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Nuclear Instruments and Methods in Physics Research A 520 (2004) 263–266

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1524-84403

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(J.K. Wigm

0168-9002/$

doi:10.1016

Phonon excitation of quasiparticles in niobium and tantalumsuperconducting tunnel junction photon detectors

J.K. Wigmore*, P. Boyd, A.C. Steele, A.G. Kozorezov, D.I. Bradley

Physics Department, Lancaster University, Lancaster LA1 4YB, UK

Abstract

We report phonon pulse measurements of quasiparticle (qp) self-recombination and trapping by Abrikosov vortices

in Nb and Ta superconducting tunnel junctions. The quasiparticle loss times, determined from the shape of the tunnel

junction output pulse, were found to be strongly correlated with flux trapping. The measured results were compared

with the model of Golubov and Houwman. It was found that qp self-recombination, as measured from the dependence

of responsivity on absorbed phonon energy, was also modified by the presence of traps. A process of phonon-mediated

de-trapping is proposed to explain the observed effects.

r 2003 Elsevier B.V. All rights reserved.

PACS: 85.25.Oj; 74.25.Kc

Keywords: Superconducting tunnel junctions; X-ray detection; Non-equilibrium phonons; Self-recombination; Fluxoid loss

1. Introduction

We have shown previously that non-equilibriumphonon pulses may be used to simulate the photo-absorption process in superconducting tunneljunctions (STJs) and hence study the quasiparticle(qp) dynamics involved [1,2]. In our experimentsthe phonons are generated as heat pulses viaelectrical excitation of a thin metal film heaterdeposited on the back of the STJ substrate. Theirfrequency distribution is approximately Planckianwith a temperature determined primarily by theincident power density. Phonons having energygreater than 2D; the energy gap of the super-conductor, are absorbed in the base electrode of

onding author. Tel.: +44-1524-593075; fax: +44-

7.

ddress: k.wigmore@lancaster.ac.uk

ore).

- see front matter r 2003 Elsevier B.V. All rights reserve

/j.nima.2003.11.340

the STJ. Because absorption is effectively uniformand instantaneous across the STJ, the excited qpdensity is spatially homogeneous. Analysis of thecurrent pulse shape gives the qp tunnelling andloss times in the electrodes whilst the chargeoutput is obtained by integration of the pulse.Previously we used non-equilibrium phonons tocharacterise Nb STJs that had been studied bycolleagues at ESTEC using X-ray photo-absorp-tion. The focus of the present paper is the effect ofAbrikosov vortices (fluxoids) on loss and self-recombination of qps excited by phonons in Nband Ta-based STJs. Full details of the techniqueand samples studied are given in Ref. [1].

2. Self-recombination

We determined the qp self-recombination coef-ficient in a Nb tunnel junction by measuring

d.

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J.K. Wigmore et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 263–266264

directly the STJ charge output as a function ofabsorbed phonon energy at a temperature of1.4 K. This was achieved by varying the inputpulse length at constant power between 15 and50 ns, an order of magnitude shorter than any lossor tunnel times of the STJ. The fraction ofphonons absorbed was calculated assuming aphonon Planck distribution with a temperaturederived empirically from a separate constant-energy calibration. It was necessary to calculatealso the anisotropy of phonon emission from theheater, phonon focussing in the substrate, andphonon transmission and reflection at the Nb–sapphire interface.

The data obtained in this experiment are shownin Fig. 1. They exhibit a slight but measurabledeviation from linearity, which is due to selfrecombination. We can write the total chargeoutput, Q, as

Q ¼ ex1N0ð1 � wN0Þ ð1Þ

where N0 is the number of qps initially excited, w isthe non-linearity parameter, and x1 a function oftunnel and loss times in the electrodes. A value forw of (2.270.5)� 10�10 was obtained from Fig. 1.For comparison we derived the following expres-sion [1]:

w ¼1

2w1L2

� �ðR12Þ

�A2

2 þ e1e2 þ ðw1=w2ÞG2t;1ðR21=R12Þ

e1e2ðe1 þ e2Þ

!ð2Þ

0

2

4

6

8

10

12

14

16

18

20

0 100 200 300 400 500

Input energy (keV)

Charg

e o

utp

ut (X

10

7 e

)

Fig. 1. Charge output from the STJ as a function of absorbed

phonon energy.

where A2, e1; e2; Gt;1 are further combinations oftunnelling and loss times, w1 and w2 are electrodethicknesses and L their lateral dimension. Herealso

R12 ¼ R�1 � R�

12

x2

x1

and R21 ¼ R�2

x2

x1

� R�21: ð3Þ

All the quantities R�1 ; R�

2 ; R�12; and R�

21 can berelated to R, the intrinsic recombination coefficientof Nb, through simple expressions containingphonon lifetimes and transmission coefficients,and electrode thicknesses. The meanings of allsymbols are fully defined in Ref. [1]. Finally thevalue of R obtained from our data was(672)� 10�16 m3 s�1. On theoretical grounds wewould expect a slightly higher value, around1.0� 10�15 m3 s�1, as was obtained in photo-absorption experiments at lower input energy insimilar samples. We will discuss the possible originof this discrepancy in Section 4.

