Solid State Sciences 13 (2011) 384e387
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Solid State Sciences
journal homepage: www.elsevier.com/locate/ssscie
Study on interactions between Cadmium and defects in Cd-doped ZnO
by first-principle calculations
Xin Tang a, b, c, *, Haifeng Lü d, Qingyu Zhang c, Jijun Zhao c, Yuyuan Lin e
a
Key Lab of New Processing Technology for Nonferrous Metal & Materials, Ministry of Education, Guilin University of Technology, Guilin 541004, China
College of Material Science and Engineering, Guilin University of Technology, Guilin 541004, China
c
Key Lab of Materials Modification by Laser, Ion, and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, China
d
Computer Network Information Center, Chinese Academy of Sciences, Beijing 10080, China
e
Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA
b
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 14 August 2009
Received in revised form
22 November 2010
Accepted 26 November 2010
Available online 1 December 2010
An ab initio calculation based on density functional theory is applied to study the formation energy and
transition energy level of defects and complexes in Cd-dopped ZnO. The calculation shows that the
incorporation of Cd into ZnO leads to the increase of the O vacancies (VO). VO exists in the form of CdZneVO
complex, which can balance the strain caused by CdZn and VO. Due to high formation energy of the Zn
interstitials (Zni) and deep transition energy level of VO, Zni and VO cannot serve singly as the source of the
n-type carriers in Cd-dopped ZnO. It is also found that the Zni-CdZn-VO complex is a shallow donor like Zni,
but has lower formation energy. Thus, the source of n-type carriers is believed to be a complex with ZniCdZn-VO structures in Cd-doped ZnO.
Ó 2010 Elsevier Masson SAS. All rights reserved.
Keywords:
Cd-dopped ZnO
n-type carrier
Density functional theory
1. Introduction
ZnO, a direct wide band gap (3.37 eV at room temperature)
semiconductor material, has been extensively studied due to its
intrinsic properties and potential applications to optoelectronic
devices [1e4], such as blue and ultraviolet light emitting diodes and
laser diodes. In order to design ZnO-based optoelectronic devices,
a critical challenge is the modulation of the band gap [5]. A further
widening of the band gap can be achieved by the incorporation of
magnesium into the ZnO layers [6,7]. On the other hand, by alloying
with CdO, which has a narrower band gap of 2.3 eV, the band gap of
ZnO can be red-shifted to a blue or even a green spectral range [8e10].
In fact, Cd incorporation can affect not only the band gap, but
also the n-type carrier concentration, which has been proved in our
recent experiments. Shan et al. [11] also found that Cd incorporation resulted in an increase of n-type carrier concentration in the
ZnCdO film. Similarly, we have reported that ZnCdO thin film
grown by the radio-frequency magnetron sputtering method has ntype conductivity with carrier concentration as high as
2.69 1020 cm3, about two orders of magnitude larger than that of
* Corresponding author. Key Lab of New Processing Technology for Nonferrous
Metal & Materials, Ministry of Education, Guilin University of Technology, Guilin
541004, China. Tel.: þ86 7735893395; fax: þ86 7735896436.
E-mail address: [email protected] (X. Tang).
1293-2558/$ e see front matter Ó 2010 Elsevier Masson SAS. All rights reserved.
doi:10.1016/j.solidstatesciences.2010.11.040
an undoped one [12]. It was also found that the n-type carrier
concentration has an increase with increasing Cd content [12]. All
of the experiments show that the source of the n-type conductivity
in Cd-doped ZnO must be related to Cd incorporation. However, Cd
incorporation in ZnO, an isovalent doping, does not create a new
donor level, which means that the only possible source of n-type
carriers are the native defects or their complexes in the ZnCdO
alloy. Cd incorporation can change the status of native defects, such
as the formation energy and the transition energy level, which
induce the increase of the carrier concentration in the ZnCdO alloy.
Therefore, it is necessary to investigate the interaction between Cd
and defects in ZnCdO alloy to understand the microscopic mechanism of the experimental phenomena as mentioned.
In this paper, we examine the important roles of Cd in the
formation of native defects. By means of first-principles calculations based on density functional theory (DFT), the formation
energies and the transition energies of native point defects and
their possible complexes in ZnCdO alloy are investigated in order to
find the source of n-type carriers. In addition, the structures of the
defects are also discussed.
