ultrafast optoelectronic study of superconducting...

Ultrafast Optoelectronic Study ofSuperconducting Transmission Lines

Shinho Cho, Chang-Sik Son and Jonghun Lyou

Presented at the 8th International Conference on ElectronicMaterials (IUMRS-ICEM 2002, Xi’an, China, 10–14 June2002)

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Ultrafast Optoelectronic Study of

Superconducting Transmission Lines

Shinho Cho1*, Chang-Sik Son

1, and Jonghun Lyou

2

1Department of Photonics, Silla University, Pusan 617-736, Korea

2School of Natural Science, Korea University, Chungnam 339-800, Korea

Keywords: Microstrip, Propagation, Thin Films, Transmission Lines *Corresponding author, Tel: +82-51-309-5698, Fax: +82-51-309-5652, E-mail:[email protected]

Advanced Nanomaterials and Nanodevices (IUMRS-ICEM 2002, Xi’an, China, 10–14 June 2002)

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Abstract

A current and temperature controlled delay in the time of flight of electrical pulses in

YBa2Cu3O7-x (YBCO) spiral transmission lines has been studied by using ultrafast

optoelectronic sampling techniques. The transmission line was configured in a

stripline type on LaAlO3 substrate. The propagation time of ultrafast electrical pulses

through the transmission line was measured as a function of temperature. The results

are used to determine the actual temperature-dependent function of the magnetic

penetration depth of the superconducting thin film. Moreover, the delay time shows a

squared dependence on the applied current, which is in good agreement with

Ginzburg-Landau theory for the case of a uniform current density through a thin film.


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1. Introduction

Recently there have been considerable interests in the development of ultrafast

electrical signals to investigate the high-speed semiconductor devices and

superconducting microwave integrated circuits [1-3]. The increase in device speeds

has resulted in the demand for higher bandwidth characterization techniques. The

time-domain ultrafast optoelectronic sampling techniques for characterization of

devices provides advantages over the frequency-domain techniques used by vector

network analyzers. The response of the devices can be windowed in the time domain

and separated from reflections due to transitions and other unwanted signals before it

is analyzed.

A new device concept for a current controlled variable delay superconducting line

is introduced by Track et al [4] and Anlage et al [5], respectively. The density of

superconducting electrons is varied by a change of the applied bias DC current. As a

consequence, the kinetic inductance of the superconducting transmission lines is

varied. Anlage et al attempted to vary the delay of the microstrip transmission line by

means of an applied DC current, but failed to observe these phenomena. The likely

reason for the their failure is considered to be the existence of strong magnetic fields

near the edge of the superconducting film before a depairing current density is

achieved in the film. These fields result from the microstrip geometry. This problem

can be minimized by using a stripline geometry, in which the presence of two ground

planes and a thin dielectric material produce a more uniform magnetic field

distribution and reduce the edge effects near the superconducting film.

In addition, there has been recently raised a question in the variational function of

the penetration depth with temperature, i.e., the actual function of the density of

superconducting electrons with temperature for the YBCO thin films. An expression

for the penetration depth was developed by the London brothers [6], and it is directly

related to the density of superconducting electrons ( )ns by λ µ= ( )m n es0

2 1 2 for a

homogeneous superconductor. The only density of superconducting electrons

depends on the temperature. Gorter and Casimir [7] found that the density of

superconducting electrons was given by n n T Ts c= −[ ( ) ]1 4 , which has been known to

be followed by many low cT materials and conventional type-II superconductors.


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Anlage et al [8] supported Gorter-Casimir temperature dependence with YBCO

microstrip resonator technique. However, Pond et al [9] and Kain et al [10] measured

a temperature-squared (T-squared) dependence in their YBCO/LaAlO3/YBCO trilayer

transmission line and YBCO coplanar waveguide resonator, respectively. This

dependence is expressed by n n T Ts c= −[ ( ) ]1 2 .

In this paper, we make use of an ultrafast optoelectronic sampling technique with

photoconductive switches to trace the variational function of penetration depth with

temperature and to investigate the applied current effects on the kinetic inductance of

superconducting YBCO delay striplines.

