The cascade theory with collision loss

Electrons are assumed to suffer a constant energy loss β by collision, and the radiation loss and pair creation are taken to be described by the formulae of Bethe and Heitler valid for complete screening. With these assumptions a solution of the cascade equations is given in the form of a series, and it is shown that the series is so rapidly convergent that in general it is necessary only to calculate the first term. Collision loss enters into each of the terms in an essential way, and as a result the first term alone gives to a very considerable degree of accuracy the whole energy spectrum of electrons from the highest energy to energies far below the critical energy . For thicknesses greater than 1.5 in the characteristic unit of length the number of particles of energy E increases monotonically with decreasing E , but the spectrum gets flattened for energies below the critical energy. For thicknesses t below 1.5, the spectrum has a very different shape, decreasing first as E decreases from the primary energy and then increasing again to the smallest E , the flattening taking place now only for E lt; β t . It is shown that neglect of collision loss sometimes causes the number of electrons of even the critical energy to be as much as seven times too large. Tables of the spectra of cascade electrons due to primaries of different energies are given for five typical thicknesses. The solution is also valid when the energy of the primary electron starting the cascade is comparable with or lower than the critical energy, and gives in a compact form the complete solution of the problem of the absorption of a low-energy electron by collision loss and cascade production.

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NON-EXPONENTIALLY LOCALIZED STATES IN A TWO-DIMENSIONAL DISORDERED SYSTEM?

International Journal of Modern Physics B ◽

10.1142/s0217979299002605 ◽

1999 ◽

Vol 13 (21n22) ◽

pp. 2705-2725 ◽

Cited By ~ 5

Author(s):

MASAKI GODA ◽

MARK YA. AZBEL ◽

HIROAKI YAMADA

Keyword(s):

Localization Length ◽

Critical Energy ◽

Low Energy ◽

Localized States ◽

Two Dimensional ◽

Disordered System ◽

Perturbed System ◽

Rate Characteristic ◽

Low Energy Electron ◽

Exponential Localization

We study the length L dependence of the forward component of the transfer matrix for an electron passing through a strip with δ-function impurity potentials, with particular attention to the slowest growth-rate characteristic. In the first step of our microscopic study we obtain the inverse localization length for low energy electron in a weakly perturbed system. We show by considering an ensemble averaged mixed tensor a critical energy dividing exponential localization and non-exponential localization in the two-dimensional disordered system.

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Applications of Low-energy Electron Diffraction to Ordering at Crystal and Quasicrystal Surfaces

Australian Journal of Physics ◽

10.1071/ph900499 ◽

1990 ◽

Vol 43 (5) ◽

pp. 499

Author(s):

EC McRae ◽

RA Malic

Keyword(s):

Electron Diffraction ◽

Surface Melting ◽

Primary Electron ◽

Low Energy ◽

Energy Electron ◽

Fold Axis ◽

Decagonal Quasicrystal ◽

Low Energy Electron Diffraction ◽

Low Energy Electron ◽

Dynamics Simulations

The value of the low-energy electron diffraction (LEED) technique for the evaluation of surface ordering depends on the ability to measure the intensity profiles of diffraction beams with respect to the associated surface component of the electron momentum transfer. Beam profiles, if measured with sufficient accuracy, may be interpreted to characterise the extent of surface order (e.g. distribution of step spacings) and to differentiate between different modes of disordering (e.g. surface melting versus roughening). The ability to measure LEED intensity profiles has been enhanced by use of low-current well-defined primary electron beams in conjunction with position-sensitive detection (PSD) of the diffracted electrons. The following are examples of applications ofLEED-PSD. Compositional Ordering at Ordering Alloy CU3Au (100) and (110) Surfaces: The ordering of the (100) surface is .believed to conform to a conventional picture in which the already-ordered bulk acts as a template, but the profiles measured in the course of ordering of the (110) surface are of the shapes expected if the ordering occurred first at the surface. Disordering of Ce(111) Surface 150 K below the Bulk Melting Temperature: The intensities and profiles are inconsistent with surface .melting or roughening, but a model based on molecular dynamics simulations is not ruled out. Order and Disordering at Decagonal Quasicrystal AI65 CUI 5 C02 0 Surfaces: At room temperature the quasi crystalline order is well developed at both the 'ten-fold' surface (perpendicular to the ten-fold surface (perpendicular to the ten-fold periodic axis) and a 'two-fold' one (parallel to the ten-fold axis) as evidenced by narrow beam profiles. The ten-fold surface undergoes a disordering transition at 700 K, but the temperature dependence of the profiles is unlike that expected for the roughening transition anticipated theoretically.

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The role of low-energy electrons in focused electron beam induced deposition: four case studies of representative precursors

Beilstein Journal of Nanotechnology ◽

10.3762/bjnano.6.194 ◽

2015 ◽

Vol 6 ◽

pp. 1904-1926 ◽

Cited By ~ 73

Author(s):

Rachel M Thorman ◽

Ragesh Kumar T. P. ◽

D Howard Fairbrother ◽

Oddur Ingólfsson

Keyword(s):

