Electron trajectories

Monte Carlo electron trajectory simulations provide a pictorial view of the complei electron—specimen interaction. As shown in Figure 2a, which depicts the interac-... 

Figure 2 (a) Monte Carlo simulation of electron trajectories in copper beam energy... 

A significant fraction—about 15% for aluminum, 30% for copper, and 50% for gold—of the beam electron trajectories intersect the surface and escape as backscat-tered electrons (BSEs), as shown in Figure 2a. The majority of BSEs escape with more than half of their incident energy. Clearly, if these electrons had remained in... 

The phenomena of beam broadening as a function of specimen thickness are illustrated in Fig. 4.20 each figure represents 200 electron trajectories in silicon calculated by Monte Carlo simulations [4.91, 4.95-4.97] for 100-keV primary energy, where an infinitesimally small electron probe is assumed to enter the surface. In massive Si the electrons suffer a large number of elastic and inelastic interactions during their paths through the material, until they are finally completely stopped. The resulting penetration depth of the electrons is approximately 50 pm and in the... 

Consider the apparatus shown in Figure 14-6. The equipment is similar to that shown in Figure 14-4 except a fluorescent screen within the tube reveals the trajectory of the particles that pass through the slot in the positive electrode. When a magnetic field is added, the electron trajectory is curved. A mathematical analysis of the curvature permits an interpretation of this experiment that leads to a determination of e/m. 

Though quantum mechanics does not tell us the electron trajectory, it does tell us how the orbital changes as n increases. It also indicates that for each value of n there are n2 different orbitals. For the hydrogen atom, the rf orbitals for a particular value of n all have the same energy,... 

Helical undulators build on this principle by using two orthogonal magnetic field arrays [82, 83]. These permit transverse excursions in perpendicular x and y directions. If the arrays have a relative longitudinal shift, this introduces a phase to the induced perpendicular excursions and when the phase is 90° the electron trajectory can follow left- or right-handed corkscrew paths The emitted radiation is correspondingly right- or left-handed CPL. 

Figure 4. Kinematics of the solid-state EMS spectrometer [11]. (a) The polar angles made by kf and k, with respect to the incident (z) direction are Of = 14° and 6% = 76°. In (b) is shown a typical sample membrane relative to the electron trajectories. The surface sensitivity is largely determined by the escape depth of the 1.2 keV electrons ( 2 nm) and is indicated by the shaded area. 

Kerkhof and Moulijn [30] suggested that a supported catalyst may be modeled as a stack of sheets of support material, with cubic crystals representing the supported particles. They used this stratified layer model, illustrated in Fig. 3.9b, to calculate the intensity ratio /P//s for electron trajectories perpendicular to the support sheets, assuming exponential attenuation of the electrons in the particles and the support. 

In fact, this attraction between negative charges (that violates the principles of electrostatics) is mediated by the crystal structure of the superconductor. In every metal lattice there is a reciprocal stripping of valence electrons between metal sites which results in these metal sites, fixed at lattice positions, assuming a positive charge. As shown in Figure 7, when a moving electron crosses these positive metal sites the metal ions are attracted towards the electron trajectory and disturbed from its equilibrium position. 

In order to estimate the contribution of secondary electrons, degradation spectrum, or in other words slowing down spectrum, is used. Degradation spectrum is defined as the length of the secondary electron trajectory, where the electron with the initial energy dissipates its energy between E and E+dE. 

In a pump-probe configuration, using photodiodes for the detection, significant absorption spectroscopic data are reported in Fig.l. Following the interaction of UV photons with aqueous OH ion, two well defined electronic trajectories are observed in the first 4 ps. 

For a same molecular ratio of aqueous NaY solutions (Y = OH, Cl), experimental data underlines specific effects of nascent OH radicals on transient UV and near-IR electronic configurations. Complex investigations of PHET reactions in the polarization CTTS well of aqueous CT and OH ions are in progress. We should wonder whether a change in the size of ionic radius (OH -1.76 A vs Cl" 2.35 A) or in the separation of the energy levels influence early branchings of ultrafast electronic trajectories. A key point of these studies is that the spectroscopic predictions of computed model-dependent analysis are compared to a direct identification of transient spectral bands, using a cooled Optical Multichannel Analyzer... 

A. H. Zewail Reaching the 100-ps time scale with our apparatus was not difficult. For the next step in reaching better resolution with a factor of 100, we had to build the system I described, which is sensitive to single-electron detection. Currently we can obtain 1 ps resolution, and with better electron trajectories we anticipate reaching the 50-fs limit outlined by Prof. Prokhorov s and Dr. Schelev s groups. We are collaborating with them to obtain electron sources to install in our apparatus to reach this time resolution. 

An interesting hybrid way of calculating the spectrum is one used by Du and Delos.24 They start with a quantum mechanical wave packet at the origin and let it propagate to r = 50ao, where they use the normals of phase fronts of the wave packets to define classical electron trajectories. These classical trajectories are then followed. Some of the trajectories are reflected back to the origin, and when... 

Fig. 4. Backscattering process is parameterized by the angles = 4>o 4>f- -r/Rc. The solid (dashed) line in (a) represents electron trajectory for B = 0 (B / 0). Different processes contributing to MR are shown in (b)-(e).

The electron trajectories in a spectrometer are affected by magnetic fields. This is demonstrated with the help of Fig. 4.40 the formerly straight path of an electron with velocity v is deflected, under the action of the magnetic field B perpendicular to the trajectory, through a distance d given by... 

Figure 452 Block diagram for electronic compensation of the geometric time spread induced by electron trajectories with A9 in the spectrometer. For the special configuration shown the delays must be chosen such that the delay times zt, with z3 < z2 < zt < compensate for these flight time differences. From [VSa83].

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