Finite Quantum Well Example
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- čas přidán 11. 09. 2024
- / edmundsj
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In this video I work out an example of the finite quantum well for typical values of the finite potential, electron mass, and quantum well length. We find a dramatic difference between the ground state energy predicted by the finite and infinite quantum well models.
This is part of my series on semiconductor physics (often called Electronics 1 at university). This is based on the book Semiconductor Physics and Devices by Donald Neamen, as well as the EECS 170A/174 courses taught at UC Irvine.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.
How do we plot the graph to get the intersection as 0.94?
If x = n*pi/2 then we step through the minimum well depth for higher harmonics of the wave function. So does that mean the minimun energy levels are given by Einf*n where n=2,3,4..? Note that the first energy level has to be found graphically. So the finite well has minimum energy levels same as the infinite well for n>1. But of course, finite well can have energy levels larger than the minimum values. In that case, we have to resort to graphical method.
I got x = 0.84 and y = 0.94 for the intersection. Thank you for the video.
Can you help me with how do you solved it to get these values?
wonderful series thank you so much
how do you put 0.94 in x direction
Is there any practical drawback if a finite QW structure supports more than one eigen-state?
Yeah - deep quantum wells usually require very different materials, which have different crystal properties, and are difficult to grow on top of each other without everything rupturing.
@@JordanEdmundsEECS Thanks. Then what is the advantage of deep QW (assuming ideal growth)?
where tf did you get 0.94?
If the circle intersect at two points or more, then how we will calculate energy, and how we will compare to infinite square well
If the circle intersects two or more points, it only means that the quantum well will support two or more states. You calculate the energy for each intersected point exactly as he calculated in the video.
Yup! This is exactly correct, thanks Joel!
why is the electrons mass only 6% of its normal mass?
You can think of the semiconductor as “lubricating” the motion of the electron, the crystal lattice actually makes it easier for it to get from point A to point B.