I am interested in any mathematical formula connecting viscosity of the solvent and thickness.
Take a look at the following papers:
Rheology and modeling of the spin coating process
Washo
IBM Journal of Research and Development, 1977, 21, 190-198
A mathematical model for spin coating of polymer resists
Flack et al.
Journal of Applied Physics, 1984, 56, 1199-1206
DOI: 10.1063/1.334049
A model for drying control cosolvent selection for spin-coating uniformity - the thin film limit
Birnie
Langmuir, 2013, 29, 9072-9078
DOI: 10.1021/la401106z
It can depend strongly on what type of system you are spin coating, but a good first-order approach is given in Eq. 1 in the publication: Vorotilov et al. J. Sol-Gel Sci. and Tech. 5, 173-183 (1995)
Publisher link: http://link.springer.com/article/10.1007%2FBF00487014
I cut the film to obtain the abrupt interface and use a-step to measure thickness.
Take a look at the following papers:
Rheology and modeling of the spin coating process
Washo
IBM Journal of Research and Development, 1977, 21, 190-198
A mathematical model for spin coating of polymer resists
Flack et al.
Journal of Applied Physics, 1984, 56, 1199-1206
DOI: 10.1063/1.334049
A model for drying control cosolvent selection for spin-coating uniformity - the thin film limit
Birnie
Langmuir, 2013, 29, 9072-9078
DOI: 10.1021/la401106z
The ellipsometry is giving you mathematical fits. Many times you can find many models with quite different thicknesses. Therefore you should be carefull when use elippsometry by limiting the numbers of parameters to be fitted and try to help the fit by giving as many exact info you are about the sample.
I have a similiar question (if not the same) and would like to refresh the topic, as I do not see any satisfying answer.
I have spin-casted PMMA layers on glass coverslips (from acetone). I do not have any acces to AFM or other equipment that would allow me to measure the layers thicknes. Is it possible to estimate the thickness of the obtained layer anyhow without measuring it? I know the molecular weight of the polymer, the concentration of PMMA in the acetone solution and the rotation speed during the process.
I've tried to find any paper with similar conditions but no one uses PMMA in acetone, most of them use toluen, or other siolvents, and as far as I know this is quite important for the calculation ;-).
Thank you in advance for any help.
I do not want to measure the thickness, as I do not have any access to any of the said devices. I would like to calculate it, from the known parameters - it does not have to be precise. Orders of magnitude would be enough.
A simple theory predicts the following relationship between the thickness of the spun film,d,the viscosity coefficient of the solution,η,its density, ρ,the angular velocity of the spinning,ω,and the spinning time,
d=[η/4πρω^2]^0.5 t^-0.5
See the same question in
https://www.researchgate.net/post/How_to_determine_a_thickness_of_a_spin_coated_polymer_film?
If you do not have access to experimental techniques like ellipsometry, spectrophotometry, profilometry etc. you can estimate approximately the thickness of your film by visual inspection of its color. Purposely you should know film refractive index. Use the following link to generate a color chart depending on the type of film and used substrate
http://www.raacke.de/index.html?airy.html
You can use nanoindentation techniques. From substrate effect, you can estimate the film thickness.
For more information go to below link.
http://www.sciencedirect.com/science/article/pii/S0032386116301227
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Semiconductor