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EE 5340 Semiconductor Device Theory Lecture 8 - Fall 2010

EE 5340 Semiconductor Device Theory Lecture 8 - Fall 2010. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc. Test 1 – W 29Sep10. 11 AM Room 108 Nedderman Hall Covering Lectures 1 through 10 Open book - 1 legal text or ref., only. You may write notes in your book.

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EE 5340 Semiconductor Device Theory Lecture 8 - Fall 2010

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  1. EE 5340Semiconductor Device TheoryLecture 8 - Fall 2010 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

  2. Test 1 – W 29Sep10 • 11 AM Room 108 Nedderman Hall • Covering Lectures 1 through 10 • Open book - 1 legal text or ref., only. • You may write notes in your book. • Calculator allowed • A cover sheet will be included with full instructions. For examples see http://www.uta.edu/ronc/5340/tests/.

  3. Star Simulation of IC Resistor

  4. Star Simulation of IC Resistor Corner

  5. The equilibrium carrier concentration ahd the Fermi energy are related as The potential f = (Ef-Efi)/q If not in equilibrium, a quasi-Fermi level (imref) is used Fermi Energy

  6. Electron quasi-Fermi Energy (n = no + n)

  7. Hole quasi-Fermi Energy (p = po + p)

  8. Ex-field when Ef - Efi not constant • Since f = (Ef - Efi)/q = Vt ln(no/ni) • When Ef - Efi = is position dependent, • Ex = -df/dx = -[d(Ef-Efi)/dx] = - Vt d[ln(no/ni)]/dx • If non-equilibrium fn = (Efn-Efi)/q = Vt ln(n/ni), etc • Exn = -[dfn/dx] = -Vt d[ln(n/ni)]/dx

  9. Si and Al and model (approx. to scale) metal n-type s/c p-type s/c Eo Eo Eo qcsi~ 4.05eV qcsi~ 4.05eV qfm,Al ~ 4.1 eV qfs,n qfs,p Ec Ec EFm EFn EFi EFi EFp Ev Ev

  10. Eo Making contact be-tween metal & s/c • Equate the EF in the metal and s/c materials far from the junction • Eo(the free level), must be continuous across the jctn. N.B.: qc = 4.05 eV (Si), and qf = qc + Ec - EF qc(electron affinity) qf (work function) Ec EF EFi qfF Ev

  11. Equilibrium Boundary Conditions w/ contact • No discontinuity in the free level, Eo at the metal/semiconductor interface. • EF,metal = EF,semiconductor to bring the electron populations in the metal and semiconductor to thermal equilibrium. • Eo - EC = qcsemiconductor in all of the s/c. • Eo - EF,metal = qfmetal throughout metal.

  12. No disc in Eo Ex=0 in metal ==> Eoflat fBn=fm- cs = elec mtl to s/c barr fi=fBn-fn= fm-fs elect s/c to mtl barr Ideal metal to n-typebarrier diode (fm>fs,Va=0) metal n-type s/c Eo qcs qfm qfi qfs,n qfBn Ec EFm EFn EFi Depl reg Ev qf’n

  13. Metal to n-typenon-rect cont (fm<fs) n-type s/c No disc in Eo Ex=0 in metal ==> Eo flat fB,n=fm - cs = elec mtl to s/c barr fi= fBn-fn< 0 Accumulation region metal Eo qcs qfm qfs,n qfi qfB,n Ec EFm EFn EFi Ev qfn Acc reg

  14. Ideal metal to p-typebarrier diode (fm<fs) p-type s/c No disc in Eo Ex=0 in metal ==> Eoflat fBn= fm- cs = elec mtl to s/c barr fBp= fm- cs + Eg = hole m to s fi = fBp-fs,p = hole s/c to mtl barr metal Eo qcs qfm qfi qfs,p qfBn Ec EFi EFm EFp qfBp Ev qfi qfp<0 Depl reg

  15. Metal to p-typenon-rect cont (fm>fs) metal n-type s/c No disc in Eo Ex=0 in metal ==> Eo flat fB,n=fm- fs,n = elec mtl to s/c barr fBp= fm- cs + Eg = hole m to s Accumulation region Eo qcs qfm q(fi) qfs,n qfBn Ec EFm EFi EfP qfp Ev qfBp qfi Accum reg

  16. Metal/semiconductorsystem types n-type semiconductor • Schottky diode - blocking for fm > fs • contact - conducting for fm < fs p-type semiconductor • contact - conducting for fm > fs • Schottky diode - blocking for fm < fs

  17. Barrier transistion region, d Interface states above fo acc, p neutrl below fo dnr, n neutrl Ditd-> oo, qfBn=Eg- fo Fermi level “pinned” Ditd-> 0, qfBn=fm - c Goes to “ideal” case Real Schottkyband structure1

  18. Fig 8.41 (a) Image charge and electric field at a metal-dielectric interface (b) Distortion of potential barrier at E=0 and (c) E0

  19. References 1Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986. See Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996, for another treatment of the m model. 2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981. 3Semiconductor Physics & Devices, 2nd ed., by Neamen, Irwin, Chicago, 1997.

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