碳纳米管的热导率:从弹道到扩散输运

采用非平衡分子动力学方法研究了300 K和1000 K时（5,5）碳纳米管热导率随长度的变化.在室温下,碳纳米管长度小于40 nm时热导率与长度呈线性关系,此时导热处于弹道输运阶段,单位面积弹道热导为5.88×10⁹ Wm^-2K^-1．随着碳纳米管长度的增加,其热导率逐渐增加,但增加速度随长度逐渐减小,此时导热处于弹道—扩散输运阶段,并随长度的增加从以弹道输运为主向以扩散输运为主转变．长度大于10 μm时由于弹道输运可以忽略,导热近似达到完全 关键词： 碳纳米管 热导率 弹道输运 低维导热     

多壁碳纳米管中的多通道弹道输运特性

借助于扫描电子显微镜中可移动金属探针的测量系统,实现了探针电极与W衬底上生长的单根多壁碳纳米管一端的完美接触.研究了单根多壁碳纳米管室温下的电输运特性,发现多壁碳纳米管具有非常高的电流承载能力.对于直径100nm的碳纳米管,其电阻为34.4Ω,流经碳纳米管的最大电流可达7.27 mA,对应的电导为 460—490G0 .这一实验结果表明,大直径的多壁碳纳米管在室温下可以实现多通道弹道输运,是未来纳电子器件与电路的理想互联导线.     

Crossover from diffusive to ballistic transport in periodic quantum maps

We derive an expression for the mean square displacement (MSD) of a particle whose motion is governed by a uniform, periodic, quantum multi-baker map. The expression is a function of both time, t, and Planck’s constant, h, and allows a study of both the long time, t→∞, and semi-classical, h→0, limits taken in either order. We evaluate the expression using random matrix theory as well as numerically, and observe good agreement between both sets of results. The long time limit shows that particle transport is generically ballistic for any fixed value of Planck’s constant. However, for fixed times, the semi-classical limit leads to diffusion. The mean square displacement for non-zero Planck’s constant, and finite time, exhibits a crossover from diffusive to ballistic motion, with crossover time on the order of the inverse of Planck’s constant. We argue that these results are generic for a large class of 1D quantum random walks, similar to the quantum multi-baker, and that a sufficient condition for diffusion in the semi-classical limit is classically chaotic dynamics in each cell. Some connections between our work and the other literature on quantum random walks are discussed. These walks are of some interest in the theory of quantum computation.     

Thermal transport associated with ballistic phonons in asymmetric quantum structures

Using the scattering matrix method, we investigate the thermal conductance associated with ballistic phonons at low temperatures in asymmetric quantum structures. The results show that when the structure is an ideal quantum wire, the universal value π ² κ _B²(3h) can be observed at very low temperatures. However, for asymmetric quantum structure, the thermal conductance is less than the universal value π ² κ _B²(3h), even at T → 0. The results also show that the thermal conductance is strongly dependent on the transport direction. The rectification effect can be observed in the asymmetric structure and can be adjusted by changing the structural parameters. A brief analysis of these results is given.      

Correlation functions for restricted Brownian motion from the ballistic through to the diffusive regimes

We calculate the spectra of the correlation functions for fields with arbitrary spatial dependence as seen by Brownian particles in bounded geometries from knowledge of the spectra of the conditional probability density functions in the infinite domain. Our results show a significant difference for the spectra for 1D, 2D and 3D motions. To our knowledge this is the first demonstration of the influence of dimensionality on the form of the correlation functions. Our results also show the different power dependence on frequency for the ballistic and diffusive cases and the treatment of the crossover is unique.     

含遮蔽抛射沉积模型的有限尺寸效应

含遮蔽抛射沉积模型是在抛射沉积(BD)模型的基础上考虑了粒子以一定的角度分布倾斜入射的情况.本文应用外推方法确定了大尺寸极限下含遮蔽抛射沉积模型的各标度指数,讨论了该模型的有限尺寸效应及其标度性质.从模拟结果可以看出含遮蔽BD模型的有限尺寸效应与BD模型有所不同,遮蔽这种非局域作用可以显著地改变BD模型的标度性质. 关键词： 遮蔽效应 抛射沉积模型 有限尺寸效应 动力学标度     

