Effective electrical resistivity in a square array of oriented square inclusions.

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, µLED 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 ρ eff of a thin sheet with resistivity ρ 1, hosting a doubly-periodic array of oriented square inclusions with resistivity ρ 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 ρ eff for an arbitrary inclusion size (0 < c < 1). We find that in the range 0.01 ≤ c ≤ 0.99, ρ eff may be approximated (to within <0.3% error with respect to finite element simulations) by: [Formula: see text] [Formula: see text] whereby at the limiting cases of c â†’ 0 and c â†’ 1, α approaches asymptotic values of α = 2.039 and α = 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 µm-scale M4PP footprint.

3ω correction method for eliminating resistance measurement error due to Joule heating.

Electrical four-terminal sensing at (sub-)micrometer scales enables the characterization of key electromagnetic properties within the semiconductor industry, including materials' resistivity, Hall mobility/carrier density, and magnetoresistance. However, as devices' critical dimensions continue to shrink, significant over/underestimation of properties due to a by-product Joule heating of the probed volume becomes increasingly common. Here, we demonstrate how self-heating effects can be quantified and compensated for via 3ω signals to yield zero-current transfer resistance. Under further assumptions, these signals can be used to characterize selected thermal properties of the probed volume, such as the temperature coefficient of resistance and/or the Seebeck coefficient.

Northward migration of the eastern Himalayan syntaxis revealed by OSL thermochronometry.

Erosion influences the dynamical evolution of mountains. However, evidence for the impact of surface processes on tectonics mostly relies on the circumstantial coincidence of rugged topography, high stream power, erosion, and rock uplift. Using the optically stimulated luminescence (OSL) thermochronometry technique, we quantified the spatial and temporal exhumation of the eastern Himalayan syntaxis. We found increasing exhumation rates within the past million years at the northeast end of the Namche Barwa-Gyala Peri dome. These observations imply headward propagation of erosion in the Parlung River, suggesting that the locus of high exhumation has migrated northward. Although surface processes influence exhumation rates, they do not necessarily engage in a feedback that sets the location of tectonic deformation.

Stimulated luminescence emission from localized recombination in randomly distributed defects.

We present a new kinetic model describing localized electronic recombination through the excited state of the donor (d) to an acceptor (a) centre in luminescent materials. In contrast to the existing models based on the localized transition model (LTM) of Halperin and Braner (1960 Phys. Rev. 117 408-15) which assumes a fixed d → a tunnelling probability for the entire crystal, our model is based on nearest-neighbour recombination within randomly distributed centres. Such a random distribution can occur through the entire volume or within the defect complexes of the dosimeter, and implies that the tunnelling probability varies with the donor-acceptor (d-a) separation distance. We first develop an 'exact kinetic model' that incorporates this variation in tunnelling probabilities, and evolves both in spatial as well as temporal domains. We then develop a simplified one-dimensional, semi-analytical model that evolves only in the temporal domain. An excellent agreement is observed between thermally and optically stimulated luminescence (TL and OSL) results produced from the two models. In comparison to the first-order kinetic behaviour of the LTM of Halperin and Braner (1960 Phys. Rev. 117 408-15), our model results in a highly asymmetric TL peak; this peak can be understood to derive from a continuum of several first-order TL peaks. Our model also shows an extended power law behaviour for OSL (or prompt luminescence), which is expected from localized recombination mechanisms in materials with random distribution of centres.