⚛️ Module 1 · Physics Foundation · Chapter 1.10 · 10 min read

Physics Module Review

Nine chapters on one page — mapped onto SIDRA.

Prerequisites

1.9 — Thermodynamics and Joule Heating

What you'll learn here

See how the 9 chapters of Module 1 connect in one concept map
Match each concept to a single formula / a single SIDRA component
Probe the module with an integrative lab task
Prepare for Module 2 (Chemistry)

Hook: Nine Chapters → One Sentence

We’ve walked nine fronts this module: atom, bands, diode, MOSFET, Ohm, RC, tunneling, electrochemistry, thermodynamics. Each is a book on its own. Yet they collapse into one sentence:

An electron, in a semiconductor lattice, flows through a channel the gate controls; in a memristor that current becomes voltage × conductance; a capacitor times it; tunneling can cross an insulator and ion motion writes conductance into memory; and all of this is paid for in heat.

This chapter turns that sentence into a concept map, a one-page cheat sheet, and an integrative lab.

Intuition: SIDRA's Bare Path

Every Module 1 chapter serves a specific SIDRA component:

Chapter	Concept	SIDRA role
1.1	Atom / electron energy levels	HfO₂ electronic states, emission spectrum
1.2	Bands, semiconductor vs insulator	Si substrate (semi) vs HfO₂ (insulator)
1.3	P-N diode + OTS analog	1S1R selector — sneak-path control
1.4	MOSFET inversion channel	Every transistor in the 28 nm CMOS base die
1.5	Ohm + KCL → MVM	Crossbar analog matrix-vector multiply
1.6	Capacitance + τ = RC	TDC readout — turning current into time
1.7	Quantum tunneling	HfO₂ gate dielectric + memristor LRS path
1.8	Ion migration + filament	Memristor SET/RESET mechanism
1.9	Joule heat + thermal budget	TDP ladder (Y1 3 W → Y100 100 W)

Formalism: One-Page Formula Card

L1 · Intro

Nine core equations, all in one place:

Topic	Formula
Bohr energy	$E_n = -13.6/n^2$ eV
Thermal voltage	$V_T = kT/q \approx 26$ mV (300 K)
Diode (Shockley)	$I = I_s(e^{V/V_T} - 1)$
MOSFET saturation	$I_D = \tfrac{1}{2}\mu_n C_{ox}(W/L)(V_{GS}-V_{th})^2$
Ohm → conductance	$I = V \cdot G$
MVM (column current)	$I_j = \sum_i V_i G_{ij}$
RC time constant	$\tau = R \cdot C$
Charging curve	$V_C(t) = V_{in}(1 - e^{-t/\tau})$
Tunneling	$T \approx e^{-2\kappa d}$
Arrhenius retention	$t \propto e^{E_a/kT}$
Joule	$P = I^2 R$
Thermal Ohm	$\Delta T = P \cdot R_{th}$

L2 · Full

What’s exponential:

Diode current in V ( $e^{V/V_T}$ ). 60 mV → 10×.
MOSFET subthreshold current in V_GS.
Tunneling in d and $\sqrt{V_0-E}$ .
Ionic drift in qaE/kT (high field).
Retention in $E_a/kT$ .
CMOS leakage in temperature.

All from the same Boltzmann family: $\exp(-E_{barrier}/k_B T)$ . Any time physics has a barrier, its crossing probability sits in an exponential of that barrier. This is the single big sentence of the module.

What’s linear:

Ohm ( $I = V/R$ ).
Analog MVM (follows from Ohm).
Derivative form of capacitor charging.
Fourier heat flux.

What’s quadratic:

MOSFET saturation current $(V_{GS}-V_{th})^2$ .
Capacitor energy $(1/2)CV^2$ .
CMOS dynamic power $CV^2f$ .
Joule heat $I^2R$ .

Quadratics sit in the “energy” family, linears in “current/voltage”, exponentials in “crossing-a-barrier”.

Experiment: Draw Your Concept Map

Take a sheet of paper. Arrange these 9 nodes on a page and draw links between them:

  [Atom] ── [Bands] ─── [P-N Diode]
     │         │             │
     │         └── [MOSFET] ─┘
     │               │
  [Ohm's Law] ──── [MVM (crossbar)]
     │               │
  [Capacitance] ─── [τ = RC] ── [TDC]
     │
  [Tunneling] ─── [Electrochemistry] ── [Memristor filament]
                       │
                  [Thermodynamics / Joule]

Next to each link, write one sentence: “How does A enable B?” Example:

Atom → Bands: “Many atoms together broaden discrete energy levels into bands.”
Bands → MOSFET: “Above-threshold gate voltage inverts the p-lattice, opening a conduction band channel.”
Ohm → MVM: “Each memristor computes V·G; KCL sums column currents.”

This map should be in your head when you walk into Module 5.

Cumulative Quiz

Each question touches 2-4 chapters. 8 total — pass with more than half.

1/8In hydrogen, the n=2 → n=1 transition releases how much energy?

Integrative Lab: A Memristor Cycle

Model the full program-read-retention cycle of one HfO₂ memristor cell.

