From 110 GHz to 220 GHz: Fixture-Invariant Extraction of Equivalent Spatial Length in 1.6T/3.2T Interconnects — A Reference-Plane Transfer Framework for Millimeter-Scale Geometric Convergence

Document status: Non-commercial technical opinion and framework-level metrology profile. This document does not request endorsement, certification, procurement, legal determination, or product approval. Companion basis: HPCA V11.7 (Zenodo DOI: 10.5281/zenodo.19822525); V7.5 TGO (Zenodo DOI: 10.5281/zenodo.19955479). Industrial Abstract. For PCB manufacturers entering the 110/220 GHz and 1.6T–3.2T generation, the real question is no longer how finely the copper can be etched, but how objectively the channel can be proven. This paper extends the author's prior physical-layer compensation framework — which converges up to 15–25% of geometric deviation into an equivalent spatial length Leq ≤ λEM/4 — by adding its measurement layer. Through a fixture-invariant de-embedding workflow, Leq can be extracted from S-parameter and TDR responses in an objective, reproducible, and traceable manner, serving as the metrological basis for first-pass yield, channel acceptance, and high-frequency ASP differentiation across advanced HDI, Ultra-HDI, and ABF substrates. The framework can be retrofitted into existing HDI, Ultra-HDI, and ABF production lines, and provides a third-party-verifiable physical observable for high-frequency channel acceptance. Academic Abstract. This paper presents a reference-plane-controlled metrology framework for extracting the equivalent spatial length Leq in 110/220 GHz interconnect channels. The framework treats the measured channel as a cascaded network composed of fixture, launch segment, probe interface, and device under test (DUT), and employs calibration and de-embedding workflows including TRL, SOLT/LRRM, and Automatic Fixture Removal (AFR, formally specified in IEEE Std 370-2020 Section 5) to rigorously transfer the measurement reference plane to the true physical boundary of the DUT. The residual phase deviation is then converted to spatial length via Leq = (Δφrad / 2π) · λEM. A publicly disclosable Measurement Hygiene Layer is further defined, covering raw S-parameter preservation (Touchstone Version 2.1 format), calibration-state evidence, repeatability and noise reporting, TDR boundary metadata, and an immutable file manifest anchored in cryptographic hashing (SHA-256). Key contributions. (i) A reference-plane-controlled Leq extraction framework assembling TRL, SOLT/LRRM, and AFR into a single metrology chain terminating in equivalent spatial length; (ii) a publicly disclosable, vendor- and tool-agnostic Measurement Hygiene Layer; (iii) the Background Quasi-Static Geometric Offloading (BQSGO) concept that separates millisecond-scale thermodynamic structural drift from picosecond-scale microwave-transport symbol response; (iv) a spatio-temporally resolved formulation Leq(f, tms) bridging quasi-static geometric drift to microwave transport; (v) the Topological Trap (Capture Basin) interpretation under topological symmetry that supports the SCD21 → 0 premise for differential-mode phase-residual extraction; and (vi) explicit instantiation of the Leq ≤ λEM/4 convergence boundary at Leq ≤ 0.5 mm @ 110 GHz and Leq ≤ 0.25 mm @ 220 GHz, providing a physical anchor that can be independently cited and verified by third parties. Public Clean Disclosure Boundary. The framework is positioned as a vendor-neutral metrology methodology and does not disclose vendor-specific calibration matrices, routing coordinates, DUT identity, or product-specific parameters. The methodology skeleton is independently reproducible by any third party with equivalent measurement capability. The open-source reference implementation of the AFR algorithm (https://opensource.ieee.org/elec-char/ieee-370) provides a concrete technical pathway for this reproducibility. Standards alignment. Complementarily aligned with IEEE Std 370, OIF CEI-05.3 (CEI-224G-LR-PAM4 Revision 05), OIF CEI-448G Framework (OIF-FD-CEI-448G-01.0, 2025-11), and IEEE P802.3dj (200/400/800/1600 Gb/s Ethernet Amendment 13). In the AI-assisted physical-modeling dimension, the framework forms a complementary relationship with recent PINN research pathways applied to Maxwell-equation inverse problems in heterogeneous media (Da-PINN) and physics-enforced modeling of transmission-line insertion loss. Index Terms: 110/220 GHz interconnects; 1.6T/3.2T channels; equivalent spatial length Leq; Fixture-Invariant Extraction; Reference-Plane Transfer Framework; Measurement Hygiene Layer; Background Quasi-Static Geometric Offloading (BQSGO); TRL; SOLT/LRRM; Automatic Fixture Removal (AFR); IEEE Std 370; Touchstone Version 2.1; Phase Unwrapping; Passivity and Causality Verification; Vector Fitting; Topological Trap / Capture Basin; SDD21/SCD21; Physics-Informed Neural Networks (PINN); OIF CEI-224G/448G; IEEE P802.3dj. No external funding, corporate sponsorship, or institutional grant support is declared. References to existing signal-integrity, calibration/de-embedding, standards, and AI-physics literature are used for scholarly positioning only; they do not constitute an admission that the Leq metrology framework, the Measurement Hygiene Layer, BQSGO, or the Topological Trap interpretation are derived from, anticipated by, or dependent on any cited reference.