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J Low Temp Phys DOI 10.1007/s10909-012-0525-7

Energy Resolution of STJ X-Ray Detectors with Killed Electrode. Simple Model
V.A. Andrianov · L.V. Filippenko

Received: 27 July 2011 / Accepted: 10 January 2012 © Springer Science+Business Media, LLC 2012

Abstract Superconducting tunnel junctions X-ray detectors Ti/Nb/Al,AlOx /Al/ Nb(2)/NbN with killed Ti/Nb electrode was studied as a function of bias voltage, energy of the absorbed quantum, and thickness of the Nb(2) layer. The data was compared with a simple diffusion model including the losses of excess quasiparticles due to self-recombination. It was shown that increasing of the electrode thickness reduces the self-recombination contribution and improves the linearity of the detector response. Keywords Detectors · Superconducting tunnel junctions · X-rays · Quasiparticles · Recombination · Phonons · Energy resolution 1 Introduction Detectors based on superconducting tunnel junctions (STJ detectors) have energy resolution of about 10­30 eV for the 5.9 keV X-ray line, that is substantially better than the resolution of 140­150 eV of typical silicon detectors [1]. Usually STJ-detectors consist of two identical superconducting electrodes separated by a thin insulating barrier and operate in multi-tunneling mode. In this case undesirable doubling of X-ray lines occurs in the measured spectra, caused by the absorption of quanta in both electrodes. STJ-detectors with killed electrode have an alternative design in which the signals of one electrode are suppressed due to the presence of the trapping layer placed at the
V.A. Andrianov ( ) Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russian Federation e-mail: andrva22@mail.ru L.V. Filippenko Institute of Radio Engineering and Electronics RAS, 103907 Moscow, Russian Federation


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side opposite to tunnel barrier [2]. The main detector signal arises from the quantum absorption in the opposite electrode. The advantages of this detector type should be the absence of line doubling and short duration of the signals. In our work [3], the STJ detectors with killed electrode on the basis of the additional titanium trapping layer were proposed. The general sequence of layers was described by the formula Ti/Nb/Al,AlOx /Al/Nb/NbN. The bottom killed electrode consisted of two layers: a Ti trapping layer and a thicker Nb layer. The main top electrode had three layers: thin Al trapping layer, the main absorbing Nb layer, and the outer reflecting NbN layer. Unfortunately the achieved energy resolution was about 90 eV for 5.9 keV line. In this work the main parameters of these detectors were studied as a function of the bias voltage, the energy of the absorbed quanta, and of the thickness of Nb layers. Data are analyzed on basis of a simple diffusion model with quasiparticle self-recombination.

2 The Diffusion Model of STJ-Detectors The main reason of degradation of energy resolution of X-ray STJ-detectors is spatial dependence of the detector signal on the photon absorption site. The amplitude of the signal is usually reduced as the photon absorption point approaches to the electrode edge. The data are considered in a framework of diffusion model of STJ-detectors. There are two main mechanisms of line broadening: the quasiparticle self-recombination [4, 5] and the edge losses of the excess quasiparticles [2]. The self-recombination causes the nonlinearity of the detector response versus the energy of the absorbed phonon as well. Figure 1 shows the dependence of the signal amplitude Q on the coordinate of the quantum absorption x0 , obtained by a diffusion model for a single electrode. a is a linear size of an electrode. We remind that the signal amplitude is proportional to the total number of tunneled quasiparticles. If the edge losses and self-recombination losses are absent, then the signal Q does not depend on the coordinate x0 . In this
Fig. 1 (Color online) The dependences of the signal amplitude Q on the coordinate of a quantum absorption x0 , obtained by a diffusion model (scheme). (1) QR = 0, QB = 0. (2) QR = 0, QB = 0. (3) QR = 0, QB = 0


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case the detector should have thin spectral line. Its width is determined by tunneling fluctuations and by an electronic noise. The self-recombination losses reduce signal Q in the center of electrode by QR and at the edge of electrode approximately by 2 QR (curve 2 in Fig. 1). The edge losses additionally reduce the signal Q by QB near the electrode boundary only (curve 3 in Fig. 1). The dependence of signal Q on the coordinate (x0 ,y0 ) causes strong broadening of the detector line. Changing of Q(x0 ) takes place in a strip near the electrode edge with the width approximately equal to the quasiparticle diffusion length = Dd , where D is the quasiparticle diffusion coefficient and d is the quasiparticle lifetime. The lifetime d is determined by the quasiparticle tunneling rate T and the loss rate L : d = (T + L )-1 . To narrow the detector line it is necessary to reduce the values QR , QB and the ratio ( /a ) (see Fig. 1). The edge losses QB depend on the methods of tunnel junction production. The ratio ( /a ) first of all depends on the detector sizes. The recombination losses QR can be described by the formula [6]: QR = P1 E 1.75
2 t

Ref ln 2D 1.89a

,
0

(1)

where P1 is the quasiparticle tunnel probability, E is the energy of the absorbed quantum, a0 is the initial radius of the excess quasiparticles distribution, and Ref is the effective recombination coefficient. In the case of a homogeneous electrode Ref is equal to R
ef

=

R l2 d4 d

1+

l2 4d

-1

,

(2)

where R is the recombination coefficient [7], is the transparency of the electrode interface for 2 -phonons; l2 is an average free path of 2 -phonons, l2 = vs pb 13 nm, where vs is the sound velocity and pb is the pair breaking time for 2 phonons [7]; d is the thickness of the electrode. From formulae (1) and (2) and Fig. 1 it follows that increasing of the electrode thickness d should decrease the recombination losses and consequently should improve the energy resolution. This conclusion was tested by experiment.

