Skip to main content
P
payman1-Visitor
1-Visitor
December 4, 2017
Solved

Fermi integral (01)

  • December 4, 2017
  • 1 reply
  • 4892 views

Hello All,

I am trying to calculate the Fermi integral of the order of 1/2 and its derivative. In the attached worksheet, the integral cannot be evaluated for x>0. I used an approximated model as is given in the following article but the result is not similar to what the article obtained.

Koroleva, Olga & V Mazhukin, A & Mazhukin, Vladimir & Breslavskiy, Pavel. (2016). APPROXIMATION OF FERMI-DIRAC INTEGRALS OF DIFFERENT ORDERS USED TO DETERMINE THE THERMAL PROPERTIES OF METALS AND SEMICONDUCTORS. MATHEMATICA MONTISNIGRI. 36. 37-53.  

 

Could you please help me with this problem. 

Thank you very much in advance.

Payman

Best answer by Werner_E

To get single values you may consider using symbolic evaluation with "float"

Bild1.png

For numeric approximation (for plotting) you may also use the same integral with a rather high upper value (not sure in which range this would be an acceptable approximation)

Bild2.png

And to make your plot to math the one you try to duplicate you will have to

  • not use the secondary y-axis (otherwise you will have different y scales)
  • set the plot-limits manually
  • notice, that the plot in the article uses a logarithmic y-scale

Bild3.png

 

 

 

1 reply

W
Werner_E25-Diamond IAnswer
25-Diamond I
December 4, 2017

To get single values you may consider using symbolic evaluation with "float"

Bild1.png

For numeric approximation (for plotting) you may also use the same integral with a rather high upper value (not sure in which range this would be an acceptable approximation)

Bild2.png

And to make your plot to math the one you try to duplicate you will have to

  • not use the secondary y-axis (otherwise you will have different y scales)
  • set the plot-limits manually
  • notice, that the plot in the article uses a logarithmic y-scale

Bild3.png

 

 

 

    W
    Werner_E25-Diamond I
    25-Diamond I
    December 4, 2017

    This is the second time I noticed it - I am not offered the option to edit my post in the 3 dots menu. Anybody else having the same problem?

     

    Just wanted to add, that you don't need to define eta as a vector and create the vectors for FF, etc.. A simple range is all thats neeed and if you are happy with the default range from -10 to 10 of the quickplot feature, you may also omit the range defintion altogether.

    Bild4.png

     

      Terms & ConditionsCookie settingsAccessibility statement