Sheet Resistance Determination Using Symmetric Structures With Contacts of Finite Size

Cornils, M.; Doelle, M.; Oliver, Paul

doi:10.1109/ted.2007.906219

Cited by 25 publications

(11 citation statements)

References 19 publications

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“…The first example has the following parameters: N = 4, 1 10 2 m a = µ , 2 10 m a = − π µ , 3 10 m a = − µ , 4 . With (C3b) we may compute the electric field inside the Hall region (Table C1).…”

Section: Appendix Cmentioning

confidence: 99%

“…Both cases can be readily computed in closed form. Then the authors found a smart power law, which interpolates the sheet resistance up to an astonishing accuracy of ±0.02% for all contact sizes ( (7) in [4], also (24) in [5]).…”

Section: Introductionmentioning

confidence: 97%

“…Van-der-Pauw measurement on Hall plates with 90˚ symmetry at zero magnetic field was discussed in [4]. There the authors focused on Hall plates with point-sized contacts and on their complementary counterparts of large contacts with no insulating boundaries in-between.…”

Section: Introductionmentioning

confidence: 99%

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Relations between Hall Plates with Complementary Contact Geometries

Ausserlechner¹

2019

JAMP

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Singly connected Hall plates with N peripheral contacts can be mapped onto the upper half of the z-plane by a conformal transformation. Recently, Homentcovschi and Bercia derived the General Formula for the electric field in this region. We present an alternative intuitive derivation based on conformal mapping arguments. Then we apply the General Formula to complementary Hall plates, where contacts and insulating boundaries are swapped. The resistance matrix of the complementary device at reverse magnetic field is expressed in terms of the conductance matrix of the original device at non-reverse magnetic field. These findings are used to prove several symmetry properties of Hall plates and their complementary counterparts at arbitrary magnetic field. Journal of Applied Mathematics and Physics mentary device (see (13a) in [6]).In [7] plane singly-connected Hall plates with four peripheral contacts and equal input and output resistances were considered. If magnetic field is impressed on such a device, it has the same output voltage as its complementary device, provided both are supplied by the same voltage source (see Figure 7 in this work). This was conjectured in [8] and proven in [7] and [9] for weak applied magnetic field (see (50) in [8], see Section 4, Appendix B, and Figure 8, all in [7]). Numerical inspection suggests that this also holds for strong magnetic field, but a rigorous proof has not been given so far. In [8] it was also implicitly mentioned that the product of input resistances of original and complementary Hall plates of that particular symmetry (i.e., input resistance equals output resistance) at zero magnetic field equals twice the square of the sheet resistance (see the paragraph after (50) in [8]).Complementary Hall plates with three extended contacts on the perimeter were studied in [10]. If such a device has single mirror symmetry, also its complementary device has single mirror symmetry. Then-analogous to above-the change of the potentials on the output contacts due to reversal of magnetic field polarity are identical in both original and complementary devices, if both devices are supplied with the same supply voltage on the other two contacts, and if the magnetic field is weak (see also Figure 6 in this work). This property also means that the ratio of Hall output signal over thermal noise under the constraint of fixed supply voltage and fixed input resistance is the same in the original Hall plate and in the complementary Hall plate [10] [11].In Section 2 we reconsider the General Formula of [12] for the electric field in the upper half of the z-plane with N contacts on the real axis. Thereby, we present a different derivation than the one given in [12]. This new approach shows how the stagnation points are linked to the electric field in the Hall plate. From this result we derive the resistance matrix of a general device at arbitrary magnetic field in Section 3. This is similar to [12]. In Section 4 we link the resistance matrices of original device and complementary device at reverse...

