Li Zhi-Bing

Mechanism of field electron emission from carbon nanotubes

Field electron emission (FE) is a quantum tunneling process in which electrons are injected from materials (usually metals) into a vacuum under the influence of an applied electric field. In order to obtain usable electron current, the conventional way is to increase the local field at the surface of an emitter. For a plane metal emitter with a typical work function of 5 eV, an applied field of over 1 000 V/μm is needed to obtain a significant current. The high working field (and/or the voltage between the electrodes) has been the bottleneck for many applications of the FE technique. Since the 1960s, enormous effort has been devoted to reduce the working macroscopic field (voltage). A widely adopted idea is to sharpen the emitters to get a large surface field enhancement. The materials of emitters should have good electronic conductivity, high melting points, good chemical inertness, and high mechanical stiffness. Carbon nanotubes (CNTs) are built with such needed properties. As a quasi-one-dimensional material, the CNT is expected to have a large surface field enhancement factor. The experiments have proved the excellent FE performance of CNTs. The turn-on field (the macroscopic field for obtaining a density of 10 μA/cm2) of CNT based emitters can be as low as 1 V/μm. However, this turn-on field is too good to be explained by conventional theory. There are other observations, such as the non-linear Fowler-Nordheim plot and multi-peaks field emission energy distribution spectra, indicating that the field enhancement is not the only story in the FE of CNTs. Since the discovery of CNTs, people have employed more serious quantum mechanical methods, including the electronic band theory, tight-binding theory, scattering theory and density function theory, to investigate FE of CNTs. A few theoretical models have been developed at the same time. The multi-walled carbon nanotubes (MWCNTs) should be assembled with a sharp metal needle of nano-scale radius, for which the FE mechanism is more or less clear. Although MWCNTs are more common in present FE applications, the single-walled carbon nanotubes (SWCNTs) are more interesting in the theoretical point of view since the SWCNTs have unique atomic structures and electronic properties. It would be very interesting if people can predict the behavior of the well-defined SWCNTs quantitatively (for MWCNTs, this is currently impossible). The FE as a tunneling process is sensitive to the apex-vacuum potential barrier of CNTs. On the other hand, the barrier could be significantly altered by the redistribution of excessive charges in the micrometer long SWCNTs, which have only one layer of carbon atoms. Therefore, the conventional theories based upon the hypothesis of fixed potential (work function) would not be valid in this quasi-one-dimensional system. In this review, we shall focus on the mechanism that would be responsible for the superior field emission characteristics of CNTs. We shall introduce a multi-scale simulation algorithm that deals with the entire carbon nanotube as well as the substrate as a whole. The simulation for (5, 5) capped SWCNTs with lengths in the order of micrometers is given as an example. The results show that the field dependence of the apex-vacuum electron potential barrier of a long carbon nanotube is a more pronounced effect, besides the local field enhancement phenomenon.

Analytic Solution of Charge Density of Single Wall Carbon Nanotube under Conditions of Field Electron Emission

We derive the analytic solution of induced electrostatic potential along single wall carbon nanotubes. Under the hypothesis of constant density of states in the charge-neutral level, we are able to obtain the linear density of excess charge in an external field parallel to the tube axis.We derived the analytic solution of induced electrostatic potential along single wall carbon nanotubes. Under the hypothesis of constant density of states in the charge-neutral level, we are able to obtain the linear density of excess charge in an external field parallel to the tube axis.

Short-Time Critical Behavior Affected by Weakly Long-Range Interactions

The theoretic renormalization group approach is applied to the study of short-time critical behavior of the Ginzburg–Landau model with weakly long-range interactions . The system initially at a high temperature is firstly quenched to the critical temperature and then released to an evolution with a model A dynamics. A double expansion in and with of order is employed, where is the spatial dimension. The asymptotic scaling laws and the initial slip exponents and for the order parameter and the response function respectively are calculated to the second order in for close to 2.

Monte Carlo Simulation of the Non-universal Short-Time Behavior for a Kinetic 2-D Ising Model*

The short-time dynamic process for the two-dimensional Ising model with the nearest-neighbor coupling and the next-nearest-neighbor antiferromagnetic coupling in the critical domain is simulated by the Monte Carlo method. From the power law behavior of the initial order increase, the critical points and the initial dynamic exponent are determined.

Particle Transport with Asymmetric Unbiased Forces and Entropic Barrier

Transport of a Brownian particle moving along the axis of a three-dimensional (3D) symmetric and periodic tube is investigated in the presence of asymmetric unbiased forces. It is found that in the presence of entropic barrier, the asymmetry of the unbiased forces is a way of inducing a net particle current. The particle current is a peaked function of temperature, which indicates that the thermal noise may facilitate the transport even in the presence of entropic barrier. There exists an optimized radius at the bottleneck at which the particle current takes its maximum value. The current can be influenced by the slope of tube walls and there exists an optimized slope for which the particle current takes its maximum value.

Dynamics of the Random Ising Model with Long-Range Interaction

Critical dynamics of the random Ising model with long-range interaction decaying as (where is the dimensionality) is studied by the theoretic renormalization-group approach. The system is released to an evolution within a model dynamics. Asymptotic scaling laws are studied in a frame of the expansion in . In dimensions , the dynamic exponent is calculated to the second order in at the random fixed point.

Noise-Induced Transition in a Voltage-Controlled Oscillator Neuron Model

In the presence of Gaussian white noise, we study the properties of voltage-controlled oscillator neuron model and discuss the effects of the additive and multiplicative noise. It is found that the additive noise can accelerate and counterwork the firing of neuron, which depends on the value of central frequency of neuron itself, while multiplicative noise can induce the continuous change or mutation of membrane potential.

Ground Band and Excited Band of Spin-1 BEC in Cigar Shaped Laser Trap

The wavefunctions that conserve the total spin are constructed for the fully condensed states and the states with one particle excited. A set of equations are deduced for the spatial longitudinal wavefunctions and the chemical potentials. These equations are solved numerically for 23Na and 87Rb condensates. The deformed trap shows significant effects on the spectrum. This implies that the spin effect of the spinor BEC are more easily detected in an optical trap of larger aspect ratio.

Population Growth of Small Harmful Rats in Grassland Subjected to Noise

The population growth of small harmful rats in grassland subjected to environment fluctuation has been modelled in a logistic equation. Two correlated random variables responsible to the fluctuation of the genetic factor and the suppression factor are used. A two-peak structure of the steady probability distribution of rate population is observed in the large fluctuation regime of the genetic factor. With the increase of correlation constant λ, the steady probability distribution can change from two peaks to a single peak. The suppression factor μ and its fluctuation also affect the steady probability distribution and can push it toward a small population.

Critical Spreading of Active Region in a Ladder Model Possessing Infinite Absorbing States

The spreading of active region of the ladder model is simulated. Finite-time scaling behaviors are observed in the vicinity of the critical point.