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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-free-standing bi-layer graphene grown on 4 inch 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 one order of magnitude across a 4 inch 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.

We present a new micro Hall effect measurement method using non-equidistant electrodes. We show theoretically and verify experimentally that it is advantageous to use non-equidistant electrodes for samples with low Hall sheet resistance. We demonstrate the new method by experiments where Hall sheet carrier densities and Hall mobilities of Ruthenium thin films (3-30 nm) are determined. The measurements show that it is possible to measure Hall mobilities as low as 1 cm2V1s1 with a relative standard deviation of 2-3%. We show a linear relation between measured Hall sheet carrier density and film thickness. Thus, the method can be used to monitor thickness variations of ultra-thin metal films.

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.

We have studied the behavior of micro four-point probe (M4PP) measurements on two-dimensional (2D) sheets composed of grains of varying size and grain boundary resistivity by Monte Carlo based finite element (FE) modelling. The 2D sheet of the FE model was constructed using Voronoi tessellation to emulate a polycrystalline sheet, and a square sample was cut from the tessellated surface. Four-point resistances and Hall effect signals were calculated for a probe placed in the center of the square sample as a function of grain density n and grain boundary resistivity ρGB. We find that the dual configuration sheet resistance as well as the resistance measured between opposing edges of the square sample have a simple unique dependency on the dimension-less parameter √nρGBG0, where G0 is the sheet conductance of a grain. The value of the ratio RA/RB between resistances measured in A- and B-configurations depends on the dimensionality of the current transport (i.e., one- or two-dimensional). At low grain density or low grain boundary resistivity, two-dimensional transport is observed. In contrast, at moderate grain density and high grain resistivity, one-dimensional transport is seen. Ultimately, this affects how measurements on defective systems should be interpreted in order to extract relevant sample parameters. The Hall effect response in all M4PP configurations was only significant for moderate grain densities and fairly large grain boundary resistivity.

Novel designs of planar Hall effect bridge sensors optimized for magnetic bead detection are presented and characterized. By constructing the sensor geometries appropriately, the sensors can be tailored to be sensitive to an external magnetic field, the magnetic field due to beads being magnetized by the sensor self-field or a combination thereof. The sensors can be made nominally insensitive to small external magnetic fields, while being maximally sensitive to magnetic beads, magnetized by the sensor self-field. Thus, the sensor designs can be tailored towards specific applications with minimal influence of external variables. Three different sensor designs are analyzed theoretically. To experimentally validate the theoretical signals, two sets of measurements are performed. First, the sensor signals are characterized as function of an externally applied magnetic field. Then, measurements of the dynamic magnetic response of suspensions of magnetic beads with a nominal diameter of 80 nm are performed. Furthermore, a method to amplify the signal by appropriate combinations of multiple sensor segments is demonstrated.

In a recent paper, Sinha et al. compared sensitivities of planar Hall effect sensors with different geometries that are all based on the anisotropic magnetoresistance of permalloy. They write that the sensitivity of a planar Hall effect sensor with a ring geometry is a factor of √2 larger than the sensitivity of the so-called planar Hall effect bridge (PHEB) sensor of equal size. Osterberg et al do not agree on the signal calculation for a ring sensor derived by Sinha et al. and claim that this adversely affects the results.

We present on-chip Brownian relaxation measurements on a logarithmic dilution series of 40 nm beads dispersed in water with bead concentrations between 16 mu g/ml and 4000 mu g/ml. The measurements are performed using a planar Hall effect bridge sensor at frequencies up to 1 MHz. No external fields are needed as the beads are magnetized by the field generated by the applied sensor bias current. We show that the Brownian relaxation frequency can be extracted from fitting the Cole-Cole model to measurements for bead concentrations of 64 mu g/ml or higher and that the measured dynamic magnetic response is proportional to the bead concentration. For bead concentrations higher than or equal to 500 mu g/ml, we extract a hydrodynamic diameter of 47(1) nm for the beads, which is close to the nominal bead size of 40 nm. Furthermore, we study the signal vs. bead concentration at a fixed frequency close to the Brownian relaxation peak and find that the signal from bead suspensions with concentrations down to 16 mu g/ml can be resolved. (C) 2012 American Institute of Physics.

The low-frequency characteristics of planar Hall effect bridge sensors are investigated as function of the sensor bias current and the applied magnetic field. The noise spectra reveal a Johnson-like spectrum at high frequencies, and a 1/f-like excess noise spectrum at lower frequencies, with a knee frequency of around 400Hz. The 1/f-like excess noise can be described by the phenomenological Hooge equation with a Hooge parameter of γH=0.016. The detectivity is shown to depend on the total length, width and thickness of the bridge branches. The detectivity is improved by the square root of the length increase. Moreover, the detectivity is shown to depend on the amplitude of the applied magnetic field, revealing a magnetic origin to part of the 1/f noise.

Sheet resistance, carrier mobility, and sheet carrier density are important parameters in semiconductor production, and it is therefore important to be able to rapidly and accurately measure these parameters even on small samples or pads. The interpretation of four-point probe measurements on small pads is non-trivial. In this paper we discuss how conformal mapping can be used to evaluate theoretically expected measurement values on small pads. Theoretical values calculated from analytical mappings of simple geometries are compared to the values found from the numerical conformal mapping of a square onto the infinite half-plane, where well-established solutions are known. Hall effect measurements are performed to show, experimentally, that it is possible to measure Hall mobility in less than one minute on squares as small as 7070 lm2 with a deviation of 66.5% on a 1r level from accurate reference measurements, when only small sheet resistance variations are present. For samples with a sheet resistance variation of more than 5%, a more time consuming method must be used. Here, the theoretically expected measurement values are computed based on the sheet resistance variation using a finite element method. This more accurate method has an experimental repeatability of 61.6% even on inhomogeneous samples.

Hall mobility and sheet carrier density are important parameters to monitor in advanced semiconductor production. If micro Hall effect measurements are done on small pads in scribe lines, these parameters may be measured without using valuable test wafers. We report how Hall mobility can be extracted from micro four-point measurements performed on a rectangular pad. The dimension of the investigated pad is 400 × 430 ¿m2, and the probe pitches range from 20 ¿m to 50 ¿m. The Monte Carlo method is used to find the optimal way to perform the Hall measurement and extract Hall mobility most accurate in less than a minute. Measurements are performed on shallow trench isolation patterned silicon wafers to verify the results from the Monte Carlo method.

In this paper, we discuss a probe spacing dependence study in order to estimate the accuracy of micro four-point probe measurements on inhomogeneous samples. Based on sensitivity calculations, both sheet resistance and Hall effect measurements are studied for samples (e.g. laser annealed samples) with periodic variations of sheet resistance, sheet carrier density, and carrier mobility. With a variation wavelength of ¿, probe spacings from 0.0012 to 1002 have been applied to characterize the local variations. The calculations show that the measurement error is highly dependent on the probe spacing. When the probe spacing is smaller than 1/40 of the variation wavelength, micro four-point probes can provide an accurate record of local properties with less than 1% measurement error. All the calculations agree well with previous experimental results.

The accumulation of magnetic beads by gravitational sedimentation and magnetic capture on a planar Hall-effect sensor integrated in a microfluidic channel is studied systematically as a function of the bead concentration, the fluid flow rate, and the sensor bias current. It is demonstrated that the sedimentation flux is proportional to the bead concentration and has a power law relation to the fluid flow rate. The mechanisms for the bead accumulation are investigated and it is found that gravitational sedimentation dominates the bead accumulation, whereas the stability of the sedimented beads against the fluid flow is defined by the localized magnetic fields from the sensor.