Masatoshi Kotera

Monte Carlo simulation of 1–10‐KeV electron scattering in a gold target

A new Monte Carlo simulation of electron scattering has been achieved for extension to the low‐energy region and to heavy elements such as Au. The Kanaya‐Okayama equation, which includes adjustable parameters, is used for the calculation of energy loss instead of the Bethe equation. Further, the Mott equation, which is obtained from a more exact treatment for elastic scattering, is used instead of the screened Rutherford equation for angular scattering. The calculated results are compared with various kinds of experimental results such as the electron range, the backscattering coefficient, and the depth distribution of energy dissipation. The theoretical results are found to be in satisfactory agreement with the experimental results.

A simulation of keV electron scatterings in a charged‐up specimen

Supposing that an insulator is charged‐up negatively by an accumulation of incident primary electrons, we study how much the subsequent incident electron is influenced by the charge in the specimen. We introduce a new Monte Carlo simulation model of electron scattering in a solid taking into account an electric field around the simulated electron. In a present study the incident electron energy is 20 keV, and the insulator is a poly‐methyl‐methacrylate wafer of 1 mm in thickness. This paper clarifies the changes in some physical quantities, e.g., the backscattering coefficient, energy deposition, etc. due to the specimen charging during an electron beam irradiation.

A Monte Carlo simulation of primary and secondary electron trajectories in a specimen

A new Monte Carlo calculation model is presented to simulate not only the primary electron behavior but also the secondary electron cascade in a specimen bombarded with an electron beam. Electrons having energy greater than 0.1 keV are treated as ‘‘fast electrons’’ and the previous single scattering Monte Carlo model is adopted. Electrons having energy smaller than 0.1 keV are treated as ‘‘slow electrons’’ and the electron cascade Monte Carlo model is used. The calculated results for the energy distribution of secondary electrons, and primary electron energy dependence of the total secondary yield and the backscattering yield are in good agreement with experimental results.

A Simulation of Electron Scattering in Metals

A Monte Carlo calculation model is developed to simulate trajectories of primary and ionized electrons in metals. It is constructed especially for a quantitative analysis of images in the scanning electron microscope. We perform a direct simulation considering each differential scattering cross section for elastic scattering, inner-shell electron ionization, conduction band electron ionization and bulk plasmon excitation. The spatial distribution of secondary electron emission calculated is narrower than that of backscattered electron emission at the Al surface for 1 keV primary electrons, but depending on the condition, this tendency may not always be found. The spatial distributions of both secondary and backscattered electrons show the size effect, and if the specimen to be observed is smaller, the practical resolution will be better in the scanning electron microscope.

Monte Carlo simulation of 1–10‐keV electron scattering in an aluminum target

New Monte Carlo simulations of electron scattering based on the single scattering model have been performed in the low‐energy region for an aluminum target, where two basic equations are required, namely the elastic scattering cross section and the energy‐loss rate. We investigated the screened Rutherford equation and the Mott equation for two different atomic potentials for the former, and the Rao Sahib‐Wittry equation (the modified Bethe equation) for the latter. The validity of each model is discussed in a comparison between Monte Carlo results and experimental results such as the electron range, electron backscattering, and electron transmission which have been reported by various authors. Consequently, it was found that a combination of the Mott cross section and the Rao Sahib‐Wittry equation showed the best accuracy. However, the accuracy of a previous model with the screened Rutherford equation is not as bad as aniticipated because of the higher accuracy of the Born approximation for light elements...

A dynamic simulation of electron beam induced charging-up of insulators

It is known that insulating materials charge-up negatively or positively depending on its condition during the electron beam (EB) irradiation. This charging disturbs various applications of EB technologies. In the present study a simulation model is proposed to express the charging mechanism of insulators as a function of time under EB irradiation The material studied here is PMMA which is a typical EB resist. In the simulation, the electron deposition distribution is calculated by a Monte Carlo simulation of electron trajectories in the specimen, where the production of secondary electrons and Auger electrons is taken into account. The electron yield obtained by the simulation for non-charged specimen agrees quite well with the experimental result, which has been obtained by using a pulse beam technique.

Quantitative electron microprobe analysis of thin films on substrates with a new Monte Carlo simulation

A new Monte Carlo simulation has been applied to the electron microprobe analysis of thin films at energies from 1–10 keV. The simulation model utilizes the Mott cross section for elastic scattering and the modified Bethe equation of Rao Sahib–Wittry for energy loss, instead of the screened Rutherford cross section and the standard Bethe equation, respectively. The new model has been examined in comparison with experimental results for the most probable angle of transmitted electrons through a thin film, and also the depth distribution of x‐ray production. Finally, the simulation was applied to thickness analysis of both aluminum and gold films on a sapphire substrate. The new results show good agreement with experimental data. It follows that the new Monte Carlo simulation is useful for electron microprobe analysis of elements, especially for heavy materials at relatively low energies.

Line edge roughness of developed resist at low dose electron beam exposure

Energy deposited in the resist is made not only by incident electrons, but also by the many secondary electrons generated, so that the influence of the exposure is spatially smoothened by the SE diffusion volume. Popular chemically amplified resists generate acid within the resist by an electron exposure, the spatial diffusion of which causes the electron exposure to be broadened and spatially smoothened. Further, by using a strong developer, which dissolves the resist with less sensitive to the electron exposure dose variation, unexposed parts of the resist can be dissolved, and the resist structure may be spatially smoothened. The influence of these factors is analyzed by simulation of the resist pattern after development. Thus, we present Monte Carlo simulations of electron trajectories in the resist.

Dependence of linewidth and its edge roughness on electron beam exposure dose

Electron beam lithography simulation is presented. A line pattern edge roughness of a resist after development process is discussed based on simulations of electron scattering in the resist film and the resist development process. Fixed threshold energy model is applied for the simulation and variations of linewidth and the line edge roughness are obtained as functions of the incident electron energy, resist thickness, and electron doses. The energy range calculated is from 1to5keV, the resist thickness ranges from 20to70nm, and the electron dose ranges from 1to100μC∕cm2. The resist assumed is poly(methylmethacrylate) and the film is on a Si substrate. In the present study, the threshold energy density is determined as 1.44×1021(eV∕cm3) to draw a given linewidth of 100nm, then the value of the line edge roughness is obtained. The minimum line edge roughness is obtained when the dose is more than that to produce the designed linewidth. As the dose is increased more than that to obtain the minimum edge roug...

Simulation of time-dependent charging of resist on Si under electron-beam irradiation

The time-dependent charging mechanism of an electrically insulating resist film on a Si substrate under electron-beam irradiation is proposed based on results obtained by a numerical simulation. The primary electron trajectory and the secondary electron cascade multiplication in the resist are calculated by Monte Carlo simulation, and spatial distributions of the electron deposition and the energy deposition in the resist are obtained. The potential distribution in and above the resist is obtained by solving the Poisson equation. The electron trajectory bending due to the electric field is calculated. The electron-beam-induced conduction is calculated based on the energy deposited. The potential distributions obtained in the resist show quite good agreement with the experimental results.