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Observation of reduction in Casimir Force Without Change of Dielectric Permittivity (?)
U. MohideenUniversity of California-Riverside
Motivation to measure Casimir force with Indium Tin Oxide (ITO)
Use Transparent Electrodes to Reduce the Casimir Force
Manipulation of the Casimir Force using UV Light
Explore same puzzles in the Lifshitz Theory with dielectrics
Transparent Electrodes to Reduce Casimir Force
Rationale:Reduce Casimir Force by Reducing Boundary Reflectivity at characteristic frequency (~c/2z)
z
In devices z~ 1mmGold Electrodes have ~100% Reflectivity
Use electrodes which are transparent around1mm to reduce reflectivity and reduce Casimir force
De Mann et al, PRL, 103,040402 (2009)
UV treatment to Reduce Casimir Force (?)
Rationale:UV treatment known to change mobility of Charge Carriers in ITO
C.N. Li et al, Appl Phys. , 80,301 (2005)
ITO Sample Properties
1. Sputter coated ITO film made in a loadlocked and cryo-pumped system with a base pressure of 5X10-7 Torr or better.
2. The substrates (Quartz) are sputter etched cleaned and then sputter coated with ITO on one side.
3. The resistivity of ITO taking by four point probe measurement is 42 ohms/sq.4. The thickness of ITO measured by AFM is 74.6 ± 0.2nm
EXPERIMENT
Experiment:i. Measure Casimir force between Au Sphere and Au plate ii.Replace Au plate with ITO plate Compareiii. UV Treat ITO plate and Measure Casimir Force Compare
Compare the Casimir force using Au & ITO Plates (with and without UV Treatment)
Results:1.Casimir force reduces by x 2 with ITO2.Casimir Force reduces additional ~35% with UV treatment
Force Measurements Using Cantilever Deflection
Plate :Au or ITO
Radius of Au coated Sphere= 101.23±0.25 µm
Smooth Au coating 0f 105±1 nm10 nm Cr followed by 20 nm of Al then Au coatingAu Coating done at 3.75 Ẩ/min
Experimental set-up scheme for contact mode
Oil Free vacuum at 10-7 TorrTemperature 2 o CVibration Isolation
100 150 200 250 300-0.5
-0.4
-0.3
-0.2
-0.1
0.0
Ca
nti
lev
er
De
fle
cti
on
(V
)
Au sphere-ITO plate relative separations (nm)
-260 mV -235 mV -225 mV -210 mV -200 mV -190 mV -175 mV -160 mV -135 mV -110 mV
Method: Measured Total Force(Electrostatic+Casimir) between Au Sphere and ITO Plate
-270 -240 -210 -180 -150 -120 -90
-0.20
-0.15
-0.10
-0.05
sig
nal
(V
)
applied voltages (mV)
Electric Force
Cantilever deflection signal:2
0 )('
)(
'''VV
k
zX
k
F
k
F
k
FS CaselectricCas
def
10 Different Voltages VV o = Residual PotentialX(z)~ Capacitancek’ = cantilever spring constant
Parabolas Drawn at each Separation
-280 -260 -240 -220 -200 -180 -160 -140 -120 -100-0.12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
applied voltages (mV)
sig
na
l (V
)
Residual Electrostatic Potential between Au Sphere and ITO Plate
<V0>=-196.81.5 mV
100 150 200 250 300
-210
-200
-190
-180
Au sphere-ITO plate separations (nm)
Res
idu
al E
lect
ros
tati
c P
ote
nti
al (
mV
)
Residual Voltage independent of Au Sphere-ITO plate separationThis allows easy subtraction of the electrostatic force
Experimental Procedure
Cantilever deflection signal: 20 )(
'
)(
'''VV
k
zX
k
F
k
F
k
FS CaseCas
def
z=z0+ zpiezo-Sphotodiode signal * m
z0 = Surface separation on contactm= cantilever deflection per signal unit
