Are the minority carriers (free electrons in p-type and holes in n-type) created after the doping of silicon or after the n or p side get voltage across from a power supply?
And my second question is in a PN junction, how are the minority carriers able to get across the diffusion barrier since their charge is the same as the charge of the atoms in the depletion layer?
Minority carriers (electrons in P type and holes in N type) are technically always there in pure semiconductor matter (such as silicon) due to the effect of heat that causes electrons to break out of their atoms leaving holes behind them, and an electron that did that can then fill a hole created by the absence of another electron and this process goes on, they just are not called minority carriers yet before doping, since it's only after doping that majority carriers exist in the semiconductor. But when doped, new electrons/holes from other atoms are now inside the semiconductor and these new electrons/holes are the ones that are called majority carriers because they are way more abundant than the ones created due to heat i.e. minority carriers. In N type, majority carriers are electrons, and due to heat electrons and holes appear, so these heat-electrons add up to the existing majority carriers (electrons that exist because of doping) and these heat-holes are now the minority carriers in this N type, similarly in P type, majority carriers are holes, and due to heat electrons and holes appear, so these heat-holes add up to the existing majority carriers (holes that exist because of doping) and these heat-electrons are now the minority carriers in this P type. (They are not called heat-elctrons/holes I just used this terminology to explain better)
Also, minority or majority carriers have nothing to do with powering the PN junction, applying a power supply or not doesn't affect their existence.
And for your second question, what you are referring to is leakage reverse current that happens when reverse biasing the PN junction, and it is a relatively small current that increases due to increase of heat, so it's this heat that causes the appearance of minority carriers that tend to create a reverse current when the PN junction is reverse biased, and the power supply that give enough energy to these electrons in the P type to overcome and cross the depletion region and go to the N type, and as I said if you increased heat more electrons will break out of their atoms and flow in the opposite direction P-to-N and you'll have a stronger current.
And here's a better explanation from "Beginner's Guide to Transistors" by J. A. Reddihough.
For your first question:
For your second question:
Are the minority carriers (free electrons in p-type and holes in n-type) created after the doping of silicon or after the n or p side get voltage across from a power supply?
They are created after doping. No power supply is required. The free electrons are originally created primarily on the N-side, and the holes are primarily created on the P side. That is, they are primarily created as majority carriers. However, because they are moving randomly due to thermal energy, they tend to diffuse from one place to another. So, some electrons from the N-side diffuse into the P-side where they become minority carriers, and some holes from the P-side diffuse into the N-side, where they are also minority carriers. As they diffuse in this way, they create an electric potential which causes an electric field to be created. This electric field causes some of the minority carriers to want to drift back in the opposite direction from which they came. When enough carriers have crossed the junction the electric field reaches a point where the diffusion current of electrons or holes in one direction matches the drift current in the other direction. A dynamic equilibrium is reached, with a net charge on each side of the junction, and an associated electric field.
And my second question is in a PN junction, how are the minority carriers able to get across the diffusion barrier since their charge is the same as the charge of the atoms in the depletion layer?
I think your question involves a misunderstanding. Carriers diffuse, and there really is no "diffusion barrier". That is, there is no barrier to diffusion in the semiconductor. It just happens, due to random thermal motion of carriers. Furthermore, it can and does happen contrary to an electric field. The effect of the electric field is to cause drift (in this case in the opposite direction).
