EE%205340%20Semiconductor%20Device%20Theory%20Lecture%207%20-%20Fall%202009

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EE 5340Semiconductor Device TheoryLecture 7 -
Fall 2009

• Professor Ronald L. Carter
• ronc_at_uta.edu
• http//www.uta.edu/ronc

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Second Assignment

• Please print and bring to class a signed copy of
  the document appearing at
• http//www.uta.edu/ee/COE20Ethics20Statement20F
  all2007.pdf

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Diffused or ImplantedIC Resistor (Fig 2.451)
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An IC Resistor with L 8W (MK)1
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Typical IC dopingprofile (MK Fig. 2.441)
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Mobilities
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IC Resistor Conductance
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An IC Resistor with Ns 8, R 8Rs (MK)1
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The effect of lateral diffusion (MK1)
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A serpentine patternIC Resistor (MK1)

• R NSRS 0.65?NCRS
• note RC 0.65?RS

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Fermi Energy

• 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

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Electron quasi-Fermi Energy (n no ?n)
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Hole quasi-Fermi Energy (p po ?p)
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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
  dln(no/ni)/dx
• If non-equilibrium fn (Efn-Efi)/q Vt
  ln(n/ni), etc
• Exn -dfn/dx -Vt dln(n/ni)/dx

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

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Ideal metal to n-typebarrier diode (fmgtfs,Va0)
n-type s/c
metal

• No disc in Eo
• Ex0 in metal gt Eoflat
• fBnfm- cs elec mtl to s/c barr
• fifBn-fn fm-fs elect s/c to mtl barr

Eo
qcs
qfm
qfi
qfs,n
qfBn
Ec
EFm
EFn
EFi
Depl reg
Ev
qfn
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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.