Superconducting Tunnel Junctions

— 27 — Superconducting tunnel junctions Didier D.E. MartinI and Peter VerhoeveI Abstract Superconducting tunnel junctions (STJ) are a class of cryogenic detectors that rely on the generation of free charge carriers by breaking Cooper pairs in a superconducting material with the use of absorbed photon energy. In an STJ, consisting of two superconducting films separated by a thin insulating barrier, the charge carriers can be detected through the tunnel-current pulse they produce if the STJ is under a finite voltage bias. The number of charge carriers generated is proportional to the energy of the absorbed photon, and, depending on the material of choice, ranges from several hundreds to a few thousand per electronvolt of photon energy. This allows STJs to be used as photon-counting detectors with intrinsic energy resolution over a wide energy band from the near infrared to well into the X-ray band. The operating temperature is typically at 10 % of the critical temperature Tc of the superconducting material and may range from 0.1 K to 1 K. Although they have not been deployed in space applications yet, they could well be envisaged as spectrometers with an energy-resolving power of several hundreds in the soft X-ray range, or as highly efficient order-sorting detectors in UV grating spectrographs. STJs can be used simultaneously as absorbers and read-out elements, or alterna- tively, if a larger sensitive area is required, two or more can be attached as read-out elements to a separate absorber. The state of the art performance comprises energy resolutions of 2 eV to 11 eV in the soft X-ray energy range from 0.4 keV to 5.9 keV, and of 0.1 eV to 0.2 eV in the near-infrared and visible range from 0.5 eV to 5 eV. Imaging arrays of >100 pixels of close-packed STJs have been made and operated in ground-based astronomical applications. Introduction Superconducting tunnel junctions (STJ) are a family of cryogenic sensors. As we shall describe in the next paragraph, they rely on the creation of ‘free’ charge carriers by the absorbed radiation. The energy required to generate these excitations is typically three orders of magnitude lower than that in classical semiconductors. This makes them extremely sensitive to radiation from the sub-millimetre to the X- ray wavelengths, in principle allowing single-photon detection with intrinsic energy IAdvanced Studies and Technology Preparation Division, ESA-ESTEC, The Netherlands 441 442 27. Superconducting tunnel junctions resolving power. STJs operate on a different principle than microcalorimeters and consequently have their own strengths and weaknesses. Although neither of them have been flown in space yet, it is expected that each will have their own domain of application. Advantages of STJs over microcalorimeters can be summarized as follows: STJs are directly grown on solid substrates (e.g., sapphire) and do not require complex micromachining processes. For a given energy resolution, operating temperatures can be substantially higher (e.g., 300 mK for STJs vs. 50 mK for transition-edge sensors, TES). Quasiparticle relaxation processes are typically faster than the thermal processes on which calorimeters rely. This makes STJs faster detectors and im- plies they could be used with higher photon-counting rates. STJs or superconductor-insulator-superconductor (SIS) junctions were first used by Giaever (1960) to study quasiparticle densities in Sn. In 1969 Wood and White (1969) observed the first α-particle induced pulses from a biased STJ made of Sn electrodes. A wider interest was generated through the efforts of Kurakado and Mazaki (1980) to further develop Sn STJs, which resulted in the first X-ray de- tections with a photon energy, E, of 5.9 keV in 1986 (Twerenbold 1986; Kraus et al 1986), still with Sn STJs. Sn proved to be unstable under thermal cycling and was replaced by materials like Nb, Al, and Ta. Since then, many other groups have been developing STJs for such different applications as particle and nuclear physics, astrophysics, material analysis, and mass spectroscopy. Principle of operation of STJs as radiation detectors In its simplest form an STJ consists of two superconducting layers, acting as radiation absorbers, separated by a thin insulating barrier (see Figure 27.1, left). Below the critical temperature Tc the electrons in a superconductor are organised in Cooper pairs, with a binding energy 2∆ with ∆ the superconductor’s energy gap which is inversely proportional to Tc. At finite temperature, a fraction of the Cooper pairs is broken into excited states, called quasi-particles (QP), through the contin- uous pair breaking by thermal phonons with energy > 2∆ and the recombination of QPs with the emission of a phonon. The rates for these processes are material dependent and tend to get slower for lower-Tc superconductors (Kaplan et al 1976). A