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SiC: A review

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Literature Survey

Polytypes

3C-SiC

4H-SiC

Point defects

Vacancy

Silicon vacancy is a high-energy defect that can only be observed in heavily irradiated {SiC}\cite{Alfieri2012a} It is experimentally observed that silicon vacancies possess a peculiar high-spin configuration($S=\frac{3}{2}$) with three aligned spin resulting in a $-1$ charge state.[ref needed] ($\mathrm{O_{Si}}$)

A Jahn-Teller distortion of the silicon vacancy is not observed in any charge state.\cite{Torpo2001}

Large energy drop when transforming into the complex made of carbon vacancy and a carbon antisite ($\mathrm{V_cC_{Si}}$).[ref needed]

Carbon vacancy exists in the \(2+\) and $0$ charge states in {3C-SiC} and in $2^+$, $0$ and $2^-$ charge states in {4H-SiC}.

substitutional oxygen at carbon site (O<sub>C</sub>) inContrary to the silicon vacancy, the carbon vacancy exhibits a strong Jahn-Teller effect.\cite{Torpo2001}

541.74452341Oxygen in 3C-SiC

Substitutional oxygen on the carbon site ($\mathrm{O_C}$) is electrically active. $\mathrm{O_C}$ is a double effective mass-like donor in {3C-SiC}, like sulfur in silicon. The one-electron level of the defect is at $E_c-0.2$~{eV}. $\mathrm{O_C}$ is an on-center defect with T$_d$ symmetry.

Single positive charge state no metastable state was found, so this is an on-center defect with T$_d$ symmetry. The Si-o distance is sligtly shorter than in the neutral state.

In the case of O$_C^{2+}$, the SI-O distance is further shortened but the geometry is essentially the same as for the neutral and the single positive defect.

The occupation levels of the $\mathrm{O_C}$ double donor are at $E\left(2+/+\right)=E_v+2.13$~{eV} and at $E\left(+/0\right)=E_v+2.09$~{eV}.

They are two metastable configurations for oxygen at the silicon site ($\mathrm{O_{Si}}$) in the neutral state. In both configuration there is a double occupied level in the gap at $E_v+0.1$ and at $+1.1$~{eV} for C$_{2v}$ and T$_d$, respectively. Therefore $\mathrm{O_{Si}}$ is a hyperdeep double donor (or rather a double hole trap).

Oxygen in 4H-SiC

Due to high formation energy of $\mathrm{O_{Si}}$ in {3C-SiC}, the \textbf{oxygen at silicon site} in {4H-SiC} was not investigated.

The formation energy of \textbf{oxygen at carbon site} ($\mathrm{O_{C}^0}$) is $1.8$~{eV} higher in {4H-SiC} than in {3C-SiC}, because of the one-electron donor level occupied by two electron is situated about 1.0~{eV} higher in {4H-SiC} than in {3C-SiC}.

The double occupied level is at $E_v+3.2$~{eV} (for the k site) [not an effective-mass-like one as in {3C-SiC}]. Possible charge states of $\mathrm{O_{C}}$ are ($2+$, with $C_{3v}$ symmetry), ($+$) and ($0$), both with $C_{1h}$ symmetry. The (2+/+) and (+/0) occupation levels at the k site are at $E_v+3.1$~{eV} and $E_v+3.2$~{eV}.

The diference between k and h site were examined only for $\mathrm{O_{C}^{2+}}$. The total energy was lower at the h site by 0.11~{eV} and the Si-O bond length were about the same.

Fluorine in SiC

None to resume?!

Chlorine in 3C-SiC

For spin-average calculations, both $\mathrm{Cl_C}$ and $\mathrm{Cl_{Si}}$ act as donors in their neutral state. $\mathrm{Cl_C}$ retains its initial $\mathrm{T_d}$ symmetry, $\mathrm{Cl_{Si}}$ lowers it from $\mathrm{T_d}$ to $\mathrm{C_{3v}}$.

[discuss energy formation differences.]

For spin-polarized calculations, $\mathrm{Cl_C}$ retains tetragonal symmetry, while $\mathrm{Cl_{Si}}$ lowers it to trigonal.substitutional oxygen at carbon site (O<sub>C</sub>) in

Regarding interstitials, $\mathrm{Cl_i}$ in $\mathrm{T_d}$ or in $\mathrm{O_h}$ both retained its symmetry. Energy-wise, they have very high $\mathrm{E_{form}}$ thus they are unlikely to occur.

