1 / 27

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

DEE4521 Semiconductor Device Physics Lecture 3: Electrons and Holes. Prof. Ming-Jer Chen Department of Electronics Engineering National Chiao-Tung University October 1, 2012. DOS (Density-of-States).

yamin
Télécharger la présentation

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 3: Electrons and Holes Prof. Ming-Jer Chen Department of Electronics Engineering National Chiao-Tung University October 1, 2012

  2. DOS (Density-of-States) • Effective masses (ml* and mt*) featuring a singlevalley in a Brillouin zone. • Effective mass in the whole Brillouin zone accounting for allvalley minima: • DOS Effective Massm*ds • States can be thought of as available seats forelectrons in conduction band and forholes in valence band.

  3. DOS • One way to derive DOS function and hence its DOS effective mass: • Solve Schrodinger equation in real space to find • corresponding k solutions in k space • Apply Pauli exclusion principle on these k solutions • Mathematically Transform an ellipsoidal energy surface to a sphere energy surface, particularly for Si and Ge

  4. Electron DOS and Hole DOS S(E): DOS function, the number of states per unit energy per unit volume in real space. mdse*: electron DOS effective mass, which carries the information about DOS in conduction band mdsh*: hole DOS effective mass, which carries the information about DOS in valence band

  5. Relation between Valley Effective Mass and DOS Effective Mass • Conduction Band • GaAs: • mdse* = me* • Silicon and Germanium: • mdse* = g2/3(ml*mt*2)1/3 • where the degeneracy factor g is the number of ellipsoidal • constant-energy surfaces lying within the Brillouin zone. For Si, g = 6; • For Ge, g = 8/2 = 4. • 2.Valence Band – Ge, Si, GaAs • mdsh* = ((mhh*)3/2 + (mlh*)3/2)2/3 • (For brevity,we do not consider the Split-off band)

  6. Fermi-Dirac Statistics Fermi-Dirac distribution function gives the probability of occupying an energy state E. 1 - f(E): the probability of not filling state E Ef: Fermi Level

  7. Fermi level is related to one of Laws of Nature: Conservation of Charge 2-13 Extrinsic case

  8. Case of EV < Ef < EC C = (Ef – EC)/kBT Electron concentration nNC exp(C) p  NV exp(V) V= (EV – Ef)/kBT Hole concentration Effective density of states in the conduction band NC = 2(mdse*kBT/2ħ2)3/2 NV = 2(mdsh*kBT/2ħ2)3/2 Effective density of states in the valence band Note: for EV < Ef< EC, Fermi-Dirac distribution reduces to Boltzmann distribution.

  9. Case of EV < Ef < EC C = (Ef – EC)/kBT nNC exp(C) p  NV exp(V) V= (EV – Ef)/kBT NC = 2(mdse*kBT/2ħ2)3/2 NV = 2(mdsh*kBT/2ħ2)3/2 • For intrinsic case where n = p, at least four statements can be drawn: • Ef is the intrinsic Fermi level Efi • Efi is a function of the temperature T and the ratio of mdse* to mdsh* • Corresponding ni (= n = p) is the intrinsic concentration • ni is a function of the band gap Eg (= Ec- Ev)

  10. Extrinsic Semiconductors in Equilibrium (Uniform and Non-uniform Doping)

  11. Uniform Doping We first focus on Non-Degenerate semiconductors, the Case of low and moderate doping of less than 1020cm-3.

  12. Intrinsic Case (No Doping, No Impurities) 2-5 Microscopic View n = p

  13. Silicon Crystal doped with phosphorus (donor) atoms. 2-6 n > p One typical method to dope or introduce impurities: High-energy ion implant at room temperature, followed by High temperature ( 1000 oC) annealing (to eliminate the defects and to place impurities on the lattice positions correctly)

  14. Acceptors in a semiconductor An electron is excited from the valence band to the acceptor state, leaving behind a quasi-free hole. 2-8 p > n

  15. 2-13 Positioning of Fermi level can reveal the doping details

  16. 2-14 n = niexp((Ef – Efi)/KBT) = NCexp((Ef - EC)/KBT) p = niexp((Efi – Ef)/KBT) = NVexp((EV - Ef)/KBT) pn = ni2 for equilibrium extrinsic intrinsic Efi = (3/4)(KBT)ln(mdsh*/mdse*) + (Ec+Ev)/2 n = p + ND+ n = p = ni Ionized donor density

  17. n + NA- = p 2-15 Ef itself reflects the charge conservation.

  18. Compensation 2-16 n = (ND+ - NA-)+p n + NA- = p ND+ NA- ND+ > NA-

  19. 2-17 Electron distribution function n(E) Evidence of DOF = 3

  20. Energy band-gap dependence of silicon on temperature 2-18

  21. 2-19

  22. 2-20 Full ionization of impurity ni versus ND or NA Ionization energy < KBT Extrinsic temperature range for ni = ND (= ND+)

  23. Ef

  24. Non-uniform Doping Case

  25. Nonuniformly doped semiconductor Only for doping with non-uniform distribution can Einstein relationship be derived. 4-2

  26. 4-8

  27. Built-in Fields in Non-uniform Semiconductors 4-9

More Related