Ultrafast Optoelectronic Study of Superconducting Transmission Lines

Ultrafast Optoelectronic Study of Superconducting Transmission Lines Shinho Cho, Chang-Sik Son and Jonghun Lyou Presented at the 8th International Conference on Electronic Materials (IUMRS-ICEM 2002, Xi an, China, 10 14 June 2002) 468

Ultrafast Optoelectronic Study of Superconducting Transmission Lines Shinho Cho 1 *, Chang-Sik Son 1, and Jonghun Lyou 2 1 Department of Photonics, Silla University, Pusan 617-736, Korea 2 School 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:scho@sillaackr 469

Abstract A current and temperature controlled delay in the time of flight of electrical pulses in YBa 2 Cu 3 O 7-x (YBCO) spiral transmission lines has been studied by using ultrafast optoelectronic sampling techniques The transmission line was configured in a stripline type on LaAlO 3 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 470

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, ie, 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 2 1 related to the density of superconducting electrons ( n s ) by λ = ( m µ 0 ne s ) 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[ 1 ( T T) 4 ], which has been known to s be followed by many low T c materials and conventional type-ii superconductors c 471

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/LaAlO 3 /YBCO trilayer transmission line and YBCO coplanar waveguide resonator, respectively This dependence is expressed by n = n[ 1 ( T T) ] s 2 c 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 υ p = 1 LC, 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] L = µ d + λ coth( t λ ) + λ coth( t λ ) + λ coth( t )] kw, where w is the width 0[ 1 1 1 2 2 2 3 3 λ3 of the strip film, µ 0 is the permeability of the free space, d is the dielectric thickness, and λ 1, λ 2, λ 3 and 1 t, t 2, t 3 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 C = ( ε r ε 0kw) d, where ε 0 is the permittivity of the free space, and ε r 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 1/ 2 [ ( )] 2 ε 1+ 3λ / υ / c = td (1) p r 472

where, c = ( ε µ 1/ 2 0 0 ), which is the speed of light in vacuum Here we have assumed that all the superconductors are identical and λ >> t Eq (1) allows the determination of the temperature dependence of the magnetic penetration depth provided that we know the relative permittivity of the dielectric ε r, the film thickness t, and the normalized phase velocity υ / p c For a thin superconducting film the kinetic inductance as a function of the applied 2 2 2 current can be derived from the Ginzburg-Landau theory L ( µ λ σ )(1 + 4i 9i ) k 0 c where σ is the cross sectional area of the strip, λ is the penetration depth, and i c is the critical current The time of flight of an electrical pulse as a function of the bias current can be expressed as 2 2 1 2 2 2 τ ( µ λ l C σ ) (1 + 2i 9i ) (2) 0 c 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 2 i 2 c 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 35 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 38 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 473

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, G ( τ ) = X( t) H ( t + τ ) dt (3) where G (τ ) is the time signal measured, X (t) is the signal propagated through the spiral line and H ( t + τ ) is the response of the photoconductive switch Note that X(t) includes the response of the generation photoconductive switch and the laser pulse width, similarly H ( t + τ ) 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 LaAlO 3 between two grounded superconductors The strip is 64-mm-long, 60- µ m -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 474

wires The stripline structure is obtained by depositiong the ground superconductors on two separate LaAlO 3 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 830 K the electrical signal occurs at 777 psec, as shown in Fig 3 As the temperature increased to 870, 875, 880, and 885 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 830 to 885 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 475

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 0277c As the temperature increases, the normalized phase velocity decreases and falls rapidly to 0267c at 885 K The difference of the change in phase velocity at 60 K and 885 K shows a 37% 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 4 1/ 2 Gorter and Casimir, λ λ [1 ( T / T ) with zero-temperature penetration depth = 0 C ] λ0 = 201nm and T = 89 K while the solid line represents a T-squared dependence of penetration depth, c λ 2 1/ 2 = λ0 [1 ( T / TC ) ] 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 885 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 600 K to avoid thermally breaking electron pairs that occurs as T c is approached At a bias current of 01 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 476

2 7 line in Fig 6 represents τ 1+ B i where B = 745 10 /ma 2, 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 15% 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) 477

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), p80 [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 478

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 2 show the measured data, while solid line indicates τ 1+ B i Inset shows the YBCO spiral line mounted between a pair of photoconductive switch 479

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