Calculations

How to Calculate Vacuum, Yield, and Alignment for Fab Equipment

Step by step math for the four calculations that matter most in fab equipment builds, from rate of rise leak testing to precision alignment time.

Building semiconductor fab equipment means proving a chamber holds vacuum, a machined body passes yield, and an assembly aligns to microns before it ships. Four calculations carry most of that load: rate of rise leak testing, rolled throughput yield on machined parts, bakeout energy, and precision alignment time. Each pulls inputs straight from shop travelers, vacuum gauges, and CNC run sheets. Below, every formula is worked with real units so an operator can reproduce it. Tools like the Vacuum Chamber Leak Rate and Chamber Machining Yield calculators automate these, but you should know the arithmetic behind the number.

Rate of rise measures leak conductance without helium. Isolate the pumped chamber, then record pressure climb over a fixed interval. The throughput leak rate Q equals chamber volume V times pressure change dP divided by elapsed time dt. Take V = 200 L, a rise from 1e-6 to 5e-6 Torr across 60 s. Q = 200 times (4e-6) divided by 60 = 1.33e-5 Torr L/s. That is your gross leak plus outgassing combined, so run a blanked baseline first and subtract it. The Vacuum Chamber Leak Rate calculator handles the subtraction and the unit math.

To compare against a UHV specification, convert Torr L/s to atmospheric cc per second. Since 1 atm equals 760 Torr, 1 atm cc/s equals 0.76 Torr L/s, so divide: 1.33e-5 divided by 0.76 = 1.75e-5 atm cc/s. That sits far above a typical helium leak spec of 1e-9 std cc/s, which tells you outgassing dominates and the joint is likely sound. A real leak shows a linear, unbounded rise, while outgassing curves and flattens as surfaces deplete. Plotting three or four dP points separates the two before you spend any helium on a mass spectrometer test.

Chamber machining yield across a multi step routing is a rolled throughput yield, the product of each operation's first pass yield, not an average. A body with 12 operations each running 99.2% gives 0.992^12 = 0.908, so 91% roll through clean even though every step looks excellent. Drop one operation to 96% and the roll falls to 0.879. Feed the per operation yields from your inspection log into the Chamber Machining Yield calculator to see which step caps the line. The lesson: long routings punish small defect rates, so attack the deepest bore and the sealing face first.

Bakeout energy has a sensible heat term plus a loss term. Sensible energy Q equals mass times specific heat times temperature rise. A 150 kg 316L chamber at Cp = 0.5 kJ per kg per K heated from 20 to 150 C needs 150 times 0.5 times 130 = 9,750 kJ, about 2.7 kWh. That is trivial next to the hold. If radiation and convection losses run 2 kW across a 24 hour bake, that is 48 kWh, so roughly 51 kWh total. At 0.12 dollars per kWh the run costs about 6 dollars in energy. The Bakeout Energy Cost calculator adds insulation and duty factors.

Precision alignment time scales with degrees of freedom and iteration count. Model it as axes times a coarse set plus iterations times a fine adjust. Six DOF at 4 min coarse each, then 3 closed loop iterations at 2 min per axis, gives 6 times (4 plus 3 times 2) = 60 min per tool. Add metrology settling of 5 min per read and the figure climbs fast. The Precision Alignment Time calculator lets you test whether tightening from 3 to 2 iterations, by improving fixture repeatability, saves the 12 minutes it predicts before you commit to new hardware.

Two more calculations round out the set. Metrology bottleneck load is demand hours divided by available hours; a CMM asked for 34 hours against 40 available runs at 85% utilization, near the queue explosion point. Test stand capacity is available hours divided by cycle time, so a stand with 6.5 productive hours per shift and a 26 minute cycle clears 15 units. Particle control risk weights exposed part time by air cleanliness class. Run these with the Metrology Bottleneck, Test Stand Capacity, and Particle Control Risk calculators to size a line before you commit floor space.

Published 2026-07-02.