A normal MOSFET usually has a gate threshold voltage too big to be controlled directly by a low voltage pin, e.g. a 3.3V output. Because of this, the manufacturers developed special MOSFETs which have a very low threshold voltage, and named them Logic Level MOSFETs.
Logic Level MOSFETs are not as common as the normal ones, so they tend to be harder to find and more expensive.
First DUT was a BUZ11A from ST. In the datasheet, the absolute maximum rating for the Vgs of a BUZ11A is +/- 20 V. By mistake, for a couple of seconds I applied +32V for Vgs. During this time the Vds was at 5V, and Ids was limited by the power supply to 3.2A only.
To my surprise, instead of a permanently damaged transistor, the result was exactly what I was looking for in the first place: a MOSFET with Vgs(th) low enough to be controlled by a 3.3V pin. Please note that a positive over voltage was applied to the transistor's gate, not a negative over voltage like in the original experiment.
So, no schematic, no setup, no measurements, no long hours of careful voltage adjustments and testing, no hard work, none of these.
Just a dumb mistake and that's it. Mission accomplished! :o)
This is the brand new BUZ11A:
and this is the same transistor after applying a Vgs of +32V for a few seconds:
The change from 3.84V to 1.57V for the threshold parameter seems to be a permanent change, but I need to experiment more before jumping to conclusion.