Supplemental Material for
Transformation from insulating p-type to semiconducting n-type conduction in
CaCu3Ti4O12-related Na(Cu5/2Ti1/2)Ti4O12 ceramics.
Ming Li, Derek C. Sinclair1
Department of Materials Science and Engineering, University of Sheffield, Sir Robert
Hadfield Building, Mappin Street, Sheffield, S1 3JD, United Kingdom.
1, Semiconductivity in CaCu3Ti4O12 (CCTO).
The origin(s) of the semiconductivity (RT resistivity ~ 10-100  cm) in CCTO is
linked to small changes in composition but remains unconfirmed despite a few
plausible models in the literature.1,2
The first model is based on anion nonstoichiometry with a low level of oxygen loss
that is accompanied with partial Ti4+ reduction to Ti3+, giving rise to the formula
CaCu 3 Ti 44 x Ti 3x O12 x/2 , according to the following reactions:
O o → Vo + 2e' + 1/2O2
(1)
2Ti4+ + 2e' → 2Ti3+
(2)
This mechanism is commonly used to explain the semiconductivity in many
perovskite-based titanates processed at high temperatures and/or inert/reducing
atmospheres.3,4 The required level of oxygen loss to give RT resistivity of ~ 10-100 
cm is low (less than 0.01 at%).3 Annealing dense CCTO ceramics (obtained by
1
Author to whom correspondence should be addressed. E-mail: d.c.sinclair@sheffield.ac.uk
1
sintering at 1115 oC) in various atmospheres (O2, air and N2) between 600 and 1000
o
C reveals negligible dependence of the bulk resistivity on oxygen partial pressure,
pO2.5 This implies that either the oxygen loss model is not suitable for CCTO or
oxygen diffusion in CCTO dense ceramics is kinetically controlled.
The second model is based on cation nonstoichiometry. A neutron and synchrotron Xray diffraction study on ‘SrCu3Ti4O12’,1 a structural analogue of CCTO, reveals the
Sr-site not to be completely occupied and a small amount of Ti to occupy the Cu-site
for charge balance, giving rise to a formula of Sr0.946(Cu2.946Ti0.054)Ti4O12 (SCTO).1
This led to a model that Cu2+ ions are partially reduced to Cu+ ions at high
temperature and charge balance is maintained by a small amount of Ti4+ ions
occupying the Cu-site according to the equation:
3Cu2+ → 2Cu+ + Ti4+
(3)
giving rise to a general formula Ca(Cu123x Cu 2x Ti 4x ) 3 Ti 4 O12 .
On cooling, Cu+ ions are reoxidized to Cu2+ ions and the released electrons enter the
Ti 3d conduction band according to the equation:
Cu+ + Ti4+ → Cu2+ + Ti3+
(4)
giving rise to the general formula Ca(Cu12x Ti 4x ) 3 (Ti 446x Ti 36x )O12 .1,2
Again, the level of nonstoichiometry required to obtain RT resistivity of ~ 10-100 
cm is small (x < 0.0001)1 and is therefore difficult to detect by most chemical
techniques. In both models outlined above, the semiconductivity is related to electrons
in the Ti 3d conduction band and is therefore n-type. There are also suggestions about
2
electron transfer between either Cu+ and Cu2+ or Cu2+ and Cu3+ ions as the source of
the semiconductivity.6-8 The valence state has been detected by X-ray Photoelectron
Spectroscopy (XPS), however, interpretation of XPS data on CCTO is rather
inconsistent in the literature.6-8 The amount of Cu+ or Cu3+, if any, is expected to be
very small as compared to that of Cu2+. Data fitting of Cu 2p3/2 XPS spectra to prove
the presence of Cu+ or Cu3+ seems, to some extent, arbitrary. In some reports XPS
spectra are fitted to show the presence of Cu+ whereas in other reports the spectra are
fitted to show the presence of Cu3+ in CCTO.6,7 In addition, XPS is a surface
technique and the results are shown to be influenced by the high vacuum requirements
for XPS measurements.8 It is not clear whether such mechanisms would give rise to por n-type behaviour.