3. Trapping by Abrikosov vortices

In both Nb and Ta samples strong flux-trappingwas observed, which was neither intentional norreproducible. Fig. 2. shows the detected currentpulses from the same Ta junction at 20 mK underidentical bias conditions in successive experiments.As observed from the pulse decay, after thermalrecycling the loss time changed significantly, from1.4 ms to 3.1 ms, which we attribute to the change in

-0.010

0.010.020.030.040.050.060.070.080.09

0.0 2.0 4.0 6.0 8.0time (µs)

sign

al (

V)

Fig. 2. Signal pulse shape in a Ta STJ before (broader trace)

and after thermal cycling.

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the number of fluxoids in the STJ. However, wenote that the pulse peak amplitude remainedalmost constant, as it should, since it was ameasure of N0; the initial number of qps excitedby the incident pulse. A previous measurement ofloss rate due to fluxoids was made by Ullom et al.via qp transport [4].

We found that the change in loss rate,3.970.2� 105 s�1, corresponded to a change inleakage current of 2.970.05 mA at the same biasvoltage (150 mV). We used this result to estimatethe additional loss introduced by a single fluxoid.Assuming that the fluxoids were aligned across thebarrier between the upper and lower electrodes, wemodelled N–I–N tunnelling as taking placethrough an area of the barrier with radius equalto the coherence length of the superconductingelectrodes [3]. Hence we calculated that eachfluxoid contributed 0.45 nA, giving a figure of6400 for the total number of fluxoids, and aloss rate contribution from each fluxoid of6175 s�1. We may compare the measured totalloss rate for the sample with the theoretical valueof 1.8� 106 s�1 calculated from the expres-sion given by Golubov and Houwman for qptrapping [5]

G ¼1:82pt0

nR2f : ð4Þ

Here t0 is the superconductor characteristic time, n

the areal density of fluxoids and Rf their effectiveradius. A similar analysis for the Nb STJ indicatedin Fig. 1 gave a calculated loss rate of 2.3� 106 s�1

for comparison with the measured rate of1.570.2� 106 s�1.

In view of the simplicity of the model, theagreement between theory and experiment forboth Nb and Ta is encouraging. Some discrepancyundoubtedly arises through taking the effectiveradius of the fluxoid for leakage current as equalto the coherence length. But the more question-able assumption is that of alignment betweenfluxoids in the two electrodes [6]. The individuallocations of fluxoids in a polycrystalline filmare significantly affected by the distribution ofpinning centres, such as grain boundaries. Ingeneral these will not be correlated in the upperand lower electrodes. However in the present

devices the base electrode is a single crystal grownepitaxially on the sapphire substrate, so it isentirely plausible that a substantial number offluxoids are aligned at locations determined by themicrostructure of the upper electrode. Finallythere is the question of whether, for alignedfluxoids, the trapping rate given by Eq. (3) isthe same quantity as the loss rate measured inour experiments. Preliminary calculations suggestthat in both sets of experiments loss by trap-enhanced recombination was indeed faster thantunnelling.

4. Effect of fluxoids on recombination

The measured fluxoid densities are unexpectedlylarge, and we believe that at the high qp densities(>1023 m�3) present in our experiments trapeffects may also be the origin of the reduced self-recombination observed. The process of shockionisation of traps was first identified by Poelaertet al. whilst studying the energy dependence of STJphoton detectors [7]. The principle is that a mobileexcited qp with sufficient excess energy canrecombine with a trapped qp to yield two excitedqps. The consequence of the high qp density willbe to excite additional mobile qps by stimulatedde-trapping, thus partly counteracting the effectsof self-recombination and reducing the effectivenon-linearity of detector responsivity. Furtherexperiments are required to explore this interestingregime.

In summary, we have shown that phonon pulsestechniques can be used, not only to provide analternative method of characterising STJ photondetectors, but also to probe basic processes of theqp dynamics.

Acknowledgements

We are grateful to A. Peacock, R. den Hartog,and P. Verhoeve at European Space Agency(ESTEC) for samples and valuable discussions,and to EPSRC for research studentships for ACSand PB.

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References

[1] J.K. Wigmore, A.C. Steele, A.G. Kozorezov, A. Peacock,

R. den Hartog, P. Verhoeve, J. Appl. Phys. 93 (2003) 5707.

[2] A.C. Steele, A.G. Kozorezov, P. Boyd, J.K. Wigmore, A.

Peacock, A. Poelaert, R. den Hartog, Nucl. Instr. and Meth.

A 444 (2000) 8.

[3] W.T. Band, G.B. Donaldson, Phys. Rev. Lett. 31 (1973) 20.

[4] J.N. Ullom, P.A. Fisher, M. Nahum, Appl. Phys. Lett. 73

(1998) 2494.

[5] A.A. Golubov, E.P. Houwman, Physica C 205 (1993)

147.

[6] V.N. Gubankov, M.P. Lisitskii, I.L. Serpuchenko, M.V.

Fistul, Sov. Phys. JETP 73 (1991) 734.

[7] A. Poelaert, A. Kozorezov, A. Peacock, J.K. Wigmore,

Phys. Rev. Lett. 82 (1999) 1257.