Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Thermal Oxidation of Si• General Properties of SiO2

• Applications of thermal SiO2

• Deal-Grove Model of Oxidation

Thermal SiO2 is amorphous.Weight Density = 2.2 gm/cm3

Molecular Density = 2.3E22 molecules / cm3

Crystalline SiO2 [Quartz] = 2.65 gm/cm3

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Thermal SiO2 Properties

(1) Excellent Electrical InsulatorResistivity > 1E20 ohm-cmEnergy Gap ~ 9 eV

(2) High Breakdown Electric Field > 10MV/cm

(3) Stable and Reproducible Si/SiO2 Interface

(4) Conformal oxide growth on exposed Si surface

Si

SiO2

Substrate

Si

SiO2

Substrate

SiO2ThermalOxidation

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

(5) SiO2 is a good diffusion mask for common dopants

D Dsio si2<< e.g. B, P, As, Sb.

(6) Very good etching selectivity between Si and SiO2.

SiO2

Si

SiSiO2

Si

HF dip

*exceptions are Ga (a p-type dopant) and some metals, e.g. Cu, Au

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Thickness of Si consumed during oxidation

si

oxoxsi N

NXX •=

oxox Xcmatoms

cmmoleculesX 46.0

/105

/103.2322

322

=×

ו=

XsiSi

Si

SiO2

originalsurface

Xox

molecular density of SiO2

atomic density of Si

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

1µm Si oxidized

2.17 µm SiO2

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Kinetics of SiO2 Growth

Gas Diffusion

Solid-stateDiffusion

SiO2

FormationSi-Substrate

SiO2

Oxidant Flow(e.g. O2, or H2O)

Gas FlowStagnant Layer

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Deal-Grove Model

CGCs

Co

Ci

X0x

stagnantlayer

SiO2 Si

F1 F2

F3

gastransportflux

diffusionflux

through SiO2

reactionflux

at interface

NoteCs > Co

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

( )F h C CG G S1 = −

x

CDF

∂∂

−=2

−⋅≅

ox

io

X

CCD

is CkF ⋅=3

Diffusivity [cm2/sec]

mass transfer coefficient [cm/sec].

Fick’s Law of Solid-state Diffusion.

surface reaction rate constant [cm/sec]

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

We use Henry’s Law to relate Co and Cs

so PHC ⋅=

( )sCkTH ⋅⋅=

use CN

Vs =

PV NkT=

partial pressure of oxidantat surface [in gaseous form].Henry’s

constant

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

HkT

CC o

s =

)( GA CHkTC ⋅≡

Fh

HkTC CG

A o1 = −( )

321 FFF ==

Define

At steady-state:

2 equations:2 unknown: Co & Ci

1 2

h≡

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

CC

k

h

k X

D

iA

s s ox=

+ +1

+⋅=

D

XkCC oxs

io 1

( )

D

Xk

h

kCk

CkFFFFoxss

Asis

++=⋅====

1321

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Now, to convert F into Oxide Thickness Growth Rate

⋅=

dt

dXNF ox

1

D

Xk

h

kCk

oxss

As

++1

oxidant molecules/unit volume required to form a unit volume of SiO2.

SiO2 Si

F

∆Xox

{ }∆t

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

++=•

D

Xk

h

kCk

dt

dXN

oxss

Asox

11

[Comment]

N cm1

22 32 3 10= ×. / for O2 as oxidant

Si O SiO+ →2 2

Si H O SiO H+ → + ↑2 22 2 2

N cm1

22 34 6 10= ×. / for H2O as oxidant

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

1

2

)11

(2

N

DCB

hkDA

A

s

≡

+≡

SiO2SiO2

Si Si

xi

xoxaftertime t

B

AXX ii +=

2

τ

Boundary Condition: At t = 0 , Xox = Xi

)(2 τ+=+ tBAXX oxoxSolution

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

XA t

AB

ox = ++

−

2

1

4

12

τ

(Case 1) Large t [large Xox]

BtXox →

(Case 2) Small t [Small Xox]

tAB

X ox →

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Bdt

dxA

dtdx

X

tBAXX

oxoxox

xox

=+

+=+

2

)(02 ττ

Deal-Grove Model

∝ t

∝ t

Xox

t

ox

ox

XAB

dtdx

2+=∴

Oxide Growth Rate slowsdown with increase oxide thickness

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

B = Parabolic ConstantB/A = Linear Constant

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Oxidation Charts

The charts arebased on

Xi=0 !

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Two Ways to Calculate Oxide ThicknessGrown by Thermal OxidationE.g.

SiO2

Si4000oA

xi=

1100oC33min

steam

SiO2

Si

xox

Method 1: Find B & B/A from Charts

Solve X AX B tox ox

2 + = +( )τ

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Method 2: Use Oxidation Charts

The charts arebased on

Xi =0 !

min244000 =⇒= τAX i at 1100oC from chart

Total effective oxidation time

min57min)3324( =+ if start with 0=iX

∴

Xox T3

T2

T1

1100o C

6500oA

4000oA

24 33 57time(min)

0

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

SiO2

Si

4000oA

SiO2

Si

4000oA

SiO2

Si

4000oAxi

CVDOxide

(1) Grown at 1000oC, t=5hrs

(2) Grown at 1100oC, 24min

(3) CVD Oxide

τ τ is the same for all threecases shown here

Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 5

Effect of Xi on Wafer Topography

SiO2 SiO2 Xi

1 32

Si

less oxide grownless Si consumed

more oxide grownmore Si consumed

32

1