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nextnano3 - Tutorial

next generation 3D nano device simulator

1D Tutorial

Two-dimensional electron gas in an AlGaN/GaN field effect transistor

Author: Stefan Birner, Zoltán Jéhn

If you want to obtain the input files that are used within this tutorial, please contact stefan.birner@nextnano.de.
->          Jogai_AlGaNGaN_FET_JAP2003_noGaNcap_Fig4Fig1Fig7_1D_nn3.in - input file for nextnano3 software  (also available as 2D input file)
->          Jogai_AlGaNGaN_FET_JAP2003_noGaNcap_Fig4Fig1Fig7_1D_nnp.in -
input file for nextnano++ software (also available as 2D input file)
->          Jogai_AlGaNGaN_FET_JAP2003_noGaNcap_Fig2Fig3_1D_nn3.in     -
input file for nextnano3 software  (also available as 2D input file)
->          Jogai_AlGaNGaN_FET_JAP2003_GaNcap_Fig4_1D_nn3.in           -
input file for nextnano3 software  (also available as 2D input file)
->          Jogai_AlGaNGaN_FET_JAP2003_GaNcap_Fig4_1D_nnp.in           -
input file for nextnano++ software (also available as 2D input file)
->          Jogai_AlGaNGaN_FET_JAP2003_GaNcap_Fig6Fig5_1D_nn3.in       -
input file for nextnano3 software  (also available as 2D input file)
->          Jogai_AlGaNGaN_FET_JAP2003_GaNcap_Fig6Fig5_1D_nnp.in       -
input file for nextnano++ software   (also available as 2D input file)
 


Two-dimensional electron gas in an AlGaN/GaN field effect transistor

This tutorial is based on:

[Jogai2003]
Influence of surface states on the two-dimensional electron gas in AlGaN/GaN heterojunction field-effect transistors

B. Jogai
J. Appl. Phys. 93, 1631 (2003)
 

For this one-dimensional simulation of an AlGaN/GaN heterojunction field effect transistor (HFET) we are solving self-consistently the Schrödinger-Poisson equation taking into account strain, and piezo- and pyroelectric charge densities.

  • At the left boundary we use a Schottky contact boundary condition with a Schottky barrier height of phiB = 1.4 eV.
    Note that in Fig. 1 of [Jogai2003], the Schottky barrier height corresponds to
       e phiB = Ec - EF
    which fixes the conduction band edge energy Ec above the Fermi energy EF. e is the elementary charge.

    Alternative boundary conditions such as
    - a fixed surface charge density or
    - surface states based on incomplete ionization of donor or acceptor states
    are described in the Schottky barrier tutorial.
  • Our simulated structure is undoped. Note that the 2DEG is present even in the absence of doping due to piezo- and pyroelectric interface charge densities.
  • The temperature is set to 300 K in all simulations.
  • We only consider cation-faced structures, i.e. we have rotated the crystal so that our [000-1] direction points along the positive x direction.

 

The following figure shows the results of these input files:
 ==> 1DJogai_AlGaNGaN_FET_JAP2003_noGaNcap_Fig4Fig1Fig7_nn3.in - input file for nextnano3 software
 ==> 1DJogai_AlGaNGaN_FET_JAP2003_noGaNcap_Fig4Fig1Fig7_nnp.in -
input file for nextnano++ software

Shown are the conduction and three valence band edges together with the probability densities of the two lowest subbands of a 30 nm Al0.3Ga0.7N / 40 nm GaN heterostructure.

 

 

Variation of the AlxGa1-xN layer thickness and alloy content x (Fig. 2 and Fig. 3 of [Jogai2003])

 ==> Jogai_AlGaNGaN_FET_JAP2003_noGaNcap_Fig2Fig3_1D_nn3.in - input file for nextnano3 software

Now we try to reproduce Fig. 2 and Fig. 3 of [Jogai2003].
We are calculating the variation of the 2DEG density with the

  • AlxGa1-xN layer thickness and
  • mole fraction (alloy content x).

 

Within the nextnano3 input file, we can perform a sweep over the alloy concentration very conveniently:
   %AlloySweepActive = yes   ! sweep alloy concentration from 0.4 to 0.0 (HighlightInUserInterface)

The thickness of the AlxGa1-xN barrier is defined as a variable.
   %ThicknessAlGaN   = 30.0  ! thickness of AlGaN spacer (ListOfValues:6,10,14,18,22,26,30,34,38)(DisplayUnit:nm)(HighlightInUserInterface)
We use nextnanomat's Template feature in order to sweep over the AlxGa1-xN barrier thickness. This is shown in the following screenshot.

The input files are created automatically and are added to the "Run" tab.

 

The 2DEG sheet carrier concentration can be found in this file: densities/int_el_dens1D.dat
This file contains the integrated electron density for each region cluster.
In our case, the total electron density is relevant which is the sum of cluster #3 (AlGaN barrier) and cluster #4 (GaN well) because the quantum cluster extends over these two clusters.
The first column contains the sweep index which is the alloy content.
 sweep_index   Cl_1[1/cm^2]  Cl_2[1/cm^2]  Cl_3[1/cm^2]  Cl_4[1/cm^2]  Cl_5[1/cm^2]  Cl_6[1/cm^2]  Total[1/cm^2]
 0.400000E+00  0.231809E-02  0.798938E+08  0.534667E+12  0.983171E+13  0.133962E+12  0.000000E+00  0.105004E+14
 ...

