A new approach to the inverse problem for current mapping in thin-film superconductors

In the critical state model, the critical current, , of a superconductor defines the upper limit of dissipation-free current flow. However conventional transport measurements of practical superconductors rely on the detection of a voltage drop along the length of the conductor. This requires that the superconductor has entered the dissipative regime, and hence inherently over-estimates the current at which geometric saturation occurs. Nonetheless, the convenience of the 1 µV cm−1 criterion means that it has become the widely adopted definition of transport . Here, we present an alternative definition for the transport critical current of a superconducting tape under self-field conditions, which is based on the concept of geometric current saturation across the full cross-sectional area. This saturation threshold can be experimentally determined through simple Hall sensor measurements of the evolving perpendicular magnetic field at the tape surface. The surface field exhibits a signature transition when the transport current increases beyond the current-saturation threshold. We present an analytical model which describes this effect and defines the critical saturated current as a function of . This definition is first validated using finite element (FE) modelling, and then experimentally demonstrated through measurements on a variety of commercial REBCO and Bi-2223 tapes of differing widths. It is found that the 1 µV cm−1 criterion consistently leads to an overestimation of the saturated critical current by ∼15% in REBCO tapes, and up to 30% in a Bi-2223 tape. FE modelling indicates that this overestimate is most prominent in superconductors exhibiting a low n-value (i.e. n ≲ 20). A key advantage of the measurement approach presented here is that it allows the unambiguous measurement of a transport value to be completed at lower currents, without entering the dissipative region in which sample damage can occur. There are also implications as to the correct choice of value which should be employed within the well-known Norris and Brandt equations for AC loss.

show abstract

“…The perpendicular component of the magnetic field measured at a location x i in the plane of the film is then given by [4,5,24]:…”

Section: Theorymentioning

confidence: 99%

Below 1 µV cm⁻¹: determining the geometrically-saturated critical transport current of a superconducting tape

Brooks¹,

Ainslie²,

Mataira³

et al. 2021

Supercond. Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…Note that this is known to be an ill-posed problem so that a unique solution does not exist: an arbitrarily large number of current configurations can sum together to produce the same magnetic field. Different techniques have been developed in attempts to constrain and solve such ill-posed inverse problems, including Tikhonov regularization [21], Fourier Filters [17,22], estimation theory [23], probabilistic multi-source reconstructions [22], least square fitting [25,26], Bayesian methods [27], genetic algorithms [28], and direct mapping and fitting in low dimensional systems [29][30][31]. Particularly in the case of failure analysis, previous approaches have tried to sidestep this obstacle by assuming specific geometries and utilizing prior knowledge of the DUT to map 3D current distributions [32][33][34].…”

Section: Figure 5(a)mentioning

confidence: 99%

Vector Magnetic Current Imaging of an 8 nm Process Node Chip and 3D Current Distributions Using the Quantum Diamond Microscope

Oliver

Martynowych

Turne

et al. 2021

International Symposium for Testing and Failure Analysis

View full text Add to dashboard Cite

The increasing trend for industry adoption of three-dimensional (3D) microelectronics packaging necessitates the development of new and innovative approaches to failure analysis. To that end, our team is developing a tool called the quantum diamond microscope (QDM) that leverages an ensemble of nitrogenvacancy (NV) centers in diamond for simultaneous wide fieldof- view, high spatial resolution, vector magnetic field imaging of microelectronics under ambient conditions [1,2]. Here, we present QDM measurements of two-dimensional (2D) current distributions in an 8 nm process node flip chip integrated circuit (IC) and 3D current distributions in a custom, multi-layer printed circuit board (PCB). Magnetic field emanations from the C4 bumps in the flip chip dominate the QDM measurements, but these prove to be useful for image registration and can be subtracted to resolve adjacent current traces on the micron scale in the die. Vias, an important component in 3D ICs, display only Bx and By magnetic fields due to their vertical orientation, which are challenging to detect with magnetometers that traditionally only measure the Bz component of the magnetic field (orthogonal to the IC surface). Using the multi-layer PCB, we demonstrate that the QDM's ability to simultaneously measure Bx, By, and Bz magnetic field components in 3D structures is advantageous for resolving magnetic fields from vias as current passes between layers. The height difference between two conducting layers is determined by the magnetic field images and agrees with the PCB design specifications. In our initial steps to provide further z depth information for current sources in complex 3D circuits using the QDM, we demonstrate that, due to the linear properties of Maxwell's equations, magnetic field images of individual layers can be subtracted from the magnetic field image of the total structure. This allows for isolation of signal from individual layers in the device that can be used to map embedded current paths via solution of the 2D magnetic inverse. Such an approach suggests an iterative analysis protocol that utilizes neural networks trained with images containing various classes of current sources, standoff distances, and noise integrated with prior information of ICs to subtract current sources layer by layer and provide z depth information. This initial study demonstrates the usefulness of the QDM for failure analysis and points to technical advances of this technique to come.

