Materials-Architecture Co-Design of 3D Integrated Circuits: Resolving the Dielectric Thermal Choke and Eliminating TSV Shear via Atomically Ordered B₅C₆N₅ Superlattices and Uncompromised PG(3, q) Routing

## Abstract Three-dimensional integrated circuits (3D-ICs) for high-density AI tensor acceleration face a fundamental physical bottleneck: conventional inter-die bonding oxides (SiO₂, kₒₓ = 1.40\,W/(m· K)) and carbon-doped silicon nitrides (SiCN, k = 2.20\,W/(m· K)) act as planar thermal blankets between stacked active tiers. In prior projective geometric 3D-IC architectures (*S3P17*), overcoming this dielectric thermal choke required drilling continuous, macro-scale copper Through-Silicon Vias (TSVs, kCu = 385\,W/(m· K)) across active silicon substrates and sacrificing k - λ channels per node of the finite projective geometry $PG(3, q)$ to serve as vertical thermal chimneys. However, macro-TSVs induce 305.59\,MPa of Lamé thermoelastic shear stress upon cool-down from back-end-of-line (BEOL) bonding (523.15\,K → 300.0\,K), enforcing 8.28\, transistor Keep-Out Zones (KOZs) that forfeit 215.41\,² of active CMOS area per via. Here we introduce a closed-loop **Materials-Architecture Co-Design** framework structured across a two-horizon foundry roadmap: (1) **Horizon 1 (Industrial Bridge)**, pairing atomic-layer-deposited AlN lateral heat spreaders with low-κ SiOC signal-pad collars (k_∥ = 162.00\,W/(m· K), κeff = 3.20); and (2) **Horizon 2 (First-Principles Target)**, synthesizing an **atomically ordered zincblende-derived B₅ C₆ N₅ superlattice** ((BN)0.625(C₂)0.375, 98.74%\,sp³ hybridization with $1.26%$ compliant insulating sp²-BN grain boundaries). By preserving translational crystal symmetry (ηorder = 0.9992), the ordered supercell suppresses Klemens ω⁴ point-defect phonon scattering, achieving k_∥ = 186.38--210.57\,W/(m· K) (23.78×--26.18× above disordered IBAD BCN alloys) and a Kapitza-coupled cross-plane effective conductivity of k⊥,eff = 116.97\,W/(m· K) across a 1.0\, isolation stack (84.60× above SiO₂). Simultaneously, matching the integrated thermal strain of silicon across the entire BEOL bonding envelope (∫300\,K523.15\,K [αBCN(T) - αSi(T)]\,dT = 0.00\,ppm) collapses residual film stress to ≤ 2.00\,MPa under ± 0.05% stoichiometric fab tolerances ($99.34%$ reduction vs. Cu TSVs). Coupled with pulsed ALD/PECVD growth, chemical-mechanical planarization (Rₐ = 0.10\,nm), and O₂/H₂O plasma B-OH hydrophilic activation, macro-TSVs are eliminated entirely in favor of BEOL-confined sub-micron direct Cu-Cu hybrid bond pads (0.00\, active silicon KOZ). In 24,000-cell anisotropic 3D Finite-Volume simulations at 225\,W/cm², peak die temperature drops from 104.68^ (clustered baseline) and 82.32^ (*S3P17*) to **61.19^**, with vertical inter-tier thermal differentials collapsing from 23.78^ to **1.34^**—liberating $100%$ of $PG(3, q)$ projective lines for non-blocking AllReduce tensor communication (2.333× to 8.111× bandwidth gain).