A Brief Introduction to Band Structure in Three Dimensions

Details A Brief Introduction to Band Structure in Three Dimensions A Brief Introduction to Band Structure in Three Dimensions

2011-05-01

arxiv.org/abs/1105.0220v1

Physics

Quantum Physics

7 pages, 4 figures; undergraduate term paper

Scientific paper

Without our ability to model and manipulate the band structure of semiconducting materials, the modern digital computer would be impractically large, hot, and expensive. In the undergraduate QM curriculum, we studied the effect of spatially periodic potentials on the spectrum of a charged particle in one dimension. We would like to understand how to extend these methods to model actual crystalline materials. Along the way, we will explore the construction of periodic potentials in three dimensions, and we use this framework to relate the single-particle Hamiltonian to the potential contribution from each atom. We then construct a crude model system analogous to the semiconductor silicon, and demonstrate the appearance of level splitting and band gaps as the strength of the potential is varied, in accordance with our intuition from the one-dimensional case. We discuss refinements of the model to include many-particle effects, and finally we show how a careful choice of the potential function leads to good agreement with the correct band diagram for silicon.

Affiliated with

Also associated with

No associations

Rating

A Brief Introduction to Band Structure in Three Dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Brief Introduction to Band Structure in Three Dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Brief Introduction to Band Structure in Three Dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-426143