Background material science ideas that may be of use.

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II Background Engineering Science Page

A) Starting Material 2- 2B) Unit Process Model for Process Control 2- 3

Crystal Gro wth Model 2- 3Growth A pproach Adjustments to Mo del Constraints 2- 3

Single Crystal Silicon Growth 2- 3Czochralski Metho d (C Z Gro wth) 2- 4Impurity Sources 2- 5

Single Crystal GaAs Growth 2- 5C) Wafer Material Performance Adjustments 2- 5

A bridged Perio dic Table of Elements 2- 6Impurities in the Crystal Structure 2- 6

Two Views of a Cubic Crystal Structure 2- 7Doping During Crystal Gro wth 2- 7 Equilibrium Segregation Coefficient 2- 8

Effective Segregation Coefficient 2- 8Two Views of a Doped Cu bic Crystal Structure 2- 9Local an d Universal Charge Characteristics 2-10 Lo w Temperature 2-10

At High Temperature 2-10After Ion A ddition 2-10

D) Bare Wafer Issues 2-11Orientation 2-12

Surface Planes an d Directions ( Miller In dices) 2-12Concentration of Constituents 2-13

Ty pical Intrinsic Densities 2-13Slab Density for Si 2-13Face Densitites for Si 2-13

Highly Doped Si Wafer Cross Section 2-13Important Parameters 2-14

Resistivity 2-14Epitaxial Film 2-15

E) Electronic Influence of Contaminates 2-15Energy Level A pproximate Values for Isolated Atom in Space 2-15Related Position of Silicon Energy Levels 2-15Compensate d Devices 2-16

Charge Neutrality 2-16

SiO2

(Quartzite)

Coke Furnace

gas

SiHCl3

Finish with EGS

Poly-crystalline

A) Starting Materials

SiCSolid

Siliquid

Heat

Exch

an

ger

SiSolid

Pulverizer

MGS

Micron sized particles

Flu

idiz

ed

BedHCl

Metallugical grade silicon

Start with Sand

Distillation Column

pureTrichorosilane

Hydrogen gas

Fuel gas

hot

Chemical Vapor Deposition Reactor

Electronic Grade solid silicon

B) Unit Process Models for Proper Control (Process control is best achieved when the equipment follows the model)

Crystal growth is an excellent example of how equipment and model cooperate to accomplish the task

Crystal Growth Model

Growth Approach Adjustments to Model Constraints (Three adjustments to equipment to make growth process match simplify model)

1)Uniformly Heat and insulate the Melt. ( This makes the liquid (dT/dx)Liquid

= 0

2)Slow Pull Rates. (This makes (dx) small value and allows use of calculus)

3)Crucible Surface Area Approximates As and Crystal Rotates Slowly. (This makes heat of fusion the only new heat source and (dT/dx)

S predictable)

This Gradient has Known Shape and Values

Thermal Conductivity for Crystal Near Liquid Interface

The small change in solid crystal mass because of a small change in time

Temperature gradient in solid crystal near the solid crystal interface

Temperature gradient in liquid at a location near the liquid interface

(dm/dt)solid

(dT/dx)Solid

- (dT/dx)liquid

s(dm dt ) s(k s Hs ) (A ) ( dT dx )s

Pulled single crystal rod is checkedby X-ray camera for crystal alignment

Aligned rod carefully polished andthen sliced to near wafer dimensions.

Wafer Finish

Linear Pull Rate

Density of Crystal Near Melt Interface

(d v dt) (ks Hs ) (1 s ) (dT dx)s

Single Crystal of Wafer Material with

know Amount of Dopent Added.Single Crystal crystal attached to chuck to obtain a specific crystalorientation with plane of melt

Seed single crystal is slowly rotatedwhile being pulled out of the melt

treated in an arc furnacefollowed by HCl rinses and

Melt comes from Sand ( Quartzite ) that has been

factional distillation to become EGS

Chuck that Holds Single Crystal

Fused Silica Crucible Adds oxygen to Melt

Crucible HolderUniformly Heated

Degenerately DopedElectronic Grade Si

Czechralski Method (CZ Growth)

=

Impurity Sources ( PPM)

MGS EGS Crucible

Metal Grade Electronic Grade Silica

B 50 0.001 0.23

Fe 2,100 5. 6

P 30 0.002 -

As - 0.01 0.005

C 80 0.6 -

0 - 0.02 0.05

“VLSI Technology”, 2nd Edition, S.M. Sze, McGraw Hill, 1988

Note:

CZ Growth used over 99% of time. Other option is Float Zone Crystal Growth Process.

