First off, a supernova is an exploding star. A star is made out of primarily hydrogen and there is so much of it that in the core there is so much pressure that it actually forces the hydrogen atoms together in a process called nuclear fusion that generates an incredible amount of energy. This can not be done without a massive, massive object, therefor you can not have a tiny supernova.
Second, it's the collapse of the supernova after it's exploded that forms the black hole.
Well, a star may not actually be necessary
as says the article:
The crux of their idea involves using using a laser to form a micro black hole, which could be used as an energy source. This would be a Schwarzschild, or non-rotating, black hole which outputs Hawking Radiation, and the smaller the black hole, the more energetic.
Of course, making a black hole isn't the world's most easy undertaking. It takes a huge amount of power to build one in the first place. To make one of these mini black holes, Crane and Westmoreland propose a 370km2 solar panel, at an orbit one million km from the surface of the sun, which, if perfectly efficient, would gather enough energy per year to make one black hole. This power would be fed to a spherically converging gamma laser, with a lasing mass of around 10^9 tonnes. However, after you make a few black holes, you can use them as a power source to make more.
