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Microelectronic Device Fabrication I (Basic Chemistry and Physics of Semiconductor Device Fabrication) Physics 445/545 David R. Evans
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Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

May 03, 2018

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Page 1: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Microelectronic Device Fabrication I (Basic Chemistry and Physics of

Semiconductor Device Fabrication)

Physics 445/545

David R. Evans

Page 2: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Atomic Orbitals

s-orbitalsp-orbitals

d-orbitals

Page 3: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

BE

*

s,p,d,etc. s,p,d,etc.

BE

*

s,p,d,etc. s,p,d,etc.

Chemical Bonding

Overlap of half-filled orbitals - bond formation

Overlap of filled orbitals - no bonding

HAHB

HA - HB = H2

Formation of Molecular Hydrogen from Atoms

Page 4: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Periodic Chart

Page 5: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Conduction Band

Valence Band

Egs3

p3

sp3

Si(separated atoms)

EV

EC

Si(atoms interact to form

tetrahedral bonding geometry )Si crystal

Crystal Bonding

sp3 bonding orbitals

sp3 antibonding orbitals

Silicon Crystal Bonding

Page 6: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Semiconductor Band Structures

Silicon

Germanium

Gallium Arsenide

Page 7: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Eg

NE

EN

V

V

C

C

EF

Conduction Band

Valence Band

Intrinsic Semiconductor

Aggregate Band Structure

Fermi-Dirac Distribution

Page 8: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

n-type Semiconductor

Aggregate Band Structure

Fermi-Dirac Distribution

Eg

NE

EN

V

V

C

C

Ei

EF

Conduction Band

Valence Band

Shallow Donor States

Donor Ionization

Page 9: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

p-type Semiconductor

Aggregate Band Structure

Fermi-Dirac Distribution

Eg

NE

EN

V

V

C

C

Ei

EF

Conduction Band

Valence Band

Shallow Acceptor States

Acceptor Ionization

Page 10: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Temperature Dependence

Fermi level shift in extrinsic silicon

Mobile electron concentration (ND = 1.15(1016) cm3)

Page 11: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Carrier Mobility

Carrier drift velocity vs applied field in intrinsic silicon

No Field Field Present

Pictorial representation of carrier trajectory

Page 12: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Effect of Dopant Impurities

Effect of total dopant concentration on carrier mobility

Resistivity of bulk silicon as a function of net dopant concentration

Page 13: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

The Seven Crystal Systems

Page 14: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Bravais Lattices

Page 15: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Diamond Cubic Lattice

a = lattice parameter; length of cubic unit cell edge

Silicon atoms have tetrahedral coordination in a

FCC (face centered cubic) Bravais lattice

Page 16: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Miller Indices

O

z

y

x

O

z

y

x

O

z

y

x

100

110

111

Page 17: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Diamond Cubic Model

100

110

111

Page 18: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Cleavage Planes

Crystals naturally have cleavage planes along

which they are easily broken. These correspond to

crystal planes of low bond density.

100 110 111

Bonds per unit cell 4 3 3

Plane area per cell a2 22a2

32a

Bond Density 24

a22

1.22

23aa

228.332

aa

In the diamond cubic structure, cleavage occurs

along 110 planes.

Page 19: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

[100] Orientation

Page 20: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

[110] Orientation

Page 21: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

[111] Orientation

Page 22: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

[100] Cleavage

Page 23: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

[111] Cleavage

Page 24: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Czochralski Process

Page 25: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Seed Rod (Single Crystal Si)

dia. = ~1 cm

Page 26: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Czochralski Process Equipment

Image courtesy Microchemicals

Page 27: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Czochralski Factory and Boules

Page 28: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

CZ Growth under Rapid Stirring

x=0

dxCs

Cl

Dopant K

B 0.72

P 0.32

As 0.27

Sb 0.020

Ga 0.0072

Al 0.0018

In 0.00036

Distribution Coefficients

0 .01

0 .1

1

10

0 0 .2 0 .4 0 .6 0 .8 1

Le ngth Fractio n

Do

pa

nt

Co

nce

ntr

ati

on

Ra

tio

0.5

0.9

0.3

0.2

0.1

0.050.01

CZ Dopant Profiles under Conditions of Rapid Stirring

Page 29: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Enrichment at the Melt Interface