Good reference for CZ growth,

“Characterization & Engineering of the Antimony Hero-Antisite Defect in LEC Gallium Arsenide, Ph.D. Dissertation, Marshall Wilson, U. South Fl. 1997

BrSeGallium Arsenic

Lewis diagrams show the atom as its symbol plus its electrons in the outer orbitEvery atom in a Group has the same number electrons in outer orbit.

Ge As

Impurities the Crystal Structure

Although unwanted impurities exist within a crystal structure, in most

micro and nano applications, a “special” impurity, the dopant, is added

to the crystal structure.

C)Wafer Material Performance Adjustments

ArAl P S ClSi

Ga

B N O FC

He

III V VI VII VIII

(with Some Lewis Electron Structures)

Group Number I

H

IV

Si

Two views of a cubic crystal structure 3 D Perspective

Ab

ou

t 6 A

Lattice Point

About 6 AO

Interstitial Location

-10o1 A = 10 Meters

About 6 A

Si

Si

Si

Si

Si Si

Si

Si

Si

Si

Si

SiSi Si SiSi

SiSiSi SiSi

Si

Si

SiSiSi

Si

Si

Si

Doping During Crystal Growth

Equilibrium Segregation Coefficient

A dopant will be driven by equilibrium considerations

to a specific concentration ratio between two possible phases

if given enough time and stable conditions to do so.Equilibrium Segregation Coefficient

With C s s = Concentration of Dopant in the Crystal Being Pulled

C ll = Concentration of Dopant in the Melt below the Crystal

kequilibrium

Cs /

C

Effective Segregation Coefficient

Often the driving equilibrium considerations are to complicatedto understand because of the arrangement of the equipment andany additional components within the melting system. In this situation an effective segregation coefficient, kseq, is used.

Segregation Coefficient

With:v = Pull Rate;

B = Boundary Layer;

D = Diffusion CoefficientNote:

kseqseq takes on values from keqeq to 1.0

kseqseq k eq ( 1 / [ keqeq +( 1 - keqeq ) ( e - (B/D) (vv ) ]=

Summary Two Views of a Doped Cubic Crystal StructurePhosphorus atom on a substitutional lattice location

n-type Doped Arrangementp-type Doped Arrangement

Boron atom on a substitutional lattice location

(Phosphorus's non-bonded outer electroncan move about the slab of material andgenerate local areas of negative charge)

(Boron’s unoccupied outer orbit hole can move about the slab of material andgenerate local areas of positive charge)

P

B P

BSi

SiSi

Si

Si

Si

Si Si

Si Si

Si

Si

Si

Si

Si

SiSi Si SiSi

SiSi Si SiSi

B Si

SiSi

Si

Si

Si Si

Si Si

Si

Si

Si

Si

Si

SiSi Si SiSi

SiSi Si SiSi

Si P

Local and Universal Charge Characteristics

The local charge around the boron adds up to zero.

Substrate withAcceptor atom

the phosphorus in the n doped slabalso adds up to zero.

The local charge around the

No localized charge inequality in eitherof these slabs of doped silicon.

1) At Low Temperatures

p-type Doped Arrangement

Both of these Slabs (n-type and p-type) Remain Overall Neutral

n-type Donor Arrangement

N =A

Substrate withDonor atom

Si Si

B

Si

Si

Si

Si

Si Si

Si Si

P

Si

Si

Si

Si

Si Si

Number Density of Acceptors N =D

Number Density of Donors

Local and Universal Charge Characteristics

3) Add ion to slab so it finally exchanges with a lattice location

An Ion

Si Si

B

Si

Si

Si

Si

Si Si

electron left this location soregion is now more positive than it was before it left.

electron has entered this location soregion is now more negative than itwas before it got there.

N = Density of Charged AcceptorsA

p = Number Density of Holes

Density of Charged Donors

n = Number Density "Free" Electrons

“Ionized” acceptor

Concentration of ions = Concentration of carrier

2) Raise the temperature of the lattice

Si Si

B

Si

SiSi

Si Si

“ionized” donor atom

Si Si

Si Si

P

Si

SiSi

Si Si

DN =

Lattice with new ion becomes charged

Orientation

(001)

(110)

(111)

a

a

Surface planes and directions based on Miller Indices

-10o1 A = 10 Meters

About 6 AO

D) Wafer Issues

(100)(010)

(001)

(100)

(100)

(The 111 perspective)

Concentration of Constituents

Typical Intrinsic Densities

Slab Density N total = 5 x 10 22 atoms/cm 3

Face Density N (100) = 6.8 x 10 14 atoms/cm 2

Face Density N (110) = 9.6 x 10 14 atoms/cm2

Highly Doped Wafer Cross-Section ( p +)

Number Density of Constituents

N Boron = 1 x 10 1818 atoms/ cm33

N Silicon = 5 x 10 2222 atoms/ cm33

Resistivity

(Sometimes before the first process step the wafer may have an excess amount of dopant that defines the wafer’s resistivity.)

