text book: silicon vlsi technology fundamentals, practice...

Crystal Growth, Si Wafers- Chapter 3

Text Book:Silicon VLSI Technology

Fundamentals, Practice and Modelingg

Authors: J. D. Plummer, M. D. Deal, and P. B. Griffina d G

SILICON VLSI TECHNOLOGYFundamentals, Practice and ModelingBy Plummer, Deal & Griffin

© 2000 by Prentice HallUpper Saddle River NJ


Crystal Growth, Wafer Fab and PropertiesProperties

• High Quality Single Crystal Wafers

• Diameter• Thickness• Thickness• Flatness• Mechanical defects (scratches)( )• Crystallographic Defects (dislocation density)• Crystal Orientation • Impurity Level• Dopant Type and Density-Resistivity



2


Silicon Structure Classification

• Single Crystal – periodic arrangement of atomsP l t lli ll t l f bit li t• Polycrystalline – small crystals of arbitrary alignment

• Amorphous Silicon – no significant ordering of atoms

• Simple Crystal Unit Cells– Cubic– Body-Centered Cubic (extra atom in the body)– Face-Centered Cubic (extra atoms centered on faces)

za

z z

y

a

y

a

y

aB

C



3x x x

A

Cubic BCC FCC


Crystal Planes• Planes and directions are defined using an x, y, z

coordinate system.– [111] direction is defined by a vector having components of 1

unit in x, y and z.

• Planes are defined by Miller indicesy– Defined as the reciprocals of the intercepts of the plane with

the x, y and z axes.

z z

y

za

za

y

za [111](100) plane (110) plane

y y y

[110] (111) plane



4

x x x[100][ ] (111) plane


Silicon Lattice

• Diamond cubic latticeT o merged FCC– Two merged FCC lattices with the origin of the second offset from the first by a/4 infrom the first by a/4 in all three directions

– Covalent bonding to four nearestfour nearest neighbors



5


Semiconductor Lattices

• 3D Model of unit cells for semiconductorshttp://jas eng buffalo edu/education/solid/unitCell/home htmlhttp://jas.eng.buffalo.edu/education/solid/unitCell/home.html– from: http://jas.eng.buffalo.edu/index.html

multiple semiconductor applets



6


Silicon Surface Plane Differences

• Bulk properties are generally isotropic with the symmetric latticesymmetric lattice

• Dopant diffusion is independent as long as surfaces play no rile in the process.p y p– However, real devices are built near surfaces.– The plane that the surface terminates on can then make a

difference.difference.– [111] has the highest number of atoms per cm2

– [100] has the lowest (dominant type used)Concerns– Concerns:

• Oxidation rates, surface defect density, “near” surface diffusion



7


Defects in Crystals

• Various types of defects can exist in crystal (or can be created by processing steps In general these arebe created by processing steps. In general these are detrimental to device performance.

Linear Defects:Di l ti d t

Volume Defects:Agglomeration of point

V Stacking Fault

Dislocation due to high stress or rapid thermal gradients

defectsPrecipitate of dopants

Point Defects:V missing/vacancyI extra atom/interstitialcy



8

I Dislocation Precipitate


Stacking Fault

• Form along the {111} planeThe insertion or remo al of an e tra {111} plane– The insertion or removal of an extra {111} plane

– Normally referred to as ABCABC…– Extrinsic adds a plane ABCACBC… (excess interstitials)

• Dominant type• Oxidation Induced Stacking Faults

– Intrinsic if a plane is missing ABCABABC…



9


Raw Material and Purification

• Raw Material – Quartzite SiO2

C t Q t it i t t ll i l d ili• Convert Quartzite into metallurgical grade silicon or (MGS) – Furnace with quartzite and carbon (coal or coke) @ 2000 ºCq ( ) @– ~ 98% pure

d l i d ili ( )• MFGS converted to electronics grade silicon (EGS)– MGS powder combined with gaseous HCl– Produce SiH4 (silane), SiH3Cl (chlorosilane), SiH2Cl24 ( ), 3 ( ), 2 2

(dichlorosilane), SiHCl3 (trichlorosilane), or SiCl4 (silicon tetrachloride)



10


Raw Material and Purification (2)

• SiHCl3 (trichlorosilane) processingRoom temperat re liq id that can be p rified sing fractional– Room temperature liquid that can be purified using fractional distillation. Boiled and condensed back into a liquid.

