Electronic Properties of Post-Transition Metal
Oxide Semiconductor Surfaces
T. D. Veal, P. D. C. King, and C. F. McConville
Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
6.1 Introduction
The post-transition metal oxides (PTMOs) have traditionally
been
classified
as
transparent
conductors.
The
normally
contradictory properties of transparency to visible light and
electrical conductivity have made materials such as Sn-doped
In O and Al-doped ZnO suitable for use as transparent electrodes
in devices such as solar cells and flat panel displays. However, the
PTMOs are increasingly being considered as semiconductors for
potential use as the active layer in a wide range of transparent
(opto)electronic devices.
Fig. 1 The post-transition metal elements and oxygen highlighted on a portion of
the periodic table. The shading corresponds to the electronegativity of the
2
elements. The atomic number (top left), atomic radius in pm (top right) and the
electronegativity in Pauling units (bottom) are also shown for each element
The electronic properties of the surfaces of semiconductors
are important for many device applications. Due to different atomic
co-ordination and broken translational symmetry at the surface, the
electronic properties can differ markedly in this region compared to
in the bulk of a semiconductor. The presence of charged surface
states can induce a macroscopic redistribution of free carriers close
to the surface, in order to screen the electric fields associated with
such a surface charge, and therefore minimize energy. Such socalled surface space-charge regions are associated with a bending of
the electronic bands relative to the Fermi level, over distances
defined by the electronic screening length of the material. Typical
length scales for such a band bending in semiconductors are on the
order of 5 to 500 nm. Therefore, while such surface electronic
properties are important for many device applications, they become
even more important in nanostructured semiconductors, where the
surface space-charge region can account for a large proportion of the
volume
of
the
material.
Indeed,
transport
properties
of
semiconductor nanowires are known to depend on the nature of the
surface space charge of the particular material. For example, in InN
nanowires the conductivity increases as the diameter is reduced due
to the presence of surface electron accumulation, while in GaN
nanowires reducing the diameter decreases the conductivity as a
3
result of the surface electron depletion layer [1, 2]. This follows the
surface space-charge behaviour of thin films of InN and GaN [3, 4].
The surface space-charge region is widely recognised as important
to the wide variety of applications of metal oxide nanostructures, but
frequently the only type of intrinsic space-charge region considered
for n-type semiconductors is an electron depletion layer [5].
However, as will be discussed below, this is generally an incorrect
assumption for PTMOs. The electronic properties of metal oxide
nanostructures provide the motivation for this chapter on the
electronic properties of the surfaces of PTMO thin films. Until
recently, many of the fundamental surface properties of these
materials were unknown or misunderstood. A knowledge and
understanding of the fundamental surface space-charge properties of
this class of materials will be of interest to those researching both
the application of these materials in transparent (opto)electronics
and the transport properties of PTMO nanostructures.
The post-transition metallic elements and oxygen are
highlighted in figure 1 on a portion of the periodic table that depicts
the electronegativity and atomic radius of the elements. This chapter
is limited to the surface electronic properties of the period 4 (ZnO
and Ga O ) and period 5 (CdO, In O , and SnO ) PTMO
semiconductors. The period 6 post-transition metal oxides (HgO,
Tl O , PbO, PbO , and Bi O ) have not yet had their surface
electronic properties investigated. In section 2, the surface spacecharge properties will be presented for each of the PTMOs of
periods 4 and 5. This will be followed in section 3 by an explanation
4
of the overriding cause of these and related properties in terms of the
nature of the bulk band structure of the materials and the location of
the band edges with respect to the charge neutrality level.
6.2 Surface Space-Charge Properties
The
surface
space-charge
properties
of
an
n-type
semiconductor can be determined, to a large extent, by measuring
the surface and bulk Fermi levels, with the difference between them
being accounted for by the band bending. In practice, the surface
Fermi level with respect to the valence band maximum (VBM) can
be determined using x-ray photoemission spectroscopy (XPS) and
knowledge of the band gap of the semiconductor enables the Fermi
level with respect to the conduction band minimum (CBM) to be
obtained. 1 The bulk Fermi level can be estimated by measuring
either the free-electron density using the Hall effect, the conduction
electron plasma frequency using infrared reflectivity, or, for a
degenerately
doped
material,
by
using
optical
absorption
spectroscopy. The determined surface and bulk Fermi levels can
then be used as boundary conditions to solve the Poisson equation
within the modified Thomas-Fermi approximation [6]. The solution
While this picture may be complicated somewhat by many-body effects within
the surface space-charge region, as will be discussed later in this chapter, it still
provides a correct qualitative and indeed semi-quantitative picture of the surface
space-charge characteristics of a given material.
1
5
of the Poisson equation gives the band bending and charge profiles
as a function of depth below the semiconductor surface and also the
surface state density. Here, the surface space-charge properties of all
the period 4 and 5 PTMOs investigated using these methods are
presented within the context of the previous understanding of their
surface electronic properties.
6.2.1 ZnO
The first member of the period 4 PTMOs, ZnO, has the
wurtzite structure and a room temperature band gap of 3.35 eV. The
electronic properties of its surfaces have been studied for over forty
years [7]. Some of the earliest work showed that it is possible to
modify the surface space charge from electron depletion to strong
electron accumulation by varying the surface treatment. Exposure of
the ZnO surface to oxygen induces an electron depletion layer,
whereas atomic hydrogen treatment produces surface electron
accumulation [7]. However, the `intrinsic' state of the space charge
at ZnO surfaces is still debated [8, 9] and the role of surface
conductivity in ZnO nanowires is far from being resolved [10].
