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Native defects and self-diffusion in GaSb

29 Mar 2002-Journal of Applied Physics (American Institute of Physics)-Vol. 91, Iss: 8, pp 4988-4994
TL;DR: In this paper, the structures and the formation energies of the stable defects and estimate the defect concentrations under different growth conditions were reported and a metastable state was observed for the SbGa antisite.
Abstract: The native defects in GaSb have been studied with first-principles total-energy calculations. We report the structures and the formation energies of the stable defects and estimate the defect concentrations under different growth conditions. The most important native defect is the GaSb antisite, which acts as an acceptor. The other important defects are the acceptor-type Ga vacancy and the donor-type Ga interstitial. The Sb vacancies and interstitials are found to have much higher formation energies. A metastable state is observed for the SbGa antisite. The significantly larger concentrations of the Ga vacancies and interstitials compared to the corresponding Sb defects is in accordance with the asymmetric self-diffusion behavior in GaSb. The data supports the next-nearest-neighbor model for the self-diffusion, in which the migration occurs independently in the different sublattices. Self-diffusion is dominated by moving Ga atoms.

Summary (2 min read)

Introduction

  • This is an electronic reprint of the original article.
  • The data supports the next-nearest-neighbor model for the self-diffusion, in which the migration occurs independently in the different sublattices.
  • In this work the authors have studied the electronic structures and the formation energies of native defects in GaSb with ab initio methods.
  • In Sec. III the authors present the results for the atomic and electronic structure of the stable native defects and study the concentrations of the defects, especially those of residual acceptors.

II. METHODS

  • The structures and the total energies of the native defects are calculated within the density-functional theory12 and the local-density approximation ~LDA!.13.
  • The formation energies of the defects are calculated following the formalism used by Zhang and Northrup.20.
  • The atomic chemical potentials obtain values below their bulk precipitates: mGa<mGa(bulk) and mSb<mSb(bulk) .
  • The electron chemical potential me is allowed to vary between zero and the experimental band gap value, 0 <me<Eg .
  • The used supercell size and the k-point sampling may also induce errors in the formation [This article is copyrighted as indicated in the article.

A. Structures and energies

  • The charge states, the symmetries and the formation energies for the native defects in GaSb are presented in Table I. charge states indicate that the partially occupied t2 level is split.
  • This is a significantly different behavior from the anion antisite defects in GaAs.
  • [This article is copyrighted as indicated in the article.
  • Finally, in the Ta site Sb is stable in the charge state ~31!, which preserves the perfect Td symmetry.

B. Concentrations

  • The p-type nature of GaSb is naturally explained by the calculations.
  • The general trends for the residual hole concentrations are shown in Fig.
  • In comparing GaSb against GaAs one also notes the absence of compensating electrically active defects.
  • [This article is copyrighted as indicated in the article.
  • Hence, experimental evidence indicates that there are two types of acceptors of which only one is present at Ga-rich conditions, while both are present in similar concentrations in the Sb-rich case.

A. Nearest-neighbor diffusion mechanism

  • The nearest-neighbor diffusion mechanism by vacancies consists of successive atomic movements where a nearestneighbor atom moves to the vacancy.
  • To the right, the Reaction ~8! is endothermic and involves electron transfer.
  • The reaction energy, calculated for the most stable charge states, increases from 0.6 eV to 1.9 eV as the Fermi level is moved from the VBM to the conduction band minimum ~CBM!.
  • Charge states, whereas VGaGaSb can be found in several negative charge states as shown in Table I. For GaSb this conclusion may not be valid since the diffusion experiments have been performed for intrinsic and p-type material.

B. Next-nearest-neighbor diffusion

  • In the next-nearest-neighbor diffusion mechanism as suggested by Bracht et al.2,3 the Ga and Sb atoms diffuse independently of each other via either vacancies or interstitials.
  • On the basis of the calculated concentrations the authors obtain a simple explanation for the large difference in the Ga and the Sb self-diffusion coefficients as found in experiments.
  • [This article is copyrighted as indicated in the article.
  • Therefore, if Reaction ~9! and the subsequent dissociation are assumed to be effective, the VGa concentration levels off as one moves toward Ga-rich conditions.
  • Reaction ~12! could thus suppress the concentration of Sb interstitials in the presence of Ga vacancies.