Page 30: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Si Ingot

Heater

Zone Refining

Ingot slowly passes through the needle’s eye heater so

that the molten zone is “swept” through the ingot from

one end to the other

Page 31: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Single Pass FZ Process

x=0 dx

L

x

C s C o

0.01

0.1

1

0 2 4 6 8 10

Zone Lengths

Do

pa

nt

Co

nce

ntr

ati

on R

ati

o

0.5

0.9

0.30.2

0.1

0.03

0.01

Page 32: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Multiple Pass FZ Process

0.01

0.1

1

0 2 4 6 8 10 12 14 16 18 20

Zone Lengths

Dopant

Co

nce

ntr

ati

on R

ati

o

0.50.9 0.3 0.2

0.1

0.03

0.01

Almost arbitrarily pure silicon

can be obtained by multiple

pass zone refining.

Page 33: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Vacancy (Schottky Defect)

“Dangling

Bonds”

Page 34: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Self-Interstital

Page 35: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Dislocations

Edge Dislocation

Screw Dislocation

Page 36: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Burgers Vector

Screw Dislocation

Edge Dislocation

Dislocations in Silicon

[100]

[111]

Page 37: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Stacking Faults

Intrinsic Stacking

Fault

Extrinsic Stacking

Fault

Page 38: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Vacancy-Interstitial Equilibrium

¬

®

Formation of a Frenkel defect - vacancy-interstitial pair

IVL +¨

“Chemical” Equilibrium

]][[ IVKeq =

Page 39: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Thermodynamic Potentials

E = Internal Energy

H = Enthalpy (heat content)

A = Helmholtz Free Energy

G = Gibbs Free Energy

For condensed phases:

E and H are equivalent = internal energy (total system energy)

A and G are equivalent = free energy (energy available for work)

T = Absolute Temperature

S = Entropy (disorder)

A E TS=

WlnkS =

Boltzmann’s relation

Page 40: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Vacancy Formation

eV 3.2~ = vE

A M E T SMv v Mv=

MvMv kS Wln=

WMv

N

N M M=

!

( )! !

==

!)!(

!lnWln

MMN

NkkS MvMv

)ln()( MNkTMN

++= MMkTNNkTEMA vMv lnln

Page 41: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Additional Vacancy Formation

MA E kT M kT N MMv v = + ln ln( )

=

kT

ENM vexp

Vacancy “concentration”

Page 42: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Equilibrium Constant

Interstitial “concentration”

NN8

5=

=

=

kT

EN

kT

ENM ii exp

8

5exp

+=

kT

EENK iv

eq exp8

5 2

¬

®

Page 43: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Internal Gettering

OO

O

OO

O

OO

O

O

O

O

O2

O2O2

O2

O2denuded zone

Gettering removes harmful impurities from the

front side of the wafer rendering them electrically

innocuous.

oxygen nuclei

oxide precipitates(with dislocations and stacking faults)

High temperature anneal - denuded zone formation

Low temperature anneal - nucleation

Intermediate temperature anneal - precipitate growth

Page 44: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Oxygen Solubility in Silicon

1.0E+17

1.0E+18

1.0E+19

900 1000 1100 1200 1300

Temperature, deg C

Inte

rsti

tia

l O

xy

gen C

once

ntr

ati

on,

per

cm

3

Page 45: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Oxygen Outdiffusion

Page 46: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Precipitate Free Energy

a) - Free energy of formation of a spherical precipitate as a function of

radius

b) - Saturated solid solution of B (e.g., interstitial oxygen) in A (e.g.,

silicon crystal)

c) - Nucleus formation

Ar

n E nT S g r= + +4

34

3

2

2 2

SiO SiO

++=

rgSnTEnrA

r84

22 SiOSiO

2

Page 47: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Critical Radius

a) – If critical radius exists, then a larger precipitate grows large

b) – If critical radius exists, then a smaller percipitate redissolves

gSnTEnrcrit

+

=

22 SiOSiO

2

Page 48: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Substrate Characterization by XRD

Constructive Interference Destructive Interference

qq

Bragg pattern - [hk0], [h0l], or [0kl]

Page 49: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Wafer Finishing

Schematic of chemical mechanical polishing

Spindle

Pad

Table

Wafer Insert

Carrier

Capture Ring

Ingot slicing into raw wafers

Page 50: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Vapor-Liquid-Solid (VLS) Growth

substrate substrate

SiH4 SiH4

H2 H2 H2 H2

substrate

catalyst

Si nanowires grown by VLS (at IBM)

