1. EE 5340 Semiconductor Device Theory Lecture 8 - Fall 2010
Professor Ronald L. Carter

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
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3. Star Simulation of IC Resistor
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4. Star Simulation of IC Resistor Corner
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5. 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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6. Electron quasi-Fermi Energy (n = no + n)
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7. Hole quasi-Fermi Energy (p = po + p)
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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
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9. 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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10. 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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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.
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12. 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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13. Metal to n-type non-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 Eo
qcs
qfm
qfs,n
qfi
qfB,n Ec
EFm
EFn
EFi Ev
qfn
Acc reg
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14. Ideal metal to p-type barrier diode (fm<fs)
p-type s/c
metal
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 Eo
qfm
qcs
qfi
qfs,p
qfBn Ec
EFi
EFm
EFp
qfBp Ev
qfi
qfp<0
Depl reg
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15. Metal to p-type non-rect cont (fm>fs)
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
qfBp
qfi Ev
Accum reg
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16. Metal/semiconductor system 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
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17. Real Schottky band structure1
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
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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
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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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