Technical Explanation
Why This Tool?
Semiconductor equipment (PVD, Etch, ALD, etc.) chamber pumpdown curves are often assumed to follow simple exponential decay. In reality, pump speed varies with pressure, conductance limits effective speed, and gas loads (leak, permeation, outgassing) create tails and floor pressure. This predictor uses a physics-based ODE model to simulate pumpdown with pump curve, conductance, and time-varying gas load, helping engineers understand why base pressure won't drop or why tails appear.
Physics Model
The governing equation is:
V · dP/dt = −S_eff(P) · P + Q_total(t)
where V is chamber volume, P is pressure (Torr), S_eff is effective pumping speed (L/s), and Q_total is total gas load (Torr·L/s). Effective speed combines pump and conductance in series:
1/S_eff = 1/S_pump(P) + 1/C
S_pump(P) is interpolated from the pump curve in log(P) space. Q_total = Q_leak + Q_perm + Q_out(t), with outgassing modeled as a two-component exponential decay (fast + slow).
Gas Load Components
- Leak (Q_leak) — Constant gas inleak. Dominates at base pressure; limits how low P can go.
- Permeation / Virtual leak — Trapped gas or permeation through seals. Often modeled as constant.
- Outgassing — Q_out(t) = Q0_fast·e^(-t/τf) + Q0_slow·e^(-t/τs). Fast: adsorbed gas (e.g. water). Slow: polymers, residual films, recontamination; creates pumpdown tail.
Throughput Balance
At steady state, S_eff·P = Q_total. The throughput balance chart plots S_eff·P (pumping term) vs Q_total (gas load). When these curves approach each other, pressure stops dropping quickly and the tail begins. The intersection indicates when gas load matches pumping capacity.
Numerical Method
The ODE has no closed-form solution for arbitrary S_pump(P) and Q_out(t). We use the RK4 (4th-order Runge–Kutta) method for numerical integration. Pressure is clamped to a minimum (e.g. 1e-12 Torr) to avoid negative values.
References & Disclaimer
Pump presets are illustrative. Use actual pump curves for accurate predictions. For critical applications, validate against real pumpdown data.