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.