After the system boundary is fixed, the review moves to the physical balance that controls the decision.
A vacuum problem starts with gas load, chamber volume and effective pumping speed. A diffusion-treatment problem starts with temperature, material response and boundary carbon or nitrogen flux.
A plasma-treatment problem starts with ion flux, bias, chemistry and surface temperature. A cathode problem starts with thermal state, gas/plasma coupling and emission drift.
The blocks below keep the same structure: variables to define, records to request, and the decision that can be made from those records.
Vacuum / gas balance
Used when chamber pressure must be checked under pump-down or process gas flow.
dP/dt = Q/V - (Seff/V)·P
P ≈ Q/Seff at steady gas load
| Inputs | V, Q, Seff, conductance, gas species |
| Records | pump-down curve, process-pressure curve, pump data |
| Decision | base-pressure and process-pressure plausibility |
Pressure rise / leak separation
Used when the chamber reaches pressure slowly or cannot hold pressure after isolation.
Qrise = V·dP/dt
Qrise = Qleak + Qoutgassing + Qvirtual
| Inputs | isolated volume, pressure-rise slope, material state |
| Records | pressure-rise curve, helium leak test, bakeout/cleaning history |
| Decision | leak repair, bakeout, cleaning, or geometry correction |
Diffusion treatment
Used for LPC, carburizing and nitriding when the required result is a measured depth/profile, not only a recipe name.
∂C/∂t = ∂/∂x[D(C,T,steel)·∂C/∂x]
-D·∂C/∂x = JC(t)
| Inputs | steel grade, temperature, time, boost/diffusion schedule |
| Records | carbon/nitrogen profile, hardness profile, microstructure |
| Decision | case depth, surface state, recipe transferability |
Thermal balance
Used when controller temperature, load temperature and thermal gradients may differ.
Cth·dT/dt = Pin - Prad - Pcond - Pgas
Prad = εσA(T⁴ - Tw⁴)
| Inputs | heater power, load mass, emissivity, fixture contact, gas state |
| Records | thermal map, ramp/soak logs, TUS/SAT where applicable |
| Decision | thermal uniformity and load-temperature validity |
Plasma surface interaction
Used when activation, nitriding, etching or coating adhesion depends on ion energy, flux and chemistry.
Γi ≈ ni·cs
Eion ≈ e·Vbias
R = f(Γi, Eion, chemistry, T)
| Inputs | pressure, gas composition, bias, current, source geometry |
| Records | bias/current log, witness coupon, profile, roughness |
| Decision | activation, nitriding, etching, adhesion risk |
Cathode emission stability
Used when ignition must be separated from stable operation, restart behaviour and drift.
Ie = f(T, φ, A, surface state)
drift = ΔI/Δt at fixed operating point
| Inputs | temperature, emitter state, gas flow, operating current |
| Records | I-V curve, restart cycles, drift, vacuum/gas log |
| Decision | activation quality and operational stability |