• Chemical vapor deposition – SiHCl3 (gas) and hydrogen (gas) with Si rod

– Deposition of polysilicon (parts per billion purity)Deposition of polysilicon (parts per billion purity)1013 to 1014 cm-3 impurities

• Polysilicon used for either:C h l ki (CZ) t l th– Czocharalski (CZ) crystal growth

– Float-Zone (FZ) crystal growth



11


Crystal Growth• The raw material contains < 1 ppb impurities. Pulled crystals contain O

(≈ 1018 cm-3) and C (≈ 1016 cm-3), plus any added dopants placed in the melt.

Seed

Single Crystal Silicon

Q t C ibl

• Essentially all Si wafers used for ICs today come from Czochralski(cho HRAL skee) grown crystalsQuartz Crucible

Water Cooled Chamber

Heat Shield

(cho-HRAL-skee) grown crystals.

• Polysilicon material is melted, held at close to 1417 ˚C, and a single

Carbon Heater

Graphite Crucible

Crucible Support

crystal seed is used to start the growth.

• Pull rate melt temperature andSpill Tray

Electrode

Pull rate, melt temperature and rotation rate are all important control parameters.

$



12

• Approximately $50 per 8 in. wafer when text writtenArgon Ambient


Crystal Growth (2)

(More information on crystal growth at http://www.memc.com)



13

(Photo courtesy of Ruth Carranza.))


Float Zone Crystal Growth

Polysilicon Ingot

• An alternative process is the float zone process which can be used for refining or single crystal growth

RF Coil

or single crystal growth.• Localized I2R heating via RF Coil

• Nitrogen or dopant ambient• Wafers < 150 mm

Single Crystal Si • Detectors and power• Doping is a challenge• Reduced C and O impurities

• Bottom in contact with single crystalBottom in contact with single crystal seed



14


Silicon Wafer Diameter



15

Martin L. Hammond, TMX International, Cupertino, Calif. -- Semiconductor International, 6/1/2004http://www.semiconductor.net/article/205503-The_Next_Wafer_Diameter_Change.php


Ingot Cutting into Wafers

After crystal pulling, the boule is shaped and cut into wafers which are then polished on one side.

(S f // )



16

(See animations of crystal polishing etc. at http://www.memc.com)


Wafer Preparation and Specification• Grind crystal to a diameter

(200mm⇔750µm) 850µm thickMark wafer earlier (laser process) (200mm⇔750µm) … 850µm thick• Grind flats (the primary and

secondary)• Saw of the boule into wafers

to track their process flow

• Lapping, etching (batch process in acids etching Si) 20 µm, polishing (chemical-mechanical) 25µm removes damage and improves flatness ±2µmdamage and improves flatness ±2µm

Suspension Al2O3

SiO2 10nm in NaOH/DI

CMP

3Si +4HNO3+18HF 3H2SiF6+4NO+8H2O




MEMC Process Animation

• Crystal PullingR d G i di• Rod Grinding– Achieving the correct diameter– Grinding flats for crystal orientationg y

• Wire Cutting– 100 mm, 150 mm, 200 mm, 300 mm, 450 mm

Ed P fili• Edge Profiling• Lapping

– Improve wafer flatnessImprove wafer flatness

• Etching and Polishing• Laser Inspection



18


Measurement Methods

• Sheet ResistanceCo linear fo r point probe– Co-linear four-point probe

– Van der Pauw

• Hot Point Probe• Hall Effect



19


Measurements of the Grown Crystal

Resistivity ρ =

1qμnn + qμpp

[Ωcm ]

rxj<<t

Φ>>s

Sheet resistance

Average resistivity



Sheet resistance


Measurements of the Grown Crystal

Conductivity Typey yp

Seebeck voltage

25-100°C hotter

Electrons move - Donors ⊕ stay Jn = qnμ nPn

dTdxElectron current

Sign of the voltage V tells what is the conductivity type




Hall Effect Measurement

Measurements of majority carrier concentrations (and type) and their wt Vx / fi ldmobility

