EE 5340 Semiconductor Device Theory Lecture 7 - Fall 2009
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EE 5340 Semiconductor Device Theory Lecture 7 - Fall 2009 Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc
description
EE 5340 Semiconductor Device Theory Lecture 7 - Fall 2009. Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc. 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. - PowerPoint PPT Presentation
Transcript of EE 5340 Semiconductor Device Theory Lecture 7 - Fall 2009
EE 5340Semiconductor Device TheoryLecture 7 - Fall 2009
Professor Ronald L. [email protected]
http://www.uta.edu/ronc
L 07 Sept 15
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
2
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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 = (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 = (Ef - Efi)/q = Vt ln(no/ni)• When Ef - Efi = is position dependent,• Ex = -d/dx = -[d(Ef-Efi)/dx] = - Vt
d[ln(no/ni)]/dx• If non-equilibrium n = (Efn-Efi)/q = Vt
ln(n/ni), etc• Exn = -[dn/dx] = -Vt d[ln(n/ni)]/dx
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Si and Al and model (approx. to scale)
qm,Al ~ 4.1 eV
Eo
EF
mEFp
EFn
Eo
Ec
Ev
EFi
qs,n
qsi~ 4.05 eV
Eo
Ec
Ev
EFi
qs,p
metal n-type s/c p-type s/c
qsi~ 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.: q = 4.05 eV (Si),and q = qEc - EF
Eo
EcEF EFiEv
q (electron affinity)
qF
q(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 = qsemiconductor in all of the s/c.• Eo - EF,metal = qmetal throughout metal.
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Ideal metal to n-typebarrier diode (m>s,Va=0)
EFn
Eo
Ec
Ev
EFi
qs,n
qs
n-type s/c
qm
EF
m
metal
qBnqi
q’n
No disc in Eo
Ex=0 in metal ==> Eoflat
Bn=m- s = elec mtl to s/c barr
i=Bn-n= m-s elect s/c to mtl barr Depl reg
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References1Device 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.
3Semiconductor Physics & Devices, 2nd ed., by Neamen, Irwin, Chicago, 1997.
