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DOPING

Fys4310 doping

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FYS4310. DOPING. Fys4310 doping. DIFFUSION. phenomenological. Ficks laws Intrinsic diffusion - extrinsic diffusion Solutions of Fick ’ s laws ’ predeposition ’ , ’ drive-in ’ electrical field enhancement Concentration dependant diffusion ( As). Diffusion program I. - PowerPoint PPT Presentation

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Page 1: Fys4310 doping

DOPING

Page 2: Fys4310 doping

Diffusion program I

Ficks laws Intrinsic diffusion - extrinsic diffusion Solutions of Fick’s laws ’predeposition’, ’drive-in’ electrical field enhancement Concentration dependant diffusion ( As)

phenomenological

atomistic

Si-Self diffusion

Vacancy diffusion

Charged vacancy model

Impurity diffusion

Vacancy -dopant interactions

Page 3: Fys4310 doping

Diffusion program II

Numerical solutions of Ficks lawsComputer packages

Math & practical

experimental./ref.reading

Measurements of diffusion

SIMS, Radio tracer, RBS

Differential Hall, SRM, CV, stain etch

High concentration effectsPairs, quartets, defects

Materials science

Bolzman Matano method

Diffusion equipment, furnaces, boilers, sources

Page 4: Fys4310 doping

Diffusion program III

B in SiAs in SiP in Si, high concentrationEmitter pushZn in GaAs

Examples

etc.

These points/topics are woven into other headings

High doping effectsSolubility, Metastable dopingDopant interactionsDefects introduced in diffusion doping, StressesDefining doping areas, masking, Diffusion in SiO2 vs SiDiffusion of metallic impurities

Page 5: Fys4310 doping

Diffusion phenomenological

Ficks laws

Ficks 1st lovDefines Dphonomenologic

Continuity equation

Ficks 2nd law

J: flux

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Continuity equation should be well known

Derivation

One dimentional

J: fluxC: concentrationt : time

x x+dx

JoutJin

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Diffusion in general microscopically

Random walkBrownian motion

Microscopic lattice modelling

Comparison gives D Phenomenologically Ficks 1. og 2.

a: jump distancev:trial rateZ: geometry

Ea= Em+Ev :migr.+vac6: std for cubic

Page 8: Fys4310 doping

Analytic solution diffusion equation 1

Boundary cond. - ”predeposition” from gas or solid source

C(z,0) =0C(0,t)=Cs

C(∞,t)=0

Solution

Total amount

Page 9: Fys4310 doping

Analytic solution diffusion equation 2

Boundary cond. - ”drive - in” on surface

Solution

no flux predep

Drive in

Dtpre<<Dtinndr

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Curve shape for idealized caseINTRINSIC Diffusion

Fig. 3-7 a b, Cambell

Pre deposition Drive in

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Electric field assisted diffusion - doping

Elec field

Flux

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Atomic diffusion -self diffusion

Usually requires little energy

exhange

vacancy-diffusion

1 2 12

Interstitialdiffusion

V V

Interstitials can knockout regular atoms - interstitialcy

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Atomic diffusion

Interstitials can move from on interstitial position to the next-Interstitial diff. Usually requires little energy

substitutional interstitial

Si

Int O, Fe, Cu, Ni, Zn

Sub P, B, As, Al, Ga, Sb, Ge

Substitutionals may move in various ways

exchange

vacancy-diffusion

1 2 12

V V

Page 14: Fys4310 doping

Atomic diffusion

Fig 3.6

Fig 3.5

Various diffusion mechanisms for doping atoms

B and P may diffuse this way -also depends whether have Si(I) or V

Frank-Turnbull

’kick out’

’Interstitialcy’

Page 15: Fys4310 doping

Atomic diffusion

Assume DSi can be measured

Si self diffusion - guess vacancy diffusionCan be measured by labeling the Si atoms by radioactive Si*

P conc.. DSi dependant on the doping density

Why?

Finds:

Page 16: Fys4310 doping

Atomic diffusion Vacancy diffusion

Vacancy concentration depends on doping concentration

Probability for jump via vacancy depends on vacancy concentration

i.e. Diffusivity D depends on doping concentration

Schematic

Diy :diffusivity

of Si by vac. w. charge y in intrinsic case

Page 17: Fys4310 doping

atomistic diffusion consequencesFor dopant atoms

n=n(C) n: electron concentrationp=p(C) C:doping concentration

i.e.D=D(C) and C=C(x)

ie EXTRINSIC DIFFUSJON

Diffusion equation Must be solved numerically

Page 18: Fys4310 doping

Diffusion, atomistic model consequences

Assume D can be measured, How?

From

With measurements of D vs. n you can determine D*, D-, D=

Fit to y: charge state *,-,+,=

Measured cm2/s eV

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Diffusion, typical profiles Fig 3.8 B high conc.

B acceptor B- V-

Fig 3.9 As high conc.

