Analytical solution for the electric field in Hall plates

Homentcovschi, Dorel; Bercia, R.

doi:10.1007/s00033-018-0989-7

Cited by 16 publications

(27 citation statements)

References 14 publications

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“…Thus, contacts 2 to N are lined up from left to right and contact 1 is at infinity. According to [12] the complex electric field ( ) E z in the point z x iy = + with 0 y ≥ (i being the imaginary unit) is given by This is opposite to the definition in [12] and therefore a different sign shows up in (1c). The applied magnetic flux density B ⊥ perpendicular to the Hall plate is counted positive, when it points out of the drawing plane.…”

Section: Introductionmentioning

confidence: 97%

“…In [12] Homentcovschi and Bercia derived their General Formula (1a) in a formal, "mathematical" way. Here we present a more intuitive derivation, which also sheds light on the physical meaning of the coefficients n c .…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

mentioning

confidence: 95%

“…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.…”

mentioning

confidence: 95%

“…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 magnetic field.…”

mentioning

confidence: 96%

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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: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 95%

mentioning

confidence: 95%

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confidence: 96%

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