2. Theory

The magnetic penetration depth λ in the superconductor affects the series

inductance of the transmission line, which in turn determines the propagation velocity

for ultrafast electrical pulses. The phase velocity of an electromagnetic wave on a

lossless transmission line can be expressed as LCp 1=υ , where L is the total

inductance per unit length and C is the total capacitance per unit length of

transmission line. The total inductance per unit length for a stripline is given by [11]

kwtttdL )]coth()coth()coth([ 3332221110 λλλλλλµ +++= , where w is the width

of the strip film, 0µ is the permeability of the free space, d is the dielectric thickness,

and λ1, 2λ , 3λ and 1t , 2t , 3t are penetration depth and thickness of the strip and

ground plane films, respectively. The factor k takes into effect the fringing fields.

The first term of the above equation represents the magnetic inductance. The second,

third and fourth terms represent the kinetic inductance of the superconducting

electrons. The capacitance per unit length is given by dkwC r )( 0εε= , where 0ε is

the permittivity of the free space, and rε is the relative permittivity of the dielectric.

Hence the phase velocity normalized to the speed of light in vacuum for a stripline is

simplified as

( )[ ] 2/12 /31/−+= tdc rp λευ (1)


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where, 2/1

00 )( −= µεc , which is the speed of light in vacuum. Here we have assumed

that all the superconductors are identical and t>>λ . Eq. (1) allows the determination

of the temperature dependence of the magnetic penetration depth provided that we

know the relative permittivity of the dielectric rε , the film thickness t , and the

normalized phase velocity cp /υ .

For a thin superconducting film the kinetic inductance as a function of the applied

current can be derived from the Ginzburg-Landau theory )941)(( 222

0 ck iiL +≈ σλµ

where σ is the cross sectional area of the strip, λ is the penetration depth, and ci is

the critical current. The time of flight of an electrical pulse as a function of the bias

current can be expressed as

)921()( 222122

0 ciiCl +≈ σλµτ (2)

where l is the length of the superconducting strip and C is the capacitance of the

stripline. Here we limits ourselves to small current biases to neglect terms of order

higher than i ic2 2 .

3. Experiment

The method used to generate and sample ultrafast electrical pulses propagating on

superconducting spiral lines is based upon the photoconductive switch techniques

described by Oshita et al. [12]. The setup used to perform this measurement is shown

in Fig. 1. A train of picosecond optical pulses is produced by a cavity-dumped

rhodamine 6G dye laser synchronously pumped by the frequency-doubled output of

an actively mode-locked Nd:YAG laser. The temporal width of the dye laser pulses is

measured to be approximately 3.5 psec full width at half maximum (FWHM) using an

optical autocorrelator. The dye laser is operated at a wavelength of approximately 620

nm with a repetition rate of 3.8 MHz and average power of 60 mW.

A beam splitter is used to define two optical paths. One path, referred to as the

generation beam, is used to generate the fast electrical transients. The generation

beam passes through a chopper and is focused onto a photoconductive switch. The


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second path, referred to as the sampling beam, travels along a path of variable length

and is focused with a 75 mm focal length lens onto another switch. The output from

the sampling switch is fed into the input of the lock-in amplifier. The path length of

the sampling beam is mechanically scanned by moving an air-spaced retroreflector

mounted on a translation stage with a computer-controlled stepping motor. By varying

the time delay τ of the sampling beam relative to the generation beam, the time

development of the electrical signal propagated through the spiral line is mapped out.

The time signal measured is an autocorrelation of the electrical signal propagated

through the spiral line and the response of the sampling photoconductive switch,

∫ += dttHtXG )()()( ττ (3)

where )(τG is the time signal measured, )(tX is the signal propagated through the

spiral line and )( τ+tH is the response of the photoconductive switch. Note that )(tX

includes the response of the generation photoconductive switch and the laser pulse

width, similarly )( τ+tH includes the contribution of the laser pulse width.

The photoconductive switches were fabricated using silicon-on-sapphire. The

central transmission line of the photoconductive switches is used for lauching fast

electrical pulses and one of the side arms is biased at 20 volts. For the

photoconductive switches used, the FWHM of the electrical autocorrelation is 8 psec

with a peak accuracy of 1± psec. One important characteristics of photoconductive

switches used for optoelectronic measurements is the variation of the photocurrent

with the applied signal. In order to take the Fourier transform of different signals and

normalize them to get scattering parameters of the device, the photocurrent has to

vary linearly with the signal on the central transmission line. The experimental setup

to measure linearity of the photoconductive switches is shown in Fig. 2.

