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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.

Pyrolytic carbon microelectrodes (PCMEs) are a promising alternative to their conventional metallic counterparts for various applications. Thus, methods for the simple and inexpensive patterning of PCMEs are highly sought after. Here, we demonstrate the fabrication of PCMEs through the selective pyrolysis of SU-8 photoresist by irradiation with a low-power, 806 nm, continuous wave, semiconductor-diode laser. The SU-8 was modified by adding Pro-Jet 800NP (FujiFilm) in order to ensure absorbance in the 800 nm range. The SU-8 precursor with absorber was successfully converted into pyrolytic carbon upon laser irradiation, which was not possible without an absorber. We demonstrated that the local laser pyrolysis (LLP) process in an inert nitrogen atmosphere with higher laser power and lower scan speed resulted in higher electrical conductance. The maximum conductivity achieved for a laser-pyrolyzed line was 14.2 ± 3.3 S/cm, with a line width and thickness of 28.3 ± 2.9 µm and 6.0 ± 1.0 µm, respectively, while the narrowest conductive line was just 13.5 ± 0.4 µm wide and 4.9 ± 0.5 µm thick. The LLP process seemed to be self-limiting, as multiple repetitive laser scans did not alter the properties of the carbonized lines. The direct laser writing of adjacent lines with an insulating gap down to ≤5 µm was achieved. Finally, multiple lines were seamlessly joined and intersected, enabling the writing of more complex designs with branching electrodes and the porosity of the carbon lines could be controlled by the scan speed.

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 → 0 and c → 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.

We present a four-probe setup for measuring temperature of Joule-heated silicon in two independent ways from the same voltage measurement: a method using the thermal dependence of resistivity and a method based on the measured sheet power density. The two methods are compared to optical temperature measurements made by fitting a gray-body model onto data from a commercial spectrometer. The two four-probe temperature measurements are conducted from 890 K to 1540 K, and they converge at temperatures above 1400 K indicating a high degree of self-consistency.

Micro four-point probes (M4PP) provide rapid and automated lithography-free transport properties of planar surfaces including two-dimensional materials. We perform sheet conductance wafer maps of graphene directly grown on a 100 mm diameter SiC wafer using a multiplexed seven-point probe with minor additional measurement time compared to a four-point probe. Comparing the results of three subprobes we find that compared to a single-probe result, our measurement yield increases from 72%-84% to 97%. The additional data allows for correlation analysis between adjacent subprobes, that must measure the same values in case the sample is uniform on the scale of the electrode pitch. We observe that the relative difference in measured sheet conductance between two adjacent subprobes increase in the transition between large and low conductance regions. We mapped sheet conductance of graphene as it changed over several weeks. Terahertz time-domain spectroscopy conductivity maps both before and after M4PP mapping showed no significant change due to M4PP measurement, with both methods showing the same qualitative changes over time.

Epitaxial graphene is a promising route to wafer-scale production of electronic graphene devices. Chemical vapor deposition of graphene on silicon carbide offers epitaxial growth with layer control but is subject to significant spatial and wafer-to-wafer variability. We use terahertz time-domain spectroscopy and micro four-point probes to analyze the spatial variations of quasi-freestanding bilayer graphene grown on 4 in. silicon carbide (SiC) wafers and find significant variations in electrical properties across large regions, which are even reproduced across graphene on different SiC wafers cut from the same ingot. The dc sheet conductivity of epitaxial graphene was found to vary more than 1 order of magnitude across a 4 in. SiC wafer. To determine the origin of the variations, we compare different optical and scanning probe microscopies with the electrical measurements from nano- to millimeter scale and identify three distinct qualities of graphene, which can be attributed to the microstructure of the SiC surface.

Hall effect metrology is important for a detailed characterization of the electronic properties of new materials for nanoscale electronics. The micro-Hall effect (MHE) method, based on micro four-point probes, enables a fast characterization of ultrathin films with minimal sample preparation. Here, we study in detail how the analysis of raw measurement data affects the accuracy of extracted key sample parameters, i.e., how the standard deviation on sheet resistance, carrier mobility and Hall sheet carrier density is affected by the data analysis used. We compare two methods, based primarily on either the sheet resistance signals or the Hall resistance signals, by theoretically analysing the effects of electrode position errors and electrical noise on the standard deviations. We verify the findings with a set of experimental data measured on an ultrashallow junction silicon sample. We find that in presence of significant electrical noise, lower standard deviation is always obtained when the geometrical analysis is based on the sheet resistance signals. The situation is more complicated when electrode position errors are dominant; in that case, the better method depends on the experimental conditions, i.e., the distance between the insulating boundary and the electrodes. Improvement to the accuracy of Hall Effect measurement results is crucial for nanoscale metrology, since surface scattering often leads to low carrier mobility.

