File:Fermi-Dirac distribution.gif

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Summary

DescriptionFermi-Dirac distribution.gif	English: Varying temperature in Fermi-Dirac distribution for chemical potential 0.55eV
Date	1 July 2024
Source	Own work
Author	Aspir8

This animation is heavily inspired by

and aims to provide a clearer view of the relevant function.

Julia 10.0.4 code

using CairoMakie
using LaTeXStrings

nfermi(ϵ,T)  = 1/(exp((ϵ-μ)*eV/T/kB) + 1)

eV = 1.602176634e−19
kB = 1.380649e−23
μ = 0.55 
ϵ = range(.45,.65, 1000) 

T = Observable(50.)
y = @lift(nfermi.(ϵ,$T))

fig = Figure(size = (800, 400),fontsize=28,linewidth=3,fonts= (; regular = "CMU Serif",bold="CMU Serif"),)
ax = Axis(fig[1, 1], xlabel = L"Energy $\varepsilon$ [eV]",
ylabel = L"$F(\varepsilon)$",
xticks=LinearTicks(5),
yticks=[0,1],)

lines!(ax, ϵ, y, color = :dodgerblue)
band!(ax,ϵ,zero.(ϵ),y,color=(:dodgerblue,0.3))
ylims!(ax,0, 1.5)
xlims!(ax,extrema(ϵ)...)
hidedecorations!(ax,label=false,ticks=false,ticklabels=false)
text!(ax, .53, 1.15, text=@lift(latexstring("\$T = $(round($T,digits=1)) \\,\\text{K}\$")),halign=:center, valign=:center,fontsize=28)
fig

## animation
framerate = 10
t_iterator = exp.(range(log(2),log(375),38))
t_iterator = [t_iterator;reverse(t_iterator)]
record(fig, "nfermi.gif", t_iterator;
        framerate = framerate) do t
    T[]=t
end

Licensing

I, the copyright holder of this work, hereby publish it under the following license:

	This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
	The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. CC0falsefalse

File history

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	Date/Time	Dimensions	User	Comment
current	10:22, 1 July 2024	1,600 × 800 (431 KB)	Aspir8	better labels
	10:14, 1 July 2024	1,600 × 800 (433 KB)	Aspir8	labels more relevant to article
	10:02, 1 July 2024	1,600 × 800 (429 KB)	Aspir8	smaller
	09:52, 1 July 2024	1,600 × 800 (651 KB)	Aspir8	Uploaded own work with UploadWizard