File:Fermi-Dirac distribution.gif

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