High-Vacuum, Semiconductor Tooling & Particle Accelerator Engineering, UHV Wall Outgassing
UHV Chamber Outgassing Load & Ultimate Base Pressure Formula
Calculate Power-Law Wall Outgassing Gas Load Q(t) (10⁻⁶ mbar·L/s), Ultimate Chamber Base Pressure P_base (10⁻⁹ mbar), Area-Specific Pumping Speed (L/s·m²), and UHV Target Ratio.
Below 10⁻⁴ mbar, chamber volume stops mattering—adsorbed water monolayers desorbing off stainless-steel walls set your ultimate vacuum floor!
Once roughing and turbomolecular pumps evacuate bulk air out of a `304L/316L` stainless-steel **High-Vacuum (`HV`) / Ultra-High-Vacuum (`UHV`)** chamber (`Internal Surface Area A` cm², `Conductance-Throttled Effective Pumping Speed S_{eff}` L/s), pressure stalls along a `1/t` plateau governed by **Thermal Desorption Outgassing** of `50–100` monolayers of adsorbed water vapor (`H_2O` binding energy `~0.8–1.0` eV)! Unbaked stainless steel exhibits a **1-Hour Specific Outgassing Rate `q_1 ~= 3.0 x 10⁻⁹` mbar·L/(s·cm²)** (`30 x 10⁻¹⁰` units) decaying hyperbolically with pumpdown hours `t` as **`q(t) = q_1 / t^alpha`** (`alpha ~= 1.0` for water desorption), creating **Total Outgassing Load `Q(t) = q(t) * A`** (`mbar·L/s`) and clamping **Ultimate Base Pressure at `P_{base} = Q(t) / S_{eff}`** (`mbar`)—which only a `150–250°C` **UHV Bakeout** (`75x–1,000x` drop in `q_1` down to dissolved `H_2` diffusion!) can break through!
Start on an Unbaked `4.50` m² (`45,000` cm²) MBE / Synchrotron Beamline Vessel—1-Hour_Outgassing_Rate `q_1` = 32.0 x 10⁻¹⁰ mbar·L/(s·cm²) (B2), Internal_Wall_Area `A` = 45,000 cm² (B3), Pumpdown_Time `t` = 10.0 h (B4), Desorption_Decay_Exponent `alpha` = 1.00 (B5), and Throttled_Effective_Speed `S_{eff}` = 420 L/s (B6). Ask the in-app assistant for a gas-throughput balance hint (`Q = P * S`): Total Outgassing Load equals `14.400 x 10⁻⁶` mbar·L/s (E2), Ultimate Base Pressure stalls at `34.286 x 10⁻⁹` mbar (`3.43 x 10⁻⁸` mbar, E3), Area-Specific Pumping Speed equals `93.33` L/(s·m²) (E4), sitting **`685.71x`** above a `0.05 x 10⁻⁹` mbar (`5 x 10⁻¹¹` mbar) UHV target (E5)!
| UHV Outgassing Balance KPI (A=45,000 cm², t=10 h, S_eff=420 L/s) | Formula | Verified Output |
|---|---|---|
| Wall Gas Load Q (10⁻⁶ mbar·L/s) | ((q1_1e10 * 1e-10 * Area_cm2) / (t^alpha)) * 1e6 | 14.400 (0.189 after 200°C bakeout!) |
| Ultimate Base Pressure (10⁻⁹ mbar) | (Gas_Load_mbar_L_s / Seff_L_s) * 1e9 | 34.286 nbar? 3.43e-8 mbar (0.450e-9 baked!) |
| Area-Specific Speed (L/(s·m²)) | Seff_L_s / (Wall_Area_cm2 / 10000) | 93.33 L/(s·m²) |
| Multiple of 5x10⁻¹¹ mbar UHV Gate | Base_Pressure_1e9_mbar / 0.05 | 685.71x unbaked (9.00x baked) |
Dayton Power-Law Water Desorption Outgassing & Throughput Base-Pressure Formula
Validate `1h_Outgassing q_1 > 0` (`x 10⁻¹⁰` mbar·L/s·cm²), `Wall_Area A >= 100` cm², `Pumpdown_Time t >= 0.1` h, `Decay_Exponent alpha` in `[0.3, 1.5]`, and `Effective_Pumping_Speed S_{eff} > 1` L/s!
=LET(q1_u, B2, aw_c, B3, tp_h, B4, al_p, B5, se_l, B6, qt_m, ((q1_u * 0.0000000001) * aw_c) / (tp_h ^ al_p), pb_9, (qt_m / se_l) * 1000000000, IF(OR(q1_u <= 0, aw_c < 100, tp_h < 0.1, al_p < 0.3, al_p > 1.5, se_l <= 1), "Invalid Outgas Input", ROUND(pb_9 / 0.05, 2)))48-Hour 200°C Bakeout Water-Stripping Gain Check (Set q1 B2 = 0.42 x 10⁻¹⁰)
Wrap heating jackets around the chamber for a `200°C` bakeout so adsorbed `H_2O` desorbs and `q_1` drops `76x` to `B2 = 0.42` (`4.2 x 10⁻¹¹` mbar·L/s·cm²): Gas Load E2 plummets to `0.189 x 10⁻⁶` mbar·L/s and Base Pressure E3 plunges into true UHV at **`0.450 x 10⁻⁹` mbar** (`4.5 x 10⁻¹⁰` mbar, E5 = `9.00x`)—ready for Ti-sublimation / NEG getter firing!
=IF(ISTEXT(E5), E5, LET(qt_m, ((B2 * 0.0000000001) * B3) / (B4 ^ B5), ROUND((qt_m / B6) * 1000000000, 3)))Try the example
Use the original values or change them to test your understanding.