Quantum Simulations for Extreme Ultraviolet Photolithography

Abstract

Extreme Ultraviolet (EUV) lithography is the state-of-the-art process in semiconductor fabrication, yet its spatial resolution is fundamentally limited by the ``blur'' originating from absorption of photons at 92 eV, which induce physical and chemical changes in the photoresist via excited state processes and electron cascades. Accurate modeling of these phenomena requires precise ab initio data for high-energy decay channels, specifically photoabsorption and photoelectron emission. These are computationally difficult for classical methods due to prohibitive scaling in simulating electron dynamics, or due to the inability to resolve the ionization continuum in an efficient manner. In this work, we present quantum simulation algorithms to compute these key observables. First, we introduce a coherent time-domain spectroscopy algorithm optimized to resolve the photoabsorption cross-section at the 92 eV operating frequency. Second, we develop a first-quantized plane-wave simulation to compute the photoelectron kinetic energy spectrum, utilizing real-time dynamics and energy windowing to treat bound and delocalized scattering states on equal footing. Additionally, we provide logical resource estimation for a model photoresist monomer, 4-iodo-2-methylphenol (IMePh), and demonstrate that 92 eV absorption sensitivity can be resolved using roughly $200$ logical qubits and $10^{9}$ total non-Clifford gates per circuit with approximately $10^3$ shots for the smallest instance. The more sophisticated photoemission algorithm that models the continuum explicitly, incurs gate costs of $\geq 10^{13}$ total non-Clifford gates per circuit, $10^4$ shots, and requires a few thousand logical qubits. These results establish high-fidelity quantum simulations as a key component to parameterize the multi-scale macroscopic models required to overcome the electron blur bottleneck in semiconductor miniaturization.

Figures (3)

• Figure 1: Our proposed workflow for the ab initio design of low-blur EUV photoresists via quantum simulation. It connects atomic-scale electronic structure to macroscopic lithographic performance through four stages: (Hamiltonian) A candidate monomer, such as 4-iodo-2-methylphenol, is selected. Its full Hamiltonian ($H_{full}$) is dimensionally reduced to an effective electronic Hamiltonian ($H_{elec}$) utilizing pseudopotentials and/or active space selection to enable efficient simulation in a chosen basis and representation. (Key Observables) Two critical properties governing EUV lithography are targeted: the absorption sensitivity at the specific 92 eV operating frequency and the kinetic energy spectrum of secondary electrons generated via Auger decay. (Quantum Simulations) Two distinct quantum algorithmic primitives are compiled: a coherent time-domain approach to estimate the dipole autocorrelation function for absorption sensitivity, and a real-time electronic dynamics simulation to resolve the kinetic energy distribution of electrons ejected into continuum states. (Quantifying Blur) These quantum observables parameterize the initial conditions of electron cascades in larger bulk materials, allowing for the computational predictions of stochastic "electron blur" which ideally enables the design of materials that support continued semiconductor miniaturization.
• Figure 2: Quantum circuit schematic for simulating the photoemission spectrum in a first-quantized plane-wave basis. The simulation operates on $\eta$ particle registers initialized as $\ket{\alpha_1}\cdots \ket{\alpha_\eta}$, where each $\alpha$ represents the integer index encoding the momentum coordinates of a single electron. The algorithm proceeds in four main stages: (1) State Preparation: The electronic ground state $\ket{\Psi_0}$ is synthesized from a compressed MPS representation of molecular orbitals, with antisymmetrization applied to enforce fermionic statistics. (2) Excitation ($W$): The electric dipole operator creates the superposition of excited states, using block-encoded position operators ($\textsc{be}(X)$) and Quantum Signal Processing to filter for eigenstates within the 92 eV bandwidth. (3) Time Evolution ($e^{-iHt}$): The wavefunction is propagated for time $t$ to simulate the Auger decay dynamics. (4) Measurement: A real-space projector $\Pi_{>R_c}$ identifies electrons in the continuum. Because the kinetic energy operator is diagonal in the plane-wave basis, the final kinetic energy spectrum is extracted by directly sampling the computational basis of these particle registers. Note that for visual clarity, the extensive ancilla registers required for block encodings and arithmetic subroutines are omitted from this high-level schematic.
• Figure 3: Molecular structure of 4-iodo-2-methylphenol (IMePh). PubChem2025_CID143713 White represents hydrogen atoms, grey for carbon, red for oxygen, and purple for iodine. For an all-electron representation of this system, $\eta = 110$.

Theorems & Definitions (3)

• Definition 1: $(\alpha, m, \epsilon)$-$\textsc{be}(A)$
• Theorem 1: Resource estimate to block encode $H$
• Corollary 1: Block encoding of IMePh Hamiltonian