Lecture 12: Oxidation

ECE418 / ECE518 – Spring 2021

Lecture 12 – Wednesday April 21st 2021

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ECE 418 / 518 – Semiconductor Processing

Spring 2021 - John Labram

Lecture 12: OxidationChapter 3 Jaeger

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Last Time

Si

SiO2SiO2

Pre-Deposition

Dopant gas

Si

Drive-in

Si

SiO2SiO2

• Before the break we covered the basics of diffusion.

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Useful LinksThis subject is widely taught, and online notes are available from

many sources. Here are some good examples:

• http://www-

inst.eecs.berkeley.edu/~ee143/fa10/lectures/Lec_06.pdf

UC Berkeley Notes:

• https://engineering.ucsb.edu/~sumita/courses/Courses/ME14

1B/ME141B_lecture_4_F10.pdf

UC Santa Barbara Notes:

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Lecture 11• Oxide Properties.

• Oxidation Process.

• Oxide Growth Model.

• Factors Influencing Oxidation Rate.

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http://www-inst.eecs.berkeley.edu/~ee143/fa10/lectures/Lec_06.pdf

https://engineering.ucsb.edu/~sumita/courses/Courses/ME141B/ME141B_lecture_4_F10.pdf



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Oxide Properties

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Oxidation• Reasons that SiO2 so widespread in VLSI:

• Forms directly from the Si substrate upon exposure to oxygen containing species (O2 or H2O):

• SiO2 is a high quality electrical insulator (low interface trap density):

Si S + O2(G) → SiO2(S)

Si S + 2H2O L → SiO2 S + 2H2(G)

“Dry”

“Wet”

• Thin (10-50 Å) gate oxide for MOS gate.

• Thick (1000-2000 Å) field oxide for transistor isolation and barrier to dopant diffusion.

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Other Compounds• This is one of the main advantages of Si, and is the main

reason why it is the commercial standard for semiconductors.

Germanium GaAs

Hu et. al. “Native Oxidation Growth on Ge(111) and (100) Surfaces” Small

1(4) (2005) 429.

Thomas et. al. “High electron mobility thin-film transistors based on Ga2O3

grown by atmospheric ultrasonic spray pyrolysis at low temperatures” APL

105 (2014) 092105.

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Structure of SiO2• Each Si surrounded tetrahedrally by 4 O atoms

• Density of SiO2 < crystalline SiO2.

• Quartz = 2.65 gm/cm3.

• Thermally grown oxide = 2.20 gm/cm3.

• Silicon = 2.33 gm/cm3.

• Open, amorphous structure.

jcrystal.com/

Si

OSi

O

O

OSi

O

OSiSi

OSi

O

O

OSi

O

OSi

OSi

O

OSi

O

OSi

O

OSi

O

OSi

O

OSi

O

OSi

O

OSi

O

1.6 A

2.27 A

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Properties of SiO2• Excellent electrical insulator.

• Resistivity > 1015 Ωcm.

• Band gap ~ 8 eV.

• Crucial in devices.

Al Al

SiO2

Si++

S D

Dielectric

Gate

e- e- e- e- e- e- e- e- e- e- e- e-

+VD

+VG

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Properties of SiO2• High breakdown electric field strength.

• >10 MV/cm.

Al Al

SiO2

Si++

S D

Dielectric

Gate

e- e- e- e- e- e- e- e- e- e- e- e-

+VD

+VG

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Properties of SiO2• Stable:

• Conformal oxide growth on exposed Si surface.

Si Si

SiO2

• Good diffusion mask for common dopants:

𝐷𝑆𝑖𝑂2 ≪ 𝐷𝑆𝑖

Si

SiO2SiO2

• Down to 10-9 Torr, T > 900°C.

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Properties of SiO2• Excellent etch selectivity between Si and SiO2.

Si

SiO2

Si

HF Dip

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Oxidation: Applications• Oxide grown by oxidation is used at two important steps in

chip manufacture.

• Field oxide.

• Gate oxide.

• Field oxide:

• Field oxide isolates different transistors on a chip.

