# 7.2. Ballistic current calculation of a GaAs nin resistor¶

This tutorial is based on the following publications: [BirnerCBR2009], [GreckPhD2012]

The following input files were used:

Input files for next

**nano**³ software`1D_nin_symmetric_PhDthesis_PeterGreck_cl_zero_bias.in`

classical calculation at zero bias, Fig. 8.1(a) of [GreckPhD2012]

`1D_nin_symmetric_PhDthesis_PeterGreck.in`

CBR calculation of Fig. 8.1 and Fig. 8.2 of [GreckPhD2012]

`1D_nin_symmetric_CBRpaper.in`

CBR calculation of Chapter 8.5 of [BirnerCBR2009], symmetric doping profile

`1D_nin_asymmetric_CBRpaper.in`

CBR calculation of Chapter 8.5 of [BirnerCBR2009], asymmetric doping profile

Input files for next

**nano**.MSB software`nin_resistor_PhDthesis_PeterGreck.xml`

MSB calculation of Fig. 8.1 and Fig. 8.2 of [GreckPhD2012]

`nin_resistor_CBRpaper_symmetric.xml`

MSB calculation of Chapter 8.5 of [BirnerCBR2009], symmetric doping profile

`nin_resistor_CBRpaper_asymmetric.xml`

MSB calculation of Chapter 8.5 of [BirnerCBR2009], asymmetric doping profile

These example input files demonstrate how to calculate the ballistic current on a GaAs nin resistor. We use the same structure as outlined in Section 8.1 of [GreckPhD2012] and section 8.5 of [BirnerCBR2009] and compare the results obtained with the MSB method to the results obtained with the CBR method.

## Example 1¶

The following figure shows the electron density and the conduction band edge profile for a 50 nm GaAs nin structure.

The following input files can be used to reproduce these results.

`1D_nin_symmetric_PhDthesis_PeterGreck_cl_zero_bias.in`

(input file for next**nano**³ code)classical calculation at zero bias, Fig. 8.1(a) of [GreckPhD2012]

`1D_nin_symmetric_PhDthesis_PeterGreck.in`

(input file for next**nano**³ code)CBR calculation of Fig. 8.1 and Fig. 8.2 of [GreckPhD2012]

`nin_resistor_PhDthesis_PeterGreck.xml`

(input file for next**nano**.MSB code)MSB calculation of Fig. 8.1 and Fig. 8.2 of [GreckPhD2012]

The MSB results are very similar to the CBR results (not shown). Note that the CBR method uses an adaptive energy grid

adaptive-energy-grid = adaptive-exponential

to improve convergence while the MSB method uses a constant energy grid spacing.

The following results of the CBR input files are consistent to the MSB results for both, zero bias and nonzero bias. This has been checked.

conduction band edges

electric field

electron density and energy resolved electron density

DOS, position resolved DOS, lead resolved DOS (although the numbers are slightly different but the energy grid is also slightly different, i.e. nonuniform (CBR) vs. uniform (MSB) energy grid)

Transmission

IV curve

## Example 2¶

The following input files can be used to reproduce the results of section 8.5 of [BirnerCBR2009].

`1D_nin_symmetric_CBRpaper.in`

(input file for next**nano**³ code)CBR calculation of Chapter 8.5 of [BirnerCBR2009], symmetric doping profile

`1D_nin_asymmetric_CBRpaper.in`

(input file for next**nano**³ code)CBR calculation of Chapter 8.5 of [BirnerCBR2009], asymmetric doping profile

`nin_resistor_CBRpaper_symmetric.xml`

(input file for next**nano**.MSB code)MSB calculation of Chapter 8.5 of [BirnerCBR2009], symmetric doping profile

`nin_resistor_CBRpaper_asymmetric.xml`

(input file for next**nano**.MSB code)MSB calculation of Chapter 8.5 of [BirnerCBR2009], asymmetric doping profile

Again, we obtained very good agreement between the CBR and the MSB algorithm.

**Important comment**

Here, we had to use more energy grid points compared to the CBR code (where we used `300`

) in order to obtain convergence.

Nodes = 501 # Comment = Number of energy grid points.

We noticed this because the number of outer Poisson iterations exceeded its maximum as can be seen in the .log file

`Poisson iteration 60`

The number of outer Poisson iterations should be increased as follows.

MaxPoissonOuterIts = 60 # Comment = Max. outer Poisson iterations where G^R is recalculated.

**Further comments regarding the MSB input file**

In order to calculate the current ballistically we switched of scattering by using the following flag.

BallisticCalculation = yes

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