Transition between grain boundary and intragrain scattering transport
mechanisms in boron-doped zinc oxide thin films
J. Steinhauser,
a兲
S. Faÿ, N. Oliveira, E. Vallat-Sauvain, and C. Ballif
Institute of Microtechnology (IMT), University of Neuchâtel, Rue A.-L. Breguet 2, CH-2000 Neuchâtel,
Switzerland
A comprehensive model for the electronic transport in polycrystalline ZnO:B thin films grown by
low pressure chemical vapor deposition is presented. The optical mobilities and carrier
concentration calculated from reflectance spectra using the Drude model were compared with the
data obtained by Hall measurements. By analyzing the results for samples with large variation of
grain size and doping level, the respective influences on the transport of potential barriers at grain
boundaries and intragrain scattering could be separated unambiguously. A continuous transition
from grain boundary scattering to intragrain scattering is observed for doping level increasing from
3⫻10
19
to 2 ⫻ 10
20
cm
−3
Transparent conductive oxides 共TCOs兲 are an essential
part of thin-film silicon solar cells. To contact the cell and act
as a transparent window, TCOs have to exhibit a high con-
ductivity and a high optical transmittance. In addition, they
have to scatter the light at the TCO-cell interface in order to
increase the effective absorption of light within the active
layers.
1,2
Boron-doped zinc oxide 共ZnO:B兲 layers deposited
by low pressure chemical vapour deposition 共LPCVD兲 have
been intensively developed in our institute.
3
This material is
especially attractive for thin-film solar cell technology, be-
cause of its low cost, and of the wide availability of its con-
stituent raw materials. Furthermore, the LPCVD technique is
well suited for large-scale device fabrication.
4
These films
are constituted of large grains with a pronounced
9–18
prefer-
ential crystallographic direction. The extremities of the
grains appear at the growing surface as large pyramids,
which yield an as-grown rough surface texture that effi-
ciently diffuses the light that enters into the solar cell.
1,3
The optical and electrical properties of TCO films have
been extensively investigated and recently reviewed. Ellmer
5
and Minami
6
discussed the limit of the resistivity of such
films by analyzing reported data for ZnO films deposited by
different techniques. They found that the electron mobility in
undoped films is mainly limited by grain boundary scatter-
ing, whereas for doped layers intragrain scattering mecha-
nism is predominant. But the transition between these two
mechanisms within a given ZnO film series could not be
evidenced yet. In the present work, the scattering mechanism
limiting the electron mobility is determined by the compari-
son, of the value of the optical mobility 共as evaluated by
using the classical Drude model兲 with the value of the Hall
mobility. When both values are markedly different, the
mechanism limiting the electron mobility is attributed to
grain boundary scattering. When both values are similar, the
limiting mechanism is attributed to intragrain scattering. This
approach is commonly applied to other TCOs.
7–11
The wide
range of carrier density easily achievable in boron-doped
LPCVD ZnO by varying the gas flow ratio allows us to
observe within one single film system the transition from one
transport mechanism to the other. The results of this contri-
bution are consistent with previous analysis of the tempera-
ture dependence of the conductivity,
12
and constitute an ex-
perimental evidence of the transition between grain boundary
scattering and intragrain scattering as the microscopic
mechanisms limiting electron mobility in LPCVD ZnO.
Consequently, further improvement of ZnO conductivity will
have to be conducted depending on the type of transport
mechanism dominant in the doping range of interest.
ZnO layers were deposited at low temperature 共155 ° C兲
by LPCVD on 0.7 mm thick Schott AF45 glass substrates.
Diethyl zinc 共DEZ兲 and water vapor were used as precursors
and directly evaporated in the system. DEZ and H
2
O flows
were set to 13.5 and 16.5 SCCM 共SCCM denotes cubic cen-
timeter per minute at STP兲, respectively. Diborane 共B
2
H
6
兲
diluted at 1% in argon was used as doping gas. The gas phase
doping ratio 关共B
2
H
6
兲/共DEZ兲兴 used during ZnO deposition
was varied from 0 共nominally undoped ZnO兲 to 2 共heavily
doped ZnO兲. The optical transmittance 共T兲 and reflectance
共R兲 of ZnO layers on glass substrates were measured in air
with a double beam Perkin-Elmer photospectrometer with
integration sphere. A 1720X Perkin-Elmer Fourier transform
infrared spectrometer was used to measure the normal reflec-
tance spectra in the infrared region. The thickness of the
layers was determined by a mechanical profiler. The resistiv-
ity
, the Hall carrier concentration N
Hall
, and the Hall mo-
bility
Hall
were deduced from Hall measurement using a
Van der Pauw configuration at room temperature. Various
grain sizes were obtained at each doping level by varying the
thickness of the films from 0.5 to 5
m. The average
projected area of the grain surface observed on scanning
electron micrographs of the polycrystalline layers surface
was measured using a commercial image analysis software
共
METRIC 8.02兲, and its square root value 共
␦
兲 was taken as the
dimensional parameter 共thereafter to be called “grain size”兲.
