// module M5 · scaling laws

Scaling Laws

Simon's Law of Crystal-Electromagnetic Scaling — projected against silicon, GAA, CNTs, 2D, photonic, and quantum trajectories.

§ governing principle

Simon's Law of Crystal-Electromagnetic Scaling

"As crystal lattice purity and electromagnetic coupling efficiency improve, transistor switching performance scales proportionally to the product of the piezoelectric coefficient and EM coupling factor of the crystal medium, independent of physical transistor size."

P(t) = P₀ × (d₃₃ × ECCF)^(t/T)

P(t)

performance at year t

P₀

starting performance (TOPS/mm²)

years from 2026 baseline

doubling period (years)

d₃₃ × ECCF

crystal-EM coupling product

d₃₃450 pC/N

ECCF0.70

T2.0 y

purity0.90

P₀0.50 TOPS/mm²

Performance Projection · 2000–2040

TOPS/mm² · log

Parameter Controls

Crystal Typed₃₃ = 450 pC/N

Crystal Purity Factor0.90

EM Coupling Efficiency0.70

Doubling Period (T)2.0 y

Starting Performance (P₀)0.50 TOPS/mm²

Breakeven Analysis

2029

crossover year

At current projections, Crystal-EM Hybrid technology surpasses silicon scaling in year 2029.

Years from now

Performance multiple

×1.0

Crossover threshold

2.48 TOPS/mm²

Confidence band

Moderate

Competitive Landscape · TRL & scaling outlook

Technology	Status	Best Mobility (cm²/V·s)	Power Efficiency	Scalability	Heat Mgmt	Cost Trend	TRL (1–9)
Silicon CMOS	Mature, plateauing	1400	Moderate	Limited <3nm	Critical	↓	9
GAA Nanosheets	Production (Intel 18A, Samsung)	1200	Good	Good to 2nm	High	→	8
FinFET	Mature	1100	Moderate	Plateaued	High	↓	9
Carbon Nanotubes	Lab demos (MIT, Stanford)	100,000	Excellent	Yield-limited	Excellent	↑↑	4
2D Materials (MoS₂)	Sub-nm prototypes (Berkeley)	200	Excellent	Excellent	Good	↑	4
Photonic Computing	Niche commercial (Lightmatter)	n/a	Excellent	Wavelength-limited	Excellent	↑	5
Quantum Computing	Research	n/a	Domain-specific	Specialized	Cryogenic	↑↑↑	3
Crystal-EM Hybrid// thesis	Thesis (Simon's Law)	1000 (GaN host)	Excellent	Geometry-independent	Excellent	↑	2