Monte Carlo method for simulating γ-ray interaction with materials: A case study on Si

Gamma-ray interaction in Ge: A Monte Carlo simulation

Yield, variance and spatial distribution of electron–hole pairs in CsI

Starting with the equation of motion for the density matrix operator of an electron gas in second quantization, a system of matrix equations is derived for matrix elements connecting states with various numbers of electron-hole pairs. Allowing up to $n$ electron-hole pairs and neglecting all states with more than $n$ pairs yields a set of ${(n+1)}^{2}$ coupled equations for the various amplitudes in close analogy to the $n\mathrm{th}$ order Tamm-Dancoff approximation. The starting point of this approximation, in which all matrix elements connecting the Fermi vacuum with any pair states are neglected (zero-order Tamm-Dancoff approximation), is an equation for the self-consistent field rather than for free particles as in the usual Tamm-Dancoff method. Correlation effects are therefore automatically taken into account when pair states are included. In a certain sense the approximation scheme given here can be thought of as being an expansion in the deviation of the Fermi surface from the sharp edge of the free-particle ground state, the deviation being caused by the Coulomb interaction among the particles. In this paper, we present calculations based on the first Tamm-Dancoff approximation (taking into account only one electron-hole pair). An expression for the dielectric constant will be derived and applied to a determination of the effects of correlations on the wavelength dependence of plasma oscillations. The theory will be compared with the experiments by Watanabe on the energy loss of fast electrons in metal foils and it will be seen that the agreement with experiment is good considering the inherent simplicity of the theory.

Energy loss of fast electrons and positrons in a plasma

: The average energy W required to create an electron-hole pair in SiO2 has been determined to be approximately 18 eV by consideration of the energy loss of fast electrons in solids. This energy is lost primarily by plasmon production and subsequent decay of the plasmons into electron-hole pairs. Also, recent data on electron-irradiated SiO2 films can be explained remarkably well by a columnar recombination model. The extrapolation to infinite electric field of the columnar model fit to the data yields a value for W that is in excellent agreement with the value obtained from the energy loss calculation.

Purpose: This study investigated the beam quality dependence of a radiophotoluminescent glass dosimeter (RGD) in megavoltage photon and electron beams. Methods: The RGD response for 4–18 MV photons and 6–20 MeV electrons was investigated by comparison with ion chamber measurements and Monte Carlo (MC) simulations in solid water phantom. The beam quality response in electron beams was determined at reference depth. The energy response for photon and electron beams was calculated with EGSnrc/egs_chamber and cavity user‐codes, respectively. The photon energy dependence was also analyzed according to Burlinˈs cavity theory. The fraction of dose due to photon interactions 1‐d for Burlinˈs theory was calculated with a modified version of egs_chamber, which allowed discarding electrons generated in surrounding medium and entering the detector. Results: The calculated and measured RGD response in photons was lower by up to 2.5% with increasing beam quality in a range of 4–18 MV. The RGD response of 20×20 cm2 for 5×5 cm2 increased by 4% in 4 MV. The RGD response as function of depth was constant within 1% except for dmax in a range of 4–18 MV. The dose in RGD resulting from 1‐d decreased with increasing photon energy and with decreasing the field size. 1 ‐d is related to the photon energy response of RGD. The RGD response at dref in electron beams was constant within 1 % but 4% lower than that for 6 MV photons. The RGD response estimated by comparison with the ion chamber measurements agreed within 1% with the MC calculations. Conclusions: The energy dependence of RGD depends on the photons energy and the field size. In electron beams, the beam quality dependence at a reference depth is insignificant but was 4% lower than 6 MV photons. The beam quality dependence depends on 1‐d in RGD, demonstrating its behavior according to Burlinˈs theory.

The integro-differential equation describing the energy distribution of very fast electrons (with negligible collision loss of energy) is reduced to a Volterra integral equation of the second kind. A rigorous solution, for an arbitrarily prescribed boundary condition, is given in terms of a convergent expansion of the Liouville-Neumann type. This method is applicable for transition probabilities of a form which is much more general than the form permitting a successful application of the Mellin transform. Since the reduction of the emission probability for Bremsstrahlung to the latter form involves an approximation in a certain region, the present method may be used in order to obtain a higher accuracy in that region.

