Photoelectron trajectory simulation in a resist for EUV lithography

Summary form only given. Intensive effort has been done to realize EUV lithography as a realistic tool for the next generation lithography. Only about 85 photons are exposed in 5 nm square at 5 mJ/cm², which is a common target to reach by laser or discharge plasma, and an extent of the statistical fluctuation in the developed resist feature is seriously concerned. To quantify the feature, the areal image of the EUV light has been used. [1] However, recently Kozawa et al. insisted that photoelectrons play an important role in EUV lithography. [2] They obtained a time dependent distribution of electron charge in a resist, and analyzed the spatial resolution. However, since a chemical reaction is caused by an energy deposited by electrons, here, we obtain a distribution of the energy deposited in a resist. EUV light has a wave length of around 13.5 nm, and the energy is 91.85 eV The absorption coefficient of such low energy photons in polymers is not well known, and also elastic and inelastic scattering cross section of photoelectrons are not well known either, and it is difficult to obtain the deposited energy with high accuracy. [3] In the present study the photo-absorption coefficient is obtained by a calculation of the dipole-oscillator-strength for a free atom with the Hartree-Fock-Slater potential. [4] Resist assumed is PMMA, and by considering binding energies and ionization cross sections of all sub-shell electrons of the consisting atoms, the photoelectron generation is obtained. Trajectory of photoelectrons in PMMA is simulated until the energy is 4 eV by our previous Monte Carlo simulation model for electron beam lithography. [5] An example of photoelectron trajectories generated in depth is shown in Fig.1, if the resist is thick enough. Fig. 1(a) shows photoelectron trajectories ionized by 100 photons incident normal to the surface, and because of the decay of the EUV light, the larger amount of electrons are generated at the shallower region. Th- e maximum depth of the EUV light to reach is almost 2 mum. Fig. 1(b) shows 5 photoelectron trajectories with an enlarged size, and because of a high probability of elastic scattering events, crooked patterns are shown. By calculating a large number of photons, a radial distribution of the energy deposition is obtained, and it is plotted in Fig.2. It is shown that the maximum radial range of those electrons is about 30 nm, and it agrees with the result of Kozawa et al. [2] The energy deposited in the first layer is almost the half of that in the other layers. The reason is that electrons emitted from the surface never come back. By using these energy deposition distributions, resist structures after development process is simulated. [6] Here, we assume sinusoidal areal image intensity distribution for the exposing EUV light with the maximum and the minimum intensity varies from 1 to 0 for the contrast (C) =1, and with the variation from 0.9 to 0.3 for C=0.5 as shown in Fig.3. The exposure pattern is 50 nm-wide lines and spaces, and the exposure dose is 5 mJ/cm². By assuming the critical absorption energy for the development process as 6.0times10²⁰ eV/cm³, the three dimensional resist structure is obtained. The top view of the resist structures for the contrast is 1 and 0.5, are shown in Fig.4. A quite rough surface at the line edge is observed, and the critical dimension error and the line edge roughness are quite severe, even if the image contrast is unity. Since the EUV exposure system consists of several reflective mirrors, an image contrast at the resist surface is always less than unity, and also the aerial image of EUV light may have a variation within the resist thickness. It is necessary to take into account non-linear characteristics of chemically amplified resist at for future precise realistic discussions.