Data:

Cell size: 100 nm × 100 nm × 5 nm (HfO₂)
V_read = 0.1 V, V_prog = 2 V
Parallel capacitance C_par = 0.5 fF
LRS conductance G_LRS = 100 µS (10 kΩ)
HRS conductance G_HRS = 1 µS (1 MΩ)
HfO₂ activation energy E_a = 1.0 eV

Questions:

(a) Under program voltage, what’s the electric field (V/m)? What is qaE in eV? (a = 0.3 nm) (b) Read currents in LRS and HRS (in µA)? (c) Read RC time, and minimum read duration? (d) If retention at 85°C is 10⁵ s, how long at 25°C? ( $E_a = 1$ eV) (e) SIDRA Y1 has 4.19 × 10⁸ cells. Power to read all in parallel? (assume column current ~ N · V · G_avg, G_avg = 50 µS)

Solutions

(a) E = 2 / 5×10⁻⁹ = 4×10⁸ V/m. qaE = 1.6×10⁻¹⁹ · 0.3×10⁻⁹ · 4×10⁸ = 0.12 eV.

(b) I_LRS = 0.1 · 100 µS = 10 µA. I_HRS = 0.1 · 1 µS = 0.1 µA. 100× ratio — easy to distinguish.

(c) R_LRS = 10 kΩ, C_par = 0.5 fF. τ = 10⁴ · 0.5×10⁻¹⁵ = 5 ps. Minimum read ≥ 5·τ = 25 ps. Real SIDRA reads at ~100 ps - 1 ns.

(d) t_25/t_85 = exp(E_a/kT_25 - E_a/kT_85) = exp(1/0.02585 - 1/0.03086) = exp(6.3) ≈ 545. So t_25 ≈ 10⁵ · 545 = 5.5×10⁷ s ≈ 1.7 years. (SIDRA 10-year target requires E_a ≈ 1.2 eV.)

(e) Column current ~ N · V · G = 256 · 0.1 · 50×10⁻⁶ = 1.28 mA. 16 CUs × 400 subarrays × 256 columns ≈ 1.6×10⁶ columns. All active → 2000 A impossible. In reality only active CUs read with ~5% activity → ~100 A × 0.1 V = 10 W. Y1 TDP is 3 W, so α < ~30%. This is exactly why activity factor matters (Ch. 1.6).

Module 1 Cheat Sheet

At a glance:

✅ Electron and atom energy levels (Bohr ladder).
✅ Band structure → metal / semiconductor / insulator classification.
✅ P-N diode (Shockley), forward/reverse bias, $V_T = 26$ mV.
✅ MOSFET 3 regimes (off / triode / saturation), CMOS inverter.
✅ Ohm + KCL = foundation of analog MVM.
✅ Capacitance + RC + CMOS dynamic power $\alpha CV^2 f$ .
✅ Quantum tunneling $T \approx e^{-2\kappa d}$ , HfO₂ high-k advantage.
✅ Memristor: oxygen-vacancy filament, SET/RESET, endurance.
✅ Joule heat + thermal balance, TDP budgets, DVFS throttling.

You’re ready for SIDRA: Module 5 dresses this same physics onto the real chip. You can skip there directly; or continue with Module 2 (Chemistry) and Module 3 (Biology→Algorithm) for the HfO₂ fab chemistry and the synapse analogy.

Vision: Beyond Physics — Modules 2–9 Preview

Module 1 laid the classical and quantum foundations. The next modules extend that foundation in different directions — each is a potential leap point for post-Y10 SIDRA:

Module 2 (Chemistry): atom-by-atom ALD-grown HfO₂, NbOx selectors, redox kinetics. Vision: ferroelectric HZO, 2D materials (MoS₂, hBN), single-molecule memristors.
Module 3 (Biology + Algorithm): brain synapse model, STDP learning, spike-timing code. Vision: organic synapses (PEDOT:PSS), biomimetic neurons, brain-matched 20 W energy budget.
Module 4 (Math): linear algebra, probability, optimization, tensor analysis. Vision: quantum linear algebra (HHL), neuromorphic optimization, stochastic computing.
Module 5 (Hardware): crossbar circuit design, ADC/DAC, sense-amp, TDC. Vision: fully digital-analog hybrid compute, photonic MVM, superconducting hybrids.
Module 6 (Software): compiler, tensor mapping, mixed precision. Vision: analog-aware compiler, HW/SW co-design tooling.
Module 7 (Manufacturing): wafer, lithography, yield, packaging. Vision: wafer-scale 3D integration, chiplet marketplace, in-memory packaging (HBM → HBM-M).
Module 8 (System): chiplet interconnect, power delivery, thermal. Vision: optical chiplet-to-chiplet links, immersion cooling, thermal-aware scheduling.
Module 9 (Top layer): AI model architectures, training, inference. Vision: brain-scale models (10¹⁴ parameters), lifelong learning, federated training.

The biggest post-Y10 SIDRA “game changer”? Most likely photonic–electronic hybrid MVM (Module 5 + 8): light for data movement, electricity for weight multiplication. Bandwidth 100×, power 10× lower. But not before 2028.

Prerequisites

What you'll learn here

🪝 Hook: Nine Chapters → One Sentence

🧭 Intuition: SIDRA's Bare Path

📐 Formalism: One-Page Formula Card

🧪 Experiment: Draw Your Concept Map

📝 Cumulative Quiz

🛠️ Integrative Lab: A Memristor Cycle

🗂️ Module 1 Cheat Sheet

🔮 Vision: Beyond Physics — Modules 2–9 Preview

📚 Further Reading