多约束纳米结构的声子热导率模型研究

纳米技术的快速发展使得对微纳尺度导热机理的深入研究变得至关重要. 理论和实验都表明, 在纳米尺度下声子热导率将表现出尺寸效应. 基于声子玻尔兹曼方程和修正声子平均自由程的方法得到了多约束纳米结构的声子热导率模型, 可以描述多个几何约束共同作用下热导率的尺寸效应. 不同几何约束对声子输运的限制作用可以分开计算, 总体影响则通过马西森定则进行耦合. 对于热流方向的约束, 采用扩散近似的方法求解声子玻尔兹曼方程; 对于侧面边界约束, 采用修正平均自由程的方法计算边界散射对热导率的影响. 得到的模型能够预测纳米薄膜(法向和面向)及有限长度方形纳米线的热导率随相应特征尺寸的变化. 与蒙特卡罗模拟及硅纳米结构热导率实验值的对比验证了模型的正确性.     

硅纳米薄膜中声子弹道扩散导热的蒙特卡罗模拟

通过建立声子散射概率函数描述声子在输运过程中的散射,提出了一种模拟声子弹道扩散导热的蒙特卡罗方法,并将其应用于硅纳米薄膜中的稳态和瞬态弹道扩散导热过程的研究. 提出的蒙特卡罗方法对边界发射的声子束进行跟踪,根据散射概率函数模拟声子束在传播区域内经历的散射过程,并通过统计声子束的分布得到温度分布. 稳态导热过程的模拟发现,尺寸效应会引起边界温度跳跃,其值随着Knudsen数的增大而增大;计算的硅纳米薄膜的热导率随着厚度的增大而增大,与文献中的实验数据和理论模型相符. 通过瞬态导热过程的模拟得到了纳米薄膜内的温度分布随时间的变化,发现瞬态导热过程中的热波现象与空间尺度相关,材料尺寸越小,弹道输运越强,薄膜中的热波现象也越显著. 关键词： 纳米薄膜 弹道扩散导热 蒙特卡罗模拟 尺寸效应     

Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides

A detailed analysis of the statistical properties of the transmitted field in corrugated waveguides in the transition from ballistic to diffusion transport is presented. The field distributions are found to be highly dependent on the incident mode excited. When the speckle contrast is one, our results agree with recent experiments where the intensity distribution follows the predictions of the random-phasor-sum model, even though the field phase is not uniformly distributed. Clear deviations from the Gaussian statistics are found which can be interpreted in terms of " K" distributions arising either from a small number of scatterers or from perturbations of the speckle pattern on propagation.     

Influence of different band masses on ballistic charge transport in ferromagnet–superconductor–ferromagnet trilayers

We study transport properties of clean FISIF double-barrier junctions consisting of metallic or semiconducting ferromagnets (F), a superconductor (S), and insulating interfaces (I). We solve the scattering problem based on the Bogoliubov–de Gennes equation and calculate differential conductance for arbitrary interface transparency, different effective band masses and Fermi wave vectors in the conductors. We analyze size and coherence effects that characterize ballistic transport: subgap transmission and geometrical oscillations of the conductance. We find that different band masses, as well as different Fermi wave vectors, affect the transport properties in a way similar to interfaces of a finite transparency. In all these cases, charge transport is reduced to resonant tunneling through the quasi-bound states in the superconducting film.     

Renormalization-convolution approach to the electronic transport in two-dimensional aperiodic lattices

A novel method combining the renormalization and convolution techniques is developed for the Kubo-Greenwood formula. Using this method, the dc and ac conductance at zero temperature in two-dimensional (2D) quasiperiodic systems are studied. The results show that the ac conductance of quasiperiodic systems could be significantly modified by the presence of periodic leads, which are usually employed as the measurement connections. Furthermore, when the system is periodic along the applied electrical field, a quantized dc conductance spectrum is observed at zero temperature and this quantized spectrum is destroyed when an oscillating electrical field is introduced. However, when the electric field is applied along a quasiperiodic direction of the system, the ac conductance spectrum shows a non-Drude behaviour, in good agreement with experiment results.     

Trend to equilibrium of weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions

Recently R. Illner and the author proved that, under a physically realistic truncation on the collision kernel, the Boltzmann equation in the one-dimensional slab [0, 1] with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense. Here it is proved that when the Maxwellians associated with the boundary conditions atx=0 andx=1 are the same MaxwellianM _w , then the solution is uniformly bounded and tends toM _w fort.     