This paper demonstrates the development of a methodology using the micro four-point probe (μ4PP) technique to electrically characterize single nanometer-wide fins arranged in dense arrays. We show that through the concept of carefully controlling the electrical contact formation process, the electrical measurement can be confined to one individual fin although the used measurement electrodes physically contact more than one fin. We demonstrate that we can precisely measure the resistance of individual ca. 20 nm wide fins and that we can correlate the measured variations in fin resistance with variations in their nanometric width. Due to the demonstrated high precision of the technique, this opens the prospect for the use of μ4PP in electrical critical dimension metrology.

We present a comparative study of electrical measurements of graphene using terahertz time-domain spectroscopy in transmission and reflection mode, and compare the measured sheet conductivity values to electrical van der Pauw measurements made independently in three different laboratories. Overall median conductivity variations of up to 15% were observed between laboratories, which are attributed mainly to the well-known temperature and humidity dependence of non-encapsulated graphene devices. We conclude that terahertz time-domain spectroscopy performed in either reflection mode or transmission modes are indeed very accurate methods for mapping electrical conductivity of graphene, and that both methods are interchangeable within measurement uncertainties. The conductivity obtained via terahertz time-domain spectroscopy were consistently in agreement with electrical van der Pauw measurements, while offering the additional advantages associated with contactless mapping, such as high throughput, no lithography requirement, and with the spatial mapping directly revealing the presence of any inhomogeneities or isolating defects. The confirmation of the accuracy of reflection-mode removes the requirement of a specialized THz-transparent substrate to accurately measure the conductivity.

We present a breakthrough in micro-four-point probe (M4PP) metrology to substantially improve precision of transmission line (transfer length) type measurements by application of advanced electrode position correction. In particular, we demonstrate this methodology for the M4PP current-in-plane tunneling (CIPT) technique. The CIPT method has been a crucial tool in the development of magnetic tunnel junction (MTJ) stacks suitable for magnetic random-access memories for more than a decade. On two MTJ stacks, the measurement precision of resistance-area product and tunneling magnetoresistance was improved by up to a factor of 3.5 and the measurement reproducibility by up to a factor of 17, thanks to our improved position correction technique.

Atomic layer deposition of ruthenium is studied as a barrierless metallization solution for future sub-10 nm interconnect technology nodes. We demonstrate the void-free filling in sub-10 nm wide single damascene lines using an ALD process in combination with 2.5 Å of ALD TiN interface and postdeposition annealing. At such small dimensions, the ruthenium effective resistance depends less on the scaling than that of Cu/barrier systems. Ruthenium effective resistance potentially crosses the Cu curve at 14 and 10 nm according to the semiempirical interconnect resistance model for advanced technology nodes. These extremely scaled ruthenium lines show excellent electromigration behavior. Time-dependent dielectric breakdown measurements reveal negligible ruthenium ion drift into low-κ dielectrics up to 200 °C, demonstrating that ruthenium can be used as a barrierless metallization in interconnects. These results indicate that ruthenium is highly promising as a replacement to Cu as the metallization solution for future technology nodes.

We demonstrate wafer-scale, non-contact mapping of essential carrier transport parameters, carrier mobility (µdrift), carrier density (Ns), DC sheet conductance (σdc), and carrier scattering time (τsc) in CVD graphene, using spatially resolved terahertz time-domain conductance spectroscopy. σdc and τsc are directly extracted from Drude model fits to terahertz conductance spectra obtained in each pixel of 10 × 10 cm 2 maps with a 400 µm step size. σdc- and τsc-maps are translated into µdrift and Ns maps through Boltzmann transport theory for graphene charge carriers and these parameters are directly compared to van der Pauw device measurements on the same wafer. The technique is compatible with all substrate materials that exhibit a reasonably low absorption coefficient for terahertz radiation. This includes many materials used for transferring CVD graphene in production facilities as well as in envisioned products, such as polymer films, glass substrates, cloth, or paper substrates.