C. Ga- and Sb-rich ambient conditions

  • In the experiment by Bracht et al.2,3 diffusion measurements were performed for both Ga- and Sb-rich ambient conditions with the temperature varying between 571 and 708 °C.2,3.
  • The main observations of these experiments were that the diffusion coefficient for Ga is identical under Sb-and Ga-rich ambient conditions, and that there is a lack of significant diffusion of Sb under Garich conditions.
  • If the surface supply of the Gai defect would be responsible for Ga diffusion, the different surface conditions should produce differing diffusion coefficients.
  • 2,3 For Ga-rich conditions the concentrations of Sb vacancies and interstitials in the as-grown material are very low, ;109 and ;0 cm23, respectively.
  • [This article is copyrighted as indicated in the article.

V. CONCLUSIONS

  • The authors have made a comprehensive study of structures, formation energies, energy levels, and concentrations of native defects in undoped GaSb.
  • The native defects show similarity in atomic and electronic structures with those in GaAs.
  • A metastable state is found for the anion antisite SbGa .
  • An important difference compared to GaAs is that in GaSb the anion antisite SbGa does not have ionization levels deep in the band gap, whereas in GaAs the ionization levels of the AsGa antisite cause the semi-insulating character of the asgrown material.
  • The concentrations of the relevant defects estimated for typical experimental conditions are used to discuss the observed highly asymmetric self-diffusion of Ga and Sb in GaSb, i.e., the phenomenon that the diffusion of Ga is several orders in magnitude faster than that of Sb.

