Power Handling and Responsivity of Submicron Wide Superconducting Coplanar Waveguide Resonators

R.M.J. Janssen 0 A. Endo 0 J.J.A. Baselmans 0 P.J. de Visser 0 R. Barends 0 T.M. Klapwijk 0 0 R. Barends Department of Physics, University of California , Santa Barbara, CA 93106, USA The sensitivity of microwave kinetic inductance detectors (MKIDs) based on coplanar waveguides (CPWs) needs to be improved by at least an order of magnitude to satisfy the requirements for space-based terahertz astronomy. Our aim is to investigate if this can be achieved by reducing the width of the CPW to much below what has typically been made using optical lithography (> 1 m). CPW resonators with a central line width as narrow as 300 nm were made in NbTiN using electron beam lithography and reactive ion etching. In a systematic study of quarter-wave CPW resonators with varying widths it is shown that the behavior of responsivity, noise and power handling as a function of width continues down to 300 nm. This encourages the development of narrow KIDs using Al in order to improve their sensitivity. Microwave Kinetic Inductance Detectors (MKIDs) [1] are showing promising results to become the future of large detector arrays for terahertz astronomy. The main advantages of MKIDs are ease of fabrication, wide dynamic range and above all their - inherent capability to read many pixels using frequency domain multiplexing [2]. This has allowed a rapid development of MKID arrays over the past decade, which has recently resulted in the first observations using cameras based on MKID technology at ground-based (sub-)mm telescopes [3, 4]. A common MKID pixel design used in these cameras is an antenna-coupled coplanar waveguide (CPW) resonator patterned in a superconducting film [5, 6]. The Al resonators of such MKID pixels have shown [7] a detector Noise Equivalent Power (NEP) as low as 3 1019 W Hz0.5. While this is close to the sensitivity required for background photon noise limited photometry in space, NEP 1019 W Hz0.5, an improvement of two orders of magnitude is required to achieve this for spectroscopy [8]: NEP 3 1021 W Hz0.5. One possible route to improve the NEP is to reduce the width of the CPW. Experiments on Al resonators wider than a few micrometers indicate that the NEP [9] scales as NEP S0.4 and NEPR S0.7 for phase and amplitude read-out, respectively. This assumes S/W is kept constant. Here S is the CPW central line width and W is the width of the CPW slots. The sensitivity improvement results from the fact that the responsivity increases more rapidly (x/Nqp S1.7) than the noise (S S1.3, SR S1) for decreasing width. The increase in responsivity is due to a change in volume (V S) and kinetic inductance [10, 11] ( S0.7), while the increase in noise is a result of decreasing read-out power handling [12] (Pread S2), which also affects the Two Level System (TLS) noise [13, 14] in phase read-out (S S1.6Prea0d.5). Because of the low background loading in space, the majority of the quasi-particles are expected to be the excess quasi-particles created by microwave read-out power [7] rather than those created by optical pair breaking. Therefore, the quasi-particle lifetime is unaffected by the reduced width. If these trends continue down to a width of e.g., S = 300 nm, the NEP would reach 6 1020 W Hz0.5, which is sufficient for space-borne photometry. However, effects negligible for wide resonators could begin to play a significant role when the width approaches the film thickness and characteristic length scales such as the magnetic penetration depth. In this study, we systematically investigate the behavior of noise, responsivity and read-out power handling of the CPW resonators that are as narrow as 300 nm, in order to find out if width reduction is a viable route to improve the sensitivity of MKIDs to a level suitable for space-borne applications. 2 Experimental Details Electron beam lithography (EBL) and reactive ion etching (RIE) are used to fabricate CPW resonators with a central line width as narrow as 300 nm. Figure 1 shows on the left an optical micrograph of such a narrow quarter-wavelength (QW) resonator coupled to a 22 m wide feedline. A close-up of the open end of the resonator, outlined by the black box, can be seen in the right image of Fig. 1. The EBL system can pattern 150 of these narrow resonators in 1 hour. Using only EBL and RIE, CPW resonators with a central line width, S, varying between 0.3 m and 3.0 m were patterned in a 100 nm thick NbTiN film, which was sputtered on a hydrogen passivated high resistivity (> 1 k cm) 100 -oriented Si substrate. These resonators have a length between 3.5 and 5.0 mm. The S/W Fig. 1 (Left) Optical micrograph of a submicron wide resonator coupled to a 22 m wide feedline. (Right) Zoom in on the black square of the optical image using a SEM. This SEM image shows the open end of a narrow CPW quarter-wavelength resonator patterned in 100 nm thick NbTiN on a Si substrate. The central line and slots are 300 nm and 200 nm wide, respectively ratio was kept constant at 3/2. The short quasi-particle lifetime (qp 1 ns) [15] of stoichiometric NbTiN prevents it from being used as the active material for MKIDs and therefore any optical experiments. However, in this work NbTiN is used instead of Al, because the higher Tc = 13.7 K (measured) allows measurements in a He-3 sorption cooler with a base temperature of T0 = 310 mK. The sample is placed in this cryostat in a gold-plated Cu box that is surrounded by a superconducting shield. The feedline transmission is measured using a signal generator, low noise amplifier (LNA) and quadrature mixer [1, 15, 16]. Detailed information on the specific design parameters and basic measurement properties of each resonator can be found in Janssen [17]. 3 Results Following Baselmans et al. [18] the phase responsivity of each resonator is determined from the change in resonance frequency, fres, as a function of temperature, T . = 4QL where QL is the resonators loaded quality factor, y = (fres(T ) fres(T0))/fres(T0) and Nqp is the number of quasi-particles in the resonator volume. The last quantity is given by the temperature under the assumption of a steady-state number density of thermally excited quasi-particles [19]. A linear least squares (LLS) fit is applied for temperatures T > Tc/6 to determine y/Nqp. Figure 2 shows that the phase responsivity increases for decreasing widths (squares). The dependency can be described by a power law /Nqp S1.200.19 (solid line). The scatter in Fig. 2 is mainly caused by the variation in the measured loaded quality factor, QLmeas, between different resonators. This is easily shown by substituting QL = 105, which for these resonators is a typical measured value log10 QLmeas = 4.90 0.12, into (1). The responsivities calculated thus are shown by the diamonds in Fig. 2. Application of a constant QL Fig. 3 (Left) The frequency noise at 1 kHz measured at an internal power of 30 dBm as a function of central line width. A fit to the data for S 1 m shows a widt (...truncated)