Source DrainSource DrainP-WellN-Well

Gate Gate

Transistor 1 Transistor 2

Fieldoxide

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Oxidation: Applications• Gate oxide

• Recall that the gate on a transistor works because the charge effects the holes and electrons across the oxide

P-Si

Insulator

N-Si

Source DrainGate

N-Si

Gate oxide

• Currently the gate oxide is only 10 - 50 Å thick. (A sheet of paper is 1,000,000 Å thick!)

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Oxidation Process

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Oxidation Techniques

• Thermal oxidation (heated in oxygen-rich environment).

• Chemical vapor deposition (CVD).

• Plasma anodization.

• Physical vapor deposition (PVD).

• Thermal oxidation is by far the prevalent in industry.

• We will focus on this technique.

• Best quality oxide.

• Unfortunately requires high temperature.

• Typically used for insulation.

• There are a few other ways to grow oxides:

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Thermal Oxidation• Two approaches:

• Dry Oxidation (O2):

• Uses oxygen gas:

• High quality.

• Slow oxidation rate.

• Small maximum thickness (i.e. gate oxide).

• Wet Oxidation (H2O):

• Diffusion speed is higher.

• Lower quality.

• Uses water vapor:

• Faster oxidation rate.


Si S + 2H2O Vapor → SiO2 S + 2H2(G)

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Oxidation: Mechanism• The oxygen containing species must diffuse through the oxide

layer to the unreacted silicon.

• This makes for a “cleaner” process.

Silicon substrate

Water vapor

OXIDEOxygen species

diffuses through

oxide Water vapor

Silicon dioxide

Silicon

Surface hydroxyl

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Oxidation: Mechanism• Oxygen reacts with silicon to form silicon dioxide:


Si S + 2H2O Vapor → SiO2 S + 2H2(G)

Si

SiO2

Si

Time

• We can work out the thickness of Si consumed from the number density.

Original

Thickness

𝑋0

𝑋𝑆𝑖

𝑋𝑆𝑖 = 𝑋0𝑛𝑜𝑥𝑛𝑆𝑖

# density of SiO2

# density of Si

𝑋𝑆𝑖 = 𝑋02.3 × 1022

5 × 1022= 0.46𝑋0

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Oxide Growth Model

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Deal & Grove Model

• It’s no accident that the world leader in Si chip technology, Intel, has been led by Andy Grove.

• As a young researcher at Fairchild Semiconductor, he “wrote the book” on SiO2

growth: the Deal-Grove model.

• Without easy growth of SiO2

on Si, there would be no semiconductor industry.

1997

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Deal & Grove Model• We will talk about dry growth (O2), but principles are the same

for H2O.

Si

SiO2

O2

Si

• SiO2 growth occurs at the Si/SiO2 interface because:

𝐷O2 SiO2 ≫ 𝐷Si SiO2

I.e. diffusion coefficient of O2 in SiO2 is much higher than the

diffusion coefficient of Si in SiO2.

• For this class we will carry out only parts of the derivation, and use the results. It closely follows the textbook.

• A more in-depth derivation can be found in ECE611.

• We want to quantify the growth rate of the oxide.

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Modelling Oxidation• The oxidation process is best visualized by this picture:

Si

SiO2

SiOriginal

Thickness

𝑋0

𝑋𝑆𝑖

• In order for oxidation to occur, oxygen must reach the silicon interface.

• As the oxide grows, the oxygen must pass through more SiO2, and the growth rate will slow.

• The figure on the right is one way to visualize the process.

SiO2 Si

𝑋0𝑥

𝑁

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Oxidation Diagram• The labels are as follows:

• 𝑁 is the concentration of O2 (# / volume).

• 𝑥 is the distance from the surface of the oxide.

• 𝑋0 is the distance of the interface between the Si and SiO2 from the surface (will change with time).

• 𝑁𝑖 is the concentration of O2 at the interface between the Si and SiO2.

• 𝐽 is the oxygen flux (# / area / time).

• We will assume the flux is the same at every position up to 𝑋0.

