1. Impedance Spectroscopy on Multiferroic BiFeO3 Epitaxial Thin Films
University of Cambridge, Department of Materials Science and Metallurgy Rainer Schmidt
Impedance Spectroscopy on Multiferroic
BiFeO3 Epitaxial Thin Films
Rainer Schmidt
Department of Materials Science
Device Materials Group
Wilma Eerenstein
Department of Earth Sciences
Centre for Ferroics
Finlay Morrison
James Scott
Electroceramics X
Toledo
17th June 2006

2. Impedance Spectroscopy on Multiferroic BiFeO3 Epitaxial Thin Films
University of Cambridge, Department of Materials Science and Metallurgy Rainer Schmidt
Impedance Spectroscopy on Multiferroic
BiFeO3 Epitaxial Thin Films
1. Multiferroic BiFeO3
2. Experimental
3. Impedance Spectroscopy
4. Data Analysis: The Brick Layer Model
5. Data Analysis: Equivalent Circuit Fitting
6. Conclusions

3. Multiferroic Magneto-Electric BiFeO3
1. Multiferroic BiFeO Rainer Schmidt
Multiferroic Magneto-Electric BiFeO3
Ferroelectric below TCurie ~ 1125K
Ismailzade, Phys.Status Solidi B, 46 (1971) K39
Antiferromagnetic below TNeel ~ 645K
Smolenskii, Yudin, Sov.Phys.JETP, 16 (1963) 622
Spontaneous Polarization at Room Temperature: – 8.9 m C/cm2 (Single Crystal/Ceramic)
Teague et al., Solid State Commun., 8 (1970) 1073
Wang et al., Appl.Phys.Lett., 84 (2004) 1731
m C/cm2 (Granular /Epitaxial Thin Film)
Wang et al., Science, 299 (2003) 1719
Yun et al., Appl.Phys.Lett., 83 (2003) 3981
Spontaneous Magnetization at Room Temperature: ~ 0.05 mB/ Unit Cell (Thin Film)
Wang et al., Science, 299 (2003) 1719 //
Eerenstein et al., Science, 307 (2005) 1203a
Rhombohedral Phase (Bulk Single Crystal) Tetragonal Phase (Thin Film Epitaxy)

4. Pulsed Laser Deposition of BiFeO3 Thin Films
2. Experimental Rainer Schmidt
Pulsed Laser Deposition of BiFeO3 Thin Films
1. Vacuum Annealing of the
STO Substrate at 700°C
for 1 h
2. Deposition at 15 Pa O2
Partial Pressure at 670°C
- Variable Deposition Time
- 1.6 J·cm-2 Laser Fluence
- 1 Hz Laser Pulse
Frequency
3. Post Deposition Annealing
at 60 kPa O2 Partial Pressure
at 500°C for 1 Hour

5. Nb-Doped STO Substrate
2. Experimental Rainer Schmidt
Sample Geometry
Copper Wires
to Impedance
Analyzer
Agilent 4294A
Spring Loaded
Stainless-Steel
Probes
Pt - Electrodes
BiFeO3 Layer
50/100/200 nm
Nb-Doped STO Substrate
AC Signal Current Path

6. Impedance Spectroscopy
3. Impedance Spectroscopy Rainer Schmidt
Impedance Spectroscopy
Application of an Alternating Voltage Signal to a Sample:
Measurement of the Alternating Current Response:
Time Dependent Definition of the Impedance:
U(w,t)=U0 cos(w t )
I(w,t) = I0 cos(w t +d )
Time Independent Complex Impedance:

7. Complex Relationship Dielectric Constant – Capacitance Relationship
3. Impedance Spectroscopy Rainer Schmidt
Complex Relationship
Dielectric Constant – Capacitance Relationship
Contact Area A d
Contact Distance
Capacitance of the Measuring Cell in Vacuum

8. 4. Data Analysis: The Brick-Layer Model Rainer Schmidt
Composite Character of the Impedance Response of a Polycrystalline Sample
Bulk
Cb ~ 1 x F
Grain Boundary
Cgb ~ 1 x 10-9 F
Electrode Interface
Cel ~ 1 x 10-6 F Rb Cb
Rgb
Cgb
Rel
Cel
Equivalent Circuit
- Z’’
Nyquist Plot
Negative Imaginary Part of Impedance –Z’’ vs Real Part Z’
frequency Z’ Rb
Rb+Rgb
Rb+Rgb+Rel

