Optical Properties of Semiconductors

The temperature dependence of the energy loss of 624-keV electrons in ferroelectric barium titanate (${\mathrm{BaTiO}}_{3}$) and triglycine sulfate [(${\mathrm{CH}}_{2}$${\mathrm{NH}}_{2}$COOH${)}_{3}$ ${\mathrm{H}}_{2}$${\mathrm{SO}}_{4}$] has been studied with the use of a single-gap magnetic spectrometer. The present measurements confirm the anomalous increase in energy loss of electrons near the Curie temperature ${T}_{C}$ and indicate its dependence on (a) the magnitude of the dielectric anomaly at ${T}_{C}$, (b) the effect of a dc electric field larger than the coercive field, and (c) the application of an alternating electric field. Probable mechanisms for the origin of the observed phenomenon are discussed.

During the interaction of a short-pulse high-intensity laser with the preplasma produced by the pulse's pedestal in front of a high-Z metal solid target, high-energy electrons are produced, which in turn create an X-ray source by interacting with the atoms of the converter target. The current brought by the hot electrons is almost completely neutralized by a return current j→ driven by the background electrons of the conductive target, and the force exerted on the hot electrons by the electric field E→ which induces Ohmic heating j→.E→, produced by the background electrons, reduces the energy of the hot electrons and thus lowers the X-ray emission and photon dose. This effect is analyzed here by means of a simple 1-D temperature model which contains the most significant terms of the relativistic Fokker-Planck equation with electron multiple scattering, and the energy equations of ions, hot, and cold electrons are then solved numerically. This Ohmic heating energy loss fraction τOh is introduced as a corrective term in an improved photon dose model. For instance, for a ps laser pulse with 10 μm spot size, the dose obtained with a tantalum target is reduced by less than about 10% to 40% by the Ohmic heating, depending upon the plasma scale length, target thickness, laser parameters, and in particular its spot size. The laser and plasma parameters may be optimized to limit the effect of Ohmic heating, for instance at a small plasma scale length or small laser spot size. Conversely, others regimes not suitable for dose production are identified. For instance, the resistive heating is enhanced in a foam target or at a long plasma scale length and high laser spot size and intensity, as the mean emission angle θ0 of the incident hot electron bunch given by the ponderomotive force is small; thus, the dose produced by a laser interacting in a gas jet may be inhibited under these circumstances. The resistive heating may also be maximized in order to reduce the X-ray emission to lower the radiation level for instance in a safety radiological goal.

: 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.

Gamma-ray interaction in Ge: A Monte Carlo simulation

Energy loss of fast electrons and positrons in a plasma

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.

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.

The fundamental reflectance of CrBr3 crystals has been measured over the energy range 2-31 eV from 300 to 30 K using synchrotron radiation. The high-frequency dielectric tensor elements epsilon xxT(E) have been determined by Kramers-Kronig analysis. Energy losses of 50 keV electrons incident along the c axis of the crystal have also been measured up to 30 eV. The results have been described in terms of single-particle excitations (charge transfer, inter-band excitons and transitions) and collective valence electron plasma oscillations. The assignments of direct inter-band transitions both at the critical points Gamma and Z and along symmetry lines of the Brillouin zone ( Lambda line) have been made by considering the intersecting-sphere model calculation of the band structure of CrBr3. The fundamental energy gap, assigned to Gamma 3- to Gamma 1+ transitions, at the zone centre is observed around 8.00 eV. Plasma resonance has been observed at 19.8 eV in the electron energy loss spectrum in fine agreement with the maximum of the optical energy loss function. Finally, the fractional ionic character fiDT=0.79 has been evaluated in the framework of the Phillips dielectric theory.

Infrared spectroscopy of solids

Studies are made of the characteristic energy losses of slow electrons during the formation of thin PTCDA films on a ZnO(0001) surface. It is shown that at low primary electron energies (<100 eV) the energy loss spectrum ( n =3.0, 6.3, and 15 eV) reflects the structure of the transitions between the valence band and the conduction band. As the primary electron energy increases, energy losses to the excitation of plasma oscillations become dominant (ħω1=6 eV — excitation of a π-plasmon and ħω2=25 eV — excitation of a σ-plasmon).

