Physical aspects of charged particle track structure

Determining the resolution limits of electron-beam lithography: direct measurement of the point-spread function

One challenge existing since the invention of electron-beam lithography (EBL) is understanding the exposure mechanisms that limit the resolution of EBL. To overcome this challenge, we need to understand the spatial distribution of energy density deposited in the resist, that is, the point-spread function (PSF). During EBL exposure, the processes of electron scattering, phonon, photon, plasmon, and electron emission in the resist are combined, which complicates the analysis of the EBL PSF. Here, we show the measurement of delocalized energy transfer in EBL exposure by using chromatic aberration-corrected energy-filtered transmission electron microscopy (EFTEM) at the sub-10 nm scale. We have defined the role of spot size, electron scattering, secondary electrons, and volume plasmons in the lithographic PSF by performing EFTEM, momentum-resolved electron energy loss spectroscopy (EELS), sub-10 nm EBL, and Monte Carlo simulations. We expect that these results will enable alternative ways to improve the resolution limit of EBL. Furthermore, our approach to study the resolution limits of EBL may be applied to other lithographic techniques where electrons also play a key role in resist exposure, such as ion-beam-, X-ray-, and extreme-ultraviolet lithography.

A Monte-Carlo code for the detailed simulation of electron and light-ion tracks in condensed matter

In an effort to understand the basic mechanism of the action of charged particles in solid radiation dosimeters, we extend our Monte-Carlo code (MC4) to condensed media (liquids/solids) and present new track-structure calculations for electrons and protons. Modeling the energy dissipation process is based on a model dielectric function, which accounts in a semi-empirical and self-consistent way for condensed-phase effects which are computationally intractable. Importantly, these effects mostly influence track-structure characteristics at the nanometer scale, which is the focus of radiation action models. Since the event-by-event scheme for electron transport is impractical above several kilo-electron volts, a condensed-history random-walk scheme has been implemented to transport the energetic delta rays produced by energetic ions. Based on the above developments, new track-structure calculations are presented for two representative dosimetric materials, namely, liquid water and silicon. Results include radial dose distributions in cylindrical and spherical geometries, as well as, clustering distributions, which, among other things, are important in predicting irreparable damage in biological systems and prompt electric-fields in microelectronics.

A Monte Carlo Code for the Simulation of Heavy-Ion Tracks in Water

TILDA, a new Monte Carlo track structure code for ions in gaseous water that is valid for both high-LET (approximately 10(4) keV/microm) and low-LET ions, is presented. It is specially designed for a comparison of the patterns of energy deposited by a large range of ions. Low-LET ions are described in a perturbative frame, whereas heavy ions with a very high stopping power are treated using the Lindhard local density approximation and the Russek and Meli statistical method. Ionization cross sections singly differential with energy compare well with the experiment. As an illustration of the non-perturbative interaction of high-LET ions, a comparison between the ion tracks of light and heavy ions with the same specific energy is presented (1.4 MeV/nucleon helium and uranium ions). The mean energy for ejected electrons was found to be approximately four times larger for uranium than for helium, leading to a much larger track radius in the first case. For electrons, except for the excitation cross sections that are deduced from experimental fits, cross sections are derived analytically. For any orientation of the target molecule, the code calculates multiple differential cross sections as a function of the ejection and scattering angles and of the energy transfer. The corresponding singly differential and total ionization cross sections are in good agreement with experimental data. The angular distribution of secondary electrons is shown to depend strongly on the orientation of the water molecule.

A Monte Carlo track structure code for electrons (approximately 10 eV-10 keV) and protons (approximately 0.3-10 MeV) in water: partitioning of energy and collision events

An event-by-event Monte Carlo simulation code for track structure studies is described. In the present form the code transports protons (approximately 0.3-10 MeV) and electrons (approximately 10 eV-10 keV) in a water medium in the gas phase approximation. For the type of particles and energy range considered, ionization, electronic excitation and electron elastic scattering are the most important collision events accounted for in the transport simulation. Efforts were made to ensure that the analytic representation of the various interaction cross sections rests on well established experimental data and theory. For example, the secondary-electron spectrum as well as partial and total ionization cross sections are represented by a semitheoretical formulation combining Bethe's asymptotic expansion and binary-encounter theory. Binding effects for five levels of ionization and eight levels of electronic excitation of the water molecule are explicitly considered. The validity of the model cross sections is examined against available experimental data and theoretical predictions from other similar studies. Results pertaining to the partitioning of energy loss and interaction events for the first-collision probability and nanometre-size track segments are presented.

Radial distribution of dose

The radial distribution of dose about the path of a heavy ion, principally from delta rays, is one of the central contributions of atomic physics to the systematization of high LET radiation effects in condensed matter, whether the detection arises in chemical, physical, or biological systems. In addition to the radial distribution of dose, we require knowledge of the response of the system to X-rays or gamma-rays or to beams of energetic electrons such that the electron slowing-down spectra from these radiations can approximate the slowing-down spectra from delta rays even at different radial distances from the ion's path. A combination of these data enables us to calculate the action cross sections ion bombardments in all detectors for which this information is available. These cross sections are indispensable for the evaluation of effects caused by high LET radiations. In this paper we focus attention principally on the calculation and measurement of the radial distribution of dose and on their limitations.