Hydrogen Related Defects (results)
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Transcript of Hydrogen Related Defects (results)
04/12/23 1GADEST 2009
Ab initio Study of Hydrogen Related Defects in Hydrogen Implanted Crystalline Silicon
Stability and Migration
Liviu BÎLTEANU1, Jean-Paul CROCOMBETTE1, Aurélie TAUZIN2
1CEA DEN/DMN/SRMP, Saclay, 91191 Gif-sur-Yvette, France.2CEA LETI/DIHS/LTFC, 17, avenue des Martyrs, 38000 Grenoble, France.
04/12/23 2GADEST 2009
Outline
1. Introduction – hydrogen behavior in silicon
2. Calculation Details
3. Hydrogen Related Defects in Silicon
4. Atomic and Molecular Defects Stability
5. Migration of Hydrogen Atoms and Molecules
6. Migration of Self-defects (vacancies and interstitials)
7. Hydrogenated Vacancies
8. Mechanisms leading to VHn type defects
9. Hydrogenated Interstitials
10. Conclusions
04/12/23 3GADEST 2009
Accumulation of hydrogen into platelets
•Context: Accumulation of hydrogen into 2D extended defects (platelets) when silicon is irradiated with highly energetic protons and then the sample is thermally annealed.
•Approach: modelization of hydrogen accumulation via elementary processes involving hydrogen related defects (see the next).
•Method: ab initio atomic scale calculations within the Density Functional Theory (DFT).
04/12/23 4GADEST 2009
CALCULATION DETAILS
DFT calculations as implemented in SIESTA.Calculation parameters: •216 Si atoms boxes that is 333 supercell +1-2 H atoms; •8 k-points that is 222 in a Monkhorst-Pack scheme;•generalized gradient approximation (GGA) of the the
exchange-correlation functionals in PBE implementation;•Mesh Cut-off 150 Ry;•Relaxation included (0.04 eV/Å)
04/12/23 5GADEST 2009
Hydrogen Related Defects
•hydrogen interstitials: – atomic Hq[X] and
– molecular H2[X-Y], whereas X, Y are label of
various sites;•self-defects:
– vacancies Vq and – interstitials Iq ;
•hydrogenated defects:
– hydrogenated vacancies (VHn)q and
– hydrogenated interstitials IHn.
04/12/23 6GADEST 2009
Atomic and Molecular Interstitials
Atomic H on different sites in [111] direction
Ato
mic
H in
ters
tital
sB
i-ato
mic
str
uctu
res
04/12/23 7GADEST 2009
Stability of Atomic and Molecular Interstitials
04/12/23 8GADEST 2009
Charged Atomic Hydrogen Diagram
Formation energy (with respect to free H atom) in function of Fermi Level for ALL sites and charge states.
Negative U – 0.32 eV
exp. 0.36 eV [1]
[1] N. M. Johnson et al., Phys. Rev. Lett. 73, 130 (1994).
NEGATIVE U - EFFECT
2H H+ + H- + 0.32 eV
2H → H+ + H-
04/12/23 9GADEST 2009
Quantitative Evaluation of H±[X] concentration
H+(BC) and H-(AB) are dominant.
Si bulk of volume V0 = 5.001022 cm-3
C0 Hydrogen (at %)
µH chemical potential of hydrogen
Eiq is the form. energy of Hq[X] calculated by DFT;
q the charge of hydrogen (q = 0, 1);
kB Boltzmann’s constant (0.861734310-4 JK-1)
T la temperature (in K);
Number of particles
exp Fq
Hq ii
B
EA
qN
k Tmeæ ö+ - ÷ç= - ÷ç ÷è ø
Mass Conservation
0,
qi
i q
c C=åCharge Conservation
0,
qi
i q
qN V n= Då
0
,
qq ii q
ii q
Nc
NC=
å
Atomic Fractions of Considered Species
04/12/23 10GADEST 2009
Migration calculations drag method •Two initial states represented by I and F containing the 3D
positions of all atoms in the calculation box.•The direct (hyper)line IF is sampled and the system is placed
in various intermediary points on this (hyper)line Rλ = I + λF with λ [0, 1]. Usually 10 – 25 points are used.
•Then the system is allowed to relax in the (hyper)plan perpendicular on the (hyper)line in the respective intermediary points.
•The collection of energy values of the system relaxed in this way describes the migration barrier.
Rλ
I F
04/12/23 11GADEST 2009
Migration of H±/H2
Migration of H± between two equiv. sites
Migration of H+ between second NN sites
Migration of H2 molecule between two T first NN sites
Atomic hydrogen migration barrier is charge independent values 0.46 eV compared with exp. 0.48 eV [Van Wieringen A., and Warmoltz N., Physica 22, 849 (1956)]. the migration barrier (of H+) between two second NN BC sites is decomposed into two elementary barriers.