From energy loss measurements of fast electrons on solid neon and methane the energy loss functions Im (−1/ε) and the dielectric constants ε = ε1 + iε2 are calculated. The ε2‐spectra of the solids are compared with the energy loss spectra of gaseous Ne and CH4.

This article presents a simplified treatment of the high density, collisionless, free-electron gas, based on the ideas of a wave number and frequency-dependent conductivity and dielectric constant. The formalism is applied to solve a number of problems: the screening of the electrostatic potential of a foreign point charge placed in the electron gas, the rate of energy loss of a charged particle moving through the electron gas, plasma oscillations, the reflection of electromagnetic waves from the electron gas, and ultrasonic attenuation in metals due to the interaction of the sound waves with the conduction electrons. In a final section it is indicated how the methods may be generalized. Explicit expressions for the conductivity of the electron gas are obtained in an appendix.

The characteristic energy loss spectrum of solids is analyzed with the aid of the dielectric formulation of the many-body problem developed by the authors. It is shown that a measurement of the angular distribution of inelastically scattered fast electrons is a direct measurement of the imaginary part of the inverse dielectric constant of the solid, at the frequency and momentum of the energy transfer to the electrons in the solid. The calculations of the dielectric constant by means of first-order perturbation theory and within the random phase approximation are discussed with regard to their implications for the characteristic energy loss spectrum. It is shown that plasmons provide the dominant excitation mode at low momentum transfer for the free electron gas and for most solids; an explicit calculation is given of the role of screening in reducing the role of the independent electron excitations in this region. A comparison is made between characteristic energy loss experiments and other techniques for exploring the energy level structure of solids, including the non-relativistic Compton effect, optical transmission and reflection experiments, and x-ray emission and absorption studies. An analogous formulation of the optical properties of solids is given, which shows that in general the transverse and longitudinal dielectric constants will not be equal. They are equal within the random phase approximation, so that a careful comparison of optical data with characteristic energy loss data permits a direct verification of the validity of the random phase approximation. Such a comparison likewise yields information on the magnitude of the screening of individual electron transitions and permits the unambiguous identification of plasmon excitations. Finally it is shown that to the extent that the random phase approximation is valid, the results of a characteristic energy loss experiment may be used for a direct experimental determination of the ground-state energy of the electrons in a solid.

Suppressed grain growth and enhanced irradiation resistance of nano-grained waste form under electronic energy loss

Total, electronic, and nuclear energy loss as well as stopping cross sections are calculated for He${}^{2+}$ ions incident on atomic hydrogen, deuterium, and tritium at low to intermediate energies by means of an ab initio, nonadiabatic approach for solving the Schr\odinger equation incorporating coupled electron and nuclear dynamics. Comparison of this ab initio treatment with classical nuclear stopping cross-section formulations obtained from Coulomb and screened potential models, and an ab initio theory, allows us to deduce scaling laws that incorporate the different target masses (target isotopic effect). We provide a discussion on the range of validity of the use of classical trajectories. We verify that the nuclear energy loss is a universal function of the center-of-mass (c.m.) scattering angle. The scattering angle in the c.m. system shows a dependence on the projectile charge due to a strong isotopic effect on the charge-transfer cross section. In the case of a Coulombic interaction, that dependence disappears, and leads to a formulation based only on the c.m. collision energy for the nuclear stopping cross section. Due to the small electron capture cross section for He${}^{2+}$ on H, D, and T in the low-energy region, it is shown that the effective charge model that assumes neutralization of the projectile does not apply to the energy loss of He${}^{2+}$ ions in the calculation of stopping cross sections. Thus, for this system, there is no influence of the charge exchange isotope effect of the target in the nuclear stopping cross section of the projectile. In the electronic energy loss, such an isotopic effect is present through Stueckelberg oscillations, but its contribution is small. Furthermore, the electronic stopping cross section shows a threshold effect that results from the minimum momentum transfer necessary to produce an electronic excitation in the target. Finally, the nuclear stopping cross section has a universal behavior as a function of the c.m. collision energy, and care must be taken when comparing ionic systems stopping cross-section results to those of neutral systems as obtained by effective charge models.