Enhanced photodecomposition of ethyl chloride (EC) adsorbed on SiO2/Si (100) supported silver nanoparticles (Ag NPs) under ultrahigh vacuum (UHV) conditions has been studied in order to assess the potential contribution of plasmonic effects. The cross section for photodecomposition of EC and overall photoyield were found to increase with increasing photon energy regardless of the plasmon resonant wavelength and with Ag coverage without any noticeable particle size effect. The influence of EC-Ag NPs separation distance on the rate of EC decomposition was studied in order to examine potential local electric field influence on the photodissociation process. Long (∼5 nm) photoactivity decay distance has been observed which excludes local surface plasmon dominance in the photodecomposition event. These findings suggest that the alignment of excited electron energy and adsorbate affinity levels is central for efficient photochemical reactions, whereas short-range electric field enhancement by plasmon excitation on top and at the immediate vicinity of silver nanoparticles does not have any measurable effect.

Carrier multiplication by generation of two or more electron-hole pairs following the absorption of a single photon may lead to improved photovoltaic efficiencies and has been observed in nanocrystals made from a variety of semiconductors, including silicon. However, with few exceptions, these reports have been based on indirect ultrafast techniques. Here, we present evidence of carrier multiplication in closely spaced silicon nanocrystals contained in a silicon dioxide matrix by measuring enhanced photoluminescence quantum yield. As the photon energy increases, the quantum yield is expected to remain constant, or to decrease as a result of new trapping and recombination channels being activated. Instead, we observe a step-like increase in quantum yield for larger photon energies that is characteristic of carrier multiplication. Modelling suggests that carrier multiplication is occurring with high efficiency and close to the energy conservation limit.

Plasmon excitation in Al by keV Ne and Ar ions

Recent work has shown that there is significant uncertainty in measuring build-up doses in mega-voltage photon beams especially at high energies. In this present investigation we used a phantom-embedded extrapolation chamber (PEEC) made of Solid Water to validate Monte Carlo (MC)-calculated doses in the dose build-up region for 6 and 18 MV x-ray beams. The study showed that the percentage depth ionizations (PDIs) obtained from measurements are higher than the percentage depth doses (PDDs) obtained with Monte Carlo techniques. To validate the MC-calculated PDDs, the design of the PEEC was incorporated into the simulations. While the MC-calculated and measured PDIs in the dose build-up region agree with one another for the 6 MV beam, a non-negligible difference is observed for the 18 MV x-ray beam. A number of experiments and theoretical studies of various possible effects that could be the source of this discrepancy were performed. The contribution of contaminating neutrons and protons to the build-up dose region in the 18 MV x-ray beam is negligible. Moreover, the MC calculations using the XCOM photon cross-section database and the NIST bremsstrahlung differential cross section do not explain the discrepancy between the MC calculations and measurement in the dose build-up region for the 18 MV. A simple incorporation of triplet production events into the MC dose calculation increases the calculated doses in the build-up region but does not fully account for the discrepancy between measurement and calculations for the 18 MV x-ray beam.

Reflectance data are presented for Si, Ge, GaP, GaAs, InAs, and InSb in the range of photon energies between 1.5 and 25 eV. The real and imaginary parts of the dielectric constant and the function describing the energy loss of fast electrons traversing the materials are deduced from the Kramers-Kronig relations. The results can be described in terms of interband transitions and plasma oscillations. A theory based on the frequency-dependent dielectric constant in the random phase approximation is presented and used to analyze these data above 12 eV, where the oscillator strengths coupling the valence and conduction bands are practically exhausted. The theory predicts and the experiments confirm essentially free electron-like behavior before the onset of $d$-band excitations and a plasma frequency modified from that of free electrons due to oscillator strength coupling between valence and $d$ bands and $d$-band screening effects. These complications are absent in Si. The energy loss functions obtained from optical and characteristic energy loss experiments are also found to be in good agreement. Arguments for interpreting structure in the reflectance curves above 16 eV in terms of $d$-band excitations are given.