Page 51: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Gold-Silicon Eutectic

A B

liquid

solid

A – eutectic melt mixed with solid gold

B – eutectic melt mixed with solid silicon

Page 52: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Silicon Dioxide Network

Silanol

Non-bridging

oxygen

SiO4 tetrahedron

Page 53: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Thermal Oxidation

Thermal SiO 2 Film

F1

Si Substrate Gas

F2

F3

C

x

CGCS

Co

Ci

One dimensional model of oxide growth

Deal-Grove growth kinetics

Page 54: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Steady-state Fluxes

)(1 SGG CChF =Mass transport flux

)(2 io CC

x

DF =

Diffusion flux

isCkF =3

Reaction “flux”

1) Diffusion flux is “in-diffusion”.

Any products, e.g., H2, must “out-diffuse”.

However, out-diffusion is fast and generally

not limiting.

2) Mass transport is generally never limiting.

Page 55: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

S

o

C

CH =

Henry's Law

Distribution equilibrium

(Henry's Law)

Reaction = Mass Transport

=

H

CChCk o

GGis

H

C

h

CkC o

G

isG +=

Page 56: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Steady-state Concentrations

Reaction = Diffusion

)( iois CC

x

DCk =

Gas phase concentration related

to reaction concentration

i

so C

D

xkC

+= 1

i

s

G

sG C

HD

xk

Hh

kC

++=

1

Page 57: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Deal-Grove Model

Relationship between thickness

and time:

+++

+=

Gs

G

Gs h

H

ktt

ND

HC

h

H

kDx

1)(

210

2

What if an oxide of thickenss, x0, is

already on the wafer?

Must calculate equivalent growth time

under desired conditions

1

3 1

++==

D

xk

h

HkHCk

dt

dxNF s

G

sGs

++= 0

2

00

12

2x

h

H

kDx

DHC

Nt

GsG

Page 58: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Deal-Grove Rate Constants

B/A => Linear Rate Constant

B => Parabolic Rate Constant

+=

Gs h

H

kDA

12

N

DHCB G2=

+

=

Gs

G

hHkN

C

A

B

11

Page 59: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Oxidation Kinetics

Reactant

Product

Transition

Ea

E

Energy‡

Process Coordinate

Process B/A for [100] B/A for [111] B

Dry Oxidation 1.03(103) kTe

00.2

1.73(103) kTe

00.2

0.214 kTe

23.1

Steam Oxidation 2.70(104) kTe

05.2

4.53(104) kTe

05.2

0.107 kTe

79.0

Note: Activation energies are in eV’s, B/A is in m/sec, B is in m2/sec

Rate constants for wet and dry oxidation on [100] and [111]

surfaces

Page 60: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Linear Rate Constant

Orientation dependence for [100] and [111] surfaces affects

only the “pre-exponential” factor and not the activation

energy

Page 61: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Parabolic Rate Constant

No orientation dependence since the parabolic rate constant

describes a diffusion limited process

Page 62: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Pressure Dependence

Oxidation rates scale linearly with oxidant pressure or partial

pressure

Page 63: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Rapid Initial Oxidation in Pure O2

This data taken at 700C in dry oxygen to investigate initial

rapid oxide growth

Page 64: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

f1

f2

+

++

++

f2 f1

EF1

EF2

EF

Evac

y =

Metal-Metal Contact

Metal 1 Metal 2

Page 65: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Metal-Silicon Contact

EFSi

fM

+

++

++

EF

Evac

EFM

Ec

Ev

fSi

fMfSi

Metal Silicon

Page 66: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Effect of a Metal Contact on Silicon

Ec

Ev

jF

EF +

++

++

Ei

Ec

Ev

jF

EF +

++

++

Ei

Depletion (p-type) Inversion (p-type)

Ec

Ev

jF

EF +

++

++

Ei

Ec

Ev

jF

EF

Ei

Accumulation (n-type) Flat Band (n-type)

+

++

++

Ec

Ev

jF

Ei

EF

Depletion (n-type)

Page 67: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Metal-Oxide-Silicon Capacitor

