Microelectronic Device Fabrication I (Basic Chemistry and Physics of

Semiconductor Device Fabrication)

Physics 445/545

David R. Evans

Atomic Orbitals

s-orbitalsp-orbitals

d-orbitals

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

Periodic Chart

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

Semiconductor Band Structures

Silicon

Germanium

Gallium Arsenide

Eg

NE

EN

V

V

C

C

EF

Conduction Band

Valence Band

Intrinsic Semiconductor

Aggregate Band Structure

Fermi-Dirac Distribution

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

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

Temperature Dependence

Fermi level shift in extrinsic silicon

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

Carrier Mobility

Carrier drift velocity vs applied field in intrinsic silicon

No Field Field Present

Pictorial representation of carrier trajectory

Effect of Dopant Impurities

Effect of total dopant concentration on carrier mobility

Resistivity of bulk silicon as a function of net dopant concentration

The Seven Crystal Systems

Bravais Lattices

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

Miller Indices

O

z

y

x

O

z

y

x

O

z

y

x

100

110

111

Diamond Cubic Model

100

110

111

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.

[100] Orientation

[110] Orientation

[111] Orientation

[100] Cleavage

[111] Cleavage

Czochralski Process

Seed Rod (Single Crystal Si)

dia. = ~1 cm

Czochralski Process Equipment

Image courtesy Microchemicals

Czochralski Factory and Boules

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

Enrichment at the Melt Interface

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

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

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.

Vacancy (Schottky Defect)

“Dangling

Bonds”

Self-Interstital

Dislocations

Edge Dislocation

Screw Dislocation

Burgers Vector

Screw Dislocation

Edge Dislocation

Dislocations in Silicon

[100]

[111]

Stacking Faults

Intrinsic Stacking

Fault

Extrinsic Stacking

Fault

Vacancy-Interstitial Equilibrium

¬

®

Formation of a Frenkel defect - vacancy-interstitial pair

IVL +¨

“Chemical” Equilibrium

]][[ IVKeq =

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

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

Additional Vacancy Formation

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

=

kT

ENM vexp

Vacancy “concentration”

Equilibrium Constant

Interstitial “concentration”

NN8

5=

=

=

kT

EN

kT

ENM ii exp

8

5exp

+=

kT

EENK iv

eq exp8

5 2

¬

®

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

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

Oxygen Outdiffusion

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

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

Substrate Characterization by XRD

Constructive Interference Destructive Interference

qq

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

Wafer Finishing

Schematic of chemical mechanical polishing

Spindle

Pad

Table

Wafer Insert

Carrier

Capture Ring

Ingot slicing into raw wafers

Vapor-Liquid-Solid (VLS) Growth

substrate substrate

SiH4 SiH4

H2 H2 H2 H2

substrate

catalyst

Si nanowires grown by VLS (at IBM)

Gold-Silicon Eutectic

A B

liquid

solid

A – eutectic melt mixed with solid gold

B – eutectic melt mixed with solid silicon

Silicon Dioxide Network

Silanol

Non-bridging

oxygen

SiO4 tetrahedron

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

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.

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 +=

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

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

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

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

Linear Rate Constant

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

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

energy

Parabolic Rate Constant

No orientation dependence since the parabolic rate constant

describes a diffusion limited process

Pressure Dependence

Oxidation rates scale linearly with oxidant pressure or partial

pressure

Rapid Initial Oxidation in Pure O2

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

rapid oxide growth

f1

f2

+

++

++

f2 f1

EF1

EF2

EF

Evac

y =

Metal-Metal Contact

Metal 1 Metal 2

Metal-Silicon Contact

EFSi

fM

+

++

++

EF

Evac

EFM

Ec

Ev

fSi

fMfSi

Metal Silicon

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)

Metal-Oxide-Silicon Capacitor

EV

EC

EFSi

fM

+

++

EF

Evac

EFM

fSi

fMfSi

SiO2

f

Metal SiliconSilicon

Dioxide

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

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

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

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

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

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

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)

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

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

Interface State Density

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

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

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

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

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

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 )+

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

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

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

Ei

EFn

EFp

Evac

Ec

Ev

EF

pn Junction

n type Silicon p type Silicon

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

Unbiased pn Junctions

EF

E

V

Electric Field

Band Diagram

Charge Density

Potential

Biased pn Junctions

IV Characteristics

V

I

I0

V

2

1

C

Vpn

CV Characteristics

Photovoltaic Effect

V

I

ISC

VOC

Solar Cell

typical cross section

equivalent circuit

Solar Cell IV Curve

ISC

VOC

I

P

Vmax

Imax

Effect of Parasitics, Temperature, etc.

effect of RS effect of RSH

effect of I0 effect of n

effect of T

Solar Cell Technology

Commercial solar cell

LED IV Characteristics

LED Technology

RGB spectrum

Commercial LED’s

white spectrum(with phosphor)

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”).

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

+ ++ ++

++

+

®

¬+ =

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

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

Solid Solubilities

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

Co-linear or “Centered” Collision

i

iv|| v̂

^v̂

iv

s

sv

k̂

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.

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.

Implant Range

Range - Total distance traversed by an ion

implanted into the substrate.

Projected Range - Average penetration depth of

an implanted ion.

Implant Straggle

Projected Straggle - Variation in penetration

depth. (Corresponds to standard deviation if the

implanted profile is Gaussian.)

Channeling

Channeling is due to the crystal structure of the

substrate.

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.

Point-Contact Transistor

Bipolar Junction Transistor

n

n p

C B E

Junction FET

n

n p

S D G

MOSFET

p

n n

S D G

enhancement mode

p

n n

S D G

depletion mode

7 V

6 V

5 V

4 V

Enhancement Mode FET