### Double Barrier Tunneling

In this tutorial we explain how a double barrier tunneling simulation can be set up with the NEGF toolbox.

The structure is a $50nm$ wide $GaAs$ chunk with two end contacts.

We choose homogeneous material properties, which means we should create artificial potential barriers. In order t achieve that the expression of the potential should be set:

inrange(-0.7, x_global, -0.5)*0.4+inrange(0.5, x_global, 0.7)*0.4

The “inrange(a,b,c)” function is $1.0$ when $a \leq b \leq c$ satisfies, otherwise $0.0$. As a result the first part of the expression creates a $0.4eV$ high barrier from $-7nm$ to $5nm$, while the second one creates one from $5nm$ to $7nm$. (We have set the global length scale to $10nm$).

We need to define the two contacts at the end of the sample, currently we don't apply any bias.

The calculated conduction band edge which is shifted with the potential, and with the artificial potential is depicted in Figure 1.

The tunneling coefficient from one contact to the another is calculated in Figure 2.