dopant diffusion revisited - university of california ...ee243/sp10/ee143/lectures/lec_10.pdf ·...

Professor N Cheung, U.C. Berkeley

Lecture 10EE143 S06

1

Dopant Diffusion Revisited

•Diffusion Mechanisms

•Dopant interactions with Point Defects of Si substrate

- Dopant Diffusivity affected by Dopant Concentration- Dopant Diffusivity affected by Point Defect Concentration- Point Defect Concentration affected by Dopant Concentration- Point Defect Concentration affected by Processing Steps


Lecture 10EE143 S06

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2) Diffusivity of Si interstitials and Si vacancies >> diffusivity of dopants

1) Thermal-equilibrium values of Si neutral interstitials and vacancies at diffusion temperatures<< doping concentration of interest (1015 –1020 /cm3)

Si Native Point Defects

At 1000oC, CIo* ~ 1012 /cm3CVo* ~ 1013 /cm3

For reference only

Si vacancy Si interstitial


Lecture 10EE143 S06

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(a) Interstitial Diffusion

Diffusion Mechanisms in Si (A) No Si Native Point Defect Required

10-6 cm2/secAu

Cu

Fast Diffusion

Example: Cu, Fe, Li, H


Lecture 10EE143 S06

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(a) Substitutional Diffusion

Diffusion Mechanisms in Si

(B) Si Native Point Defects Required (Si vacancy and Si interstitials)

(b) Interstitialcy Diffusion

Example: Dopants in Si ( e.g. B, P,As,Sb)


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(c) Kick-Out Diffusion (d) Frank Turnbull Diffusion

(B) Si Native Point Defects Required (Si vacancy and Si interstitials)continued

10-12 cm2/sec

B,P

As

Slow Diffusion


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Diffusivity Comparison:Dopants, Si interstitial, and interstitial diffusers

108 times higher

For reference only


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High Concentration Diffusion Effects

Log C(x)

x

Low conc profile:Erfc or gaussian

Log C(x)

x

J large

J small

High conc. profile:D gets largerwhen C(x) is large

* C(x) looks “flatter”at high conc. regions

1) E-Field Enhanced Diffusion2) Charged point defects enhanced diffusion


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(1) Electric-field Enhancement

Example: Acceptor Diffusion

Na(x)

Na(x)=Na-(x)

p(x)

hole gradient

x

Hole diffusion tendency

E build-in

Complete acceptorionization at diffusion temperature

At thermal equilibrium, hole current =0Hole gradient creates build-inelectric field to counteract the hole diffusion tendency


Lecture 10EE143 S06

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B-

+[p]holes tends to moveaway due to holeconcentration gradient

Ebuild-in

B- acceptorsexperiencean additionaldrift force

Enhanced Diffusion for B- acceptor atoms


Lecture 10EE143 S06

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[ ]dx

pdq

kTdxdp

pqkT

E

mequilibriuthermalatdxdp

qDEpqJ ppp

ln

1.

0

⋅=

⋅⋅=⇒

=⋅−⋅⋅⋅= µ

Calculation of build-in Electric Field E


Lecture 10EE143 S06

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Since

Total acceptor atom flux

A =µ

NEDF AAA ⋅⋅--= µdNA/dx

= (diffusion + drift) components

DA/[kT/q] from Einstein’s Relationship

Na-(x)

E

x

Calculation of total diffusion flux F


Lecture 10EE143 S06

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[ ]

[ ]22

22

2

4

1ln2

4)2(&)1(

)2(

)1(

ln

iA

A

iAA

i

A

AA

A

nNdxdN

dxpd

nNNp

ActionMassofLawnpn

NeutralitychargeNnpFrom

Ndx

pddx

dNDF

+⋅=∴

++=∴

=

+=

⋅+⋅−=

−


Lecture 10EE143 S06

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2

1

41

11

2

2

→<<→>>

+

+⋅⋅−=

−

hNn

hNnIf

Nndx

dNDF

Ai

Ai

factorh

A

i

AA

44 344 21

high dopant conc.

∴

low dopant conc.

Value of h depends on concentration NA


Lecture 10EE143 S06

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Temp range for dopant diffusion

Intrinsic Carrier Concentration ni

If n or p > ni(Tdiffusion), we will expect to observe high concentration diffusion effects.


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E-Field Effect ExampleHow the uniform substrate concentration is perturbed by E-field of diffusion specie

Asdiffusion

Uniform B conc in substrate

caused by Asconc gradient

B-


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(2) Diffusion Enhanced by Charged Point Defects (e.g. Vacancies)

Vo = neutralV+ = + vacancyV- = - vacancyV= = - - vacancy

…..