Molecular hydrogen migration barrier is 5 times higher (~2.5 eV), hence H2 is immobile when compared to H±)
04/12/23 12GADEST 2009
Migration and accumulation of intrinsic defects
0,0 0,1 0,2 0,3 0,4-0,05
0,00
0,05
0,10
0,15
0,20
Reaction Coordinate
En
erg
y [
eV
]
- In Si self-defects are rapidly migration species- Vacancies tend to accumulate.- The migration and accumulation barriers are less than the H± migration barrier vacancies diffuse and accumulate quicker.
Wright and Wixom, J. Appl. Phys. 106 (2008)
Migration of silicon self-interstitial
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00,00
0,02
0,04
0,06
0,08
0,10
0,12
0,14
0,16
4V → V + 3V
Reaction Coordinate
En
erg
y [
eV
]
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0-0,50
0,00
0,50
1,00
1,50
2,00
2V → V + V
Reaction Coordinate
En
erg
y [e
V]
04/12/23 13GADEST 2009
Hydrogenated Vacancies
q = -2 q = -1 q = 0 q = +1 q = +2
04/12/23 14GADEST 2009
Possible elementary process
1.20 1.4131.82 1.652
2 41.13 2.233
H VHV H VH H VH VH
H VH
- -+ +- -- + - +
- -- -
ì üï ï+ ¾¾¾¾® ¾¾¾¾®ï ïï ï+ ¾¾¾¾® + ¾¾¾¾® ®í ýï ï+ ¾¾¾¾® ¾¾¾¾®ï ïï ïî þ
1.92 1.432 22 2 3V H VH H VH- -- - + -+ ¾¾¾¾® + ¾¾¾¾®
Elementary processes involving H atoms
Reaching the most stable VHn type structure, that is VH4
Elementary processes involving also H2 molecules
04/12/23 15GADEST 2009
Decomposition of VHn type structures
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
Reaction Coordinate
En
erg
yV2- + H+ → VH-
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00,00
0,50
1,00
1,50
2,00
2,50
Reaction CoordinateEn
erg
y [
eV
]
VH2 → VH- + H+
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00,00
0,20
0,40
0,60
0,80
1,00
1,20
1,40
1,60
1,80
2,00
2,20
Reaction Coordinate
Energ
y [
eV
]
VH3+ → VH2
+ H+
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00,00
0,25
0,50
0,75
1,00
1,25
1,50
1,75
2,00
2,25
2,50
2,75
Reaction Coordinate
En
erg
y [
eV
]
VH4 → VH3- + H+
• H+ migrates via a hoping like mechanism.• The interm. barriers are ~0.5 eV or less.• H- does not have any « barrier » to reach VHn defects.
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00,00
0,25
0,50
0,75
1,00
1,25
1,50
1,75
2,00
2,25
2,50
Reaction Coordinate
En
erg
y [
eV
]
VH3- → VH2
2- + H+
04/12/23 16GADEST 2009
Ejection of H2 molecule
•Hydrogen molecule barrier stays unchanged in the presence of a vacancy.
•The migration can be associated to a hoping-like behavior.
•The H2 barrier is ~5 times higher than that of an atomic hydrogen which might explain its lack of mobility.
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,70,00
0,40
0,80
1,20
1,60
2,00
2,40
2,80
3,20
3,60
4,00
Reaction Coordinate
En
erg
y [
eV
]
VH22- → V2- + H2
04/12/23 17GADEST 2009
Hydrogenated Interstitials
•Structures found by Random Structure Search;
•IH2 is the most stable structure.
•Possible mechanism to reach IH2 structure:
Morris et al. PRB 78 (2008)
{I,H}
{I,H2} {I,H2}*
{I,H3} {I,H4}0.77 0.53 0.16
2 22I H I H IH H IH+ - -+ ¾¾¾¾® + ¾¾¾¾® + ¾¾¾¾®
04/12/23 18GADEST 2009
Conclusions
•Hydrogen related defects in silicon have been studied at atomic scale.
•One has identified the main migrating species (atomic hydrogen) that have been revealed to be charged.
•The calculated negative-U effect leading to the formation of charged atomic defects is in perfect agreement with the experimenal values DLTS.
•The migration energy of both H± species is charge independent being almost equal to the experimental value obtained via permeation experiments.
•Several reaction-type mechanisms that can be elementary processes in hydrogen accumulation have been investigated.
•Close to vacancy dominated region, the migration of H+ is done through a hoping-like mechanism, while the H- seems to have no barrier.
•Hydrogen molecule has a ~2.2 eV migration barrier, which indicates that the molecule is highly immobile with respect to the hydrogen atoms, a fact that has been implied previously from the experimental measurements.