X-ray microscopy at photon energies above 15 keV is very attractive for the investigation of atomic and nanoscale properties of technologically relevant structural and bio materials. This method is limited by the quality of X-ray optics. Multilayer Laue lenses (MLLs) have the potential to make a major impact in this field because, as compared to other X-ray optics, they become more efficient and effective with increasing photon energy. In this work, MLLs were utilized with hard X-rays at photon energies up to 34.5 keV. The design, fabrication, and performance of these lenses are presented, and their application in several imaging configurations is described. In particular, two "full field" modes of imaging were explored, which provide various contrast modalities that are useful for materials characterisation. These include point projection imaging (or Gabor holography) for phase contrast imaging and direct imaging with both bright-field and dark-field illumination. With high-efficiency MLLs, such modes offer rapid data collection as compared with scanning methods as well as a large field of views.

The total electron emission yield (TEEY), at very low energy, is investigated with a Monte Carlo (MC) technique and compared with experimental results. The important points of an MC tool for the simulation of electron emission are presented. The tool is based on a combination of properly selected models taking into account plasmon excitations at the surface and the effect of the crossing surface-barrier potential. The reflectivity is calculated as a function of the primary energy using an analytical expression found in the literature. By comparing MC results with the measurements, a good correspondence between obtained curve shapes is observed. Irregularities in measured and simulated yields are identified and explained by considering plasmon excitations. This comparison allows one, among other things, to remove the ambiguity on the variation of the yield obeying the change in reflectivity as a function of primary energy. In fact, some results reported in the literature claim that the TEEY coefficient approaches unity when the primary electron energy tends to zero. This occurs due to nearly total electron reflection from the surface, for electron energy less than an electron volt. In this paper, we summarize comprehensive studies rendering this claim inaccurate. Aluminum, a free-electron-like metal, will be considered here as a representative illustration.

Electron energy-loss spectroscopy (EELS) using high-energy incident electrons has been known to be a powerful tool for studies of electronic structure in solids. The main energy-loss mechanisms in thin solid samples are due to single-particle excitations such as interband and core-level transitions, and collective excitations such as bulk plasmons and surface plasmons. In EELS, the intensity of inelastically scattered incident electrons could be measured as a function of energy-losses and scattering angles (reciprocal space) under the condition of parallel beam illumination. Energy-loss spectra obtained as a function of scattering angles can yield the dispersion relations, i.e., the excitation energy vs. wave vector, of the corresponding excitations. The angular (wave vector) dependence of the EELS spectra plays an important role for us to fully understand the elementary excitations in solids. High resolution spatially-resolved EELS spectra can be obtained from different areas of interest in a sample when a convergent beam electron nanoprobe is utilized. In this case, the spatial resolution is determined primarily by the electron probe size. This is readily accomplished when EELS is performed in conjunction with a modern scanning transmission electron microscope (STEM) which can deliver an electron probe ∼ 0.2 nm or smaller. The combination of EELS with a STEM is a very powerful tool for the studies of local electronic structures on an atomic-scale for complex materials. This is particularly suitable for studies of nanomaterials in which inhomogeneity of sizes, shapes and structures often can not be avoided. The combination of STEM/EELS can circumvent this difficulty and allows us to study each nano-object individually. It should be noted, however, that the use of nanoprobes under convergent beam conditions for spatially resolved EELS inevitably collected electrons inelastically scattered through a wide angle. The measured scattering cross-section is, therefore, angle-integrated in this case. In most solids, the character of collective plasmon excitations normally can be easily distinguished from single particle excitations such as interband and core-level transitions. This is particularly true for metals well described by the nearly free electron-gas model in which the energies of these two types of excitations are well separated. Aluminum which exhibits a bulk plasmon peak at 15 eV and an interband transition at 1.5 eV is an excellent example in this category. The situation,