Supporting Information for
Ultrafast Atomic Layer-by-Layer Oxygen Vacancy-Exchange Diffusion in DoublePerovskite LnBaCo2O5.5- Thin Films
ShangyongBao, Chunrui Ma, Garry Chen, Xing Xu, Erik Enriquez, and Chonglin Chen*
Department of Physics and Astronomy, University of Texas at San Antonio, TX 78249, USA
Yamei Zhang
Department of Physics, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu
212003, China
Jerry L. Bettis, Jr. and Myung-Hwan Whangbo
Department of Chemistry, North Carolina State University, Raleigh, NC 27695-8204, USA
Chuang Dong and Qingyu Zhang
Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Ministry of
Education, Dalian University of Technology, Dalian 116024, China.
1. Experimental
Under the laser energy density of about 1.5 - 2.0 J /cm2 at a repetition rate of 5 Hz, good
single crystalline LnBCO epitaxial films are grown on (001) LaAlO3 substrates under the
optimized growth condition of an oxygen pressure of 250 mTorr at 850 C, similar to that for the
growth of other LaBCO epitaxial thin films, as shown in Fig. S1. Details of the optimized film
growth were presented in the previous studies.i,ii,iiiThe crystallinity and epitaxial nature were
checked by XRD and confirmed by TEM microscopy. The XRD measurements indicate that the
all epitaxial films are c-axis oriented, namely, the ab-plane of the ErBCO lattice is parallel to the
substrate surface. The redox reactions on the ErBCO films were conducted by using a Lake
Shore 370 AC Precise Resistance Bridge System in the range of 200 - 700oCunder a switching
flow of O2 and H2 at 1 atm. Platinum leads were glued on the film surface with high temperature
silver paste, which was air-dried at room temperature and annealed at 800
o
C before
measurements.
Fig. S1 (a) x-ray diffraction, (b) cross sectional TEM image and diffraction pattern, iv (c) high
resolution TEM image and EDX showing the excellent epitaxial nature of single crystalline
LaBCO thin films on LAO.v
(c)
(a)
(b)
2. R vs. t and dR/dt vs. t plots obtained for the A-site disordered LaSrCo2O5.5+
The resistance of single crystalline LaSCO thin films grown on (001) LaAlO3 was
examined at various temperatures under the switching flow of the reducing (H2) and oxidizing
(O2) gases. As shown in Fig. S2 for the results obtained at 300 C, oscillation peaks are not
found in the dR/dt vs. t plot. The inset of Fig. S2 shows a zoomed-in view of the resistance
change during t = 9810  9834 s.
Figure S2.
3. Diffusion of carriers through thin layers of thickness L
The carrier density c(x, t) at the distance x from the center of the layer (so that the
distance between the center to the surface is L/2) at the time t is related to the diffusion
coefficient D of the redox gas as followsvi

c(x, t)  c1
4(1)i
x
Dt
 1 
cos[(2i  1) ]exp[2 (2i  1) 2 2
c2  c1
L
L
i  0 (2i  1)
(1)
If the conductivity is dominated by one type of charge carrier, the mean conductance (x, t) is
written as
  1
8 
1
t
 1 2 
exp[(2i  1)2 ] ,
2
2  1
 i 0 (2i  1)

(2)
where 1 and 2 are the conductance at the initial and final states, respectively, and  is the
relaxation time
L2
 2 .
D
(3)
For small times (t <<), Eq. (2) is simplified as
  1
t
 43/2
.
 2  1

(4)
where 1 and 2 are the conductance at the initial and final states, respectively, and this
expression is valid when t is small compared to the relaxation time  
conductance change  during a short time interval t is given by
L2
. Then, the
2 D
 
C
t ,
t
where C  23/2 (2  1 ) 1/  . Using this expression we analyze the resistance oscillations
observed during the oxidation cycle at various temperatures ranging from 240 to 400 oC to
deduce the associated relaxation times , and subsequently the diffusion coefficients D by taking
L/2 as the c-axis lattice constant. Table 1 summarizes our results obtained at various
temperatures ranging from 240 to 400 oC.
4. Comparison of the diffusion rates
The oxygen diffusion in ErBCO is faster than that in YSZ, Gd:CeO2 and other similar
perovskite oxides by several orders of magnitude,vii,viii,ix,x while the hydrogen diffusion in ErBCO
is comparable in rate to the silver diffusion in -Ag2+S and -Ag2Te.xi
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