Note that, due to the growth mechanism, the grain size in-
creases linearly over the film thickness.
3
This effect has no
influence on the optical measurements, whereas the conduc-
tivity and Hall mobility are slightly reduced compared to
the case where the grain size would be constant over the
thickness.
Figure 1 shows the reflectance 共R兲 and transmittance 共T兲
spectra for 2.1
m thick ZnO layers grown with various gas
a兲
Electronic mail: jerome.steinhauser@unine.ch
Published in Applied Physics Letters 9, issue 142107, 1-3, 2007
which should be used for any reference to this work
1
phase doping ratios 关共B
2
H
6
兲/共DEZ兲兴. These films have an
average transmittance superior to 80% and an absorbance
close to zero in the visible range 共0.4–0.8
m兲. In the near
infrared 共NIR兲 region 共wavelength between 0.8 and 2.5
m兲,
T decreases. The inflection point in the transmittance curves
is shifted towards shorter wavelengths with increasing dop-
ing ratio due to the related increase of free carrier absorption
共FCA兲. At longer wavelengths, R abruptly increases after the
plasma resonance wavelength, which is progressively low-
ered as the boron content 共and consequently the free carrier
density兲 is increased. This behavior is generally described by
the Drude model;
8–10
some authors use an extended Drude
model including a Lorentz oscillator term
11
or a frequency
dependent damping term.
13
Indeed, the Drude model in its
simplest form is sufficient to describe the NIR optical behav-
ior of LPCVD ZnO films. Consequently, the dielectric func-
tion can be expressed as
共
兲 =
⬁
− 共
N
2
/共
2
+ i⌫
兲兲, 共1兲
where
⬁
is the high frequency dielectric constant, ⌫ is a
damping frequency, and
N
2
= N
optic
e
2
/
0
m
*
, 共2兲
where N
optic
is the free electron density, e the electron charge,
0
the permittivity of free space, and m
*
the electron effec-
tive mass. The optical mobility
optic
is calculated using the
relation
optic
= e/⌫m
*
. 共3兲
Assuming
⬁
=4 and m
*
=0.28m
e
where m
e
is the elec-
tron mass,
5,8
the reflectance spectra of ZnO films were fitted
to this model taking into account the multiple reflection due
to the air/glass/ZnO structure of our samples and using
N
and ⌫ as fit variables. Examples of fits for ZnO layers with
different doping ratios are given in Fig. 2. A good conver-
gence of the fitted curves is obtained in the range of validity
of the Drude model. The optical mobility
optic
and carrier
density N
optic
are then extracted using Eqs. 共2兲 and 共3兲. The
calculated electron mean-free path is in the range of a few
nanometers and under the application of a rapidly oscillating
electric field, the average electron path length is also much
smaller than the typical grain size.
6,14
Therefore, grain
boundary scattering will not influence the measured value for
the optical mobility, and only intragrain scattering will influ-
ence
optic
. Note that the depleted region at grain boundaries
occupies only a small volume compared to the bulk of the
grain and will not affect the optical measurements. In the
case of the Hall effect measurement, electrons cross several
grain boundaries, and consequently the grain boundary den-
sity will influence the measured value of
Hall
.
For all measured samples, the value of the Hall electron
density is the same as the one deduced from the optical mea-
surements. As shown in Fig. 3,
Hall
and
optic
are both mea-
sured as a function of the grain sizes
␦
for ZnO series with
two different carrier concentrations. For ZnO layers with low
carrier concentration 共N= 3.8⫻10
19
cm
−3
兲, the Hall mobility
depends on
␦
: it increases from 22 to 36 cm
2
V
−1
s
−1
with
increasing grain size. The optical mobility of these samples
remains constant at a high value of 38 cm
2
V
−1
s
−1
for all
grain sizes. For heavily doped samples 共N =2⫻10
20
cm
−3
兲
both Hall and optical mobilities remain nearly constant at a
value around 25 cm
2
V
−1
s
−1
while
␦
is increased.
In lightly doped ZnO films, the observed differences be-
tween optical intragrain mobility and Hall mobility values
are due to a grain barrier limited mobility, in agreement with
previous observations described, for instance, by Seto
15
or
Bruneaux et al.
16
As the grain size is increased, the grain
boundaries influence on
Hall
is reduced and
Hall
and
optic
become almost identical. For
␦
larger than 600 nm, the grain
boundary density becomes too low to influence the measured
Hall mobility. Consequently, efforts to improve the film con-
ductivity by increasing the grain size beyond this value are
useless. At heavy doping level, grain boundary scattering
FIG. 1. Total transmittance 共T兲 and reflectance 共R兲 for 2
m thick ZnO
films, for which the gas phase doping ratios 共B
2
H
6
/DEZ兲 used during the
deposition was varied from 0 共undoped兲 to 1.5 共higly doped兲.