Carrier mobility and chemical doping level are essential figures of merit for graphene, and large-scale characterization of these properties and their uniformity is a prerequisite for commercialization of graphene for electronics and electrodes. However, existing mapping techniques cannot directly assess these vital parameters in a non-destructive way. By deconvoluting carrier mobility and density from non-contact terahertz spectroscopic measurements of conductance in graphene samples with terahertz-transparent backgates, we are able to present maps of the spatial variation of both quantities over large areas. The demonstrated non-contact approach provides a drastically more efficient alternative to measurements in contacted devices, with potential for aggressive scaling towards wafers/minute. The observed linear relation between conductance and carrier density in chemical vapour deposition graphene indicates dominance by charged scatterers. Unexpectedly, significant variations in mobility rather than doping are the cause of large conductance inhomogeneities, highlighting the importance of statistical approaches when assessing large-area graphene transport properties.

The electrical performance of graphene synthesized by chemical vapor deposition and transferred to insulating surfaces may be compromised by extended defects, including for instance grain boundaries, cracks, wrinkles, and tears. In this study, we experimentally investigate and compare the nano- and microscale electrical continuity of single layer graphene grown on centimeter-sized single crystal copper with that of previously studied graphene films, grown on commercially available copper foil, after transfer to SiO2 surfaces. The electrical continuity of the graphene films is analyzed using two noninvasive conductance characterization methods: ultrabroadband terahertz time-domain spectroscopy and micro four-point probe, which probe the electrical properties of the graphene film on different length scales, 100 nm and 10 μm, respectively. Ultrabroadband terahertz time-domain spectroscopy allows for measurement of the complex conductance response in the frequency range 1-15 terahertz, covering the entire intraband conductance spectrum, and reveals that the conductance response for the graphene grown on single crystalline copper intimately follows the Drude model for a barrier-free conductor. In contrast, the graphene grown on commercial copper foil shows a distinctly non-Drude conductance spectrum that is better described by the Drude-Smith model, which incorporates the effect of preferential carrier backscattering associated with extended, electronic barriers with a typical separation on the order of 100 nm. Micro four-point probe resistance values measured on graphene grown on single crystalline copper in two different voltage-current configurations show close agreement with the expected distributions for a continuous 2D conductor, in contrast with previous observations on graphene grown on commercial copper foil. The terahertz and micro four-point probe conductance values of the graphene grown on single crystalline copper shows a close to unity correlation, in contrast with those of the graphene grown on commercial copper foil, which we explain by the absence of extended defects on the microscale in CVD graphene grown on single crystalline copper. The presented results demonstrate that the graphene grown on single crystal copper is electrically continuous on the nanoscopic, microscopic, as well as intermediate length scales.

Experimental advances allow for the inclusion of multiple probes to measure the transport properties of a sample surface. We develop a theory of dual-probe scanning tunneling microscopy using a Green's function formalism, and apply it to graphene. Sampling the local conduction properties at finite length scales yields real space conductance maps which show anisotropy for pristine graphene systems and quantum interference effects in the presence of isolated impurities. Spectral signatures in the Fourier transforms of real space conductance maps include characteristics that can be related to different scattering processes. We compute the conductance maps of graphene systems with different edge geometries or height fluctuations to determine the effects of nonideal graphene samples on dual-probe measurements.

Fabrication of ultra-high aspect ratio exchangeable and customizable tips for atomic force microscopy (AFM) using lateral focused ion beam (FIB) milling is presented. While on-axis FIB milling does allow high aspect ratio (HAR) AFM tips to be defined, lateral milling gives far better flexibility in terms of defining the shape and size of the tip. Due to beam-induced deformation, it has so far not been possible to define HAR structures using lateral FIB milling. In this work we obtain aspect ratios of up to 45, with tip diameters down to 9 nm, by a deformation-suppressing writing strategy. Several FIB milling strategies for obtaining sharper tips are discussed. Finally, assembly of the HAR tips on a custom-designed probe as well as the first AFM scanning is shown.

We demonstrate a combination of micro four-point probe (M4PP) and non-contact terahertz time-domain spectroscopy (THz-TDS) measurements for centimeter scale quantitative mapping of the sheet conductance of large area chemical vapor deposited graphene films. Dual configuration M4PP measurements, demonstrated on graphene for the first time, provide valuable statistical insight into the influence of microscale defects on the conductance, while THz-TDS has potential as a fast, non-contact metrology method for mapping of the spatially averaged nanoscopic conductance on wafer-scale graphene with scan times of less than a minute for a 4-in. wafer. The combination of M4PP and THz-TDS conductance measurements, supported by micro Raman spectroscopy and optical imaging, reveals that the film is electrically continuous on the nanoscopic scale with microscopic defects likely originating from the transfer process, dominating the microscale conductance of the investigated graphene film.

