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Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
A. P. Zhuravel*, S. M. Anlage#, and A. V. Ustinov
Physikalisches Institut, Universität Erlangen-Nürnberg, Erlangen, Germany
* Institute for Low temperature Physics and Engineering, Kharkov, Ukraine# Physics Department, Center for Superconductivity Research, University of Maryland, USA
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in
Superconducting Resonators
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Motivation / Goals
To image rf currents in operating superconducting microwave circuits and devices
To identify sources of microwave nonlinearities in superconductors
To investigate how rf currents are redistributed by m- and nm-scale defects
To develop new methods to investigate microwave nonlinearities in superconductors
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Conventional Laser Scanning Microscopy (LSM)
patterned superconducting film
V
laser beam
laser powerac modulated
lock-involtmeter
V(x,y) measured signal
y
x
dccurrent dc
current
2 – 300 K
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Microwave imaging LSM
combiner
f1
spectrum analyzerlock-incomputer
77 – 95 K
laser beam
YBCO film
LAO substrate
ground plane
isolatorssources
f2
crystal detector
PIN
POUT
amplifier
switch
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
LSM
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Erlangen LSM setup
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Imaging modes of LSM
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
optical contrast
dc voltage contrast;
thermoelectric response imaging
linear microwave contrast
nonlinear (intermodulation distortion) microwave contrast
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Principle of the measurement
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Pout
ff0
|S21(f0)|2
|S21(f0)|2laser OFF
laser ON
co-planar resonator f0 ~ 5.2 GHz
Pin
modulatedlaser
resonator transmission
|S12|2 ~ [JRF(x,y)]2
Local heating produces a change in transmission coefficient proportionalto the local value of JRF
2
J. C. Culbertson, et al. J.Appl.Phys. 84, 2768 (1998)
A. P. Zhuravel, et al., Appl.Phys.Lett. 81, 4979 (2002)
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Intermodulation distortion LSM imaging
f1
f2
deviceundertest
LSM induced changes in the amplitude of transmitted microwave signals
note 100 kHz square wave laser power modulation (red arrows).
LSM
5,9670 5,9685 5,9700-100
-80
-60
-40
-20
0
Pou
t [dB
m]
Frequency [GHz]
POUT(f1)
2f2 – f1
+IMD3
2f1 – f2
-IMD3
f0
Df=1 MHz
laser
100 kHz
POUT(f2)
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
spectrum analyser
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Device Under Test
Meandering microstrip resonator (Agile Devices, USA)
Capacitive coupling(g = 200 mm)
Patternedcenter line
top view of the
resonator topology
YBCO film
HTS strip:
YBa2Cu3O7-d
TC = 92 K, DTC = 6 K
Thickness = 1 mm, Width W = 250 mm
Substrate:
LaAlO3 (er =24.2) 5x10x0.5 mm3
Resonator at 77 K:
loaded QL~2000, f0 = 1.85 GHz
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Global microwave response
-10 0 10 20 30-100
-50
0
PO
UT [d
Bm
]
PIN
[dBm]
RF IM
slope=1
slope=3
Pd=4 dBm
Log-log plot of input power dependence of the fundamental RF signals (black diamonds) and two-tone the third order IMD (blue circles) measured at T = 83 K.
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
POUT(f1)
POUT(2f1-f2)
1 mm
RFIN
RFOUT
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Spatially-resolved microwave photo-response
- YBCO film- LAO substrate
1 mm
1x1 mm
XY
XY
JRF
0
max
Frequency
Pow
er [
dBm
]
f1 f2
- 42
-14 -14
- 43
2f1 -f2 2f2 –f1
- 43- 42
- 49- 55
1x1 mm
IMD PRJrf
x
y
1x1 mm
0 max
(a) (b) (c)
RFIN
RFOUT
XY
JRF
XY
JIMD
(a) Top view of the resonator topology along with overall and (b, c) detailed 1x1 mm 3-d LTLSM plots (bottom images) showing (b) JRF(x,y) and (c) IMD PR distribution. The upper part of (b) shows the two input tones at –14 dBm as well as the output tones. The upper part of (c) shows the signals entering the spectrum analyzer after the primary tones have suffered partial cancellation.
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
2 2(2 / )'2
( , , ) (1 )L Mr r i tzLL
L
PP r z t e e e
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Laser-induced signal generation model
The power distribution induced by a focused modulated laser beam can be described as:
temporalspatial
x-y z t
focused laser beam(lLAS = 670 nm, PL = 1 mW)
substrate
HTS film
d
heatsource
x
z
The thermally induced changes of S21(f) in the probe are understood as LSM photo-response (PR) that can be expressed as:
2 2 2 22 12 12 120 12
12 20 12
( ) ( ) ( )1 (1/ 2 )( )
2 (1/ 2 )
S f S f S ff SQPR S f T
f T Q T TS
inductive PR + resistive PR + insertion loss PR 2
2 1212 2 2
0
( )1 4 ( / 1)
SS f
Q f f
where
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
~2121 21
21
2121
21
21
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Modeling of the linear photo-response (PR)
5.8 5.9 6.0 6.1
-2
0
2
PR
x 1
08
Frequency, (GHz)
0
2
4
|S21
|2 x103
d|S12|2
inductive PRX
resistive PRR x100 total PR
f
f0
insertion loss PRIL x 100
laser OFF
laser ON (a) Microwave transmittance |S21|2(f) of a resonator at РIN=0 dBm at a fixed temperature T = 80.7 K
(b) difference between the traces in (a) that is proportional to the total PR, along with the inductive, insertion loss (IL) and resistive components
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Partition of inductive and resistive components
f1= 5.957 GHz
PR (f2)±
=
reflectiveLSM image
resistive component
inductive component
PRR(x,y)
PR(f2) and PR(f1) are the LSM PR at equidistant frequencies f2 (above) and f1 (below) from f0
f2= 5.977 GHz
PR (f1)
300x300 mm2
RF photoresponse maps obtained at T = 78 K, PRF(f1) = PRF(f2) = 0 dBm, and laser power PL = 123 mW. Areas A and B are chosen for detailed spatial analysis of the resonator RF properties.