In sum, it is found that vacancies arising after implantation, rather than $\mathrm{Cl}$, can be held responsible for carrier compensation in n-type {SiC}, while for p-type {SiC} the presence of a compensating center, such as the $\mathrm{Cl_CAl_{Si}}$ complex, can be put forwsubstitutional oxygen at carbon site (O<sub>C</sub>) inard.substitutional oxygen at carbon site (O<sub>C</sub>) in

Method

Convergency Tests

Energy Cut-off

Ecut (eV)FFT gridEtotal (eV)ΔE (eV)
35058x58x64-542.46690454+0.0000
40062x62x68-542.40930972+0.0576
45066x66x72-542.32762253+0.1393
50068x68x76-542.22542586+0.2415
55072x72x80-542.24431883+0.2223
60074x74x84-542.25605694+0.2108
Ecut (eV)FFT gridEtotal (eV)ΔE (eV)
35058x58x64-538.17052187+0.0000
40062x62x68-538.07438469+0.0961
45066x66x72-537.98184250+0.1887
50068x68x76-537.87645909+0.2941
55072x72x80-537.89586716+0.2757
60074x74x84-537.90935670+0.2612
Ecut (eV)FFT gridEtotal (eV)ΔE (eV)
35058x58x64-541.99735253+0.0000
40062x62x68-541.90696915+0.0904
45066x66x72-541.81475011+0.1826
50068x68x76-541.71212207+0.2852
55072x72x80-541.72749107+0.2699
60074x74x84-541.74452341+0.2528
Ecut (eV)FFT gridΔEform (eV)
35058x58x64-3.7074
40062x62x68-3.7009
45066x66x72-3.6994
50068x68x76-3.6952
55072x72x80-3.6995
60074x74x84-3.6962

Bibliography

[1]
A. Mattausch, Ab-Initio Theory of Point Defects and Defect Complexes in SiC, University of Erlangen-Nuremberg, 2005.
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VASP: Band-structure calculation Tutorial

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In this tutorial, I will describe how to calculate the Band Structure using VASP, taking Si as an example. In the calculation, I chose a FCC primitive unit cell with 2 atoms in the unit cell. But first lets take some considerations regarding Accurate Band Structure Calculations.

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Mount remote file systems over SSH

The following example is for mounting your blafis home folder as a ‘private’ media, not accessible to other local users.

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E-MRS 2014 Fall Meeting

Overall considerations regarding the talks from Symposium K (Computer Modelling …):

  • Not many “pure” DFT works, mainly there were discussed Monte Carlo, Molecular Dynamics and DFT-“something” works.
  • Many works were Van der Waals interaction plays important role (DFT-vdW).
  • In the few DFT-U works presented, the U-value convergence was not discussed or was fitted for one structure and “reused” in several different structures.
  • Quantum Espresso widely used!
  • Interesting talk about DFT used in “curved” space.

Regarding my talk:

  • I was unsuccessfully to gain many “followers” mainly because none of the attendees knew AIMPRO and were septic regarding the results.
  • Few questions/comments were made:
    1. They were intriguing about how much the wavefunction was delocalized to the neighboring NC;
    2. They were septic about the practicability of making experimentally films with the properties of these NC-SL.
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Metalic Silicides Interfaces

[toc][mathjax]

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Doping Si NCs with TCNQ and F2-TCNQ

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Doping Si NCs with Li and Na

Workplan

  • (done) Partir da bulk-superlattice e dopar com Na e Li nos sites T e O
  • (done) Criar base da densidade de carga tipo 2 para o Na e Li

A supercelula do bulk está em:
blafis:/home/coutinho/research/f4-tcnq/fcc-si317/bulk/res.fcc-si317h172

