Escape probability of signal photoelectrons from non-crystalline solids: influence of anisotropy of photoemission

The escape probability of photoelectrons as a function of depth of orgin haa been studied experimentally, analytically and by the Monte Carlo (MS) technique. The depth distribution function (DDF) describing the probability for an electron emitted at a certain depth to leave a surface without being scattered inelastically has been obtained by solving a kinetic equation in the transport approximation. The analytically derived DDF is a universal function of the ratio of the inealstic to the transport mean free paths and the asymmetry parameter. In the directions of minima of the angular distribution, this function is no longer exponential, but it may be essentially nonmonotonic, reaching its maximum value at the depth comparable with the inelastic mean free path. The maximum value of the DDF exceeds its surface value by about 50% for the asymmetry parameter being equal to 2 in the emission directions close to that of X-ray propagation. Under the same conditions, the mean escape depth of electrons may be several times larger than the value predicted by the usual XPS formalism. Such behaviour of the escape probability is explained by elastic scattering of photoelectrons.The solution to the kinetic equation for a uniform target is generalized for a sample with an arbitrary depth profile and depth-dependent elastic and inelastic scattering cross-sections under the condition of the ratio of the inelastic to the transport mean free paths being independent of depth. Analytical formulas for the photoelectron yield from overlayer/substrate structure have been derived and studied in detail. The analytical predictions are compared with the experimental and Monte Carlo simulation data obtained for aluminium oxide/aluminium specimen. A satisfactory agreement is observed between the experimental and theoretical results.     

Photoelectron escape from iron oxide

Iron oxide of nanometer thickness were grown in situ by step-by-step oxidation of an iron foil to measure the escape probabilities of O 1s photoelectrons as a function of depth of origin, the so-called emission depth distribution function (EDDF), and the mean escape depth (MED). To record photoelectron spectra for a wide range of emission angles, the X-ray excitation source was positioned on the opposite side of the iron foil with respect to the analyzer. To excite photoelectrons on the side of the foil surface adjacent to the analyzer, the foil was made thin enough to be semitransparent to the X-ray radiation. The O 1s spectra were recorded for a wide range of oxide thicknesses until no features of metallic iron were recognized in the photoelectron spectra. The escape probability of the O 1s photoelectrons in the iron oxide was derived from the oxide-thickness dependence of the O 1s peak areas. The resulting EDDF reached a maximum beneath the oxide surface for X-ray incidence and electron-emission angles located along the surface normal. For the same incidence angle and an emission angle of 60°, the escape probability could be well approximated by a simple exponential function. The mean escape depths were obtained for both experimental geometries and agreed well with the available theory.     

Zur Lage des Maximums der Ausbeutekurve bei der Sekundärelektronenemission

There exists a quantitative connection between penetration depth of primary electrons, the maximum escape depth of secondary electrons and the position of the maximum of the yield curve if one assumes: (1) the maximum of the yield curve is determined by an energyE _p ^max of the primary electrons where the maximum penetration depth of primary electrons equals the maximum escape depth of the secondary electrons; and (2) the maximum escape depth of secondary electrons is given by 10 atomic layers for all metals investigated as it has been found earlier by Mayer and Hölzl for potassium. These assumptions are confirmed experimentally by measurements of yield curves and energy distributions at defined conditions and by variation of several parameters as temperature, contamination of the surface, surface roughness, evaporation conditions, and angle of incidence of the primary electrons.     

