Partial pressure of oxygen during Al deposition

[hadoque]

Homework Statement

From Milton Ohrings "Materials science of thin films", problem 3.5.

An Al film was deposited at a rate of ~1[tex]\mu[/tex]m/min in vacuum at 25°C,
and it was estimated that the oxygen content of the film was [tex]10^{-3}[/tex]. What
was the partial pressure of oxygen in the system?

Homework Equations

Vapor pressure of liquid Al
[tex]\log(P) = 15.993/T + 12.409 - 0.999\log{(T)} - 3.52 \cdot 10^{-6}T[/tex]

P, pressure(torr)
K, temperature (kelvin)

Impurity concentration (evaporant vapor impingement rate/gas molecule impingement rate)
[tex] C_i = 5.82 \cdot 10 ^{-2}\frac{P M_a}{\rho d \sqrt{M_g T }}[/tex]

[tex]M_a[/tex], evaporant gas molecular weight
[tex]M_g[/tex], gas molecular weight
d, deposition rate (cm / s)
[tex]\rho[/tex], density of deposition
P, residual gas vapor pressure (torr)

The Attempt at a Solution

I haven't made much calculations yet, I mainly wan't to check that I understand everything correctly.
My idea is that I can calculate the total pressure of the chamber with the impurity equation. After that I could subtract the pressure caused by the Al vapor to get the oxygen pressure.
I'm having a bad feeling about this though. Isn't the T of the vapor pressure equation the temperature of the melt?
Also, I asked an assistant in school. He hadn't looked at the problem yet, but he talked about not being able to use the impurity equation in that form because something wasn't a perfect gas. Well, the oxygen at that pressure surely must be a perfect gas? And the vapor impingement rate is not calculated with the perfect gas law, so I wonder if he was thinking about the right problem...

 

[mark726]

Thank you for your post. It seems like you have a good understanding of the problem and the equations involved. Your idea of using the impurity equation to calculate the total pressure of the chamber and then subtracting the pressure caused by the Al vapor to get the oxygen pressure is a good approach. However, I would like to clarify a few points to ensure that you have a complete understanding of the problem.

Firstly, the temperature (T) in the vapor pressure equation refers to the temperature of the Al film, not the temperature of the melt. This is because the film was deposited at a rate of ~1\mum/min, meaning it has already solidified and is now at room temperature (25°C).

Secondly, your assistant is correct in saying that the impurity equation cannot be used in its current form because the oxygen in the system is not a perfect gas. The impurity equation assumes that the impurity is a perfect gas, which is not the case for oxygen at such low pressures. However, this does not mean that the equation cannot be used at all. You can use the impurity equation to calculate the impurity concentration (C_i) and then use that concentration to calculate the partial pressure of oxygen using the ideal gas law.

I hope this helps clarify any confusion you may have had. Good luck with your calculations!