The superconducting spiral line was fabricated in the geometry of a stripline. The

YBCO strip is embedded in a dielectric medium of LaAlO3 between two grounded

superconductors. The strip is 64-mm-long, 60- mµ -wide and 130-nm-thick as

measured by a Dektak 3030. The superconducting film is defined by standard

photolithography and connected to two sets of photoconductive switches via bonding


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wires. The stripline structure is obtained by depositiong the ground superconductors

on two separate LaAlO3 substrates. The YBCO transition temperature was measured

to be 89 K.

The spiral line and the switches were mounted on a cryostat insert in a variable

temperature dewar with an optical access window. For the current dependence

measurement, a DC current source is connected to the central transmission line, as

shown in the inset of Fig. 6. For temperature measurement, a 50 Ω terminator was

placed on the transmission line instead.

4. Results and discussion

The films exhibit a linear resistivity versus temperature above the transition

temperature and a sharp transition begins at 89 K. In order to see how

superconductivity influences ultrafast pulse propagation on the YBCO transmission

line, we measured the time of flight of electrical pulse as a function of temperature.

The zero time delay between the generation and the sampling beam was set using one

set of photoconductive switches. This sets the 0 psec reference for the time of flight

measurements. At 83.0 K the electrical signal occurs at 777 psec, as shown in Fig. 3.

As the temperature increased to 87.0, 87.5, 88.0, and 88.5 K, the peak of the electrical

pulse shifted to 788, 797, 814, and 837 psec, respectively. In addition to the delay in

the time of flight, an increase in temperature caused a gradual increase in the FWHM

of the electrical pulse. The increase in temperature from 83.0 to 88.5 K was

accompanied by an increase in the pulse width from 38 to 90 psec. The dispersive

nature, attenuation in amplitude and widening in width of the electrical pulse, is

considered to be due to the increase in surface resistance and dielctric substrate

properties [10].

We can estimate the phase velocity by assuming non-dispersive pulse, where the

group velocity is the same as the phase velocity. This assumption is valid if the

change in time of flight of the pulse is only due to the kinetic inductance effect, and

the surface resistance and dielectric effects are negligible. The phase velocity is given

by the distance an electrical pulse has travelled per the delay time it takes for the pulse

to propagate in the superconducting delay line. Therefore, the normalized phase

velocity can be obtained from measuring the temperature dependence of the delay


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time of the electrical pulse. The measured temperature dependence of phase velocity

normalized to the speed of light in vacuum c is shown by the solid circles in Fig. 4.

The phase velocity at 60 K is approximately 0.277c . As the temperature increases,

the normalized phase velocity decreases and falls rapidly to 0.267c at 88.5 K. The

difference of the change in phase velocity at 60 K and 88.5 K shows a 3.7% change.

This small percentage change in the phase velocity is probably due to the bigger

dimensions of the delay stripline [13]. Hence we can investigate the actual functional

formula of the penetration depth of YBCO delay line. The dashed line in Figure 4

indicates the normalized phase velocity plotted using the two-fluid model proposed by

Gorter and Casimir, 2/14

0 ])/(1[ −−= CTTλλ with zero-temperature penetration depth

2010 =λ nm and 89=cT K while the solid line represents a T-squared dependence of

penetration depth, 2/12

0 ])/(1[ −−= CTTλλ . Our measured data are relatively good

agreement with a T-squared dependence even though they show a slightly deviation

below 70 K.

In order to examine the frequency-dependent characteristics of the electrical

pulses, we have performed a Fast Fourier Transform (FFT) of the input and output

signal data obtained in the time-domain. Figure 5 displays the amplitude spectra of

the input signal at 83, 88 and 88.5 K, and they show that our optoelectronic system

has a bandwidth of approximately 150 GHz.

