A method of making given field distribution within thin electro-optical layers by using narrow band electrodes placed at the same electric potential. A formula for electric field intensity produced by a single band electrode is obtained. Electric field modeling for different band electrode configurations is undertaken. It was shown, by applying piezoresponse force microscopy, that in case of highly inhomogeneous field the polarization of lithium niobate electro-optical film persisted only in the area above
the band electrode.
Lithium niobate, electro-optical structures, piezoresponse force microscopy, Computer
simulation

Bykov, A.S.

Kiselev, D.A.

Ksenich, S.V.

Kubasov, I.V.

Malinkovich, M.D.

Parkhomenko, Yu.N.

Temirov, A.A.

Timushkin, N.G.

Zhukov, R.N.

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 8 No 3, 03011(4pp) (2016) Том 8 № 3, 03011(4cc) (2016) 
 
 
2077-6772/2016/8(3)03011(4) 03011-1  2016 Sumy State University 
Formation of the Electric Field Distribution in Thin Electro-Optic Layers for Precision 
Correction their Optical Characteristics  
 
R.N. Zhukov*, S.V. Ksenich, I.V. Kubasov, A.A. Temirov, N.G. Timushkin, D.A. Kiselev, A.S. Bykov, 
M.D. Malinkovich, Yu.N. Parkhomenko 
 
National University of Science and Technology "MISiS", 4, Leninskiy pr., 119049 Moscow, Russian Federation  
 
(Received 20 April 2016; published online 03 October 2016) 
 
A method of making given field distribution within thin electro-optical layers by using narrow band 
electrodes placed at the same electric potential. A formula for electric field intensity produced by a single 
band electrode is obtained. Electric field modeling for different band electrode configurations is 
undertaken. It was shown, by applying piezoresponse force microscopy, that in case of highly 
inhomogeneous field the polarization of lithium niobate electro-optical film persisted only in the area above 
the band electrode. 
 
Keywords: Lithium niobate, Electro-optical structures, Piezoresponse force microscopy, Computer 
simulations. 
 
DOI: 10.21272/jnep.8(3).03011 PACS numbers: 77.80.Dj, 68.55. – a, 77.55.H – 
 
 
                                                        
* rom_zhuk@mail.ru 
1. INTRODUCTION 
 
Electrooptics and electro-optic effect find widespread 
application in most diverse devices such as Pockels and 
Kerr cells, electro-optic modulators [1, 2]. Most of the 
existing electro-optic devices are made on the basis of 
single-crystalline bulk materials and significantly fewer 
of them are made on the basis of film materials. 
Nevertheless, electro-optic films with given optical axis 
orientation and spontaneous polarization vector 
nonreversing [3, 4], which are integrated in thin-film 
multilayer structures, including gradient ones [5], can 
be a fine alignment tool for optical cavities of moderate- 
and high-precise laser gyroscopes, optical narrow band-
pass filters, phase shifters and other advanced. 
Managing effect is obtained due to precise modifying the 
reflex index of electro-optic films or layers by applying 
external electric field. At that, the correction of optical 
path can be performed within the accuracy of a few 
angstroms. 
Electrical intensity needed to modify refraction 
index in lithium niobate films several hundreds 
nanometers thick up to ~ 1,5-3 % for optical elements 
fine adjusting, must 105-106 V/cm.   
Here we report the possibility of making an electric 
field with given intensity in thin layers of lithium 
niobate or any other material with electro-optical effect 
by applying a system of electrodes placed on the 
substrate and at the same potential and using an 
electrode out of operational structure, at infinite, as a 
second potential. The results of field distribution 
modeling depending on electrode size-shape factor and 
experimental studies are introduced. 
 
2. MODEL DESCRIPTION 
 
Create a given distribution of the electric field in 
the thin film of lithium niobate is possible by means of 
thin electrode system under the same potential. 
Another potential to be supplied with the freeform 
electrode located at a distance much greater than the 
film thickness. Create a given distribution of the 
electric field in the thin film of lithium niobate is 
possible by means of thin electrode system under the 
same potential. Another potential to be supplied with 
the freeform electrode located at a distance much 
greater than the film thickness. 
Consider the distribution of the electric field 
generated by a single thin conductive strip width (m) 
and length (l). 
On the perpendicular at a distance z from the origin, 
located in the center of the strip, the electric field 
strength, calculated by integration over m and l (Figure 
1), is given by: 
 
, 
 
         (1) 
 
 
where zmax – distance to the second electrode provided 
zmax  m, Δφ – potential difference between electrodes, 
as well as the condition m  l. 
 
