Application of Heisenberg uncertainty principle in semiconductor diode Is there a way to apply the Heisenberg uncertainty principle in a p-n junction? For an electron or hole in the p-n junction diode, using the uncertainty principle can i get a probability curve as follows:

 A: The Heisneberg uncertainty principle , HUP, is  not yet relevant in electronics:

The fact that quantum mechanics and the Heisenberg uncertainty principle place limits on our ability to make measurements would, at first glance, seem to have little relevance to experiments in the solid state; the measurement precision achieved in such experiments is usually limited by more mundane concerns (for example, thermal fluctuations of voltages and currents). However, this seemingly innocuous expectation is now being challenged by a number of experiments in quantum nanoscience that are pushing the boundaries of measurement sensitivity ever closer towards ultimate quantum limits.

This is also interesting, in eliminating noise in nanotechnology, as noise comes from the Heisenberg uncertainty at that level. 
If you are asking whether you could get the probability distribution for position and momentum for the electron or a hole, using the HUP, the answer is no. The HUP imposes an envelope in which one distribution will be measured if the other is known but it cannot give the probability distribution for the position and momentum of the electron/hole. It can only show whether it is obeyed or not when both position and momentum are measured. To get the probability distributions you have to solve for  the quantum mechanical boundary conditions of your solid, and and once you have the wavefunction the corresponding x and p operators will give the distributions.
A: In theory, you should be able to observe the Heisenberg uncertainty principle in angstrom-size semiconductor devices.  In practice, it might be challenging.
I would suggest the following experiment:  Instead of a p-n junction consider growing a very thin metal film on a semiconductor (a so-called quantum well).  Such systems are ubiquitous in advanced semiconductor devices.  Since the Heisenberg uncertainty principle is a measurement-based phenomenon you will need:


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*A way of fabricating very thin, atomically uniform films of known thickness.  A technique such as molecular beam epitaxy under ultra-high vacuum would work.

*A way to measure the electron's momentum in the $z$-direction.  I would suggest normal-emission photoemission spectroscopy.  You can convert energy to momentum since they commute.

*A way of cooling the film to liquid-helium temperatures for measurement might be advisable (to reduce thermal broadening).


When electrons are confined to very thin films (where film thicknesses are much smaller than the coherence length of the elections), the band structure of the film becomes quantized in the $z$-direction.  By varying the film thickness, you should (in theory) be able to observe changes in the observed spectral band thicknesses.  In practice, this may be difficult for a number of reasons:


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*Depending on the film thickness (your $\Delta x$), the changes in $\Delta P$ might be very small compared to the intrinsic thickness of the spectral peak.

*Thermal broadening will introduce additional spectral width. Cooling the system to liquid-helium temperatures will help with this.

*Creating atomically uniform films is not trivial (but can be done).

*Knowing your exact film thickness is not trivial (but can be done).

*You will need a very flat substrate.  Consider purchasing semiconductor wafers with the smallest miscut you can afford.


Anyway, this is how I would do it.
