H.-J. Fitting

Monte Carlo simulation of electron emission from solids

Abstract Electron emission and spectroscopy has been simulated by a new Monte Carlo program which has been adapted especially to low energy electron scattering. The underlying physic model in based on elastic Mott cross sections and inelastic losses with full dispersion Δ E=hω( q ) . Charge carrier multiplication by secondary electron creation and subsequent cascading processes have been included. Surface effects like surface plasmons and the quantum mechanical surface transmittivity have also been taken into account. Results are obtained for the materials Be, C, Al, Si, Ag, Au, and SiO2. They include energy spectra of secondary and characteristic electrons. We find that attenuation lengths and related escape depths approach the inelastic mean free path λin only in higher electron energy regions; below 100 eV they drop down to roughly 20% of λin. The results should find application in spectroscopic microscopy by means of low energy electrons in the sub-keV range.

Monte Carlo simulation of secondary electron emission from the insulator SiO2

Abstract Low energy electron scattering and transport in the dielectric and insulating material silicon dioxide is simulated by a Monte Carlo program based on the electron interaction with polar-optical and acoustic phonons, intervalley and interband scattering as well as impact ionization. These scattering processes for higher electron energies are considered and proved in a one-, three-, or five-band structure of amorphous SiO2. The acoustic screening and the impact ionization as the most elastic and the most inelastic processes, respectively, have been optimized by ‘backscattering-versus-range’ calculations in connection with respective experimental data. We may show that the one-band model is already sufficient for description of the ballistic electron scattering in amorphous SiO2. Finally the simulation is applied to secondary electron (SE) generation, relaxation and SE emission with trajectories, field-dependent escape depths, energy distributions and the SE yield.

Electron beam charging of insulators: A self-consistent flight-drift model

Electron beam irradiation and the self-consistent charge transport in bulk insulating samples are described by means of a new flight-drift model and an iterative computer simulation. Ballistic secondary electron and hole transport is followed by electron and hole drifts, their possible recombination and/or trapping in shallow and deep traps. The trap capture cross sections are the Poole-Frenkel-type temperature and field dependent. As a main result the spatial distributions of currents j(x,t), charges ρ(x,t), the field F(x,t), and the potential slope V(x,t) are obtained in a self-consistent procedure as well as the time-dependent secondary electron emission rate σ(t) and the surface potential V0(t). For bulk insulating samples the time-dependent distributions approach the final stationary state with j(x,t)=const=0 and σ=1. Especially for low electron beam energies E0<4keV the incorporation of mainly positive charges can be controlled by the potential VG of a vacuum grid in front of the target surface. For...

Self-consistent electrical charging of insulating layers and metal-insulator-semiconductor structures

By means of a computer simulation the self-consistent charge transport with the current densities j(x,t), the respective charges ρ(x,t), field strengths F(x,t), and potential distributions V(x,t) in SiO2 layers are obtained as a function of the insulator depth x and the injection time t. The SiO2 layers are considered as open layers on silicon substrate or they are embedded in metal-oxide-semiconductor (MOS) structures. The given currents of primary electrons, the field-dependent ballistic currents of secondary electrons and holes as well as the Fowler–Nordheim injection of electrons from the substrate into the dielectric layer are taken into account. This method allows a defined charge storage and the explanation of complicated emission, charging-up, and breakdown processes within insulating layers during electron bombardment and/or high-field charge injection from adjacent electrodes, e.g., in MOS structures.

Attenuation and escape depths of low-energy electron emission

Abstract Electron transport and emission is simulated by two Monte Carlo (MC) programs. The first version is based on elastic Mott cross sections and inelastic loss functions with full dispersion Δ E = ℏω ( q ), including electron impact and subsequent cascading processes. Surface effects like surface plasmons and the quantum mechanical surface transmittivity have been taken into account too. Especially for dielectric materials like SiO 2 and applied electric fields a second MC version is developed based on the electron scattering with acoustic and optical phonons, intra- and intervalley scattering and impact valence band ionization. A comparison of both versions results in a good agreement still in the energy region of several eV, but a predominance of the phonon-based second version is found for very low electron energies, e.g., for hot and ballistic electrons in dielectric materials.

