[Study] Homemade Hall Effect Sensor (PCB integrated)

The progress made in applied physics and electronics, helped to produce thousands of different sensors on the market. Some of them use a classic physics phenomenons (Thermopile, Hall-sensor, Moisture, etc..) or could be a mix of physics and microelectronics (Microphone, Pixel-Matrix, self-compensated sensors,etc..).

But the main feature of theses is that they are produced with Semi-Conductors materials in a Micro/Nano scale.

As you could imagine, no one, in the maker/DIY community, have a SC processing facility or the gears to produce 10nm lithography.

If we want to make the innovation more accessible and provide homemade solutions, we need to find out how we can produce sensor with civilians skills. It will not be as good as industrial ones but it’s still a first step.

As you guess, the studied sensor here is the Hall sensor.

As a quick reminder of the Hall effect here’s a schematic :

image5

The sensor is a semi conductive materials (see later) current provided (I), one side to another.

When we put a magnetic field (H) trough the plate (up or down), the Laplace Forces (Fm) moves the electrons aside of the current output-face. This create a polarization between the side faces. And because the flow need to be the same in input and output, the Hall polarization is created to compensate the forces.

That’s the voltage which need to be observed for linear magnetic measurement.

The Hall voltage is characterized with the law : {\displaystyle U_{H}=R_{H}{\frac {IB}{a}}}With : {\displaystyle R_{H}=-{\frac {1}{ne}}}
I -> Current in Amperes / B -> Magnetic field in Tesla / a -> the thickness of the plate
n -> the electrons density / e-> the charge of the electron

As you can see, the less we have electrons (carry electrons) the more sensitive we are. Same with the thickness.

That’s exactly why semi-conductors are used. Because a micro-sensor with medium conductance have a perfect behavior for magnetic measurements.

But could we use conductive materials ? It will be way bigger , less efficient , but easier to integrate on PCB and cheaper to produce (for a low-money maker for example T_T).

Let’s do some science !

If we consider the copper thickness on 1 Oz PCB’s, factories are mainly agree on 35µm.

So , if we conceive a large sensor (there is absolutely no interest of building a large sensor except for current dissipation) of 10 mm over 5mm, the volume of the sensor will be:

0.000035 * 0.01 * 0.005 = 1.75x10e-9 m3

Once the volume calculated , we need to find how many electrons there are in the plate. So we take the volumetric mass of copper => 8920 kg/m3

So for a volume of 1.75x10e-9 m3 we have => 1.75x10e-9 m3 * 8920 = 15,61 mg

However the molar mass of copper is => 63,546 g/mol

So 15.61mg / 63.546g/mol = 0.0002456 mol

When we applied Avogadro laws, 1 mol = N.

So 0.0002456 * N(avogadro) = number of electrons for 1.75x10e-9 m3 = 1.479x10e20

So Rh = -1/(1.479x10e20 * -1.602x10e-19) = 0.04220.

With the Rh set, we need to adjust the other values for characterizing the sensor.

I could be at 10mA so we have : (0.04 * (0.01/0.000035)) * B = Uhall

For 1 Tesla => 11.428 * 1T = 11.428 V

For 1 mili-Tesla => 11.428 * 1mT = 11.428 mV

For 1 micro-Tesla =>11.428 * 1µT = 11.428 µV

Which is absolutely accessible for Earth magnetic field at approx. 200µT (so 2.2mV).

Even more interesting with parameters like Current who is adjustable (and a large plate allows more heat dissipation).

/!\ Remember to not put isolation material or Mass plane under / on the sensor !

As usual, we could imagine even more with this study !

A small-volume sensor allows to build a matrix of Hall sensor on PCB, and the use of  capacitive straps as a measurement involve less amplitude but no bias current in the hall sensor.

screenshot-from-2017-02-19-12-30-07

Civilians appropriation of science is amazing when simple concepts are hacked and this one could be very interesting (and feel free to use and modify it , as specified in the creative commons terms)

[ I asked myself a long time on the patent opportunity of the Capacitor PCB Hall Sensor, but my soul feel better to share it with you ;)]

That’s all for the Hall sensor and I hope you are all following your dreams and projects because Art & Science is the best 😀

-> If you find errors / mistakes / orthographic monstrosity , come back to me on my twitter account (PM) !

 

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