ee 5340 semiconductor device theory lecture 08 – spring 2011
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EE 5340 Semiconductor Device Theory Lecture 08 – Spring 2011. Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc. Second Assignment. Submit a signed copy of the document posted at www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf. Test 1 – Tuesday 22Feb11. - PowerPoint PPT PresentationTRANSCRIPT
EE 5340Semiconductor Device TheoryLecture 08 – Spring 2011
Professor Ronald L. [email protected]
http://www.uta.edu/ronc
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Second Assignment• Submit a signed copy of the
document posted at
www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf
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Test 1 – Tuesday 22Feb11• 11 AM Room 129 ERB• Covering Lectures 1 through 9• 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 http://www.uta.edu/ronc/5340/tests/.
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Diffused or ImplantedIC Resistor (Fig 2.451)
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An IC Resistor with L = 8W (M&K)1
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Typical IC dopingprofile (M&K Fig. 2.441)
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Mobilities**
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IC Resistor Conductance
g1R dxxnxqg
dxxnxqLWG
dxLWxnxqdG
sx
0n
x
0n
n
j
j
,
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An IC Resistor with Ns = 8, R = 8Rs (M&K)1
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The effect of lateral diffusion (M&K1)
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A serpentine patternIC Resistor (M&K1)
R = NSRS + 0.65NCRS
note: RC = 0.65RS
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• 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
kT
EEnn and , n
nkTEE fif
i
o
i
ofif expln
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Electron quasi-Fermi Energy (n = no + n)
kTEE
nnn
:is density carrier the and
, nnnkTEE
:defined is (Imref) level Fermi-Quasi The
fifn
i
o
i
ofifn
exp
ln
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Hole quasi-Fermi Energy (p = po + p)
kTEE
npp
:is density carrier the and
, nppkTEE
:as defined is Imref the holes, For
fpfi
i
o
i
ofpfi
exp
ln
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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 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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Si and Al and model (approx. to scale)
qfm,Al ~ 4.1 eV
Eo
EF
mEFp
EFn
Eo
Ec
Ev
EFi
qfs,n
qcsi~ 4.05 eV
Eo
Ec
Ev
EFi
qfs,p
metal n-type s/c p-type s/c
qcsi~ 4.05 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
Eo
EcEF EFiEv
qc (electron affinity)
qfF
qf(work function)
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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 (fm>fs,Va=0)
EFn
Eo
Ec
Ev
EFi
qfs,n
qcs
n-type s/c
qfm
EF
m
metal
qfBnqfi
qf’n
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
Depl reg
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Metal to n-typenon-rect cont (fm<fs)
EFn
Eo
Ec
Ev
EFi
qfs,n
qcs
n-type s/c
qfm
EF
m
metal
qfB,n
qfn
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
Acc reg
qfi
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Ideal metal to p-typebarrier diode (fm<fs)
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 barr.
fi = fm-fs,p = hole s/c to mtl barr.
EFp
Eo
Ec
Ev
EFi
qfs,pqcs
p-type s/c
qfm
EF
m
metal
qfBn
qfi
qfp<0Depl regqfBp
qfi
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Metal to p-typenon-rect cont (fm>fs)
No disc in Eo
Ex=0 in metal ==> Eo flat
fB,n = fm - cs = elec mtl to s/c barr
fBp= fm- (cs + Eg) = hole m to s
fi = fm-fs,n = s/c to mtl barr.
EFi
Eo
Ec
Ev
EfP
qfs,n
qcs
n-type s/c
qfm
EF
m
metal
qfBnq(fi)
qfpAccum reg
qfBp qfi
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Metal/semiconductorsystem typesn-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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References1 and M&KDevice 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 model.
2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981.
3 and **Semiconductor Physics & Devices, 2nd ed., by Neamen, Irwin, Chicago, 1997.
Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989.