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This is an electronic reprint of the original article.
This reprint may differ from the original in pagination and typographic detail.
Author(s):
Hakala, M. & Puska, M. J. & Nieminen, Risto M.
Title:
Native defects and self-diffusion in GaSb
Year: 2002
Version: Final published version
Please cite the original version:
Hakala, M. & Puska, M. J. & Nieminen, Risto M. 2002. Native defects and self-diffusion
in GaSb. Journal of Applied Physics. Volume 91, Issue 8. 4988-4994. ISSN 0021-8979
(printed). DOI: 10.1063/1.1462844.
Rights: © 2002 American Institute of Physics. This is the accepted version of the following article: Hakala, M. &
Puska, M. J. & Nieminen, Risto M. 2002. Native defects and self-diffusion in GaSb. Journal of Applied
Physics. Volume 91, Issue 8. 4988-4994. ISSN 0021-8979 (printed). DOI: 10.1063/1.1462844, which has
been published in final form at http://scitation.aip.org/content/aip/journal/jap/91/8/10.1063/1.1462844.
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Native defects and self-diffusion in GaSb
M. Hakala, M. J. Puska, and R. M. Nieminen
Citation: Journal of Applied Physics 91, 4988 (2002); doi: 10.1063/1.1462844
View online: http://dx.doi.org/10.1063/1.1462844
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/91/8?ver=pdfcov
Published by the AIP Publishing
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Native defects and self-diffusion in GaSb
M. Hakala,
a)
M. J. Puska, and R. M. Nieminen
Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Finland
Received 19 July 2001; accepted for publication 29 January 2002
The native defects in GaSb have been studied with first-principles total-energy calculations. We
report the structures and the formation energies of the stable defects and estimate the defect
concentrations under different growth conditions. The most important native defect is the Ga
Sb
antisite, which acts as an acceptor. The other important defects are the acceptor-type Ga vacancy and
the donor-type Ga interstitial. The Sb vacancies and interstitials are found to have much higher
formation energies. A metastable state is observed for the Sb
Ga
antisite. The significantly larger
concentrations of the Ga vacancies and interstitials compared to the corresponding Sb defects is in
accordance with the asymmetric self-diffusion behavior in GaSb. The data supports the
next-nearest-neighbor model for the self-diffusion, in which the migration occurs independently in
the different sublattices. Self-diffusion is dominated by moving Ga atoms. © 2002 American
Institute of Physics. DOI: 10.1063/1.1462844
I. INTRODUCTION
Gallium antimonide is a technologically interesting ma-
terial due to its applications to high speed electronic and long
wavelength photonic devices for a review, see Ref. 1. The
narrow, direct band gap of 0.73 eV at 300 K of GaSb en-
ables its use in the fabrication of infrared detectors and
sources. GaSb can be lattice matched with ternary and qua-
ternary III-V compounds to form a substrate material for
various optical communication devices, which operate in the
2–4
m regime. Furthermore, GaSb has a high electron mo-
bility and saturation velocity, which can be utilized in high
electron mobility transistors. In these devices band offsets of
GaSb with similar compounds can be used to create the con-
ducting two-dimensional electron gas. Interesting basic prob-
lems in GaSb are the origin of its residual acceptor concen-
tration and the recently observed strongly asymmetric
self-diffusion.
2,3
GaSb is always p type irrespective of
growth techniques and conditions.
1
The typical residual ac-
ceptor concentration is 10
17
cm
3
, and the acceptors are
associated with native Ga vacancies and antisite defects.
1
Nonstoichiometric growth conditions have been used to re-
duce the acceptor concentration and increase the hole
mobility.
4,5
Self-diffusion is related to material degradation,
and it is strongly correlated to lattice defects and the diffu-
sion of impurities.
The recent experiments by Bracht et al.
2,3
have demon-
strated that Ga diffuses several orders of magnitude faster
than Sb. The authors have proposed a model according to
which the diffusion takes place independently in the different
sublattices, which points to a next-nearest-neighbor diffusion
mechanism. According to the model Ga diffuses via vacan-
cies, whereas Sb diffuses via interstitials. The large differ-
ence in the diffusion coefficients derives from a significant
concentration difference between the Ga vacancies and the
Sb interstitials. The concentrations are explained to be
strongly affected by amphoteric transformations, which in-
crease the number of Ga vacancies and reduce the number of
Sb interstitials. Since the defects may possess several charge
states, the energetics of amphoteric reactions is proposed to
depend on the Fermi level position.
Electronic structure calculations have been extensively
used in the analysis of properties of native defects in III-V
materials. GaAs is the most studied material, and to a large
extent the results can be generalized to other III-V materials.
6
The defects with intrinsic metastabilities have attracted par-
ticular interest in III-V materials.
7
For example, the detection
of a defect may depend on whether it is in the stable or the
metastable configuration. It is interesting to see whether this
structural property is found in GaSb. For GaSb, there are few
electronic structure calculations available. The existing data
is usually calculated as a part of a series where the chemical
trends of III-V materials have been analyzed. Ku
¨
hn et al.
8
have studied vacancies and antisite defects using charge-self-
consistent empirical tight-binding methods. Xu
9
has studied
vacancies with semiempirical tight-binding methods, while
Talwar and Ting
10
have studied vacancies and antisites using
Green’s function tight-binding methods. Puska
11
has studied
vacancies and antisites with linear-muffin-tin-orbital Green’s
function methods. All the above-mentioned studies are for
ideal atomic structures.
In this work we have studied the electronic structures
and the formation energies of native defects in GaSb with ab
initio methods. The calculations have been performed for
