01. The working principle of Hall sensor

1 ● Hall effect

The physical basis of the Hall sensor is the Hall effect. As shown in Figure 1, on a cuboid conductive plate with length l, width b, and thickness d, electrodes are installed on the left, right, front, and rear sides. A current I is passed in the length direction, and a magnetic field with a magnetic induction intensity B is applied in the thickness direction.

■ Figure 1 Schematic diagram of the Hall effect

The free electrons in the conductive plate move directionally along the opposite direction of the current, with an average speed of v. Under the action of a magnetic field, electrons are subject to the Lorentz force. The magnitude of the Lorentz force fL on each electron is

Among them, e is the electric charge of an electron, e=1.6×10 -19 C. According to the left-hand rule, it can be judged that the direction of the Lorentz force fL is from outside to inside.

In addition to directional movement, electrons also drift inward under the action of Lorentz force. As a result, electrons are accumulated on the inner surface of the conductive plate, and positive charges are accumulated on the outer surface. In this way, an additional electric field EH is formed in the conductive plate. called the Hall electric field.

Under the action of the Hall electric field, electrons will experience an electric field force in the opposite direction to the Lorentz force

The role of this force prevents the continued accumulation of charges. When the accumulation of electrons in the conductive plate reaches a dynamic balance, the charge no longer increases, and the Lorentz force and electric field force on the electrons are equal in size, that is

simplified

At this time, a potential difference is generated between the outer surface and the inner surface of the conductive plate, and the magnitude is

Putting the formula in:

When a current-carrying conductor or semiconductor is in a magnetic field perpendicular to the current, a potential difference will be generated at its two ends perpendicular to the direction of the current and the direction of the magnetic field. This phenomenon is called the Hall effect, and the electromotive force generated by the Hall effect is called Hall electromotive force, the cuboid conductive plate is called Hall plate. The Hall effect is the result of the Lorentz force on the moving charge in the magnetic field, and the sensor based on the Hall effect is called a Hall sensor.

It can be seen from the above formula that the Hall electromotive force UH has a linear relationship with the magnetic induction B, therefore, B can be obtained by measuring UH. This is how Hall sensors work.

1879年，美国物理学家霍尔（Edwin H. Hall，1855-1938）在研究金属导电机制时发现了霍尔效应，但是，由于金属材料的霍尔效应太弱，霍尔效应没有得到应用。随着半导体技术、材料科学和电子技术的发展，使用半导体材料制作的霍尔片具有明显的霍尔效应，并且出现了高强度的恒定磁体以及工作于小电压输出的信号调节电路，霍尔式传感器迅速发展起来了。霍尔式传感器用于测量电磁、电力、加速度、振动等物理量，应用非常广泛。例如，汽车上就使用了多种霍尔式传感器。

2●霍尔灵敏度

设导电板中自由电子浓度为n，电子定向运动的平均速度为v，则电流的大小为

霍尔片在单位控制电流和单位磁感应强度时产生的霍尔电动势，称为霍尔灵敏度，记为KH，即

代入公式，得

从公式可见，霍尔灵敏度与霍尔片的厚度d成反比，因此，常把霍尔片做成薄片状，其厚度一般为0.1~0.2mm。另外，霍尔灵敏度还与自由电子浓度n成反比。因为金属的自由电子浓度过高，所以，金属不适合用于制作霍尔片。

在使用霍尔传感器进行测量时，常用恒压源提供激励电流，电源电压是一个常量，U=El。设霍尔片材料的迁移率为μ，则电子在电场中的平均迁移速度为v=μE，从而有

结合以上公式可得：

从以上公式可见，霍尔灵敏度与载流子的迁移率µ成正比。因为电子迁移率远大于空穴，所以，常用N型半导体材料制作霍尔片。

3●霍尔元件

霍尔元件的结构如图2所示，由霍尔片、4根引线和壳体组成。在霍尔片长度方向的两侧焊有两根控制电流引线“输入1”和“输入2”，它们在薄片上的焊点称为激励电极。在霍尔片宽度方向的两侧焊有两根输出引线“输出1”和“输出2”，它们在薄片上的焊点称为霍尔电极。霍尔元件的壳体用非导磁金属、陶瓷或环氧树脂封装而成。