0V
- Curvature
- residual potential differencebetween the sphere and the plate
'
)(
k
zX
Parameters defined from parabolas:
'k
0z
Use sphere- plate electrostatic formula
100 150 200 250 300-0.5
-0.4
-0.3
-0.2
-0.1
0.0
Ca
nti
lev
er
De
fle
cti
on
(V
)
Au sphere-ITO plate relative separations (nm)
-260 mV -235 mV -225 mV -210 mV -200 mV -190 mV -175 mV -160 mV -135 mV -110 mV
-270 -240 -210 -180 -150 -120 -90
-0.20
-0.15
-0.10
-0.05
sig
na
l (V
)
applied voltages (mV)
-270 -240 -210 -180 -150 -120 -90-0.30
-0.25
-0.20
-0.15
-0.10
sig
nal
(V
)
applied voltages (mV)
m from
<z0>=29.50.4 nm
Determination of contact separation zo & cantilever spring constant k
<k>=0.01390.0001 N/m
0 200 400 600 800 1000
-3.0x10-5
-2.0x10-5
-1.0x10-5
0.0
Experiment Theory
Au sphere-ITO plate separations (nm)
Par
abo
la C
urv
atu
re
Both zo & k independent of separationCritical for precision measurement
200 400 600 800 100027
28
29
30
31
Ave
arag
e sp
her
e-p
late
sep
arat
ion
on
co
nta
ct (
nm
)
End point of the fit (nm)
100 200 300 400 500 600 700 800 900 10000.0134
0.0136
0.0138
0.0140
0.0142
0.0144
Can
tiliv
er S
pri
ng
Co
nst
ant
(N/m
)
End point of the fit (nm)
Will lead to Dependence of Vo on Separation Distance (Anamalous Behaviour Due to Skewed Parabola)
0
Correction for Sphere or Plate Movement during Measurement
Sphere- Plate separation (nm)
Force vs. Separation Curves for Same Applied Voltage Shifted due to Sphere/Plate Movement
1st time
2nd time
Canti
leve
r Defl
ectio
n
Correction due to Sphere-Plate Drift
01000200030004000
-4
-3
-2
-1
0
4114.34114.44114.54114.64114.74114.84114.9
-3.6
-3.4
-3.2
-3.0
-2.8
-2.6
Sd
ef(a
rbit
rary
un
its
)
yx
w
Piezo extension, d (nm)
C
y
x
w
2. Repeat Electrostatic Force Measurement for same applied V and look at change in contact point.
1600 1620 1640
-1.70
-1.65
-1.60
Ca
nti
lev
er
De
fle
cti
on
(V
)
0.08 nm/sec
1. Find Precise Sphere Plate Contact Point- Extrapolate
Contact points as a function of time
200 400 600 800 1000
25.5
26.0
26.5
27.0
27.5
28.0
End point of the fit (nm)
Av
eara
ge
sph
ere-
pla
te s
ep
arat
ion
on
co
nta
ct (
nm
)
100 150 200 250 300
-210
-200
-190
-180
Sphere-plate separations (nm)
Sp
he
re-p
late
co
nta
ct
po
ten
tia
l (m
V)
100 150 200 250 300-210
-205
-200
-195
-190
-185
Sp
he
re-p
late
co
nta
ct
po
ten
tia
l (m
V)
Sphere-plate separations (nm)
<V0>=-196.81.5 mV
Errors due to Sphere-Plate Separation DriftCorrected Uncorrected
<z0>=29.50.4 nm
200 400 600 800 100028.0
28.5
29.0
29.5
30.0
30.5
31.0
Ave
arag
e sp
her
e-p
late
sep
arat
ion
on
co
nta
ct (
nm
)
End point of the fit (nm)
50 100 150 200 250 300-350
-300
-250
-200
-150
-100
-50
0
Ca
sim
ir F
orc
e (p
N)
Au sphere-ITO plate separations (nm)
60 70 80 90 100-350
-300
-250
-200
-150
-100
-50
Measured Casimir Force from Au Sphere- ITO Plate
20 )()( VVzXFFFF TotalElectricTotalCasimir
Subtract Electric Force from Total Force
100 Voltages Applied to Plate
Measured Casimir Force Comparison of Au plate to ITO plate
100 150 200 250 300
-300
-250
-200
-150
-100
-50
0
Au sphere-ITO plate separations (nm)
ITO before UV Gold
C
as
imir
Fo
rce
(p
N)
Number of voltages V = 10Number of repetitions = 10
FCas (pN)z (nm)
100
85
120 -50.1
-123.42
-81.62
ITO/Au
0.57
0.61
