Tunneling time in space fractional quantum mechanics

We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for $b\to \infty$ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.     

Tunneling time based on the quantum diffusion process approach in multichannel and optical potential cases

We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson’s quantum mechanics. This generalization enables us to describe quantum system with channel couplings and optical potential in a real time stochastic approach, which seems to give us a new insight into quantum mechanics beyond Copenhagen interpretation     

Tunneling times through a barrier with inelasticity

Tunneling delay times of wavepackets in quantum mechanical penetration of rectangular barriers have long been known to show a perplexing independence with respect to the width of the barrier. This also has relevance to the transmission of evanescent waves in optics. Some authors have claimed that in the presence of absorption or inelastic channels (which they model by taking a complex barrier potential) this effect no longer exists, in that the time delay becomes proportional to the barrier width. Taking the point of view that complex potentials imply non-Hermitian Hamiltonians and are as such fraught with conceptual pit-falls particularly in connection to problems involving time evolution, we have constructed a two-channel model which does not suffer from such limitations in order to examine this issue. We find that the conclusions arrived at by the earlier authors need to be more precisely specified.     

Tunneling time and stochastic-mechanical trajectories for the double-barrier potential

Quantum motion of particles tunneling a double barrier potential is considered by using stochastic mechanics. Stochastic-mechanical trajectories give us information about complex motion of tunneling particles that is not obtained within the framework of ordinary quantum mechanics. Using such information, we calculate the tunneling times within each of the barriers which depend on the distance between them. It is found that the stochastic-mechanical tunneling time shows better asymptotic behavior than the quantum-mechanical dwell time and presence time.     

Influence of field evaporation treatment on the field emission properties of carbon nanotubes array

Field evaporation was used in the post-fabrication treatment of a carbon nanotubes (CNTs) array and effectively modified the CNTs morphology in favor of the field emission under a moderate field. After the field evaporation treatment, the uniformity of the emission site distribution improved but the onset voltage rose. Using the Fowler-Nordheim theory, the actual onset field and the evaporation field around the CNT were calculated to be −4.6-5 and 9-12 V/nm, respectively. These values are close to those obtained from the individual CNT samples. The above results have provided an alternative to modify the configuration of an array sample and demonstrated the feasibility of tackling the problem of the disparity in the field emission capability of different CNTs in an array.     

Tunneling times for opaque barriers

We propose new criteria to evaluate the average time spent by particles in a tunneling barrier. First we construct asojourn time, on the basis of statistical information provided by quantum mechanics, which seems to be an appropriate measure of the time spent byall particles within the barrier. A simple, stochastic treatment is then used to deal with the particles that actually traverse the barrier, in order to study their interaction time. The results obtained show that opaque barriers have important effects on the particlesbefore they enter the potential region, confirming previously published numerical findings. No arbitrarily high effective velocities appear anywhere in the present treatment.     

Tunneling Times with Covariant Measurements

We consider the time delay of massive, non-relativistic, one-dimensional particles due to a tunneling potential. In this setting the well-known Hartman effect asserts that often the sub-ensemble of particles going through the tunnel seems to cross the tunnel region instantaneously. An obstacle to the utilization of this effect for getting faster signals is the exponential damping by the tunnel, so there seems to be a trade-off between speedup and intensity. In this paper we prove that this trade-off is never in favor of faster signals: the probability for a signal to reach its destination before some deadline is always reduced by the tunnel, for arbitrary incoming states, arbitrary positive and compactly supported tunnel potentials, and arbitrary detectors. More specifically, we show this for several different ways to define “the same incoming state” and “the same detector” when comparing the settings with and without tunnel potential. The arrival time measurements are expressed in the time-covariant approach, but we also allow the detection to be a localization measurement at a later time. Dedicated to Pekka Lahti on the occasion of his 60th birthday.     

Synthesis and efficient field emission of ZnO nanoinjectors

ZnO nanoinjectors were synthesized on Au-coated Si substrate by direct thermal evaporation of zinc powder at a low temperature of 600 °C and atmospheric pressure. Field-emission scanning electron microscopy and X-ray diffraction were applied to study the structural characteristics of the sample. The result indicated that the nanoinjector sample consisted of single-crystalline wurtzite structures which were preferentially oriented in the 0 0 1 direction. The field emission of the sample started at a turn-on field of 1.5 V/μm at a current density of 1 μA/cm², while the emission current density reached about 1 mA/cm² at an applied field of 5.0 V/μm.     