Fig. 2 Valence-band XPS spectra from the Zn-polar and O-polar faces of (a) the
same bulk c-axis HT ZnO wafer and (b) the same bulk c-axis PM ZnO wafer,
showing the extraction of , the valence-band maximum to Fermi level separation,
for each face. The inset of (a) shows the spectrum from the m-plane face of a
separate HT ZnO wafer. The inset of (b) shows the spectrum from the a-plane face
6
of a separate PM ZnO wafer. Figure reproduced with permission from M. W.
Allen, C. H. Swartz, T. H. Myers, T. D. Veal, C. F. McConville, and S. M. Durbin,
Physical Review B 81, 075211 (2010). Copyright (2010) by the American Physical
Society.
Figure 2 shows valence band XPS of bulk ZnO crystals
grown by both the hydrothermal (HT) and pressurized-melt (PM)
techniques. Spectra were collected from both the Zn- and O-polar
faces of the same c-axis crystals grown by each method and also
from non-polar crystals (m-plane and a-plane). The room
temperature bulk electron densities were found, from multiple field
Hall effect measurements, to be 2-3
5
10
cm
10
cm
for the HT ZnO,
for the a-plane PM ZnO, and 1.5
10
cm
for
the c-plane PM ZnO [9]. The separation, , between the VBM and
the Fermi level at the surface is determined by extrapolating a linear
fit to the lower binding energy edge of the valence band
photoemission to a line fitted through the background data. The
Fermi level is calibrated to be the zero of the binding energy scale
by using the Fermi edge of a silver reference sample.
From the XPS data, the surface Fermi level was found to be
located between 3.50 and 3.71 eV above the VBM, with the highest
values being for the Zn-polar surface, the lowest values for the Opolar surface, and the non-polar surfaces in between [9]. Since the
measured bulk carrier densities correspond to bulk Fermi levels
ranging from 3.10 to 3.27 eV above the VBM, the surface Fermi
level is always higher than the bulk Fermi level, indicating the
7
presence of surface electron accumulation for all samples
investigated. A greater difference between the surface Fermi levels
of the Zn- and O-polar surfaces was found for the HT ZnO than for
the much higher bulk carrier density PM ZnO. The greater electron
accumulation at the Zn-polar face, particularly for the HT ZnO, is
attributed to the spontaneous polarization [11] associated with the
wurtzite structure. The effect is reduced for the PM ZnO due to
partial screening by the higher bulk electron density of these
samples. The surface band bending and carrier concentration profiles
for the various ZnO samples were determined by numerical solution
of
Poisson's
equation
within
the
modified
Thomas-Fermi
approximation [6] and are shown in figure 3.
From the measured amount of band bending, solving the
Poisson equation enabled the surface sheet densities to be
determined as 7
10
cm
[3
10
[O-polar] face of the HT ZnO and 5
cm
cm
10
] for the Zn-polar
cm
[2.5
10
] for the Zn-polar [O-polar] face of the PM ZnO. These
surface electrons have been found to have a significant influence on
the electrical properties of high resistivity HT ZnO at temperatures
below 200 K, and are a major cause of the anomalously low
maximum electron mobility measured using single magnetic field
Hall effect measurements. For PM ZnO, the surface layer has little
effect on its electrical properties above 50 K due to the higher
concentration of uncompensated shallow donors in this material [9].
Surface electron accumulation appears to be the natural state of both
polar and non-polar ZnO surfaces and can significantly influence
8
electrical measurements made on heavily compensated ZnO
material. Consequently it must be taken into account when
investigating the electrical properties of potentially -type material.
Additionally, it can be seen from figure 3 that, for the HT ZnO, the
free-electron density 100 nm away from the surface is still
significantly higher than the bulk value, illustrating how important
surface properties can be for nano-scale structures.
6.2.2 Ga O
The second member of the period 4 PTMOs, Ga O ,
exhibits five different polymorphs [12], with the most stable being
-Ga O with a monoclinic structure and a room temperature band
gap in the range of 4.4-4.9 eV [13, 14]. In spite of the surface
electronic properties of Ga O
not receiving much attention, thin
films of this material have been successfully used as gas sensors.
Rather than exhibiting sensitivity to anion-like chemisorption, such
as O , they have been found to be good sensors of reducing gases,
such as H
and CO, when chemisorption of donor-like species
occurs [15]. This behaviour was explained in terms of an electron
accumulation layer model of the Ga O surface [16]. The presence
of an electron accumulation is also suggested by recent
photoemission data, where the surface Fermi level can be seen to be
approximately 4.5 eV above valence band maximum [17]. Such a
surface Fermi level, very close to or above the conduction band
9
minimum, is above typical Ga O
bulk Fermi levels, indicating
downward band bending and surface electron accumulation. Further
investigations of Ga O are, however, required to verify the nature
of its surface electronic properties.
Fig. 3 Poisson-MTFA calculations of the band banding and the carrier
concentration profiles in the electron accumulation layer at the Zn-polar [(a) and
(c)] and O-polar faces [(b) and (d)] of HT ZnO; and at the Zn-polar face [(e) and
(g)] and O-polar face [(f) and (h)] of PM ZnO. Figure reproduced with
permission from M. W. Allen, C. H. Swartz, T. H. Myers, T. D. Veal, C. F.
