Details

Autor(en) / Beteiligte

• Guralnik, Benny
• Hansen, Ole
• Henrichsen, Henrik H
• Caridad, José M
• Wei, Wilson
• Hansen, Mikkel F
• Nielsen, Peter F
• Petersen, Dirch H

Titel

Effective electrical resistivity in a square array of oriented square inclusions

Ist Teil von

• Nanotechnology, 2021-04, Vol.32 (18), p.185706-185706

Ort / Verlag

England: IOP Publishing

Erscheinungsjahr

2021

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The continuing miniaturization of optoelectronic devices, alongside the rise of electromagnetic metamaterials, poses an ongoing challenge to nanofabrication. With the increasing impracticality of quality control at a single-feature (-device) resolution, there is an increasing demand for array-based metrologies, where compliance to specifications can be monitored via signals arising from a multitude of features (devices). To this end, a square grid with quadratic sub-features is amongst the more common designs in nanotechnology (e.g. nanofishnets, nanoholes, nanopyramids, LED arrays etc). The electrical resistivity of such a quadratic grid may be essential to its functionality; it can also be used to characterize the critical dimensions of the periodic features. While the problem of the effective electrical resistivity eff of a thin sheet with resistivity 1, hosting a doubly-periodic array of oriented square inclusions with resistivity 2, has been treated before (Obnosov 1999 SIAM J. Appl. Math. 59 1267-87), a closed-form solution has been found for only one case, where the inclusion occupies c = 1/4 of the unit cell. Here we combine first-principle approximations, numerical modeling, and mathematical analysis to generalize eff for an arbitrary inclusion size (0 < c < 1). We find that in the range 0.01 ≤ c ≤ 0.99, eff may be approximated (to within <0.3% error with respect to finite element simulations) by: e f f = 1 ( c ) − 1 − 2 1 1 + 2 1 ( c ) + 1 − 2 1 1 + 2 1 c ( c ) , ( c ) = 1 + 0.9707 0.9193 + c 1 − c 2.1261 0.4671 . whereby at the limiting cases of c → 0 and c → 1, approaches asymptotic values of = 2.039 and = 1/c − 1, respectively. The applicability of the approximation to considerably more complex structures, such as recursively-nested inclusions and/or nonplanar topologies, is demonstrated and discussed. While certainly not limited to, the theory is examined from within the scope of micro four-point probe (M4PP) metrology, which currently lacks data reduction schemes for periodic materials whose cell is smaller than the typical m-scale M4PP footprint.