In a vapor-assisted process, a solution-coated precursor film is converted by a vapor inside a low-pressure chamber. How the vapor reaches the film depends on the mean free path of gas molecules compared with the chamber dimensions. This guide explains the mean free path, the Knudsen number and flow regimes, pump-down time, and why ultimate pressure is not the same as operating pressure.
In one paragraph: Mean free path is inversely proportional to pressure at fixed temperature and, in the hard-sphere model, proportional to temperature and inversely proportional to molecular collision cross-section [4]. Comparing it with a characteristic chamber dimension gives the Knudsen number: viscous flow is typically associated with Kn < 0.01 and molecular flow with Kn > 1 [4]. For nitrogen in a 10 mm gap, the illustrative calculation gives viscous flow at 100 Pa and molecular flow at 0.1 Pa. Outgassing can become important during pump-down, depending on the chamber and its condition. Ultimate pressure is not a validated operating pressure for a vapor process [4].
1. What Vapor-Assisted Film Conversion Is
Some thin films are made in two steps: a precursor layer is first deposited from solution, and it is then converted by exposing it to a vapor. Because the second step takes place in the gas phase, the pressure, temperature and geometry of the chamber in which it happens decide how vapor molecules reach the film. This guide is not a recipe for any particular chemistry.
The published literature gives examples of this class of process:
- Vapor-assisted solution process (VASP) for perovskites. Chen and co-workers demonstrated a low-temperature vapor-assisted solution process to make polycrystalline perovskite films with full surface coverage, small surface roughness and grain size up to the microscale [1]. Li and co-workers later described a low-pressure vapor-assisted solution process in which a spin-coated lead iodide layer containing an additive reacted with an organic ammonium halide vapor in a low-pressure heating oven [2].
- Vapor priming of substrates. In photolithography, the adhesion promoter HMDS is transported as a vapor in a bubbler by dry nitrogen to a substrate heated to 75–120 °C, where it bonds chemically as a monolayer; spun-on liquid HMDS, by contrast, is bound only physically and can release ammonia that affects the resist [3].
These are published examples of the technology class, cited to illustrate why vapor transport matters. They are not described here as uses of any particular instrument. Solution-based perovskite film formation is covered in Perovskite Film Fabrication: Spin Coating, Antisolvent Timing and Annealing.
2. Mean Free Path: Pressure, Temperature and Molecular Size
The mean free path λ is the average distance a molecule travels between collisions with other molecules [4]. In the hard-sphere approximation it is:
λ = kBT / (√2 π d2 p)
where kB is the Boltzmann constant, T the absolute temperature, d the molecular diameter and p the pressure [4].
For practical work, the product λ·p at room temperature is tabulated for common gases. For nitrogen it is 6.4 × 10−3 m·Pa; for comparison, the same lecture gives 7 × 10−3 for argon, 12 × 10−3 for hydrogen, 19 × 10−3 for helium and 4 × 10−3 for carbon dioxide, all in m·Pa [4]. Dividing by the pressure gives the mean free path:
| Pressure (Pa) | Approximate equivalent | Mean free path of N2 at room temperature |
|---|---|---|
| 101,325 | Atmospheric pressure | About 63 nm |
| 1,000 | 10 mbar | 6.4 µm |
| 100 | 1 mbar | 64 µm |
| 10 | 0.1 mbar | 0.64 mm |
| 1 | 0.01 mbar | 6.4 mm |
| 0.1 | 0.001 mbar | 64 mm |
Calculated as λ = (6.4 × 10−3 m·Pa) / p, from the value tabulated by Vandoni [4].
Temperature. Because λ is proportional to T at fixed pressure, heating the gas from 20 °C (293 K) to 100 °C (373 K) lengthens the mean free path by a factor of 373/293, about 1.27, if the pressure stays the same. A tenfold change of pressure has a far larger effect.
Molecular size. Larger molecules have larger collision cross-sections and shorter mean free paths at the same pressure and temperature [4]. A precursor vapor will not have the same mean free path as nitrogen, so read the table as orders of magnitude for the background gas.