2. Method of calculation
The calculations were performed in the framework of DFT with
the projected augmented wave (PAW) method [13e15], using the
X. Tang et al. / Solid State Sciences 13 (2011) 384e387
Vienna ab initio simulation package (VASP) [16], which is effective
in describing the crystal and electronic structure of the condensed
matter [17,18]. The interaction between ions and electrons were
described by the Perdew-Wang (PW91) [19] generalized gradient
approximation (GGA). For valence electrons, the outermost s and
d states of Zn and Cd atoms, s and p states of O atoms are employed
in the work. The plane-wave energy cutoff is set to 400 eV and a Gpoint centered 3 3 3 k-point mesh [20,21] is used for Brillouin
zone. The formation energy of a defect a with charge state q is
defined as [22,23]
DEf ða; qÞ ¼ DEða; qÞ þ
X
(1)
Defect
Undoped ZnO
VO
Zni-oct
Oi-oct
VZn
0.60
3.51
6.38
5.35
where DEða;qÞ ¼ Eða;qÞEðhostÞþ
P
is the total energy of the defect, and EðhostÞ is the total energy of
the host (ZnO or Zn36-nCdnO36, which is represented by a 72-atom
ZnO supercell where n Zn atoms are substituted by Cd atoms). EF is
the Fermi level, referenced to the valence-band maximum in the
bulk, 3VBM, and varies from the valence-band maximum (VBM) to
the conduction-band minimum (CBM). ni indicates the number of
atoms of type i (host atoms or impurity atoms) that have been
added to (ni < 0) or removed from (ni > 0) the supercell. mi is the
chemical potential of constituent i reference to elemental solid/gas
with energy EðiÞ . mZn and mO obey the equilibrium condition
mZn þ mo ¼ DHf ðZnOÞ, where DHf ðZnOÞ ¼ 3:51 eV is the calculated
enthalpy of formation of ZnO, compared to the experimental value
of 3.6 eV [24]. Here, we only report our results under Zn-rich
condition, i.e. mZn ¼ 0 , as most epitaxial growth occurs in oxygendeficient conditions. The defect transition energy level 3a ðq=q0 Þ is
Fermi energy EF in Eq.(1) at which the formation energy DEf ða;qÞ of
defect a and charge q is equal to that of another charge q’ of the
same defect. 3a ðq=q0 Þ can be obtained from
i.
ðq0 qÞ
(2)
In order to describe the defect level, we use a hybrid scheme to
combine k-points sampling and G-point-only approaches to
calculate the transition energy level and the formation energy of
a charged defect [22,23]. This new approach has been used
successfully for studying defects in various semiconductors [25,26].
In this scheme, the ionization energy Eion ð0=qÞ for donor (q > 0)
with respect to CBM is given by
Eion ð0=qÞ ¼ 3Gg ðhostÞ 3ð0=qÞ
i h
h
¼ 3GCBM ðhostÞ 3GD ð0Þ þ Eða; qÞ Eða; 0Þ
i.
q
q3kD ð0Þ
(3)
where 3kD ð0Þ and 3GD ð0Þ are the defect levels at the special k-points
(averaged) and at the G-point, respectively; 3GVBM ðhostÞ and
3GCBM ðhostÞ are the VBM and CBM energy, respectively, of the host
supercell at the G-point, and 3Gg ðhostÞ is the calculated band gap.
The formation energy of a charged state is then given by:
DEf ða; qÞ ¼ DEf ða; 0Þ q3ð0=qÞ þ qEF
(0.81a
(2.71a
(5.88a
(5.06a
1.00b
2.50b
6.20b
5.35b
0.69c)
2.76c)
6.36c)
5.94c)
Defects far
from Cd atom
Defects connected
with Cd atom
0.63
3.28
6.10
5.38
0.13
3.41
6.38
5.38
Reference 17.
Reference 18.
Reference 27.
ni EðiÞþq3VBM ðhostÞ. Eða;qÞ
i
3a ðq=q0 Þ ¼ DEf ða; qÞ DEf ða; q0 Þ
b
c
i
h
Table 1
Calculated formation energies DEf(a,0) (in eV) at EF ¼ 0 for native point defects in
ZnO and ZnCdO alloy under Zn-rich condition. The values in parenthesis are the
calculated data from Ref. 17,18,27 respectively. Ref.17:DFT, GGA; Ref.18:DFT, GGA;
Ref.27:DFT, LDA.
a
ni mi þ qEF
385
calculated, as shown in Table 1. As the interstitials at octahedral
(oct) sites are more stable than those at tetrahedral (tet) sites [17],
only the octahedral interstitials are considered. For the formation
energies of the defects, compared with the theoretical calculations
[17,18,27], our results are believed to be reasonable despite the
presence of tiny differences. The differences in formation energies
can be attributed to the differences in computational details,
especially the functions for exchange-correlation potentials, pseudopotential types, k-points sampling, and relaxation approaches.