Confinement of the field electron emission to atomic sites on ultra sharp tips

The spatially controlled field assisted etching method for sharpening metallic tips, in a field ion microscope (FIM), is used to study the evolution of the field emission when the tip apex radius is decreased below 1 nm. Unlike the conventional image formation in a field emission microscope (FEM), we demonstrate that at this scale the field emission is rather confined to atomic sites. A single atom apex fabricated at the end of such tips exhibits an outstanding brightness compared to other atomic tips. The measurements have been repeated for two double atom tips, with different atom-atom separations, and images of atomic field emission localization have also been obtained. We have found that the field emission intensity alternates between adjacent atoms when the applied voltage is gradually increased beyond a threshold value.     

碳纤维阴极的场致发射特性实验研究

 研究了具有一定导电性能的碳纤维的直流场致发射电子束特性,实验分别在大气环境、低真空（10^-1 Pa）及高真空(10^-5 Pa)环境下进行。实验结果表明,碳纤维具有一定的场致发射能力,并且发射特性和发射环境的真空度密切相关。在大气环境下,发射电子束流与所施加的电压符合Fowler-Nordheim关系,当电压为7 kV,电流为61.4 μA时,根据Fowler-Nordheim定理推算出碳纤维场致发射场增强因子为3.75×10⁵。在低真空条件下阳极只收集到微弱的电流;在高真空条件下,阴极发射明显,在较低电压下就能观测到阳极电流,放电前阳极最高电流是大气条件下的3~4倍,发射的束流大小和所施加在尖端的电压关系接近Child-Langmiur定律。     

Simulation and fabrication of carbon nanotubes field emission pressure sensors

A novel field emission pressure sensor has been achieved utilizing carbon nanotubes (CNTs) as the electron source. The sensor consists of the anode sensing film fabricated by wet etching process and multi-wall carbon nanotubes (MWNTs) cathode in the micro-vacuum chamber. MWNTs on the silicon substrate were grown by thermal CVD. The prototype pressure sensor has a measured sensitivity of about 0.17-0.77 nA/Pa (101-550 KPa). The work shows the potential use of CNTs-based field-emitter in microsensors, such as accelerometers and tactile sensors.     

Model calculation and empirical investigation of enhanced field emission behavior of branched carbon nanostructures

In this paper, we propose the novel branched carbon nanotubes (B-CNTs) as efficient candidate for field emission applications. We believe that the double-stage structure of B-CNTs, beside formation of multiple thin branches at the apex of each vertical CNT, is responsible for the observed enhanced field emission behavior in B-CNTs. In this regard, we have derived an analytical model to evaluate the field enhancement factor (β) of the B-CNTs in comparison with CNTs, as the most popular cathode for field emission applications in the scientific society. The presented model also allows investigating the effect of different structural parameters on the field emission characteristic. We have also, compared the field emission characteristics of the B-CNTs with vertical CNTs experimentally. We observed a β value for B-CNTs which was around three times higher than CNTs. The observed enhancement in the experimental data was in good agreement with the presented analytical model.     

Modeling and simulation for the field emission of carbon nanotubes array

To optimize the field emission of the infinite carbon nanotubes (CNTs) array on a planar cathode surface, the numerical simulation for the behavior of field emission with finite difference method was proposed. By solving the Laplace equation with computer, the influence of the intertube distance, the anode–cathode distance and the opened/capped CNT on the field emission of CNTs array were taken into account, and the results could accord well with the experiments. The simulated results proved that the field enhancement factor of individual CNT is largest, but the emission current density is little. Due to the enhanced screening of the electric field, the enhancement factor of CNTs array decreases with decreasing the intertube distance. From the simulation the field emission can be optimized when the intertube distance is close to the tube height. The anode–cathode distance hardly influences the field enhancement factor of CNTs array, but can low the threshold voltage by decreasing the anode–cathode distance. Finally, the distribution of potential of the capped CNTs array and the opened CNTs array was simulated, which the results showed that the distribution of potential can be influenced to some extent by the anode–cathode distance, especially at the apex of the capped CNTs array and the brim of the opened CNTs array. The opened CNTs array has larger field enhancement factor and can emit more current than the capped one.     

