Among the common vacancy-related point defects in silicon, the E center is one of the most prominent due to its degrading effect in silicon-based technology. Even though it has been the subject of extensive experimental and theoretical studies, a comprehensive theoretical model capable of reproducing the experimental evidence for all three dopants (P, As, and Sb) is still missing. Guided by a Jahn-Teller model, we are able to reproduce the absorption bands and the transition probability between equivalent geometries of the defect at low temperatures by including many-body-perturbation corrections based on the GW approximation on top of the density functional theory. At higher temperatures, vacancies become mobile centers, enabling the reorientation of the whole defect and contributing to the dopant diffusion. The underlying mechanisms of the vacancy-mediated dopant diffusion are revisited, characterizing the activation energies of such technologically relevant processes and obtaining quantitative results in good agreement with experiment.

1.
P.
Pichler
,
Intrinsic Point Defects, Impurities, and Their Diffusion in Silicon
(
Springer Science & Business Media
,
2012
), Chap. 5.
2.
I. H.
Hopkins
and
G. R.
Hopkinson
, “
Further measurements of random telegraph signals in proton irradiated CCDs
,”
IEEE Trans. Nucl. Sci.
42
,
2074
2081
(
1995
).
3.
D.
Smith
,
A.
Holland
, and
I.
Hutchinson
, “
Random telegraph signals in charge coupled devices
,”
Nucl. Instrum. Methods Phys. Res. A
530
,
521
535
(
2004
).
4.
T.
Nuns
,
G.
Quadri
,
J.
David
, and
O.
Gilard
, “
Annealing of proton-induced random telegraph signal in CCDs
,”
IEEE Trans. Nucl. Sci.
54
,
1120
1128
(
2007
).
5.
C.
Virmontois
,
V.
Goiffon
,
P.
Magnan
,
O.
Saint-Pe
,
S.
Girard
,
S.
Petit
,
G.
Rolland
, and
A.
Bardoux
, “
Total ionizing dose versus displacement damage dose induced dark current random telegraph signals in cmos image sensors
,”
IEEE Trans. Nucl. Sci.
58
,
3085
3094
(
2011
).
6.
A.
Ural
,
P. B.
Griffin
, and
J. D.
Plummer
, “
Fractional contributions of microscopic diffusion mechanisms for common dopants and self-diffusion in silicon
,”
J. Appl. Phys.
85
,
6440
6446
(
1999
).
7.
G. D.
Watkins
and
J. W.
Corbett
, “
Defects in irradiated silicon: Electron paramagnetic resonance and electron-nuclear double resonance of the Si-E center
,”
Phys. Rev.
134
,
A1359
A1377
(
1964
).
8.
E. L.
Elkin
and
G. D.
Watkins
, “
Defects in irradiated silicon: Electron paramagnetic resonance and electron-nuclear double resonance of the arsenic- and antimony-vacancy pairs
,”
Phys. Rev.
174
,
881
897
(
1968
).
9.
G. D.
Watkins
, “
Optical properties of group-V atom-vacancy pairs in silicon
,”
Radiat. Eff. Defects Solids
111-112
,
487
500
(
1989
).
10.
G.
Watkins
, “
Understanding the Jahn–Teller distortions for the divacancy and the vacancy–group-V-atom pair in silicon
,”
Phys. B: Condens. Matter
376-377
,
50
53
(
2006
).
11.
R.
Virkkunen
and
R.
Nieminen
, “
First-principles study of the phosphorous-vacancy pair in silicon
,”
Comput. Mater. Sci.
1
,
351
357
(
1993
).
12.
G.
Pfanner
,
C.
Freysoldt
,
J.
Neugebauer
, and
U.
Gerstmann
, “
Ab initio EPR parameters for dangling-bond defect complexes in silicon: Effect of jahn-teller distortion
,”
Phys. Rev. B
85
,
195202
(
2012
).
13.
M. G.
Ganchenkova
,
A. Y.
Kuznetsov
, and
R. M.
Nieminen
, “
Electronic structure of the phosphorus-vacancy complex in silicon: A resonant-bond model
,”
Phys. Rev. B
70
,
115204
(
2004
).
14.
A. N.
Larsen
,
A.
Mesli
,
K.
Bonde Nielsen
,
H. K.
Nielsen
,
L.
Dobaczewski
,
J.
Adey
,
R.
Jones
,
D. W.
Palmer
,
P. R.
Briddon
, and
S.
Öberg
, “
e center in silicon has a donor level in the band gap
,”
Phys. Rev. Lett.
97
,
106402
(
2006
).
15.
M.
Ganchenkova
,
L.
Oikkonen
,
V.
Borodin
,
S.
Nicolaysen
, and
R.
Nieminen
, “
Vacancies and E-centers in silicon as multi-symmetry defects
,”
Mater. Sci. Eng. B
159–160
,
107
111
(
2009
). eMRS 2008 Spring Conference Symposium K: Advanced Silicon Materials Research for Electronic and Photovoltaic Applications.