ρ =wts

Vx

Ixw/o B field

Test structure

Electrons at the bottom




Measuring ImpuritiesFourier Transport Infrared Spectroscopy (FTIR)

For Interstitial Oxygen incorporated during CZ growth and SubstitutionalC b (d i li i O 2 1015 3Carbon (detection limit O- 2x1015cm-3, C- 5x1015cm-3 )

Fourier transformFourier transform Sweep the wavelength of incident energy look for absorption




SEM and TEM

• Scanning Electron MicroscopeMicroscope– Large depth of focus– Magnification 300,000x– Resolution below 5 nm

• Transmission Electron• Transmission Electron Microscope– Prepared samples

(1 um thickness)– Resolution is about 0.2 nm



8


Models and Simulation

• Czochralski Crystal GrowthD t I ti i CZ• Dopant Incorporation in CZ

• Zone Refining and FZ Growth• Point Defects• Point Defects• Oxygen in Silicon• Carbon in Silicon



9


Modeling Crystal GrowthSeed • We wish to find a relationship between

pull rate and crystal diameter.• Freezing occurs between isotherms X1

Solid Si

dxC

B Isotherm X 2

and X2.• Heat balance:

• latent heat of crystallization + heat conducted from melt to crystal

Liquid Si

A

Isotherm X 1

= heat conducted away.

fusion ofheat latent =dmL

liquid ofty conductivi thermal

unit timeper freezing ofamount

=

=

dTkdtdm

L

22

11

AdxdTkA

dxdTk

dtdmL SL =+ 1

1

solid ofty conductivi thermal

isothermat gradient thermal

=

=

dTk

xdxdT

S

(1)



10

22

at xgradient thermal=dxdT


Model Crystal Growth (2)• The rate of growth of the crystal is

where vP is the pull rate and N is the density and A the cross sectional area.

NAvdtdm

P ⋅⋅=(2)

density and A the cross sectional area.

• Neglecting the middle term in Eqn. (1) we have: 2

2

AdxdTk

dtdmL S≤

Seed

dxC

22

AdxdTkLNAv SP ≤⋅⋅⋅

2dxdT

NLkv S

PMAX ⋅= (3)

Solid Si

dx

B

A

Isotherm X 2

Liquid Si Isotherm X 1



11


Model Crystal Growth (3)• In order to replace dT/dx2, we need to consider the heat transfer processes.• Latent heat of crystallization (A) transfers up the crystal (B) and is lost by

di ti (C)radiation (C).

Seed

• Heat radiation from the crystal (C) is given by the Stefan-Boltzmann law

dxC ( ) ( )42 TrdxdQ σεπ ⋅= (4)

• Heat conduction up the crystal is given by

Solid Si

i i Si

B

A

Isotherm X 2

Isotherm X 1

given by

( )dxdTrkQ S ⋅⋅= 2π (5)

• Differentiating (5), we haveLiquid Si Isotherm X 1

( ) ( ) ( ) 2

222

2

22

dxTdrk

dxdk

dxdTr

dxTdrk

dxdQ

SS

S πππ ≅+=

(6)



12

(6)


Model Crystal Growth (4)

• Substituting (6) into (4), we have 02 42

2

=− Trkdx

Td σε (7)rkdx S

• kS varies roughly as 1/T, so if kM is the thermal conductivity at the melting point, T

Tkk MMS = (8)

y g p ,

02 52

2

=−∴ TrTkdx

Td

MM

σε(9)

• Solving this differential equation, evaluating it at x = 0 and substituting the result into (3), we obtain

Tk21 5σε (10)2

12

14

133

−

⎟⎞

⎜⎛

⎟⎞

⎜⎛⎞⎛ rkrTk

rTk

LNv MM

PMAX 321 σε

= (10)

• Using the example on p. 124, this gives a max pull rate of ≈ 24 cm hr-1 for 6” t l (A t l l 2X l th thi )

383

83

⎟⎟⎟

⎠⎜⎜⎜

⎝⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅⎟

⎠⎞

⎜⎝⎛=

M

MMM

TrkxrTkT

σεσε



13

a 6” crystal (Actual values are ≈ 2X less than this).