We present measurements of the electronic properties of graphene using a repositionable micro four-point probe system, which we show here to have unique advantages over measurements made on lithographically defined devices; namely speed, simplicity and lack of a need to pattern graphene. Measurements are performed in ambient, vacuum and controlled environmental conditions using an environmental scanning electron microscope (SEM). The results are comparable to previous results for microcleaved graphene on silicon dioxide (SiO(2)). We observe a pronounced hysteresis of the charge neutrality point, dependent on the sweep rate of the gate voltage; and environmental measurements provide insight into the sensor application prospects of graphene. The method offers a fast, local and non-destructive technique for electronic measurements on graphene, which can be positioned freely on a graphene flake.

We introduce a highly compact fiber-optic Fabry-Pérot refractive index sensor integrated with a fluid channel that is fabricated directly near the tip of a 32 μm in diameter single-mode fiber taper. The focused ion beam technique is used to efficiently mill the microcavity from the fiber side and finely polish the end facets of the cavity with a high spatial resolution. It is found that a fringe visibility of over 15 dB can be achieved and that the sensor has a sensitivity of ~1731 nm/RIU (refractive index units) and a detection limit of ~5.78 × 10(-6) RIU. This miniature integrated all-in-fiber optofludic sensor may find use in minimal-invasive biomedical applications.

Nano- and microelectromechanical structures for in situ operation in a transmission electron microscope (TEM) were fabricated with a turnaround time of 20 min and a resolution better than 100 nm. The structures are defined by focused ion beam (FIB) milling in 135 nm thin membranes of single crystalline silicon extending over the edge of a pre-fabricated silicon microchip. Four-terminal resistance measurements of FIB-defined nanowires showed at least two orders of magnitude increase in resistivity compared to bulk. We show that the initial high resistance is due to amorphization of silicon, and that current annealing recrystallizes the structure, causing the electrical properties to partly recover to the pristine bulk resistivity. In situ imaging of the annealing process revealed both continuous and abrupt changes in the crystal structure, accompanied by instant changes of the electrical conductivity. The membrane structures provide a simple way to design electron-transparent nanodevices with high local temperature gradients within the field of view of the TEM, allowing detailed studies of surface diffusion processes. We show two examples of heat-induced coarsening of gold on a narrow freestanding bridge, where local temperature gradients are controlled via the electrical current paths. The separation of device processing into a one-time batch-level fabrication of identical, generic membrane templates, and subsequent device-specific customization by FIB milling, provides unparalleled freedom in device layout combined with very short effective fabrication time. This approach significantly speeds up prototyping of nanodevices such as resonators, actuators, sensors and scanning probes with state-of-art resolution.

Background: Many clinicians and researchers believe that there are subgroups of people with spinal pain who respond differently to treatment and have different prognoses. There has been considerable interest in this topic recently. However, problems occur when conclusions about subgroups are made that are inappropriate given the randomized controlled trial design used. The research design to choose, when developing a study protocol that investigates the effect of treatment subgroups, depends on the particular research question. Similarly, the inferences that can be drawn from an existing study will vary, depending on the design of the trial., Objectives: This paper discusses the randomized controlled trial designs that are suitable to answer particular questions about treatment subgroups. It focuses on trial designs that are suitable to answer four questions: (1) 'Is the treatment effective in a pre-specified group of patients?'; (2) 'Are outcomes of treatment applied using a subgrouping clinical reasoning process, better than a control treatment?'; (3) 'Are the outcomes for a patient subgroup receiving a particular treatment (compared to a control treatment) better than for patients not in the subgroup who receive the same treatment?'; and (4) 'Are outcomes for a number of treatments better if those treatments are matched to patients in specific subgroups, than if the SAME treatments are randomly given to patients?'. Illustrative examples of these studies are provided., Conclusion: If the clinical usefulness of targeting treatments to subgroups of people is to be determined, an important step is a shared understanding of what different RCT designs can tell us about subgroups.