SiO2 Si

𝑋0

𝑁𝑖

𝑥

𝑁

𝐽

𝑁0

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Modelling Oxidation• We can describe the flux (𝐽) using Fick’s First Law:

𝐽 = −𝐷𝜕𝑁 𝑥, 𝑡

𝜕𝑥

• Where 𝐷 is the diffusion coefficient of O2 in SiO2.

• The negative sign means that particles tend to move from regions of high concentration to regions of low concentration.

• For our derivation we are going to make the approximation that oxygen flux is constant everywhere and that 𝑁 ∝ 𝑥.

• In this case we can just approximate Fick’s First Law as:

𝐽 = −𝐷𝑁𝑖 − 𝑁0𝑋0 − 0

SiO2 Si

𝑋0

𝑁𝑖

𝑥

𝑁

𝐽

𝑁0

= −𝐷𝑁𝑖 − 𝑁0𝑋0

(3.3)

(3.4)

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Oxidation Reaction

• At the interface between the SiO2 and Si we assume the oxidation rate (𝑘𝑠) is proportional to the concentration of O2 at the interface (𝑁𝑖):

𝐽 = −𝐷𝑁𝑖 − 𝑁0𝑋0

SiO2 Si

𝑋0

𝑁𝑖

𝑥

𝑁

𝐽

𝑁0

𝐽 = 𝑘𝑠𝑁𝑖

• We quantify the conversion of silicon and oxygen into + O2 to SiO2 via a chemical reaction rate: 𝑘𝑠 . This has units of length / time, (e.g. cm/s).

• Equating 𝑁𝑖’s in these two equations:

𝐽 =𝐷𝑁0

𝑋0 + Τ𝐷 𝑘𝑠I.e. the flux is

limited/defined by the reaction rate

(3.4)

(3.5)

(3.6)

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Oxide Growth Rate• So, by balancing diffusion with reaction rate we can describe

the O2 flux as:

𝐽 =𝐷𝑁0

𝑋0 + Τ𝐷 𝑘𝑠

• Recall, our goal is to determine the rate of oxide growth:

𝑑𝑋0𝑑𝑡

• We define the number of oxygen molecules incorporated into a unit volume of the resulting oxide as 𝑀.

• 𝑀 is a number density and has dimensions of #/[length]3.

• We can hence infer through dimensional analysis:

𝑑𝑋0𝑑𝑡

=𝐽

𝑀=

𝐷𝑁0𝑀 𝑋0 + Τ𝐷 𝑘𝑠

(3.6)

(3.7)

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Oxide Growth Rate

• We identify this a first order ordinary differential equation.

𝑑𝑋0𝑑𝑡

=𝐷𝑁0

𝑀 𝑋0 + Τ𝐷 𝑘𝑠

• We are not going to solve it, we will just take the solution:

𝑋0 𝑡 = 0.5𝐴 1 +4𝐵

𝐴2𝑡 + 𝜏

Τ1 2

− 1

(3.7)

(3.9)

• Where:

𝐴 =2𝐷

𝑘𝑠𝐵 =

2𝐷𝑁0𝑀

• And 𝜏 is the time it would have taken to grow the initial oxide.

• Bare silicon is very reactive, and in air you will always find your wafer has some native oxide (even if it is only ~10Å).

• You can think of 𝜏 as the time before 𝑡 = 0 required to grow this native oxide.

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Oxide Thickness𝑋0 𝑡 = 0.5𝐴 1 +

4𝐵

𝐴2𝑡 + 𝜏

Τ1 2

− 1 (3.9)

• Growth parameters are often quoted with this notation:

• This is the equation that tells us how thick our oxide would be for a certain oxidation time (𝑡) and certain parameters (𝐴, 𝐵, 𝜏).

• Be aware of the non-standard units for length and time.

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Growth Regimes𝑋0 𝑡 = 0.5𝐴 1 +

4𝐵

𝐴2𝑡 + 𝜏

Τ1 2

− 1 (3.9)

• It turns out we can simplify this equation for different times.