As donor, As+

As+ V- , As+ V+

n>>ni : h=2,

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Diffusion, High doping effects

Cluster formation

Dislocations

Band gap shrinkage

Segregation

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Diffusion, High doping effects Dislocations

Stress-no disloc.f.example B doping

Disadvantage for stress in membranes for MEMS, ie for pressure sensors

Stress in heavy B doping of Si tried compensated by adding Ge

Elastic energy released by creating a dislocation

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Diffusion, High doping effects Band-gap narrowing

Very low doping conc. High doping conc.

e-e int.act.. Donor donor interaction.Ed

Eg variesni varies[V] varies.

Page 23: Fys4310 doping

Diffusion, High doping effects Band-gap narrowing, qualitatively?

Van Overstraeten, R. J. and R. P. Mertens, Solid State Electron. 30, 11 (1987) 1077- 1087.

For 1017 ≤ N ≤ 3·1017 cm-3       .∆Eg

el ~ 3.5·10-8·Nd1/3 (eV)

(Nd in cm-3)

Page 24: Fys4310 doping

Diffusion, High doping effects Cluster formation

Various reactions

ln(C)ln

(n) solubility

VAs2-complexSi

Si

V

As

As

V=+2As+=VAs2

kVl+mAs++ye=(VKAsm)(m+lk-y)

Complex neutral, el.neg, [V]>>[2V]Gives k=1 and m=1,2,4

Complexes/clustersMaybe precursor to segregation

One model

Page 25: Fys4310 doping

Diffusion, High doping effects Cluster formation

How to find out about cluster models.?

ln(C)ln

(n) solubility

V2As2-complex

2V-+2As+=V2As2

kVl+mAs++ye=(VKAsm)(m+lk-y)

Én model

As

AsSi

V

V

Page 26: Fys4310 doping

Diffusion, High doping effects Segregation

Requires nucleation of new phase,

i.e. the concentration must correspond to super saturation before precipitation occurs, The density of precipitates depends upon nucleation rate and upon diffusion. It means measurements of solubility can require patience particularly at low temperatures.

r* r

∆G

surface

volumebulk

∆G*

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Diffusion, Numerical calculation considerations

Finite differencing

Solving the diffusion equations (by simulations)

General methods

Finite elementMonte CarloSpectral

Variational

Page 28: Fys4310 doping

Diffusion, numeric ’finite difference’Representations of time and space differentials

example. diff.eq.

Combining a and b giver representation FTCS Forward Time Centered Space

Forward Euler differentiation, Accuracy to 1ste order ∆t

NB Unstable*

FTCS explicit so Ujn+1 can be calculated for each j from known points

Stability achieved by Stability just as much art as science

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Diffusion, numeric ’finite difference’

Leapfrog

accuracy 2nd order in ∆t

FTCS:

Often stability means many time steps

Here

F: Flux

C: Flux

(explicitly)

Stab. criteria:

Diffusion equation in simple case

Page 30: Fys4310 doping

FTCS:

=Crank-Nicholson method

(explicit)

(implicit) Backward time

Combining the two

(explicit)(implicit) Crank-Nicholson

Allows large time-steps

Diffusion, numeric ’finite difference’

Page 31: Fys4310 doping

Diffusion equation w. Crank -Nicholsen

collect left and right

ie

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Diffusion equation w Crank -Nicholsen

A and B tridiagonal i.e.

Boundary cond , j=1 i.e. surface

R=1 reflectionR=0 trapping

R=0.5 segregation coeff

j=2

ie.

ie.

Page 33: Fys4310 doping

Diffusion equation w Crank -Nicholsen

unknown

=

known

If D=D(C) i.e. we have a nonlinear set of equations

Can readily be solved when D only a function of x and t but not of C.

Page 34: Fys4310 doping

Diffusion, numeric examplesschematic

Implanted profileVacancy creation on surfaceVacancy annihilation in ion-damaged regionGe i Si

Implanted profileVacancy creation on surfaceVacancy annihilation in ion-damaged region Surface segregationAs i Si

Page 35: Fys4310 doping

Diffusion, numeric general

unknown known

If D=D(C) ie

we have a nonlinear system of equations

But assume

as 1st approx. then calculate Cn+1, and put in A for next it.

vector matrix Initial conditions

This equation is solved for example by Newton’s method in the general case

Page 36: Fys4310 doping

Diffusion, numeric SOFTWARE PACKAGES

SUPREM III (1D), SUPREM IV(2D) [Stanford] TSUPREM4, SSUPREM4[Silvaco],ATHENA[Silvaco]ICECREAM, DIOS, STORM Floops, Foods, ACES,

’curve-fitting' models / physical models

1D, 2D, 3D

All processing stages/ all thermal/ just diffusion

Integrated, -masks, device, system-simulation (icecream silvaco)

Required for ULSI

Page 37: Fys4310 doping

Diffusion, Measurements of diffusion profiles, D(C)

SIMS, TOFSIMSNeutron activationRBS, ESCA, EDAXIR abs.

