amplitude E0 and the photon energy ℏΩ of an IEMW, the energy ℏωp and the temperature for a specific n-i-p-i superlattice of GaAs : Si / GaAs : Be is achieved due to a numerical method. The computational results show that not only the dependence of IDAC on ℏΩ but also the dependence of IDAC on ℏωp can be applied to optically detect the electric subbands in a DSSL.

Nonreciprocal Wave Transmission in Metastable Modular Metastructures Utilizing Asymmetric Dual-Threshold Snap-Through

2019 ◽  
Author(s):  
Xiang Liu ◽  
Guoping Cai ◽  
K. W. Wang
Keyword(s):  
Potential Energy ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Wave Transmission ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
One Dimensional ◽  
Threshold Phenomenon ◽  
Energy Equilibrium ◽  
Nonreciprocal Transmission

Abstract In this research, the nonreciprocal wave transmission features in one-dimensional and two-dimensional metastable modular metastructures are studied. Unlike previous work, in which the nonreciprocal transmission in metastable metastructures is realized by utilizing the supratransmission phenomenon when the excitation frequency is inside the linearized bandgap, a new approach is explored to achieve nonreciprocal wave transmission exploiting metastability and asymmetric dual-threshold snap-through. It is found that because of the asymmetry of potential energy wells of the equilibria, there will be two excitation amplitude thresholds for a metastable component when it is initially at the high-potential-energy equilibrium with excitation frequency within the passband. When the excitation amplitude increases and exceeds the first threshold, the metastable component will snap to the low-potential-energy equilibrium and maintain intrawell motion around this stable point, which will cause a significant decrease of the wave transmission. And when the excitation amplitude exceeds the second threshold, the metastable component will start to perform interwell motion, and now the wave transmission will increase suddenly. By using this “dual-threshold” phenomenon, nonreciprocal wave transmission in a one-dimensional structure is realized by connecting a metastable chain with a linear periodic part. Because of the wave attenuation effect of the linear part of the system, the excitation amplitude thresholds on different sides of the one-dimensional structure will be discrepant. Therefore, nonreciprocal wave transmission can be developed when the excitation amplitude is within certain ranges. It is interesting to note that the direction of nonreciprocal wave transmission can be changed by setting the excitation amplitude to different values. By changing the configuration of the metastable chain, the operation frequency and excitation amplitude ranges of the nonreciprocal transmission can be tuned. For a two-dimensional metastable metastructure, nonreciprocal wave transmission can be realized by adjusting the parameters of some metastable modules in the metastructure in the manner that the potential energy and energy thresholds of the adjusted modules and the unadjusted modules are different, but the passbands of the adjusted modules and the unadjusted modules will overlap in some frequency regions. Numerical studies provide clear insight of the proposed nonreciprocal wave transmission approach.

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