Issue 015 - Semiconductors - Infrastructure scaling
Are AI-chip fabs city-scale infrastructure?
Reuters reported that South Korea's planned Honam semiconductor industrial complex could cost at least 800 trillion won, about $540 billion, and include four planned chip fabrication plants. Analysts said those fabs alone could require 70% to 80% of the current annual electricity use of Gwangju, North Jeolla, and South Jeolla combined.
The problem
Estimate the daily electricity demand and water demand of one large advanced semiconductor fab.
Then scale that to four fabs. Would a four-fab AI-chip hub consume resources more like a large factory, a small city, or a major metropolitan region?
Because Fermi problems target an order of magnitude, I normally use no more than two significant digits and write most calculations in scientific notation; the Fermi reference explains both conventions.
Before checking sources
Matt's first pass
I felt like the problem gave too much information, so I did not have to estimate very much. I tried to approach it from a slightly different angle so I could introduce more guessing.
For water, I assumed an average person might consume 40 gallons daily between showering, bathroom use, cooking, drinking, and other household needs. In a household with 2.5 people, that is about 100 gallons per household per day.
single-fab water use ~= 2.5 x 10^6 gallons/day
household equivalent per fab ~= (2.5 x 10^6 gallons/day) / (100 gallons/household/day)
~= 2.5 x 10^4 households
four-fab water equivalent ~= 4 x 2.5 x 10^4 households
~= 1 x 10^5 householdsFor electricity, I assumed an average house consumes electricity at a rate of about 1.2 kW. Then I assumed a spun-up chip fab consumes power at a rate of about 1 GW. I treated that as equivalent to about 1,000 households, and four fabs as about 4,000 households.
So my first-pass conclusion was that a four-fab hub would consume about the same electricity as a small town and the same water as a large town, approaching the volume of consumption of a small metro area.
Calibration Score
Matt's Calibration Score: 40 / 100
Higher is better: earn points for accurate pegs, sound models, correct math, and a result close to the sourced answer. The image shows percent full of it: 100 minus the Calibration Score.
Pegs: 0/30. The water comparison was good, but the power-unit peg missed the MW-to-GW relationship.
Model: 30/30. Fab power and water scaled cleanly to household equivalents once the units were corrected.
Math: 0/10. The thousandfold power-conversion slip substantially changed the household-equivalent answer.
Result: 10/30. The final conclusion was directionally right, but the electricity result was several orders too small.
Grounding facts
A continuous 1-GW load consumes 24 GWh per day. Four such loads consume 96 GWh per day. That is why grid planning matters: a fab hub is not just a one-time construction project, but a permanent high-reliability utility customer.
Water has a different shape. Ten million gallons/day is about 100,000 households at 100 gallons/household/day. Sixty-six million gallons/day, the Reuters dam-system planning figure, is more like hundreds of thousands of households.
After checking sources
Check and recalibrate
The water structure was good. The electricity comparison had a unit-conversion slip: 1 GW is 1,000 MW, and 1 MW is 1,000 kW, so 1 GW is 1,000,000 kW.
1 GW = 1 x 10^9 W
= 1 x 10^6 kWIf an average household draws about 1.2 kW continuously, then one 1-GW fab is not 1,000 households. It is closer to 800,000 households:
household equivalents per 1-GW fab ~= (1 x 10^6 kW) / (1.2 kW/household)
~= 8.3 x 10^5 households
four 1-GW fabs ~= 4 x 8.3 x 10^5 households
~= 3.3 x 10^6 householdsA useful power range is broad. CSIS describes TSMC Arizona's first phase at roughly 200 MW, with planned expansion potentially above 1 GW. For one large advanced fab, use roughly 200 MW to 1 GW. For four fabs:
four-fab power ~= 4 x (0.2 to 1.0 GW)
~= 0.8 to 4 GW
daily electricity ~= power x 24 hours
~= 19 to 96 GWh/dayThat is a city or metropolitan-region-scale electricity load, not a normal-factory load. The Reuters claim that four fabs could require 70% to 80% of the current annual electricity consumption of Gwangju, North Jeolla, and South Jeolla combined is consistent with that scale.
For water, Matt's 2.5 million gallons/day per fab is in the right range for many 300-mm fab estimates, though some large campuses and advanced fabs can be higher. Use 2.5 to 10 million gallons/day per fab as a rough range:
four-fab water ~= 4 x (2.5 to 10 million gallons/day)
~= 10 to 40 million gallons/dayUsing 100 gallons/household/day or 40 gallons/person/day:
household water equivalent ~= (10 to 40 million gallons/day) / (100 gallons/household/day)
~= 1 x 10^5 to 4 x 10^5 households
person water equivalent ~= (10 to 40 million gallons/day) / (40 gallons/person/day)
~= 2.5 x 10^5 to 1 x 10^6 peopleThe Reuters water-planning figure is even larger: an additional 250,000 metric tons/day is about 66 million gallons/day. If that is used as the broader water-system planning load, it is equivalent to about 660,000 households or 1.7 million people at Matt's residential-use assumptions.
A good Fermi answer is therefore: four advanced fabs could demand roughly 1 to 4 GW of continuous power and 10 to 60+ million gallons/day of water infrastructure, depending on scope and recycling. That is much more like adding a city or major metropolitan utility load than adding a normal factory.
Post-check reflection
Matt's reflection
I really blew it on the electricity. For some reason I continued my calculations assuming 1,000 kW per GW, and I missed the MWs. That put me off by several orders of magnitude for the electricity calculation.
I knew the fab plants would be on the order of a city, but it was still shockingly high. This question really helped establish the appropriate perspective: these plants are using the equivalent of hundreds of thousands of households worth of electricity and water, maybe on the order of millions of people.
That is a really big deal, and clearly something that will require careful consideration and planning.
Recommended memory peg
Remember 1 GW = 1,000 MW = 1,000,000 kW, and 1 GW continuous = 24 GWh/day. For large fabs, use a rough peg of hundreds of MW to about 1 GW and millions of gallons of water per day.
Reader results
Bars show how submitted estimates sort into the answer choices from the gut-check prompt.