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| author | Ian Jauslin <jauslin@ias.edu> | 2019-05-22 22:59:03 -0400 |
|---|---|---|
| committer | Ian Jauslin <jauslin@ias.edu> | 2019-05-22 22:59:03 -0400 |
| commit | df7449e4a29ec8d3182cf7b2aebcb86f7ac596c2 (patch) | |
| tree | 182c5c85f57264b38c60a02ec268e5c00d937b34 /figs/fowler-nordheim.fig/asymptotic.jl | |
Diffstat (limited to 'figs/fowler-nordheim.fig/asymptotic.jl')
| -rw-r--r-- | figs/fowler-nordheim.fig/asymptotic.jl | 46 |
1 files changed, 46 insertions, 0 deletions
diff --git a/figs/fowler-nordheim.fig/asymptotic.jl b/figs/fowler-nordheim.fig/asymptotic.jl new file mode 100644 index 0000000..fd1d492 --- /dev/null +++ b/figs/fowler-nordheim.fig/asymptotic.jl @@ -0,0 +1,46 @@ +using QuadGK +using SpecialFunctions +using FFTW + +# numerical values +hbar=6.58e-16 # eV.s +m=9.11e-31 # kg +Vn=9 # eV +En=14e9 # V/m +Kn=4.5 # eV + +V=1 +E=En*hbar/(2*Vn^1.5*m^0.5)*sqrt(1.60e-19) +k0=sqrt(Kn/Vn) + +# rescale x to nm +nm_scale=sqrt(2*m*Vn)/hbar*1e9*sqrt(1.60e-19) + +# cutoffs +p_cutoff=20*k0 +p_npoints=256 + +# airy approximations +airy_threshold=30 +airy_order=5 + +# xbounds +xmax=10 +xmin=-10 +x_npoints=200 + +include("FN_base.jl") + +# compute asymptotic values +ps_asym=Array{Complex{Float64}}(undef,x_npoints) +dps_asym=Array{Complex{Float64}}(undef,x_npoints) +for i in 1:x_npoints + x=xmin+(xmax-xmin)*i/x_npoints + ps_asym[i]=psi_pole(x,k0,E,V) + dps_asym[i]=dpsi_pole(x,k0,E,V) +end + +# print asymptotic values +for i in 1:x_npoints + print((xmin+(xmax-xmin)*i/x_npoints)*nm_scale,' ',abs(ps_asym[i])^2,' ',J(ps_asym[i],dps_asym[i]),'\n') +end |