Twin-Wire Networks for Zero Interconnect, High-Density 4-Wire Electrical Characterizations of Materials

Abstract

Four-wire measurements have been introduced by Lord Kelvin in 1861 and have since become the standard technique for characterizing small resistances and impedances. However, high-density 4-wire measurements are generally complex, time-consuming, and inefficient because of constraints on interconnects, pads, external wires, and mechanical contacts, thus reducing reproducibility, statistical significance, and throughput. Here, we introduce, systematically design, analyze, and experimentally validate zero interconnect networks interfaced to external instrumentation by couples of twin wire. 3D-printed holders with magnets, interconnects, nonadhesive layers, and spacers can effortlessly establish excellent electrical connections with tunable or minimum contact forces and enable accurate measurements even for delicate devices, such as thin metals on soft polymers. As an example, we measured all the resistances of a twin-wire 29-resistor network made of silver-nanoparticle ink printed on polyimide, paper, or photo paper, including during sintering or temperature calibration, resulting in an unprecedentedly easy and accurate characterization of both resistivity and its temperature coefficient. The theoretical framework and experimental strategies reported here represent a breakthrough toward zero interconnect, simple, and efficient high-density 4-wire characterizations, can be generalized to other 4-wire measurements (impedances, sensors) and can open the way to more statistically meaningful and reproducible analyses of materials, high-throughput measurements, and minimally invasive characterizations of biomaterials.

Twin‐Wire Sensor Networks

“…The twin‐wire network strategy, which has been recently proposed for enabling zero interconnect, high‐density 4‐wire electrical characterizations of materials, can also be applied to networks of resistive or impedance sensors. The general results [ 11 ] for network generation, iterations, numbers of pads/wires/resistors and multiply‐by‐M expansions (i.e., bifurcation for M = 2, trifurcation for M = 3,…) apply, but twin‐wire sensing networks do not necessarily have the zero‐interconnect property. As an example, Figure 1b schematically shows a twin‐wire network of 29 resistive sensors which may be formally generated by applying three bifurcation steps [ 11 ] to an initial resistor R A .…”

“…Recently, twin‐wire networks [ 11 ] have been proposed for enabling zero interconnect and high‐density 4‐wire material characterizations (e.g., silver‐nanoparticle conductive inks printed on polyimide, paper, or photo paper [ 11 ] ), which are more efficient than conventional 4‐wire systems in terms of the numbers of pads and wires. The twin‐wire network strategy can be generalized to other 4‐wire measurements, but networks of resistive sensors do not necessarily inherit the zero‐interconnect property.…”

“…In some cases, the sensors can be made of the same conductive material used for connecting the sensors to the electronic interface. For instance, an array of twin‐wire resistors printed by silver nanoparticles conductive ink, [ 11 ] once the temperature coefficients of the resistors are calibrated, can be seen as an array of resistive temperature sensors and, if the entire network is printed by the same silver nanoparticles conductive ink without adding any other conductive material, the resulting twin‐wire sensor network has the zero‐interconnect property. [ 11 ] However, in practical systems, discrete components are often employed as sensors or, in microsystems, the sensing elements may be made of a different material in comparison with the connections or must be smaller than the area required for connections, so parasitic resistances must be taken into account.…”

“…For instance, an array of twin‐wire resistors printed by silver nanoparticles conductive ink, [ 11 ] once the temperature coefficients of the resistors are calibrated, can be seen as an array of resistive temperature sensors and, if the entire network is printed by the same silver nanoparticles conductive ink without adding any other conductive material, the resulting twin‐wire sensor network has the zero‐interconnect property. [ 11 ] However, in practical systems, discrete components are often employed as sensors or, in microsystems, the sensing elements may be made of a different material in comparison with the connections or must be smaller than the area required for connections, so parasitic resistances must be taken into account. Additionally, non‐idealities of both the sensors and the electronic interface translate into measurement errors, so that accurate measurements may be hindered by the uncertainties on the biasing current and the non‐idealities of the instrumentation amplifier, with special reference to the gain error and to the input offset and low‐frequency noise voltages.…”

Thin PDMS-on-Sacrificial-PCB Devices

“…As a proof of concept, we tested the strain sensor or stretchable interconnect shown in Figure 1f. The small resistance can be accurately measured by connecting a couple of twin wires 63 to each pad and performing four-wire measurements. Figure 4a shows the resistance during strain cycles (no strain up to 0.57% peak strain).…”