STM Simulations Using VASP
Theory of STM:
References
J. Tersoff and D. R. Hamann, PRL 50, 1998
(1983).
J. Tersoff and D. R. Hamann, PRB 31, 805
(1985).
Scripts for processing VASP output:
To compute the simulated STM image we compute the integrated LDOS ---typically
integrated over an energy of 1 eV
below the Fermi level--- and then construct the corresponding height
contour for a fixed value of this integrated LDOS.
This can be accomplished running the ground state and then computing
the "charge density" corresponding to a set of
fixed input occupation numbers. The occupation numbers can be specified
in VASP with the tokens ISMEAR = -2
and FERWE set to the desired occupation. For a spin-polarized calculation
one also sets FERDO to the occupation
numbers for the spin minority channel. Both these setttings are "automated"
with the script "stm_occup" below:
Run the ground state with specified occupancies (to get the integrated
LDOS): stm_occup
Atom coordinates from the OUTCAR file: vp
Construct an STM image file for use with the mathematica notebook below:
stm_atom_positions
Mathematica Notebook for processing STM images: stm.nb
Simulations of XSTM ([110]) Image ofAs Antisite
in [001] GaAs
References
Expt: R. M. Feenstra, J. M. Woodall, and G. D.
Pettit, PRL 71, 1176, (1993).
Theory: R. B. Capaz, K. Cho, and J. D. Joannopoulos,
PRL 75, 1811 (1995).
Simulations of STM ([001]) Image of Mn dopant in
[001]-grown GaAs
** Ground state can be difficult to converge, depending sensitively
on the Fermi smearing and the type of
mixing scheme adopted. As a small test, the GaAs [001] surface was
used with a MnGa impurity at the surface.**
In this plot we show the number of SCF steps and the total energies
(free energy, energy w/o entropy and energy w/ sigma->0)
versus the Fermi smearing for both the default mixing scheme and one
with better mixing parameters (from Erwin.):
GaAs_100_surf_MnGa.png
Clearly the improved mixing scheme speeds up the convergence (vs. SCF
steps) of the total energy (by more than a factor of 2
for a smearing of 0.5 eV).
Files (for SIGMA=0.5 eV) |
| STM image of GaAs [001] Surface (unreconstructed, Ga-termination):
GaAs_001_stm.gif |
STM image of GaAs [001] Surface with MnGa dopant (unreconstructed),
bias = 1.0 eV: GaAs_001_MnGa_stm.gif
STM image of GaAs [001] Surface with MnGa dopant (unreconstructed),
bias = 4.0 eV: GaAs_001_MnGa_4_stm.gif
Note that the Mn d DOS
occurs between ~4 and ~1.5 eV below the Fermi level, so that the 2nd image
above is a more realistic depiction of the STM image due to Mn.
|
Simulations of XSTM ([110]) Image of Mn dopant in
[001]-grown GaAs
| The unit cell is large in this case (360 atoms = 6x6x1 surface unit
cell with 5 layers in the slab) and difficult to converge. The real space
projection technique is slightly faster ---by about 20%--- than the reciprocal
space technique:
Recip. Space
Real Space Proj.
Time for one Electronic SCF Loop (sec:)
4639.90 sec
3627.65 sec (About 20 % faster). |
| Tests of the convergence properties of the ground state have been performed
for a smaller unit cell (40 atoms) with a MnGa dopant with Mn
at the surface and in the 2nd layer.
MnGa at the surface: Test_GaAs_110_Mn_Energy_Convergence.png
MnGa in the 2nd layer from the surface: Test_GaAs_110_Mn_2ndLayer_Energy_Convergence.png |
| In the end the problem with the large unit cell is due to an empty
d-band
just above the Fermi level. For the 360 atom unit cell (6x6 surface unit
cell) this band is only ~46 meV above the highest occupied state. Thus
a finite temperature scheme with a large temperature smearing will give
severe charge sloshing problems. To avoid this problem one can either use
a very small temperature smearing (effectively zero temperature) or setting
the occupation numbers by hand (ISMEAR = -2 and FERWE and FERDO tokens
set in the INCAR file).
Density of states for small (40 atoms) cell with MnGa in
the 2nd layer: dos_gaas_110_40atoms.png |
|
|
For interstitial Mn, calculations in a smaller supercell have been
used to determine realistic atomic relaxations that might take place near
the surface. These include interstitial positions with tetrahedral coordination
to Ga and As in the atomic planes below the surface and for a surface interstitial
site. The starting configuration of the Mn interstitial atoms is represented
schematically here.
