1 / 13

Prof. Ming-Jer Chen Department of Electronics Engineering National Chiao-Tung University

IEE5501 Solid State Physics. Lecture 8a: Bloch Electrons in a Brillouin Zone. Prof. Ming-Jer Chen Department of Electronics Engineering National Chiao-Tung University 04/02/2014. Felix Bloch (awarded the 1952 Nobel Prize in Physics).

tokala
Download Presentation

Prof. Ming-Jer Chen Department of Electronics Engineering National Chiao-Tung University

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. IEE5501 Solid State Physics Lecture 8a: Bloch Electrons in a Brillouin Zone Prof. Ming-Jer Chen Department of Electronics Engineering National Chiao-Tung University 04/02/2014

  2. Felix Bloch (awarded the 1952 Nobel Prize in Physics) His doctoral thesis (1928), under Heisenberg, established the Quantum theory of solids, using Bloch waves to describe the electrons in the solids. Solid line: A schematic of a typical Bloch wave in one dimension. (The actual wave is complex; this is the real part.) The dotted line is from the eik·r factor. The light circles represent atoms. This leads to the concept of electronic band structures. From Wikipedia

  3. Leon Brillouin under Paul Langevin In his dissertation (1920), Brillouin studied the atomic vibrations (phonons). In 1926, he independently developed what is known as WKB approximation. In 1930, he introduced the concept of Brillouin zones to address the propagation of electron waves in a crystal lattice. From Wikipedia

  4. 1-D r-space 1-D k-space (reciprocal space) First Brillouin zone (-/a  k  /a) of 1-D lattice in r-space Also, Wigner-Seitz lattice of reciprocal lattice in k-space of 1-D lattice in r-space

  5. 2-D Brillouin-zone construction by 300keV electrons The reciprocal lattices (dots) and corresponding first Brillouin zones of (a) square lattice and (b) hexagonal lattice. From Wikipedia

  6. 3-D FCC in r-space, and its two BCC in k-space and two Brillouin zones in k-space Reciprocal Wigner-Seitz of BCC Brillouin Zones

  7. First Brillouin Zone <001> (out-of-plane) The zone center (Gamma at k = 0) The zone end along <100> 3-D View On (001) Wafer <100> (in-plane) Length = 2/a (Gamma to X) <010> (in-plane) Length =( )2/a (Gamma to L) The zone end along <111> (001) a: Lattice Constant by Robert F. Pierret All distinct Bloch waves occur for k-values within the first Brillouin zone. The information of a solid is self-contained in the zone and all k’s are completely diffracted by the boundaries of the zone.

  8. Band Structure M.J. Chen, et al.

More Related