0.59
40% Reduction in Casimir Force with ITO
UV Treatment of ITO Plate
• Penray Hg Lamp 9.0 inch long and 0.375 inch diameter
• λ=254 nm 5.4 mWatt/cm2 at 1.9 cm• λ=365 nm 0.2 mWatt/cm2 at 1.9 cm• 12 hr• Cleaned as before (Acetone, Methanol,
Ethanol, water rinse and Nitrogen dry)
Insert UV Treated ITO Plate& Repeat Measurement
100 150 200 250 300
-0.4
-0.3
-0.2
-0.1
0.0
Au sphere-ITO plate relative separations (nm)
Can
tile
ve
r D
efl
ect
ion
(V
)
-25 mV 0 mV 25 mV 50 mV 60 mV 70 mV 85 mV 100 mV 125 mV 150 mV
-40 0 40 80 120 160-0.20
-0.16
-0.12
-0.08
-0.04
sig
na
l (V
)
applied voltages (mV)
-40 0 40 80 120 160
-0.12
-0.08
-0.04
0.00
sig
na
l (V
)
applied voltages (mV)
Measured Total Force(Electrostatic+Casimir) between Au Sphere and ITO Plate
Electric Force
20 )(
'
)(
'''VV
k
zX
k
F
k
F
k
FS CaselectricCas
def
10 Different Voltages V on plateV o = Residual PotentialX(z)= Capacitancek’ = cantilever spring constant
Cantilever deflection signal:
0V
Parabola Curvature
- residual potential differencebetween the sphere and the plate
'
)(
k
zX
'k
0z
Use sphere- plate electrostatic formula
Check Stability of Measurements of Au Sphere and ITO Plate (after UV treatment)
<z0>=290.6 nm
<V0>=65 2 mV
<k>=0.01380.0001 N/m
100 150 200 250 30050
55
60
65
70
75
80
Res
idu
al E
lect
rost
atic
Po
ten
tial
(m
V)
Au sphere-ITO plate separations (nm)
1. Distance independence of residual potential Vo
2. Distance independence of contact separation zo 3. Distance independence of Spring constant
100 200 300 400 500 600 700 800 900 100028.2
28.4
28.6
28.8
29.0
29.2
29.4
Av
erag
e S
epar
ati
on
on
Sp
her
e-P
late
Co
nta
ct (
nm
)
Au sphere-ITO plate separations (nm)
200 400 600 800 10000.0134
0.0136
0.0138
0.0140
0.0142
Ca
nti
live
r S
pri
ng
Co
ns
tan
t (N
/m)
Au sphere-ITO plate separations (nm)
Fit Electrostatic Force Curve
Repeat Casimir Force between Au Sphere and ITO Plate (after UV treatment)
100 150 200 250 300
-250
-200
-150
-100
-50
0
Ca
sim
ir F
orc
e (
pN
)
Au sphere-ITO plate separations (nm)
60 70 80 90 100
-250
-200
-150
-100
-50
Grey Bars represent the complete range of data every 5 nm
20 )()( VVzXFFFF TotalElectricTotalCasimir
Subtract Electric Force from Total Force
100 Voltages Applied to Plate
Casimir Force between Au Sphere and ITO Plate (Before and After UV comparison)
After UV/Before UVz (nm)
100
120
85 0.72
0.68
0.66
100 150 200 250 300
-300
-250
-200
-150
-100
-50
0
Au sphere-ITO plate separations (nm)
ITO after UV ITO before UV
C
asim
ir F
orc
e (p
N)
21-35% Reduction with UV treatment21% at 60 nm and 35% at 130 nm
440 460 480 500 520 5400.0
0.1
0.2
0.3
0.4
Casimir Force (pN)
140 1600.0
0.1
0.2
0.3
0.4
Casimir Force (pN)
60 80 1000.0
0.1
0.2
0.3
0.4
Casimir Force (pN)
240 260 280 300 320 3400.0
0.1
0.2
0.3
0.4
Casimir Force (pN)
100 1200.0
0.1
0.2
0.3
0.4
Casimir Force (pN)
40 600.0
0.1
0.2
0.3
0.4
Casimir Force (pN)
ITO Before UVITO After UV
60 nm
80 nm
100 nm
Histograms of the Experimental Data- No Overlap
100 150 200 250 3000.0
0.5
1.0
1.5
2.0
2.5
3.0
Total error Systematic error Random error
Au sphere-ITO plate separations (nm)
Err
or
(pN
)
100 150 200 250 3000.0
0.5
1.0
1.5
2.0
2.5
3.0
Total error Systematic error Random error
Au sphere-ITO plate separations (nm)
Err
or
(pN
)