Figure 6 displays the delay of a ultrafast electrical pulse propagating through a 64

mm spiral line as a function of the applied dc current in order to investigate the effect

of an applied current on the kinetic inductance of the YBCO spiral line. The operating

temperature was set at 60.0 K to avoid thermally breaking electron pairs that occurs as

cT is approached. At a bias current of 0.1 mA the peak of the electrical transient

occurs at 770 psec. As the bias current was increased to 70, 100, 160 and 190 mA the

peak of the electrical pulse shifted to 774, 777, 781, and 786 psec, respectively. No

significant delay in the time of flight was observed up to 50 mA, while beyond this

point the delay increases rapidly as the bias is increased up to 190 mA. The pulse

becomes asymmetric as the current is increased. This is attributed to the variation in

current density transverse to the propagation direction in the stripline. These results

are in relatively good agreement with those presented by Enpuku et al. [14]. The solid


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line in Fig. 6 represents 21 iB ⋅+≈τ where 71045.7 −×=B /mA2, which is that

calculated by using the Ginzburg-Landau theory in a sample with uniform current

distribution (see equation 2). The measured data are well consistent with an applied

DC current-squared dependence within 1.5% error. This can beexplained as follows:

as the applied current increases the time of flight increases due to the increase in

kinetic inductance, which is manifested due to the decrease in the density of available

superconducting electrons.

5. Conclusion

We have observed a delay in the time of flight of an electrical pulse propagating

in a superconducting transmission line by means of an applied current and change of

temperature. The tuning range was measured to be 16 psec for a change of 190 mA in

bias. The delay in the time of flight results from the change in kinetic inductance of

superconductors and is found to behave as a function of the applied current squared.

This is in good agreement with the Ginzburg-Landau theory. Field edge effects which

cause the breakdown of superconductivity before a propagation time is observed are

avoided by using a stripline configuration. The actual function of penetration depth of

YBCO thin film is found to be T-squared dependence.

Acknowledgments

This work was supported by Korea Research Foundation Grant (KRF-2001-015-

DP0166).


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References

[1] D. R. Dykaar and U. D. Keil, Optical and Quantum Electronics, 28 (1996) 731.

[2] Y. Liu, J. F. Whitaker, C. Uher, S. Y. Hou, and J. M. Phillips, Appl. Phys. Lett.

67 (1995) 3022.

[3] S. Cho, Supercond. Sci. Technol. 9 (1996) 788.

[4] E. K. Track, M. Radparvar, and S. M. Faris, IEEE Trans. Magn. 25 (1989) 1096.

[5] S. M. Anlage, H. J. Snortland, and M. R. Beasley, IEEE Trans. Magn. 25 (1989)

1388.

[6] F. London and H. London, Proc. Roy. Soc. (London), A149 (1935) 71.

[7] M. Tinkham, Introduction to Superconductivity (McGraw-Hill, New York,

1974), p.80.

[8] S. M. Anlage, H. Sze, H. J. Snortland, S. Tahara, B. Langley, C. B. Eom, and M.

R. Beasley, Appl. Phys. Lett. 54 (1989) 2710.

[9] J. M. Pond, K. R. Carroll, J. S. Horwitz, D. B. Chrisey, M. S. Osofsky, and V.

C. Cestone, Appl. Phys. Lett. 59 (1991) 3033.

[10] A. Z. Kain, J. M. Pond, H. R. Fetterman and C. M. Jackson, Microwave and

Optical Technology Letters, 6 (1993) 755.

[11] B. W. Langley, S. M. Anlage, R. F. W. Pease, and M. R. Beasley, Rev. Sci.

Instrum. 62 (1991) 1801.

[12] F. Oshita, M. Martin, M. Matloubian, H. R. Fetterman, H. Wang, K. Tan, and D.

Streit, IEEE Microwave Guided Wave Lett. 2 (1992) 340.

[13] W. H. Henkels and C. J. Kircher, IEEE Trans. Magn. 13 (1977) 63.

[14] K. Enpuku, M. Hoashi, H. Doi, and T. Kisu, Jpn. J. Appl. Phys. 32 (1993) 3804.


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Figure Captions

Figure 1. Experimental setup for ultrafast optoelectronic characterization of the

YBCO transmission stripline.

Figure 2. Experimental setup to measure the linearity of photoconductive switches.

Figure 3. Pulse shape after propagating a distance of 64 mm on a YBCO spiral line

at various temperatures. The time delay in each case was taken as the peak position of

the electrical pulse.

Figure 4. The normalized phased velocity as a function of temperature is shown by

the solid circles. The solid line is for temperature-squared dependence of λ , and the

dashed line is for the two-fluid-model.

Figure 5. The normalized amplitude spectra of the electrical pulses at several

temperatures.

Figure 6. Delay time as a function of applied bias current at 60 K. Solid circles

show the measured data, while solid line indicates 21 iB ⋅+≈τ . Inset shows the

YBCO spiral line mounted between a pair of photoconductive switch.


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