Doping by Large-Size-Mismatched Impurities: The Microscopic Origin of Arsenic-
or Antimony-Doped p-Type Zinc Oxide
Sukit Limpijumnong,1,2S. B. Zhang,1Su-Huai Wei,1and C.H. Park1,3
1National Renewable Energy Laboratory, Golden, Colorado 80401, USA
2School of Physics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand
3Research Center for Dielectric and Advanced Matter Physics, Pusan National University, Pusan 609-735, Korea
(Received 12 September 2003; published 15 April 2004)
Based on first-principles calculations, a model for large-size-mismatched group-Vdopants in ZnO is
proposed. The dopants do not occupy the O sites as is widely perceived, but rather the Zn sites: each
forms a complex with two spontaneously induced Zn vacancies in a process that involves fivefold As
coordination. Moreover, an AsZn-2VZncomplex may have lower formation energy than any of the parent
defects. Our model agrees with the recent observations that both As and Sb have low acceptor-ionization
energies and that to obtain p-type ZnO requires O-rich growth or annealing conditions.
DOI: 10.1103/PhysRevLett.92.155504 PACS numbers: 61.72.Vv, 61.72.Bb, 61.72.Ji, 71.55.Gs
Chemical and size proximities are among the top con-
siderations for choosing a ‘‘good’’ semiconductor dopant
with low formation energy, and thus high solubility. For
p-type doping, it is also desirable to have a dopant with
high electronegativity . For materials involving first-
row anions such as ZnO, however, choices meeting these
criteria are often lacking, because no p-type dopant has a
size similar to the first-row anion and is also more elec-
tronegative. This lack of dopant candidates often consti-
tutes a major hurdle for turning first-row wide-gap
materials into useful electronic materials: p-type zinc
oxide is one such example, for which cation substitution
produces only deep acceptor levels . Until recently, it
was virtually impossible to dope ZnO p type even with
nitrogen, the element that is most similar to O in terms of
atomic size. ZnO is the II-VI analogy of gallium nitride,
having a direct band gap of about 3.4 eV and an excep-
tionally large exciton binding energy of 60 meV .Were
it not for the p-doping bottleneck, ZnO would be an ideal
material for blue and ultraviolet laser and light-emitting
diode applications [4,5].
Recently, codoping was suggested as a possible means
to enhance nitrogen solubility in ZnO and to lower its
ionization energy, thereby obtaining p-type ZnO [6,7].
More recent studies [1,8,9], however, questioned the basic
principles of codoping.The results in Ref.  are, instead,
attributed to the use of metastable dopants and growth
kinetics . It is now clear that the level of the nitrogen
atom on the oxygen site, NO, is relatively deep, making
acceptor ionization difficult [2,10], and N-doped ZnO
could be unstable. To further pursue p-type ZnO, other
group-V dopants have been tried. Interestingly, several
research groups have recently reported p-type conductiv-
ity in ZnO with exceptionally large-size-mismatched
dopants such as P , As [12,13], and Sb 
(atomic radius ? 1:06, 1.20, and 1:40?A vs 0:73?A for
O). This is quite puzzling because not only have the basic
principles regarding dopant size been violated, but also
recent first-principles total energy calculations show that
PO, AsO, or SbOall have very high acceptor-ionization
energies. For example, the calculated AsOacceptor level
is deep, about 930 meV  above the valence band
maximum (VBM). Thus, the probability for acceptor
ionization at room temperature is less than one in 1019,
making it impossible for AsOto dope ZnO efficiently
In this Letter we present a theory for large-size-
mismatched impurities by first-principles calculations.
Isolated As may form donor (AsZn), deep acceptor
(AsO), or amphoteric interstitial (Asi), but none of these
could result in p typeness, so one must consider As-
related defect complexes. Guided by strain relief and
Coulomb interaction, we find that among the complexes
an AsZn-2VZncomplex represents a new class of low-
energy defects with shallow acceptor levels. In this com-
plex, the core As occupies the Zn antisite, which is
energetic enough to spontaneously induce two Zn vacan-
cies.The resulting AsZn-2VZncomplex is an acceptor with
both low formation energy, ?Hf?q ? 0? ? 1:59 eV, and
low ionization energy, "?0=?? ? 0:15 eV, in agreement
with experiments, 0.12  to 0.18 eV . Because the
As atom has fivefold coordination, the complex has its
own identity that is qualitatively different from either
AsZnor VZn. The same is true for Sb with ?Hf?0? ?