16.
S.
Öğüt
and
J. R.
Chelikowsky
, “
Charge state dependent Jahn-Teller distortions of the E-center defect in crystalline Si
,”
Phys. Rev. Lett.
91
,
235503
(
2003
).
17.
G.
Henkelman
,
B. P.
Uberuaga
, and
H.
Jónsson
, “
A climbing image nudged elastic band method for finding saddle points and minimum energy paths
,”
J. Chem. Phys.
113
,
9901
9904
(
2000
).
18.
J. S.
Nelson
,
P. A.
Schultz
, and
A. F.
Wright
, “
Valence and atomic size dependent exchange barriers in vacancy-mediated dopant diffusion
,”
Appl. Phys. Lett.
73
,
247
249
(
1998
).
19.
X.
Gonze
,
F.
Jollet
,
F.
Abreu Araujo
,
D.
Adams
,
B.
Amadon
,
T.
Applencourt
,
C.
Audouze
,
J.-M.
Beuken
,
J.
Bieder
,
A.
Bokhanchuk
,
E.
Bousquet
,
F.
Bruneval
,
D.
Caliste
,
M.
Côté
,
F.
Dahm
,
F.
Da Pieve
,
M.
Delaveau
,
M.
Di Gennaro
,
B.
Dorado
,
C.
Espejo
,
G.
Geneste
,
L.
Genovese
,
A.
Gerossier
,
M.
Giantomassi
,
Y.
Gillet
,
D.
Hamann
,
L.
He
,
G.
Jomard
,
J.
Laflamme Janssen
,
S.
Le Roux
,
A.
Levitt
,
A.
Lherbier
,
F.
Liu
,
I.
Lukačevié
,
A.
Martin
,
C.
Martins
,
M.
Oliveira
,
S.
Poncé
,
Y.
Pouillon
,
T.
Rangel
,
G.-M.
Rignanese
,
A.
Romero
,
B.
Rousseau
,
O.
Rubel
,
A.
Shukri
,
M.
Stankovski
,
M.
Torrent
,
M.
Van Setten
,
B.
Van Troeye
,
M.
Verstraete
,
D.
Waroquiers
,
J.
Wiktor
,
B.
Xu
,
A.
Zhou
, and
J.
Zwanziger
, “
Recent developments in the ABINIT software package
,”
Comput. Phys. Commun.
205
,
106
131
(
2016
).
20.
D. R.
Hamann
, “
Optimized norm-conserving Vanderbilt pseudopotentials
,”
Phys. Rev. B
88
,
085117
(
2013
).
21.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
, “
Generalized gradient approximation made simple
,”
Phys. Rev. Lett.
77
,
3865
3868
(
1996
).
22.
G.
Makov
and
M. C.
Payne
, “
Periodic boundary conditions in ab initio calculations
,”
Phys. Rev. B
51
,
4014
4022
(
1995
).
23.
A.
Kokalj
, “
XCrySDen–a new program for displaying crystalline structures and electron densities
,”
J. Mol. Graph. Model.
17
,
176
179
(
1999
).
24.
F.
Bruneval
,
N.
Vast
, and
L.
Reining
, “
Effect of self-consistency on quasiparticles in solids
,”
Phys. Rev. B
74
,
045102
(
2006
).
25.
L.
Hedin
, “
New method for calculating the one-particle Green’s function with application to the electron-gas problem
,”
Phys. Rev.
139
,
A796
A823
(
1965
).
26.
L.
Hedin
and
S.
Lundqvist
,
Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids
(
Academic Press
,
1970
), pp.
1
181
.
27.
P.
Rinke
,
A.
Janotti
,
M.
Scheffler
, and
C. G.
Van de Walle
, “
Defect formation energies without the band-gap problem: Combining density-functional theory and the GW approach for the silicon self-interstitial
,”
Phys. Rev. Lett.
102
,
026402
(
2009
).
28.
L.
Martin-Samos
,
G.
Roma
,
P.
Rinke
, and
Y.
Limoge
, “
Charged oxygen defects in SiO2: Going beyond local and semilocal approximations to density functional theory
,”
Phys. Rev. Lett.
104
,
075502
(
2010
).
29.
G.
Watkins
, “
An EPR study of the lattice vacancy in silicon
,”
J. Phys. Soc. Jpn.
18
(
Suppl. II
),
22
(
1963
).
30.
X.-Y.
Liu
,
W.
Windl
,
K. M.
Beardmore
, and
M. P.
Masquelier
, “
First-principles study of phosphorus diffusion in silicon: Interstitial- and vacancy-mediated diffusion mechanisms
,”
Appl. Phys. Lett.
82
,
1839
1841
(
2003
).
You do not currently have access to this content.