Arun Waves

November 8, 2009

Formation of a quantum wire – Parabolic potential well

This post deals with a Matlab simulation showing the formation of a quantum wire, i.e. a parabolic potential well.

Such potential profiles can be easily realized by negatively biasing 2 metallic plates (also known as gates) separated by a short distance as shown in the figure below. Split-gate technique is one method used to form (fabricate) such structures.

Split gates

2 plates (on top) with negative charge

In the following movie, the potential starts with a flat profile (at zero/ground potential) when there is no charge on the plates. As the negative potential is increased the potential under the plates rises and the fringing field (field that is not directly under the plates) pulls the neighboring potential along with it – almost like lifting the ends of a bed sheet. The title calls it the ‘Parabolic potential well’ since the transverse cross section (section along the width) shows a parabolic shape for the potential along the width of the wire.

The Length and Width axis of the wire are in units of nano-meter (1 nm = 1*10^-9 m, i.e. 1 billionth of a meter). Nanometer is the typical unit for length used for measuring dimensions in the nano world. The Potential axis is in arbitrary units of electric potential. All the numeric values are chosen to represent typical values seen in actual experiments.

Once the wire is formed in the simulation, it is rotated (in the above video) to give a clear view of its shape (remember the edges are electric potential and not physical walls/matter). The last segment of the video shows the top view of the wire which will be a useful view to get used to when we will pass electrons through the wire. The color bar on the right hand side gives the value of the potential at any point in the wire based on the color gradient; maximum is 25 (red) and minimum is 0 (blue).

Feel free to post any questions…………… thanks 🙂



  1. Awesome video, I have been working on quantum wells and was curious if I could use a screen capture of your video if I reference it as your picture (please let me know how you would like me to cite you), additionally if this Matlab code is available somewhere?

    Comment by Ryan Aridi — November 8, 2018 @ 1:24 pm | Reply

    • Cool. Feel free to use it with reference. Sorry about the delayed response. I will fish out a link for the code but I must tell you that it was written before I knew how to write good code! I had never taken any CS course.

      Comment by Arun — January 26, 2019 @ 4:18 pm | Reply

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