McConville, and S. M. Durbin, Physical Review B 81, 075211 (2010). Copyright
(2010) by the American Physical Society
6.2.3 CdO
The first member of the period 5 PTMOs, CdO, has the
rocksalt structure and a room temperature direct band gap of 2.2 eV
[18, 19], with two indirect band gaps of less than 1.1 eV [19, 20,
21]; the valence band maximum is not at the
-point due to
repulsion between the Cd 4d and O 2p states being symmetry
forbidden at
for the rock-salt structure [22]. Until recently, CdO
had long been assumed to exhibit surface electron depletion [23].
However, several recent studies have contradicted this, finding
evidence of surface electron accumulation [24, 25, 26].
10
Fig. 4 (a) Valence-band XPS, (b) squared optical-absorption coefficient, and (c)
measured (points) and simulated (line) IR reflectivity spectra for an undoped CdO
sample following annealing at 600
C in UHV for 2 h. (d) Band bending [CBM,
indirect (L-point) and direct ( -point) VBMs] and (e) carrier concentration as a
function of depth below the surface in the electron accumulation layer. Figure
reproduced with permission from P. D. C. King, T. D. Veal, P. H. Jefferson, J.
Zúñiga-Pérez, V. Muñoz-Sanjosé, and C. F. McConville, Physical Review B 79,
035203 (2009). Copyright (2009) by the American Physical Society
Specifically, a combination of valence-band XPS, Hall effect
and optical absorption and reflectivity has been used to determine
the surface and bulk Fermi levels of CdO(001) films grown by metal
organic vapour phase epitaxy on sapphire substrates. The valenceband XPS measurements, shown in Fig. 4(a), give the L-point
(indirect) VBM to surface Fermi level separation as =1.29 0.05
eV. Taking the separation of the -point and L-point maxima of the
valence band as 1.2 eV from calculations [24], the surface Fermi
level is found to be 2.49 eV above the -point VBM. Meanwhile,
from Hall effect measurements (n=1.6 10
cm V
s
cm
,
=106
) and the optical absorption and IR reflectivity data
shown in Figs. 4(b) and 4(c), the -point VBM to bulk Fermi level
separation was determined as
= 2.23
0.05 eV. Therefore, the
Fermi level lies higher relative to the band extrema at the surface
than in the bulk, implying a downward bending of the bands at the
surface of 0.26 eV. The calculated band bending is shown in Fig.
11
4(d) along with the large accumulation of electrons in the near
surface region shown in Fig. 4(e).
The surface electron accumulation has additionally been
found to be quantized. Angle-resolved photoemission spectroscopy
(ARPES) has revealed that the conduction electrons at the surface
occupy two-dimensional subbands created by the confining potential
well associated with the downward band bending [24, 26]. The
photoemission maps for a CdO surface quantized two-dimensional
electron gas (Q2DEG) are shown in Fig. 5. Similar Q2DEG states
are expected at the surface of PTMO nanowires. However, if the
nanowire size is sufficiently small, the wavefunction tails from the
Q2DEG states of one surface may overlap with those from the
surface on the opposite side of the nanowire. In this case, these
states could interact, potentially giving rise to novel physics between
two spatially separated, but nonetheless coupled, Q2DEGs.
Fig. 5 (a) Quantized conduction-band subbands of a surface Q2DEG. (b) E vs k
and (c) constant energy cuts through the subband dispersions measured by
ARPES, shown here for a CdO(001) surface recorded with a photon energy of
h = 30 eV at room temperature. The constant energy cuts are integrated over
3
meV about (c1) the Fermi level and (c2) 0.15, (c3) 0.30, and (c4) 0.45 eV below
the Fermi level, respectively. (d) Schematic of downward bending of the
conduction band and (inset) corresponding increase in free-carrier density within
the semiconductor surface electron accumulation layer (Q2DEG). (e) angleintegrated PES measurements of the valence bands and Cd 4d core levels in CdO,
recorded at a photon energy of h
= 120 eV. Figure reproduced with permission
12
from P. D. C. King, et al., Physical Review Letters 104, 256803 (2010). Copyright
(2010) by the American Physical Society
Intriguingly, such detailed spectroscopic measurements of the electronic
states within a surface electron accumulation layer reveals a discrepancy with the
simple band-bending picture discussed so far. While the valence band bending
determined by XPS (Fig. 4a) as well as core-level and other valence-band
photoemission measurements (Fig. 5e) indicate a downward band bending of only
0.25 eV, a deep enough quantum well to give the measured conduction-band
subband as low as 0.5 eV below the Fermi level requires the conduction band to
bend downwards by 1.1 eV. This discrepancy between the amount of valence and
conduction band bending can be resolved by considering many-body effects
within the electron accumulation layer [26]. Instead of the conduction and valence
bands undergoing the same amount of band bending as in the conventional oneelectron picture of surface space charge, band gap renormalization occurs in the
accumulation layer where the electron density is highest, shrinking the band gap
close to the surface, as illustrated in Fig. 6. This band gap shrinkage has a large
influence on the surface sheet density; within the one-electron picture, the valence
band bending implies a sheet density of 1
density, determined from the Luttinger area,
vector,
10
cm
=
, taken directly from the ARPES data, is 4.4
, while the actual sheet
, with the Fermi wave
10
cm
. Such
many-body effects probably increase the surface sheet electron densities of other
materials discussed elsewhere in this chapter compared with the reported values
based on valence-band photoemission data.
