1. Impedance Spectroscopy on Nano-sized Multiferroic Thin Films
University of Cambridge, Department of Materials Science and Metallurgy Rainer Schmidt
Impedance Spectroscopy on Nano-sized Multiferroic Thin Films
Rainer Schmidt
Department of Materials Science
Device Materials Group
Wilma Eerenstein
Department of Earth Sciences
Centre for Ferroics
Finlay Morrison
James Scott
26th July 2006
ICYS-ICMR Summer School
on Nanomaterials
Poster II-26

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. Introduction
2. Impedance Spectroscopy
3. Multiferroic BiFeO3
4. Thin Film Epitaxy
5. Equivalent Circuit Analysis
6. Conclusions

3. Any Useful for Interface
1. Introduction Rainer Schmidt
Dielectric and Resistive Characterisations by Impedance Spectroscopy
Well Established:
Never Used:
Polycrystalline Bulk Material
Separation of Contributions from
Electrode - Sample Interface Layer
Grain Boundary Areas
Grain Interior Bulk Material
Thin Epitaxial Layers
Epitaxial Layer
Electrodes
Waver Substrate
No Grain Boundaries
Any Useful for Interface
and Film Separation ???

4. Impedance Spectroscopy
2. 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 )
U(w,t ) U0 cos(w t )
Z(w,t )
I(w,t ) I0 cos(w t + d )
Time Independent Complex Impedance: Z*
(d )
(d )
(id )

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

6. Multiferroic Magneto-Electric BiFeO3
3. 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 RT:
3.5 – 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 RT:
~ 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) Pseudo-Tetragonal Phase (Thin Film Epitaxy)

7. Pulsed Laser Deposition of BiFeO3 Thin Films
4. Thin Film Epitaxy 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 7 Pa O2
Partial Pressure, 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

8. Nb-Doped STO Substrate
4. Thin Film Epitaxy Rainer Schmidt
Sample Geometry
Copper Wires
to Impedance
Analyzer
Agilent 4294A
Spring Loaded
Stainless-Steel
Probes
Pt - Electrodes
Film Thickness d:
50/100/200 nm
BiFeO3 Layer
Nb-Doped STO Substrate
r ~ 5 mΩ·cm
AC Signal Current Path

9. Data Collected at 150ºC / 50 nm Film
5. Equivalent Circuit Analysis Rainer Schmidt
Equivalent Circuit
[C1]
[C2]
Irvine et al., Advanced Materials,
Vol. 2 (3), (1990) p132
Data Collected at 150ºC / 50 nm Film
Frequency in Hz Z’
108
107
106
105
104
103
10-10
10-11
10-12
10-13 C’ R1 R2 R0 C1 C2

10. Film Thickness Dependence of C1 and C2
5. Equivalent Circuit Analysis Rainer Schmidt
Film Thickness Dependence of C1 and C2
Data Normalisation d A
Interface : A
Film : A / d
A / d
Capacitance Conversion: Hsu, Mansfeld, Corrosion 57, (2001), p747

11. Temperature Dependence of Resistance
5. Equivalent Circuit Analysis Rainer Schmidt
Temperature Dependence of Resistance

12. Temperature Dependence of the Dielectric Constant e’2
5. Equivalent Circuit Analysis 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

13. 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 two Contributions Suggests That
Single Frequency Measurements are Unreliable
Contributions from Measuring Leads and Electrodes can be Separated and Quantified
Poster II-26

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

15. Temperature Dependence of R0 and L1
Equivalent Circuit Analysis Rainer Schmidt
Temperature Dependence of R0 and L1

16. 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

17. 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’

18. - Z’’ Z’ Brick Layer Model Narrow, Homogeneous
Data Analysis: The Brick-Layer Model Rainer Schmidt
Brick Layer Model
Narrow, Homogeneous
Distribution of Grain Sizes
Identical Grain Boundary,
Electrode and Bulk
Properties and
Homogeneous Shapes
Bulk
Cb ~ 1 x F
Grain Boundary
Cgb ~ 1 x 10-9 F
Electrodes
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

19. Identification of the Origin of Relaxation Times
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
10-11 – 10-8
10-10 – 10-9
10-9 – 10-7
10-7 – 10-5
10-4
bulk
minor second phase
grain boundary
bulk ferroelectric
surface layer
sample – electrode interface
electrochemical reaction
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