The following figure shows the total integrated electron density (Total[1/cm^2]) as a function of alloy concentration for various AlGaN thicknesses.
Note that these results were obtained by using one input file template only: 1DJogai_AlGaNGaN_FET_JAP2003_nn3_Fig2Fig3.in

For a given barrier thickness, the 2DEG sheet carrier concentration varies almost linearly with alloy concentration x.
The 2DEG density approaches saturation as the barrier thickness is increased.
This fact can be better seen in the next plot where we show exactly the same data.

Our results seem to be in reasonable agreement to the simulations of [Jogai2003] (Fig. 2 and Fig. 3).

 

 

Variation of the Schottky barrier height (Fig. 7 of [Jogai2003])

 ==> Jogai_AlGaNGaN_FET_JAP2003_noGaNcap_Fig4Fig1Fig7_1D_nn3.in - input file for nextnano3 software
 ==> Jogai_AlGaNGaN_FET_JAP2003_noGaNcap_Fig4Fig1Fig7_1D_nnp.in -
input file for nextnano++ software

Now we vary the Schottky barrier height phiB and calculate for each value the 2DEG density.
 %SchottkyBarrierHeight = 1.4 ! Schottky barrier height phi_B = E_c - E_F, used by [Jogai2003], see p. 1634, column 1 (ListOfValues:1.40,1.42,1.65)(RangeOfValues:From=0.0,To=4.0,Step=0.25)(DisplayUnit:V)
This situation is equivalent to fixing the surface potential to
   e phiB = Ec - EF.

 

The following figure shows the calculated 2DEG density as a function of Schottky barrier height, i.e. surface potential.
We used a 30 nm Al0.3Ga0.7N barrier.
Again, the 2DEG sheet carrier concentration can be found in this file: densities/int_el_dens1D.dat (Total[1/cm^2])
The results are in reasonable agreement to Fig. 7 of [Jogai2003].

 

 

AlGaN/GaN FET including a GaN cap layer

 ==> Jogai_AlGaNGaN_FET_JAP2003_GaNcap_Fig4_1D_nn3.in           - input file for nextnano3 software
 ==> Jogai_AlGaNGaN_FET_JAP2003_GaNcap_Fig4_1D_nnp.in           -
input file for nextnano++ software
 ==> Jogai_AlGaNGaN_FET_JAP2003_noGaNcap_Fig4Fig1Fig7_1D_nn3.in -
input file for nextnano3 software
 ==> Jogai_AlGaNGaN_FET_JAP2003_noGaNcap_Fig4Fig1Fig7_1D_nnp.in -
input file for nextnano++ software

Now we compare HFET structures with and without a GaN cap layer.
GaN-capped HFETs have a lower 2DEG density compared to uncapped structures.

When introducing a GaN cap layer, the density of the 2DEG is reduced.

  • 5 nm cap,     30 nm Al0.3Ga0.7N barrier. The calculated 2DEG density is n = 1.03 * 1013 cm-2 (n = 1.20 * 1013 cm-2 [Jogai2003]).
  • without cap, 30 nm Al0.3Ga0.7N barrier. The calculated 2DEG density is n = 1.25 * 1013 cm-2 (n = 1.47 * 1013 cm-2 [Jogai2003]).

The following figure shows the conduction and valence band edges of an Al0.3Ga0.7N/GaN FET with (solid lines) and without (dotted lines) a 5 nm GaN cap layer.

 

 

 ==> Jogai_AlGaNGaN_FET_JAP2003_GaNcap_Fig6Fig5_1D_nn3.in - input file for nextnano3 software
 ==> Jogai_AlGaNGaN_FET_JAP2003_GaNcap_Fig6Fig5_1D_nnp.in -
input file for nextnano++ software

The following figure shows the band edges and the electron and hole densities for a 14 nm GaN cap layer.
The Al0.3Ga0.7N barrier thickness is 30 nm.
For GaN cap layers thicker than 14 nm, a 2DHG forms.
The density of the 2DHG screens the surface potential so that the density of the 2DEG is maintained at a constant level even if the GaN cap layer thickness increases further.



The calculated 2DHG density is p = 0.513 * 1012 cm-2 (p = 1.77   * 1012 cm-2 [Jogai2003]).
The calculated 2DEG density is n = 0.839 * 1013 cm-2 (n = 1.009 * 1013 cm-2 [Jogai2003]).

 

 

Variation of the GaN cap layer thickness (Fig. 5 of [Jogai2003])

 ==> Jogai_AlGaNGaN_FET_JAP2003_GaNcap_Fig6Fig5_1D_nn3.in - input file for nextnano3 software
 ==> Jogai_AlGaNGaN_FET_JAP2003_GaNcap_Fig6Fig5_1D_nnp.in -
input file for nextnano++ software

Now we are going to vary the GaN cap layer thickness.
 %ThicknessGaNcap = 5.0 ! thickness of GaN cap layer for GaN cap simulation (Fig. 4, Fig. 5), (ListOfValues:1,2,3,4,5,7,9,11,12,13,14,15,17,20,25,30)(DisplayUnit:nm)(HighlightInUserInterface)
 

 

The following figure shows the 2DEG density vs. GaN cap layer thickness for a 30 nm Al0.3Ga0.7N barrier.
Beyond a GaN cap layer thickness of ~13 nm (12 nm [Jogai2003]) the 2DEG density saturates.

 

 

Additional comments

In contrast to the article of [Jogai2003], we did not include exchange-correlation effects. (To do: Add to this tutorial.)
In contrast to the article of [Jogai2003], we used a single-band model for the 2DHG rather than a 6-band k.p model. (To do: Add 6-band k.p for the holes to this tutorial.)

 

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