A stochastic approach to hopping transport in semiconductors

Generalized charge carrier equations for hopping transport in semiconductors are derived which include also the widely used Van Roosbroeck equations. The approach is based on a microscopic stochastic interacting particle system which models the hopping of electrons on a random set of states.     

Number-resolved master equation approach to quantum measurement and quantum transport

In addition to the well-known Landauer–Büttiker scattering theory and the nonequilibrium Green’s function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.     

Nonlinear transport in a dilute binary mixture of mechanically different particles

The hierarchy of moments of the Boltzmann equation for a binary mixture of mechanically different Maxwell molecules is exactly solved. The solution corresponds to a nonequilibrium homogeneous steady state generated by an external force that accelerates particles of each species (or color) along opposite directions. As a consequence, macroscopic fluxes are induced in spite of the absence of concentration gradients. Explicit expressions for the fluxes of mass and momentum as functions of the field strength, the mass ratio, the molar fractions, and the interaction constant ratio are obtained. In particular, the color conductivity coefficient reduces to the mutual diffusion coefficient in the zero-field limit. Some physically interesting limiting cases are discussed. The maximum-entropy method is used to construct an approximate velocity distribution function from the exact knowledge of the mass and momentum fluxes. This distribution is exact up to second order in the color field and also in the limit of large color field.     

耦合不可压流场输运方程的格子Boltzmann方法研究

基于格子Boltzmann方法,提出了求解耦合不可压缩流场输运方程的一种改进数值方法. 该方法使用格子Boltzmann方法求解流场方程,并根据流场格子模型的密度分布函数构建了输运方程的二阶离散格式. 通过二维平板通道流场输运系统验证了该方法的有效性.数值结果表明,该方法可以有效地减少计算过程中出现的非物理耗散, 并克服了传统模型所需巨大存储量的缺点.     

Green function solution of the Boltzmann transport equation for semiconducting thin film with rough boundaries

In this study the Green function solution of the Boltzmann transport equation on semiconducting thin film with irregular walls has been applied for the first time. The effects of electron scattering caused by these irregularities on the electrical conductivity have been investigated. First of all by using coordinate transformations, the irregularities on the walls have been transferred into the volume and in this way the both surfaces have been brought into flat forms. By taking two models, Gaussian and exponential, for random potential energy term contained in the transformed Hamiltonian as the perturbation, the resistivity results have been calculated and compared with the ones obtained from the methods widely known in the literature. The Boltzmann transport equation has been solved in relaxation time approximation for the irregular walled system in the case of no magnetic field.     

Convective scheme solution of the Boltzmann transport equation for nanoscale semiconductor devices

A model for the simulation of the electron energy distribution in nanoscale metal–oxide–semiconductor field-effect transistor (MOSFET) devices, using a kinetic simulation technique, is implemented. The convective scheme (CS), a method of characteristics, is an accurate method of solving the Boltzmann transport equation, a nonlinear integrodifferential equation, for the distribution of electrons in a MOSFET device. The method is used to find probabilities for use in an iterative scheme which iterates to find collision rates in cells. The CS is also a novel approach to 2D semiconductor device simulation. The CS has been extended to handle boundary conditions in 2D as well as to calculation of polygon overlap for polygons of more than three sides. Electron energy distributions in the channel of a MOSFET are presented.     

Relaxation and transport in FCHC lattice gases

FCHC lattice gases are the basic models for studying flow problems in three-dimensional systems. This paper presents a self-contained theoretical analysis and some computer simulations of such lattice gases, extended to include an arbitrary number of rest particles, with special emphasis on non-semi-detailed balance (NSDB) models. The special FCHC lattice symmetry guarantees isotropy of the Navier-Stokes equations, and enumerates the 12 spurious conservation laws (staggered momenta). The kinetic theory is based on the mean field approximation or the nonlinear Boltzmann equation. It is shown how calculation of the eigenvalues of the linearized Boltzmann equation offers a simple alternative to the Chapman-Enskog method or the multi-time-scale methods for calculating transport coefficients and relaxation rates. The simulated values for the speed of sound in NSDB models slightly disagree with the Boltzmann prediction.     

Quantum scattering in the strip: From ballistic to localized regimes

Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined. Received: 28 January 1998 / Revised: 16 June 1998 / Accepted: 6 July 1998