EE 5340Semiconductor Device TheoryLecture 8 - Fall 2010

Professor Ronald L. Carterronc@uta.edu

http://www.uta.edu/ronc

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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 http://www.uta.edu/ronc/5340/tests/.

Star Simulation of IC Resistor

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Star Simulation of IC Resistor Corner

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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

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 = (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 EFi

Ev

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

qBn

qi

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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Metal to n-typenon-rect cont (m<s)

EFn

Eo

Ec

Ev

EFi

qs,n

qs

n-type s/c

qm

EF

m

metal

qB,n

qn

No disc in Eo

Ex=0 in metal ==> Eo flat

B,n=m - s

= elec mtl to s/c barr

i= Bn-n<

0Accumulatio

n region

Acc reg

qi

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Ideal metal to p-typebarrier diode (m<s)

EFp

Eo

Ec

Ev

EFi

qs,p

qs

p-type s/c

qm

EF

m

metal

qBn

qi

qp<0

No disc in Eo

Ex=0 in metal ==> Eoflat

Bn= m- s = elec mtl to s/c barr

Bp= m- s + Eg = hole m to s

i = Bp-s,p = hole s/c to mtl barr

Depl reg

qBpqi

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Metal to p-typenon-rect cont (m>s)

No disc in Eo

Ex=0 in metal ==> Eo flat

B,n=m- s,n = elec mtl to s/c barr

Bp= m- s + Eg = hole m to s

Accumulation region

EFi

Eo

Ec

Ev

EfP

qs,n

qs

n-type s/c

qm

EF

m

metal

qBn

q(i)

qpAccum reg

qBpqi

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Metal/semiconductorsystem types

n-type semiconductor

• Schottky diode - blocking for m > s

• contact - conducting for m < s

p-type semiconductor

• contact - conducting for m > s

• Schottky diode - blocking for m < s

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Real Schottkyband structure1

• Barrier transistion region,

• Interface statesabove o acc, p neutrl

below o dnr, n neutrl

Dit -> oo, qBn= Eg- o

Fermi level “pinned”

Dit -> 0, qBn= m - Goes to “ideal” case

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Fig 8.41 (a) Image charge and electric field at a metal-dielectric interface (b) Distortion of potential barrier at E=0 and (c) E0

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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.