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Technology / Re: What are the assumptions of the hydrogenic model in semiconductors?
« on: 24/02/2024 22:50:50 »
I hadn't come across the first equation previously (must have been asleep in one of the solid state physics lectures!) but it does look like a statement of electrostatics. The neat thing is that the answer matches the highest energy of the absorption line spectrum, so we do at least know it is correct!
We have experimental methods for estimating effective mass and permittivity so it could be said that no assumptions are required to propose the hydrogenic model, it just happens to work. Or you could argue that it is actually a circular argument because me* is derived from a knowledge of electron resonance and ε, which makes it a somewhat fictitious interpretation of "mass" with an apparently enormous range for 0 to 1000 me or more!
We have experimental methods for estimating effective mass and permittivity so it could be said that no assumptions are required to propose the hydrogenic model, it just happens to work. Or you could argue that it is actually a circular argument because me* is derived from a knowledge of electron resonance and ε, which makes it a somewhat fictitious interpretation of "mass" with an apparently enormous range for 0 to 1000 me or more!
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