Definite 4D integral evaluation (Fuchs-Sondheimer Resistivity model for Nanowires)

[bmulyanto]

Hello, 

I really appreciate it if someone can help me to double check the following equation by running my sheet in their Mathcad. I attached my sheet.

This time, I use different formula from my previous post here.

In the mean time, I am writing matlab code to double check as well.

I run my sheet, it took so much time with my pc and at the end it show error.

The formula to compute:

[terryhendicott]

Hi,

You need to be very patient for a result

[terryhendicott]

Hi

[bmulyanto]

@terryhendicott
hi...thank you.
could you run it once again from w: 20-70 nm?
The motivation is to see the w around lambda and thickness h.

I tried in my pc from w: 25 - 50 nm. it still takes long time.
is there tips to speed up the calculation? 

I use ORIGIN=0,  TOL=10^-3, CTOL=10^-3

@LucMeekes
Hi..yes, the integral notation confused me.
But after reading the very original paper, which use such a notation, nested integration is my conclusion.
In your sheet, your third term uses +, it should be -.
You might got that from the paper, which shows double minus sign.
Thank again for your help.

[terryhendicott]

Hi,

Cheers Terry

[LucMeekes]

The third term is negative, due to the -6 that it starts with. If used the expression continuation (continues the expression from the previous line). In Mathcad that is only possible with an addition, so I just add a negative expression...

Luc

[LucMeekes · Accepted solution]

And YES, there are ways to speed it up.

This is the time to calculate 6 points on my pc:

If you notice that the integrand function to dTheta is symmetric around pi/2, we can omit half of the integration:

Down from 203 to 92 seconds.

Success!
Luc

[bmulyanto]

deleted

[LucMeekes]

Assuming that weird integral notation actually is intended to mean the nested integrals below:...

Success!

Luc

P.S. It also means that the expression in your other thread was actually meant to be a nested integral, rather than a product of integration results. That other expression easily runs into overflows when trying to (numerically) integrate. No symbolic solution was found.