As we focus on the origin of n-type carriers, more attention is
paid to the donor like defects. Zni and VO are main intrinsic donors
in ZnO. From Table 1, we find that the formation energy of Zni is
relatively high, with the value of 3.51 eV, and VO has the lowest
formation energy 0.60 eV in undoped ZnO. That is to say, VO is the
most abundant native defect in ZnO and acts as the dominant
intrinsic donor. Fig. 1 presents the calculation ionization energies of
donors in ZnO reference to the CBM. As shown in Fig. 1, it is also
confirmed that Eion ð0=þ2Þ < Eion ð0=þ1Þ for VO according to Eq. (3),
implying that the chargeestate transition of VO is directly from 0 to
2 þ charge state and VO is a “negative-U” center. The result is in
agreement with the previous experiment [28] and calculations
[29,30]. For Zni, the ionization energy is over the CBM with the
value of 0.15eV, which means that Zni is easy to ionize to
1 þ charge state and gives electrons. So, Zni is generally considered
to the source of the intrinsic n-type in ZnO in early research [30].
For the defect formation energies in ZnCdO, two configurations
are discussed. One is that defects are far from the Cd atoms and
the other is that defects are connected with the Cd atoms. When the
defects are far from the Cd atoms, the interaction between the
defects and the Cd atoms is very weak and the expanded lattice
caused by Cd incorporation into ZnO is the only factor that affects
the defect formation energies. As the expanded lattice can increase
the interstitial room and facilitate the formation of interstitials, the
formation energies of interstitials decrease a little, as shown in
Table 1. On the other hand, the expanded lattice also hinders the
(4)
where DEf ða; 0Þ is the formation energy of the neutral charge
defect.
3. Results and discussion
The formation energies (Ef) of native point defects (including Zn
interstitials (Zni), O vacancies (VO), O interstitials (Oi), Zn vacancies
(VZn) in the ZnO and Zn35Cd1O36) at neutral charge states are
Fig. 1. The calculation ionization energies (in eV) of donors in undoped ZnO reference
to the CBM.
386
X. Tang et al. / Solid State Sciences 13 (2011) 384e387
formation of vacancies, for example, the formation energies of VO
and VZn increase to 0.63 and 5.38 eV, respectively. When defects are
connected with Cd atoms, the results show that the formation
energies of the defects almost remain unchanged except for VO. It is
interesting to find that the formation energy of VO decreases from
0.60 eV to 0.13 eV and the difference reaches 0.73 eV unexpectedly. The negative formation energy indicates that CdZn is accompanied by VO in Zn-rich conditions.
In order to explain the large decrease of the formation energy of
VO, the atomic configurations of neutral VO in ZnO and ZnCdO are
presented in Fig. 2. Due to the existence of VO in ZnO, the
surrounding four Zn atoms are displaced inward by 15%, as shown
in Fig. 2(a). Once the Cd atom substitutes one of the four Zn atoms
around VO, CdZneVO complex forms. In the complex, the displacement of the other three Zn atoms around VO decreases by 7%,
which is only half of the case of pure ZnO, as shown in Fig. 2(b).
Moreover, the Cd atom moves towards VO and the bonds between
Cd and O atoms become longer, with the bond length of 2.25 Å. The
value is very close to 2.24 Å, the calculated CdeO bond length in
wurtzite CdO [31]. The structure of CdZneVO complex suggests that
the complex can balance the strain caused by VO and CdZn, and
reduce the formation energy effectively.
Generally speaking, if the donor defects can be seen as the
source of n-type conductivity, two requirements are needed: one is
low formation energy; the other is a low ionization energy, i.e. the
donor defects are the shallow donors. For Zni in ZnCdO alloy, the
formation energy is high, with the value of 3.28 eV. The high
formation energy of Zni implies that Zni is not the main donor to
provide n-type carriers in ZnCdO alloy. For CdZneVO in ZnCdO alloy,
as discussed above, the formation energy is very low and even
negative, and CdZneVO is likely to be a candidate for the source of ntype carriers. To verify this hypothesis, we need to check the ionization energy of CdZneVO. The calculation ionization energies of
donors in Cd-doped ZnO reference to the CBM are presented in
Fig. 3. As shown in Fig. 3, CdZneVO in ZnCdO alloy still is a “negative-U” center and Eion ð0=þ2Þ for CdZneVO in ZnCdO is 0.41 eV
under CBM. The ionization energy of CdZneVO in ZnCdO is very high
and it is a very deep donor, which means that CdZneVO is not the
source of n-type carriers either. Therefore, in ZnCdO, single donor
cannot serve as the source, which is similar to the case in pure ZnO.
