Amihai Silverman -  Research Notes
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A study of the growth process of nano-diamond films

The role the Hydrogen atoms in the
nano-diamond films growth process

Diamond Sample

Samples of 512 Carbon atoms were simulated to for a structure of a diamond core
surrounded by amorphous Carbon.

The initial samples were [100] cubes of 512 Carbon atoms in a diamond structure.
Below are two different views of the initial samples. Click image for a 3D animations.




Initial Sample

Initial Sample


Below are the calculated Radial Distribution Function (RDF) and Density of States (DOS) for this initial sample (click image for a large view).
The red line in the DOS plot depicts the Fermi level which is set such that the integrated density of states up to this point equals the number of electrons in the system.


diamond.rdf.png
dos_diamond.png

On the next stage, a 216 atoms diamond sample was used to study the H interstitials sites. H atom were inserted into different sites in the diamond sample, the sample was then relaxed using alternatively Steepest Descent algorithm or Conjugate Gradient (CG) algorithm, using the Frauenheim's Tight Binding (FTB) model with cyclic boundary conditions The energy of the different sites interstitials were calculated. Two different interstitials sites  for the H atom were predicted  by the FTB model, the  energies of these sites were calculated.

Two H interstitial sites were observed. The Body-Centered (BC) site and the Tetrahedral (T) Site. The BC site energy was lower that the T site energy. In the BC site the two C atom neighbors of the H atoms are displaced from their site locations, where in the T site the neighboring C atoms are in their site locations.

Below is a close views of the Body-Centered (BC) site. Click image for a 3D animations.

H_in_BC_site.png



BC_site_Diamond.png
Below is a close views of the Tetrahedral (T) site. Click image for a 3D animations.


H_in_T_site.png


T_site_Diamond.png

The calculation of the Density of States (DOS) show that the H interstitial adds states at the band-gap near the Fermi energy level. For comparison, below are plots of the DOS of the following samples:
1. Pure diamond 216 sample
2. The diamond sample with the BC site H
interstitial
3. 
The diamond sample with the T site H interstitial
The Y axis scale was increased in the two latest plots in order to observe the additional states. Note the the DOS of the two different
H interstitials is very similar.
(click image for a large view).

1. Pure diamond 216 sample DOS
dos_xtal_216.png
2. The diamond sample with the BC site H interstitial DOS


dos_H_BC_site.png
3.  The diamond sample with the T site H interstitial DOS



dos_H_T_site.png



Amorphous Carbon

A molecular dynamics algorithm was used.
The Simulation algorithm was a Parrinello-Rahman NPT Molecular Dynamics (MD) with cyclic boundary conditions. The Stillinger-Weber type inter-atomic potentials, improved by Barnard-Russo for tetrahedral Carbon were used for the inter-atomic forces and energy calculations.
On the next stage MD simulations were performed using Frauenheim's Tight Binding (FTB) model, starting rom 1200K and reducing gradualy to zero. Than a Steepest Descent (SD) relaxation algorithm using the Frauenheim's Tight Binding was applied and the sample energy was calculated.





Below is a view of the final amorphous carbon sample. Click image for a 3D animations.
amor_sample.png
Below are the calculated Radial Distribution Function (RDF) and Density of States (DOS) for this amorphous Carbon sample (click image for a large view).
The red line in the DOS plot depicts the Fermi level which is set such that the integrated density of states up to this point equals the number of electrons in the system.



rdf-amor.png
dos_amor_sample.png


On the next stage, H atom interstitials were inserted into different sites in the amorphous carbon sample, the sample was then relaxed using a Steepest Descent algorithm and the energy of the different sites interstitials were calculated. The average over all these sites was calculated as the average energy of an H atom interstitial in an amorphous carbon.

Two kind of sites for the H atoms in the amorphous Carbon were obserevd. Below are views of a portions of different simulated sample of an
H atom in the amorphous carbon with the two kinds of sites. Click image for a 3D animations.


H1_in_amor_C.png
H2_in_amor_C.png

From these views we learn the followings:
1. The H atoms minimum energy location is in the largest cavity in its neighborhood.
2. Two different sites are observed:
  A site where the H atoms is connected to one Carbon atom. This site is similar in its characters to the
Tetrahedral (T) site in a diamond.
 
A site where the H atoms is connected to two Carbon atoms. This site is similar in its characters to the Body-Centered (BC) site in a diamond.


Mixed Sample

A molecular dynamics algorithm was used.
The Simulation algorithm was a Parrinello-Rahman NPT Molecular Dynamics with cyclic boundary conditions. The Stillinger-Weber type inter-atomic potentials, improved by Barnard-Russo for tetrahedral Carbon were used for the inter-atomic forces and energy calculations.

