A Tale of Two Vacancies
Peter Y. Yu
Department of Physics, University of California
&
Materials Science Division, Lawrence Berkeley
National Laboratory, Berkeley, CA 94720
Acknowledgments: Collaborators are Lei Liu, Wei Cheng,
Zixun Ma and Samuel S. Mao. This work was supported by the
Us Department Of Energy NNSA/NA-22, under Contract No.
De-Ac02-05ch11231
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OUTLINE
• INTRODUCTION
• MOTIVATIONS
• VACANCIES IN GROUP III-NITRIDES
– FERROMAGNETISM DUE TO Ga VACANCIES
– DOPING BY Gd
• VACANCIES IN Cd-CHALCOGENIDES
– CODOPING WITH OXYGEN
– EVIDENCE OF O2 MOLECULES
• CONCLUSIONS
• ACKNOWLEDGMENTS
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INTRODUCTION
• Vacancies are often introduced during
crystal growth at high temperature
• Vacancies are important in determining the
quality and electrical properties of
semiconductors:
– Vacancies allow impurities to diffuse more
easily throughout a crystal
– Vacancies involve dangling bonds and are
electrically active, vacancies can cause selfcompensation
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MOTIVATIONS
• Vacancies are detected mainly by two methods:
High Resolution TEM and Positron Annihilation.
Otherwise they are difficult to detect
• Recent advances in First-Principle Density
Functional Theory (DFT) make it possible to
calculate the properties of vacancies
• Present work attempts to study their role in
– (1) room temperature Ferromagnetism in GaN:Gd
– (2) incorporation of Oxygen into CdTe in the
formation of O2
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STORY 1
How Vacancies Produce Room
Temperature Ferromagnetism In
GaN
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Ferromagnetism in GaN:Gd
Room temperature Ferromagnetism was reported by at least 2
groups in GaN doped with Gd :
“Magnetic, optical and electrical properties of GaN and AlN doped with rareearth element Gd” by S. W. Choi, Y. K. Zhou, S. Emura, X. J. Lee, N. Teraguchi, A.
Suzuki, and H. Asahi (2002-2006):
[Gd]:2-6%
Tc~400K
sample n-type with [e]>5x1019 cm-3.
“Gd-doped GaN: A very dilute ferromagnetic semiconductor with a Curie
temperature above 300 K” by S. Dhar, L. Pérez, O. Brandt, A. Trampert,
and K. H. Ploog (2005-2007)
[Gd]:1016-1019 cm-3
Tc>300K
magnetic moment /Gd~4000mB
magnetic moment/Gd increases with defect concentration since ionimplanted sample has large moment than sample after annealing
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Ferromagnetism in GaN:Gd
Results of Ploog’s Group suggested that
intrinsic defects played an important role in
the Ferromagnetism.The nature and role of
the intrinsic defect are, however, unclear.
Our First-Principle Calculation suggests that:
GaN:Gd is paramagnetic
GaN containing GdGa+VN is also paramagnetic
GaN containing GdGa+VGa is ferromagnetic
Surprisingly GaN containing only VGA is also
ferromagnetic!
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Computation Method
•Use spin-polarized DFT within the Generalized
Gradient Approximation (GGA).
•Electron correlation important for the d and f
electrons of Gd ions are included (approximation
known as GGA+U )
