Incorporating Inelastic Scattering into Multislice Simulation

Abstract

Existing Scanning/Transmission Electron Microscopy (S/TEM) image simulation algorithms such as Multislice and Bloch Wave are based exclusively on elastic scattering. At thicker specimens inelastic scattering may affect image intensity and contrasts. Previous semi-quantitative incorporation of inelastic plasmon scattering into the output of Multislice simulated diffraction patterns has improved the agreement between experimental and simulation results from ~ 30 % to less than 10 % [1]. In this study, a full quantitative plasmon scattering algorithm was incorporated into multislice method [2] by allowing the wavefunction of the propagating beam to interact inelastically within each slice [3].Crystalline Si samples with 4 x 4 nm supercells oriented along <100> crystallographic direction with various thicknesses were used in this simulation. STEM operated at 100 kV accelerating voltage and 11.4 mrad convergence angle giving about 2 Å diameter probe was used here. High-angle annular darkfield (HAADF) STEM images and Electron Energy Loss Spectroscopy (EELS) signals were calculated. For HAADF-STEM images 54 -150 mrad detector was used and 20 mrad collection angles was used for EELS.The modified "inelastic-elastic" multislice method first takes into account the plasmon scattering by calculating the energy loss for each scattering angles before undergoing the elastic scattering through transmission operation. Then beam propagates to the next slice using propagation operator. Simulated EELS spectra in Si using new "inelastic-elastic" multislice method for thicknesses of 42, 74, 83, and 130 nm are shown in Figure 1 comparable with early experiments performed under similar conditions [4]. An energy dispersion of 1 eV (for energy loss up to 60 eV) was used in the simulation to monitor single, double, and triple plasmon scattering in these Si samples. A good agreement was achieved for the range of specimen thicknesses.

Gel-based thermocells for low-grade heat harvesting

“…where ΔE and ΔT are the potential difference and temperature difference between two parallel electrodes, S R and S O are the partial molar entropy of the reductant and oxidant, respectively, n is the number of electrons transferred in the redox reaction, and F is the Faraday's constant [26]. It is worth noting that the sign of S tg is determined by the type of the redox couple, with positive and negative signs corresponding to p-type and n-type thermocells, respectively.…”