Fig. 6 One-electron (solid line) and schematic renormalized (dashed line) band
bending at the surface of CdO, and corresponding calculated one-electron (solid)
and measured renormalized (dashed) subband energies. Figure reproduced with
13
permission from P. D. C. King, et al., Physical Review Letters 104, 256803
(2010). Copyright (2010) by the American Physical Society
6.2.4 In O
The second member of the period 5 PTMOs, In O , has the
body-centred-cubic (bcc) bixbyite structure or the less stable
rhombohedral (rh) structure. The direct band gap of cubic In O
was long thought to be 3.7 eV, based on the onset of optical
absorption, with an indirect gap of about 2.6 eV [27, 28]. However,
recent theoretical studies have found no evidence for any significant
difference between the direct and indirect band gaps [29, 30].
Experimental studies using photoemission, x-ray emission and
absorption and optical absorption are consistent with a band gap in
the range 2.6--2.95 eV [29, 31]. The theoretical calculations indicate
that the weak nature of optical absorption around this energy can be
attributed to transitions between the highest valence-band states and
states at the CBM being dipole forbidden or having only minimal
dipole intensity [29, 30].
This revision of the band gap has brought about a reevaluation of the surface space-charge properties of In O . Before
2008, photoemission spectroscopy had been used to locate the
surface Fermi level at about 3 eV above the VBM [32, 33]. With the
accepted band gap at that time being 3.7 eV, this, along with a bulk
Fermi level close to the CBM, implied the presence of upward band
14
bending and a surface electron depletion layer. However, with the
recently established band gap of 2.9 eV ( 3.0 eV) for bcc (rh)
In O , this and more recent photoemission data, such as that shown
in figure 7 for both bcc- and rh-In O , indicate that the surface
Fermi level is above the bulk Fermi level, corresponding to
downward band bending and electron accumulation [31, 34].
For In O , with the shallow dispersion of its topmost
valence bands [30], the VBM position with respect to the Fermi
level cannot be accurately determined by extrapolating the leading
edge of the valence band photoemission; this method leads to an
underestimation of the VBM to surface Fermi level separation due to
the effects of instrumental and lifetime broadening. Instead, as
shown in figure 7, the experimental data is compared with the
broadened calculated valence band density of states (VB-DOS). A
3.4 eV (3.5 eV) shift is required to align the calculated VB-DOS
with the XPS data from undoped bcc (rh) In O , indicating that the
surface Fermi level is 0.5 eV above the CBM for both bcc and rh
In O . Along with the bulk Fermi levels for the different samples,
determined from Hall effect and infrared reflectivity measurements,
the downward band bending was found to be in the range 0.4-0.5 eV
[31]. When heavily Sn-doped, the bulk Fermi level is much closer to
the surface Fermi level, resulting in approximately flat bands. The
band bending and carrier concentration profiles as a function of
depth below the surface, calculated by solving the Poisson equation,
are shown in figure 8 [31]. The surface sheet density can be
15
estimated from these calculations to be 1.3 10
cm
for all of
the undoped In O samples.
Fig. 7 Background-subtracted valence-band photoemission spectra from (a)
undoped and Sn-doped bcc-In O (001) and undoped (111) (grown by plasmaassisted molecular-beam epitaxy and metal organic vapour phase epitaxy) and (b)
undoped rh-In O (0001). The conduction-band emission is magnified 25 times.
The density functional theory calculated valence-band density of states is shaded
in grey and is also shown after lifetime and instrumental broadening. Figure is
adapted from ref. [31]
Fig. 8 Poisson-MTFA calculations of band bending [(a) and (c)] and carrier
concentration profiles [(b) and (d)] in the electron accumulation layer at the
surface of bcc-In O
[(a) and (b)] and rh-In O
[(c) and (d)]. Figure is
adapted from ref. [31]
The presence of surface electron accumulation is further
corroborated by a comparison of Al K
XPS (h = 1486.6 eV) and
synchrotron radiation high energy XPS (h = 6000 eV) [35]. As can
be seen in figure 7, an additional peak is present in the
photoemission spectra just below the Fermi level. This corresponds
to photoemission from the occupied conduction band states which
have predominantly In 5
character. After correcting for matrix
element effects, Zhang et al. found a larger contribution from filled
conduction band states in the more surface sensitive 1486.6 eV XPS
16
than for the 6000 eV XPS [35]. This indicates that there is an
increased concentration of conduction electrons close to the surface
than deeper in the bulk, confirming the picture of a surface electron
accumulation layer in In O .
6.2.5 SnO
The third and final member of the period 5 PTMOs, SnO ,
has the rutile structure and a band gap of 3.59 eV (3.50 eV at room
temperature) [36, 37]. The surface properties of SnO
have been
comprehensively reviewed quite recently [38]. The surface of SnO
can exhibit surface electron depletion or accumulation, depending on
the stoichiometry of the surface and the bulk Fermi level. Similarly
to ZnO, adsorption of anion species leads to electron depletion,
while cation adsorption leads to accumulation, making SnO a good
material for gas sensing via corresponding changes in conductivity.
Indeed, nanoscale structures of SnO
are particularly suited to this
task [39], where the larger surface to bulk ratio provide a relatively
higher density of surface adsorption sites compared to thin films,
enabling the adsorbed species to have an even greater influence on
the total measured conductivity. The presence of an electron
accumulation layer at the surface of SnO
under certain conditions
is long established [40], but whether it is the `intrinsic' state' of the
surface is not yet well established.
Valence-band XPS from an undoped bulk SnO (100) crystal
after cleaning by 2 hours of vacuum annealing at 400 C is shown in
17
figure 9. The VBM to surface Fermi level separation is 3.70 eV.
With a room temperature band gap of 3.50 eV, this corresponds to
the surface Fermi level being 0.20 eV above the CBM. This is well
above the non-degenerate bulk Fermi level of undoped SnO ,
indicating the presence of downward band bending and electron
accumulation. Before annealing a VBM to surface Fermi level
separation of 3.60 eV was observed, again indicating electron
accumulation but to a lesser extent than after the surface was
reduced by annealing.