•Use Full-potential Linearized Augmented Plane
Wave (FLAPW) as basis functions for calculating
the electron eigenvalues and functions.
Lei Liu, Peter Y. Yu, Zhixun Ma, and Samuel S. Mao.
Ferromagnetism in GaN:Gd: A Density Functional Theory Study.
Phys. Rev. Lett. 100, 127203 (2008)
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Supercell model:GdGa7N8
Gd atoms are
separated by 3 atom
layers to simulate
long range
interaction between
Gd atoms.
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GaN:Gd is Paramagnetic
f electrons
Band Structure of GaN:Gd: f-electrons in Gd ions are magnetized
but the coupling between the moments is paramagnetic
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GdGa6N8 Supercell containing Gd and VGa
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Ferromagnetism in GaN:Gd
GaN containing GdGa+VGa is ferromagnetic!
Top valence bands are 100% Polarized!
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Ferromagnetism in GaN:Gd
What is the source
of the strong
coupling between
the Gd ions?
Answer: coupling
with the spin of
holes introduced by
Ga vacancies
Spin-resolved DOS of Ga Vacancy in GaN
Pratibha Dev, Yu Xue, and Peihong Zhang. Defect-induced intrinsic
magnetism in wide-gap III-nitrides. Phys. Rev. Lett. 100, 117204 (2008).
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Ferromagnetism in GaN:Gd
How come the Gd magnetic moment is
so large?
(1)Local strain of Gd
ion induces
vacancies in the
vicinity
GdGa6N8
10
0.7
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(2)The magnetic
moment of Gd is
enhanced by the 3
spins of each Ga
vacancy nearby
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Ferromagnetism in GaN:Gd
Summary:
Gd introduces Ga vacancies by producing tensile local
strain
Ga vacancies produce holes
When the hole wave functions are localized enough (as in
case of nitrides) they become spin polarized according to
Hund’s Rule
Coupling between the Gd and hole spins produce a strong
ferromagnetic state.
When the hole or Ga vacancy concentration is much higher
than the Gd concentration the magnetic moment of Gd
appears to be enhanced
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STORY 2
How Cd Vacancies allow
O2 Molecules to be
incorporated into CdTe
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BACKGROUND
• CdTe is an important semiconductor for thin film
solar cells
• Oxygen is a common impurity in the manufacture of
solar cells.
• O replacing Te (OTe) is an isovalent impurity. Since
electronegativity of O>>electronegativity of Te, O will
attract an electron to form O- which is a shallow
acceptor.
• Mass of O<<Mass of Te so vibration of OTe is highly
localized around O. These are called local vibration
mode (LVM).
• LVM are very sharp and, therefore, sensitive probes
of light impurities
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Infrared Absorption Spectra of CdTe:O
(G. Chen, I. Miotkowski, S. Rodriguez, and A. K. Ramdas, Phys. Rev. B 75, 125204
(2007).)
Sample Growth strategies:
CdO to provide oxygen
and Excess Cd to
suppress VCd
Absorption Coefficient (cm-1)
T=5K
Res. = 0.02 cm-1
FWHM = 0.24 cm-1
30

