Charge fluctuators, their temperature and their response to sudden electrical fields Outline Charge two-level fluctuators Measuing noise with an SET Temperature and bias dependence of the noise TLF temperature Measuring step response with an SET Slow charge drift, logaritmic increase Extracting TLF densities TEM Studies of tunnel barriers Histogram of barrier thicknesses Conclusion M.V. Gustafsson et al. PRB 88, 245410 (2013) A. Pourkabirian, et al., PRL 113, 256801 (2014) L.J. Zheng et al. J. Phys. D, 48, 395308 (2015)
Two-level fluctuators (TLFs) Physical origin of 1/f charge noise is still an unsolved problems From superposition of individual charged two-level fluctuators (TLFs) Where? How many? Microscopic origin
Where are the background charges? Background charges give rise to 1/f noise in SETs and decoherence in qubits In spite of extensive research we still know rather little about them In the island oxide? In the junctions? In the substrate? At the interface? Bulk distribution or surface distribution? What is the microscopic origin? Zimmerli et al., Appl. Phys. Lett. 61, 237 (1992) Song et al., IEEE Trans. Appl. Supercond. 5, 3085 (1995) Krupenin et al., J. Appl. Phys. 84, 3212 (1998) Verbrugh et al., J. Appl. Phys. 78, 2830 (1995) Bouchiat, Doctoral Thesis, (Paris 6, 1997) Starmark et al., J. Appl. Phys. 86, 2132 (1999). Zorin et al., Phys. Rev. B 53, 13682 (1996) Kenyon et al., J. Appl. Phys., 88, 6536 (2000) O. Astafiev, et al., Phys. Rev. Lett. 96, 137001 (2006) S. Kafanov, et al., Phys. Rev. B 78, 125411 (2008)
TLFs measured with a SET Two methods to gain information about the TLFs Noise measurements Step response measurements M. V. Gustafsson et al., PRB 88, 245410 (2013) A. Pourkabirian, et al., PRL 113, 256801 (2014)
Sample design and setup Sample layout, 5 SETs on each chip B=1T => Normal state SET, E C 6K Aluminum on different substrates Oxidized silicon, glass, saphire
Noise measurements Noise spectrum = transimpedance amplifier Pilot tone at 377Hz! SQ = S Q (390 Hz)
Charge noise: bias and temperature dependence Linear temperature dependence Saturation at lower temperatures Saturation strongly depends on the bias point Allows us to extract the TLF temperature Qg=e/2 Qg=0 Others have claimed S Q ~T 2. Astafeiev et al. PRL 2006 Kenyon et al. JAP 2000
Charge noise: temperature dependence We find a linear temperature dependence Dutta Horn Kenyon Brown Kafanov S S Q ~T 2 Q ~T S Q ~T Others have claimed S Q ~T 2. Astafeiev et al. PRL 2006 Kenyon et al. JAP 2000
Charge noise: Bias dependence We measure the noise at 300 different bias point with varying bias voltage and bias current. T=20 mk Aim: How does the noise change with voltage, current, and power
The noise increases with dissipated power The noise increases with Power not with only voltage not with only current Same color same current
Comparing temperatures substrate T ph T TLF cooling stage Electron temperature: Estimated from theory and and extracted from exp. (x in right Fig.) TLF temperature from bias dependence of the noise Phonon temperature; from FEM simulations
The TLFs are most likely heated by the island electrons The TLFs are hot The TLFs cannot be heated by via the phonons The TLFs are likley heated by electrons tunneling from the SET island The linear T dependence also speaks in favour of a single well trap. SET island trap M. V. Gustafsson et al., PRB 88, 245410 (2013)
What about parity effect? If the electrons tunnel in and out of the SET Island, that changes the parity on the island 1.0 0.8 0.6 0.4 0.2 0.0 0.5 1.0 1.5 2.0 3.0 2.5 2.0 1.5 1.0 0.5-3 -2-1 0 1 2 3 Parity effects in Superconducting SETs should still be there. Noise is similar in S and N state This has however only been observed at high bias voltage, close to the gap, i.e. when qp are injected on the island. Comparison of 1/f noise in S and N state should be revisited.
