atomic orbitals s-orbitals p-orbitals d-orbitals

Microelectronic Device Fabrication I (Basic Chemistry and Physics of

Semiconductor Device Fabrication)

Physics 445/545

David R. Evans

Atomic Orbitals

s-orbitals p-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 formtetrahedral 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

VV

CC

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

VV

CC

E i

EF

Conduction Band

Valence Band

Shallow Donor States

Donor Ionization

p-type Semiconductor

Aggregate Band Structure

Fermi-Dirac Distribution

Eg

NE

EN

VV

CC

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 PresentPictorial 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 edgeSilicon 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 22a 232a

Bond Density 24

a 221.2

223

aa 22

8.332aa

In the diamond cubic structure, cleavage occurs along 110 planes.

[100] Orientation

[110] Orientation

[111] Orientation

[100] Cleavage

[111] Cleavage

Czochralski Process

Czochralski Process Equipment

Image courtesy Microchemicals

Czochralski Factory and Boules

CZ Growth under Rapid Stirring

x=0

dxCs

Cl

Distribution Coefficients

0.01

0.1

1

10

0 0.2 0.4 0.6 0.8 1

Length Fraction

Dop

ant

Con

cent

rati

on R

atio

0.5

0.9

0.3

0.2

0.10.05 0.01

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

Dop

ant

Con

cent

rati

on R

atio

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

Dop

ant

Con

cent

rati

on R

atio

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 EnergyH = Enthalpy (heat content)

A = Helmholtz Free EnergyG = 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 TemperatureS = Entropy (disorder)

A E TS

WlnkS

Boltzmann’s relation

Internal Gettering

OO

O

OO

O

OO

O

O

O

O

O2O2

O2

O2

O2denuded zone

Gettering removes harmful impurities from thefront side of the wafer rendering them electricallyinnocuous.

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

tial

Oxy

gen

Con

cent

rati

on,

per

cm3

Oxygen Outdiffusion

Precipitate Free Energy

a) - Free energy of formation of a spherical precipitate as a function of radiusb) - Saturated solid solution of B (e.g., interstitial oxygen) in A (e.g., silicon crystal)c) - Nucleus formation

Substrate Characterization by XRD

Constructive Interference Destructive Interference

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-bridgingoxygen

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

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)

kTe00.2

0.214 kTe

23.1

Steam Oxidation 2.70(104) kTe

05.2 4.53(104)

kTe05.2

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

1

2

2 1

EF1

EF2

EF

Evac

=

Metal-Metal Contact

Metal 1 Metal 2

Metal-Silicon Contact

EFSi

M

EF

Evac

EFM

Ec

Ev

Si

MSi

Metal Silicon

Effect of a Metal Contact on Silicon

Ec

Ev

FEF

Ei

Ec

Ev

F

EF

Ei

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

Ec

Ev

F

EF

Ei

Ec

Ev

FEF

Ei

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

Ec

Ev

FEi

EF

Depletion (n-type)

Metal-Oxide-Silicon Capacitor

EV

EC

EFSi

M

EF

Evac

EFM

Si

MSi

SiO2

Metal SiliconSilicon Dioxide

MOS Capacitor on Doped Silicon

EV

EC

EFM

EiFEFSi

EV

EC

EFM

Ei

FEFSi

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

Vg

0 vSchematic of biased MOS capacitor

EV

EC

FEiEi

EFSi

EFM

EV

EC

EFM

FEi

EFSi

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

EV

EC

EFM

EiFEFSi

EV

ECEFM

FEi

EFSi

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

EV

EC

EFM

EiFEFSi

EV

EC

EFM

F Ei

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 frequencydepletion

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 chargered: negative

surface charge

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

onle

ss li

near

sca

le)

0.1

1

10

100

1000

-150 -100 -50 0 50 100

Cap

acit

ance

(dim

ensi

onle

ss lo

gari

thm

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 sweepfastvery 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

FEF

Ei

Interface states – caused by broken symmetry at interface

Interface states – p-type depletion

Interface states – n-type depletion

EV

ECEFM

FEi

EFSi

+++++

EV

EC

EFM

EiFEFSi

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

total charge, Qtime, t, or

100%

0%

FailedPer cent

good reliabilitypoor reliability

“ infant” mortality

Oxide Reliability

QBD - “charge to breakdown” - constant current stressTDBD - “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

roID

(cm2/sec)

rIQ

(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

sv

k̂

tangent plane(edge on)

Elementary “hard sphere” collision

Co-linear or “Centered” Collision

iiv|| v̂

v̂

iv

ssv

k̂

tangent plane(edge on)b=0

==0

isi

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