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MOSLab.jl

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MOSLab.jl

From Semiconductor to TransistorLevel Modeling in Julia, including:

  1. Material properties analysis of electronical characteristics using Fermi-Dirac distribution, Boltzmann-Maxwell distribution, and Blakemore distribution (at this stage limited to Silicon)
  2. Numerical Simulations of MOS structures and MOS transistors in 1D and 2D powered by VoronoiFVM.jl
  3. Implementation of industry and research standard MOSFET models (Pah-Sah, Brews, BSIM 6, PSP 103, UICM and EKV), with different mobility models.
  4. Circuit Level Simulation including DC operating Point, Transient analysys ( Powered by ModelingToolkit.jl ), Ac Analysis ( Powered By ControlSystems.jl )
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Getting Started

To get a local copy up and running follow these simple steps.

Prerequisites

A Julia instalation with version 1.6 or higher

Installation

  ] add MOSLab
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Usage: MOS Cap Band Diagram

using MOSLab
using Plots
T = 300.0 # Temperature Kelvin
N_a = 5e18 # Bulk Doping in cm^-3
E_a = 0.044 #  The ground state energy of the acceptor in eV
t_ox = 4e-7 # oxide thickness in cm
t_si = 2.5e-5 # Silicon thickness
Vgv = 1.0 # Gate Voltage
PB = SemiconductorData(T,BoltzmanDist(),PSilicon(N_a,E_a))
MOS = MOSStructure(Alluminium(),SiO2(),PB,t_ox,t_si)
sol = PoissonVoronoi(Vgv,MOS,201)
BandDiagram(sol)
plot!(legend=:topright)
savefig("BandDiagram.png")

BandDiagram

PBFermi = SemiconductorData(T,FermiDist(),PSilicon(N_a))
MOSFermi = MOSStructure(Alluminium(),SiO2(),PBFermi,t_ox,t_si)
plot(-2.3:0.05:2.3,x-> ψs(x,MOS),label="Boltzmann Distribution")
plot!(-2.3:0.05:2.3,x-> ψs(x,MOSFermi),label="Fermi Distribution",legend=:topleft)
xlabel!("Vg [V]")
ppsi = ylabel!(L"\psi_s \  [V]")
savefig("psi_comp.png")

psi_comp

Usage: Simple 2D MOSFET Simulation

  using MOSLab
   using Plots
   using LaTeXStrings
   Vg = 0.1 # Gate Voltage
   Vd = 1.0 # Dain Voltage
   Nx = 101 # Number of grid points on the x direction
   Ny = 101 # Number of grid points on the y direction
   N_d = 6e16 # Dopants density at the drain and source side  in cm ^-3
   T = 300.0 # Temperature in Kelvin
   Nb = 5.7e17 # Dopants ensity at the bulk in cm ^-3
   l = .180e-4 # Channel length
   h = 0.5e-4 # Silicon depth
   t_ox = 4e-7 # Oxide thickens in cm
   Ms = MOSFETInputDeck(N_d,Nb,T,l,h,h/2.0,l,t_ox,:NMOS) # Create the input deck for an NMOS transistor
   Vs = ψs_PSP(Vg,Ms.Gate) # Calculate the surface potential at the gate
   G,psi,nn,pp = MOSFETSimulation(Ms,Vs,Vd,Nx,Ny;verbose=false,ξ₀=0.01) # run 2D MOSFET simulation
   gr()
   X = unique(G[1,:])
   Y = unique(G[2,:])
   contour(X,Y,psi,fill=true)
   surface(G[1,:],G[2,:],psi,fill=true)
   xlabel!(L"x \ [\mu m]")
   ylabel!(L"y \ [\mu m]")
   plot!(zlabel = L"\psi \ [V]")

Transitor Surface Potential at bias

PsiImage

   yvals = unique(G[2,:])
   ySel = G[2,:] .== yvals[end-1]
   sum(ySel)
   minimum(psi[ySel])
   plot(G[1,ySel],psi[ySel],label="\$ \\psi (x,$(yvals[end-1]) ) \$",legend=:bottomleft)

Surface Potential Allong Channel

PsiImage

    savefig("Psi_channel.png")
    plot(G[1,ySel],nn[ySel],label="\$ E_C (x,$(yvals[end-1]) ) \$",legend=:topright)
    savefig("nn_channel.png")

Electron Concentration Allong Channel

PsiImage

Usage: Plot Id x Vd and Id Vg curve of an Mosfet using

using MOSLab
using Plots
using LaTeXStrings
NpolyDoping = 5.5e17 # Gate Npoly doping concentration in cm^-3
N_a = 5.5e17 # Bulk doping concentration in cm^-3
E_a = 0.0# The ground state energy of the acceptor in eV
t_ox = 3.8e-7 # oxide thickness in cm
t_si = 1e-6
CList2 = reshape( range(colorant"blue", stop=colorant"red",length=7), 1, 7 );