Background: A central element in the current debate about best practice management of non-specific low back pain (NSLBP) is the efficacy of targeted versus generic (non-targeted) treatment. Many clinicians and researchers believe that tailoring treatment to NSLBP subgroups positively impacts on patient outcomes. Despite this, there are no systematic reviews comparing the efficacy of targeted versus non-targeted manual therapy and/or exercise. This systematic review was undertaken in order to determine the efficacy of such targeted treatment in adults with NSLBP., Method: MEDLINE, EMBASE, Current Contents, AMED and the Cochrane Central Register of Controlled Trials were electronically searched, reference lists were examined and citation tracking performed. Inclusion criteria were randomized controlled trials of targeted manual therapy and/or exercise for NSLPB that used trial designs capable of providing robust information on targeted treatment (treatment effect modification) for the outcomes of activity limitation and pain. Included trials needed to be hypothesis-testing studies published in English, Danish or Norwegian. Method quality was assessed using the criteria recommended by the Cochrane Back Review Group., Results: Four high-quality randomized controlled trials of targeted manual therapy and/or exercise for NSLBP met the inclusion criteria. One study showed statistically significant effects for short-term outcomes using McKenzie directional preference-based exercise. Research into subgroups requires much larger sample sizes than traditional two-group trials and other included studies showed effects that might be clinically important in size but were not statistically significant with their samples sizes., Conclusions: The clinical implications of these results are that they provide very cautious evidence supporting the notion that treatment targeted to subgroups of patients with NSLBP may improve patient outcomes. The results of the studies included in this review are too patchy, inconsistent and the samples investigated are too small for any recommendation of any treatment in routine clinical practice to be based on these findings. The research shows that adequately powered controlled trials using designs capable of providing robust information on treatment effect modification are uncommon. Considering how central the notion of targeted treatment is to manual therapy principles, further studies using this research method should be a priority for the clinical and research communities.

We show that accurate sheet resistance measurements on small samples may be performed using microfour-point probes without applying correction factors. Using dual configuration measurements, the sheet resistance may be extracted with high accuracy when the microfour-point probes are in proximity of a mirror plane on small samples with dimensions of a few times the probe pitch. We calculate theoretically the size of the "sweet spot," where sufficiently accurate sheet resistances result and show that even for very small samples it is feasible to do correction free extraction of the sheet resistance with sufficient accuracy. As an example, the sheet resistance of a 40 microm (50 microm) square sample may be characterized with an accuracy of 0.3% (0.1%) using a 10 microm pitch microfour-point probe and assuming a probe alignment accuracy of +/-2.5 microm.

Nanorobotic handling of carbon nanotubes (CNTs) using microgrippers is one of the most promising approaches for the rapid characterization of the CNTs and also for the assembly of prototypic nanotube-based devices. In this paper, we present pick-and-place nanomanipulation of multi-walled CNTs in a rapid and a reproducible manner. We placed CNTs on copper TEM grids for structural analysis and on AFM probes for the assembly of AFM super-tips. We used electrothermally actuated polysilicon microgrippers designed using topology optimization in the experiments. The microgrippers are able to open as well as close. Topology optimization leads to a 10-100 times improvement of the gripping force compared to conventional designs of similar size. Furthermore, we improved our nanorobotic system to offer more degrees of freedom. TEM investigation of the CNTs shows that the multi-walled tubes are coated with an amorphous carbon layer, which is locally removed at the contact points with the microgripper. The assembled AFM super-tips are used for AFM measurements of microstructures with high aspect ratios.

Free-standing epitaxially grown nanowires provide a controlled growth system and an optimal interface to the underlying substrate for advanced optical, electrical, and mechanical nanowire device connections. Nanowires can be grown by vapor-phase epitaxy (VPE) methods such as chemical vapor deposition (CVD) or metal organic VPE (MOVPE). However, VPE of semiconducting nanowires is not compatible with several microfabrication processes due to the high synthesis temperatures and issues such as cross-contamination interfering with the intended microsystem or the VPE process. By selectively heating a small microfabricated heater, growth of nanowires can be achieved locally without heating the entire microsystem, thereby reducing the compatibility problems. The first demonstration of epitaxial growth of silicon nanowires by this method is presented and shows that the microsystem can be used for rapid optimization of VPE conditions. The important issue of the cross-contamination of other parts of the microsystem caused by the local growth of nanowires is also investigated by growth of GaN near previously grown silicon nanowires. The design of the cantilever heaters makes it possible to study the grown nanowires with a transmission electron microscope without sample preparation.