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Supporting Information
Giant Electrocaloric Effect in PZT Bilayer Thin Films by
Utilizing the Electric Field Engineering
Tiandong Zhang,1 Weili Li,1,2,a) Wenping Cao,1 Yafei Hou,1 Yang
Yu,1 Weidong Fei,1,3,b)
Figure. S1 XRD patterns and SEM cross-section image (inset) of PZ0.95T0.05/PZ0.52T0.48 bilayer thin films.
The total (Gibbs) free energy density of such a bilayer structure is given as the volumetric weighted
sum of the free energies of contributing layers such that
G  1G1   2G2
(S1)
Here,  i is the volume fraction of layer i, 1   2  1 .
G  U  TS  PE
(S2)
and thus,
dG   SdT  PdE
(S3)
Insert Eq. S1 into Eq. S3 and after arranging terms yield
dG  1dG1   2 dG2  SdT  1P1dE1   2 P2 dE2
(S4)
where S  1S1   2 S 2 , Pi is the polarization of layer i, E is total electric field applied in bilayer films,
the allocated electric field in layer i is Ei.
Based on the voltage allocation’s law, Eq. S5 can be obtained:
E1l1  E 2 l2  E (l1  l2 )  El
where, li is the thickness of layer i, and  i  li /
(S5)
n
l
i
, l is the total thickness.
i 1
Combined with Eq. S4 and Eq. S5, the Eq. S4 can be expressed as
dG   SdT  P1dE1   （
2 P1  P2 )dE2
(S6)
By considering a solid as an isolated material, the following is obtained from the derivative of Gibbs
free energy:
 G 
S  

 T  E , E2
 G 
P1  

 E T , E2
(S7)
Further derivations obtained from Eq. S7 are the Maxwell relations:
 P 
 S 

  1
 E T  T  E
In a similar way, the Eq. S9 can be obtained:
(S8)
 P 
 S 

  2 
 E T  T  E
(S9)
Combined with Eq. S8 and Eq. S9, one finds
 P
 P 
 P 
 S 
 S 
 S 
 2
 
  1  1    2  2   
 E T
 E T  E T
 T  E
 T  E  T
1 
where



E
(S10)
P  1P1   2 P2 is the average polarization of bilayer films[1,2].
and thus,

E
0
(
 P
T
) E dE  S  1S1   2 S 2  1

E1
0
(
P1
) E dE   2
T

E2
0
(
P2
) E dE
T
(S11)
The dielectric constant dependence of frequency of PZ0.95T0.05/PZ0.52T0.48 bilayer thin films, PZ0.95T0.05
single layer and PZ0.52T0.48 single layer was given in Figure. S2. We assuming that the bilayer films is
the series connection model of ideal capacitors.
1
1
1


C C1 C 2
(S12)
where C1 is the capacitance of PZ0.95T0.05 layer and C1 is the capacitance of PZ0.52T0.48 layer, C is the
total capacitance of bilayer films. The average dielectric constant of bilayer films can be given by
l
r

l1
 r1

l2
r2
(S13)
where εr, εr1, εr2, represent the dielectric constant of PZ0.95T0.05/PZ0.52T0.48 bilayer thin films, PZ0.95T0.05
layer and PZ0.52T0.48 layer, respectively. In our work, the total thickness l is 350 nm, and l1 = l2 = 175
nm. The εr, εr1, εr2 (at 100 Hz) can be obtained in Figure. S1, which is 1202, 880 and 2145, respectively.
These values are plugged into the Eq. S13, and the left hand side approximately equals the right hand
side, it proves that the bilayer films accord with the series connection model of ideal capacitors.
Figure. S2 The dielectric constant dependence of frequency of PZ0.95T0.05/PZ0.52T0.48 bilayer thin films, PZ0.95T0.05
single layer and PZ0.52T0.48 single layer.
Now, the process of amplifying effect of electric field is needed to illustrate in detail.
According to the Gauss law, the continuity of electric displacement (D) at the interfaces can be
obtained, these result in
 r1E1   r 2 E2
(S14)
where, εri is the dielectric constant of layer i. It is easy to understand that the layer with a smaller εr can
be allocated a higher E according to the Eq. S14.
Combined with Eq. S14 and Eq. S5, the electric field E1 allocated in layer 1 can be expressed as
E1 
1
1  (1  1 )
 r1
 r2
E
(S15)
If the values of εr1/εr2 is much less than 1 with a fixed α1 , it should be possible to obtain a higher E1 in
layer 1, and the E1 > E > E2 can be obtained.
It is necessary to give an example for us to create a better understand of the E1 which will be amplified
once again due to the redistributed electric field with poling process.
(i) When the electric field E is applied, the allocated Ei follows the Gauss law,
 r1，0 E1，0   r 2，0 E 2，0
(S16)
where εri,0 denotes the zero-field dielectric constant value. In our work, ε1,0 = 880 for PZ0.95T0.05 layer,
ε2,0 = 2145 for PZ0.52T0.48 layer, and thus
1
E  1.418 E
1 1 880
 