 
 R.N. ZHUKOV, S.V. KSENICH, I.V. KUBASOV ET AL. J. NANO- ELECTRON. PHYS. 8, 03011 (2016) 
 
 
03011-2 
 
 
Fig. 1 – Determination of the field at the point with 
coordinate z, generated elements dx and dy with coordinates 
+ y, – y (a) and the + x, – x (b) 
 
The electric field generated by the conductive strip 
at a distance r0 from the origin in the direction of α was 
calculated according to the scheme shown in Figure 2. 
 
 
 
Fig. 2 – Determination of resulting electric field that 
created by two elements with area of dx and coordinates 
of + x and – x in direction  at the distance of r0 from 
origin 
 
After integration and some transformations, we obtain 
Eq (2): 
 
(2) 
 
3. COMPUTER SIMULATION 
 
Using the equation (2), computer modeling was 
carried out distribution of the electric field created by 
any number of strip electrodes arranged at an arbitrary 
distance from each other. 
 
 
 
Fig. 3 – The vector distribution of the electric field E, V/m 
generated by a single stripe electrode with width of 2 m 
 
Vector distribution of electric field, which formed by 
single strip electrode is presented at the Fig. 3. We used 
the following parameters of electrodes for simulation: 
the width of electrode – 2 m, voltage – 1000 V, distance 
from external electrode 1 cm. 
One can achieve high homogeneity of electric field by 
varying width of strips and distance between the mas it 
shown at Fig. 4. The simulation was made for 10 
electrodes with width of 400 nm, distance between 
strips of 400 nm, voltage of 1000 V and distance from 
external electrode of 1 cm. Here electric field is almost 
constant (approx. 106 V/m) at the distance of 300 nm 
and more from the strip electrodes. 
 
 
 
Fig. 4 – Projection of electric field E, V/m to z axis. The plot is 
calculated for 10 strips with width of 400 nm and distance 
between electrodes of 400 nm 
 
 
 
Fig. 5 – Projection of electric field E, V/m to z axis. The plot is 
calculated for 3 strips with width of 4μm and distance between 
electrodes of 200 μm 
 
In order to verify mathematical model we calculated 
electric field of 3 electrodes with a width of 4μm with 
and a distance of 200 m between electrodes. The distance 
from an external electrode and applied voltage were 1 cm 
and 1000 V, correspondingly (high inhomogeneity of 
electric field distribution), Fig. 5. Accordingly to this 
distribution samples for experiments were prepared.  
 
4. EXPERIMENTAL DETAILS 
 
The LiNbO3 films 200 nm thick were deposited on 
 FORMATION OF THE ELECTRIC FIELD DISTRIBUTION… J. NANO- ELECTRON. PHYS. 8, 03011 (2016) 
 
 
03011-3 
Al2O3 substrate (with pre-coated gold stripe electrodes) 
by RF magnetron sputtering of the single-crystalline 
target in Ar/O  1 atmosphere and under the working 
pressure of 0.6 Pa. After sputtering process the films 
were annealed in a furnace at 700 °C for two minutes. 
The electrodes have a width of 4 m, a length through 
the sample, the distance between the electrodes was 
200 m, the system of plane-parallel electrodes had 
dimensions of 14  14 mm (Fig. 6).  
 
 
 
 
 
Fig. 6 – Schematic representation (1 – LiNbO3, 2 – Au 
electrodes, 3 – Al2O3 substrate), photo image (b) of the EO 
structure based on LiNbO3 thin films 
 
The surface morphology, ferro- and piezoelectric 
properties of the LN thin films were characterized by 
the piezoresponse force microscopy using commercial 
scanning probe microscopes MFP-3D (Asylum Research) 
and NTEGRA Prima (NT-MDT) with Asyelec Ti/Ir 
coated conductive probes (Asyelec-01, Asylum 
Research, USA). Out-of-plane PFM images (OOP-PFM) 
of the samples were obtained by applying AC voltage 
(5V peak-to-peak) with the frequency around 300 kHz. 
 
