imaging of microwave currents and microscopic sources of nonlinearities in superconducting...

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,


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




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


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


LSM


Erlangen LSM setup



Imaging modes of LSM


optical contrast

dc voltage contrast;

thermoelectric response imaging

linear microwave contrast

nonlinear (intermodulation distortion) microwave contrast


Principle of the measurement


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)


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)


spectrum analyser


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



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.


POUT(f1)

POUT(2f1-f2)

1 mm

RFIN

RFOUT


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.


2 2(2 / )'2

( , , ) (1 )L Mr r i tzLL

L

PP r z t e e e


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


~2121 21

21

2121

21

21


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



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


PRR=|PR (f2)+PR (f1)| / 2

PRx=|PR (f2)-PR (f1)| / 2


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)

(b)

inductive

resistitive


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



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



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



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.



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)



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.


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


SUMMARY


Appl.Phys.Lett. 81, 4979 (2002).

IEEE Trans.Appl.Superc. 13, 340 (2003).

Low Temp.Phys. 32, 592 (2006).

Appl.Phys.Lett. 88, 212503 (2006).

cond-mat/0609244 (2006).

Steven Anlage Alexander Zhuravel

Thanks to my collaborators

We are now looking for new

applications, collaborations

and funding sources

imaging of microwave currents and microscopic sources of nonlinearities in superconducting...

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