CdZneVO has low formation energy and Zni has low ionization
energy, which is over CBM with the value of 0.13 eV, as shown in
Fig. 3. If a complex can combine CdZneVO with Zni, it may be
possible that the complex has low formation energy and low ionization energy. Following this idea, a complex including CdZneVO
and Zni is constructed, as presented in Fig. 4. In the complex, a Zni in
octahedral interstitial is connected with the Cd atom in CdZneVO
Fig. 2. Atomic structure of neutral (a) VO in ZnO and (b) CdZneVO in ZnCdO. The red
(blue) balls denote O (Zn) atoms. The atoms marked with A, B, C, D are the Zn atoms
around VO.
Fig. 3. The calculation ionization energies (in eV) of donors in Cd-doped ZnO reference
to the CBM.
complex. According to Eq. (1), the neutral complex has formation
energy of 2.72 eV, about 0.7 eV lower than that of Zni in ZnCdO alloy.
The decrease in formation energy is just close to the difference
between the formation energies of VO and CdZneVO complex in
ZnO. Similarly, the structure of the complex is also investigated. In
the complex, the bonds between Cd and O are 2.35 Å and 2.56 Å,
respectively, which expand the room of octahedral interstitial, and
the three Zn atoms around VO move outward by only 1%. The strain
caused by VO and Zni is released effectively in the complex.
For the ionization energy of the complex, as shown in Fig. 3, the
lowest one is Eion ð0=þ1Þ , with the value of 0.72 eV, which is much
lower than Eion ð0= þ 1Þ for Zni. The result suggests that the complex
is also a shallow donor like Zni. The decrease of ionization energy in
the complex may be attributed to the donoredonor pair (VO-Zni
pair), which can lower the donor ionization energy [32].
The lowered formation energy and ionization energy show that
the Zni-CdZn-VO complex concentrates the features of CdZn-VO and
Zni successfully. Although the complex still has high formation
energy, it can be obtained in non-equilibrium processes. Additionally, the complex also gives us a clue to the source. We believe
that the source is a kind of complex with Zni-CdZn-VO structures,
such as Zni-2CdZne2VO or Zni-3CdZne3VO. There are three Zn atoms
around Zni and only one of the three atoms is substituted by Cd
atom in Zni-CdZn-VO structure. If another one or two Zn atoms of
the three atoms are also substituted by Cd atoms which are in
CdZneVO complexes, Zni-2CdZne2VO or Zni-3CdZn-3VO complex can
be formed. Due to the presence of Zni and more CdZn-VO in these
complexes, they are expected to be a shallow donor and to have
lower formation energy than that of Zni-CdZn-VO. Additionally, we
also calculated the dependence of the formation energies of neutral
Zni and VO on the Cd concentration, as shown in Fig. 5. The
formation energies of Zni and VO keep decreasing with the
increasing Cd concentration and VO decreases more dramatically,
with the formation energy of 2.01 eV at 11.11% Cd, which indicates
that the Zni-CdZn-VO complex also has lower formation energy in
high Cd concentration than in low Cd concentration. This result is
also consistent with the recent experiments [11,12].
Fig. 4. Atomic structure of neutral Zni-CdZn-VO complex in ZnCdO. The red (blue) balls
denote O (Zn) atoms.
X. Tang et al. / Solid State Sciences 13 (2011) 384e387
387
References
Fig. 5. Formation energies of neutral Zni and VO as a function of Cd concentration.
4. Conclusion
In conclusion, our first-principles calculation reveals that the
incorporation of Cd into ZnO results in the increase of VO defect
under Zn-rich condition and VO exists in the form of CdZneVO
complex, which can balance the strain caused by VO and CdZn. In
addition, Zni-CdZn-VO complex has lower formation energy than
CdZneVO complex and lower ionization energy than Zni. The
complexes with Zni-CdZn-VO structure are believed to be the source
of n-type carriers in ZnCdO alloy.
Acknowledgements
The work is supported by the National Natural Science Foundation of China under Grant Nos.10904021 and 10774018 and the
Ministry of Science and Technology of China under Grant No.
2007CB616902. X. Tang, one of the authors, also acknowledges the
support from Scientific Research Foundation of Guilin University of
Technology under Grant No. 002401003267.
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