# Hall Effect Sensors Design, Integration and Behavior Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Hall Effect Sensors Design and Integration

#### 2.1 Hall Effect Sensors Basic Considerations

_{H}is the scattering factor of Silicon, (usually 1.15), n is the carrier density, t is the thickness of the active region, I

_{bias}is the biasing current, and B is the magnetic field induction, [7].

_{H }is the Hall angle [8].

#### 2.2. Hall Effect Sensors Geometry Selection and Design Guidelines

**Figure 2.**Guiding procedure for L and W selection for rectangular Hall Effect structures with small sensing contacts.

**Figure 3.**Variation of L/W with respect to the area A, for different small sensing contact sizes, s.

## 3. Experimental Section

#### 3.1. Hall Effect Sensor Measurements

_{0}, absolute sensitivity S

_{A}, offset drift, etc. The design parameters include L, W, and s, which stand for sensors length, width, and sensing contacts length respectively.

Geometry Type | Basic | Low-doped | L | XL | 45 Deg | Narrow Contacts | Borderless | Square | Optimum |
---|---|---|---|---|---|---|---|---|---|

Shape | |||||||||

R_{0} (kΩ) @ T=300 K, B=0 T | 2.3 | 5.6 | 2.2 | 2.2 | 2.1 | 2.5 | 1.3 | 4.9 | 1.5 |

S_{A} (V/T) @ Ibias = 1 mA | 0.0807 | 0.3392 | 0.0804 | 0.0806 | 0.0807 | 0.0822 | 0.0325 | 0.0884 | 0.0635 |

Offset drift (μT/°C) (4-phases current spinning) | 0.409 | 0.067 | 0.264 | 0.039 | 0.373 | 0.344 | 0.526 | 0.082 | 0.328 |

L, W (μm) of the Active Area (n-well) | L = 21.6 | L = 21.6 | L = 32.4 | L = 43.2 | L = 21.6 | L = 21.6 | L = 50 | L = 20 | L = 50 |

W = 9.5 | W = 9.5 | W = 14.25 | W = 19 | W = 9.5 | W = 9.5 | W = 50 | W = 20 | W = 50 | |

L/W | 2.27 | 2.27 | 2.27 | 2.27 | 2.27 | 2.27 | 1 | 1 | 1 |

s (μm) for Sensing Contacts | 8.8 | 8.8 | 13.55 | 18.3 | 8.8 | 1.5 | 2.3 | 2.3 | 4.7 |

#### 3.2. Offset Temperature Drift Measurement Results Using a DC Measurement Setup and Manual Phase Switching

_{p1,2,3,4}are the individual phases offsets.

**Figure 4.**Hall cells polarization for Greek-cross cells (

**a**), borderless cell (

**b**) and optimum cell (

**c**).

Phases | I_{bias} | V_{HALL} |
---|---|---|

(biasing) | (sensing) | |

Phase 1 | a to c | b to d |

Phase 2 | d to b | a to c |

Phase 3 | c to a | d to b |

Phase 4 | b to d | c to a |

_{bias }= 0.5 mA and I

_{bias }= 1 mA respectively. The samples were placed into an oven and the temperature was cycled between −40 and 125 °C. We can observe the parabolic temperature dependence of the residual offset.

**Figure 5.**Magnetic-equivalent offset vs. absolute temperature for the basic (

**left**) and L (

**right**) Hall cells, for I

_{bias }= 0.5 mA.

**Figure 6.**Magnetic-equivalent offset vs. absolute temperature for the XL Hall cell, for I

_{bias }= 0.5 mA (

**left**) and I

_{bias }= 1 mA (

**right**).

**Figure 7.**Magnetic-equivalent offset vs. absolute temperature for the borderless Hall cell, for I

_{bias }= 0.5 mA (

**left**) and I

_{bias }= 1 mA (

**right**).

#### 3.3. Room Temperature Offset Measurement Results Using an Automated AC Measurement Setup

## 4. Three-Dimensional Physical Simulations

^{15}cm

^{−3}is used while the active n-well region is implanted with an Arsenic doping concentration of 1.5 × 10

^{17}cm

^{−3}with a Gaussian profile. The thickness of the p-substrate is 5 μm while the n-profile implantation depth is 1 μm. In this case, the average mobility is 0.0630 m

^{2}·V

^{−1}·s

^{−1}.

## 5. Results and Discussion

Hall Structure | L (μm) | W (μm) | s (μm) |
---|---|---|---|

Basic | 21.6 | 9.5 | 8.8 |

L | 32.4 | 14.25 | 13.55 |

XL | 43.2 | 19 | 18.3 |

Borderless | 50 | 50 | 4.7 |

Optimum | 50 | 50 | 2.3 |

## 6. Conclusions

## References

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**MDPI and ACS Style**

Paun, M.-A.; Sallese, J.-M.; Kayal, M. Hall Effect Sensors Design, Integration and Behavior Analysis. *J. Sens. Actuator Netw.* **2013**, *2*, 85-97.
https://doi.org/10.3390/jsan2010085

**AMA Style**

Paun M-A, Sallese J-M, Kayal M. Hall Effect Sensors Design, Integration and Behavior Analysis. *Journal of Sensor and Actuator Networks*. 2013; 2(1):85-97.
https://doi.org/10.3390/jsan2010085

**Chicago/Turabian Style**

Paun, Maria-Alexandra, Jean-Michel Sallese, and Maher Kayal. 2013. "Hall Effect Sensors Design, Integration and Behavior Analysis" *Journal of Sensor and Actuator Networks* 2, no. 1: 85-97.
https://doi.org/10.3390/jsan2010085