1.Quantum Bankruptcy of Copper Interconnects Numerical Proof of the d⁻³ Resistance Singularity and Critical Length Collapse at the 1nm Node

[Zenodo Submission: Paper I — Cu Interconnect Quantum Bankruptcy] 1. Title Quantum Bankruptcy of Copper Interconnects: Numerical Proof of the d⁻³ Resistance Singularity and Critical Length Collapse at the 1nm Node 2. Identifiers Series DOI: 10.5281/zenodo.18325543 Patent: KR 10-2026-0017941 SHA-256: 42dbcbc0c8d41c0951134847814ae7e584854adc654939647e2570359931b020 3. AbstractThis paper provides a fully reproducible numerical proof of copper interconnect failure at the 1nm logic node, derived exclusively from bulk Cu physical constants (ρ0=1.7×10−8\rho_0 = 1.7\times10^{-8} ρ0=1.7×10−8 Ω⋅\Omega\cdot Ω⋅m, λ=39\lambda = 39 λ=39 nm, RQ=12.9R_Q = 12.9 RQ=12.9 kΩ\Omega Ω). No process-specific fitting parameters are used. The resistance model incorporating Fuchs–Sondheimer surface scattering yields a dominant w−3w^{-3} w−3 singularity with analytically fixed coefficient ρ0Cλ=3.315×10−16\rho_0 C\lambda = 3.315\times10^{-16} ρ0Cλ=3.315×10−16 Ω⋅\Omega\cdot Ω⋅m3^3 3. At w≤8w \leq 8 w≤8 nm, this cubic term accounts for more than 70% of total resistance. The ratio test at w=6w = 6 w=6 nm vs. w=3w = 3 w=3 nm yields Rratio=7.06R_\text{ratio} = 7.06 Rratio=7.06, converging to the exact 23=82^3 = 8 23=8 scaling of a pure w−3w^{-3} w−3 singularity. A critical length Lcrit(w)=RQw3/ρ0CλL_\text{crit}(w) = R_Q w^3 / \rho_0 C\lambda Lcrit(w)=RQw3/ρ0Cλ is derived, below which wire resistance exceeds the quantum of resistance RQR_Q RQ. Numerical results: Lcrit=2.49 μL_\text{crit} = 2.49\,\mu Lcrit=2.49μm, 1.05 μ1.05\,\mu 1.05μm, 0.311 μ0.311\,\mu 0.311μm for w=4w = 4 w=4, 33 3, 22 2 nm respectively. Since minimum back-end-of-line routing lengths exceed 1 μ1\,\mu 1μm, copper at w≤3w \leq 3 w≤3 nm operates in a state of Quantum Bankruptcy. The paper concludes that only transport architectures structurally decoupled from w−3w^{-3} w−3 scaling can sustain signal integrity at and beyond the 1nm node. All results are reproducible with a scientific calculator from the stated constants. 4. Source of Truth Declaration All numerical values are derived from tabulated bulk Cu constants. No experimental dataset is required for reproduction. This paper is Paper I of the SVRN-OS research series. 5. Author Minsu Cho (조민수) [e-mail] linkedin.com/in/minsu-cho-a3750a393 KR 10-2026-0017941