CRYSTALSIM

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Understanding Simon's Law Projections

Lesson 4 of 6·15 min read·+80 XP
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Projections are arguments, not predictions

Simon's Law tells you what could happen if the underlying parameters hold. It says nothing about whether they will. Mastery means choosing parameters you can defend with evidence — and presenting a range of scenarios, not a single confident line.

Key Concept
Technology Readiness Level (TRL)
NASA's 1–9 scale for tech maturity. TRL 1 = basic principles observed. TRL 5 = component validated in relevant environment. TRL 9 = system proven in full operational use. Most Crystal-EM pillars sit between TRL 3 (lab demos) and TRL 5 (pilot lines).
Key Concept
Scenario analysis
Building 2–4 distinct futures (pessimistic / moderate / optimistic) instead of one point estimate. Forces you to defend the *range* and exposes which parameters drive the outcome.
Key Concept
Conservative estimate
A number you'd defend in front of skeptical reviewers. Use measured data only, no speculative improvements. The pessimistic scenario should be a conservative estimate.

Choosing parameters

Three knobs drive the curve:

- d₃₃ (piezo coefficient) — bench-demonstrated values: ZnO ≈ 12 pC/N, GaN ≈ 3 pC/N, AlN ≈ 5 pC/N, PZT ≈ 250–600 pC/N. PZT is mature; integrating it into CMOS is the bottleneck. - ECCF (electromechanical coupling) — ratio (d₃₃·E·Q) / (δ·f). Today's RF MEMS reach 0.3–0.6. Lab cavities have hit 0.85. - T (doubling period) — argue from analogous tech. Moore's Law had T ≈ 2 yr (early), now ≈ 3–4 yr. EUV-driven nodes: ≈ 3 yr. Crystal-EM has no track record yet — pessimists assume 5 yr; optimists 2 yr.

Build three scenarios

Use the scenario builder below. Each card shows the 10-year projection for that parameter set and a one-line rationale. Click Snap to copy the values to your clipboard for your write-up.

Interactive · Pessimistic / Moderate / Optimistic
Simon's Law · scenario analysis
Pessimistic
T
5 yr
ECCF
0.30
d₃₃
80 pC/N
10-yr
2.8×
TRL 3 — bench prototypes
Conservative: assumes only what has already been demonstrated in single labs.
Moderate
T
3 yr
ECCF
0.60
d₃₃
250 pC/N
10-yr
21.0×
TRL 5 — fab pilot lines (5–7 yr horizon)
Industry-typical: assumes EM-coupling efficiencies similar to today's RF MEMS.
Optimistic
T
2 yr
ECCF
0.90
d₃₃
500 pC/N
10-yr
97.7×
TRL 7 — system demos (10 yr horizon)
Aggressive: assumes PZT-class piezo + tuned-cavity Q ≥ 2000 in production.
Exercise: snap each scenario, paste into your notes, and write one sentence justifying which scenario you'd defend in front of investors.

Cross-check on the Scaling Laws page

For high-fidelity charts and for screenshots you can drop into a slide deck, replicate each scenario in the Scaling Laws module. Set d₃₃, ECCF, and T to match each card; capture the chart for pessimistic, moderate, and optimistic.

Checkpoint · +5 XP
What's the right way to defend a doubling period T = 3 years?
Lesson Summary
  • Set realistic Simon's Law parameters.
  • Build pessimistic, moderate, and optimistic scenarios.
  • Argue for a doubling period T from real evidence.
  • Tie projections to Technology Readiness Levels.
Test Your Knowledge · +80 XP
1
Why present three scenarios instead of one number?
2
TRL 5 means:
3
Which parameter would a *pessimistic* scenario use?
4
What's a 'conservative estimate'?
5
PZT's d₃₃ is roughly: