1 / 15

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

DEE4521 Semiconductor Device Physics Lecture 2: Band Structure. Prof. Ming- Jer Chen Department of Electronics Engineering National Chiao -Tung University 09/24/2013. Electron Distribution Function f(x, y, z, k x , k y , k z , t). According to Heisenberg’s Uncertainty Principle,

colby-palmer
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. DEE4521 Semiconductor Device Physics Lecture 2: Band Structure Prof. Ming-Jer Chen Department of Electronics Engineering National Chiao-Tung University 09/24/2013

  2. Electron Distribution Function f(x, y, z, kx, ky, kz, t) According to Heisenberg’s Uncertainty Principle, We have a 6 dimensionality space at a time for a Semiconductor in a Realx-y-z Space; and at each point (x,y.z), Electrons, Holes, Phonons, and Photons are all better dealt with in another space: kx-ky-kz Space or Wavevector Space or Momentum Space

  3. by Analogy • De Broglie’s Wave and Particle Duality • Degree of Freedom (DOF) – Kinetic Energy • Potential Energy and its Reference

  4. Electrons in Solid A ball in the air Electron Effective Mass mx* in x direction Crystal Momentum ħkx (kx: wave vector in x direction) Electron Momentum ħ(kx-kxo) Electron Kinetic Energy Ek = ħ2(kx-kxo)2/2mx* Ball’s Mass m in x direction Ball’s Momentum mvx Ball’s Kinetic Energy mvx2/2 Effective Mass m* Crystal momentum Ek = ħ2kx2/2m* 1. kxo: a point in k space around which electrons are likely found. 2. Crystal momentum (global) must be conserved in k space, not Electron Momentum (local).

  5. Si Conduction-Band Structure in wave vector k-space (Constant-Energy Surfaces in k-space) Effective mass approximation: m* (to reflect electron confinement in solid) Ek = ħ2(ky – kcy)2/2m* Kinetic energy + ħ2kx2/2m* + ħ2kz2/2m* Ellipsoidal energy surface (silicon) E = Ek + Ec 6-fold valleys Potential energy total electron energy Kcy 0.85 (2/a); Longitudinal Effective Mass m* (or ml*)= 0.92 mo Transverse Effective Mass m* (or mt*)= 0.197 mo a: Lattice Constant

  6. Effective Masses of Commonly Used Materials (You may then find that these effective masses are far from the rest mass. This is just one of the quantum effects.) Electron and hole effective mass are anisotropic, depending on the orientation direction. Electron (not hole) effective mass is isotropic, regardless of orientation. Rest mass of electron mo = 0.9110-30 kg GeSi GaAs ml*/mo 1.588 0.916 mt*/mo 0.081 0.190 me*/mo 0.067 mhh*/mo 0.347 0.537 0.51 mlh*/mo 0.0423 0.153 0.082 mso*/mo 0.077 0.234 0.154 (by Prof. Robert F. Pierret)

  7. Electron Energy E-k Relation in a Crystal Zinc blende a = 5.6533 Å Diamond a = 5.43095 Å Diamond a = 5.64613 Å ( )2/a Quasi-Classical Approximation Bottom of valley

  8. k-Space Definition <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 (Principal-axis x, y, and z coordinate system usually aligned to match the k coordinate system)

  9. Electron E-k Diagram Indirect gap Direct gap EG: Energy Gap

  10. Comparisons between Different Materials (Constant-Energy Surface) Conduction Band one valley at the zone center 8-fold valleys along <111> (half-ellipsoid in Brillouin) (sphere) 6-fold valleys along <100> (ellipsoid)

  11. Valence-Band Structure

  12. Conduction-Band Electrons and Valence-Band Holes and Electrons Hole: Vacancy of Valence-Band Electron

  13. No Electrons in Conduction Bands All Valence Bands are filled up.

  14. Work Function  (Electron Affinity) (= 4.05 eV for Si) Ec E x

More Related