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 dimensionless metric — the Crystal-EM Enhancement Factor (CEF). When CEF > 1, hybrid architectures resume the historical doubling curve. We call this extension Simon's Law: P(t) = P_Si(t) · CEF, with CEF = (μ_crystal/μ_Si)·(1 + κ·η_EM).
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 device architectures at the intersection of crystallography, piezotronics, and electromagnetic resonance. CrystalSim originated from a hypothesis that the deceleration of Moore's Law admits a non-geometric scaling solution — one based on materials and field coupling rather than miniaturization. The simulator implements textbook compact models calibrated against published silicon and GaN data, with an open-source parameter database. All findings are pre-publication; collaboration with academic and industrial partners is actively sought.
Background: independent research, 2024–present. Prior work in software architecture and platform engineering. Self-directed study of semiconductor device physics, drawing primarily from Sze's Physics of Semiconductor Devices, Taur & Ning's Fundamentals of Modern VLSI Devices, and the IRDS technical roadmap.
CrystalSim is open to collaboration with:
- • Materials scientists who can validate predicted properties
- • Device engineers with TCAD experience who can cross-check models
- • Foundry researchers exploring post-silicon paths
- • Academic groups with thin-film or piezo characterization capability
- • Independent researchers and students
Open questions and data requests welcome via GitHub issues.
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
Performance at time t is the silicon-equivalent trajectory amplified by a dimensionless Crystal-EM Enhancement Factor:
P(t) = P_Si(t) · CEF
P_Si(t) = P₀ · 2^((t − t₀) / τ_eff) [τ_eff > 2 yr; default 3.5]
CEF = (μ_crystal / μ_Si) · (1 + κ · η_EM) [dimensionless]
ECCF = κ · η_EM
= clamp01(d₃₃ · σ_max / V_th) · clamp01(Q / Q_critical) [Q_critical ≈ 100]Dimensional check: [pC/N · Pa] / [V] = [C·m⁻²·V⁻¹·V] / [V] = [F/m²] / [F/m²] = dimensionless ✓
κ captures piezoelectric gating contribution (saturation stress vs threshold voltage); η_EM captures resonator coupling efficiency. Both are clamped to [0,1] before multiplication.
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.