2:00 eV and "?0=?? ? 0:16 eV. Our finding could
explain the puzzling experimental observations that
oxygen-rich growth/annealing conditions, which would
severely suppress the formation of AsOand SbO, are
required for successful p-type doping.
We used the density functional theory, as implemented
in the VASP codes , with local density approximation
and ultrasoft pseudopotentials . Zinc 3d states were
included in the valence. The cutoff energy for the plane
wave expansion is 300 eV , with additional tests carriedout
at 400 eV.We used a supercell approach and Monkhorst-
Pack k-point mesh for Brillouin zone integration. For
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16 APRIL 2004
VOLUME 92, NUMBER 15
2004 The American Physical Society155504-1
charged defects, a jellium background was used. In the
case of As, we calculated for each defect the energy with
36-, 64-, and 96-atom cells. Good linearity with inverse
cell volume was observed, which allows for an extrapo-
lation of the defect energies to their dilute limits . In
the case of Sb, we used a 64-atom supercell, with cell
corrections taken from the corresponding As complex.
The defect formation energy is defined  as
?Hf? Etot?D;q? ? Etot?0? ? ?nZn?Zn? ?nO?O
? ?nX?X? qEF;
where Etot?D;q? and Etot?0? are the total energies of the
supercell with and without the defect, D, and X ? As and
Sb. Quantities ?nAand ?Aare the number of species A
(?Zn;O;As;Sb) removed from a defect-free cell to its
respective reservoir to form the defect cell and the cor-
responding reservoir chemical potential, respectively.
The upper limits for ?Zn, ?O, ?As, and ?Sbare the
energies of metallic Zn, gaseous O2, and solid state As
and Sb, which are offset to zero in the present study. To
keep the ZnO thermodynamically stable, it also requires
that ?Zn? ?O? ?ZnO;calc? ?3:58 eV. This further im-
poses ?Oto be in the range ?3:58 eV ? ?O? 0 and
redefines ?Zn? ?3:58 eV ? ?O. Because both As and
Sb prefer to bind with O more strongly than among
themselves, the precipitation of As2O3
thus redefines at the oxygen-rich limit (?O? 0),
?4:05 eV for Sb). In Eq. (1), q and EFare the defect
charge state and Fermi level with respect to theVBM. For
shallow defects, the procedure in Ref.  is used to
calculate the ionization energy.
Figure 1 shows the defect formation energy calculated
under the oxygen- and arsenic-rich conditions, i.e., ?O?
0 and ?As? ?3:63 eV. Formation energy under other
growth conditions can be readily obtained by using
Eq. (1) and Table I, where ?Hfat a specific set of EF,
?O, ?As, or ?Sbis given. Consider isolated As defects:
The formation energies of AsOare greater than 6.0 eVfor
all charge states in the band gap. These energies are high
because of the very large size mismatch between As and
O.Thus, the relevant isolated defects in Fig. 1are the zinc
vacancy (VZn) and arsenic antisite (AsZn). Two or more
such isolated defects can form complexes.We find that the
As?or Sb????As2O3?or Sb2O3?? 3?O?=2??3:63 eV
Zn! ?AsZn? VZn??
is exothermic with a binding energy of 1.14 eV. The
resulting AsZn-VZnis, however, still energetic. It combines
with another VZnto form AsZn-2VZn,
?AsZn? VZn??? V2?
with another1.70 eV binding energy.The overall reaction
can be written as
Zn! ?AsZn? 2VZn??
Zn! ?AsZn? 2VZn??
with the total binding energy ? 2:84 eV.