ITO Before UV ITO After UV
Experimental Errors at 95% Confidence Level
Error due to use of Proximity Force Approx <0.3%Radius of Sphere= 101.2±0.5 mm
Comparison with Lifshitz Theory
Lifshitz Formula
lk
l
lk
li
kk
llk
l
kll
kl
ik
qK
qKKr
Kq
KqKr
)(
)()(
)()(
)()()(
// ),(,),(
]})()(1ln[])()(1{ln[)1()( 2,
)2(
,
)1(
0 0
2,
)2(
//,
)1(
//021 zq
lll
zqlllBc
ll eKrKreKrKrdKKTRKzF
2/12)()(2/12 ])([,)( 2
2
2
2
KiKKqcl
kklcl
ll
R
z
R>>z
2
1
TlkB
l
2 At l=0, =0xMatsubara Freqs.
Reflection Coeffs:
Measure PermittivityEllipsometry Measurements
VUV-VASESpectral range 0.14 – 1.7 µm;Angle of incidence is computer controlled from 10° to 90° ;
IR-VASE
Spectral range 1.7–33 µm; Angle of incidence is computer controlled from 30° to 90°.
J.A. Woollam Co., Inc.
Comparison with Theory: Casimir Force between Au Sphere and ITO Plate
Dielectric Permittivity Measured by Ellipsometry from 0.04 eV to 8.47 eV. Fit to Lorentz oscillators and Drude type free electron behavior
14.5 15.0 15.5 16.0 16.5 17.00
2
4
6
8
10
12
ITO(i
)
Log10[(rad/s)]
0 2 4 6 8 10 120
1
2
3
4
5
Im IT
O
(eV)
220
220
20
)( WW
WAOsc
xgwx
xga
aA=111.52; w0=8.eV, g0= 4.eV.
Extrapolated to lower Frequency with Drude Model [wp =1.5 eV, g=0.128 eV]
15.0 15.5 16.0 16.5 17.00
2
4
6
8
10
12
ITO(i)
Log10[(rad/s)]
14.5 15.0 15.5 16.0 16.5 17.00
2
4
6
8
10
12
ITO(i
)
Log10[(rad/s)]
No UV
After UV
Dielectric Permittivity in Imaginary Frequency
0 2 4 6 8 10 120
1
2
3
4
5
Im IT
O
(eV)
0 2 4 6 8 10 120
1
2
3
4
5
Im IT
O
(eV)
Very Little Difference between Before and After UV in imaginary frequency
Drude Model Parameters [wp =1.5 eV, g=0.128 eV (No UV), g=0.132 eV (UV)]
220
220
20
)( WW
WAOsc
xgwx
xga
aA=111.52; w0=8.eV, g0= 4.eV;aA=240.54, w0=9.eV, g0=8.5eV.
RMS Roughness=2.04 nm
hi, nm vi
0.097 4.40E-040.483 1.50E-04
0.87 0.001021.257 0.00161.644 8.70E-04
2.03 0.002622.417 0.001892.804 0.002773.191 0.004083.577 0.004523.964 0.003354.351 0.00514.738 0.006415.124 0.0083
5.511 0.0086
5.898 0.01049
6.285 0.01311
6.671 0.01734
7.058 0.01734
7.445 0.02273
7.832 0.02389
8.218 0.03395
8.605 0.04006
8.992 0.05041
9.379 0.05522
9.765 0.06148
10.152 0.08421
10.539 0.08362
10.926 0.08858
11.312 0.09237
11.699 0.07605
12.086 0.05478
12.473 0.04691
12.859 0.02608
13.246 0.02171
13.633 0.00874
14.02 0.00758
14.406 0.00626
14.793 000262
15.18 0.00102
Fractions vi of the surface area covered by roughnesswith heights hi
ITO Plate Roughness
Roughness effect<0.5 % for >116 nm<1% for > 90 nm<2.2% at 60 nm
Carrier Density Measurement
dneIB
HV
Slope = B/dne is sameSame Carrier Density = 7 x 1020 /cc
wikipedia
-1000 -500 0 500 1000-5.38
-5.36
-5.34
-5.32
-5.30
-5.28
-5.26
-5.24
-5.22
magnetic flux density (Gauss)
VH
all (
mv)
No UVAfter UV
100 150 200 250 300
-300
-250
-200
-150
-100
-50
0
Au sphere-ITO plate separations (nm)
Ca
sim
ir F
orc
e (
pN
)
60 70 80 90 100-300
-250
-200
-150
-100
-50
0
Comparison with Theory: Casimir Force between Au Sphere and ITO Plate Before UV
ITO Before UV DC Conductivty Included – Good Agreement
Comparison with Theory: Casimir Force between Au Sphere and ITO Plate After UV
No Agreement if we include Free Carriers
----Theory with DC Conductivity
Effect of inclusion of DC Conductivity
++ Data
60 80 100 120 140 160 180 200
-300
-250
-200
-150
-100
-50
0
Au sphere-ITO plate separations (nm)
Ca
sim
ir F
orc
e (
pN
)
ITO After UV
100 150 200 250 300
-300
-250
-200
-150
-100
-50
0
Au sphere-ITO plate separations (nm)
Ca
sim
ir F
orc
e (
pN
)
60 70 80 90 100-300
-250
-200
-150
-100
-50
Comparison with Theory: Casimir Force between Au Sphere and ITO Plate After UV
Good Agreement only if we drop the DC conductivity of ITO Afer UV Assume it to be a perfect dielectric
ITO After UV
DC Conductivity Not Inclduded
Understanding the Patch Effectby
Electrostatic Simulation
Electrostatic simulation with COMSOL software package
Plate size = 32×32 m;Patch size = 0.6×0.6 m;Vplate=0.018 mV , Vsphere=0, Vpatches=random in [-90;90] mV, ~0.7 mV.