fully relaxed vacancies, interstitials, and antisite defects. We
show that the defects behave to a large extent in a similar
way to those in GaAs. We calculate the defect concentrations
at typical growth temperatures. We show that the residual
acceptor is the gallium antisite defect and estimate the effect
of growth conditions on the residual hole concentration. We
study the model by Bracht et al.
2,3
for the asymmetric self-
diffusion, the proposed amphoteric transformations, and
comment on the probability of the nearest-neighbor diffusion
mechanism.
a
Electronic mail: moh@fyslab.hut.fi
JOURNAL OF APPLIED PHYSICS VOLUME 91, NUMBER 8 15 APRIL 2002
49880021-8979/2002/91(8)/4988/7/$19.00 © 2002 American Institute of Physics
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The paper is organized as follows. In Sec. II we describe
the theoretical methods and the calculation of the defect for-
mation energies and concentrations. In Sec. III we present
the results for the atomic and electronic structure of the
stable native defects and study the concentrations of the de-
fects, especially those of residual acceptors. In Sec. IV the
self-diffusion is discussed in the light of our data. Finally,
Sec. V presents the conclusions.
II. METHODS
The structures and the total energies of the native defects
are calculated within the density-functional theory
12
and the
local-density approximation LDA.
13
The plane-wave
pseudopotential method
14
is used with nonlocal norm-
conserving pseudopotentials: for Ga a Hamann type
15
and for
Sb a Troullier-Martins type.
16
The 3d and 4d electrons of Ga
and Sb, respectively, are included in the core. The nonlinear
core-valence exchange-correlation scheme
17
is used for both
elements. With these pseudopotentials the theoretical
experimental
1
lattice constant is 6.01 Å 6.10 Å, the bulk
modulus 0.548 Mbar 0.563 Mbar and the band gap is 0.31
eV 0.82 eV at 0 K. The band gap underestimation is typical
for the LDA calculations.
We have used a 64-atom supercell with the optimized
lattice constant and a k-point sampling proposed by Makov
et al.
18
The sampling consists of points 0, 0, 0 and
1
2
,
1
2
,
1
2
in units of (2
/a), where a is the lattice constant of the
supercell. This sampling and supercell size have been found
to be a good approximation for the formation energies for
point defects in semiconductors,
19
tending to minimize the
interactions between a defect and its periodic replica.
18
The
approximation may lead to a slight indefiniteness in the point
symmetry group of the defects.
19
We use a 22-Ry kinetic
energy cutoff, which leads to well-converged atomic struc-
tures. Our starting configurations are the ideal structures for
vacancies, antisites, and interstitials. For interstitials we use
as starting configurations the two inequivalent tetrahedral
sites and the hexagonal site. A small random component is
added to the initial atomic coordinates to break the high sym-
metry of the initial configuration. The ions are allowed to
relax with no symmetry restrictions following the
HellmannFeynman forces until the largest force component
on any atom is less than 5 meV/Å.
The formation energies of the defects are calculated fol-
lowing the formalism used by Zhang and Northrup.
20
The
formation energy of a defect is written as
E
f
E
D
q
e
E
v
n
Ga
Ga
n
Sb
Sb
, 1
where E
D
is the total energy of the supercell containing the
defect in question, q the charge electrons or holes trans-
ferred to the defect from a reservoir,
e
the chemical poten-
tial of the reservoir, and E
v
the valence band maximum
VBM.
e
corresponds to the Fermi level calculated from
the VBM. To account for the Coulomb interaction between a
charged defect and its periodic replicas, we have added a
Madelung-type monopole correction term to E
D
.
21
n
Ga
and
n
Sb
are the number of each element in the supercell. The
atomic chemical potentials obtain values below their bulk
precipitates:
Ga
Ga(bulk)
and
Sb
Sb(bulk)
. It is also re-
quired that the sum of the chemical potentials equals the
chemical potential per atom pair in the bulk compound:
Ga
Sb
GaSb
.
Equation 1 can be rewritten as
E
f
E
D
q
e
1
2
n
Ga
n
Sb
, 2
where
E
D
E
D
1
2
n
Ga
n
Sb
GaAs
1
2
n
Ga
n
Sb
Ga
bulk
Sb
bulk
qE
v
3
and
Ga
Sb
Ga
bulk
Sb
bulk
. 4
Ga(bulk)
and
Sb(bulk)
are calculated from their elemental
bulk phases. The electron chemical potential
e
is allowed to
vary between zero and the experimental band gap value, 0
e
E
g
. The limits for the chemical potential
are
given by the heat of formation H of GaSb, H⭐⌬
⭐⌬H. The values closer to H correspond to Sb-rich
growth conditions and values closer to H to Ga-rich
growth conditions. If
were defined using the chemical
potentials of other than the elemental solid phases, i.e., those
of the elemental molecular gases, the range of variation of
would increase. We use the experimental value of 0.43
eV for H.
22
Our calculated theoretical value is ( 0.1
0.3) eV; the discrepancy may be explained by the short-
comings of the LDA calculation, since H requires a very
accurate calculation of the energy difference between the
compound and the elements in bulk phase.
The concentration of a given defect is
C
D
z
D
N
s
exp
F
f
/k
B
T
, 5
where z
D
is the number of equivalent configurations for a
particular defect per sublattice site, N
s
the density of sublat-
tice sites (1.710
22
cm
3
), F
f
the free energy of defect
formation, k
B
the Boltzmann constant, and T the equilibrium
sample temperature. In our calculations we have omitted the
entropy part in F
f
and use only the formation energies when
estimating the concentrations. The entropy differences can be
of the order of 3k
B
,
6
which corresponds to internal energies
0.2 eV in the temperature range of 400 to 500 °C. The
charge neutrality condition is used to define the Fermi level
position.
20
Thermally created charge carriers in the valence
and the conduction bands are included in the self-consistent
determination of the Fermi level. The effective densities of
states of the valence and conduction bands are calculated
from the effective masses of electrons and holes.
1
In showing
the relative defect concentrations we use the temperature
450 °C, which corresponds to the growth temperature of the
molecular beam epitaxy MBE method used in the experi-
