EE 5340Semiconductor Device TheoryLecture 08 – Spring 2011

Professor Ronald L. Carterronc@uta.edu

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

g1

R dxxnxqg

dxxnxqLW

G

dxLW

xnxqdG

s

x

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

EE

nn and ,

nn

kTEE fif

i

o

i

ofif expln

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Electron quasi-Fermi Energy (n = no + n)

kT

EE

nnn

:is density carrier the and

, n

nnkTEE

: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)

kT

EE

npp

:is density carrier the and

, n

ppkTEE

: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 EFi

Ev

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

qfBn

qfi

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 reg

qfBpqfi

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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

qfBn

q(fi)

qfpAccum reg

qfBp qfi

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Metal/semiconductorsystem 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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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 m 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.