Lecture7 Doping Ion Implantation

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For the exclusive use of adopters of the bookIntroduction to Microelectronic Fabrication,Second Edition by Richard C. Jaeger. ISBN0-201-

44494-1.

© 2002 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is protected under all copyright laws as they currently exist. Noportion of this material may be reproduced, in any form or by any means,

without permission in writing from the publisher.

Introduction toMicroelectronic Fabrication

Richard C. JaegerDistinguished University Professor

ECE Department

Auburn University

Chapter 4Diffusion

For the exclusive use of adopters of the bookIntroduction to Microelectronic Fabrication, SecondEdition by Richard C. Jaeger. ISBN0-201-44494-1.

© 2002 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. Thismaterial is protected under all copyright laws as they currently exist. No portion of thismaterial may be reproduced, in any form or by any means, without permission in writing

from the publisher.

Copyright Notice

reproduced, in any form or by any means, without permission inwriting from the publisher.

• For the exclusive use of adopters of the book Introduction to

Microelectronic Fabrication, Second Edition by Richard C.Jaeger. ISBN0-201-44494-1.

from the publisher.

Impurity Diffusion

•Diffusion Mechanisms

• Substitutional

• Interstitial

from the publisher.

DiffusionFick’s First Law

Particle flux J is proportional to the negativ

of the gradient of the particle concentratio

J = − D∂ N

D = diffusion coefficient

from the publisher.

DiffusionFick’s Second Law

Continuity Equation for Particle Flux :

Rate of increase of concentration is equal to the

negative of the divergence of the particle flux

∂ t = −

(in one dimension)

Fick's Second Law of Diffusion :

Combine First Law with Continuity Eqn.

∂ t = D

∂ 2 N

∂ x 2

D assumed to be independent of concentration!

from the publisher.

Constant Source DiffusionComplementary Error Function Profiles

Concentration : N x, t ( )= N 0erfc x2 Dt

Total Dose : Q = N x, t ( )dt = 2 N 00

∫ Dt

N 0 =Surface Concentration

D =Diffusion Coefficient

erfc = Complementary Error Function

erfc z( )=1− erf z( )

erf z( )=2

π exp − x

2[ ] dx0

from the publisher.

Limited Source DiffusionGaussian Profiles

Concentration:

N x,t ( )= N 0 exp − x

π Dt exp −

N 0 =Surface Concentration N 0 = Q

D = Diffusion Coefficient

Gaussian Profile

Initial Impulse with Dose Q

from the publisher.

DiffusionProfile Comparison

Complementary Error Function and

Gaussian Profiles are Similar in Shape

erfc z( )=1− erf z( )

erf z( )=2

π exp − x 2[ ] dx

from the publisher.

Diffusion Coefficients

Substitutional

Diffusers Interstitial

Diffusers

from the publisher.

Diffusion Coefficients

D = DO

exp − E A

Arrhenius Relationship

EA = activation energy

k = Boltzmann's constant =1.38 x10-23 J/K

T = absolute temperature

from the publisher.

Successive Diffusions

• Successive Diffusions Using Different Times and

Temperatures

• Final Result Depends Upon the Total Dt Product

Dt ( )tot = Di

∑ t i

from the publisher.

DiffusionSolid Solubility Limits

• There is a limit to the amount of agiven impurity that can be “dissolved”

in silicon (the Solid Solubility Limit)

• At high concentrations, all of the

impurities introduced into silicon willnot be electrically active

For the exclusive use of adopters of the book

Introduction to Microelectronic Fabrication, SecondEdition by Richard C. Jaeger. ISBN0-201-44494-1.

material is protected under all copyright laws as they currently exist. No portion of thismaterial may be reproduced, in any form or by any means, without permission in writing

from the publisher.

Diffusionp-n Junction Formation

x j =Metallurgical Junction Depth

P - n junction occurs at the point x j where the net impurity

concentration is zero

(i. e. p - type doping cancels out n - type doping)

Gaussian Profile : x j = 2 Dt ln N0

Error Function profile : x j = 2 Dt erfc -1 N0

from the publisher.

DiffusionResistivity vs. Doping

ρ =σ −1 = q µ n n + µ p p( )[ ]−1

n − type: ρ ≅ q µ n N D − N A( )[ ]−1

p − type: ρ ≅ q µ p N A − N D( )[ ]−1

from the publisher.