3. Knudsen Number and Flow Regimes
The mean free path matters only in comparison with the size of the space the gas moves through. That comparison is the Knudsen number:
Kn = λ / D
where D is a characteristic dimension, for example the gap between a vapor source and the substrate or the diameter of a tube. The flow regimes are [4]:
| Regime | Condition | What it means |
|---|---|---|
| Viscous (continuum) flow | Kn < 0.01 (λ < D/100) | Molecules collide mostly with each other; gas moves as a fluid, and vapor reaches the surface by diffusion and flow |
| Transitional flow | 0.01 < Kn < 1 | Collisions with other molecules and with walls both matter |
| Free molecular flow | Kn > 1 (λ > D) | Molecules travel from wall to wall with few collisions in between; line of sight and geometry dominate |
Regime limits as given by Vandoni [4].
For nitrogen at room temperature, the same source gives the practical rule that flow is molecular when the product p·D is below 0.064 mbar·mm and viscous when it is above 6.4 mbar·mm [4].
Worked example: a 10 mm gap
Take a gap of D = 10 mm between a vapor source and a substrate, filled with nitrogen at room temperature:
| Pressure (Pa) | λ (N2) | Kn = λ/10 mm | Regime |
|---|---|---|---|
| 1,000 | 6.4 µm | 6.4 × 10−4 | Viscous |
| 100 | 64 µm | 6.4 × 10−3 | Viscous |
| 10 | 0.64 mm | 0.064 | Transitional |
| 1 | 6.4 mm | 0.64 | Transitional |
| 0.1 | 64 mm | 6.4 | Molecular |
Illustrative calculation from the tabulated λ·p value and regime limits [4].
The regime is set by pressure and geometry together: halving the gap doubles Kn, just as halving the pressure does.
Transport, flow and surface reaction
In a vapor conversion step, vapor leaves the source, travels to the film and reacts with or diffuses into it; the slowest of these steps sets the overall rate. In the viscous regime, vapor arrives by diffusion through the background gas and by any flow, so background pressure and gas flow affect how quickly and how uniformly it arrives. In the molecular regime, molecules travel in straight lines, so arrival depends on the source temperature, the substrate’s view of the source and the spacing. If the surface reaction is slower than arrival, the film chemistry sets the rate. Which step limits a given process has to be established experimentally.
4. Pump-Down, Outgassing and Ultimate vs Operating Pressure
Pump-down time
For an idealized chamber with constant effective pumping speed S and negligible leaks and outgassing, pressure falls exponentially. The time to go from p0 to p is [4]:
t = (V/S) ln(p0/p)
Vandoni’s idealized example uses a 50 L volume and an effective pumping speed of 1 L/s, giving a time constant V/S of 50 s. Each decade of pressure takes about 115 s, so the idealized time from 1000 mbar to 1 mbar is about 345 s [4]. Actual pump-down time can be longer because of conductance restrictions, leaks, outgassing and changes in effective pumping speed.
Ultimate pressure is not operating pressure
In Vandoni’s treatment, below about 1 Pa the pressure curve departs from the simple exponential because gas released from the chamber walls (outgassing) can no longer be neglected [4]. Where this happens in a given system depends on the chamber and its condition. When the pressure stops falling on the time scale of observation, it is set by the balance between the total gas load Q and the pumping speed: pultimate = Q/S [4]. This has two consequences for a vapor process:
- The ultimate pressure of a system describes the empty, pumped chamber. As soon as a vapor source is heated or a gas flow is admitted, that source adds to Q, and the pressure rises to a new balance.
- The operating pressure of a process is therefore a process parameter, set by vapor generation, gas flow and pumping together. It has to be measured and validated for each process; a low ultimate pressure shows that the chamber can be pumped well, not that a particular process will run at that pressure.
5. What to Record for a Vapor Conversion Step
| Parameter | Why it matters |
|---|---|
| Base (ultimate) pressure before the process | Shows chamber condition and leaks or outgassing [4] |
| Operating pressure during the process | Sets mean free path and Knudsen number [4] |
| Gas type and flow rate | Background gas changes λ and transport [4] |
| Source and substrate temperatures | Control vapor generation and surface reaction; λ scales with T |
| Source-to-substrate spacing and geometry | Defines D in the Knudsen number |
| Pump-down and process times | Exposure history of the film |
| Vapor source mass or amount before and after | Indicates how much vapor was generated |
| Film checks after conversion | Thickness, appearance, structure; see the measurement guide |
A minimum record for a vapor conversion step; general practice.
