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EE 5340 Semiconductor Device Theory Lecture 7 - Fall 2009

EE 5340 Semiconductor Device Theory Lecture 7 - Fall 2009. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc. Second Assignment. Please print and bring to class a signed copy of the document appearing at http://www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf.

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EE 5340 Semiconductor Device Theory Lecture 7 - Fall 2009

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  1. EE 5340Semiconductor Device TheoryLecture 7 - Fall 2009 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

  2. Second Assignment • Please print and bring to class a signed copy of the document appearing at http://www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf

  3. Diffused or ImplantedIC Resistor (Fig 2.451)

  4. An IC Resistor with L = 8W(M&K)1

  5. Typical IC dopingprofile (M&K Fig. 2.441)

  6. Mobilities**

  7. IC Resistor Conductance

  8. An IC Resistor with Ns = 8, R = 8Rs (M&K)1

  9. The effect of lateral diffusion (M&K1)

  10. A serpentine patternIC Resistor (M&K1) R = NSRS + 0.65NCRS note: RC = 0.65RS

  11. 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

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

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

  14. 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

  15. 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

  16. 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

  17. 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.

  18. 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

  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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