Si vacancy


Lecture 10EE143 S06

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Possible Point Defect Configurations

For reference only


Lecture 10EE143 S06

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• Neutral interstitial and vacancy point defects present at thermal equilibrium

• Charged Point Defects enhanced by heavy doping; total point defect concentrations enhanced by ~10x

I+, Io, I-

V+, Vo, V-, V=

•Point defects Injected by interfaces during oxidation(total point concentrations enhanced by ~10x)

• Implantation collisions (total point defect concentration enhanced by ~ 1000X)

How processing steps affect point defect concentrations

At 1000oC, CIo* ~ 1012 /cm3

CVo* ~ 1013 /cm3


Lecture 10EE143 S06

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K c = [Vo] nr

[V -r ]=

[Vo] n ir

[V i -r ]

[V -r]

[V i -r ]= [

nni

] r

where n = electron concentration , [ ] denotes the concentrations ,subscript i denotes condition for intrinsic Si

1) Negatively charged vacanciesVo + r • electrons ↔ V -r (r = 1,2,3…)

2) Positively charged vacanciesVo + r • holes ↔ V +r (r =1,2,3…)

[V +r]

[V i +r]= [

pni

] r = [nin ] r

p =hole concentration

Law of Mass Action

For the reaction : a•A + b • B ↔ c • C

[A] a [B]b

[C]c= Kc

[ ] denotes concentrationKc = equilibriumConstant at Temp T

Derivation of charged vacancy concentration

same Kc for undoped Si


Lecture 10EE143 S06

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...2

+

⋅+

⋅+

⋅+= =−+

ii

ii

ii

o

nn

Dnn

Dnp

DD

Why each diffusivity written with ni as normalization factor ?

Dtotal

Consider the +charge vacancy first , D+ ∝ [V+].From Law of Mass Action: [V+] ∝ p Therefore , D+ ∝ p and can be written as D+ = K• p where K is a proportionality constant

Let us multiply K by ni and call it Di+, then D+ = Di

+• (p / ni )The physical meaning of Di

+ is diffusivity D+ for undoped siliconbecause p = ni for undoped silicon

Similarly, Di- and Di

= are diffusivity values for undoped Si due to –charge and = charge vacancies

Charged Vacancy Enhanced Diffusion


Lecture 10EE143 S06

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...++++= =−+ DDDDD ov

...2

+

⋅+

⋅+

⋅+= =−+

ii

ii

ii

o

nn

Dnn

Dnp

DD

Do = Dio exp(-Eia / kT) <-- diffusion coefficient for diffusion vianeutral vacancies

Di+ = Do

+ exp(-Ea+/kT) <-- diffusion coefficient for diffusion via

singly positively charged vacancies

Di- = Do

- exp(-Ea-/kT) <-- diffusion coefficient for diffusion via

singly negatively charged vacancies

Di= = Do

= exp(-Ea=/kT) <-- diffusion coefficient for diffusion via

doubly negatively charged vacancies

Note that p/ni = n/ni = 1 for intrinsic (i.e. undoped) material!

Charged Vacancy Enhanced Diffusion


Lecture 10EE143 S06

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Example : High Concentration Arsenic diffusion profile becomes “box-like”


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First, Check if doping concentration is > ni(T) or < ni(T)

If doping conc < ni:D= Do

Use constant diffusivity solutions(profile is erfc or half-gaussian)

If doping conc > ni:

Use D = Dv = h [ Do + D+ + D- + D= + ...](Solution requires numerical techniques)

Summary of High-Concentration Diffusion


Lecture 10EE143 S06

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Oxidation Enhanced Diffusion (OED)

Field Oxide

Example:Channel-stop implant diffuses faster during field oxidation

Diffusivity is enhanced for B and P underneath a growing oxide

SiO2

SiSi[I]

Injected Si[I] interstitialsenhance dopant diffusion

Note: The dopant Sb shows retarded diffusivity during oxidation=> it diffuses primarily via the vacancy mechanism

DOED = D + ∆D ∆D ∝ [dXox / dt]n where 0.4 < n < 0.6


Lecture 10EE143 S06

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Transient Enhanced Diffusion (TED)

Dopant Implantation

Sisubstrate

Implantationinduced excesspoint defects

x

C(x)

no annealing

900oC, several sec (TED)Extremely rapid diffusion due to excess point defects

Implantation createslarge number of excess Siinterstitials and vacancies.(1000X than thermal process).After several seconds of annealing, the excess point defects recombine.

900oC, several minutes(After excess point defects recombine. slower diffusion)


Lecture 10EE143 S06

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•Difficult to make ultra-shallow (< 0.1µm) junctionswith implantation and annealing

Annealingtime

JunctionDepth xj

TED

Normal diffusion (with high concentration effects)

seconds

Junction Depth versus post-implantation annealing time

dopant diffusion revisited - university of california ...ee243/sp10/ee143/lectures/lec_10.pdf ·...

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