Supplemental Material
for
Electro-Mechanical Response of Top-Gated LaAlO3/SrTiO3
Feng Bi,1 Mengchen Huang,1 Chung Wung Bark,2 Sangwoo Ryu,2 Sanghan Lee, 2 ChangBeom Eom,2 Patrick Irvin1 and Jeremy Levy1,*
1
Dept. of Physics & Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania,
15260, USA
2
Dept. of Materials Science, University of Wisconsin-Madison, Madison, Wisconsin,
53706, USA
Quantitative analysis of PFM measurement:
Piezoresponse Force Microscopy is based on the detection of electrical bias-induced
surface deformation. The excitation voltage: V  t   Vdc  VPFM cos(2 FPFM t ) is applied to the
LAO/STO interface with the top electrode held at virtual ground. The surface deformation will
be:
Vdc
z  zdc  Az ( FPFM ,VPFM ,Vdc )  cos(2 FPFM t  0 )   d33eff (Vdc )  dV 
0
d (Vdc )  VPFM  cos(2 FPFM t )
(2).
eff
33
Here Az ( FPFM ,VPFM ,Vdc ) is surface deformation amplitude under bias modulation, d 33eff is the
effective strain tensor component that directly couples into the vertical motion of the cantilever
and 0  0 or  , depending on the sign of d 33eff (Vdc ) . The surface deformation couples to the
cantilever displacement, which results in a change of deflection that is monitored with a lock-in
1
amplifier. Due to the contact resonant enhancement, the surface deformation will be amplified by
Q times, the quality factor of the tip-surface contact resonant system. If the lock-in X-output is
denoted by X (0 ,Vdc ) and  as the sensitivity of AFM, then
d33eff (Vdc )VPFM Q  X (0 ,Vdc )
(3).
. The sensitivity   67.75 nm/V can be obtained from the AFM force curve (Fig. S1). The
tensor component d 33eff (VDC ) is calculated as follows:
d33eff (Vdc ) 
X (0 , Vdc )
QVPFM
(4).
The surface displacement at the location of the AFM tip can be obtained by integrating with
respect to the applied voltage
Vdc
zdc (Vdc )  zdc (0 V)   d33eff (Vdc )dV
(5).
0V
The surface displacement is calculated under different VDC based on the high frequency PFM
measurement on device A. PFM spectral measurements (from 285 kHz to 305 kHz) are
performed under different VDC modulated from 0V-10V10V0V with step size 0.2V
(Fig. 5(a)). During the measurement, the ac excitation voltage is given by VPFM=20 mV.
Each spectrum is then fitted to a simple harmonic oscillator (SHO) model:
A   
Amax02
( 2  02 ) 2  (0 / Q) 2
2
(6).
where 0 is the resonant frequency, Amax is the amplitude and Q is the quality factor. With 0
and Q at each dc bias, one obtains:
X (Vdc ) 
X 0 ,Vdc 
Q
(7).
Equation (4) and (5) can be simplified to
X (Vdc )  67.75nm/V
VPFM
d33eff (Vdc ) 
zdc (Vdc )  
VDC
0
X (Vdc )  67.75 nm/V
 dV
VPFM
(8).
(9).
Eq. (8) and Eq. (9) give the result of d 33eff (Vdc ) and surface displacement zdc (Vdc ) , which are
plotted in Fig. 5(c) and Fig. 6(a) separately. Fig. 6(a) shows the quantitative distortion within
LAO/STO during the interface MIT.
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Fig. S1 AFM deflection versus Z piezo extension as tip engage to and retrace from the sample
surface (known as AFM force curve). By linear fit the tip/sample engaged part, the AFM
sensitivity  can be obtained.
4