ments by Bracht et al.
2,3
The additional error sources in the formation energy are
as follows. The plane-wave convergence error was found to
be 0.05 eV and the convergence error in the atomic chemi-
cal potentials 0.25 eV. The used supercell size and the
k-point sampling may also induce errors in the formation
4989J. Appl. Phys., Vol. 91, No. 8, 15 April 2002 Hakala, Puska, and Nieminen
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energy. We assume that these deviations are not critical for
the formation energy and concentration differences.
Finally, the ionization level (q/q
) of a defect is defined
as the position of the Fermi level when two given charge
states have the same total energy:
E
D
q
Q
E
v
q
e
q/q
E
D
q
q
E
v
q
e
q/q
. 6
One should note that the used monopole correction see
above affects the level positions strongly for the higher
charge states. For example, the 3/2 level is corrected by
0.6 eV. As the higher-order terms in the expansion for the
electrostatic energy decrease the magnitude of the correction,
the monopole shifts provide an upper bound.
III. NATIVE DEFECTS
A. Structures and energies
The charge states, the symmetries and the formation en-
ergies for the native defects in GaSb are presented in Table I.
The ionization levels are given in Table II. In general, the
electronic structure of the vacancies, antisites and interstitials
is in qualitative agreement with the other III-V compounds.
6
The formation energy is affected by the Fermi level position
due to the fact that the defects can exist in different charge
states. Among the vacancy defects, V
Ga
acts as a triple ac-
ceptor: 13 electrons can be added to the defect with a posi-
tive extra energy per each added electron. The electrons are
distributed to the four Sb dangling bonds. In the 3 charge
state the defect preserves the T
d
symmetry with an inward
relaxation 12% of the nearest neighbor atoms of the va-
cancy. For the 2 and 1 charge states there is an addi-
tional symmetry-breaking distortion, which indicates that the
partially occupied t
2
level is split. V
Sb
can be found with the
charge states 1, 0 and 1.Inthe1 charge state the
symmetry group is T
d
Ref. 23 with an inward relaxation
of 5%. The smaller relaxation indicates that the accompany-
ing energy release is smaller than for V
Ga
. The 1/0 and
0/1 levels were found close to each other at 0.2 eV. In
the 0 charge states the symmetry of V
Sb
is lowered to C
2
v
as a gap state is occupied. Double occupancy of the gap level
leads to a very strong inwards relaxation 共⬃20% with the
symmetry of D
2d
. The strong relaxation is very similar to
that found for the negatively charged V
As
in GaAs.
24
The
systematic feature in the present calculation is that the relax-
ation is always towards the vacancy. In GaAs, an outward
relaxation for V
As
for the 1 and 0 charge states has
been reported.
24
The antisite Ga
Sb
is stable in the 0, 1, and 2
charge states and acts as a double acceptor. In the 2
charge states the bonding t
2
level is fully occupied and the
defect preserves the T
d
symmetry relaxing inwards 9%.
The transition levels are in the lower half of the band gap.
The additional symmetry-breaking distortions for the 1
and 0 charge states indicate that the partially occupied t
2
level is split. The double acceptor behavior is similar to the
Ga antisite in GaAs.
20,25
For the Sb
Ga
antisite in the 0
charge state two electrons occupy the antibonding a
1
state.
The T
d
symmetry is preserved and the defect relaxes out-
wards 11%. As electrons are removed from the single-
particle state the anionanion distance decreases. The donor
levels 2/1 and 1/0 as calculated from the total en-
ergies are, however, below the VBM. This is a significantly
different behavior from the anion antisite defects in GaAs. In
GaAs and InP the donor levels of the anion antisites are
located at midgap or above.
7
For the interstitial defects we studied Ga and Sb atoms at
the hexagonal H and the two tetrahedral sites (T
a
,T
c
). At
the T
a
(T
c
) site the defect has four anions cations as near-
est neighbors. We find that the interstitials stabilize at posi-
tive charge states due to the removal of high-energy dangling
bond electrons. Ga
i
is found stable only at the T
c
site at the
1 charge state with a rather low formation energy. In fact,
the T
a
and H starting configurations relax to the T
c
configu-
ration. The absence of states in the band gap indicates that
the a
1
level is within the valence band and the unoccupied t
2
level in the conduction band. Sb
i
is found stable at the H site
and both the T sites. For the T
c
site the stable charge state is
1. In fact, the point symmetry is lowered to D
2d
. This
is the energetically most favored configuration for all Fermi
level positions. The small symmetry-breaking distortion sug-
TABLE I. Charge states, point symmetry groups, and formation energies of
the native defects in GaSb. The point symmetries are deduced from the
converged positions of the ions neighboring the defect.
Defect Symmetry
a
E
f
eV
V
Ga
3
T
d
2.62 (1/2)
3
e
V
Ga
2
T
d
2.07 (1/2)
2
e
V
Ga
1
D
2d
1.76 (1/2)
e
V
Sb
1
T
d
1.93 (1/2)
e
V
Sb
0
C
2
v
1.11 (1/2)
V
Sb
1
D
2d
2.31 (1/2)
e
Ga
Sb
2
T
d
1.43
2
e
Ga
Sb
1
T
d
1.17
e
Ga
Sb
0
C
3
v
1.13
Sb
Ga
0
T
d
1.33
Ga
i
1
(T
c
)
T
d
0.77 (1/2)
e
Sb
i
3
(T
a
)
T
d
3.77 (1/2)
3
e
Sb
i
1
(H)
C
3
v
2.80 (1/2)
e
Sb
i
1
(T
c
)
D
2d
2.96 (1/2)
e
(V
Ga
Ga
Sb
)
3
C
3
v
2.70 (1/2)
3
e
(V
Ga
Ga
Sb
)
2
C
3
v
2.18 (1/2)
2
e
(V
Ga
Ga
Sb
)
1
C
3
v
1.90 (1/2)
1
e
(V
Sb
Sb
Ga
)
1
C
1h
2.35 (1/2)
e
(V
Ga
Sb
i
)
0
C
3
v
1.56
a
Reference 23.
TABLE II. Ionization levels for the stable native defects.
Defect
Ionization
level
Energy
eV
Ga
Sb
0/1 E
v
0.04
1/2 E
v
0.26
V
Ga
0/1 E
v
0.00
1/2 E
v
0.31
2/3 E
v
0.55
V
Sb
1/0 E
v
0.18
0/1 E
v
0.20
V
Ga
Ga
Sb
1/2 E
v
0.28
2/3 E
v
0.52
4990 J. Appl. Phys., Vol. 91, No. 8, 15 April 2002 Hakala, Puska, and Nieminen
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Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors examined the growth of strained layer superlattice (SLS) structures for the purpose of characterizing and improving the minority carrier lifetime and found that higher growth temperatures were beneficial for both binaries, although the improvement for InAs was less than that of InAs.

