Impact of thickness of metal on hall effect

Question

I was reading the paper on the Hall Effect and found that the initial experiment was performed on a metal strip. The experiment on the metal failed to provide any useful results, and then it was stated that

Owing probably to the fact that the metal disk used had considerable thickness, the experiment at that time failed to give any positive result.

Later when the same experiment was performed with a gold leaf, the experiment gave satisfactory results.

So, I wanted to know how thickness impacted the results of the Hall Effect Experiment.

Answer 1

According to Wikipedia - Hall effect - Theory the measured Hall voltage is $$V_H = \frac{IB}{nte}$$ where $I$ is the current, $B$ is the magnetic field strength, $n$ is the number density of free charge carriers, $t$ is the thickness, and $e$ is the charge of an individual charge carrier.

You see, you get larger voltages for thin foils (small $t$), and for materials with only few free charge carriers (small $n$). That is why nowadays Hall sensors are made of semiconductors (e.g. silicon, with $n\approx 10^{16}\text{ m}^{-3}$) instead of metals (with $n\approx 10^{28}\text{ m}^{-3}$).