Spreadsheet program for calculating secondary electron trajectories in electrostatic fields

Author(s):  
Grady F. Bradley ◽  
David C. Joy

With the increasing importance of Low Voltage Scanning Electron Microscopy, the problem of describing the influence exerted by Secondary electron detectors on the path of primary electrons as well as its effects on the trajectories followed by secondary electrons become increasingly important. In situations where uncoated, insulating specimens are studied in an SEM, the additional problem of sample charging also has to be considered. Characterizing these interactions can be very difficult by conventional programming methods. The large number of points and the interdependence of the potentials at all of the points make the “bookkeeping” very difficult to manage. Spreadsheet programs with macroinstruction languages, however, can make these calculations much easier to perform. Not only can spreadsheets be used to calculate the potential field within a microscope column, macro programming can be used to calculate trajectories throughout that field. For the computations described in this paper, Microsoft Excel for the Macintosh was the spreadsheet chosen because of its effective use of the graphics capabilities of the Macintosh.

Author(s):  
Zbigniew Czyzewski ◽  
David C. Joy

Electron microscope use an electron beam to obtain various kind of information about specimen. The electron beam is focussed by electrostatic and magnetic fields and electron detectors employ electrostatic fields to attract or deflect electrons. In many cases the demand to calculate the electron trajectories in a fast and visual way is very strong. One of the most important questions is the problem of the secondary electron (SE) trajectories inside the SEM chamber and the effect of sample charging on detector yield. This is especially important in the low voltage SEM when investigating an uncoated, non-conductive specimen. A relatively large number of calculated trajectories gives a possibility to optimize SE detector placement as well as detector bias.The main problem is solving the Laplace equation in a 3-D space. In the 3-D space composed of cubic cells of dimension Δ3, the Laplace equation takes the following form:


2020 ◽  
Vol 10 (1) ◽  
Author(s):  
W. Han ◽  
M. Zheng ◽  
A. Banerjee ◽  
Y. Z. Luo ◽  
L. Shen ◽  
...  

AbstractThis paper demonstrates how secondary electron energy spectroscopy (SEES) performed inside a scanning electron microscope (SEM) can be used to map sample atomic number and acquire bulk valence band density of states (DOS) information at low primary beam voltages. The technique uses an electron energy analyser attachment to detect small changes in the shape of the scattered secondary electron (SE) spectrum and extract out fine structure features from it. Close agreement between experimental and theoretical bulk valance band DOS distributions was obtained for six different test samples, where the normalised root mean square deviation ranged from 2.7 to 6.7%. High accuracy levels of this kind do not appear to have been reported before. The results presented in this paper point towards SEES becoming a quantitative material analysis companion tool for low voltage scanning electron microscopy (LVSEM) and providing new applications for Scanning Auger Microscopy (SAM) instruments.


2016 ◽  
Vol 24 (04) ◽  
pp. 1750045 ◽  
Author(s):  
A. G. XIE ◽  
Z. H. LIU ◽  
Y. Q. XIA ◽  
M. M. ZHU

Based on the processes and characteristics of secondary electron emission and the formula for the yield due to primary electrons hitting on semiconductors and insulators, the universal formula for maximum yield [Formula: see text] due to primary electrons hitting on semiconductors and insulators was deduced, where [Formula: see text] is the maximum ratio of the number of secondary electrons produced by primary electrons to the number of primary electrons. On the basis of the formulae for primary range in different energy ranges of [Formula: see text], characteristics of secondary electron emission and the deduced universal formula for [Formula: see text], the formulae for [Formula: see text] in different energy ranges of [Formula: see text] were deduced, where [Formula: see text] is the primary incident energy at which secondary electron yields from semiconductors and insulators, [Formula: see text], are maximized to maximum secondary electron yields from semiconductors and insulators, [Formula: see text]; and [Formula: see text] is the maximum ratio of the number of total secondary electrons produced by primary electrons and backscattered electrons to the number of primary electrons. According to the deduced formulae for [Formula: see text], the relationship among [Formula: see text], [Formula: see text] and high-energy back-scattering coefficient [Formula: see text], the formulae for parameters of [Formula: see text] and the experimental data as well as the formulae for [Formula: see text] in different energy ranges of [Formula: see text] as a function of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] were deduced, where [Formula: see text] and [Formula: see text] are the original electron affinity and the width of forbidden band, respectively. The scattering of [Formula: see text] was analyzed, and calculated [Formula: see text] values were compared with the values measured experimentally. It was concluded that the deduced formulae for [Formula: see text] were found to be universal for [Formula: see text].