9. Identification of the Origin of Relaxation Times
4. Data Analysis: The Brick Layer Model Rainer Schmidt
Identification of the Origin of Relaxation Times
Normalised Capacitance in F/cm
Origin of the RC Element
10-12
10-11 – 10-8
10-10 – 10-9
10-7 – 10-5
Bulk
Grain Boundary
Bulk Ferroelectric
Sample – Electrode Interface
Irvine et al., Advanced Materials, 2 (3) (1990) 132
The Values are Valid Only for Samples of the Size 1 cm x 1cm x 1cm
For Bulk Contributions Data can be Normalized Using the
Geometrical Factor g: d
For Electrode Contributions Data can be Normalized Using the Contact Size A

10. Data collected at 150ºC / 50 nm film
5. Data Analysis: Equivalent Circuit Fitting Rainer Schmidt
Equivalent Circuit
[C1]
[C2]
Frequency in Hz Z’
108
107
106
105
104
103
10-10
10-11
10-12
10-13 C’ R1 R2 R0 C1 C2
Data collected at 150ºC / 50 nm film

11. Thickness Dependence of C1 and C2
5. Data Analysis: Equivalent Circuit Fitting Rainer Schmidt
Thickness Dependence of C1 and C2
Capacitance Conversion: Hsu, Mansfeld, Corrosion 57 (2001) 747

12. Temperature Dependence of Resistance
5. Data Analysis: Equivalent Circuit Fitting Rainer Schmidt
Temperature Dependence of Resistance

13. Temperature Dependence of the Dielectric Constant e 2
5. Data Analysis: Equivalent Circuit Fitting Rainer Schmidt
Temperature Dependence of the Dielectric Constant e 2
Dielectric Constant of BiFeO3 Epitaxial Layer: ~ 285 ± 75
Dielectric Constant for Polycrystalline Films : ~ 110
V R Palkar et al., Appl.Phys.Lett. 80(9) 1628, 2002

14. Temperature Dependence of R0 and L1
5. Data Analysis: Equivalent Circuit Fitting Rainer Schmidt
Temperature Dependence of R0 and L1

15. Conclusions Impedance Spectroscopy is a Useful Tool for Dielectric
6. Conclusions Rainer Schmidt
Conclusions
Impedance Spectroscopy is a Useful Tool for Dielectric
Characterization of Multiferroic Thin Films
Multiferroic BiFeO3 Thin Film Impedance Spectra
Display an Interface and a Film Contribution
Strong Overlap of the two Contributions Suggests That
Single Frequency Measurements are Unreliable
Contributions from Measuring Leads and Wires can be
Separated and Quantified

16. Acknowledgments Paul Midgley University of Cambridge
7. Acknowledgments Rainer Schmidt
Acknowledgments
Paul Midgley
University of Cambridge
Department of Materials Science

17. U, I Time Dependent Notation Arrow Diagram
Impedance on the Complex Plane Rainer Schmidt
Time Dependent Notation
Arrow Diagram
U, I
U=U0 cos(w t)
IC=I0 cos(w t-p/2) C R
IRC=I0 cos(w t –d ) d
IR=I0 cos(w t) g
CPE
IC-CPE=I0 cos(w t -p/2+g)
ZC-CPE=1/[(iw)n C ]; n ~ 1
ZR=R
ZC=1/iwC
IL=I0 cos(w t +p/2)
ZL=iwL
Time Independent Complex Impedance

18. Equivalent Circuit wmax = 2p fmax - Ferroelectrics - Dielectrics
Impedance on the Complex Plane Rainer Schmidt
Equivalent Circuit
- Ferroelectrics
- Dielectrics
- Thermistors R
Real – and Imaginary Parts of the Impedance
Nyquist Plot
106
105
104
103
102
101
100
10-1
10-2
106
105
104
103
102
101
100
10-1
10-2
1.0E5
7.5e4
5.0E4
2.5E4
wmax
= 2p fmax Z’
-Z’’
-Z’’
R = 100 kΩ
C’ = 10 nF
E E E E5
Frequency in Hz Z’