粒子在二维开放型四分之一圆形微腔中的逃逸研究

利用半经典理论对粒子在开放型四分之一圆形微腔中的逃逸过程进行了研究,推导出了逃逸几率密度的计算公式.我们研究了一簇从四分之一圆形微腔的左下方的入口出射、并从该微腔右边界逃逸的粒子轨迹.对于粒子的每一条逃逸轨迹,记录下它的传播时间和逃逸的位置.结果发现逃逸时间图随着逃逸点的位置的变化曲线呈现出振荡结构.随着碰撞次数的增加,逃逸点的位置越靠近该腔的右顶端.对一系列的探测点,找到从源点出发到达探测点的轨迹,然后应用半经典理论来构造波函数,进而给出逃逸几率密度的计算公式.研究结果标明,逃逸几率密度与探测平面上逃逸点的位置、粒子的动量、初始出射角及与微腔的碰撞次数有关.为了更清楚的看出量子力学和经典力学之间的联系,我们对体系的半经典波函数进行傅里叶变换,给出了粒子的路径长度谱.路径长度谱的每个峰值对应于一条粒子逃逸轨迹的长度.本文的研究对理解量子力学和经典力学之间的联系以及研究粒子在微腔中的的逃逸和输运过程有一定的参考价值.     

粒子在二维开放型四分之一圆形微腔中的逃逸研究

利用半经典理论对粒子在开放型四分之一圆形微腔中的逃逸过程进行了研究,推导出了逃逸几率密度的计算公式。我们研究了一簇从四分之一圆形微腔的左下方的入口出射、并从该微腔右边界逃逸的粒子轨迹。对于粒子的每一条逃逸轨迹,记录下它的传播时间和逃逸的位置。结果发现逃逸时间图随着逃逸点的位置的变化曲线呈现出振荡结构。随着碰撞次数的增加,逃逸点的位置越靠近该腔的右顶端。对一系列的探测点,找到从源点出发到达探测点的轨迹,然后应用半经典理论来构造波函数,进而给出逃逸几率密度的计算公式。研究结果标明,逃逸几率密度与探测平面上逃逸点的位置、粒子的动量、初始出射角及与微腔的碰撞次数有关。为了更清楚的看出量子力学和经典力学之间的联系,我们对体系的半经典波函数进行傅里叶变换,给出了粒子的路径长度谱。路径长度谱的每个峰值对应于一条粒子逃逸轨迹的长度。本文的研究对理解量子力学和经典力学之间的联系以及研究粒子在微腔中的的逃逸和输运过程可以提供一定的参考价值。     

GaN光电阴极表面势垒对电子逸出几率的影响

针对GaN光电阴极表面势垒对电子逸出几率的影响问题,应用玻尓兹曼分布和基于Airy函数的传递矩阵法计算了GaN光电阴极的电子逸出几率,发现电子逸出几率主要由I势垒决定,II势垒对电子逸出几率的影响有限.利用自行研制的GaN光电阴极激活评估实验系统,测试了透射式GaN光电阴极样品的激活光电流.实验发现,Cs单独激活引起电子逸出几率的显著增加,而Cs单独充分激活后的Cs/O交替激活对电子逸出几率的影响有限.理论计算结果与激活光电流测试结果一致,其原因是Cs单独激活对降低真空能级的贡献远大于Cs/O共同激活.     

Resonant escape over an oscillating barrier in underdamped Josephson tunnel junctions

The escape from a metastable state over an oscillating barrier of an underdamped Josephson tunnel junction has been experimentally investigated with oscillation frequency well separated from the plasma frequency of the junction. The resonant escape, namely, a minimum of the average escape time as a function of the oscillation frequency, was observed. For the oscillation frequency much smaller than the "resonant frequency," the average escape time is the average of the times required to cross over each of the barriers. On the other hand, for the oscillation frequency much greater than the "resonant frequency," the average escape time is that required to cross the average barrier.     

The escape factor in plasma spectroscopy—I. The escape factor defined and evaluated

In plasma spectroscopy, it is frequently convenient to treat the effect of self-absorption parametrically, as a reduction in the spontaneous transition probability by a parameter known in the literature relating to laboratory sources as the escape factor. The concept of the escape factor is here developed in a systematic way, within a framework into which the many contributions of individual authors to particular aspects of the subject have been fitted. A general definition of the escape factor is presented from which other definitions are shown to follow. The escape factor has been evaluated for Gaussian, Lorentzian and Holtsmarkian profiles, for upper and lower limits to the source function and for infinite plane-parallel slab and infinite cylinder geometries. A comparison is made with other calculations of the escape factor from the literature. Where appropriate, reference is made to the astrophysical literature, particularly to that concerning the net radiative bracket.     