Monitoring Ingot Growth

Seed • Automation of the process incorporates numerousSingle Crystal Silicon

Quartz Crucible

Water Cooled Chamber

incorporates numerous sensors and feedback– Optical monitoring of resulting

Heat Shield

Carbon Heater

Graphite Crucible

crystal diameter– Infrared sensing of

temperatureCrucible Support

Spill Tray

Electrode

– Thermocouples for specific temperatures within chamber



14


Modeling Dopant Behavior During Crystal GrowthCrystal Growth

• Dopants are added to the melt to provide a controlled N or P doping level in the ingot and resulting wafersN or P doping level in the ingot and resulting wafers.

– The dopant incorporation process is complicated by dopant p p p p y psegregation, a difference in the impurity concentration between the liquid and solid.

– Segregation occurs between the liquid and solid phase of g g q pmaterial when they are in intimate contact. An experimentally measured segregation coefficient defines the difference between the two.

L

SO C

Ck =



15


Segregation CoefficientDopant kO

As 0.3 Bi 7 x 10-4

k O = CS

CL

Bi 7 x 10C 0.07 Li 10-2 O 0.5 P 0 35P 0.35

Sb 0.023 Al 2.8 x 10-3 Ga 8 x 10-3

0 8B 0.8Au 2.5 x 10-5

• Most k values are <1; therefore the impurity prefers to stay in the liquid• Most k0 values are <1; therefore, the impurity prefers to stay in the liquid.• Thus as the crystal is pulled CL increases.• As the melt concentration increases, the silicon crystal doping, NS,

will also increase.



16


Dopant Model• If during growth, an additional volume dV freezes, the impurities (I)

incorporated into the volume dV are given by

dIkdkd L (12)dVVV

IkdVCkdISO

LOLO −

−=−= (12)

∫∫ =SL VI dVkdI (13)

VS, CS

IL, CLVO, IO, CO

∫∫ −−=

O SOO

I L VVk

I 0

( 3)

⎟⎟⎞

⎜⎜⎛

⋅−=⎟⎟⎞

⎜⎜⎛ O

OL VkI loglog

Ok

SVII ⎟⎟⎞

⎜⎜⎛−= 1 (14)

⎟⎟⎠

⎜⎜⎝ −⎟⎟

⎠⎜⎜⎝ SO

OO VV

kI

loglog

OOL V

II ⎟⎟⎠

⎜⎜⎝−= 1 (14)

• This equations defines the number of impurities in the melt as a function of how much of the melt has solidified



17

of how much of the melt has solidified.


Dopant Model (2)• Knowing the number of impurities in the melt as a function of how much

of the melt has solidified. We define the fraction of melt “frozen” as f .

• The impurities in the crystal (C )

0VVf S= ( ) Ok

OL fII −= 1

VS, CS

• The impurities in the crystal (CS) can then be computed usingt

LdIC ∝ (15)IL, CLVO, IO, CO S

LS dV

C −∝ (15)

( ) 1k( ) 11 −−= OkOOS fkCC (16)

• This equations defines expected impurity concentration in the resulting wafers based on their location in the crystal This is directly related to the



18

wafers based on their location in the crystal. This is directly related to the amount of melt solidified in the ingot pulling process, f=0 to f=1.


Doping Concentration vs. Position

10

1Boron

CO

• Plot of Eq. (16).

f f

0.1

Phosphorus, Arsenic

CS/

C • Note the relatively flat profileproduced by boron with a kSclose to 1.

0 01

Antimony • Dopants with kS << 1 produce much more variation in dopingconcentration along the crystal.