Electron Beam ◽

Gas Phase ◽

Primary Electron ◽

Low Energy ◽

Primary Electron Beam ◽

Secondary Electrons ◽

Low Energy Electrons ◽

Low Energy Electron ◽

Precursor Molecules ◽

Insight Into

Focused electron beam induced deposition (FEBID) is a single-step, direct-write nanofabrication technique capable of writing three-dimensional metal-containing nanoscale structures on surfaces using electron-induced reactions of organometallic precursors. Currently FEBID is, however, limited in resolution due to deposition outside the area of the primary electron beam and in metal purity due to incomplete precursor decomposition. Both limitations are likely in part caused by reactions of precursor molecules with low-energy (<100 eV) secondary electrons generated by interactions of the primary beam with the substrate. These low-energy electrons are abundant both inside and outside the area of the primary electron beam and are associated with reactions causing incomplete ligand dissociation from FEBID precursors. As it is not possible to directly study the effects of secondary electrons in situ in FEBID, other means must be used to elucidate their role. In this context, gas phase studies can obtain well-resolved information on low-energy electron-induced reactions with FEBID precursors by studying isolated molecules interacting with single electrons of well-defined energy. In contrast, ultra-high vacuum surface studies on adsorbed precursor molecules can provide information on surface speciation and identify species desorbing from a substrate during electron irradiation under conditions more representative of FEBID. Comparing gas phase and surface science studies allows for insight into the primary deposition mechanisms for individual precursors; ideally, this information can be used to design future FEBID precursors and optimize deposition conditions. In this review, we give a summary of different low-energy electron-induced fragmentation processes that can be initiated by the secondary electrons generated in FEBID, specifically, dissociative electron attachment, dissociative ionization, neutral dissociation, and dipolar dissociation, emphasizing the different nature and energy dependence of each process. We then explore the value of studying these processes through comparative gas phase and surface studies for four commonly-used FEBID precursors: MeCpPtMe3, Pt(PF3)4, Co(CO)3NO, and W(CO)6. Through these case studies, it is evident that this combination of studies can provide valuable insight into potential mechanisms governing deposit formation in FEBID. Although further experiments and new approaches are needed, these studies are an important stepping-stone toward better understanding the fundamental physics behind the deposition process and establishing design criteria for optimized FEBID precursors.

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Surface Chemical Reactions Stimulated by Low Energy Electron Bombardment

MRS Proceedings ◽

10.1557/proc-75-609 ◽

1986 ◽

Vol 75 ◽

Cited By ~ 3

Author(s):

R. R. Kunz ◽

T. M. Mayer

Keyword(s):

Electron Beam ◽

Chemical Reactions ◽

Secondary Electron ◽

Incident Angle ◽

Oxide Thickness ◽

Iron Pentacarbonyl ◽

Primary Electron ◽

Low Energy ◽

Low Energy Electrons ◽

Low Energy Electron

AbstractA low energy, broad beam electron source was used to induce chemical reactions on surfaces. Electron beam energies were selected to maximize the emission of secondary electrons, for the purpose of determining if these low energy electrons contributed to the overall reaction. Room temperature silicon oxidation showed maximum terminal oxide thickness (35 Å) at the primary electron energy that produced the maximum secondary electron flux (300 eV). XPS showed these films to be mostly sub-oxide in nature. Similar results were obtained in analogous experiments using tetraethoxysilane to deposit SiO2 and using iron pentacarbonyl to deposit Fe. By increasing the incident angle of the electron beam to 70 degrees from the normal, the deposition yields of SiO2 and Fe increased by 45% and 30%, respectively. This again was thought to be a result of secondary electron contributions, as the secondary yield increased by a factor of two upon tilting the beam.

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Performance Evaluation of a Novel Type of Low-Energy Electron Microscope

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100180525 ◽

1990 ◽

Vol 48 (1) ◽

pp. 354-355

Author(s):

Bertholdand Senftinger ◽

Helmut Liebl

Keyword(s):

Electron Microscope ◽

High Resolution ◽

Field Strength ◽

Numerical Aperture ◽

Low Energy ◽

Energy Electron ◽

High Resolution Imaging ◽

Lens System ◽

Resolution Imaging ◽

Low Energy Electron

During the last few years the investigation of clean and adsorbate-covered solid surfaces as well as thin-film growth and molecular dynamics have given rise to a constant demand for high-resolution imaging microscopy with reflected and diffracted low energy electrons as well as photo-electrons. A recent successful implementation of a UHV low-energy electron microscope by Bauer and Telieps encouraged us to construct such a low energy electron microscope (LEEM) for high-resolution imaging incorporating several novel design features, which is described more detailed elsewhere.The constraint of high field strength at the surface required to keep the aberrations caused by the accelerating field small and high UV photon intensity to get an improved signal-to-noise ratio for photoemission led to the design of a tetrode emission lens system capable of also focusing the UV light at the surface through an integrated Schwarzschild-type objective. Fig. 1 shows an axial section of the emission lens in the LEEM with sample (28) and part of the sample holder (29). The integrated mirror objective (50a, 50b) is used for visual in situ microscopic observation of the sample as well as for UV illumination. The electron optical components and the sample with accelerating field followed by an einzel lens form a tetrode system. In order to keep the field strength high, the sample is separated from the first element of the einzel lens by only 1.6 mm. With a numerical aperture of 0.5 for the Schwarzschild objective the orifice in the first element of the einzel lens has to be about 3.0 mm in diameter. Considering the much smaller distance to the sample one can expect intense distortions of the accelerating field in front of the sample. Because the achievable lateral resolution depends mainly on the quality of the first imaging step, careful investigation of the aberrations caused by the emission lens system had to be done in order to avoid sacrificing high lateral resolution for larger numerical aperture.

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