The influence of frequency redistribution on the transfer of gyroresonant photons in the atmospheres of compact stars: Monte-Carlo analysis

We numerically model the frequency redistribution of gyroresonant photons in a plane-parallel semi-infinite plasma atmosphere of a compact star by means of the Monte-Carlo method. We calculate the mean frequency shift and the mean number of scatterings for photons leaving the atmosphere as functions of the optical depth at emission, plasma temperature, and magnetic field strength. The probability of the escape of cyclotron-radiation photons from the atmosphere as a function of their optical depth at birth is calculated. The influence of the frequency redistribution effects on the spectrum of emergent radiation is studied.     

Dependence of ESCA signal intensities of ionic compounds on chemical environment

Variation in ESCA signal intensities for ionic compounds is interpreted in terms of the dependence of photoelectron escape probability on the immediate environment of the emission center. A model has been developed to estimate this escape probability by the fractional solid angle not blocked by the nearest neighbors of the emission center. A linear correlation is found between the normalized intensity ratios for simple alkali halides and the fractional escape solid angle ratios. Absolute intensity measurements have been carried out for alkali perchlorates and alkali chlorides. The chlorine signal intensities were constant for perchlorates but decrease steadily from LiCl to CsCl. These observations are consistent with the chlorine atom in the perchlorate groups always being surrounded by four oxygens; therefore its fractional escape solid angle is independent of the compound.     

重力驱动下运动物体在颗粒介质中的最大穿透深度

通过高速摄像的跟踪，研究了重力场中球形下落物体对松散颗粒床进行撞击并进入颗粒床内的运动过程.运用已得到的颗粒体系中运动物体的阻力模型，分析了物体质量对穿透深度的影响.研究表明，当物体与颗粒床撞击的初始速度较小时，物体在颗粒床中的最大穿透深度与物体质量呈近似线性关系. 实验得到的结果与模型符合很好. 关键词： 颗粒体系 阻力 动力学过程     

Escape by diffusion from a square well across a square barrier

The problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time. In the limit of a high barrier the rate of escape is given by an asymptotic result similar to that derived by Kramers for a curved well and a curved barrier. An approximate analytic formula is derived for the outward time-dependent probability current in terms of the width and depth of the well and the width and height of the barrier. A similar expression holds for the complete probability distribution.     

A prediction theory of random level distribution based on a generalized difference type of Fokker-Planck equation and its application to environmental noise and vibration,II: Experimental study

In a companion paper [1], a procedure for solving the short time prediction problem in terms of the transition probability distribution has been theoretically derived, for discrete time-sampled data. Explicit algorithms for estimating the non-stationary moment statistics of arbitrary order also have been derived, based on a generalized difference equation of Fokker-Planck type for the conditional probability distributed function, which is central to the theory. In this paper, evidence for the validity and effectiveness of the proposed method is presented, as obtained not only by means of digital simulation but also by using road traffic noise data obtained experimentally in Hiroshima. For several non-stationary random processes simulated by means of random numbers, the theoretical and experimental conditional probability functions are compared. For non-stationary road traffic noise data the theoretically predicted and experimentally determined confidence intervals are compared; in these comparisons several types of conditional probability function and various values of weighting parameter are used in the algorithm. All of the theoretical results show good agreement with the experimental results.     

Canopy spectral invariants, Part 2: Application to classification of forest types from hyperspectral data