Cd
O
20
Cd
Cd
Cd
10
0
340
344
348
352
356
360
A single sharp line is
observed:
0 = 349.8 cm-1
FWHM = 0.24 cm-1
Selection rule:
1  5
Wave number (cm-1)
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High Frequency Mode when VCd Is Present
Absorption Coefficient (cm-1)
60
In CdTe:O without excess Cd
T=5K
Res. = 0.01 cm-1
FWHM1 = 0.165 cm-1
FWHM2 = 0.137 cm-1
I2 / I1 = 1.7
Chen et al. observe 2 high
frequency modes at :

1 = 1096.78 cm-1;
2 = 1108.35 cm-1.
40
20
At high T 1 and 2
merged into one mode
with frequency:1104cm-1.

OTe-VCd
0
1092
1096
1100
1104
1108
-1
Wave number (cm )
1112
They attributed these 2
modes to vibration of a
complex: OTe-VCd
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Model Proposed by Chen et al.
Te
Te
3
Te
N=1
1
VCd
1
Cd
c
O
1
Cd
2
2
Cd
N=0
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1
E || c
E c
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Dynamic Switching of VCd-O complex
VCd
Wave number (cm-1)
1108


c
1104
Cd
3
Cd

0
100
4
O
0*
( + 2 * ) / 3
1100
Cd
1
2
200
300
Temperature (K)
As T increases Oxygen switches
between sites: 1, 2 , 3 and 4
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Activation Energy for Switching
0
In [ 1 - ( - )T/( - )0 ]
0
-0.2
-2
-0.4
-4
-0.6
-6
-0.8
0.0036
0
0.1
0.2
0.3
1 / T (1 / K)
0.4
( 2   1 ) T  ( 2   1 ) 0 [1  e
 W / kT
0.5
]
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0.004
0.0044
0.0048
1/T
W=42 meV
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MOTIVATION FOR PRESENT WORK
L. Zhang, J. T-Thienprasert, M.-H. Du, D. J. Singh, and S.
Limpijumnong, Phys. Rev. Lett. 102, 209601 (2009)
calculated, from first principle, the frequency of the
OTe-VCd complex and obtained <500 cm-1.
Similar high frequency modes (>1000 cm-1)have also
been observed by Chen et al. in CdSe (G. Chen, J. S.
Bhosale, I. Miotkowski, and A. K. Ramdas, Phys. Rev.
Lett. 101, 195502 (2008)) so this complex is rather
common in Cd chalcogenides.
What is the identity of this complex of O in
CdTe and CdSe? How to explain the dynamic
switching?
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Computational Method
First-Principle density-functional
theory based on the GGA-PBE
potential (J.P. Perdew, K. Burke, and M.
Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) )
Two commercial softwares:
VASP (Vienna ab initio simulation
package ) and MedeA (by Material
Design )
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Tests Of Softwares
CdTe Lattice
Constant (nm)
Our result
Experiment
0.641
0.646
O-O bond length 0.1236 ;
(nm) &
1548.20
stretching mode
frequency (cm-1)
0.1208 ;
1580
Local mode
331.86
frequency of OTe
(cm-1)
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349.8
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New Model of Oxygen-VCd Complex in CdTe
Ball-and-Stick model of the
cell: Cd31Te32O2 containing a
VCd (blue ball) and a O2
molecule (red balls). The
golden and green balls
represent Te and Cd atoms,
respectively.
O-O is oriented along the
[111] axis and is displaced
from the Cd site.
Symmetry of complex is C3v
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Defect Formation Energies in CdTe
Defect
Formation
Energy (our
result) eV
VoCd
2.1
Formation
Energy (Wei, Zhang
and Zunger*) eV
2.30
V-Cd
2.42
V-2Cd
2.69
VCd-O2
1.2
*S. H. Wei, S. B. Zhang, and A. Zunger J. Appl. Phys. 87, 1304
(2000).
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Normal Modes of O2 Molecule in CdTe Vacancy
O-O stretch:1112.5 cm-1
Rocking of the O2 molecule:192.1 cm-1
A1 Modes
Libration Mode at 315.7 cm-1
Rocking of the O2 molecule:176.6 cm-1
E Modes
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IR activity of O-O Stretching Mode in CdTe
• O-O Stretching Mode of O2 in gas form is not
infrared-active since it has even parity
• O2 in VCd of CdTe has no inversion symmetry
and therefore can be infrared-active.
• The calculated charge difference between the
two O atoms in CdTe is ~0.05e and the bond
length is ~0.13 nm (0.1208 nm in gaseous
O2) giving an electric dipole moment of ~3
Debye.
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Existence of Two IR modes in VCd-O2
1 peak (singlet)
2 peak (doublet)>1
The energy to rotate the O2 molecule by 90o~ energy of the
libration mode=39 meV
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LVM of Oxygen in CdTe
Summary:
Oxygen replacing Te has a LVM at ~350 cm-1.
In the presence of VCd Oxygen prefers to form molecule inside the VCd
The O2 molecule is oriented along the [111] direction but displaced from
the center of the vacancy. The two O atoms occupy in-equivalent
sites so the O-O stretching mode is IR-active
Charge transfer to the neighboring Te atoms weakens the O-O bond
and lowers the O-O stretching mode frequency. The calculated O-O
stretching mode frequency is in good agreement with experiment
The existence of two modes at low T and their convergence at high T
are also explained by theory
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CONCLUSIONS
Using first-principle density-functional theory we have studied the
electronic and vibrational properties of vacancies in CdTe and
GaN.
In GaN vacancies can be induced by replacing the cations with
large rare-earth ions like Gd.
The Ga vacancies produce holes which are spin polarized.
They strongly coupled to each other and to the Gd spins.
These results explains recently reported observation of
ferromagnetism in GaN:Gd above room temperature and the
enhancement of the magnetic moment per Gd by intrinsic defects.
In CdTe the cation vacancies are large thus allowing small
molecules like oxygen to be located inside them and forming a
new kind of molecular complex.
The vibrational modes of these molecular-vacancy complexes in
CdTe explain the sharp high frequency local vibration modes
reported in CdTe.
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