Electron Beam Charging of Insulators with Surface Layer and Leakage Currents

The electron beam induced self-consistent charge transport in layered insulators (here, bulk alumina covered by a thin silica layer) is described by means of an electron-hole flight-drift model and an iterative computer simulation. Ballistic secondary electrons and holes, their attenuation and drift, as well as their recombination, trapping, and detrapping are included. Thermal and field-enhanced detrapping are described by the Poole–Frenkel effect. Furthermore, an additional surface layer with a modified electric surface conductivity is included which describes the surface leakage currents and will lead to particular charge incorporation at the interface between the surface layer and the bulk substrate. As a main result, the time-dependent secondary electron emission rate σ(t) and the spatial distributions of currents j(x,t), charges ρ(x,t), field F(x,t), and potential V(x,t) are obtained. For bulk full insulating samples, the time-dependent distributions approach the final stationary state with j(x,t)=c...

Monte-Carlo simulation of low energy electron scattering in solids

A new Monte-Carlo program for simulation of low energy electron scattering in solids is presented. Applications to electron microscopy and electron microprobe analysis are discussed. Elastic interactions are described by Mott cross sections within the framework of partial wave analysis (PWA) whereas the inelastic collisions are based upon the momentum dependent dynamic form factor S(q, ω). For inelastic interactions with weakly bound valence electrons, S(q, ω) is expressed in terms of the energy loss function Im {—/1e(q, ω)} of the linear dielectric theory. On the other hand, generalized oscillator strengths (GOS) are chosen in case of excitation of tightly bound core level electrons. The electron energy range extends from several keV down to energies of about 10 eV, i.e. just above the vacuum level. Secondary electron (SE) creation and cascade processes have been included, where the SE transport has been treated in the same way as the scattering of the primary electrons.

Si and Ge Nanocluster Formation in Silica Matrix

High resolution transmission electron microscopy, scanning transmission electron microscopy, and cathodoluminescence have been used to investigate Si and Ge cluster formation in amorphous silicon-dioxide layers. Commonly, cathodoluminescence emission spectra of pure SiO2 are identified with particular defect centers within the atomic network of silica including the nonbridging oxygen hole center associated with the red luminescence at 650 nm (1.9 eV) and the oxygen deficient centers with the blue (460 nm; 2.7 eV) and ultraviolet band (295 nm; 4.2 eV). In Ge+ ion-implanted SiO2, an additional violet emission band appears at 410 nm (3.1 eV). The strong increase of this violet luminescence after thermal annealing is associated with formation of low-dimension Ge aggregates such as dimers, trimers, and higher formations, further growing to Ge nanoclusters. On the other hand, pure silica layers were modified by heavy electron beam irradiation (5 keV; 2.7 A/cm2), leading to electronic as well as thermal dissociation of oxygen and the appearance of under-stoichiometric SiOx. This SiOx will undergo a phase separation and we observe Si cluster formation with a most probable cluster diameter of 4 nm. Such largely extended Si clusters will diminish the SiO2-related luminescence and Si-crystal-related luminescence in the near IR.

Dose effects of cathodoluminescence in SiO2 layers on Si

Abstract Cathodoluminescence (CL) of thermal SiO2 layers is performed in a digital scanning electron microscope (SEM) and wavelength, dispersed registered by a CCD-camera. The CL-spectrum of SiO2 shows three characteristic bands at 650 nm (red), 460 nm (blue) and 285 nm (UV) that all change their intensity during the time of electron bombardment. This different excitation dose behaviour of the luminescence bands was investigated in a wide range of current densities (10−5–10−3 A cm−2) and temperatures (90–500 K). Some interpretation is made by a model of precursor transformation and quenching. The UV and blue luminescence is attributed to twofold-coordinated silicon in SiO2. Contrary to thermal SiO2 films TEOS-CVD SiO2 shows only the red band which is generally associated with non-bridging oxygen.

Time-dependent start-up and decay of secondary electron emission in dielectrics

Electron beam induced selfconsistent charge transport and secondary electron emission in insulators are described by means of an electron-hole flight-drift model implemented by an iterative computer simulation. Ballistic secondary electrons and holes, their attenuation and drift, as well as their recombination, trapping, and field-dependent and temperature-dependent detrapping are included. As a main result the time dependent secondary electron emission rate σ(t) and the spatial distributions of currents j(x,t), charges ρ(x,t), field F(x,t), and potential V(x,t) are obtained. Whereas the switching-on of the secondary electron emission proceeds over milliseconds due to selfconsistent charging, the switching-off process occurs much faster, even over femtoseconds.