The formation of the AsZn-VZncomplex is a result of
Coulomb binding between two oppositely charged de-
fects. The subsequent formation of the AsZn-2VZncom-
plex is, however, more complicated, involving both the
optimization of the Madelung energy and, for certain
charge states, the transformation of the As atom into a
newfivefold coordination. Figures 2(a) and 2(b) show two
characteristic atomic structures for the complexes for
q ? 0 and 3 ? . For q ? 0 and ?, the As atom is a triple
donor, donating all of its three electrons to the two VZn
(each can accept up to two electrons). This high 3?
charge leaves the As atom
while sitting in an environment that is highly electro-
negativewith negatively charged oxygen ions.The unique
Fermi level (eV)
Formation energy (eV)
AsZn + VZn + VZn [AsZn-2VZn]
[AsZn-VZn] + VZn [AsZn-2VZn]
AsZn + VZn [AsZn-VZn]
tion energy, as a function of the Fermi level for various As-
related defect complexes in ZnO, under the O- and As-rich
conditions (?O? 0 and ?As? ?3:63 eV). In (b) the slope of
the curves reflects the charge state of the defects and the solid
dots denote the energy positions at which transition from one
charge state to another takes place.
(a) Calculated binding energy and (b) defect forma-
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16 APRIL 2004
VOLUME 92, NUMBER 15
geometry of the wurtzite structure allows for the fifth
oxygen (which ideally would be 12
along the ?0001? direction) and the As to approach each
other. The presence of the two neighboring vacancies
further assists such displacements by locally softening
the lattice. These result in, as indicated in the inset in
Fig. 2(a), a strong As-O bond that is 5% shorter than a
nominal Zn-O bond. The energy gain is 0.61 eV , in com-
parison with a configuration of the same charge state but
without fivefold coordination, similar to the one in
Fig. 2(b). It is interesting to note that for larger impurities
such as Sb, the fourfold structure in Fig. 2(b) spontane-
ously transforms into the fivefold structure without any
energy barrier. For the 3? charged complex, however,
while both VZnare doubly negatively charged, the (1?)-
3bond length away
charged AsZnis not electropositive enough to induce such
fivefold-coordinated As configuration.
The solid dots in Fig. 1(b) show the transition energy
level positions for these defects. In particular, VZnis a
moderately deep double acceptor with the transition en-
ergy at "?0=2?? ? 0:39 eV(measured from theVBM). On
the other hand, AsZnis a multicharge donor with the
transition energy at "?3?=?? ? 0:95 eV. The AsZn-VZn
complex is an amphoteric defect with the donor/acceptor
transition energy at "??=?? ? 1:13 eV. In contrast, the
AsZn-2VZncomplex is a multicharge acceptor with two
calculated ionization energies at "?0=?? ? 0:15 eV
(0.16 eV for SbZn-2VZn) and "??=3?? ? 1:37 eV, respec-
tively. In addition, the metastable AsZn-2VZn, with four-
fold-coordinated Asatom, hasthe"?0=??levelat 0.25eV.
The reason that the AsZn-2VZncomplexes could have
shallower ?0=?? acceptor levels than VZncan be under-
stood as follows: The ?0=?? level of AsZn-2VZnis derived
mainly from the low-lying t2-like acceptor level of VZn,
which could couple to a high-lying t2-like ??=0? level of
AsZn. The level repulsion between the two, upon the
complex formation, pushes the low-lying t2-like level
down, therefore leading to shallower "?0=?? levels for
the AsZn-2VZncomplexes. Moreover, the formation of the
fifth As-O bond lowers the energy of the q ? ? state
slightly more than that of the q ? 0 state, hence further
lowering the "?0=?? level.
Recent experiments showed that ZnO could be doped p
type using P , As [12,13], or Sb  as the dopant to a
hole concentration higher than 1017cm?3. The doping
techniques may vary, e.g., radio frequency sputtering for
P, hybrid beam deposition for As, and excimer laser
doping for Sb, but all have one thing in common: One
needs to apply an oxygen-rich ambient, either during
growth or during postgrowth thermal treatment. Within
the framework of the previous As-on-O acceptor model,
this is quite difficult to reconcile. (i) The AsOhas high
white spheres are the Zn, the large shaded spheres are the As, and the large dashed spheres are the missing Zn atoms.The arrows in
(a) indicate selectively the displacements of the O atoms with large atomic relaxations. The insets in the middle show bond lengths
between the As and neighboring O atoms with respect to that of ideal Zn-O bond (in terms of the percentage difference).
Atomic structures of the AsZn-2VZncomplexes, (a) q ? 0 and (b) q ? 3 ? . The small white spheres are the O, the large
EF? 0, ?O? 0, ?As? ?3:63, and ?Sb? ?4:05 eV. The
energy of H?is with respect to H in a free H2molecule.
