Martin Cornils

Explicit connection between sample geometry and Hall response

The linear galvanomagnetic response of four-contact devices to the presence of a magnetic field B is deduced from two normalized current densities ja0 and jb0 in the device under rotated biasing conditions in the absence of B. When B and the transport coefficients are homogeneous, the integrals of the scalar and cross products of ja0 and jb0 over the device volume fully capture the influence of the device geometry on the measured offset signal and Hall voltage, respectively. As a consequence, the galvanomagnetic response of homogeneous planar devices exhibiting fourfold rotational symmetry is parameterized by a single geometric parameter.

Sheet Resistance Determination Using Symmetric Structures With Contacts of Finite Size

This paper proposes an extension of van der Pauws celebrated method for the extraction of the sheet resistance Rsq of planar homogeneously conducting samples with four point-like contacts to symmetric samples with contacts of finite length. Using the method, Rsq can be extracted, e.g., from symmetric integrated Hall plates and stress sensors, without having to resort to dedicated van der Pauw structures. First, the analog of van der Pauws formula for arbitrarily shaped samples with four extended contacts separated by point-like insulations is derived. Based on this and van der Pauws original result, an interpolation formula applicable to symmetric samples with contacts of arbitrary length is constructed. The new formalism was successfully put to the test using ten widely differing CMOS sensor structures, with contacts covering between 10.1% and 91.3% of the device periphery. The extracted Rsq values lie within the range specified by the CMOS foundry used for the fabrication of the samples and show a relative standard deviation of 1.04%.

Fully symmetric vertical hall devices in CMOS technology

We present a novel CMOS-integrated, vertical Hall sensor (VHS) with optimized symmetry for the measurement of in-plane magnetic field components. Due to the junction field effect, conventional five-contact VHS (5CVHS) suffer from considerable offsets caused by their inherent electrical asymmetry under contact permutations. The novel device achieves a higher degree of symmetry by the appropriate connection of four identical three-contact elements. As a result, with a bias voltage of 3.5 V and after current switching a mean residual offset of 2.5 μV with a standard deviation of 33.8 μV is achieved among 45 samples on an 8-inch wafer. This represents an improvement by a factor of more than 4 over 5CVHS fabricated on the same wafer. In addition, the power consumption is reduced by 47%.

Reverse-magnetic-field reciprocity in conductive samples with extended contacts

This paper reports on the extension of the reverse-magnetic-field reciprocity (RMFR) principle to electrically linear devices with arbitrary shape and extended contacts. The RMFR principle is a consequence of Onsager’s relation for the conductivity tensor depending on the magnetic field. It states the identity of resistance measurements on linearly conductive four-contact samples in a magnetic field B upon contact switching and magnetic field reversal. The previously available proof was restricted to samples with pointlike contacts and thus did not directly apply to real devices. Implications for two-contact and three-contact structures, for planar and symmetric devices, and the use of the structures as magnetic sensors are discussed. Experimental results obtained with complementary metal oxide semiconductor test structures of different geometries are in excellent agreement with the theoretical findings.

How to Extract the Sheet Resistance and Hall Mobility From Arbitrarily Shaped Planar Four-Terminal Devices With Extended Contacts

Van der Pauws method enables the sheet resistance Rsq and the Hall mobility μH to be extracted from arbitrarily shaped simply connected planar samples with four peripheral pointlike contacts. This paper generalizes the method for devices with extended contacts. It is found that Rsq and μH can be extracted using only six resistance measurements in the absence of a magnetic field and a single magnetic sensitivity measurement. Conversely, if the μH of a simply connected planar conducting device with peripheral contacts is known, the magnetic sensitivity of the device can be predicted based on six resistance measurements in the absence of a magnetic field, without any further knowledge of the device geometry. The new method is applied to a variety of differently shaped diffused silicon n-wells with peripheral contacts. The extracted sheet resistance and Hall mobility values show excellent consistency and are in agreement with the fabrication specifications.

Sheet resistance determination of electrically symmetric planar four-terminal devices with extended contacts

This paper reports an analytic method to determine the sheet resistance Rsq of symmetric planar four-terminal devices based on resistance measurements. Using the technique of conformal mapping it is first shown that any such device is electrically equivalent to a corresponding symmetric unit disk with the same Rsq and invariant under rotations by 90°. Two independent resistances measurable on these devices are expressed analytically as a function of Rsq and of the contact opening angle α. These two resistances fully characterize the electrical properties of such planar conductive devices. A simple procedure to extract both α and Rsq from the resistance values is then presented. These findings are corroborated by the experimental characterization of four-contact devices of ten different geometries fabricated using a commercial complementary metal oxide semiconductor process. From these widely different devices, the sheet resistance of a n-well is extracted to be 1042Ω with a relative uncertainty of only 0.45%.

Cantilever-Based Tactile Sensor with Improved Sensitivity for Dimensional Metrology of Deep Narrow Drillings

The paper reports on a tactile force sensor for the dimensional metrology of deep narrow drillings. The sensor consists of an up to 7-mm-long cantilever with a width of 150 mum suspended by a thin silicon membrane hinge comprising an implanted piezoresistive stress sensor. The device is microstructured using deep reactive etching of single-crystal silicon. A quadratic p-well with four peripheral p+-contacts serves as stress sensor element. To investigate and improve the stress sensitivity of these elements, 90times90 mum2 p-wells comprising non-conducting islands of different sizes were implemented. In comparison to sensor elements without island, the introduction of a non-conducting region of 60times60 mum2 improves the sensitivity by 41% consistent with Finite Element simulations. Depending on the size of the island, force sensitivities between 7.74 mV/V/mN and 10.9 mV/V/mN were achieved.

The magnetic calibration of arbitrarily shaped Hall sensors in the absence of magnetic fields

This paper presents a method to calibrate arbitrarily shaped planar Hall plates without the need for applying a magnetic field. Using the method of conformal mapping, it is shown that magnetic sensitivity parameters can be extracted from six independent resistance values measurable in the absence of a perpendicular magnetic field B⊥. Remarkably, no prior knowledge of the device geometry is required. As a consequence, numerical simulations of Hall plate sensitivities can be performed by solving electrical conduction problems without magnetic effects, and using the appropriate value of the Hall mobility μH. Experimental data measured with CMOS sensors corroborate the theoretical findings.

The magnetic calibration and optimization of symmetric hall plates may be accomplished even in the absence of a magnetic field

This paper presents a method to calibrate symmetric Hall plates with four terminals without the need for applying a magnetic field. We show that magnetic sensitivity parameters can be extracted from two independent resistance measurements in the absence of a perpendicular magnetic field Bperp. As a consequence, for known Hall mobility muH the optimization of symmetric Hall sensors is reduced to electrical conduction problems at Bperp = 0, thus avoiding finite-element simulations including magnetic effects. The results are obtained using the method of conformal mapping. They were verified using finite-element analysis. Experimental results from CMOS sensors are in excellent agreement with the theoretical predictions.

Sensor Calibration of Planar Four-Contact Devices with up to Two Extended Contacts

This paper reports on a novel method for the calibration of planar four-contact sensors making it possible to extract the sheet resistance Rsq of their conducting layer with minimal effort. We present extensions of van der Pauws method to determine Rsq holding for arbitrarily shaped four-terminal devices with one and two extended contacts. This is achieved by performing three and four electrical resistance measurements, respectively, on these devices. The results are obtained using the method of conformal mapping in combination with the method of images. Using finite-element analysis, our findings were verified to hold with a relative accuracy of better than 0.055%. Experimental tests with differently shaped structures corroborate the theoretical results.