DiffusionTwo Step Diffusion

• Short constant source diffusion used toestablish dose Q (“Predep” step)

• Longer limited source diffusion drives

profile in to desired depth (“drive in”step)

• Final profile is Gaussian

from the publisher.

Diffusion CalculationExample 4.3 - Boron Diffusion

• A boron diffusion is used to form the base region of an npn

transistor in a 0.18 Ω-cm n-type silicon wafer. A solid-

solubility-limited boron predeposition is performed at 900o

C for 15 min followed by a 5-hr drive-in at 1100o

C. Findthe surface concentration and junction depth (a) after the

predep step and (b) after the drive-in step.

from the publisher.

Diffusion CalculationExample 4.3 - Boron Diffusion

Predeposition step is solid- solubility limited.

T1 = 900

C =1173K →NO =1.1x10

D1 =10.5exp −

3.69eV

8.614 x10−5eV / K ( )1173K

=1.45 x10

−15cm2 /sec

t 1 =15 min = 900 sec D1t 1 =1.31 x10−12 cm2

N x( )=1.1 x1020

erfc x

2.28 x10

Dose: Q = 2 N O D1t 1

π =1.42 x10

14 / cm

T2 =1100oC =1373K

D2 =10.5exp −3.69eV

8.614 x10−5 eV / K ( )1373K

= 2.96 x10

−13cm2 /sec

t 2 = 5 hr =18000 sec D2

t 2 = 5.33 x10

−9cm2

N 2 x( )=1.42 x10

14 / cm2

π 5.33 x10−9cm2( )

exp − x

2 D2t 2

=1.1 x1018 exp − x

1.46 x10−4

from the publisher.

Diffusion CalculationExample 4.3 (cont.)

N 1 x( )=1.1 x1020 erfc x2.28 x10−6 cm

x j1 = 2 D

1t 1erfc−1 N o

= 2.28 x10

−6cm( )erfc−1 3 x1016

1.1 x1020

= 2.28 x10

−6cm( )erfc−12.73 x10

−4( )

x j1 = 2.28 x10−6cm( )2.57( )= 5.86 x10

−6cm = 0.058

N 2 x( )=1.1 x1018 exp − x

1.46 x10−4

x j 2 =1.46 x10

−4 cm ln1.1 x1018

3 x1016

= 2.77 x10

−4 cm = 2.77 µ m

from the publisher.

Diffusion CalculationExample 4.3 (cont.)

Starting Wafer : n - type 0.18Ω− cm

n - type 0.18 Ω− cm →ND = 3 x 1016 /cm3

from the publisher.

Two Step Diffusion

• Short constant source diffusion used toestablish dose Q (“Predep” step)

• Longer limited source diffusion drives

profile in to desired depth (“drive in”

• Final profile is Gaussian

from the publisher.

Lateral DiffusionUnder Mask Edge

• Diffusion is really a 3-D process.

As impurities diffuse vertically,

they also diffuse horizontally in

both directions.

• Diffusion proceeds laterally under

the edge of the mask opening

from the publisher.

Lateral DiffusionUnder Mask Edge

Original Mask

from the publisher.

Concentration DependentDiffusion

Second Law of Diffusion

∂ t = ∂

∂ x D x( )

Profiles More Abrupt at High Concentrations

from the publisher.

Concentration DependentDiffusion

from the publisher.

ResistorsSheet Resistance

A =W • t

R = ρ

RS = ρ

t = Sheet Resistance [Ohms per Square]

=Number of Squares of Material

from the publisher.

ResistorsCounting Squares

Figure 4.14

• Top and Side Views ofTwo Resistors of Different

• Resistors Have Same

Value of Resistance

• Each Resistor is 7 in

Length

• Each End ContributesApproximately 0.65

• Total for Each is 8.3

from the publisher.

ResistorsContact and Corner Contributions

• Effective SquareContributions of Various

Resistor End and Corner

Configurations

Figure 4.15

from the publisher.

Sheet ResistanceIrvin’s Curves

• Irvin Evaluated this Integral andPublished a Set of NormalizedCurves Plot SurfaceConcentration Versus AverageResistivity

• Four Sets of Curves

– n-type and p-type– Gaussian and erfc

σ x( )dx0

RS = ρ x j

σ x( )dx0

RS ≅ q µ N x( )dx0

ρ = RS x j

from the publisher.