0.010 0.2 0.4 0.6 0.8 1

Fraction of Melt Solidified



19


Float Zone Growth and RefiningRF -> melt zone moving

Poly-SiL

Zone

C0 original concentration in the rod

COCS(x)

I - impuritiesin the liquid dI=(C0-k0CL)dx

the rod

dx

• In the float zone process, dopants and other impurities tend to stay in the liquid; therefore, refining can be accomplished, especially with multiple passes

• See the text for models of this process.

( ) ( ) ⎬⎫

⎨⎧ ⋅

−L

xkO

kCC 11



20

( ) ( )⎭⎬

⎩⎨ ⋅−−⋅= L

OOS ekCxC 11


FZ Impurity Behavior



21


Modeling Point Defects

• Vacancies (V) and Interstitials (I)Th i t f d f t i i i th t t l f• The existence of defects minimizes the total free energy of the crystal. Therefore, they will exist for all temperatures above absolute zero.p– The concentrations can be related as

⎟⎟⎞

⎜⎜⎛ −

⎟⎟⎞

⎜⎜⎛

=HSN

ff

expexpCC **

– Sf is the formation entropy of the defectf

⎟⎟⎠

⎜⎜⎝

⎟⎟⎠

⎜⎜⎝

=kTk

NS expexpC,C VI 00

– Hf is the enthalpy of formation of the defect– NS is the number density of lattice sites– * denotes equilibrium



22


Point Defect Equilibrium

• The Frenkel process: moving a silicon atom off from a lattice site inside a crystal. It creates equal number of V and I.inside a crystal. It creates equal number of V and I.

• I created if silicon atom moves from the surface into the bulk.• V and I can be recombined removing one of each

Stacking fault can capture either V or I by growing or shrinking• Stacking fault can capture either V or I by growing or shrinking but one lattice site

• In general, there is an assumption that the equilibrium population rate of change is due to kinematics and is assumedpopulation rate of change is due to kinematics and is assumed to change “immediately” with respect to temperature.– With the exception of ion implantation and CZ growth

⎞⎛ V83• Estimated values for Silicon

⎟⎠⎞

⎜⎝⎛ −≅

kTeVxC

I

8.3exp101 27*0

⎟⎞

⎜⎛ − eVC 6.2109 23*



23

⎟⎠⎞

⎜⎝⎛≅

kTeVxC

V

6.2exp109 23*0


Concentration Example

• At 1000 ºC3-510 × 343 8.617 −≅ cmk

312* 1010−≅ cmxCI

312* 105 −≅ cmxC

3181014.7 −≅ cmxni

32015 1010, −≅ cmtoNN AD1050 ≅ cmxCV

, AD

Defects are present but a concentrations significantly less than carriers and difficult to detect.



24


Point Defect Diffusivities

• Point defects are extremely mobile. Cr stal kinematics– Crystal kinematics.

– Not directly measured, but has been inferred from dopant diffusivity.

12 sec8.1exp51 −⋅⎟⎠⎞

⎜⎝⎛ −≅ cm

kTeVdI p

⎠⎝ kTI

124 sec58.1exp10653 −− ⋅⎟⎞

⎜⎛ −⋅×≅ cmeVdV secexp1065.3 ⎟

⎠⎜⎝

×≅ cmkT

dV



25


Modeling Point Defects in Silicon

• Point defects (V and I) will turn out to play fundamental roles in many process technologies.

• The total free energy of the crystal is minimized when finite concentrations of these defects exist.

Stacking FaultV Stacking Fault

• In general and both are strong functions of temperature.

CI0* ≠ C

V0*

• Kinetics may determine the concentration in a wafer rather than thermodynamics.

I Dislocation Precipitate



26


Charged Point Defects

• Shockley and Last (1957) first described these charged defect concentrationscharged defect concentrations

• V and I also exist in charged states with discrete energies in the Si bandgap.g g p– In N type Si, V= and V- will dominate– In P type, V+ and V++ will dominate.

