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bmulyanto1-Visitor
1-Visitor
January 14, 2019
Solved

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

  • January 14, 2019
  • 2 replies
  • 3884 views

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.

image.png

 

The formula to compute:

image.png

Best answer by LucMeekes

And YES, there are ways to speed it up.

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

LM_20190115_Speed14.png

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

LM_20190115_Speed15.png

Down from 203 to 92 seconds.

 

Success!
Luc

2 replies

T
terryhendicott21-Topaz II
21-Topaz II
January 14, 2019

Hi,

 

You need to be very patient for a result

Capture2.JPG

 

T
terryhendicott21-Topaz II
21-Topaz II
January 14, 2019

Hi

 

Capture.JPG

B
bmulyanto1-VisitorAuthor
1-Visitor
January 15, 2019

@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.

 

L
LucMeekes23-Emerald IV
23-Emerald IV
January 14, 2019

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

LM_20190114_Resistivity.png

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.

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