Sheet ResistanceIrvin’s Curves

from the publisher.

Sheet ResistanceIrvin’s Curves (cont.)

from the publisher.

Two Step DiffusionSheet Resistance - Predep Step

Initial Profile

N o =1.1 x1020 / cm3

N B = 3 x1016 / cm3

x j = 0.0587 µ m

p− type erfc profile

RS x j = 50 Ω - µ m

RS =32 Ω - µ m

0.0587 µ m= 850 Ω /Square

from the publisher.

Two Step DiffusionSheet Resistance - Drive-in Step

Final Profile

N o =1.1 x1018 / cm3

N B = 3 x1016 / cm3

x j = 2.73 µ m

p− type Gaussian profile

RS x j = 700 Ω - µ m

RS =700 Ω - µ m

2.73 µ m= 260 Ω /Square

from the publisher.

Resistivity MeasurementFour-Point Probe

ρ = 2π sV

I [Ω - m] for t >> s

ρ = π t

[Ω - m] for s >> t

RS = ρ

t = π

I ≅ 4.53

I [Ω /square]

Four Terminal Resistance Measurement

from the publisher.

Four-Point ProbeCorrection Factors

Correction Factors

(a) Wafers Thick Relative to the Probe Spacing

(b) Wafers of Finite Diameter

ρ = F ρ measured

from the publisher.

Sheet Resistancevan der Pauw’s Method Van der Pauw's Theory

Any Four - Terminal Region without Holes

exp -π t R AB ,CD

+ exp -π t

R BC , DA

R AB,CD =

I AB and R BC , DA =

For symmetrical structure R AB ,CD = R AB ,CD

RS = ρ

Four Terminal Resistance Measurement

from the publisher.

Junction Depth Measurement

• Groove and StainMethod

= a+ b( ) a− b( )

from the publisher.

Junction Depth Measurement

• Angle Lap Technique

x j = d tanθ = N λ 2

from the publisher.

Impurity ProfilingSpreading Resistance

• Region of Interest is Angle-

Lapped

• Two-Point Probe Resistance

Measurements vs. Depth• Profile Extracted

from the publisher.

Impurity ProfilingSecondary Ion Mass Spectroscopy (SIMS)

For the exclusive use of adopters of the bookIntroduction to Microelectronic Fabrication, Second

Edition by Richard C. Jaeger. ISBN0-201-44494-1.

material may be reproduced, in any form or by any means, without permission in writingfrom the publisher.

Diffusion Systems

Open Furnace Tube Systems(a) Solid source in platinum

source boat

(b) Liquid Source - carrier gaspassing through bubbler

(c) Gaseous impurity source

Wafers in Quartz Boat

Scrubber at Output

Diffusion SystemsPhosphorus Diffusion

Gaseous Source : Phosphine PH3 (Extremely Toxic)

2P H 3 + 4O2 → P2O5 + 3 H 2O

All systems need careful scrubbing!

P2O5 POCl3 Cl2

Surface Reaction:

2P2O5 + 5Si↔ 4P + 5SiO2

Solid Sources:

Phosphorus Pentoxide

Ammonium monophosphate NH4H2PO4

Ammonium diphosphate NH4( )2H2PO4

Liquid Source : Phosphorus Oxychloride POCl3

4POCl3 + 3O2 → 3P2O5 + 6Cl2

Diffusion SystemsArsenic & Antimony Diffusion

Arsenic Surface Reaction

2 As2O3 + 3Si↔ 3SiO2 + 4 As

Solid Sources : Possible - Low Surface Concentations

Gaseous Source: Arsine AsH3 (Extremely Toxic)

Ion− Implantation Is Normally Used for Deposition

Antimony Surface Reaction

2Sb2O3 + 3Si↔ 3SiO2 + 4Sb

Liquid Source : Antimony Pentachloride Sb3Cl5

Ion− Implantation Is Normally Used for Deposition

DiffusionToxicity of Gaseous Sources

Silane and Dichlorosilane Used for

Polysilicon Deposition

DiffusionGettering

• Improves Quality of Wafers

– Removes Metallic Impurities: Cu, Au, Fe, Ni (Rapid Diffusers)

– Removes Crystal Defects: Dislocations

• Backside Treatment

– Surface Damage e. g. Sandblasting

– Phosphorus Diffusion

• Argon Implantation

• Internal Stress

• Crystal Defects

• Oxygen Incorporation

– During Growth

– Implantation

DiffusionReferences

For the exclusive use of adopters of the bookIntroduction to Microelectronic Fabrication,

Second Edition by Richard C. Jaeger. ISBN0-201-44494-1.

portion of this material may be reproduced, in any form or by any means,without permission in writing from the publisher.