2 2 2145
 2 E  E1,0  0.582 E
E1,0 
E 2, 0
E1,0
E 2, 0

(S17)
 2, 0
 2.4375
 1,0
(ii) we hypothesis that the allocated electric field is keep to Eq. S17 and remain unchanged with poling
process. As shown in Figure. S3, If the allocated voltage of PZ 0.52T0.48 layer is 5 V, and the voltage
distributed in PZ0.95T0.05 layer is about 5 V×2.4375≈12 V. If the hypothesis is true, which yields
E1 V1 12V


 2.4
E2 V2
5V
(S19)
However, according to the CV results in Figure. S3,
 2 C2 (5V ) 1.12 nF


 3.56
1 C1 (12V ) 0.314 nF
(S20)
Figure. S3 The CV curves of PZ0.95T0.05 single layer and PZ0.52T0.48 single layer at selected voltage.
Thus, it is ambivalent between the Gauss law and our hypothesis, which is caused by the εr1 of
PZ0.95T0.05 layer dropped rapidly compared to the εr2 of PZ0.52T0.48 layer with poling process. The
electric field will be redistributed and E1 will be amplified once again with poling process due to the εr1
is decreased rapidly according to the Gauss law, and there are two possibilities:
   r1 E1   r 2 E 2 
corresponding to the situation of E2,0 > Ec,2 (Ec,2 is the coercive field of PZ52T48 thin film, as shown in
Figure. S4.
Figure. S4 Schematic diagram of the amplifying effect of electric field E and the evolution of the dielectric
constant and allocated electric filed of each layer (c) the initial state of polarization (d) final state of polarization.
   r1 E1   r 2 E 2 
corresponding to the situation of E2,0 < Ec,2, as shown in Figure. S5.
Figure. S5 Schematic diagram of the amplifying effect of electric field E and the evolution of the dielectric
constant and allocated electric filed of each layer (c) the initial state of polarization (d) final state of polarization.
and both situations (   r1 E1   r 2 E 2  and   r1 E1   r 2 E 2  ) are impossible according to
Eq.S5, where “  ” represent “decreasing”, “  ” represent “increasing”.
The P(E) loops of PZ0.52T0.48 layer (thickness=175 nm) and PZ0.95T0.05 layer (thickness=175 nm) are
given in Figure. S6. The Ec,2 of PZ0.52T0.48 film is lower than 100 kV/cm. When the total electric field E
= 566 kV/cm is applied, the allocated electric field E2,0 in PZ0.52T0.48 layer is about 329 kV/cm at the
initial state of polarization, in our work, the situation of E2,0 > Ec,2 can be found, so the Figure. S4,
rather than Figure. S5, is given in Figure. 1(d) in the manuscript.
Figure. S6 P(E) loops of single layer thin film and bilayers films with the same electric field at room temperature.
It can be seen that the ratio of dielectric constant (εrFE/εrAFE) between FE to AFE films decreases
with the temperature increasing slowly as shown in Fig. S7, resulting in the slow decreasing of
effective electric field (E1) in AFE layer. But the effective electric filed in AFE layer is larger than the
external field (E) when temperature is lower than 160 oC. Therefore, the amplifying effect of field in
AFE layer is still presence below 160 oC.
Figure. S7 The temperature dependence of the ratio of εrFE/εrAFE and E1/E.
1
M. B. Okatan, J. V. Mantese, S. P. Alpay, Phys. Rev. B. 79, 174113, (2009).
2
S. Zhong, S. P. Alpay, Appl. Phys. Let. 87, 102902, (2005).