FIG. 2. Example of fits 共solid lines兲 of near normal reflectance spectra of
ZnO films 共symbol兲 deposited with different gas phase doping ratios
共B
2
H
6
/DEZ兲 using the Drude model.
FIG. 3. Optical 共circles兲 and Hall 共squares兲 electron mobilities as a function
of grain size for films with carrier densities N= 3.8⫻ 10
19
cm
−3
共open sym-
bol兲 and N =2⫻ 10
20
cm
−3
共filled symbol兲. The lines are guides for the eyes.
2
plays only a minor role compared to intragrain scattering
mechanisms. Here, the optical and Hall mobility values be-
come almost identical and the variation of grain size does no
longer affect the Hall mobility.
To find the doping level at which the main limiting scat-
tering factor changes from grain boundary scattering to bulk
scattering, films with a varying doping concentration at con-
stant grain size have been fabricated. In Fig. 4, the optical
and the Hall mobilities for samples with a variation of gas
phase doping ratio 关共B
2
H
6
兲/共DEZ兲兴 from 0 to 2 are plotted
versus the carrier density. The resistivity of these films de-
creases almost by a decade 共from 1.4⫻ 10
−2
to 1.2
⫻10
−3
⍀ cm兲. This variation is mainly caused by an increase
of free carrier density from 2.0⫻ 10
19
to 2.2⫻10
20
cm
−3
.
For lightly doped layers,
optic
has a value of 41 cm
2
V
−1
s
−1
,
much higher than the value of
Hall
=23 cm
2
V
−1
s
−1
, which
confirms that, at this doping level, the grain boundary scat-
tering effect is predominant. As long as N is inferior to
10
20
cm
−3
,
Hall
increases with the increasing carrier density.
This behavior is explained by an increasing carrier concen-
tration which facilitates the transport by creating a lower and
narrower potential barrier at grain boundaries. For N superior
to 1.0⫻ 10
20
cm
−3
, tunneling through potential barrier occurs
and grain boundaries do not limit the conductivity anymore.
In this case
optic
and
Hall
are close and decrease with the
increasing carrier density, indicating that the bulk scattering
becomes the main limiting factor of the electron mobility.
A high mobility value of 44.2 cm
2
V
−1
s
−1
was
reported
17
for heavily doped sputtered ZnO:Al, in which mo-
bility is limited by intragrain ionized impurity scattering. The
relatively low mobility of LPCVD ZnO 共23 cm
2
V
−1
s
−1
at
2.0⫻ 10
20
cm
−3
兲 indicates that additional bulk scattering
phenomena occur. Ionized impurity scattering is usually con-
sidered as the limiting factor for heavily doped ZnO.
5,6,18
But, as reviewed by Ellmer,
5
several other mechanisms could
explain this low mobility value, such as formation of impu-
rity clusters, higher charge states of ionized donors 共due to
self-doping by oxygen vacancies兲, or extrinsic dopants on
interstitial sites. Further investigations, such as temperature
dependence of mobility measurements, are needed to gain
insight into this phenomenon. Finally, our results are consis-
tent with the temperature dependence of the resistivity of
these ZnO films,
12
for which negative and positive tempera-
ture coefficients have been found near room temperature for
lightly and heavily doped films, respectively. These coeffi-
cient signs are linked to transport influenced either by ther-
mally activated potential barriers or by an intragrain scatter-
ing which increases with the temperature.
In summary, the experimental observation of a continu-
ous transition between grain boundary scattering and intra-
grain scattering limited mobility is reported. This study gives
a comprehensive picture of transport mechanisms in LPCVD
ZnO films. It points out that, for lightly doped film 共with N
⬍10
20
cm
−3
兲, the mobility can be improved by increasing
the grain size. Furthermore for grain size
␦
⬎600 nm, grain
boundary density is too low to influence the measured
mobility. For heavily doped film 共with N⬎ 10
20
cm
−3
兲, the
mobility is limited by intragrain scattering, and improve-
ments of the grain bulk quality are mandatory to increase the
conductivity of the polycrystalline layers. A high mobility
value of 36 cm
2
V
−1
s
−1
is measured for thick, lightly doped
共N = 3.8⫻10
19
cm
−3
兲 ZnO films having a large grain size
共
␦
⬃500 nm兲. This film is particularly appropriate as TCO in
thin-film solar cells due to its reduced FCA, its good conduc-
tivity, and its ability to scatter light efficiently. Indeed, mi-
crocrystalline solar cells with a conversion efficiency of 10%
could be fabricated on such substrate.
19
The authors thank the Swiss Federal Government
共OFEN兲 and the Swiss Commission for Technology and In-
novation 共CTI兲 for financial support.
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FIG. 4. Optical and Hall mobilities vs free carrier density for ZnO films
grown with gas phase doping ratio 共B
2
H
6
/DEZ兲 varied from 0 to 2. The
lines are guides for the eyes.
3