We solved the Poisson equation for conductive plate (variable potential Vplate) with dielectric patches on the surface (random potential distribution in [-90;90] mV) and conductive sphere on the distance z from the plate
Area filled by patches has been chosen according to condition: Surface area > Aeff=2Rd (for z=0.1 m plate size should be higher then 8 m)
Ftotal (Vplate) between
the sphere and plate = 0Vplate =V0
Aeff=2Rd
Patches
- 0r
V=0 r – relative permittivity
Electrostatic simulation with COMSOL software package
In the pictures:Sphere radius R = 100 m; Plate size = 32×32 m;Patch size = 0.3×0.3 m to 0.9×0.9 m;Vpatches=random in [-90;90] mV, ~0.7 mV.
We solved the Poisson equation for conductive plate (variable potential Vplate) with dielectric patches on the surface (random potential distribution in [-90;90] mV) and conductive sphere on the distance d from the plate
Plate
Patches
Aeff=2Rd
Sphere
Apply voltages to the plate and find voltage when electrostatic force goes to zeroThis compensating voltage (Vo) is found for different separations.
- 0r
V=0 r – relative permittivity
Simulation Results of Compensating Voltage
0.0 0.2 0.4 0.6 0.8 1.0
0.009
0.012
0.015
0.018
0.021
sphere-plate separations (m)
Co
mp
en
sa
tin
g V
olt
ag
e (
mV
)
300 nm 300 nm 600 nm 600 nm 900 nm 900 nm
size distance between
Distance IndependentAs in Observed in Experiment –WellCompensated
Conclusions1. UV Modification of the Casimir Force was demonstrated.
2. No Anamalous distance dependence of the Compensating Voltage
3. 21-35% reduction of Casimir force by UV treatment even though there is not much change in e(ix)
4. The Casimir force measurements have the correct distance dependence.
5. Inclusion of DC conductivity in the Lifshitz formula for the ITO after UV leads to disagreement with the experimental results.
6. A Study of the Temperature Dependence of the Carrier Mobility might shed light on the discrepancy.
• Precision Measurement of Casimir Force with Au Using a
Dynamic AFM at 15:30 pm
AcknowledgementsExperimentC.C. ChangA. Banishev
R. Castillo
Theoretical AnalysisV.M. Mostepanenko
G.L. Klimchitskaya
Research Funded by: DARPA, National Science Foundation & US Department of Energy
100 150 200 250 300
-300
-250
-200
-150
-100
-50
0
Au sphere-ITO plate separations (nm)
Cas
imir
Fo
rce
(pN
)
60 70 80 90 100-300
-250
-200
-150
-100
-50
0
100 150 200 250 300
-300
-250
-200
-150
-100
-50
0
Au sphere-ITO plate separations (nm)
Cas
imir
Fo
rce
(pN
)
60 70 80 90 100-300
-250
-200
-150
-100
-50
100 150 200
-300
-250
-200
-150
-100
-50
0
Au sphere-ITO plate separations (nm)
Cas
imir
Fo
rce
(pN
)
Comparison with Theory: Casimir Force between Au Sphere and ITO Plate
Good Agreement only if we dropthe DC conductivity of ITO
Afer UV
ITO Before UV ITO After UV
ComparisonDC Conductivty Included DC Conductivity Not Inclduded
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