The Crystal-EM Hybrid Thesis
Why we built CrystalSim, what it models, and where it's going.
Moore's Law is decelerating. Below 3 nm, silicon transistors run into quantum tunneling, runaway leakage current, and thermodynamic limits that no amount of lithographic refinement can repair. The industry has spent the last decade buying performance with capex rather than physics.
The Crystal-EM Hybrid thesis proposes that scaling does not end with silicon — it migrates to crystals. Wide-bandgap semiconductors (GaN, ZnO), 2D crystals (MoS₂), crystalline oxides (InGaOₓ), and piezoelectrics (PZT, LiNbO₃) collectively offer 3-10× the carrier mobility, sub-femtojoule switching energy, and gate-less control via electromagnetic coupling.
We quantify the opportunity with a single coupling factor — ECCF, the Electromagnetic-Crystal Coupling Factor. When ECCF > 1, hybrid architectures resume the historical doubling curve. We call this extension Simon's Law: S(t) = S₀ · 2(t−t₀)/τ · ECCF(crystal, ω).
Top 5 indexed studies
- Piezotronics and Piezo-PhototronicsGeorgia Tech · 2010
Demonstrated that piezoelectric potential can gate transistors without an external voltage source.
- Gate-All-Around Nanosheet Oxide Semiconductor Transistor by Selective Crystallization of InGaOxUniversity of Tokyo · 2025
Achieved 44.5 cm²/V·s mobility with crystalline oxide channel, stable for 3 hours under stress.
- Single-Crystal PZT Piezo-Phototronic Adaptive TransistorMulti-institutional · 2026
Record memory window capacity factor of 0.87, ON/OFF ratio >10⁵, 90% neural network accuracy.
- Piezoelectricity in 2D MoS₂ SemiconductorBerkeley Lab · 2014
First quantitative measurement of piezoelectricity in a single molecular layer; coefficient 2.9×10⁻¹⁰ C/m.
- Skoltech / IBM Optical SwitchSkoltech / IBM · 2021
1 trillion operations per second — 100–1000× faster than commercial transistors.
Simon's Law of Crystal-Electromagnetic Scaling
A New Paradigm for Transistor Performance Beyond Moore's Law. The full pre-publication draft introducing Simon's Law, the ECCF metric, and the Crystal-EM Hybrid architecture — with experimental evidence, competitive landscape, and research roadmap.
Independent researcher exploring post-silicon transistor architectures at the intersection of crystallography, piezotronics, and electromagnetic coupling. Bio placeholder — full version forthcoming.
The physics models
Drift-diffusion with long-channel saturation: I_D = ½ · μ · C_ox · (W/L) · (V_GS − V_T)². Applied uniformly across all crystal channels.
μ ∈ [ZnO 200, Si 1400, GaN 2000] cm²/V·s C_ox = ε₀ · εᵣ / t_ox
Direct piezo effect: V_piezo = d₃₃ · σ / (ε₀ · εᵣ). Mechanical stress σ generates a gating voltage proportional to the d₃₃ tensor.
d₃₃ ∈ [ZnO 12, PZT 600] pC/N ε₀ = 8.854 × 10⁻¹² F/m
Electromagnetic-Crystal Coupling Factor: ECCF = (ε_r · μ_eff · Q) / (ω · t_channel), normalized so silicon at 1 GHz ≈ 0.1.
Q (resonance) ∈ [Si 50, GaN 800, PZT 2000] ω = 2π · f
From simulator to silicon-killer
- Phase 1SimulatorQ2 2026 · current
Eight calibrated modules covering crystal selection, transistor sim, EM coupling, and hybrid design.
- Phase 2Lab ValidationQ4 2026
Partner with a thin-film growth facility to verify ZnO and PZT mobility / d₃₃ predictions.
- Phase 3Prototype Crystal-EM Transistor2027
Fabricate a single-device demonstrator with EM-coupled gating and benchmark vs. silicon.
- Phase 4Patent & Publication2028
File IP on the Crystal-EM hybrid architecture and submit findings to a top-tier journal.