124 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a comprehensive account of semiconductor defect charging, identifying correspondences and contrasts between surfaces and the bulk as well as among semiconductor classes (group IV, groups III-V, and metal oxides).
Abstract: Native point defects control many aspects of semiconductor behavior. Such defects can be electrically charged, both in the bulk and on the surface. This charging can affect numerous defect properties such as structure, thermal diffusion rates, trapping and recombination rates for electrons and holes, and luminescence quenching rates. Charging also introduces new phenomena such as nonthermally photostimulated diffusion, thereby offering distinctive mechanisms for defect engineering. The present work incorporates the first comprehensive account of semiconductor defect charging, identifying correspondences and contrasts between surfaces and the bulk as well as among semiconductor classes (group IV, groups III–V, and metal oxides). For example, small lattice parameters, close-packed unit cells, and basis atoms with large atomic radii all inhibit the formation of ionized interstitials and antisites. The charged defects that exist in III–V and oxide semiconductors can be predicted with surprising accuracy from the chemical potential and oxygen partial pressure of the ambient. The symmetry-lowering relaxations, formation energies, and diffusion mechanisms of bulk and surface defect structures often depend strongly on charge state with similar qualitative behavior, although for a given material surface defects do not typically take on the same configurations or range of stable charge states as their counterparts in the bulk.