All the Mn(int) considered have a moment of 3 mb regardless of location,
coordination, or atomic relaxation.
|
Defect Type
|
Maximum Atomic Relaxation (A)
|
Relaxed Atomic Coordinates (jmol format)
|
|
As4-1
|
0.370
|
As4-1 |
|
As4-2
|
0.284
|
As4-2 |
|
As4-3
|
0.332
|
As4-3 |
|
As4-4
|
|
|
|
As4-5
|
0.077
|
As4-5 |
|
|
|
|
Ga4-1
|
0.501
|
Ga4-1 |
|
Ga4-2
|
0.347
|
Ga4-2 |
|
Ga4-3
|
0.221
|
Ga4-3 |
|
Ga4-4
|
0.158
|
Ga4-4 |
|
Schematic of interstitial Mn configurations near the surface considered
in this work. See jmol files at left to see the actual relaxed geometries.
|
Based on these results, we assume no coordinate relaxation---beyond the
surface [110] buckling---for supercells with Mn more than 3 layers removed
from the surface. Thus only cells like As4-1, As4-2, As4-3, Ga4-2 and Ga4-3
need to include atomic relxatioins.
| For the case of Mn(Ga) substitutionals, no atomic relxation (beyond
the [110] buckling) was included. This would seem a poor approximation
for the case of Mn(Ga) on the [110] surface. However, simulating atomic
relaxations of Mn(Ga) at the surface shows theres is only a 81 meV gain
in energy in including these relaxations and a maximum atomic displacement
of 0.12 Angstroms (for the surface As atoms to which Mn bonds, the As atoms
move slightly towards Mn). Thus we use the ideal (unrelaxed) coordinates. |
|
Calculations in the large unit cell (360 atoms) suggest that
there are no satellite peaks associated with Mn(Ga) that extend much beyond
the first near neighbor Ga atoms in the plane. Hence, we will test the
use of a much smaller unit cell (5+1 layers w/ 3x3x1 surface unit cell
= 108 atoms in total).
| Pure GaAs:
Number of Atoms: 9 H(0.75) + 9H(1.25) + 45Ga + 45As = 1 Layer of 18
"H" atoms + 5 Layers of Ga9As9
Number of Electrons = 378
Number of Up Bands = 189
Number of Dn Bands: = 189
Test:
NBANDS = 234
ISMEAR = -2
FERWE = 189*1.0 45*0.0
FERDO = 189*1.0 45*0.0
ENCUT = 227.24
1x1x1 K-Point Sampling
Timing (16 procs): 4345.70 secs |
GaAs with Mn(Ga) in 2nd layer:
Number of Atoms: 9 H(0.75) + 9H(1.25) + 44Ga + 45As + 1Mn = 1 Layer
of 18 "H" atoms + 5 Layers of Ga9As9 with Mn(Ga)
Number of Electrons = 382
Number of Up Bands = 193
Number of Dn Bands = 189
Test:
NBANDS = 234
ISMEAR = -2
FERWE = 193*1.0 41*0.0
FERDO = 189*1.0 45*0.0
ENCUT = 227.24
1x1x1 K-Point Sampling
Timing (16 procs): 4729.71 secs |
GaAs with Mn(int) Ga4-4layer:
Number of Atoms: 9 H(0.75) + 9H(1.25) + 45Ga + 45As + 1Mn = 1 Layer
of 18 "H" atoms + 5 Layers of Ga9As9 with Mn(int)
Number of Electrons = 385
Number of Up Bands = 194
Number of Dn Bands = 191
Test:
NBANDS = 234
ISMEAR = -2
FERWE = 194*1.0 40*0.0
FERDO = 191*1.0 43*0.0
ENCUT = 227.24
1x1x1 K-Point Sampling
Timing (16 procs): 5139.77 secs |
| Pure GaAs:
Number of Atoms: 16 H(0.75) + 16H(1.25) + 80Ga + 80As = 1 Layer of 32
"H" atoms + 5 Layers of Ga16As16
Number of Electrons = 672
Number of Up Bands = 336
Number of Dn Bands: = 336
Test:
NBANDS = 350
ISMEAR = -2
FERWE = 336*1.0 14*0.0
FERDO = 336*1.0 14*0.0
ENCUT = 227.24
1x1x1 K-Point Sampling
Timing (16 procs): 16480.23 |
GaAs with Mn(Ga) in 2nd layer:
Number of Atoms: 16 H(0.75) + 16H(1.25) + 79Ga + 80As +1Mn= 1 Layer
of 32 "H" atoms + 5 Layers of Ga16As16 with Mn(Ga)
Number of Electrons = 676
Number of Up Bands = 336
Number of Dn Bands: = 336
Test:
NBANDS = 350
ISMEAR = -2
FERWE = 340*1.0 10*0.0
FERDO = 336*1.0 14*0.0
ENCUT = 227.24
1x1x1 K-Point Sampling
Timing (24 procs): 12703.18 |
|
|
|
MnGa Substitutional
XSTM Simulations
Mnint Interstitial
XSTM Simulations: As Coordinated Defects
Mnint Interstitial
XSTM Simulations: Ga Coordinated Defects