Many studies have been conducted to demonstrate the ability of hyperspectral data to discriminate plant dominant species. Most of them have employed the use of empirically based techniques, which are site specific, requires some initial training based on characteristics of known leaf and/or canopy spectra and therefore may not be extendable to operational use or adapted to changing or unknown land cover. In this paper we propose a physically based approach for separation of dominant forest type using hyperspectral data. The radiative transfer theory of canopy spectral invariants underlies the approach, which facilitates parameterization of the canopy reflectance in terms of the leaf spectral scattering and two spectrally invariant and structurally varying variables—recollision and directional escape probabilities. The methodology is based on the idea of retrieving spectrally invariant parameters from hyperspectral data first, and then relating their values to structural characteristics of three-dimensional canopy structure. Theoretical and empirical analyses of ground and airborne data acquired by Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) over two sites in New England, USA, suggest that the canopy spectral invariants convey information about canopy structure at both the macro- and micro-scales. The total escape probability (one minus recollision probability) varies as a power function with the exponent related to the number of nested hierarchical levels present in the pixel. Its base is a geometrical mean of the local total escape probabilities and accounts for the cumulative effect of canopy structure over a wide range of scales. The ratio of the directional to the total escape probability becomes independent of the number of hierarchical levels and is a function of the canopy structure at the macro-scale such as tree spatial distribution, crown shape and size, within-crown foliage density and ground cover. These properties allow for the natural separation of dominant forest classes based on the location of points on the total escape probability vs the ratio log-log plane.     

表面势垒对梯度掺杂GaN光电阴极电子逸出几率的影响

研究表面势垒对梯度掺杂GaN光电阴极电子逸出几率的影响.计算梯度掺杂透射式GaN光电阴极的电子能量分布及逸出几率,结果显示梯度掺杂与均匀掺杂相比,可以获得更大的电子逸出几率;I势垒对电子逸出几率的影响显著,而Ⅱ势垒影响较小.利用GaN光电阴极多信息量测试系统,测试两种GaN阴极样品的光电流.实验结果表明,梯度掺杂GaN样品比均匀掺杂电子逸出几率更大;单独进行Cs激活形成的I势垒对电子逸出几率有显著影响,而Cs/O共同激活形成的Ⅱ势垒对其影响较小.     

Influence of cesium atoms on the field electron emission from multi-walled carbon nanotubes

It has been shown that the deposition of cesium atoms on multi-wall carbon nanotubes abruptly increases the current of the field electron emission, decreases the threshold electric field by a factor of three (to 0.8 V/m), and decreases the work function to 2.1–2.3 eV. It has been found that the flowing of the large emission current I ≥ 2 × 10^?6 A leads to a change in the current-voltage characteristics and a decrease in the emission current. This effect has been explained by escape of cesium atoms from the tips of most nanotubes into the nanotube depth due to desorption or intercalation. At the same time, the low work function is retained for some nanotubes, probably, due to the stronger bonding of Cs atoms with these nanotubes.     

The mean probability of photon capture of resonance radiation in atomic absorption spectroscopy

The mean probability of photon capture Ψ, obtained via an approximation to the complementary escape factor Λ, for calcium and zinc resonance lines at 4226.73 and 2138.56 Å have been determined from their atomic absorption measurements. Calculations are performed for Gaussian, Lorentzian, and Voigt spectral line shapes. Tabulations and graphical plots of the mean probability of photon capture, Ψ, with the optical depth in the center of Doppler profile, τ_D, and the number density of free atoms in the ground state N, are provided.     

Equilibrium measure and Brownian escape process

The probability density of Brownian escape process has been obtained recently by R. K. Getoor. In this note we illustrate that Getoor's result can also be obtained by considering equilibrium charge distribution on a metal ball of radiusr>0. This approach reveals a connection between Brownian escape process and classical potential theory.     

Fresnel biprism as a 1D refractive axicon

Fresnel biprism is a one dimensional refractive element that has a lateral linear phase. Having been considered this element as a refractive axicon, its focal depth was evaluated theoretically and experimentally by means of Fresnel–Kirchhoff integral. It is shown that its focal length is a function of its refractive index and its apex angle. Experimental results are in very good agreement with theoretical work.     

Optical chaos and hysteresis in a laser-diode pumped Nd doped fibre laser

Modulated pumping of a Nd³⁺ doped silica monomode fibre laser has been investigated experimentally. For small modulation depths the laser exhibits a resonance at the relaxation oscillation frequency, providing pulses of a few microseconds duration at a repetition rate in the region of 10 kHz, dependent on the average pump level above threshold. As the pump modulation depth is increased, hysteresis is observed as a function of modulation frequency, along with optical bistability. For further increase in modulation depth, optical chaos and period doubling are observed. Gain-switching has also been demonstrated.