Growth and field emission properties of globe-like diamond microcrystalline-aggregate

The globe-like diamond microcrystalline-aggregates were fabricated by microwave plasma chemical vapor deposition (MPCVD) method. The ceramic with a Ti mental layer was used as substrate. The fabricated diamond was evaluated by Raman scattering spectroscopy, X-ray diffraction spectrum (XRD), and scanning electron microscope (SEM). The field emission properties were tested by using a diode structure in a vacuum. A phosphor-coated indium tin oxide (ITO) anode was used for observing and characterizing the field emission. It was found that the globe-like diamond microcrystalline-aggregates exhibited good electron emission properties. The turn-on field was only 0.55 V/μm, and emission current density as high as 11 mA/cm² was obtained under an applied field of 2.9 V/μm for the first operation. The growth mechanism and field emission properties of the globe-like diamond microcrystalline-aggregates are discussed relating to microstructure and electrical conductivity.     

On the alleged equivalence of certain field theories

We critically examine some recent claims that certain field theories with and without boson kinetic energy terms are equivalent. We point out that the crucial element in these claims is the finiteness or otherwise of the boson wavefunction renormalisation constant. We show that when this constant is finite, the equivalence proof offered in the literature fails in a direct way. When the constant is divergent, the claimed equivalence is only a consequence of improper use of divergent quantities.     

The field emission of vacuum filtered graphene films reduced by microwave

A green, convenient, and inexpensive approach to producing graphene field emitters has been developed. Graphite oxide (GO) produced by hummer method was reduced to graphene in a microwave synthesis system. The vacuum filtration method made it possible to form pure and uniform graphene thin films without any additives and it's easy to transfer to other substrates. Transmission electron microscopy (TEM), X-ray diffraction (XRD), and UV-vis diffuse reflectance spectroscopy (UV-vis) measurements proved that the graphene prepared by microwave has nearly the same reduction level as that prepared by hydrazine. The results of field emission testing demonstrated that graphene films reduced by microwave are more suitable as field emitters than those reduced by hydrazine, which pave a way to mass-produce low-cost graphene emitter for field emission applications.     

Simulations of barrier traversal and reflection times based on event enhanced quantum theory

The formalism of event enhanced quantum theory is used to simulate traversal and reflection times of electrons through a one-dimensional barrier. The dependence of these times on the parameters of the barrier and the detectors is examined and the results are compared with those of selected approaches.     

单晶LaB6场发射阵列的电化学腐蚀工艺

 六硼化镧（LaB₆）场发射尖锥阵列的刻蚀工艺是制备LaB₆场发射阵列阴极的关键。在(111)面单晶LaB₆基片上,用等离子体增强化学气相沉积法制备氮化硅层做掩膜,光刻后采用电化学腐蚀方法对基片进行刻蚀,得到具有一定高度的LaB₆尖锥场发射阵列。讨论了单晶LaB₆的电化学腐蚀机理。改变各种电化学腐蚀参数,包括电解液成分、电解液浓度、阳极所加电压,用电子扫描显微镜观察样品形貌。结果发现H₃PO₄是刻蚀单晶LaB₆的理想电解液,它克服了过去电化学实验中经常遇到的尖锥各向异性问题。随着电解液浓度或阳极电压的增大,尖锥高度增加,但是基底表面变得更为粗糙。另一方面,阳极电压太小时,有横向刻蚀现象产生,不利于提高发射体的场增强因子。此外,在二极管结构中初步测试了LaB6尖锥场发射阵列的电流发射特性,在真空度2×10^-4 Pa、极间距离0.1 mm、阳极电压900 V下,发射电流达到13 mA。     

Carbon nanotube field emission cathodes fabricated with chemical displacement plating

A new approach for making field emission cathodes consisting of carbon nanotubes (CNTs) is discussed. The authors used a chemical displacement technique to fabricate field emission cathodes by co-depositing CNTs/nickel composite onto the surface of a zinc-coated soda-lime glass. There are several advantages of this displacement method for preparing field emission cathodes such as the uniform distribution of CNTs in the composite cathodes, low cost of consumed CNTs, low cost of instrument and equipment, feasibility of large-area mass production, and stability of plating solution, which can be used for many times and still remain useful after a long-time storage. The results show that, after the CNT purification and dispersion processes, a CNT content of 1.0 g/L, a pH value of 7.0, and a temperature of 50 ± 3 °C are the optimal process conditions which give better CNT distribution in the CNTs/Ni composite emitter and better field emission performance. The CNTs/Ni composite deposited with a plating solution which has been used for tens of times has an emission effect similar to those deposited with a new solution.     

Tunneling time distribution by means of Nelson’s quantum mechanics and wave-particle duality

We construct a tunneling time distribution by means of Nelson’s quantum mechanics and investigate statistical properties of the tunneling time distribution. As a result, we find that the relationship between the average and the variance of the tunneling time shows ‘wave-particle duality’.