114 citations

Journal ArticleDOI
TL;DR: The successful growth of high-quality GaAs1-xSbx nanowires with near full-range bandgap tuning may speed up the development of high -performance nanowire devices based on such ternaries.
Abstract: Here we report on the Ga self-catalyzed growth of near full-composition-range energy-gap-tunable GaAs1–xSbx nanowires by molecular-beam epitaxy. GaAs1–xSbx nanowires with different Sb content are systematically grown by tuning the Sb and As fluxes, and the As background. We find that GaAs1–xSbx nanowires with low Sb content can be grown directly on Si(111) substrates (0 ≤ x ≤ 0.60) and GaAs nanowire stems (0 ≤ x ≤ 0.50) by tuning the Sb and As fluxes. To obtain GaAs1–xSbx nanowires with x ranging from 0.60 to 0.93, we grow the GaAs1–xSbx nanowires on GaAs nanowire stems by tuning the As background. Photoluminescence measurements confirm that the emission wavelength of the GaAs1–xSbx nanowires is tunable from 844 nm (GaAs) to 1760 nm (GaAs0.07Sb0.93). High-resolution transmission electron microscopy images show that the grown GaAs1–xSbx nanowires have pure zinc-blende crystal structure. Room-temperature Raman spectra reveal a redshift of the optical phonons in the GaAs1–xSbx nanowires with x increasing fro...

65 citations

Journal ArticleDOI
TL;DR: Visible/extended short–wavelength infrared photodetectors with a bandstructure–engineered photo–generated carrier extractor based on type–II InAs/AlSb/GaSb superlattices have been demonstrated, with sensitivity down to visible wavelengths.
Abstract: Visible/extended short–wavelength infrared photodetectors with a bandstructure–engineered photo–generated carrier extractor based on type–II InAs/AlSb/GaSb superlattices have been demonstrated. The photodetectors are designed to have a 100% cut-off wavelength of ~2.4 μm at 300K, with sensitivity down to visible wavelengths. The photodetectors exhibit room–temperature (300K) peak responsivity of 0.6 A/W at ~1.7 μm, corresponding to a quantum efficiency of 43% at zero bias under front–side illumination, without any anti–reflection coating where the visible cut−on wavelength of the devices is <0.5 µm. With a dark current density of 5.3 × 10−4 A/cm2 under −20 mV applied bias at 300K, the photodetectors exhibit a specific detectivity of 4.72 × 1010 cm·Hz1/2/W. At 150K, the photodetectors exhibit a dark current density of 1.8 × 10−10 A/cm2 and a quantum efficiency of 40%, resulting in a detectivity of 5.56 × 1013 cm·Hz1/2/W.

64 citations

Journal ArticleDOI
TL;DR: A unidirectional propagation effect due to a self-induced compositional variation in GaAsSb nanowires (NWs) is reported, where the rectifying direction is determined by the NW growth direction.
Abstract: Device configurations that enable a unidirectional propagation of carriers in a semiconductor are fundamental components for electronic and optoelectronic applications. To realize such devices, however, it is generally required to have complex processes to make p–n or Schottky junctions. Here we report on a unidirectional propagation effect due to a self-induced compositional variation in GaAsSb nanowires (NWs). The individual GaAsSb NWs exhibit a highly reproducible rectifying behavior, where the rectifying direction is determined by the NW growth direction. Combining the results from confocal micro-Raman spectroscopy, electron microscopy, and electrical measurements, the origin of the rectifying behavior is found to be associated with a self-induced variation of the Sb and the carrier concentrations in the NW. To demonstrate the usefulness of these GaAsSb NWs for device applications, NW-based photodetectors and logic circuits have been made.

64 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the Hartree and Hartree-Fock equations are applied to a uniform electron gas, where the exchange and correlation portions of the chemical potential of the gas are used as additional effective potentials.
Abstract: From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of $\frac{2}{3}$.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.

