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The electronic band structure is dependent on the static electric bias voltage, which determines the electron and hole current densities?

Physics Asked on April 25, 2021

I am currently studying the textbook Physics of Photonic Devices, second edition by Shun Lien Chuang. Chapter 1.4 Overview of the Book says the following:

In the presence of injection of electrons and holes using a current bias or an optical source, the semiconductor materials may change from being absorptive to gain media due to population inversion effect. This implies that the optical dielectric function is also changed. This change can be modeled with the knowledge of the electronic band structures, which require the solutions of the Schrödinger equation or the so-called effective-mass equation for the given bulk or quantum-well semiconductors. By solving Maxwell’s equations, we obtain the optical field from the dielectric function of the semiconductors. The electronic band structure is also dependent on the static electric bias voltage, which determines the electron and hole current densities.

I didn’t understand this part:

The electronic band structure is also dependent on the static electric bias voltage, which determines the electron and hole current densities.

What is meant by this? What is the "static electric bias voltage", and how does it determine the electron and hole current densities?

One Answer

It’s means that the accumulation of charge, either via injection or optical generation causes the semiconductor bands to bend.

You will be familiar with band bending in PN junction due to distribution of charges.

Well the same happens if the charges are present for other reasons. Main difference is the charges are mobile when injected.

See this paper https://engineering.purdue.edu/~ee606/downloads/T3.PDF

The equation that you will solve to figure this out is called Poisson-Boltzmann.

Correct answer by boyfarrell on April 25, 2021

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