EV

EC

EFSi

fM

+

++

EF

Evac

EFM

fSi

fMfSi

SiO2

f

Metal SiliconSilicon

Dioxide

Page 68: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

MOS Capacitor on Doped Silicon

EV

EC

EFM

EijFEFSi

+

++

EV

EC

EFM

Ei

jF

EFSi

+

++

Depletion (p-type) Accumulation (n-type)

Vg

0 v

Schematic of biased MOS capacitor

Page 69: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

EV

EC

jF

EiEi

EFSi

EFM

EV

EC

EFM

jF

Ei

EFSi

Accumulation (p-type) Inversion (n-type)

EV

EC

EFM

EijFEFSi

EV

ECEFM

jF

Ei

EFSi

Depletion (p-type) Depletion (n-type)

EV

EC

EFM

EijFEFSi

EV

EC

EFM

jFEi

EFSi

Inversion (p-type) Accumulation (n-type)

Biased MOS Capacitors

Page 70: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

CV Response

n-type substrate

p-type substrate

0

1

2

3

4

5

6

7

8

9

10

-100 -50 0 50 100

Bias Voltage

Ca

pa

cit

an

ce

quasistatic

high frequency

depletion

approximation

0

1

2

3

4

5

6

7

8

9

10

-50 -40 -30 -20 -10 0 10 20 30 40 50

Bias Voltage

Ca

pa

cit

an

ce

quasistatic

high frequency

depletion

approximation

Page 71: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Surface Charge Density

1

10

100

1000

10000

100000

1000000

10000000

-30 -20 -10 0 10 20 30

Bias Voltage

Su

rfa

ce

Ch

arg

e D

en

sit

y

inversion

accumulation

depletion

1

10

100

1000

10000

100000

1000000

10000000

-30 -20 -10 0 10 20 30

Bias Voltage

Su

rfa

ce

Ch

arg

e D

en

sit

y

accumulation

depletion

inversion

n type substrate

p type substrate

blue: positive

surface charge

red: negative

surface charge

Page 72: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

s

x

dx

d

=

j )(2

2

Capacitance, Charge, and Potential

Poisson’s equation (1-D)

Charge density for a uniformly

doped substrate

AD NNxnxpqx += )()()(

i

si

nq

kT22

=

Intrinsic Debye Length:

a measure of how much an external

electric field penetrates pure silicon

Page 73: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

The Depletion Approximation

)()(

2

2

xNxNq

dx

dAD

s

=j

Carrier concentrations are negligible

in the depletion region

=

i

DA

DA

sd

n

NN

NNq

kTx ln

42

max

Maximum depletion width

DA

sD

NNq

kT

=

2

Extrinsic Debye Length:

a measure of how much an external

electric field penetrates doped silicon

Page 74: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

CV vs Doping and Oxide Thickness

Substrate

Doping

Oxide

Thickness

p-type substrate0

1

2

3

4

5

6

7

8

9

10

-100 -50 0 50 100 150

Cap

acit

ance

(dim

ensi

on

less

lin

ear

scal

e)

0.1

1

10

100

1000

-150 -100 -50 0 50 100

Cap

acit

ance

(dim

ensi

on

less

logar

ithm

ic s

cale

)

Bias Voltage (dimensionless linear scale)

Page 75: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

CV Measurements

V

C

Cmin

Cox

Quasi-static CV

V

C

Cmin

Cox

High Frequency CV

V

C

Cox

Cmin slow sweep

fast

very fast

extremely fast

Deep Depletion Effect

V

C

Cmin

Cox

FBC

VFB

VFB

Ideal

Actual

Flat Band Shift

V

C

Cmin

Cox

FBC

VFB

Ideal

Actual

Fast Interface States

Page 76: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Interface States

EV

EC

jF

EF

Ei

Interface states – caused by

broken symmetry at interface

Interface states – p-type depletion

Interface states – n-type depletion

EV

ECEFM

jF

Ei

EFSi

+++++

EV

EC

EFM

EijFEFSi

Page 77: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Interface State Density

Interface state density is always higher on [111] than [100]

Page 78: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

IV Response

log J

E10 MV/cm

T hick

T hin

Very T hin

Logarithm of current density (J) vs applied electric field (E)

Fowler-Nordheim

tunneling

avalanche breakdown

Page 79: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Conduction Mechanisms