EC

V=

V-

EF EF for an N type

t i l V

V++

Ei material



27

EVV+ V++


Charged Point Defects

• For intrinsic silicon, no change in charge occupationF t i i N t Si V d V ill d i t th• For extrinsic N type Si, V= and V- will dominate as the Fermi energy rises– The dominant vacancy charge state becomes V- acting like y g g

an acceptor

• For extrinsic P type Si, V+ and V++ will dominate. As the Fermi energy fallsthe Fermi energy falls– The dominant vacancy charge state becomes V-+acting like

an donor EC

V=V

V-

Ei

EF

EF for an N type material



28 EVV+ V++

yp


Charge Defect Concentrations

• Shockley and Last (1957) first described these

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

+

+

kTEE

CC FVVV

exp**0

• Shockley and Last (1957) first described these charged defect concentrations (see text).

Note: • The defect concentrations are always ⎠⎝ kT

⎟⎟⎞

⎜⎜⎛ −

=−

−

EECC VF

VVexp**

0

<< ni. ( doping EF point defect concentrations)

• As doping changes, the neutral point defect concentrations are constant.⎟⎟

⎠⎜⎜⎝

−

kTCC

VVe p0 defect concentrations are constant.

• However, the charged defect concentrations change with doping. ∴ the total point defect concentrations

h ith d ichange with doping.



29


Point Defect Example

N 5 x 1019 cm-3 • At 1000 ˚C, the P region will be intrinsic, the N region is extrinsic.E 0 7778 V

P 1015 cm-3

• Eg ~ 0.7778 eV• Compute ni and check ND and NA• Construct energy band diagram

Intrinsic:Fermi

Extrinsic: Fermi L lLevel in

middleLevel shifted



30


Point Defect ExampleN 5 x 1019 cm-3

• Compute V0 and I0

P 1015 cm-3

P R i N R i

p• Compute P-type V and I

P Region N RegionDoping 1 x 1015 cm-3 5 x 1019 cm-3

ni 7.14 x 1018 cm-3 7.14 x 1018 cm-3 V0 4.6 x 1013 cm-3 4.6 x 1013 cm-3

Note:• ni relative to doping in the

two regions.V- 2.37 x 1014 cm-3 1.61 x 1015 cm-3 V= 1.85 x 1013 cm-3 8.50 x 1014 cm-3 V+ 2.08 x 1012 cm-3 3.06 x 1011 cm-3 V++ 1 94 x 1011 cm-3 4 23 x 109 cm-3

two regions.• V0 is the same in the two

regions.• Different charge states

d i t i th diff tV 1.94 x 1011 cm 3 4.23 x 109 cm 3

I0 9.13 x 1011 cm-3 9.13 x 1011 cm-3 I- 4.02 x 1011 cm-3 2.73 x 1012 cm-3 I 8 32 1010 3 1 48 1011 3

dominate in the different regions.



31

I+ 8.32 x 1010 cm-3 1.48 x 1011 cm-3


Oxygen and Carbon in CZ SiliconTh CZ th i h tl i t d O d C• The CZ growth process inherently introduces O and C.

• Typically, CO ≈ 1018 cm-3 and CC ≈ 1016 cm-3.

• The O in CZ silicon often forms small SiO2 precipitates in the Si crystal under normal processing conditions.

StackingFault

V I

OI

OI

OI SiO • O and these precipitates can

[OI]

OIOI

OI SiO2O and these precipitates can actually be very useful.• Provide mechanical strength.• Internal gettering (described

l t i Ch t 4)OI Diffusion

I

SiO2

later in Chapter 4).



32


Summary of Key Ideas

• Raw materials (SiO2) are refined to produce electronic grade silicon with a purity unmatched by any other commonly available material on earth.p y y y y

• CZ crystal growth produces structurally perfect Si single crystals which can then be cut into wafers and polished as the starting material for IC manufacturing.

• Starting wafers contain only dopants, O, and C in measurable quantities. • Dopant incorporation during crystal growth is straightforward except for

segregation effects which cause spatial variations in the dopant t ticoncentrations.

• Point, line, and volume (1D, 2D, and 3D) defects can be present in crystals, particularly after high temperature processing.P i t d f t "f d t l" d th i t ti d d• Point defects are "fundamental" and their concentration depends on temperature (exponentially), on doping level and on other processes like ion implantation which can create non-equilibrium transient concentrations of these defects.



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