2014 ◽  
Vol 28 (06) ◽  
pp. 1450046 ◽  
Author(s):  
Ai-Gen Xie ◽  
Chen-Yi Zhang ◽  
Kun Zhong

Based on the main physical processes of secondary electron emission, experimental results and the characteristics of backscattered electrons (BE), the formula was derived for describing the ratio (β angle ) of the number of secondary electrons excited by the larger average angle of emission BE to the number of secondary electrons excited by the primary electrons of normal incidence. This ratio was compared to the similar ratio β obtained in the case of high energy primary electrons. According to the derived formula for β angle and the two reasons why β > 1, the formula describing the ratio β energy of β to β angle , reflecting the effect that the mean energy of the BE W AV p0 is smaller than the energy of the primary electrons at the surface, was derived. β angle and β energy computed using the experimental results and the deduced formulae for β angle and β energy were analyzed. It is concluded that β angle is not dependent on atomic number z, and that β energy decreases slowly with z. On the basis of the two reasons why β > 1, the definitions of β and β energy and the number of secondary electrons released per primary electron, the formula for β E-energy (the estimated β energy ) was deduced. The β E-energy computed using W AV p0, energy exponent and the formula for β E-energy is in a good agreement with β energy computed using the experimental results and the deduced formula for β energy . Finally, it is concluded that the deduced formulae for β angle and β energy can be used to estimate β angle and β energy , and that the factor that W AV p0 increases slowly with atomic number z leads to the results that β energy decreases slowly with z and β decreases slowly with z.


The velocity distribution of the secondary electrons produced by bombarding a metallic face with a stream of primary electrons has been a matter of interest ever since the beginning of the study of secondary electron emission. As early as in 1908, Richardson and von Baeyer independently showed that slow moving electrons were copiously reflected from conducting faces. Farnsworth showed that for primary electrons having velocities less than 9 volts, most of the secondary electrons had velocities equal to the primary. As the primary potential was increased, the percentage of the reflected electrons decreased gradually but was appreciable at 110 volts. Davisson and Kunsman obtained reflected electrons even at primary potentials of 1000 and 1500 volts in the cases of some metal faces. At higher potentials we have also the electrons that undergo the Davisson and Germer scattering from the many crystal facets on the bombarded targets. As the potential is increased, the number of electrons with low velocities increases steadily and at large applied potentials, we have a large percentage of these in the secondary beam. These conclusions followed as a result of the work of Farnsworth who studied the distribution of velocities of the secondary electrons by the retarding potential method. He did not actually calculate the energy distribution from his curves but has drawn attention to the above conclusions. A careful investigation of the velocity distribution of the secondary electrons from various conducting faces was made by Rudberg at primary potentials ranging up to about 1000 volts. He adopted a magnetic deflection method similar to the one used in the analysis of the β rays and of the electrons excited by X-rays. The method had indeed been used by previous workers for the study of secondary emission, but Rudberg improved the technique considerably and obtained better focussing conditions. His results suggest that there are three groups of electrons in the secondary beam. The first group contains electrons returning with the same velocity as the primary. In the second group of electrons, we have those which undergo inelastic collisions with the orbital and structure electrons and hence are returned with some loss of energy. Richardson has drawn attention to the well-marked minimum between the two groups in Rudberg’s curves and infers that free electrons are not involved in the collisions. Finally there is the third group which contains the slow secondary electrons. The second and the third groups appear to be definitely connected with each other since they are both predominant at high primary potentials and become negligible at low primary potentials. Richardson suggests that the third group is the result of the excitation accompanying the inelastic collisions.