The 512 Carbon atom sample was simulated where 150 atoms in the center of the sample were pinned. Pinned means that these atoms were not allowed to move during the simulation. Cyclic boundary conditions were applied to all the boundaries of the sample.
At the first stage, the sample was gradually heated until a total disorder in the active atoms was observed. Then the sample was
gradually cooled so the volume could reduce. At the end of the process, a long simulation at  a temperature of 300K was run to verify that the sample is stable. Samples which didn't have enough disorder collapsed in this stage back to diamond crystals with local defects. Samples with enough disorder didn't change after a long time of run in 300K, the volume decreased to stabilization and the disordered atoms remained in a stable amorphous phase.

Many such attempt were done until a stable sample was formed.
The Radial Distribution Function (RDF) of the active atoms was calculated to verify that these atoms are in the amorphous structural phase.

Simulations Results

Below are two different views of the final sample. Click image for a 3D animations.


fin_sample1
fin_sample2



Below are plots of the
Radial Distribution Function (RDF) and Density Of States (DOS) of the pinned crystalline atoms, and of the active atoms (click image for a large view).


              CrystallineAtoms             
                 Active Atoms               
rdf-final-frozen1_atoms-plot.png
C_final_active_rdf.png
dos_fin_frozen.png
dos_fin_active.png





On the next stage, an Orthogonal Tight Binding (TB) Molecular Dynamic (MD) algorithm was applied to
all the atoms in the sample. The sample was relaxed in a room temperature T=300 for 50fs, and than a static relaxation Steepest Descent algorithm was applied using the Orthogonal tight binding model to relax the atoms to their energy minima spacial locations.
After the relaxation, the sample was examined, the Radial Distribution Function (RDF) and electronic Density Of States (DOS) were calculated.

Below are plots of the RDF and DOS of the core atoms and the amorphous atoms (click image for a large view). The core atoms are the atoms which were pinned in the sample formations process, but now they were active as a part of the sample MD simulations and static relaxation.  The amorphous atoms are the other atoms which were active in the formations process.
The DOS plot of the
core atoms is an average of the local DOS Orthogonal Tight Binding calculation of all core atoms, where the DOS plot of the amorphous atoms is an average of the local DOS results of all the other atoms.


Core Atoms Amorphous Atoms
rdf-core1.png rdf-amor2.png
dos_Wnew2_core.png
dos_Wnew2_amor.png

Below is the average DOS of all the atoms in the sample. Note that it is very close to the amorphous atoms average DOS plotted above.

dos_fin.png


As can be observed from the RDF plots, the amorphous layer remained amorphous, where the core inside atoms are now strained, therefore the widening of the atomic location lines. The crystalline RDF pattern is  preserved, no lines is absent, therefore we deduce that the crystalline core inside the sample remains crystalline.



Observing the sample form, one can see that the core atoms are still ordered, which means that they were not changed their form into amorphous structure, but rather distorted. See the figures of this sample below
(click image for a large view).


Wnew2-2.png Wnew2-3.png



Experimental NEXAFS versus Calulated Density of States

Below
are plots of the simulated samples DOS calculation versus experiment results of Near Edge X-ray Absorption Fine Structure (NEXAFS) which were performed on a Chemical Vapor Deposition (CVD) diamond film. The NEXAFS experiment was done on CVD diamond film that was amorphized using high dose Ion Implantation (Xe+, 5E15 ions/cm2).

The first plot shows the DOS calculation of a crystalline diamond sample (red line) versus NEXAFS results for a diamond film (blue line). The plot depicts the DOS above the Fermi level.


diamond_dos_nexafs.png


The second plot shows the DOS of 512 atoms amorphous carbon simulated sample versus EXAFS results of CVD amorphous carbon films.




amorph_dos_vs_nexafs.png
30 hydrogen atoms were inserted into interstitial sites of a 512 atoms a-C sample. After a relaxation using the Tight Binding Model, the local DOS of the hydrogen atoms was calculated for each atom separately.
This procedure was done 4 times for 4 different a-C samples with
30 hydrogen atoms in interstitial sites. The average local DOS of all the hydrogen atoms was calculated and plotted in the figure below (red line) versus NEXAFS photo desorption of the H+ in polycrystalline hydrogenated diamond film.



amor_H+_dos_nexafs.png


Below is a figure of one such sample. The red circles depict the hydrogen atoms.