Thickness measurement methods are compared in How to Measure Thin Film Thickness: Profilometry, Ellipsometry and Interference. Substrate preparation before the precursor coat is covered in Substrate Cleaning Protocol for Thin-Film Devices: Solvents, UV-Ozone, Plasma and Queue Time, and thermal treatment in an inert atmosphere in Annealing Under Nitrogen: Inert Hot Plates for Air-Sensitive Films.
6. Levon™ VCD Vapor Deposition System: Specifications
The Levon™ VCD is a compact vapor deposition system with an ultimate pressure below 0.5 Pa, a 6 mm substrate chamber height, a vacuum pump and a flow meter. Heating is customizable, and the final configuration is confirmed on quotation. These specifications describe the hardware; they do not establish compatibility with a particular vapor chemistry or qualify the system for a specific film-conversion process. Confirm the intended process, vapor source, gas and chemical compatibility, operating conditions and required controls with us.
| Specification | VCD |
|---|---|
| Maximum substrate | 150 × 150 mm (other sizes available on request) |
| Substrate chamber height | 6 mm |
| Heating | Customizable |
| Vacuum pump | 90 m3/h; pump-down from atmosphere to 1 Pa in 12 s; test conditions not specified |
| Ultimate pressure | <0.5 Pa |
| Vacuum gauge | Pirani gauge |
| Flow meter | Side-mounted, 0.1–1 L/min |
| Operating pressure for a given process | — |
| Display | 7-inch touchscreen |
| Dimensions (W × D × H) | 300 × 372 × 300 mm; 15 kg |
Source: ACS Material product specifications (October 2026). The supplied configuration is confirmed in the quotation. A dash means the specification is not listed.
How this connects to the guide: the specified values illustrate some quantities discussed in Sections 2–4. The 6 mm chamber height is a possible geometric length scale, but the appropriate dimension D for the Knudsen number depends on the actual flow path and process geometry. The specified ultimate pressure does not establish operating pressure, and the flow meter range does not identify a supported gas or vapor chemistry. Details of the Levon™ VCD Vapor Deposition System can be discussed through the contact form.
7. Keep Exploring the Thin-Film Processing Knowledge Hub
Related guides
- Substrate Cleaning Protocol for Thin-Film Devices: Solvents, UV-Ozone, Plasma and Queue Time — preparing the substrate before the precursor coat
- Annealing Under Nitrogen: Inert Hot Plates for Air-Sensitive Films — thermal treatment under nitrogen
- PECVD: Low-Temperature Thin-Film Deposition — another low-pressure thin-film process
- Perovskite Film Fabrication: Spin Coating, Antisolvent Timing and Annealing — solution-based perovskite film formation
- How to Measure Thin Film Thickness: Profilometry, Ellipsometry and Interference — measuring film thickness before and after conversion
Equipment
- Levon™ VCD Vapor Deposition System — ultimate pressure below 0.5 Pa; 6 mm substrate chamber height
Questions about a specific instrument can be sent through the contact form.
8. FAQ
What is a vapor assisted solution process?
A two-step method in which a solution-coated precursor film is converted by exposure to a vapor; for perovskites it was demonstrated by Chen and co-workers [1] and later in a low-pressure oven by Li and co-workers [2].
What is the mean free path of nitrogen at 1 Pa?
About 6.4 mm at room temperature, from λ·p = 6.4 × 10−3 m·Pa [4].
What is the Knudsen number?
The mean free path divided by a characteristic dimension: below 0.01 the flow is viscous, between 0.01 and 1 transitional, above 1 molecular [4].
Does temperature change the mean free path?
Yes. At fixed pressure it is proportional to absolute temperature, so 20 to 100 °C lengthens it by about 27% [4].
Why does the pressure stop falling during pump-down?
Outgassing; when the pressure stops falling it is set by gas load divided by pumping speed, Q/S [4].
Is ultimate pressure the pressure a process runs at?
No. It describes the empty, pumped chamber; vapor and gas flow add load, so operating pressure must be measured for each process [4].