Part II · The future chip · Chapter 15 of 18

Light and heat

How many units one laser can feed, what the phase shifters cost to hold, and what heat from the stacked logic does to their phases.

One laser, more and more unitsillustrative

Each step doubles the units on one 20 dBm laser at 4 λ and 112 GBd. Losses and the power at each receiver come from the browser’s port of the simulator’s laser budget; the margins are the simulator’s own (experiment 14).

Data table

Margin vs units on one laser
units U	4 λ, 112 GBd
1	14.37
2	11.06
4	7.425
8	3.323
16	−1.379
32	−6.715
64	−12.6

P_{\text{mod}} = \alpha\,\frac{P_{\text{laser}}}{W\,U}\,\frac{10^{-L/10}}{4}\,10^{-\text{IL}_{\text{MZM}}/10}

L = L_{\text{coupler}} + L_{\text{WDM}} + L_{\text{split}}\,\log_2(8U) + L_{\text{prop}}

What this stage does

Two physical budgets limit how far the stacked chip can scale before any arithmetic is done. Light: one external laser is split on chip to every unit’s four modulators and four LO ports, so each doubling of U halves the power at every receiver. Heat: every unit holds dozens of phase shifters at a set phase, which costs power, and the logic stacked underneath heats the photonic layer unevenly, which moves those phases.

How it’s modelled

The laser budget follows the light: a fibre coupler (1.5 dB illustrative), WDM when W > 1 (1.5 dB illustrative), a binary splitter tree with 0.1 dB illustrative of excess loss per stage, propagation across the layer (1 dB/cm illustrative) and the modulator’s insertion loss (4 dB illustrative). The signal/LO split is optimised per point, and the margin is Part I’s: how far every noise term can grow before the worst output reaches the SER target, with the receiver noise from the transimpedance limit of chapter 12. A design must hold 6 dB illustrative.

Phase shifters sit at a mean phase of π and hold it at 10 mW illustrative per π (thermo-optic; the simulator sweeps the range reported for silicon heaters), with MEMS and non-volatile trimming as low-power options. Heat from the logic is a flux map (an even 0.5 W/mm2 illustrative with hot spots at 2 W/mm2 illustrative) through the stack’s thermal resistance (5 K mm2/W illustrative), spread sideways over 0.5 mm illustrative. A TEC holds the mean; each heater’s phase moves by 0.08633 rad/K of local temperature change.

What we found

One laser feeds a handful of units. At 112 GBd with the bonded receiver, one laser holds a 6 dB margin for at most U × W = 20 at four wavelengths (26 at one), and 8 (12) at 10 dB. The margin falls from 14.37 dB with one unit to −12.6 dB with 64, so lasers multiply with U. At Part I’s 14 GBd one laser would feed 233: speed costs light.

Max U × W per laser vs laser powerillustrative

The largest U × W one laser can feed, at 4 λ and 112 GBd, against its power. Where a laser cannot hold the margin for even one unit the value is 0, which a log axis cannot show; it is in the data table.

Data table

Max U × W per laser vs laser power
laser (dBm)	6 dB margin	10 dB margin
13	4	0
17	8	4
20	20	8
23	36	16
27	92	44

Many wavelengths on one mesh. The simulator’s v0.4 adds a term these limits leave out: every phase in a mesh scales with wavelength, so each channel sees a slightly different transform. Restated with each channel’s own transform, the laser limits do not move: one laser still feeds U × W = 20 at four wavelengths and a 6 dB margin. Where the wavelength term does cost is in chapter 18.

Phase shifters, not the laser, dominate static power. At 10 mW per π a unit holds 0.5 W (1.25 W/mm² of photonics), so the phase shifters alone reach the 500 W cap at U = 1,000. MEMS or non-volatile trimming would remove nearly all of it, at the price of slower settling.

Phase-shifter power vs Uillustrative

Phase shifter:

thermo-optic 10 mW/π: 10 mW per π to hold, 10 µs to settle. Its hold power alone reaches the 500 W cap by U = 1,024.

Hold power of the phase shifters (4 λ) against U, with the chip's power cap. The non-volatile line is zero, drawn at the plot floor.

Data table

Phase-shifter power vs U
units U	thermo 2 mW/π	thermo 10 mW/π	thermo 30 mW/π	mems	nv
4	0.4	2	6	0.0002	1 × 10⁻⁹
16	1.6	8	24	0.0008	1 × 10⁻⁹
64	6.4	32	96	0.0032	1 × 10⁻⁹
256	25.6	128	384	0.0128	1 × 10⁻⁹
1,024	102.4	512	1,536	0.0512	1 × 10⁻⁹
4,096	409.6	2,048	6,144	0.2048	1 × 10⁻⁹

An idle-to-busy step of the stacked logicillustrativetextbook

The vendored temperature map for U = 64 (experiment 14), relative to the TEC-held mean; each unit’s heater phase errors are computed in your browser from it, with the simulator’s heater layout, and match its rms and maximum.

Heat moves phases a little at the default flux, a lot at hot-spot flux. An idle-to-busy step spans 3.192 K across the layer and moves heater phases by up to 0.05947 rad (0.01407 rad rms), which pushes 0 units past the error target. From 2 W/mm² some units fail, and at the top of the swept flux 62.5 % do. A TEC cannot help: it holds the mean temperature, and phases are differences. Each such step costs a recalibration, which is where chapter 16 picks up. Thermal crosstalk between neighbouring heaters leaves 0.03818 rad rms after one ordered calibration sweep and 0.0008615 rad after three.

Idle → busy logic step vs heat fluxillustrative

Data table

Idle → busy logic step vs heat flux
logic heat flux (W/mm²)	rms	max
0.1	0.003411	0.01214
0.25	0.008528	0.03034
0.5	0.01706	0.06068
1	0.03411	0.1214
2	0.06823	0.2427
4	0.1365	0.4854

What would need measured data

Every loss and thermal figure here is illustrative except silicon’s thermo-optic coefficient. A real design would need the coupler, splitter and propagation losses of the actual photonic layer, the laser’s power and wall-plug efficiency, the phase shifters’ hold power and settle time, the stack’s thermal resistance and spreading, and a measured heat map of the logic under the workload.