MOSf(T) = MOSStructure(NPoly(NpolyDoping),SiO2(),SemiconductorData(T,BoltzmanDist(),PSilicon(N_a,E_a)),t_ox,t_si) ## Calculate Parameters of a MOS Structure the given parameters using Boltzman Distribution at temperature T 
transistor_model(T) = BSIM6Model(MOSf(T),1.0e-4,1.0e-4)
Idf(Vg,Vd,T) = Id(Vg,Vd,0.0,transistor_model(T)) ## Calculate the Current using the ACM Model of a transistor having the parameters from MOSf(T) and W =1.0 um, L = 1.0 um, similar contructors are available for the other models
plot()
for Vgv in 0.2:0.2:1.8
    plot!(0:0.05:1.8,x->1e6*Idf(Vgv,x,300.0),label="\$V_{GB} = $(Vgv) V\$") # plot Id, Vd characteristics for different VGB
end
PSPG = plot!(xlabel=L"V_{DS} \ [V]",ylabel=L"I_{DS} \ [\mu A]",legend=:topleft)

plot()
for (i,Tv) in enumerate(LinRange(200,500,5))
    plot!(0:0.05:1.0,x->1e6*Idf(x,0.1,Tv),label="\$T = $(Tv) K\$",linecolor=CList2[i]) # plot Id, Vg characteristics for different Temperatures
end
PSPD = plot!(xlabel=L"V_{GS} \ [V]",ylabel=L"I_{DS} \ [\mu A]",legend=:topleft,yaxis=:log10)
plot(PSPG,PSPD) # plot both graphs side by side 
savefig("TransistorCurves.png")

PsiImage

gmIdf(Vg,Vd,T) = gm(Vg,Vd,0.0,transistor_model(T))/Idf(Vg,Vd,T)
plot()
for (i,Tv) in enumerate(LinRange(200,500,5))
    plot!(0:0.01:1.0,x->gmIdf(x,0.1,Tv),label="\$T = $(Tv) K\$",linecolor=CList2[i]) # plot Id, Vg characteristics for different Temperatures
end
PSPD = plot!(xlabel=L"V_{GS} \ [V]",ylabel=L"I_{DS} \ [\mu A]",legend=:topright)
savefig("gmId.png")

PsiImage

Circuit Simulation

using Plots
using MOSLab


NpolyDoping = 5e17 # Gate Npoly doping concentration in cm^-3
N_a = 5e17 # Bulk doping concentration in cm^-3
E_a = 0.044 # The ground state energy of the acceptor in eV
t_ox = 4e-7 # oxide thickness in cm
t_si = 1e-6
MOSf(T) = MOSStructure(NPoly(NpolyDoping),SiO2(),SemiconductorData(T,BoltzmanDist(),PSilicon(N_a,E_a)),t_ox,t_si) ## Calculate Parameters of a MOS Structure the given parameters using Boltzman Distribution at temperature T 
g = 1
d = 2
s = 0
M1 = CircuitComponent("M1",ACMModel(MOSf(300.0),1000.0e-4,1.0e-4))
netT = Netlist()
addComponent(netT,M1,Dict("g"=>1,"d"=>d,"s"=>s))
addComponent(netT,CircuitComponent("Vg",VoltageSource(0.3)),Dict("p"=>g,"n"=>s))
addComponent(netT,CircuitComponent("Vd",VoltageSource(1.0)),Dict("p"=>d,"n"=>s))
ckt = Circuit(netT)
res = dc_op(ckt)
for i in 2:length(netT.nodes) # exclude ground
    println("$(netT.nodes[i].name): $(res[i-1])")
end

V_n1: 0.3
V_n2: 1.0
J_Vg: 0.0
J_Vd: -0.0005823007996463166
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Roadmap

See the open issues for a list of proposed features (and known issues).

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Contributing

Contributions are what make the open source community such an amazing place to learn, inspire, and create. Any contributions you make are greatly appreciated.

  1. Fork the Project
  2. Create your Feature Branch (git checkout -b feature/AmazingFeature)
  3. Commit your Changes (git commit -m 'Add some AmazingFeature')
  4. Push to the Branch (git push origin feature/AmazingFeature)
  5. Open a Pull Request
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License

Distributed under the MIT License. See LICENSE for more information.

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Contact

João Roberto Raposo de Oliveira Martins - jrraposo1@gmail.com

Project Link: https://github.com/Rapos0/MOSLab.jl

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Acknowledgements