  • (done) Calculate Na$^{(0/+)}$ and Li$^{(0/+)}$ in a Si-NC in a box to understand the effect of the superlattice
  • Produce figures with levels of Li, Na and TCNQ without charge correction;
  • Calculate migration barrier of Li$^{(0)}$ and Na$^{(0)}$ in the NC core (9 NEB images);
  • Calculate absorption barrier of Li$^{(0)}$ and Na$^{(0)}$ into the NC (9 NEB images);
  • Calculate migration barrier of Li$^{(+)}$ and Na$^{(+)}$ in the NC core (9 NEB images);
  • Calculate absorption barrier of Li$^{(+)}$ and Na$^{(+)}$ into the NC (9 NEB images);

Basis

parameter{ecut=200}
species{pot=11-Na-9, wfbas=atom-pppp, cdbas=atom-2-5xs, normalize}
species{pot=3-Li-3,  wfbas=atom-pppp, cdbas=atom-2-5xs, normalize}

Energies and Levels

==============================================================================================================================
str            E(0)            E(+)            E_rel       E(0)-E(+)   E(-)-E(0)   E(0)-E*(+)  E*(-)-E(0)
               [Hr]            [Hr]            [eV]        [eV]        [eV]        [eV]        [eV]
------------------------------------------------------------------------------------------------------------------------------
fcc-bulk      -1353.86075     -1353.92476                  1.74180     3.60905     1.61979     3.73106
------------------------------------------------------------------------------------------------------------------------------
Na - fcc
   Th         -1401.44947     -1401.58313      0.02503     3.63707                 3.51506
   Oh         -1401.42752     -1401.56457      0.62232     3.72932                 3.60731
   [111]      -1401.45039     -1401.58465      0.00000     3.65340                 3.53139
   c-Th       -1401.39612     -1401.52659      1.47676     3.55027                 3.42826
------------------------------------------------------------------------------------------------------------------------------
Li - fcc
   Th         -1361.17023     -1361.29105      0.50178     3.28768                 3.16567
   Oh         -1361.14869     -1361.26373      1.08791     3.13040                 3.00839
   [111]      -1361.16714     -1361.29867      0.58586     3.57911                 3.45710
   c-Th       -1361.18867     -1361.31927      0.00000     3.55381                 3.43180
==============================================================================================================================
fcc-bulk   E(-)=-1353.72812 Hr

Starred values include a Madelung correction (see F4-TCNQ molecules in Si-NC superlattices).

Increasing superlattice parameter

==============================================================================================================================
str            E(0)            E(+)            E_rel       E(0)-E(+)   E(-)-E(0)   E(0)-E*(+)  E*(-)-E(0)
               [Hr]            [Hr]            [eV]        [eV]        [eV]        [eV]        [eV]
------------------------------------------------------------------------------------------------------------------------------
fcc80-bulk    -1353.67707     -1353.60655                 -1.91895     0.14585    -2.09223     0.31914
------------------------------------------------------------------------------------------------------------------------------
Na - fcc80
   Th         -1401.23826     -1401.24548      0.85770     0.19647                 0.02319
   Oh         -1401.23834     -1401.24591      0.85553     0.20599                 0.03271
   [111]      -1401.26978     -1401.27374      0.00000     0.10776                -0.06552
   c-Th       -1401.21868     -1401.21753      1.39050    −0.03129                -0.20457
------------------------------------------------------------------------------------------------------------------------------
Li - fcc80
   Th         -1360.95887     -1360.92842      1.22179    −0.82859                -1.00187
   Oh         -1360.95934     -1360.92641      1.20900    −0.89607                -1.06935
   [111]      -1360.97748     -1360.97515      0.71539    −0.06340                -0.23668
   c-Th       -1361.00377     -1361.00300      0.00000    −0.02095                -0.19423
==============================================================================================================================
fcc80-bulk E(-)=-1353.67171

As F4-TCNQ molecules in Si-NC superlattices, we applied a Madelung correction (starred values), using the following parameters. The super-lattice constant is now $a_0=4.2334~~\text{nm}$ (80.00 a.u.) and the nanocrystal’s volume is maintained, so the new estimation for the macroscopic dielectric constant is $\epsilon_{SL}=4.50$. For a fcc lattice we have $E_M(q=1)=0.17328~\text{eV}$.
No structural relaxation was performed in these cases.

Results from the previous tables are pictured below.

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Levels (0/+) of Na (black) and Li (orange) with Madelung corrections for several structures (solid lines) and the effect of increasing superlattice constant (dashed lines).