Fig. 9 Background-subtracted valence-band photoemission spectrum from bulkgrown SnO (100)
These results, parallels with the other PTMOs, some recent
studies [37, 41] and the discussion in the next section indicate that
SnO
surfaces do have an inherent tendency to exhibit electron
accumulation in contrast to the surface depletion layer of the
majority of n-type semiconductors. However, the presence of anion
species when used as a gas detector or exposure to oxygen plasma
treatment can result in surface electron depletion [38, 41].
18
6.3 Bulk Band Structure Origin of Electron
Accumulation Propensity
From the preceding sections, it is clear that the PTMOs
exhibit a tendency towards surface electron accumulation, rather
than the charge depletion common to almost all conventional
semiconductors. This raises the question whether some universal
characteristic of the PTMOs drives this apparently unconventional
surface behaviour. In addition to their propensity for strongly -type
surfaces, these materials also have a proclivity towards -type bulk
properties, with many defect centres that are traditionally considered
to counteract the prevailing conductivity, including hydrogen
impurities [42, 43, 44, 45] and several native defects, exhibiting an
extreme propensity for donor behaviour in PTMOs. Any model
which explains the surface properties of these materials must also be
consistent with these striking bulk properties.
In fact, both the surface and bulk characteristics of PTMOs
can naturally be explained from gross features of their bulk band
structure. A typical PTMO bulk band structure, for In O , is shown
in Fig. 10. While multiple and quite complex valence bands are
observed, the conduction band is characterized by a single low-lying
band at the zone centre. Throughout the rest of the Brillouin zone,
the conduction band lies much higher. The character of so-called
deep, that is localized, defects, is determined from the band structure
across the Brillouin zone (that is, they have a very extended k-space
19
nature). Indeed, for broken-symmetry defect states such as surface
states, native defects, or hydrogen impurities, it is possible to define
an energy level at the mid-point of the average band gap across the
Brillouin zone which determines the charge transition from
positively to negatively charged defect centres [46, 47, 48, 49]. If
this so-called charge neutrality level (CNL) lies within the
fundamental band gap, it is generally favaourable for compensating
defect centres and surface charge depletion, as shown in Fig. 11.
However, for a bulk band structure of the form depicted in Fig. 10,
the low-lying CBM can actually occur below the mid-gap position
averaged across the entire Brillouin zone. In this case, even for bulk
Fermi levels above the bottom of this CBM, it remains favourable
for donor-like surface states to donate their electrons into the
conduction band, forming a surface electron accumulation.
Similarly, native defects and hydrogen impurities can both gain
energy by donating free-carriers into the conduction band (see Fig.
11).
Fig. 10 Calculated band structure of In O . Figure adapted from Ref. [30]
Fig. 11 Schematic formation energies for dominant native defects and interstitial
hydrogen impurities and schematic band bending in conventional semiconductors
(left) and PTMOs (right). The influence of the CNL, within the band gap in
20
conventional semiconductors but above the CBM in PTMOs, can clearly be seen.
Figure adapted from Ref. [25]
Consequently, the general propensity for donor-type surface
states as well as donor bulk defects and hydrogen in PTMOs can all
be understood to result from the bottom of the conduction band lying
below the charge neutrality level in these materials. Indeed, from a
number of direct measurements [25, 34], relative valence band
alignments from valence-band offset measurements [50, 51, 52], and
calculations [53, 54], the CNL lying above the bottom of the
conduction band can indeed be seen as a universal property of the
PTMOs, as shown in Fig. 12. In all of these cases, the low-lying
CBM gives rise to this band alignment: such features of the bulk
band structure are apparent in electronic structure calculations for
many PTMOs [22, 37, 55]. This itself can be understood as a
consequence of the large size and electronegativity mismatch
between the constituent post-transition metal element and oxygen
[56] (see Fig. 1). A similar situation occurs in the semiconductor
InN, with the CBM also located below the CNL [56], as shown in
Fig. 12. Indeed, the properties of InN exhibit many similarities with
the PTMOs [56, 57, 58]. While we stress that this is not a
microscopic model, such similarities, and their differences from
conventional semiconductors such as Si and GaAs, are well
explained by the charge neutrality level concept (see Fig. 12).
21
Fig. 12 Band lineup of a number of PTMOs and other semiconductors, relative to
the charge neutrality level. The PTMOs and InN are highlighted and compared
with the conventional semiconductors, Si and GaAs. Ga O
is omitted due to the
lack of quantitative information about the location of its band edges with respect
to the CNL. The positions of the bands relative to the CNL are derived from the
measurements and calculations in Refs. [25, 31, 50, 51, 52, 53, 56]
6.4 Conclusion
Evidence of electron accumulation at the surfaces of the
PTMOs, ZnO, Ga O , CdO, In O and SnO has been presented.
For the most ionic and cation-anion mismatched compounds, CdO
and In O , electron accumulation is universally observed (in the
absence of extremely high doping levels). The other PTMOs have a
strong tendency to exhibit surface electron accumulation, but can
also have an electron depletion layer under the appropriate surface
stoichiometry conditions or when certain anions are adsorbed.
This proclivity towards surface electron accumulation shown
by the PTMOs is due to their bulk band structure, whereby the point band extrema are low with respect to the charge neutrality
level, enabling donor surface states to be unoccupied and therefore
positively charged for typical bulk Fermi levels. These surface states
donate their electrons into the conduction band, resulting in surface
electron accumulation and a corresponding downward band bending.
