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Semiconductor Device Theory - Lecture 7: IC Resistors and Metal-Semiconductor Contacts

This lecture covers the theory behind integrated circuit (IC) resistors, focusing on the effects of lateral diffusion, doping profiles, and conductance. It explores the relationship between equilibrium carrier concentration, Fermi energy, and quasi-Fermi levels. Additionally, the lecture discusses the formation of contacts between metals and semiconductors, ensuring thermal equilibrium at the junctions. Essential references are provided for further understanding of semiconductor devices and their fundamentals. Students are also reminded to bring a signed ethics statement to class.

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Semiconductor Device Theory - Lecture 7: IC Resistors and Metal-Semiconductor Contacts

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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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