Tong Predictions for w310

This is re-do of a post I made before the new year regarding the predictions of the ‘Tong equation’ for wafer 310 (I deleted the earlier post because I came to the wrong conclusion). I wrote MATLAB files to calculate the predictions of the Tong equation from porosity, pore diameter, pressure and membrane thickness. Also, because the equation predicts a flow per pore, I wrote a second m-file to predict the flow through any calibrated TEM image that has been processed through Mike B’s processing program. Mike’s program creates a ‘results’ file which can be read by my m-file to calculate flow or hydraulic permeability assuming the Tong equation applies. I’ll repost the m-files on the software pages with the date January 8th, 2008 to distinguish them from a buggy version I had up last week.

For wafer 310:

If one plugs in the mean pore diameter (23 nm), and mean porosity (1.8%), thickness (15 nm), pressure (3.3 PSI), the Tong equation produces 442 ul/(min-cm2-PSI). This is effectively a calculation assuming all pores are 23 nm.

If one calculates the flow, pore-by-pore using the histogram (with the second program I wrote) the answer comes back 700 ul/(min-cm2-PSI). I’ve double checked this now after missing a calibration factor in my earlier version of the code. Still, if someone can check my code for accuracy, that would be great.

With the new calculations of permeability in the EQ format, we measured around 310 ul/(min-cm2-PSI) for w310 for an outer membrane (like the image). I think the theory – which is much older than Tong’s paper (I’ll explain later) – is pretty solid. Still I’m not surprised by some disparity difference with this untested theory. We’ll try Shigeru’s treatment with UV/ozone and isopropanol to see if air or wetting issues are getting in our way of higher numbers.

Here is the image of w310 that I used.

Here is the pore distribution I found with Mike’s program.

Here is the way individual pores in the image contribute to the overall porosity (according to Tong). Notice how little small pores contribute compared to large pores. The Tong equation predicts that permeability depends very strongly on pore size.