End of Chapter 4

For the exclusive use of adopters of the bookIntroduction to Microelectronic Fabrication,

Second Edition by Richard C. Jaeger. ISBN0-201-44494-1.

portion of this material may be reproduced, in any form or by any means,without permission in writing from the publisher.

Introduction to

Microelectronic Fabrication

Richard C. JaegerDistinguished University Professor

ECE Department

Auburn University

Chapter 5

Ion Implantation

Copyright Notice

• © 2002 Pearson Education, Inc., Upper Saddle River, NJ. Allrights reserved. This material is protected under all copyrightlaws as they currently exist. No portion of this material may bereproduced, in any form or by any means, without permission in

writing from the publisher.

• For the exclusive use of adopters of the book Introduction toMicroelectronic Fabrication, Second Edition by Richard C.

Jaeger. ISBN0-201-44494-1.

Ion ImplantationHigh Energy Accelerator

1. Ion Source

2. Mass Spectrometer

3. High-Voltage Accelerator (Up to 5 MeV)

4. Scanning System

5. Target Chamber

Force on charged particle F = q v x B( )

Magnetic Field B =2mV

Implanted Dose Q =1

mqA I t ( )

∫ dt

m =mass

v = velocity

V = acceleration potential

A = wafer area

Ion ImplantationOverview

• Wafer is Target in High Energy Accelerator

• Impurities “Shot” into Wafer

• Preferred Method of Adding Impurities to Wafers

– Wide Range of Impurity Species (Almost Anything)

– Tight Dose Control (A few % vs. 20-30% for high temperaturepre-deposition processes)

– Low Temperature Process

• Expensive Systems

• Vacuum System

Ion ImplantationMathematical Model

Gaussian Profile

N x( )= N p exp − x − R p( )

2∆ R p

R p = Projected Range

∆Rp =Straggle

Dose Q = N x( )dx = 2π 0

∫ N p∆ R p

Ion ImplantationProjected Range

Ion ImplantationStraggle

Ion ImplantationSelective Implantation

N x, y( )= N x( )F y( )

F y( )=1

y − a

2∆ R⊥

− erfc

2∆ R⊥

∆ R⊥ = transverse straggle

N x( ) is one - dimensional solution

Figure 5.4

Contours of equal ion concentration for an implantationinto silicon through a 1-µm window. The profiles are

symmetrical about the x-axis and were calculated using

the equation above taken from Ref. [3].

• Desire Implanted Impurity

Level to be Much Less

Than Wafer Doping

N(X0) << NB

N(X0) < NB /10

X 0 ≥ R p + ∆ R p 2ln 10 N p

= R p + m∆ R p

Ion ImplantationJunction Depth

N x j( )= N B

N p exp − x j − R p( )

2∆ R p

x j = R p ± ∆ R p 2ln N p

from the publisher.

Ion ImplantationLattice Damage and Annealing

• Implantation Causes

Damage to Surface

• Typically Removed by

Annealing Cycle 800-

C for 30 min.• Rapid Thermal Annealing

(RTA) Now Used for

Lower Dt Product

from the publisher.

Ion ImplantationDeviation from Gaussian Theory

• Curves Deviate from

Gaussian for Deeper

Implantations (> 200 keV

• Curves Fit Four-Moment(Pearson Type-IV)

Distribution Functions

from the publisher.

Ion ImplantationShallow Implantation

Ion Implantation

from the publisher.

Ion ImplantationReferences

For the exclusive use of adopters of the bookIntroduction to Microelectronic Fabrication,Second Edition by Richard C. Jaeger. ISBN0-201-

44494-1.

© 2002 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.This material is protected under all copyright laws as they currently exist. Noportion of this material may be reproduced, in any form or by any means,

without permission in writing from the publisher.

End of Chapter 5

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