Electronic Structure

Abstract

Given that all matter consists of atoms, there are only 90 naturally occurring elements on the planet Earth (Elements with atomic numbers 1 through 92 (except elements with atomic numbers 43 and 61) occur naturally.). However, if one looks at the naturally occurring or even man-made materials in daily life, there is an enormous range of structures and properties. Such a diversity is precisely due to the various arrangements at the atomic scale of an otherwise finite set of elements. In the previous chapter about the atomic arrangement, we motivated the reader by stating that it is indispensable to understand how atoms interact with each other and how this arrangement affects the nanoscale properties. In this chapter, we focus on the role that atomic arrangement in various dimensions plays in determining the physical and chemical properties of a material.

Appendices

Problems

5.1 For a parabolic band, plot the approximate density of states for a 1D structure.

5.2 For a parabolic band, plot the approximate density of states for a 2D structure.

5.3 For a parabolic band, plot the approximate density of states for a 3D structure.

5.4 What is the physical meaning of f(E)?

5.5 What is the physical meaning of $[1-f(E)]$?

5.6 Calculate the value of the Fermi’s function at $E = 0$ for $\mu = 0$, and $k_\mathrm{B}T = 25\,\mathrm{meV}$.

5.7 Give an example of an insulator. Comment on its band gap.

5.8 Give an example of a semiconductor. Comment on its band gap.

5.9 Give an example of a semi-metal. Comment on its band gap.

5.10 Give an example of a metal. Comment on its band gap.

5.11 Comment on the velocity of electrons for a material with linear bandstructure like that of a monolayer graphene.

Research Assignment

R5.1 Nanobiotechnology and bionanotechnology are important aspects of nanotechnology. This area is expected to revolutionize nanomedicine. The medical applications include equipment sanitation, implant disinfection, lab on chip, medical implant, tissue engineering, drug screening, drug delivery, bionanosensors, nanobiosensors, pathogen detection, medical imaging (e.g. fMRI, functional medical resonance imaging), targeted drug delivery, dentistry (nanocomposites, nanoclusters, implants, bone replacement cements, nano-needles), ophthalmology, surgical robots, artificial organs, etc. Pick a topic of your choice about how nanotechnology is affecting healthcare in contemporary society, and write a one-page summary.