5. RESULTS 
 
The surface morphology of the LiNbO3 film 
synthesized on Al2O3 substrate include a single 
electrode as shown in Fig. 7a. OOP-PFM image obtained 
simultaneously with the topography image are shown in 
Fig. 7b. As known, PFM can to used to characterize the 
polarization states in the ferroelectric materials. The 
maximum piezoelectric response (negative value a 
signal or dark contrast) observed in the film with the 
lower electrode area, and this signal is uniform over the 
entire length of the electrode, which implies that the 
polarization vector in this area is directed toward the 
upper interface. Outside this area the OOP-PFM signal 
has a zero piezoresponse.  
To confirm the presence of the ferroelectric 
properties of the investigated heterostructures based on 
LiNbO3, a series of experiments on the local polarization  
 
 
 
 
Fig. 7 – Topography (a), OOP-PFM image before (b) and 
after poling experiment (c) of LN heterostructure  
 
of the surface at DC voltage (Fig. 7c). Since the 
cantilever in scanning probe microscope in a contact 
mode plays the role of the upper electrode during the 
scanning process, it is possible to supply a DC voltage to 
subsequent visualization a remnant piezoelectric 
response. After applying an outside 18  18 m2 square 
with + 50 V voltage and an inside 8  8 m2 square with 
– 50 V, a large OOP-PFM contrast is observed (Fig. 7c). 
The structure «box-in-box» (or remnant piezoelectric 
response) characterized of the local polarization 
switching effect under a DC voltage. However, as can be 
seen from Fig. 7c polarized only part of the film, which 
"lies" on the lower gold electrode. Outside electrode 
(LiNbO3 on sapphire) the poling area do not appear, 
since the density of the lines of force arising under the 
cantilever during the polarization is considerably 
smaller than the electrode area. 
А 
B 
А 
B 
(а) 
(c) 
(b) 
+50 V 
+50 V 
-50 V 
(b) 
(а) 
 R.N. ZHUKOV, S.V. KSENICH, I.V. KUBASOV ET AL. J. NANO- ELECTRON. PHYS. 8, 03011 (2016) 
 
 
03011-4 
0 5 10 15 20 25
-1
0
1
B
 
 
P
ie
zo
re
sp
o
n
se
, 
n
A
Distance, m
1  before poling
2  after poling
1
2
А
 
 
Fig. 8 – OOP-PFM image before (curve 1) and after poling 
experiment (curve 2) of LN heterostructure along line AB in 
Fig. 2b, c 
 
Fig. 8 shows the profiles of OOP-PFM piezoelectric 
response signal before and after polarization, conducted 
along the lines "A-B" indicated on scans Fig. 7b, c. The 
level of the remnant signal for the piezoelectric response 
poled at + 50 V by absolute values compare with the 
original piezoelectric response, which demonstrates the 
effect of the full polarization switching under the 
influence of a DC voltage applied to the cantilever. 
When a voltage of – 50 V is "recovery" values 
piezoelectric response to the original state. It is worth 
noting that the poling area is stable over time and does 
not disappear after a few hours of uninterrupted 
scanning. 
 
6. CONCLUSIONS 
 
In summary, the electric field produced by a single 
electrode strongly inhomogeneous and reaches a 
maximum value immediately above this electrode in the 
perpendicular direction. In this case, the vertical 
component of the electric field rapidly decreased from 
right and left edges of electrode consistent with some 
experimental observations. Experimentally is observed 
that the piezoresponse value (polarization of the 
ferroelectric film) is stable only in the film area located 
directly above the bottom electrode. At the same time, 
the simulation shows that at a sufficient distance from 
the electrode along the z-axis of the electric field 
becomes uniform. The distance at which the electric 
field increases uniformity decreases with decreasing 
width of the electrode.  
 
ACKNOWLEDGEMENT 
 
The research was financially supported by the 
Federal Target Program “Investigation and Engineering 
in High-Priority Lines of Development of Science and 
Technology in Russia for 2014-2020” (unique project 
identifier RFMEFI57814X0071, contract no. 
14.578.21.0071)
 
 
REFERENCES 
 
1. R.L. Holman, L.M. Johnson, D.P. Skinner, Opt. Eng. 26, 
134 (1987).  
2. B. Wessels, Annu. Rev. Mater. Res. 37, 659 (2007).  
3. C. Xiong, W.H.P. Pernice, J.H. Ngai, J.W. Reiner, 
D. Kumah, F.J. Walker, H. Charles, C.H. Ahn, H.X. Tang, 
Nano Lett. 14, 1419 (2014).  
4. D. Sando, P. Hermet, J. Allibe, J. Bourderionnet, S. Fusil, 
C. Carretero, E. Jacquet, J.-C. Mage, D. Dolfi, 
A. Barthelemy, Ph. Ghosez, M. Bibes, Phys. Rev. B. 89, 
195106 (2014).  
5. A.B. Shvartsburg, A.A. Maradudin, Waves in Gradient 
Metamaterials (Singapore: WSPC: 2013). 
 


Formation of the Electric Field Distribution in Thin Electro-Optic Layers for Precision Correction their Optical Characteristics

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Formation of the Electric Field Distribution in Thin Electro-Optic Layers for Precision Correction their Optical Characteristics

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