An Integrated Multimethod Simulation Framework for Tin Debris Control in Extreme Ultraviolet Lithography

Summary

This protocol aims to guide users through an integrated simulation framework to achieve tin debris control in extreme ultraviolet (EUV) and emerging Blue-X lithography, integrating kinetic modeling, the Boltzmann transport equation (BTE), and density functional theory (DFT)–based methods to evaluate ion interactions and hydrogen-assisted cleaning.

Abstract

This protocol is a conceptual, integrated modeling framework illustrated with representative results and instructs users on combining the Boltzmann transport equation (BTE), particle-in-cell (PIC), and kinetic simulations to investigate tin (Sn) debris mitigation in extreme ultraviolet (EUV) lithography. The protocol includes the reflectivity of Mo/Si multilayer mirrors (MLM), sputtering yield, implantation depth, kinetic modeling, and BTE computation. BTE and PIC simulations are used to resolve the electron energy distribution function (EEDF) of hydrogen plasmas and analyze the generation and acceleration of energetic Sn ions under different plasma conditions. The influence of hydrogen flow on ion slowing and radiation efficiency is also quantified. Based on the ionization cross sections and dissociation channels of Sn_xH_y species, the interaction potentials for Sn-H collision are computed using the density functional theory (DFT) method, which are used to calculate the implantation depth. In addition, the MLM reflectivity and sputtering yield from the interaction between Sn debris and the Ru coating on the MLM are calculated using a semi-empirical formula. By following this protocol, users can obtain key physical parameters relevant to Sn debris control, including sputtering yields, implantation depths, MLM reflectivity, and SH₄ formation under various hydrogen plasma EEDFs. These outputs enable systematic evaluation of contamination, cleaning, and detection processes in EUV lithography systems.

Introduction

Extreme-ultraviolet lithography (EUVL) is the state-of-the-art technology for advancing integrated circuit miniaturization, enabling patterning of features smaller than 2 nm. In a typical EUV source, a tin (Sn) microdroplet is first vaporized and ionized by a prepulse from a Nd:YAG laser, and the resulting plasma cloud is reheated by a CO₂ laser operating at 10.6 µm, thereby generating EUV radiation, which is collected by Mo/Si multilayer mirrors (MLM)^1,2. For commercial systems such as those developed by ASML, source power has reached levels sufficient for mass production. Nevertheless, ongoin....

Protocol

NOTE: The overall workflow, including the integration of fluid, kinetic, and quantum-chemical approaches. The workflow is illustrated in Figure 1 (highlighted in the red box).

Figure 1. Schematic of the integrated simulation framework for extreme ultraviolet lithography. Abbreviatio....

Results

Sputtering yield calibration and validation
Calculate the sputtering yield of Ar atoms in Ru as a calibration step. These sputtering yields represent output from protocol step 2.1 (Yamamura model). The results are shown in Figure 5 (left). Experimental data reported by Wu et al.²⁶ and Laegreid et al.²⁷ are largely consistent. The theoretical results from the present model show good agreement with experimental measurements a.......

Discussion

The integrated methodology that combines the Boltzmann transport equation (BTE), particle-in-cell (PIC), and kinetic simulations establishes a unified framework for investigating tin (Sn) debris mitigation in extreme ultraviolet (EUV) lithography. Specifically, the fluid simulation yields the plasma parameters—density and temperature, which can be integrated into a PIC program to obtain the spatiotemporal distribution of Sn_xH_y molecules. By coupling these PIC results with reaction rates obtain.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
BOLSIG+	Laboratory Plasma et Conversion d'Energie, University Paul Sabatier	The version updated on April 24, 2025
Gaussian	Gaussian Inc.	Gaussian 16
RustBCA	Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana-Champaign	1.2.0