show abstract

“…The perpendicular component of the magnetic field measured within the plane of the conductor is then given by [39,40,109]:…”

Section: Identifying the Saturation Currentmentioning

confidence: 99%

Modelling of Saturation Currents and Dynamic Resistance in High-Temperature-Superconductors

Brooks¹

View full text Add to dashboard Cite

High temperature coated conductors are useful for their large Tc, Jc and Bc2values. They are manufactured in long lengths and are available from numerouscommercial distributors around the world. As a result, they have found use inmany applications that can utilise the large magnetic fields that these materialscan produce. In any complex circuit that incorporates superconducting components, it can bedesirable to include superconducting analogues of semiconducting power electronics,such as switches, and transistors. The ideal switch in a superconducting circuit haszero resistance when the switch is closed and infinite resistance when open. Onlysuperconductors can provide the zero resistance closed state. Thus it is the onset ofresistive phenomenon, the conditions under which a non zero resistance is inducedin a superconducting tape, stack, or loop, that are the subject of this thesis. The two phenomena that are examined are: geometric current saturation, and dynamicresistance. Both are investigated using existing finite element models employing the H-formulation and a power-law resistivity in the software COMSOL, accompaniedby experimental verification. Flux flow resistance arises when the transport current in a high temperature superconductor is larger than the critical current I c. This current produces asufficiently large Lorentz force such that there is continuous vortex motion through the superconductor. This results in an effective DC resistance. Today, the criticalcurrent is universally identified using an arbitrary voltage measurement criterion. In this thesis, it is demonstrated that current filling and eventual saturation acrossthe width of a HTS tape can be observed using magnetic field imaging near to the tape surface and correlated with changes in the measured I-V characteristics. Asimple model is presented to explain this behaviour which requires only that the material have a non-linear resistivity. The current filling behaviour is modelledusing numerical methods and validated against experimental data obtained from commercial wires. Finally, it is shown that the saturation determined using eithermagnetic field imaging or voltage measurements is sensitive to the rate of change of current. Dynamic resistance is a resistive phenomenon that occurs when an AC magnetic field interacts with a high temperature superconductor that is simultaneously carrying aDC transport current lower than the critical current. Dynamic resistance occurs when the AC field amplitude is larger than some sample dependent threshold. Comparison between numerical models and measured data demonstrate that field dependent Jc values are required to reproduce the experimentally observed transientvoltage waveforms. The finite element models were then used to analyse the transient current distributions inside of vertical stacks of parallel connected tapesand predict values for the threshold magnetic field. The threshold fields exhibit a transition from ’tape-like’ to ’slab-like’ behaviour as the stack aspect ratio varies. Finally, the effective resistance of a current carrying hollow superconducting strip exposed to an alternating perpendicular magnetic field is presented and analysedvia finite element modelling.

show abstract

A new approach to the inverse problem for current mapping in thin-film superconductors

Cited by 7 publications

References 43 publications

Below 1 µV cm⁻¹: determining the geometrically-saturated critical transport current of a superconducting tape

Below 1 µV cm⁻¹: determining the geometrically-saturated critical transport current of a superconducting tape

Vector Magnetic Current Imaging of an 8 nm Process Node Chip and 3D Current Distributions Using the Quantum Diamond Microscope

Modelling of Saturation Currents and Dynamic Resistance in High-Temperature-Superconductors

Contact Info

Product

Resources

About

A new approach to the inverse problem for current mapping in thin-film superconductors

Cited by 7 publications

References 43 publications

Below 1 µV cm−1: determining the geometrically-saturated critical transport current of a superconducting tape

Below 1 µV cm−1: determining the geometrically-saturated critical transport current of a superconducting tape

Vector Magnetic Current Imaging of an 8 nm Process Node Chip and 3D Current Distributions Using the Quantum Diamond Microscope

Modelling of Saturation Currents and Dynamic Resistance in High-Temperature-Superconductors

Contact Info

Product

Resources

About

Below 1 µV cm⁻¹: determining the geometrically-saturated critical transport current of a superconducting tape

Below 1 µV cm⁻¹: determining the geometrically-saturated critical transport current of a superconducting tape