There are also disagreements on the nature of the major charge carrier in CCTO. Most
reports show evidence of n-type behaviour in CCTO ceramics and thin films based on
Thermopower measurements and pO2 dependence of resistivity.1,9-11 In a few reports,
Hall effect measurements suggest the electrical conduction is p-type.7,12,13 The
dependence of resistivity on pO2 for CCTO thin films at 100-200 oC is consistent with
p-type behaviour.14 Annealing CCTO thin films at 680 oC in O2 however suppresses
the semiconductivity,13 implying n-type electrical conduction. In a more recent report,
both Hall effect and Seebeck coefficient measurements suggest electrons to be the
main charge carrier in CCTO.11
2, Analysis of Impedance Spectroscopy data using combined spectroscopic plots
of the imaginary components of impedance, Z" and electric modulus, M".
3
In the previous report,15 only Impedance, Z*, complex plane plots were used to
analyse the IS data, see Fig. 6 in Ref15. This is not always enough to probe the
electrical homogeneity of the grains/ceramic, as demonstrated below by a simple
simulation based on the idealised brick layer model.
For simplicity, assume a model based on two phases that are connected (electrically)
in series. Both phases have a cross-sectional area (A) = 1 cm2 but a different path
length (l); l = 2 cm for phase 1 and l = 1 cm for phase 2. The volume fraction of
phases 1 and 2 is therefore 2/3 and 1/3, respectively. The intrinsic relative permittivity,
r, is the same for both phases (r = 113) but phase 1 is more resistive with a
resistivity, , of 1 M cm compared to 10 k cm for phase 2. Thus the capacitance
(C = 0rA/l where 0 is the permittivity of free space, 8.854×10-14 F cm-1) and
resistance (R = l/A) of phase 1 and phase 2 are C1 = 5 pF, R1 = 2 M and C2 = 10
pF, R2 = 10 k and can be modelled using the equivalent circuit in Fig. S1a.

The simulated Z* plot, Fig. S1b, is dominated by the arc associated with the resistive
phase 1. Most of the arc associated with phase 2 is swamped by the arc associated
with phase 1. Even the high frequency data (> 1 MHz) on an expanded scale, inset in
Fig. S1b, shows limited evidence for the presence of phase 2. In practice, this
frequency range is close to the upper frequency limit of most Impedance analysers (~
10 MHz). In the case of experimental IS data, the arc in the Z* plot is likely to be
depressed due to non-ideal behaviour of real materials and thus further obscure
evidence for the presence of the arc associated with phase 2. In addition, as both
phases have low capacitance there is no apparent high permittivity capacitance
plateau in the C' spectroscopic plot (not shown). The above factors make it difficult to
4
get a conclusive judgement about the presence of any conductive phase 2 from
analysis of IS data using either Z* or C' spectroscopic plots.
In contrast, both phases are clearly visible in a combined spectroscopic plots of the
imaginary components of impedance, Z" and electric modulus, M", Fig. S1c. Each
phase gives rise to a Debye peak in the Z" and M" spectroscopic plot and can be
described by the following equations:16,17
RC
]
1  (RC ) 2
(5)
C0
RC
[
]
C 1  (RC ) 2
(6)
Z" = R [
M" =
where C0 is the capacitance of the empty cell (C0 = 0A/l), = 2f and f is the applied
frequency in Hz. At the peak maxima maxRC = 1 holds and it follows that:
Z" =
R
2
(7)
M" =
C0
2C
(8)
A few parameters can be obtained from Z" and M" peaks. Firstly, both resistance and
capacitance can be calculated using equations (7) and (8). Obviously the Z" spectrum
is dominated by the most resistive element (this is why only the Z" peak associated
with resistive phase 1 is visible in the current case), whereas the M" spectrum is
dominated by the element with the smallest capacitance. As C1 and C2 are comparable
in this simulation, the M" peaks associated with phases 1 and 2 are clearly and easily
detectable, Fig. S1c.
5
Secondly, the ratio of the M" peak heights associated with phase 1 and phase 2 is 2:1,
as expected by the inverse proportionality relationship between M" and C, equation 8.
On the condition that both phases have the same intrinsic permittivity, the effective
capacitance for each phase is related to its volume fraction. The M" peak height can
therefore be used to estimate the volume fraction of the phases present in a sample. In
this simplified case, the ratio of the M" peak heights is the same as the ratio of volume
fraction for the two phases. In practice, the relationship between volume fraction and
capacitance for each phase is more complex and depends on many factors, including
how the phases are distributed, their relative time constants (RC product) and volume
fractions. We are currently developing a quantitative relationship between M" peak
height and volume fraction for each phase by Finite Element simulations. The results
will be reported in the future. Nevertheless, at this stage M" spectroscopic plots can
provide useful information about the presence, electrical properties and qualitative
volume fraction of phases in heterogeneous electroceramics.