Step response: Nonequilibrium probing of TLFs We start from equilibrium (24 hours waiting time) Then we apply an abrupt voltage step to the gate (~10V) We measure the drift of the charge induced on the SET island A. Pourkabirian, et al., PRL 113, 256801 (2014)
Charge drift is measured with the SET. We can extract the charge by counting the oscillations Drift continues for more than 20 hours after the step. The charge increases logarithmically with time Charge drift T 30 mk Substrate: Oxidized silicon V=9.8 V
Different step heights The drift increases linearly with step height De define the logarithmic slope of the drift normalized to the voltage step
Charge drift for different substrates # substrate T(mK) H 1 SiOx 2000 0.26 1 SiOx 30 0.22 2 SiOx 20 0.22 3 glass 20 0.37 4 sapphire 20 0.19 H is very similar for different materials Similar at 30 mk and 2K Steps are larger in sappire indicating larger e d but fewer TLFs Sometimes step in opposite direction (sapphire)
Thermal activation or quantum tunneling? Absence of temperature dependence Linear step height dependence Excludes thermal activation of the TLFs but agrees with quantum tunneling Thermal activation Quantum tunneling
Modelling the charge drift We define the gate field e G =E G /V G, which is due to the gate voltage (Green). We define the (virtual) field e V =E V /V 0, which is the field produced by putting the island potential to V 0, and all other electrodes to zero (Dashed black).
Energy shift for the TLF Before the step After the step e G determines if the TLF will switch or not
Induced charge e V determines how much charge a switching TLF will induce
Step response, what to expect induced charge Which TLFs switch switching prob. after time t
Extracting the density of TLFs Homogeneous volume distribution, n V (red) Kevin Osbornes group, SiN n v 7.8 10 24 m -3 ev -1 Homogeneous surface distribution, n S (black) S. Sendelbach et al. PRL 100, 227006 (2008) Densities calculated by numerically computing the integral, assuming 1e and a tunnel distance d=1nm i.e. assuming a dipole moment of 1 e nm 50 Debey
Densities for different materials Comparing different materials, H is similar but SiO x and glass show many small steps, whereas sapphire show fewer but larger steps. Thus e d, is larger for sapphire. n H d 2 #1,2 SiOx #3 glass #4 Sapphire Larger steps in sapphire thus indicates lower density in sapphire
Explaining the steps in opposite direction Steps in both directions are visible The induced charge depends on the scalar product of e V and e G. Q ~ e V e G Underneath, the island e V and e G point in opposite directions. Underneath the leads they point in the same direction. Sapphire
Meassuring the barrier thickness TEM work by Eva Olssons group L.J. Zheng et al., J. Phys. D: Appl. Phys. 48 (2015) 395308
Histograms of the barrier thickness Barrier thickness measured at over 300 different positions for each sample For each sample, 50 STEM images from ~20 different grains Sample P t <l> σ σ/<l> # (mbar) (min) (nm) (nm) Thermal oxide 1 0.1 3 1.66 0.35 21.1% 2 0.1 30 1.88 0.32 17.0% 3 1 3 1.73 0.37 21.4% Epitaxial Plasma oxide 3.95 0.37 9.4% Chris Richardson, LPS Less than 10% of the junction area carries more than 90% of the current L.J. Zheng et al., J. Phys. D, 48, 395308 (2015)
How big fraction of the junction is active Fraction of the current that flows in fraction of the junction area Less than 10% of the junction area carries more than 90% of the current L.J. Zheng et al., J. Phys. D, 48, 395308 (2015)
Conclusions The TLFs are hot: they are heated by electrons on the SET island The noise increases linearly with temperature TLFs are possibly single traps within tunnel distance from the SET The step response causes charge drift which increases logarithmically in time The logarithmic slope of the drift, H, depends linearly on the voltage does NOT depend on the temperature does NOT depend strongly on material This rules out thermal activation of the TLFs, but is consistent with quantum tunneling We have extracted the densities of the TLFs from the drift n S =1.6 10 16 m 2 ev -1 decade 1, n V =1.6 10 24 m 3 ev -1 decade 1 The thickness of the tunnel barrier varies by 20% in a polycrystalline film. M. V. Gustafsson et al., PRB 88, 245410 (2013) A. Pourkabirian, et al., PRL 113, 256801 (2014) L.J. Zheng et al., J. Phys. D, 48, 395308 (2015)