47,477 citations

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TL;DR: In this article, the ground state of an interacting electron gas in an external potential was investigated and it was proved that there exists a universal functional of the density, called F[n(mathrm{r})], independent of the potential of the electron gas.
Abstract: This paper deals with the ground state of an interacting electron gas in an external potential $v(\mathrm{r})$. It is proved that there exists a universal functional of the density, $F[n(\mathrm{r})]$, independent of $v(\mathrm{r})$, such that the expression $E\ensuremath{\equiv}\ensuremath{\int}v(\mathrm{r})n(\mathrm{r})d\mathrm{r}+F[n(\mathrm{r})]$ has as its minimum value the correct ground-state energy associated with $v(\mathrm{r})$. The functional $F[n(\mathrm{r})]$ is then discussed for two situations: (1) $n(\mathrm{r})={n}_{0}+\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}(\mathrm{r})$, $\frac{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}}{{n}_{0}}\ensuremath{\ll}1$, and (2) $n(\mathrm{r})=\ensuremath{\phi}(\frac{\mathrm{r}}{{r}_{0}})$ with $\ensuremath{\phi}$ arbitrary and ${r}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$. In both cases $F$ can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.

38,160 citations

17 Jun 1964

28,969 citations

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TL;DR: It is found that these pseudopotentials are extremely efficient for the cases where the plane-wave expansion has a slow convergence, in particular, for systems containing first-row elements, transition metals, and rare-earth elements.
Abstract: We present a simple procedure to generate first-principles norm-conserving pseudopotentials, which are designed to be smooth and therefore save computational resources when used with a plane-wave basis. We found that these pseudopotentials are extremely efficient for the cases where the plane-wave expansion has a slow convergence, in particular, for systems containing first-row elements, transition metals, and rare-earth elements. The wide applicability of the pseudopotentials are exemplified with plane-wave calculations for copper, zinc blende, diamond, \ensuremath{\alpha}-quartz, rutile, and cerium.

13,174 citations

01 Jan 1992

12,636 citations

Frequently Asked Questions (16)
Q1. What are the contributions in "Native defects and self-diffusion in gasb" ?

This is the accepted version of the following article: Hakala, M. & Puska, M. J. & Nieminen, Risto M. 2002. 

Due to the long diffusion times the material is actually assumed to reach a thermal equilibrium state which corresponds to Sb-rich growth conditions at ;700 °C.3 

For the Sb defects the formation energies of both vacancies and interstitials would decrease, but their concentration would still be small compared to that of Ga vacancies and interstitials. 

The reaction energy for the complex to dissociate decreases from 1.0 to 0.25 eV as the Fermi level is moved from the VBM to the CBM. 

The authors estimate that an extreme p-type doping would lower the formation energy of the Ga defect by ;0.1–0.3 eV ~at 450 °C! for stoichiometric or Ga-rich growth conditions thus increasing its concentration. 

In the case of the Sb diffusion, a high temperature and Sb-rich ambient conditions are found to increase the concentration of Sb interstitials and thereby the Sb self-diffusion. 

In order to resolve the actual atomistic diffusion mechanism ~vacancy or interstitial! for both elements, it would be necessary to perform simulations for the diffusivities. 

The other mechanisms, such as the antisite exchange or the collective diffusive mechanisms, have been neglected in these calculations. 

When moving toward Ga-rich conditions the increase of the GaSb acceptor concentration is seen to pull the Fermi level downward from its intrinsic value. 

For Ga-rich growth conditions at T5450 °C the Fermi level is at 0.15 eV ~Fig. 2!, which corresponds to the value ;20.3 eV for the reaction energy. 

In showing the relative defect concentrations the authors use the temperature 450 °C, which corresponds to the growth temperature of the molecular beam epitaxy ~MBE! 

The recombination of Sb interstitials and Ga vacancies is a reaction which has been proposed to explain the loss of Sb interstitials:2,3SbGa VGa2Sbi . 

3. There is a decrease in the hole concentration when moving from higher to lower temperatures and from Ga-rich to Sbrich conditions. 

The effective densities of states of the valence and conduction bands are calculated from the effective masses of electrons and holes. 

The entropy differences can be of the order of 3kB ,6 which corresponds to internal energies ;0.2 eV in the temperature range of 400 to 500 °C. 

In contrast, due to the long diffusion times the Sb diffusion experiments performed under Sb-rich ambient conditions were considered to change the sample composition to correspond to Sb-rich growth conditions.