Thirdly, the Z", M" Debye peak frequency is determined by fmax =
1/(2RC)=1/(20r). fmax is therefore determined by fundamental parameters
(resistivity and permittivity) and is independent of sample geometry. Based on the
assumed resistivity and permittivity values given above, fmax for phase 1 and 2 is 15.9
kHz and 1.59 MHz, respectively, Fig. S1c. In addition, the temperature dependence of
permittivity is generally much smaller than the temperature dependence of resistivity
(exceptional cases exist in some ferroelectrics/relaxors near their Curie point/Tmax),
the temperature dependence of fmax reflects the temperature dependence of the
resistivity and the slope of an Arrhenius-type plot of log fmax versus 1/T can be used to
estimate the activation energy, Ea, of the conduction process.
6
Finally, equation 8 can be rewritten as:
M" =
1
2 r
(9)
So M" peak is unit less and scales inversely with relative permittivity. Some software
packages such as ZView tend to automatically present relative M" (absolute value of
M" divided by 0). In this case, it follows:
M"
0
=
1
2 0  r
=
1
2Ccorr
(10)
where Ccorr is capacitance corrected after pellet geometry (pellet thickness/area). Both
methods of presentation (equation 9 and 10) are used in the literature.
References
1
J. Li, M. A. Subramanian, H. D. Rosenfeld, C. Y. Jones, B. H. Toby, and A.
W. Sleight, Chem. Mater. 16, 5223 (2004).
2
M. Li, A. Feteira, D. C. Sinclair, and A. R. West, Appl. Phys. Lett. 88, 232903
(2006).
3
F. D. Morrison, D. C. Sinclair, and A. R. West, J. Am. Ceram. Soc. 84, 474
(2001).
4
F. D. Morrison, D. C. Sinclair, and A. R. West, J. Am. Ceram. Soc. 84, 531
(2001).
5
T. B. Adams, D. C. Sinclair, and A. R. West, J. Am. Ceram. Soc. 89, 3129
(2006).
7
6
T. T. Fang, L. T. Mei, and H. F. Ho, Acta Mater. 54, 2867 (2006).
7
G. Deng, N. Xanthopoulos, and P. Muralt, Appl. Phys. Lett. 92, 172909
(2008).
8
T.-T. Fang and Y.-H. Wang, J. Electrochem. Soc. 158, G207 (2011).
9
S. Y. Chung, I. D. Kim, and S. J. L. Kang, Nat. Mater. 3, 774 (2004).
10
I.-D. Kim, A. Rothschild, T. Hyodo, and H. L. Tuller, Nano Lett. 6, 193
(2006).
11
A. Ismayil, T. Nakamura, R. Kamiya, M. Nakamura, Y. Nakanishi, T. Naito,
H. Fujishiro, T. Watanabe, G. Sawada, M. Toita, K. Takegahara, and M. Yoshizawa, J.
Phys. Soc. Jpn. 80, SA113 (2011).
12
G. Deng, T. Yamada, and P. Muralt, Appl. Phys. Lett. 91, 202903 (2007).
13
G. Deng and P. Muralt, Phys. Rev. B: Condens. Matter 81, 224111 (2010).
14
E. Joanni, R. Savu, P. R. Bueno, E. Longo, and J. A. Varela, Appl. Phys. Lett.
92 (2008).
15
B. Rivas-Murias, M. Sanchez-Andujar, J. Rivas, and M. A. Senaris-Rodriguez,
Mater. Chem. Phys. 120, 576 (2010).
16
D. C. Sinclair and A. R. West, J. Appl. Phys. 66, 3850 (1989).
17
J. T. S. Irvine, D. C. Sinclair, and A. R. West, Adv. Mater. 2, 132 (1990).
8
Fig. S1. (a) An equivalent circuit consisting of two parallel RC elements connected in
series to model impedance data associated with two phases. Simulated (b) Z* plot and
(c) a combined spectroscopic plot of the imaginary components of impedance, Z" and
electric modulus, M", by fixing C1 = 5 pF, R1 = 2 M and C2 = 10 pF, R2 = 10 k.
Inset in (b) shows an expanded scale of the high frequency Z* data. Filled symbols
indicate selected frequencies in Hz.
9