3 Experiment and Discussion The samples of STJ-detectors Si-substrate/Ti/Nb/Al,AlOx /Al/Nb(2)/NbN were fabricated by magnetron sputtering. Five rhomb-shaped STJ detectors with a ratio of diagonals of 2:1 or 4:1 and different electrode areas, S = 400, 400, 1600, 6400, and 20000 µm2 , were arranged on one chip. The scheme of the STJ-detector is shown in Fig. 2. The layer thicknesses were as follows: Ti and NbN (30 nm each), base Nb layer (100 or 150 nm), Al/AlOx oxide layer (4 nm/2 nm), top Nb(2) layer (150, 200, or 250 nm), and trapping top Al layer (11­13 nm). The width of current leads was about 10 µm. The superconducting gaps for the bottom and top electrodes were base = 1.36 meV and top 0.95 meV. The normal resistance of the tunnel barrier was RN S 400 µm2 . The best resolution was achieved for detectors with maximum areas S = 6400 and 20000 µm2 .


J Low Temp Phys Fig. 2 Scheme of the STJ-detector: 1--Si substrate; 2--the base lead (Nb/Ti); 3--Ti trapping layer; 4--Nb base layer; 5--isolating layer (Al2 O3 ); 6--SiO2 isolation; 7 --Al trapping layer of the top electrode; 8--Nb top layer; 9--NbN outer layer; 10--the top lead (Nb)

Fig. 3 (Color online) Bias voltage dependence of the initial slope aini (a) and the nonlinearity b (b)

The pulse height spectra were measured at different bias voltages Vd at the temperature 1.25 K. The samples were irradiated by MnK and MnK X-rays (5.9 and 6.4 keV) from a 55 Fe radioactive source, by fluorescent TiK and TiK X-rays (4.5 and 4.9 keV) from a Ti foil shield placed around the source and with fluorescent SiK X-rays from Si substrate [5]. The detectors had noticeable nonlinearity of the response relative the energy of the quantum. The dependence Q(E ) was determined at every bias voltage and was described by the formula [6]: Q(0) = aini E(1 - bE ), (3)

where aini is the initial slope coefficient and b is the nonlinearity coefficient. Expressions for aini and b follow from formula (1): a
ini

=

P1 , 1.7 t

b=

1 1.7

t

Ref ln 2D 1.89a

.
0

(4)

Figure 3 shows the dependences of coefficient aini and nonlinearity b on the detector voltage Vd for several samples. aini (Vd ) has a maximum and the b(Vd ) has a


J Low Temp Phys Fig. 4 (Color online) Quasiparticle lifetime d -top as function of thickness of Nb(2)-layers. Labels show the thickness of Al-trapping layers in top electrodes in nm

minimum at the voltage Vd ( base - top )/e . This behavior is explained by the maximum in the tunneling rate T for the electrode with a narrower band gap in the asymmetric tunnel junction [6]. The maximum in T is accompanied with the minimum in d and . One can see from Fig. 3b that detectors with thicker top electrode have lower nonlinearity b . This means that increasing of the electrode thickness d really decrease the recombination losses QR . Unfortunately changing of the electrode thickness did not improve the energy resolution. For all samples the best energy resolution at Vd ( base - top )/e was about 90 eV at 5.9 keV. This behavior can be explained by changing of quasiparticle lifetime d . Figure 4 shows the dependence of the lifetime d on the thickness of Nb layer. The lifetime d was determined as a risetime of signal pulses at Vd ( base - top )/e . One can see that the thicknesses of Nb layer and Al layer influence the quasiparticle lifetimes. In particular, increasing of the thickness of Nb layer increases the lifetime. This means that the diffusion length increases also. As the result, the factor ( /a ) deteriorates the energy resolution. Changing of d with the thickness of the layers is due to the tunneling rate T . This means that the Al/Nb quasiparticle trap in this range of the layer thicknesses is not saturated. To exclude the dependence of d on the electrode thickness one has to select thicker Al layers and consequently deeper quasiparticle traps. 4 Conclusion The experimental data obtained for STJ-detectors with killed electrode are consistent with a simple diffusion model. It is shown that the self-recombination of excess quasiparticles gives the noticeable contribution to line broadening. Increasing of the electrode thickness reduces the self-recombination losses and improves the linearity of the detector response as a function of the photon energy. The improvement of energy resolution in STJ-detectors under study is blocked by decreasing of tunneling rate with increasing of the top electrode thickness. To improve energy resolution, the usage of thicker Al trapping layers is recommended. The confirmation of the diffusion model was obtained in some other publications also [1]. The only exception is the series of the works performed by the lowtemperature scanning synchrotron microscope method [8, 9]. The abnormal behavior


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observed in these works may be considered as an evidence of an additional mechanism of the resolution degradation which appears in STJ-detectors with large electrode sizes and deep quasiparticle traps.
Acknowledgements This study was supported by the Ministry of Education and Science of the Russian Federation (Contract No. 02.740.11.0242).

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