=

E

EEAJ o

FN exp2 Fowler-Nordheim tunneling

f= kT

qEqEAJ

ox

BFP exp

Frenkel-Poole emission

f= kT

qEqTAJ

ox

B4

exp* 2

Schottky emission

kTEqEAJ aee = expOhmic (electronic)

conduction

kTEq

T

EAJ ai

i = exp Ionic conduction

3

2

8

9

o

ox

eox

x

VJ

=

Mobility limited breakdown

current

Page 80: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

total charge, Qtime, t, or

100%

0%

FailedPer cent

good reliabilitypoor reliability

“ infant” mortality

Oxide Reliability

QBD - “charge to breakdown” - constant current

stress

TDBD - “time dependent breakdown” - constant

voltage stress

Each point represents a failed MOS structure - stress is

continued until all devices fail

Page 81: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Linear Transport Processes

Ohm’s Law of electrical conduction: j = E = E/

J = electric current

density, j

(units: A/cm2)

X = electric field,

E = V

(units: volt/cm)

V = electrical potential

L = conductivity,

= 1/

(units: mho/cm)

= resistivity ( cm)

Fourier’s Law of heat transport: q = T

J = heat flux, q

(units: W/cm2)

X = thermal force,

T

(units: K/cm)

T = temperature

L = thermal

conductivity,

(units: W/K cm)

Fick’s Law of diffusion: F = DC

J = material flux, F

(units: /sec cm2)

X = diffusion force,

C

(units: /cm4)

C = concentration

L = diffusivity, D

(units: cm2/sec)

Newton’s Law of viscous fluid flow: Fu = u

J = velocity flux, Fu

(units: /sec2 cm)

X = viscous force,

u

(units: /sec)

u = fluid velocity

L = viscosity,

(units: /sec cm)

J = LX

J = Flux, X = Force, L = Transport Coefficient

Page 82: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Diffusion

Diffusion in a rectangular bar of constant cross section

C

tD

C

x=

2

2

Fick’s Second Law

Dtxx

eDt

NtxC 4

20

2,

=

Instantaneous Source - Gaussian profile

Constant Source - error function profile

=

Dt

xxNtxC

2erfc

2, 00

A

x

x

F(x) xF(x )+

Page 83: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Instantaneous Source Profile

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5

0.1

1.0

0 0.5 1 1.5 2

Linear scale

Log scale

Page 84: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Constant Source Profile

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5

0.1

1.0

0 0.5 1 1.5 2

Linear scale

Log scale

Page 85: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Surface Probing

I

r

Substrate

Single probe injecting

current into a bulk

substrate

s ss

1 2 3 4

I I

Substrate

Four point probe

I

r

Substrate

T hin Film

xf

Single probe injecting

current into a

conductive thin film

Page 86: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Ei

EFn

EFp

Evac

Ec

Ev

EF

pn Junction

n type Silicon p type Silicon

Page 87: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Junction Depth

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5

0.01

0.10

1.00

0 0.5 1 1.5 2

xJ

xJ

red: background

doping

black: diffused

doping

Page 88: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Unbiased pn Junctions

EF

E

V

Electric Field

Band Diagram

Charge Density

Potential

Page 89: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Biased pn Junctions

IV Characteristics

V

I

I0

V

2

1

C

Vpn

CV Characteristics

Page 90: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Photovoltaic Effect

V

I

ISC

VOC

Page 91: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Solar Cell

typical cross section

equivalent circuit

Page 92: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Solar Cell IV Curve

ISC

VOC

I

P

Vmax

Imax

Page 93: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Effect of Parasitics, Temperature, etc.

effect of RS effect of RSH

effect of I0 effect of n

effect of T

Page 94: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Solar Cell Technology

Commercial solar cell

Page 95: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

LED IV Characteristics

Page 96: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

LED Technology

RGB spectrum

Commercial LED’s

white spectrum(with phosphor)

Page 97: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Diffusion Mechanisms

Vacancy Diffusion - Substitutional impurities,

e.g., shallow level dopants (B, P, As, Sb, etc.),

Diffusivity is relatively small for vacancy

diffusion.

Interstitial Diffusion - Interstitial impurities,

e.g., small atoms and metals (O, Fe, Cu, etc.),

Diffusivity is much larger, hence interstitial

diffusion is fast compared to vacancy diffusion.

