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# nextnano3 - Tutorial

## Local density of states

Note: This tutorial's copyright is owned by Stefan Birner, www.nextnano.com.

Authors: Stefan Birner

If you want to obtain the input files that are used within this tutorial, please contact stefan.birner@nextnano.de.
```-> 1D_LDOS_GaAs.in  ```

## Local density of states

`-> 1D_LDOS_GaAs.in`

Here, we calculate the local density of states LDOS(z,E) for a one-dimensional system of GaAs which is restricted to z > 0 nm.
At z <= 0 nm, there is an infinite barrier.

This LDOS can be derived analytically and reads

LDOS1D(z,E) = 2 / (pi hbar) (2m*/E)1/2 sin2(kz)

where k = (2m*E)1/2 / hbar.

The following figure shows the calculated LDOS1D(z,E) for z = [0 nm, 20 nm] and E = [0 eV, 0.3 eV].
The GaAs conduction band edge is set to 0 eV.
The units are ` [nm-1 eV-1]`.

The local density of states output LDOS(z,E) is contained in these files:
```   Schroedinger_1band/LocalDOS_cb001_qc001_sg001_deg001_dir_Kz001.dat / *.coord / *.fld```

## Local density of states for a 3D system restricted to z > 0 nm

The following plot is based on Fig. 1.11 (p. 30) of
The Physics of Low-Dimensional Semiconductors - An Introduction
John H. Davies
Cambridge University Press (1998)

• Please help us to improve our tutorial. Send comments to``` support [at] nextnano.com```.