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 nextnano³ 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 nextnano.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.

nin resistor

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

  • 1D_nin_symmetric_PhDthesis_PeterGreck_cl_zero_bias.in (input file for nextnano³ code)

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

  • 1D_nin_symmetric_PhDthesis_PeterGreck.in (input file for nextnano³ code)

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

  • nin_resistor_PhDthesis_PeterGreck.xml (input file for nextnano.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 nextnano³ code)

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

  • 1D_nin_asymmetric_CBRpaper.in (input file for nextnano³ code)

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

  • nin_resistor_CBRpaper_symmetric.xml (input file for nextnano.MSB code)

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

  • nin_resistor_CBRpaper_asymmetric.xml (input file for nextnano.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 Comment="Number of energy grid points.">501</Nodes>

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 Comment="Max. outer Poisson iterations where G^R is recalculated.">60</MaxPoissonOuterIts>

Further comments regarding the MSB input file

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

<BallisticCalculation Comment="yes or no (default is no)">yes</BallisticCalculation>