This band structure property of the PTMOs is also responsible for
22
the favourability of donor native defects, high dopability and donor
hydrogen in already n-type material.
The surface electronic properties of the PTMOs determine
the Ohmic or Schottky behaviour of contacts, are important for their
use as gas sensors and contribute to their conductivity. The
electronic properties of thin films and bulk crystals of the PTMO
surfaces also provide information vital for the interpretation of
conductivity measurements of PTMO nanostructures, which are
often dominated by surface effects.
Acknowledgements
The following people are gratefully acknowledged for fruitful
collaborations on determining the surface electronic properties of
PTMOs: P. H. Jefferson, J. Zúniga-Peréz, V. Muñoz-Sanjosé, Ch. Y.
Wang, V. Cimalla, and O. Ambacher, A. Bourlange, D. J. Payne, K.
H. L. Zhang, R. G. Egdell, M. W. Allen, S. M. Durbin, N. Peng, G. R.
Bell, I. Maskery, L. F. J. Piper, K. E. Smith, E. D. L. Rienks, M.
Fuglsang Jensen, Ph. Hofmann, F. Fuchs, A. Schleife, J.
Furthmüller, and F. Bechstedt. The Engineering and Physical
Sciences Research Council, UK, is acknowledged for funding a
Career
Acceleration
EP/G004447/1).
Fellowship
for
TDV
(Grant
no.
23
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Calarco, R., Marso, M.: GaN and InN nanowires grown by MBE: A comparison. Appl.
Phys. A 87, 499-503 (2007)
Richter, T., Lüth, H., Schäpers, Th., Meijers, R., Jeganathan, K., Estévez Hernández,
S., Calarco, R., Marso, M.: Electrical transport properties of single undoped and ntype doped InN nanowires. Nanotechnol. 20, 405206:1-6 (2009)
Mahboob, I., Veal, T.D., McConville, C.F. Lu, H., Schaff, W.J.: Intrinsic electron
accumulation at clean InN surfaces. Phys. Rev. Lett. 92, 036804:1-4 (2004)
King, P.D.C, Veal, T.D., Lu, H., Jefferson, P.H., Hatfield, S.A., Schaff, W.J.,
McConville, C.F.: Surface electronic properties of n- and p-type InGaN alloys. Phys.
Stat. Sol. (b) 245, 881-883 (2008)
Comini, E., Baratto, C., Faglia, G., Ferroni, M., Vomiero, A., Sberveglieri, G.: Quasione dimensional metal oxide semiconductors: Preparation, characterization and
application as chemical sensors. Prog. Mat. Sci. 54, 1-67 (2009)
King, P.D.C, Veal, T.D., McConville, C.F.: Nonparabolic coupled PoissonSchrödinger solutions for quantized electron accumulation layers: Band bending,
charge profile, and subbands at InN surfaces. Phys. Rev. B 77, 125305:1-7 (2008)
Heiland, G., Kunstman, P.: Polar surfaces of ZnO crystals. Surf. Sci. 13, 72-84 (1969)
Schmidt, O., Kiesel, P., Ehrentraut, D., Fukuda, T., Johnson, N.M.: Electrical
characterization of ZnO, including analysis of surface conductivity. Appl. Phys. A 88,
71-75 (2007)
Allen, M.W., Swartz, C.H., Myers, T.H., Veal, T.D., McConville, C.F., Durbin, S.M.:
Bulk transport measurements in ZnO: The effect of surface electron layers. Phys. Rev.
B 81, 075211:1-6 (2010)
Chiu, S.-P., Lin, Y.-H., Lin, J.-J.: Electrical conduction mechanisms in natively doped
ZnO nanowires. Nanotechnol. 20, 015203:1-8 (2009)
Posternak, M., Baldereschi, A., Catellani, A., Resta, R.: Ab initio study of the
spontaneous polarization of pyroelectric BeO. Phys. Rev. Lett. 64, 1777-1780 (1990)
Roy, R., Hill, V.G., Osborn, E.F.: Polymorphism of Ga2O3 and the System Ga2O3H2O. J. Am. Chem. Soc. 74, 719-722 (1952)
Passlack, M., Schubert, E.F., Hobson, W.S., Hong, M., Moriya, N., Chu, S.N.G:
Ga2O3films for electronic and optoelectronic applications. J. Appl. Phys. 77, 686-693
(1995)
Orita, M., Ohta, H., Hirano, M., Hosono, H.: Deep-ultraviolet transparent conductive
β- Ga2O3thin films. Appl. Phys. Lett. 77, 4166-4168 (2000)
Fleischer, M., Meixner, H.: Sensing reducing gases at high temperatures using longterm stable Ga2O3thin films. Sens. Actuators B 7, 257-261 (1992)
16. Geistlinger, H.: Accumulation layer model for Ga O thin-film gas sensors based
on the Volkenstein theory of catalysis. Sensors and Actuators B 18-19, 125-131 (1994)
17. Lovejoy, T.C., Yitamben, E.N., Shamir, N., Morales, J., Villora, E.G., Shimamura, K.,
Zheng, S., Ohuchi, F.S., Olmstead, M.A.: Surface morphology and electronic
structure of bulk single crystal β-Ga2O3(100). Appl. Phys. Lett. 94, 081906:1-3 (2009)
18. Jefferson, P.H., Hatfield, S.A., Veal, T.D., King, P.D.C, McConville, C.F., ZúñigaPérez, J., Muñoz-Sanjosé, V.: Bandgap and effective mass of epitaxial cadmium oxide.