Under the O-rich limit, however, it increases by 1.45 eVdue to
the precipitation of H2O.
Calculated defect formation energy (in eV) at
X ? As
X ? Sb
PH YSICA L R EVI EWL ET T ERS
16 APRIL 2004
VOLUME 92, NUMBER 15
formation energy, therefore it is unlikely to form in any Download full-text
appreciable concentrations. (ii) Even if they do form, the
acceptor level of AsOis too deep to provide sufficient
holes. (iii) Moreover,theuse of the O-rich growth/anneal-
ing condition is expected to suppressthe formation of AsO
toa level at which AsZn(a donor)shouldbe more abundant
Within the framework of the present AsZn-2VZncom-
plex model, however, all the three major difficulties of the
As-on-O model are removed. (i) The formation energy is
reasonably low. Figure1(b) shows that during equilibrium
growth the AsZn-2VZncomplex would act as the leading
acceptor while AsZnwould act as the leading donor. This
results in a Fermi level, EF? 0:61 ?1
0:60 eV, at a typical growth temperature of TG?
430?C. The equilibrium concentration of AsZn-2VZn
would be on the order of 1015cm?3. The actual con-
centration could, however, be higher, either by high-
temperaturegrowth followed by rapid cooling that results
in supersaturation of AsZnand VZn, or by nonequilibrium
growth inwhich theAschemicalpotentialexceedsthat of
As2O3. In addition,Table I suggests that a large amount of
H could be incorporated, which shifts the Fermi level
higher. This suppresses isolated AsZnand AsZn-VZndo-
nors, while enhancing AsZn-2VZnacceptors. It is known
that H could be annealed out relatively easily. (ii) The
ionization energy is low.The calculated ionization energy
of 0.15 eVis in fact in reasonable agreement with experi-
ments, 0.12 eV  or 0.18 eV . (iii) Low formation
energy is achieved and is only achievedunder the oxygen-
rich condition, also in line with experiments.
There are other ways to construct complexes between
AsZnand native defects. However, most of them could be
readily ruled out based on their expected electrical be-
haviors and on their dependence on the growth condition
. For example,AsZn-VOwould not form because of the
high energy of VOat the O-rich condition. Moreover, both
AsZnand VOare donors. The resulting complex is also a
donor that cannot explain p-type ZnO. Among the com-
plexes that may compete with AsZn-2VZn, we have calcu-
lated the following: (a) AsO-VZn. While this complex
serves to release the large AsOstrain and could, in prin-
ciple, be a triple acceptor, it spontaneously transforms
into AsZn-VO, which is a donor. (b) Off-center AsO(also
known as Asi-VOpair). Despite the high formation energy
of AsO, the displaced Asistill spontaneously moves back
into the vacant oxygen site (VO). (c) AsZn-2Oi. This is the
most probable competing acceptor that works the same
way as AsZn-2VZn. It deserves attention because,while the
formation energy of Oiis considerably larger than VZn,
the distance to AsZn can be substantially smaller.
However, we find that Oiprefers to form split interstitial
with oxygen (e.g., with about 1.4 eV binding energy for
even larger amount, but also pushes the ?0=2?? transition
level 1.5 eVabove theVBM. This makes the Oiunattrac-
tive to AsZnunless EF> 1:5 eV.
i). This not only increasesthe Oidiffusion barrier by an
In summary, our AsZn-2VZn(and SbZn-2VZn) model
provides a possible answer to a number of mysterious
key experimental observations in As- (and Sb)-doped
ZnO. The significance of the model could go beyond
p-type ZnO: It reveals that one could in fact maximize
the formation energies of the compensating native defects
such as VOand Zni, while minimizing that of the dopant
by adequate chemical potentials. This is in contrast to
currently used doping schemes in which the formation
energies of the compensating defects are often mini-
mized along with that of the dopant. So far, complex
formation by codoping has been largely discredited be-
cause a mechanism in which Coulomb binding could
compensate the cost of creating extra defects in the com-
plex is still lacking. Our model here provides a mecha-
nism through which complexes could become more
important than their parent defects.
This work was supported by the U.S. DOE/BES and
DOE/EERE under Contract No. DE-AC36-99GO10337
and by the NERSC for MPP time. The work in
Thailandwassupportedby theThai Research Fund under
Contract No. BRG4680003.
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