# Tutorial 20: Top-of-the-barrier model for graphene

The following tutorial compute the transfer characteristics, the charge density and the potential in correspondence of graphene in a double gate FET through the top-of-the-barrier model.

Top and bottom oxides are supposed to be 0.5 nm thick and made of SiO2.

We first set the top and bottom capacitance

`C1=3.9*eps0/0.5e-9;`
`C2=3.9*eps0/0.5e-9;`

and we set Vds=1.5 V.

We then create the tuple to store the main electrical quantities

`Phi_channel=[];`
`Vg=[]`
`Id=[];`
`Phi_c=Vg1;`
`rho=[];`

We set the minimum Vg1 to -5V and the delta Vg equal to 0.01 V

`Vg1=-5;`
`delta_Vg=0.01`

We now initialize the top-of-the-barrier graphene class

`TOB=graphene_TOB(C1,C2,Vg1,Vg2,Vds,Phi_c);`

Let’s then sweep Vgs up to 5V, and impose Vg2 equal to Vg1.

At each step, the method charge_I return the potential in the graphene (Phi_c), the current (curr) and the charge in graphene (charge), which are then stored in the corresponding tuples, defined before.

`while (Vg1<=5):`
`    print Vg1`
`    TOB.Vg2=Vg1;`
`    [Phi_c,curr,charge]=TOB.charge_I();`
`    Phi_channel.append(Phi_c)`
`    Vg.append(Vg1)`
`    Id.append(curr)`
`    Vg1=Vg1+delta_Vg;`
`    rho.append(charge)`
`    TOB.Vg1=Vg1;`

Let’s then store all the information in three different files, which can then be plotted with gnuplot.

`a=[array(Vg),array(Id)]`
`savetxt("Id.out",transpose(a));`
`a=[array(Vg),array(Phi_channel)]`
`savetxt("Pot_c.out",transpose(a));`
`a=[array(Vg),array(rho)]`
```savetxt("rho.out",transpose(a));
```

The complete script can be found here.

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