Interstitialcy Mechanism - Enhances the

diffusivity of substitutional impurities due to

exchange with silicon self-interstitials. This

leads to enhanced diffusion in the vicinity of the

substrate surface during thermal oxidation (so-

called “oxidation enhanced diffusion”).

Page 98: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Defect-Carrier Equilibria

Vacancies interact with mobile carriers and

become charged. In this case, the concentrations

are governed by classical mass action equilibria.

V V h KV

Vpx

V x

®

¬

+

+ =

V V h KV

VpV

= + =

=

®

¬+ =

V V e KV

Vnx

V x

®

¬

+ +

+

+ =

V V e KV

VnV

+ ++ ++

++

+

®

¬+ =

Page 99: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Arrhenius Constants for Dopant Atoms

Atomic Species

I

Diffusion Mechanism rV

r

oID

(cm2/sec)

r

IQ

(eV)

Si xV

V

=V

+V

0.015

16

10

1180

3.89

4.54

5.1

5.09

As xV

V

0.066

12.0

3.44

4.05

B xV

+V

0.037

0.76

3.46

3.46

Ga xV

+V

0.374

28.5

3.39

3.92

P xV

V

=V

3.85

4.44

44.2

3.66

4.00

4.37

Sb xV

V

0.214

15.0

3.65

4.08

N xV 0.05 3.65

Page 100: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Arrhenius Constants for Other Species

Atomic Species Mechanism,

Temperature, etc.

DoI

(cm2/sec)

QI

(eV)

Ge substitutional )10(25.6 5 5.28

Cu (300-700C)

(800-1100C)

)10(7.4 3

0.04

0.43

1.0

Ag )10(2 3 1.6

Au substitutional

interstitial

(800-1200C)

)10(8.2 3

)10(4.2 4

)10(1.1 3

2.04

0.39

1.12

Pt 150-170 2.22-2.15

Fe )10(2.6 3 0.87

Co )10(2.9 4 2.8

C 1.9 3.1

S 0.92 2.2

O2 0.19 2.54

H2 )10(4.9 3 0.48

He 0.11 1.26

Page 101: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Solid Solubilities

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Ion Implantation

Dopant species are ionized and accelerated by a

very high electric field. The ions then strike the

substrate at energies from 10 to 500 keV and

penetrate a short distance below the surface.

b

iv

|| v̂

^v̂

iv

i

s

q

sv

k̂ q

c

tangent plane(edge on)

Elementary “hard sphere” collision

Page 103: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Co-linear or “Centered” Collision

i

iv|| v̂

^v̂

iv

s

sv

tangent plane(edge on)b=0

c=

q=0

i

si

isi

si

sii v

mm

mvv

mm

mmv

+=

+

=

2 ;

Clearly, if mi<ms, then iv is negative. This means that light implanted ions tend to be

scattered back toward the surface. Conversely, if mi>ms, then iv is positive and heavy

ions tend to be scattered forward into the bulk. Obviously, if mi equals ms, then 0|| v̂v i

vanishes. In any case, recoiling silicon atoms are scattered deeper into the substrate.

Page 104: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Stopping Mechanisms

Nuclear Stopping - Direct interaction between

atomic nuclei; resembles an elementary two

body collision and causes most implant damage.

Electronic Stopping - Interaction between

atomic electron clouds; sort of a “viscous drag”

as in a liquid medium. Causes little damage.

Page 105: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Implant Range

Range - Total distance traversed by an ion

implanted into the substrate.

Projected Range - Average penetration depth of

an implanted ion.

Page 106: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Implant Straggle

Projected Straggle - Variation in penetration

depth. (Corresponds to standard deviation if the

implanted profile is Gaussian.)

Page 107: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Channeling

Channeling is due to the crystal structure of the

substrate.

Page 108: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Implantation Process

For a light dose, damage is isolated. As dose is

increased, damage sites become more dense and

eventually merge to form an amorphous layer.

For high dose implants, the amorphous region

can reach all the way to the substrate surface.

Page 109: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Point-Contact Transistor

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Bipolar Junction Transistor

n

n p

C B E

Page 111: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

Junction FET

n

n p

S D G

Page 112: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

MOSFET

p

n n

S D G

enhancement mode

p

n n

S D G

depletion mode

Page 113: Microelectronic Device Fabrication I - Portland State …web.pdx.edu/~davide/slides.pdfA = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent

7 V

6 V

5 V

4 V

Enhancement Mode FET