• We define Short Times as 𝑡 + 𝜏 ≪ Τ𝐴2 4𝐵:

𝑋0 𝑡 =𝐵

𝐴𝑡 + 𝜏 (3.10)

• We define Long Times as 𝑡 + 𝜏 ≫ Τ𝐴2 4𝐵, 𝑡 ≫ 𝜏:

𝑋0 𝑡 = 𝐵𝑡 (3.11)

• For this reason, sometimes Τ𝐴 𝐵 is the called the Linear Coefficient and 𝐵 is called the Parabolic Coefficient.

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Growth Regimes• If we plotted the oxide thickness (𝑋0) as a function of growth

time, we would hence expect to observe something like this:

Parabolic

𝑋0 ∝ 𝑡

𝑡

𝑋0

𝑋0 ∝ 𝑡

Linear

𝑡 ≈𝐴2

4𝐵− 𝜏

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Factors Influencing

Oxidation Rate

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Diffusion Coefficient• As we talked about in the last lecture, diffusion is a

temperature-activated process:

𝐷 = 𝐷0 exp−𝐸𝐴𝑘𝐵𝑇

(3.12)

• Where:

• 𝐷 is the diffusion coefficient (of oxygen in SiO2).

• 𝐷0 is the diffusion pre-factor.

• 𝐸𝐴 is the activation energy.

• 𝑘𝐵 is the Boltzmann Constant.

• 𝑇 is the Temperature.

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Diffusion Coefficient

• Dry oxide:

• 700-1,200 °C.

• 1 atm (101325 Pa).

• Typical = 100nm/hr.

• SiO2 Density is higher.

• Used for gate oxide.

• Wet oxide:

• 750-1,100 °C.

• 25 atm (2.5 × 106 Pa).

• Typical = 1μm/hr.

• SiO2 Density is lower, more porus.

• Used for field oxide and etch oxide.

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Growth Rate Constants

• The rate constants / coefficients are also 𝑇-dependent.

𝐴 =2𝐷

𝑘𝑠𝐵 =

2𝐷𝑁0𝑀

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Oxide Growth in Practise

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First Substrates are Cleaned• RCA Clean (Lecture 2)

• Organic strip.

• Piranha Solution.

• Native oxide removal.

• HF.

• Heavy metal removal.

• HCl:H2O2:H2O.

• Dump rinse.

• 18 MΩcm DI H2O.

• Spin Dry.

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Initial Oxidation Regime• Experimentally, this is observed:

How do we explain this?

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Initial Oxidation Regime• Many models have been proposed.

• It is likely the O2:SiO2 interface is not abrupt:

O2 SiO2 Si

𝑥

O2 Conc.

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Dopants• Common dopants in Si enhance oxidation at higher

concentration

Boron

Oxide thickness vs. wet oxidation time at 640 mTorr for three different boron concentrations (Sze)

Phosphorus

Data for dry oxidation at 1 atm and 900˚C

Linear, B/A, and parabolic, B, rate

constants vs. phosphorus concentration.

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Oxidation Reactor• Oxidation is carried out in a horizontal or vertical reactor.

• Many wafers are held in a vertical holder and pure water is pumped through.

Wafers

Hydrogen

Water vapor

Oxygen

Exhaust

• Pressure = 760 Torr (typical)

• High concentration to help diffusion.

• Temperature = 900 ± 1 oC (typical)

• High temperature to help diffusion.

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Equipment• You will become familiar with this

equipment during lab sessions.

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Summary• We will have covered the

growth of silicon oxide.

Wafers

Hydrogen

Water vapor

Oxygen

Exhaust

SiO2 Si

𝑋0

𝑁𝑖

𝑥

𝑁

𝐽

𝑁0

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Next Time…• Next time will start to cover

transistors.

S D

𝐿

𝑊

𝐿

𝑊

𝐷

DS

Gate

Dielectric

Semiconductor

Substrate

𝐼𝐷

𝑉𝐷

𝑉𝐺

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Documents

Lecture 12: Oxidation