Appl. Phys. Lett. 92, 022101:1-3 (2008)
19. Benko, F.A. and Koffyberg, F.P.: Quantum efficiency and optical transitions of CdO
photoanodes. Solid State Comm. 57, 901-903 (1986)
20. Koffyberg, F.P.: Thermoreflectance spectra of CdO: Band gaps and band-population
effects. Phys. Rev. B 13, 4470-4476 (1976)
21. King, P.D.C, Veal, T.D., Schleife, A., Zúñiga-Pérez, J., Martel, B., Jefferson, P.H.,
Fuchs, F., Muñoz-Sanjosé, V., Bechstedt, F., McConville, C.F.: Valence-band
24
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
electronic structure of CdO, ZnO, and MgO from x-ray photoemission spectroscopy
and quasi-particle-corrected density-functional theory calculations. Phys. Rev. B 79,
205205:1-6 (2009)
Schleife, A., Fuchs, F., Furthmüller, J., Bechstedt, F.: First-principles study of groundand excited-state properties of MgO, ZnO, and CdO polymorphs. Phys. Rev. B 73,
245212 (2006)
Makuta, I.D., Poznyak, S.K., Kulak, A.I.: Hole diffusion transport and photocurrent
generation in the degenerate n-CdO/electrolyte junction. Solid State Comm. 76, 65-68
(1990)
Piper, L.F.J., Colakerol, L., King, P.D.C, Schleife, A., Zúñiga-Pérez, J., Glans, P.-A.,
Learmonth, Federov, T.A., Veal, T.D., Fuchs, F., Muñoz-Sanjosé, V., Bechstedt, F.,
McConville, C.F., Smith, K.E.: Observation of quantized subband states and evidence
for surface electron accumulation in CdO from angle-resolved photoemission
spectroscopy. Phys. Rev. B 78, 165127:1-5 (2008)
King, P.D.C, Veal, T.D., Jefferson, P.H., Zúñiga-Pérez, J., Muñoz-Sanjosé, V.,
McConville, C.F.: Unification of the electrical behavior of defects, impurities, and
surface states in semiconductors: Virtual gap states in CdO. Phys. Rev. B 79,
035203:1-5 (2009)
King, P.D.C, Veal, T.D., McConville, C.F., Zúñiga-Pérez, J., Muñoz-Sanjosé, V.,
Hopkinson, M., Rienks, E.D.L., Fuglsang Jensen, M., Hofmann, Ph.: Surface bandgap narrowing in quantized electron accumulation layers. Phys. Rev. Lett. 104,
256803:1-4 (2010)
Weiher, R.L., Ley, R.P.: Optical properties of indium oxide. J. Appl. Phys. 37, 299302 (1966)
Matino, F., Persano, L., Arima, V., Pisignano, D., Blyth, R.I.R., Cingolani, R.,
Rinaldi, R.: Electronic structure of indium-tin-oxide films fabricated by reactive
electron-beam deposition. Phys. Rev. B 72, 085437:1-6 (2005)
Walsh, A., Da Silva, J.L.F., Wei, S.-H., Körber, C., Klein, A., Piper, L.F.J., DeMasi,
A., Smith, K.E., Panaccione, G., Torelli, P., Payne, D.J., Bourlange, A., Egdell, R.G.:
Nature of the band gap of In 2O3 revealed by first-principles calculations and x-ray
spectroscopy. Phys. Rev. Lett. 100, 167402:1-4 (2008)
Fuchs, F., Bechstedt, F.: Indium-oxide polymorphs from first principles: Quasiparticle
electronic states. Phys. Rev. B 77, 155107:1-10 (2008)
King, P.D.C, Veal, T.D., Fuchs, F., Wang, Ch.Y., Payne, D.J., Bourlange, A., Zhang,
H., Bell, G.R., Cimalla, V., Ambacher, O., Egdell, R.G., Bechstedt, F., McConville,
C.F.: Band gap, electronic structure, and surface electron accumulation of cubic and
rhombohedral In2O3. Phys. Rev. B 79, 205211:1-10 (2009)
Christou, V., Etchells, M., Renault, O., Dobson, P.J., Salata, O.V., Beamson, G.,
Egdell, R.G.: High resolution x-ray photoemission study of plasma oxidation of
indium–tin–oxide thin film surfaces. J. Appl. Phys. 88, 5180-5187 (2000)
Gassenbauer, Y., Schafranek, R., Klein, A., Zafeiratos, S., Hävecker, M., KnopGericke, A., Schlögl, R.: Surface states, surface potentials, and segregation at
surfaces of tin-doped In2O3. Phys. Rev. B 73, 245312:1-11 (2006)
King, P.D.C, Veal, T.D., Payne, D.J., Bourlange, A., Egdell, R.G., McConville, C.F.:
Surface electron accumulation and the charge neutrality level in In 2O3. Phys. Rev.