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Section: Appendix Cmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Relations between Hall Plates with Complementary Contact Geometries

Ausserlechner¹

2019

JAMP

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“…Although Vertical Hall effect devices of Figure 1(c) have different orientations than Hall plates of Figure 1(a) & Figure 1(b), the plane which we refer to is orthogonal to the detectable magnetic field B ⊥ in both cases. in λ is a ratio of two parameters sh , in R R which are accessible to electricalmeasurements: in R is simply measured with an Ohm-meter and sh R is measured according to a generalization of van der Pauw's method[10]…”

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confidence: 99%

An Analytical Theory of the Signal-to-Noise Ratio of Hall Plates with Four Contacts and a Single Mirror Symmetry

Ausserlechner¹

2018

JAMP

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This work gives an analytical theory of the signal-to-thermal-noise ratio (SNR) of classical Hall plates with four contacts at small magnetic field. In contrast to previous works, the symmetry of the Hall plates is reduced to only a single mirror axis, whereby the average of potentials of the two output contacts off this mirror axis differs from the average of potentials at the two supply contacts on the mirror axis, i.e. the output common mode differs from 50%. Surprisingly, at fixed power dissipated in the Hall plate, the maximum achievable SNR is only 9% smaller for output common modes of 30% and 70% when compared to the overall optimum at output common modes of 50%. The theory is applied to Vertical Hall effect devices with three contacts on the top surface and one contact being the buried layer in a silicon BiC-MOS process. Geometries are found with large contacts and only a moderate loss in SNR.

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“…홀 플레이트의 오프셋 및 1/f 잡음은 수십 mV로 낮은 홀 전압 출력 환경에서 센서의 정확도를 감소시키는 핵 심요소이다. 이러한 오프셋 및 1/f 잡음을 감소시키기 위해 다양한 구조의 홀 플레이트 연구 [5] , 두 개 이상의 홀 플레이트 어레이(orthogonal array) 기반 불균등 저 항성분 제거기술 [6] 및 전류 스피닝(current spinning)기 반 잡음성분 제거기술 [7] 등 다양한 연구가 진행되었다. .…”

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A Design Of Cross-Shpaed CMOS Hall Plate And Offset, 1/f Noise Cancelation Technique Based Hall Sensor Signal Process System

Hur¹,

Jung²,

Lee³

et al. 2016

Journal of the Institute of Electronics and Information Enginee

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본 논문은 CMOS 자기센서(hall Sensor) AbstractThis paper describes an offset and 1/f noise cancellation technique based hall sensor signal processor. The hall sensor outputs a hall voltage from the input magnetic field, which direction is orthogonal to hall plate. The two major elements to complete the hall sensor operation are: the one is a hall sensor to generate hall voltage from input magentic field, and the other one is a hall signal process system to cancel the offset and 1/f noise of hall signal. The proposed hall sensor splits the hall signal and unwanted signals(i.e. offset and 1/f noise) using a spinning current biasing technique and chopper stabilizer. The hall signal converted to 100 kHz and unwanted signals stay around DC frequency pass through chopper stabilizer. The unwanted signals are bloked by highpass filter which, 60 kHz cut off freqyency. Therefore only pure hall signal is enter the ADC(analog to dogital converter) for digitalize. The hall signal and unwanted signal at the output of an amplifer and highpass filter, which increase the power level of hall signal and cancel the unwanted signals are -53.9 dBm @ 100 kHz and -101.3 dBm @ 10 kHz. The ADC output of hall sensor signal process system has -5.0 dBm hall signal at 100 kHz frequency and -55.0 dBm unwanted signals at 10 kHz frequency , 이와 함께 자기센서의 선형성 향상을 위 (798)

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Sheet Resistance Determination Using Symmetric Structures With Contacts of Finite Size

Cited by 25 publications

References 19 publications

Relations between Hall Plates with Complementary Contact Geometries

Relations between Hall Plates with Complementary Contact Geometries

An Analytical Theory of the Signal-to-Noise Ratio of Hall Plates with Four Contacts and a Single Mirror Symmetry

A Design Of Cross-Shpaed CMOS Hall Plate And Offset, 1/f Noise Cancelation Technique Based Hall Sensor Signal Process System

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