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.