Lett. 101, 116808:1-4 (2008)
Zhang, K.H.L., Payne, D.J., Palgrave, R.G., Lazarov, V.K., Chen, W., Wee, A.T.S.,
McConville, C.F., King, P.D.C, Veal, T.D., Panaccione, G., Lacovig, P., Egdell, R.G.:
Surface Structure and Electronic Properties of In 2O3(111) Single-Crystal Thin Films
Grown on Y-Stabilized ZrO2 (111). Chem. Mat. 21, 4353-4355 (2009)
Fröhlich, D., Kenklies, R., Helbig, R.: Band-gap assignment in SnO2 by two-photon
spectroscopy. Phys. Rev. Lett. 41, 1750-1751 (1978)
25
37. Schleife, A., Varley, J.B., Fuchs, F., Rödl, C., Bechstedt, F., Rinke, P., Janotti, A.,
Van de Walle, C.G.: Tin dioxide from first principles: Quasiparticle electronic states
and optical properties. Phys. Rev. B 83, 035116 (2011)
38. Batzill, M., Diebold, U.: The surface and materials science of tin oxide. Prog. Surf.
Sci. 79, 47-154 (2005)
39. Comini, E.: Metal oxide nano-crystals for gas sensing. Anal. Chim. Acta 568, 28-40
(2006)
40. De Frésart, E., Darville, J., Gilles, J.M.: Surface properties of tin dioxide single
crystals. Surf. Sci. 126, 518-522 (1983)
41. Nagata, T., O. Bierwagen, M. E. White, M-Y. Tsai, and J. S. Speck: Study of the Au
Schottky contact formation on oxygen plasma treated n-type SnO2 (101) thin films. J.
Appl. Phys. 107, 033707:1-7 (2010)
42. Van de Walle, C.G., Neugebauer, J.: Universal alignment of hydrogen levels in
semiconductors, insulators and solutions. Nat. 423, 626-628 (2003)
43. Cox, S.F.J., Davis, E.A., Cotrell, S.P., King, P.J.C., Lord, J.S., Gil, J.M., Alberto,
H.V., Vilão, R.C., Piroto Duarte, J., Ayres de Campos, N., Weidinger, A., Lichti, R.L.,
Irvine, S.J.C.: Experimental Confirmation of the Predicted Shallow Donor Hydrogen
State in Zinc Oxide. Phys. Rev. Lett. 86, 2601-2604 (2001)
44. King, P.D.C, McKenzie, I., Veal, T.D.: Observation of shallow-donor muonium in
Ga2O3: Evidence for hydrogen-induced conductivity. Appl. Phys. Lett. 96, 062110
(2010)
45. King, P.D.C, Lichti, R.L., Celebi, Y.G., Gil, J.M., Vilão, R.C. , Alberto, H.V., Piroto
Duarte, J., Payne, D.J., Egdell, R.G., McKenzie, I., McConville, C.F., Cox, S.F.J.,
Veal, T.D.: Shallow donor state of hydrogen in In2O3 and SnO2 : Implications for
conductivity in transparent conducting oxides. Phys. Rev. B 80, 081201(R):1-4 (2009)
46. Heine, V.: Theory of surface states. Phys. Rev. 138, A1689-A1696 (1965)
47. Inkson, J.C.: Deep impurities in semiconductors. I. Evanescent states and complex
band structure. J. Phys. C 13, 369-381 (1980)
48. Tersoff, J.: Schottky barriers and semiconductor band structures. Phys. Rev. B 32,
6968–-6971 (1985)
49. Mönch, W., Electronic Properties of Semiconductor Interfaces. Springer (2004)
50. Veal, T.D., King, P.D.C, Hatfield, S.A., Bailey, L.R., McConville, C.F., Martel, B.,
Moreno, J.C., Frayssinet, E., Semond, F., Zúñiga-Pérez, J.: Valence band offset of the
ZnO/AlN heterojunction determined by x-ray photoemission spectroscopy. Appl. Phys.
Lett. 93, 202108:1-3 (2008)
51. King, P.D.C, Veal, T.D., Jefferson, P.H., McConville, C.F., Wang, T., Parbrook, P.J.,
Lu, H., Schaff, W.J.: Valence band offset of InN/AlN heterojunctions measured by xray photoelectron spectroscopy. Appl. Phys. Lett. 90, 132105:1-3 (2007)
52. King, P.D.C, Veal, T.D., Kendrick, C.E., Bailey, L.R., Durbin, S.M., McConville,
C.F.: InN/GaN valence band offset: High-resolution x-ray photoemission spectroscopy
measurements. Phys. Rev. B 78, 033308:1-3 (2008)
53. Falabretti B., Robertson, J.: Electronic structures and doping of SnO2, CuAlO2, and
CuInO2. J. Appl. Phys. 102, 123703:1-5 (2007)
54. Schleife, A., Fuchs, F., Rödl, C., Furthmüller, J., Bechstedt, F.: Branch-point energies
and band discontinuities of III-nitrides and III-/II-oxides from quasiparticle bandstructure calculations. Appl. Phys. Lett. 94, 012104:1-3 (2009)
55. H. He, R. Orlando, M. A. Blanco, and R. Pandey, E. Amzallag, I. Baraille, and M.
Rérat: First-principles study of the structural, electronic, and optical properties of
Ga2O3 in its monoclinic and hexagonal phases. Phys. Rev. B 74, 195123:1-8 (2006)
56. King, P.D.C, Veal, T.D., Jefferson, P.H., Hatfield, S.A., Piper, L.F.J., McConville,
C.F., Fuchs, F., Furthmüller, J., Bechstedt, F., Lu, H., and Schaff, W.J.: Determination
of the branch-point energy of InN: Chemical trends in common-cation and commonanion semiconductors. Phys. Rev. B 77, 045316:1-6 (2008)
26
57. Veal, T.D., McConville, C.F., Schaff, W.J. (eds.), Indium Nitride and Related Alloys.
CRC Press (2009)
58. King, P.D.C, Veal, T.D., McConville, C.F.: Unintentional conductivity of indium
nitride: transport modelling and microscopic origins. J. Phys.: Condens. Matter 21,
174201:1-7 (2009)