1. EE 5340 Semiconductor Device Theory Lecture 7 - Fall 2009
Professor Ronald L. Carter

2. Second Assignment
Please print and bring to class a signed copy of the document appearing at
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3. Diffused or Implanted IC Resistor (Fig 2.451)
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4. An IC Resistor with L = 8W (M&K)1
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5. Typical IC doping profile (M&K Fig. 2.441)
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6. Mobilities**
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7. IC Resistor Conductance
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8. An IC Resistor with Ns = 8, R = 8Rs (M&K)1
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9. The effect of lateral diffusion (M&K1)
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10. A serpentine pattern IC Resistor (M&K1)
R = NSRS NCRS
note: RC = 0.65RS
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11. 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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12. Electron quasi-Fermi Energy (n = no + n)
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13. Hole quasi-Fermi Energy (p = po + p)
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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
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15. 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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16. 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 Eo
qc (electron affinity) qf
(work function) Ec EF
EFi
qfF Ev
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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.
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18. Ideal metal to n-type barrier diode (fm>fs,Va=0)
n-type s/c
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 Eo
qfm
qcs
qfi
qfBn
qfs,n Ec
EFm
EFn
EFi
Depl reg Ev
qf’n
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19. References
1Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 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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