Ion diffusion

Absorption barriers

A work in progress …
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Migration barriers

A work in progress …
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Dielectric constant calculation of Si-NC

Si-NC in Vacuum

An atom-centered Si-NC (Si211H140) was placed in the corner of a simple cubic box (80 a.u.). Self-consistent electron relaxation cycle was performed to find the minimized total energy and then the process was repeated after adding a point charge in the center of the box.

Dump files of electron density and potencials are no longer available in blafis due to its large size (~40GB per file). They are still available upon request.

After fiddling with the code, I got the following result using these conditions

SiNC.dump
SiNCpc.dump
1.0                           ! Localized charge [...,-2,-1,+1,+2,...]
0.0 0.0 0.0                   ! Averaging stencil diameters along X, Y and Z [Bohr]
1                             ! nspin [1 - Spin average, 2 - Spin polarized]
450 450 450                   ! Grid [nga, ngb, ngc]
 80.000     0.000     0.000   ! a1 lattice vector [Bohr]
  0.000    80.000     0.000   ! a2 lattice vector [Bohr]
  0.000     0.000    80.000   ! a3 lattice vector [Bohr]
0.0 0.0 0.0                   ! Center of symmetry sphere/slab (z-coord) [Bohr]
20.000                        ! Cut-off radius/half-width sphere/slab [Bohr]
200                           ! Number of bins for plot

Note that the stencil diameter is zero, ie, no local averaging is carried out. The source code can be found at blafis:/home/coutinho/aimpro/screening/devel/screen.f90

Stencil diameter dependency

Now we need to make a few tests, namely, increase the stencil diameter and produce (1) a plot with local rho functions vs radius for several stencil diameters, and (2) a plot with cumulative rho functions vs radius for several stencil diameters. Use stencil diameters of D = (0, 1, 5, 10, 20) atomic units. Mind that the stencil diameters are directly set at the input files (and not its radii as in some input file comments suggest).
Results are pictured below.
Calculations with stencil diameters of D= (30, 40) were abandoned due to high computational costs.

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Size effects

Tests with smaller and larger SI-NCs are in progress …

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Surface modification

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Data available in the following files:
blafis:~tiago/queue/sinc/radial.Si377.*.norm.dat.d0 (normalized)
blafis:~tiago/queue/sinc/nc-sc.Si377.H196/scr/radial.dat.d0 (un-normalized charge density for -H)
blafis:~tiago/queue/sinc/nc-sc.Si377.F196/scr/radial.dat.d0 (un-normalized charge density for -F)

The same atom-centered Si-NC passivated with hydrogen was also passivated with Fluorine (Si211F140) and -OH (Si211O100H80) and placed in the same simple cubic box (80 a.u.). After structural relaxation, self-consistent electron relaxation cycle was performed to find the minimized total energy and then the process was repeated after adding a point charge in the center of the box. The following plots sumarize the obtained results.

H passivation

F passivation

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OH passivation

Summary

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Medium (host) effects

Calculations for SiNC embeded in diferent mediums are on hold!

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Si-NC superlattices

I. Optimization of the Si-NC superlattice

We produced superlattices of atom-centered H-terminated Si-NCs. We performed a self-consistent lattice/atom/electron relaxation cycle to find the Si-NC superlattices that minimized the total energy. Two situations were study, stacked and connected NCs arranjed in two superlattices, simple cubic (sc) and face-centered cubic (fcc) superlattices.

          | stacked             | connected           |
diameter  | fcc      | sc       | fcc      | sc       |
-------------------------------------------------------
 ~ 2 nm   | 63.3929    42.0278    52.1310    40.4852

*all values in a.u.

Soon, I’ll be adding the other NCs sizes.

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ABINIT: Basic Tutorial

The following tutorial is based on the binaries of version 6.8.2 found in
blafis:/home/tiago/bin/abinit-6.8.2-ser for the serial version and
blafis:/home/tiago/bin/abinit-6.8.2-mpi for parallel runs.

Typical job.files structure:

job.in         # main output file
job.out # main output file
job.xi # root input file
job.xo # root output file
job.x # root temporary files
pseudo_1.hgh # pseudopotencial file of species 1
pseudo_2.hgh # pseudopotencial file of species 2, and so on ... ...