semiconductor representation of the energy-level diagram with electron-like and hole-like quasiparticles for a biased STJ at T > 0 is shown in Figure 27.1, middle. The charge carriers associated with QPs can tunnel quantum-mechanically across the insulating barrier. Four different tunnel processes are possible, two of which are depicted in Figure 27.2 for the case of a symmetric STJ under a bias voltage Ub. The other two (3 and 4) are the reverse processes of these. Processes 1 and 3 involve the direct transfer of a quasiparticle from left to right and vice versa, respectively, and correspond to an electron transferred in the same direction. Processes 2 and 443 e Figure 27.1: Left: Schematic representation of a superconducting tunnel junction. Middle: the energy level diagram in the semiconductor representation for an STJ, voltage biased at Ub. Right: The current-voltage characteristic for this structure. e Figure 27.2: Left: Schematic representation of the possible tunnel processes that can occur in an STJ. Processes 3 and 4 (not indicated) are the exact opposite of 1 and 2. The vertical scale represents energy. Right: Resulting current-voltage characteristic for an STJ at T > 0, in arbitrary units. 4 involve the additional annihilation of a Cooper pair in one film and creation in the other film. Effectively in process 2 a QP is transferred from right to left, but an electron is still going from left to right, as in process 1. At sufficient high bias voltage, the occupancy of the higher energy levels is sufficiently low to leave only processes 1 and 2 significantly contributing to the tunnel current (see Figure 27.2, right). The resulting I-V curve is schematically shown in Figure 27.1, right. For bias voltages Ub < 2∆/e (the sub-gap region), the current is weakly dependent on bias voltage and scales with the temperature dependent quasiparticle density 1 ∆ − k T as n(T ) T 2 e B , with kB the Boltzmann constant. Above 2∆/e the device exhibits the∝ normal resistance of the barrier (represented by the dashed line). The absorption of a photon with energy E in a superconductor is followed by a series of fast processes involving both electrons and phonons (Kozorezov et al 2000, and references therein), in which the photon energy is converted into quasiparticles in excess of the thermal density by the breaking of Cooper pairs. For typical transition metals the time scale of this conversion process ranges from nanosec- onds (niobium) to microseconds (hafnium). The average number of excess carriers 444 27. Superconducting tunnel junctions is N0(E) = E/(1.7∆) (Kurakado 1982; Rando 1992). Thus, in a superconductor such as tantalum (∆=0.7 meV), the initial mean number of free charge carriers 3 created is N0(E) 10 per electronvolt of photon energy. The excess quasiparticle population produced≈ through photo-absorption in one of the electrodes of a voltage-biased STJ will be detected as a tunnel-current pulse with amplitude proportional to the incoming photon’s energy. Absorptions in either electrode of the STJ will give rise to the same polarity current pulse, and moreover, quasiparticles that have been transferred to the other electrode by one of the two processes 1 or 2 described above, can continue to contribute to the signal by ‘backtunnelling’ (Gray 1978) as long as they are available in the electrode volume. On average each quasiparticle will contribute <n> times to the signal before it is lost from the system through recombination or trapping. Hence the mean number of detected charge carriers N =<n> N0. The detector responsivity R is referred to as the number of tunnelled electrons per electronvolt of photon energy: R =<n> /(1.7∆). For a symmetric STJ the value of <n> Γ /Γ , with Γ the tunnel rate across ≈ tun loss tun the barrier and Γloss the loss rate in the system. The tunnel rate for bias voltages k T eU < 2∆ can be approximated as (de Korte et al 1992): B ≪ b 1 (∆ + eU )2 Γ = b , (27.1) tun 4 e2ρ N(0)d (∆ + eU )2 ∆2 n s b − with ρn the resistivity of the barrier, N(0) the normal-state single spin density of state of the superconductor, d the electrode thickness. Typical values for Γtun in a Ta STJ with d = 100 nm and ρ =2 10−6 Ω cm2, are of the order of 106 s−1. The n × loss rate Γloss is ultimately limited by quasiparticle recombination and can be orders of magnitude slower than the tunnel rate. In practice however, other processes like diffusion of the QPs out of the electrode volume or trapping and recombination in defects at surfaces, edges or bulk impurities will dominate the loss rate. Multiple tunnelling can be enhanced by including layers of a lower-gap material on either side of the barrier, such that quasiparticles are collected and confined close to the barrier and the tunnel rate is enhanced (Booth 1987), and away from possible loss sites such as surfaces.

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