10 -4

10 +2

10 +3

10 0

10+1

10 -1

10 -2

10 -3

1014

1015

10 1017

1018

1019

1020

Dopant Density #/cm3

Conductivity = (Charge/Carrier)(Mobility of Carrier)(Density of Carrier)

Conductivity = (1/ Resistivity)

When Dopant is an n-type Material

When Dopant is a p-type Material

Graph for Educational Value Only.Do not use Values for Accurate Work.

16

Important Parameters

Res

isti

vely

Oh

m-C

m

5 x 10 atoms/cm15 -310 ohm-cm

5 x 10 atoms/ cm16 -31 ohm-cm;

How many Boron (dopant) atoms should be put into an epi layer with a resistivity of;

B) 10 ohm-cm

Primary reason to build an epi layer coated substrate is to adjustthe resistance between the circuit to be built on the top of the epi layer

and the back side of the wafer below the epi layer.

Resistance of a Material

Resistance = (resistivity) ((length material)/ (cross-section area))

R = ( )

A) 1 ohm-cm;from Resistivity plot, 5 x 10 atoms/ cm are needed.16 -3 (i.e. about 1 PPM)

Epitaxial Film

665 micrometers

Less than 20 micrometersepi layer

Common p-epi layer resistivities values are from 1 0hm-cm through 10 ohm-cm.

Example- Epitaxial Film Concentration

5 x 10 atoms/cm are needed.15 -3 (i.e. about 0.1 PPM)from Resistivity plot,

(( L ) / ( A ))

Energy Levels(levels further away from the nucleus)

Energy of Orbit closest to nucleus

E5

E4

( E - E ) =5 4

Conductance Band

TheBandGap

(Alone and Lonely)Single Atom

Many Atoms Close Together

(In a Solid Crystal Lattice)E

E9

6E5

En

erg

y V

alu

es

Hig

her

Neg

ati

ve V

alu

es

With n being integer energy levelsand 13.6 electron volts being Bohr’senergy value for the first orbit of a hydrogen atom

Energy Levels from Bohr’s Model

En (1/n) (13.6 ev)2

=Not

to

Scale

1 2 3 4 5 6 7 8 9 10

-13.6 ev

-0.136 ev

-3.40 ev

-1.51 ev

-0.85 ev

-0.21 ev-0.55 ev

Related Position of Silicon Energy Levels

More

Posit

ive E

nerg

y V

alu

es

E4

E

E3

2E1

More

Posit

ive E

nerg

y V

alu

es

Valance Band

E1

E2

E3

E5

E9

Energy Level Approximate Values for Isolated Atom in Space

E) Electronic Influence of Contaminates

( -0.55 - [ -0.85] ) = + 0.30 ev

Phosphorous in Interstital Spaces

Phosphorous in Substitutional Spaces

p-type Dopent at Substitutional SitesMetallurgical Junction

(Equal Density of Positive and Negative Entities)

(the letter Sigma indicates that all of the items in the region of interested are added together.)

Note:Charge neutrality occurs when;

( NA

n )

(If both n-type and p-type materials are present, the device is said to be compensated)

Compensated DeviceMask Protecting a Piece of Boron Doped Silicon

( D

p )

N

Number of ionized acceptors

Number of holes

Image Triggering Vocabulary

Metallurgical Grade Silicon (MSG)

Electronic Grade Silicon (ESG)

CZ Growth

Lattice

Interstitial Locations

Substitutional Locations

Lewis Diagrams

Miller Indicies

Resistivity

Epitaxial Film

Compensated Device

Donors

Acceptors

Equal Charge Density

Metallurigical Junction

Image Triggering Vocabulary

Metallurgical Grade Silicon (MSG)

Electronic Grade Silicon (ESG)

CZ Growth

Lattice

Interstitial Locations

Substitutional Locations

Lewis Diagrams

Miller Indicies

Resistivity

Epitaxial Film

Compensated Device

Donors

Acceptors

Equal Charge Density

Metallurigical Junction