So measurement of C, and n el. P is needed

In many situations we have C=C(x), We can find D(C) by measuring C(x) at different T

Can find D*, D+, D-, D= from the dependency D(n)

Example P in simple caseMethods for C Methods for n

Spreading ResistanceDifferential Hall i.e.. +stripCapacitance, C-V + stripSCM, SRM

Page 38: Fys4310 doping

Diffusion, Measurement of diffusion, process surveillance

sphere

sphere

Top view

Page 39: Fys4310 doping

Diffusion, Measurement of diffusion, process surveillance

’Four-point probe’

Measures so-called sheet resistance

Can find resistivity if the depth distribution of n and µ is found

Mostly for process surveillance-reproducibility tests

Page 40: Fys4310 doping

Diffusion, Measurements of diffusion profiles

van der Peuw method

2

1

4

3

More common geometry

12

3

4

Page 41: Fys4310 doping

Diffusion, Measurement of electric profileHall measurements

Measurement-procedure

Measure s, RHS gives µH

Strip a layerRepeat to d

Calc individual n and µ

Page 42: Fys4310 doping

Diffusjon, Measurement of electric profile

Schottky

p-n junction

electrolyte

Page 43: Fys4310 doping

Diffusion, Measurement of diffusion profile

ScanningProbeMicroscopy

SSRMSCM

Page 44: Fys4310 doping

Diffusion, Measurement of diffusion profile

Page 45: Fys4310 doping

Diffusion, Measurement of diffusion profile

Page 46: Fys4310 doping

Diffusion, Measurement of diffusion profileSpreading resistancemeasurements

beveling

needle

Page 47: Fys4310 doping

Diffusion, Measurement of diffusion profileScanning capacitance microscopy

Electric

Page 48: Fys4310 doping

Diffusion, Measurement of diffusion profileScanning capacitance microscopy

Elektriske

Page 49: Fys4310 doping

Diffusion, Measurement of diffusion profileScanning capacitance microscopy

Elektriske

Page 50: Fys4310 doping

Diffusion, Measurement of diffusion profileSIMS,

Page 51: Fys4310 doping

Physical ElectronicsUniversity of Oslo

Equipment at MRL-UiO:

Installed April-Aug. 2004

principle

SIMS Cameca 6F

UiO SIMS

Page 52: Fys4310 doping

Characteristics of SIMS:

SIMS karakteristiske trekk

Sensitivity: All elements can be detected Sensitivity depends on element. in Si: B, P 1014cm-3

Accuracy: Through standards ( not absolute spectro-scopy/-metry) Good reproducibility Matrix-effects: Ionization coeff. depends on surface, oxidation, sputter w. oxygen yields good reproducibility Interface-effects

Depth resolution: Limited by sputter process, 2 nm - 50 nm ion mixing, segregation, run away erosion

Well suited for measurements of diffusion profiles in high tech 1/2 conductors:

Page 53: Fys4310 doping

Diffusion, Measurement of diffusion profile

RBS

Absolute measurement

Depth resolution 10-30 nm

Sensitivity: Matrix effects. Heavy in light matrix 1018 cm-3

Page 54: Fys4310 doping

Detection limits

Page 55: Fys4310 doping

Analysis depths

Page 56: Fys4310 doping

Diffusion, doping sources

Page 57: Fys4310 doping

Bolzman Matano method

Point: Extract D(C) from C(x)

Introduce a new coordinate system x’ by

C=C(x’,t) is a function only of i.e. C=C()

We may write Ficks 2 law by

LHS

RHS

Setting LHS=RHS

Page 58: Fys4310 doping

Bolzman Matano method

Here we have the same differential on both sides, so we integrate

Integration between C=0 and C=C1 and assume

C1 is one particular conc. we wish to investigate

Slight rewriting:

I

Put in to [I ] and choose a particular experimentally measured time for diffusion t1:

A

B

1. x’ origo from B2. dC/dx’ from curve3. Int(x’,C=C1..C0)

1+2+3 gives D from A

Method

Page 59: Fys4310 doping

Diffusjon, example P

P donor, P+

P+ V- , P+ V+

?observations

Vacancies are created at the surfaceConc of vac depends on n at surfaceV= + P+ -> VP-

EC-EF depends on depth when dC/dx <0VP- breaks up -> exess vac’Conc. of vacancy controlled by surface and not by local doping

Fair -Tsai model

Page 60: Fys4310 doping

Diffusion, ”Emitter-push”

Many models

Fair-Tsai diff. Model for P +Band gap narrowing

Describes results adequately

Page 61: Fys4310 doping

Diffusion, Example: Zn i GaAs

Zn acceptor in GaAs , Substitutes for Ga

VGa+ , VGa

* ..Zni+, Zns

-

Confinement of waveguides, etc..