### n-i-n resistor

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#### Introduction

Today's down-scaling of microelectronics devices led to size regime, where the classical semiconductor device equations can not be used. In this region the quantum effects can not be neglected, and a new theory should be applied. With the Non-equilibrium Green function (NEGF) approach we can simulate reliably quantum devices, even with included scattering effects.

#### Structure

The device is built from doped GaAs layers, as it is depicted in figure 1.

It is built from two highly doped layers near the contacts and from an insulator layer, where the electron density should be low.

#### Band-structure

From classical calculation the conduction band profile is depicted in figure 2. It shows, that the 50nm of insulator layer creates a potential barrier for the electrons, which reduces the transport across the device. This effect can be used in nano-scale field effect transistors, that with the height of the internal barrier the current through the transistor can be controlled.

#### Density calculations

With the NEGF method one can calculate the transport properties, and charge carrier densities in the device including non-equilibrium effects. In this example we are comparing the results of this method with our existing different methods of device simulation.

The three methods tat we are using:

**NEGF**We calculate the electron density from the correlation function $G_n$, which we calculated self consistently with the potential in the device, according to ref(Datta), with the kinetic equation.**Classical**It simply assumes that the electron density is defined by the local potential, and fermi level. It doesn't take the Quantum mechanical effects into account.**Schrodinger equation**with effective mass} According to this method we calculate the eigenfunctions in the device, and we calculate the 2 dimensional density of states locally in the sample, respecting these eigenfunctions. The population of these states are simply following the fermi-statistics.

The calculated profiles with the different methods are depicted in figure 3. It shows that in equilibrium all three methods converges for the same results. The Schrödinger equation based method converges at the boundary to oscillatory solutions, which can be the result of the boundary conditions.

#### Density of states and spectral function

According to quantum mechanical calculation we simulated the electron wave-functions in the system which would contribute to the density of states which is plotted in figure 4. This also can be done with the NEGF method in 5., which overlaps with the Schrödinger equation based method.