The results of the various investigations which have been carried out during the last few years on the critical potentials for the excitation of soft X-rays, and for the production of secondary electrons, from solids, have shown that the effects occurring at solid surfaces under electronic bombardment in vacuo are more complex than was anticipated when this line of investigation was begun, and that they cannot be interpreted in any simple way in terms of the displacements of electrons within the atoms of the target. The work of various investigators* on the distribution of velocities among the electrons leaving a surface subjected to bombardment by primary electrons of known energy, has shown that a certain number of the electrons leaving the bombarded surface have energies practically equal to that of the primary stream, suggesting that a readily detectable proportion of the primary electrons is scattered or reflected at the target surface without appreciable loss of energy. The proportion of such electrons is greatest for small bombarding energies, e.g ., about 10 volts, and decreases as the voltage accelerating the primary electrons increases. The other marked feature in the velocity distribution curves, for bombarding voltages up to about 1000, is a group having a sharp maximum at about 10 volts. Apart from these features the distribution is a more or less continuous one, the number of electrons having a given velocity increasing as that velocity increases, except that after achieving a small maximum at about 25 volts less than the primary voltage, the curve falls to a minimum before rising to the very sharp peak indicating true reflection There are no indications of maxima for electron energies differing from the primary by amounts corresponding to those required to effect characteristic electron transitions within the atoms of the target. Moreover, there appears to be nothing in the velocity distribution curves for the secondary emission to correspond to the discontinuities which have been found by various investigators to occur in the current-voltage curves of the secondary electron current from a bombarded surface, or in the current-voltage curves of the photoelectric effect of the soft X-radiation excited by the bombardment. As regards the latter effect an explanation is to hand on the view that the proportion of the primary electrons whose energy is converted, in part, to photoelectrically active radiation is so small that indications of the various different energy transfers suggested by the critical potential curves are swamped in the velocity distribution curves of the secondary electrons. It is, however, more difficult to reconcile the absence of any correlation between the discontinuities which have been observed in the current-voltage curves for secondary electron emission, and the velocity distribution of the latter.


2012 ◽  
Vol 18 (2) ◽  
pp. 385-389 ◽  
Author(s):  
Daisuke Tsurumi ◽  
Kotaro Hamada ◽  
Yuji Kawasaki

AbstractThe reproducibility of contrast in secondary electron (SE) imaging during continuous electron irradiation, which caused surface contamination, was investigated using SE high-pass energy filtering in low-voltage scanning electron microscopy (SEM). According to high-pass energy-filtered imaging, dopant contrast in an indium phosphide remained remarkably stable during continuous electron irradiation although the contrast in unfiltered SE images decreased rapidly as a contamination layer was formed. Charge neutralization and the SE energy distributions indicate that the contamination layer induces a positive charge. This results in a decrease of low-energy SE emissions and reduced dopant contrast in unfiltered SE images. The retention of contrast was also observed in high-pass energy-filtered images of a gold surface. These results suggest that this imaging method can be widely used when SE intensities decrease under continuous electron irradiation in unfiltered SE images. Thus, high-pass energy-filtered SE imaging will be of a great assistance for SEM users in the reproducibility of contrast such as a quantitative dopant mapping in semiconductors.


Author(s):  
Vincent J. Coates

Recent improvements in the design of the Coates and Welter field emission electron gun have resulted in very small probe sizes (less than 50A) with low voltage (0.5 to 2 KV) electron beams operated at probe currents in excess of 1 nanoampere. Such weak electrons do not penetrate deeply into the sample. This results in images which often show more topographical detail of surface features than can be obtained using conventional high voltage scanning electron microscopy. At low voltages, the number of secondary electrons produced for each primary electron in the beam is often greater than one.


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