amor_H+_dos_nexafs_sample.png

H Interstitial

On the next stage, a single H atom was inserted to the sample.
The previous sample of 150 crystalline pinned atoms are surrounded by amorphous atoms was relaxed to its local minimum energy with a Conjugate Gradient
(CG) relaxation algorithm using the Frauenheim's Tight Binding (FTB) model with cyclic boundary conditions, while the 150 crystalline core atoms remain pinned. The energy of this sample was calculated (we denote it by Es).
H atoms were inserted to different site locations of this sample. For each sample a CG relaxation algorithm using the FTB model with cyclic boundary conditions was applied. The Energy of this sample was calculated (we denote it by Es_h).
For a reference,
H atoms were inserted to different site locations in a pure 512 atoms diamond crystalline sample. A CG relaxation algorithm using the FTB model with cyclic boundary conditions was applied to each such sample and the average energy of these sample was calculated (we denote Ex_h). The energy of the pure diamond crystalline sample is denoted by Ex. The difference Ex_h - Ex is the energy of an H atom interstitial in a diamond crystal.
(In the previous session we learned that since the crystalline atoms are at a minority in the sample, than the amorphous disorder diffuses into the crystalline core. Keeping the core crystalline atoms pined simulates a sample with a larger crystalline core.)

Below is a plot of the energy difference Es_h - Es for various H interstitial sites. The plot X axis is the radial distance of the H atom interstitial from the interface between the crystaline and amorphous regions, where the interface is in X=0.
On the left hand side of the plot, points with the value of
Ex_h - Eof the lowest H interstitial energy in a diamond were added. On the right hand side of the plot, points with the value of Ex_h - Ex of the average H interstitial energy in an amorphous carbon were added. The red curved line depicts the calculations of a spline curve.
We learn from the plot followings:
1. The H interstitial reduces the sample energy.
2. In the amorphous region, the
H interstitial energy reduction is 50% more than the H interstitial energy reduction in a crystalline sample.
3. The interface creates a barrier of 3-4eV for the diffusion of the H atoms.
4. A potential well is observed in the interface between the interface and the diamond regions, as well as between the interface and the amorphous carbon region.
The observed major reduction in the
H interstitial energy between the diamond and amorphous carbon is a driven force for H atoms diffusion from the crystalline region to the and amorphous region.


energy.1-H-pinned.png



Below are 2 views of the a final sample with an H atom interstitial in yellow (click image for a large view).




Sample_with_H_2.png
Sample_with_H_1.png



H Atoms Dynamics

In the following animations,
a Molecular Dynamic (MD) algorithm using the Frauenheim's Tight Binding (FTB) model was applied. One H atom was inserted in an interstitial near the center of the sample. The crystalline atoms were pinned during the Md simulations in order to simulate a sample with a larger crystalline core.
(Click the link to start the animation).

Animation of an H atom diffusion at 300K

Animation of an H atom diffusion at 800K  (note in this simulation that the H atom jumps from one side of the sample to the other side because of the cyclic boundary conditions of these two boundaries).


From these animations we observe the followings:
1. The H atom diffusion is extreamly fast. The time interval of one whole simulation is 200 femto seconds (10-15sec).
2. As was observed in the H interstitial energy plot (above) the H atom thends to diffuse from the
crystalline region to the amorphous region.
3. During the diffusion, H atom experience an energy barier the interface between the crystalline and the amorphous regions. The H atom moves forward and backward near the interface, and after some attempts, the H atom finds a site with a lower barrier and diffuses to the amorphous region.

Following is an animation of 5 H atoms in the same sample. The H atoms start at the crystalline region, and only one pass the interface into the amorphous region, while the other 4 H atoms are trapped beyond the interface barrier.
Animation of 5H atom diffusion
Type here to view this sample at the end of the simulation from a different angles.

Here is an animation of 36 H atoms located at interstitial sites in the crystalline region near the interface. Than during MD at 800K where 50 atoms at the core of the sample are pinned they diffuse out to the amorphous region. Type the image to start the animation.
init_sample_icon.png

Below is the sample at the end of the animation. Type the image to view
3D animations of this sample.
final_sample_icon.png

The next plot show the density of the H atoms along the radial distance, starting from the center of the sample where the structure is crystalline (the left hand side of the plot) to the surface of the sample in the amorphous regions (the right hand side of the plot). The red histogram shows the H atoms at the beginning of the simulations, where the green histogram shows the H atoms at the end of the simulations.
The simulations started where all the H atoms were in the crystalline region near the interface. At the end of the simulation the H atoms diffused to amorphous regions and concentrated near the crystalline-amorphous region. 




h_atoms_histogram.png



The initial 64 atoms diamond sample
diamond 64 atoms

A diamond sample with 15 at.% hydrogen atoms
CH-9

A diamond sample with 25 at.% hydrogen atoms

CH-15




A diamond sample with 50 at.% hydrogen atoms

many H in diamons



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Copyright Notice
All rights reserved. The material in this page including the plots, pictures and animations may not be published, broadcast, rewritten or redistributed in a whole or part in any medium without a written permission. Contact: "amihai" at "technion.ac.il"


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NEXAFS Results: Structural, electrical, and optical properties of diamondlike carbon films deposited by dc magnetron sputtering, Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films -- November 2003 -- Volume 21, Issue 6, pp. L23-L27