1 mm
A
B
YBCO
LAO
=
LSM PRmin max
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
PRR=|PR (f2)+PR (f1)| / 2
PRx=|PR (f2)-PR (f1)| / 2
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Simplified estimate of resistive photo-response
5.967 5.968 5.969 5.970-40000
-20000
0
20000
40000
PR
R/P
RX, (
a.u.
)
frequency, (GHz)
5.967 5.968 5.969 5.970-10
-5
0
5
10
LSM
PR
, (a.
u.)
FB
LSM PRmin max
F1
PRX >> PRR
PRX << PRR
25 mm
(a) resistive and inductive components of LSM photo-response (PR)
(b) their ratio
F2
PRX >> PRR
PRX ~ PRR
FA
F1
FA
FB
F2
Resistive PRx400
Inductive PR
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
(a)
(b)
inductive
resistitive
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Results: In-plane rotated grain
Grain Boundaries
LAO
YBCO
Large Grain position
200x100 m reflectivity LSM image
0 20 40 60 80 1000.0
0.5
1.0
Averr
aged J R
F [a
.u.]
Y - position [m]
-10 dBm
0 dBm
+10 dBm
2D and 3D maps of RF current distribution in a YBCO film on LAO substrate
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Results: Crack
LAO
YBCOreflectivity
Position of a crack
JRF(x,y) x
y
Evident spatial modulation of rf current density along the crack formed by localized vortices pinning on a twin-domain structure of the YBCO film
0
JRFMAX
50 mm
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Results: Standing wave
82.2 K
0
PRmax
0 5 10 15 20 25
0
50
100
150
LSM
PR
[a.u
.]
Distance [mm]
5.9 GHz standing wave of YBCO/LAO 1850 MHz resonators.
AB
CD
E FG
H
Points A-H are the same for both figures. LSM PR data on the graph corresponds to the PR averaged in each cross section of the HTS strip along the path from A to H.
Only a very small fraction of the structure contributes to the global RF response.
RF currents are peaked at the edges, however, interior corners give at least three times higher densities.
F
B
A
F
G
EDC
H
Reflectivity LSM image
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Results: Power dependence of LSM PR
Resistive,
PRR(x,y)
Inductive,
PRX(x,y)
25 mm
10 mm
0
peak
PR
+12 dBm
+12 dBm
0 dBm
0 dBm
-12 dBm
-12 dBm
Power-dependent penetration of PRX is spatially aligned with the direction of twin-domain blocks (TDB), whereas the development of the resistive state is uncorrelated with the TDBs.
Note the different spatial scale for the upper and bottom figures.
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Results: Power dependence of PRR(x,y)
LAO
YBCO10 mm
0 dBm
+6 dBm+4 dBm
+2 dBmLAO
50x50 mm
Images of resistive LSM PR penetrating into HTS film (area B) at the different input HF power indicated in the images. White dotted boxes show the YBCO/LAO patterned edge. Brighter regions correspond to larger amplitude of PRR(x,y).
3D plot of resistive LSM PR at +6 dBm
LAO
YBCO
PRR(x,y)
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
Results: Corners and grain boundaries
ILT
0.5 mm
ReflectivityLAO
YBCO
100 mm
IMD PR
GBs
Vortices
XY
Intermodulation LTLSM image showing a spatial modulation of the photoresponse at PIN = 4 dBm. Two different mechanisms of the LSM PR are shown. First one is the increasing of PR produced by grain boundaries (GBs) while in the second the LSM PR is reduced due to spatial vibration of RF induced vortices at the corner leading to an opposing electric field produced by the moving vortices.
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,
The laser scanning microscope (LSM) is a convenient tool for imagingRF currents in superconducting microwave devices
Many irregularities can be identified in the RF current flow:grain boundaries, cracks, defects, vortices, phase slips,current peaks at device edges and corners (IMD generation)
Linear RF photo-response LSM images show JRF2(x,y)
Our partition method allows to separate inductive and resistive changes inthe microwave impedance
Nonlinearities are mapped by intermodulation distortion (IMD) imaging:IMD features ~ JRF
4(x,y) are thus sharper than linear responseIMD response strongly varies at defects and device corners
Imaging of Microwave Currents and Microscopic Sources of Nonlinearities in Superconducting Resonators
SUMMARY
A.P. Zhuravel, S. M. Anlage and A.V. Ustinov,