Session 3B - Penn Engineeringnanosop/documents/... · Session 3B Using the Gen-Osc Layer to Fit Data UPenn, February 2014 ©2014 J.A. Woollam Co., Inc. 2 Using Gen-Osc to Fit Data

©2014 J.A. Woollam Co., Inc. www.jawoollam.com 1

Andrew Martin

Session 3B Using the Gen-Osc Layer to Fit Data

UPenn, February 2014


Using Gen-Osc to Fit Data

Pre-built Existing Genosc Layer

Library optical constants GENOSC

Cauchy Point-by-Point GENOSC

Choosing the correct oscillators

– Fitting out-of-range oscillators

– Parameter correlation


GENOSC Process Overview

Use Oscillator

To Fit DATA

Create

Oscillator Model

Existing

Oscillator Model

Tabulated

Optical Constants

Pt-by-Pt Fit

Reference

optical constants

itera

te


1 Example_1_a-si_on_glass.dat

Use 7059_u.mat for substrate

Use a-si_asp.mat as Reference

Remember to add

surface oxide

– Very important for

semiconductors


1 Example_1_a-si_on_glass.dat REPEAT

Compare Tauc-Lorentz to Cody-

Lorentz.

Use pre-existing Genosc layer for a-

Si available in the library and

repeat the example.


Procedure for UV Absorbing Films

6

1. Cauchy Fit

– transparent region only

2. Pt-by-Pt Fit – all wavelengths

– fix thickness, then perform pt-by-pt fit

– Build Genosc from tabulated ‘cauchy’

3. Match n,k using Genosc

– fit reference – first e2, then e1

4. Fit Y & D data using new Genosc model


2 Example_2_Thin_Dielectric_on_Si.dat

Use Si_vuv.mat for substrate

Cauchy PBP Gen-Osc


Example 2: Thin Dielectric on Silicon

Select Transparent

Region

Build Model with Single-

layer Cauchy

Fit thickness and

Cauchy parameters

Extend range further

toward absorbing

region until MSE climbs

Generated and Experimental

Wavelength (nm)

600 800 1000 1200 1400 1600 1800

Y

in

degre

es

3

6

9

12

15

18

21

24

Model Fit

Exp E 60°

Exp E 75°

0 si_vuv 1 mm

1 cauchy 22.541 nm



Fix Thickness and

Cauchy parameters

Select data at ALL

wavelengths

Fit n & k using Pt-by-Pt fit


Wavelength (nm)

0 300 600 900 1200 1500 1800

Y in

de

gre

es

0

10

20

30

40

50

60

70

Model Fit Exp E 60°Exp E 75°



PBP fit result n,k



Shortcut: Build GenOsc from tabulated‘cauchy’

0 si_vuv 1 mm

1 genosc 22.522 nm

If you have

tabulated optical

constants from any

layer you would like

to use as reference in Genosc, use

right-click menu.



Tabulated n & k is

loaded as Reference

Material

Note this particular

dielectric has Tauc-

Lorentz absorption shape in UV

Select Fit e2 only



Add Oscillators to match e2 shape of Reference material.

~ 5eV



Fit Oscillator Parameters to match Reference e2.



Select “Fit e1 Only”

Fit e1 with poles & offset


Example 2: Thin Dielectric on Silicon Generated and Experimental

Wavelength (nm)

0 300 600 900 1200 1500 1800

Y in

de

gre

es

0

10

20

30

40

50

60

70



Wavelength (nm)

0 300 600 900 1200 1500 1800

D in

de

gre

es

-100

0

100

200

300


Generate data

before fitting to insure

that the new layer

agrees with point-by-

point result.

Generated curves

should be close to

Experimental data.




Wavelength (nm)

0 300 600 900 1200 1500 1800

D in

de

gre

es

-100

0

100

200

300


Allow oscillator parameters and thickness to fit.

Watch for

correlation

between

parameters.

MSE=1.36

SAVE Model File for FUTURE!


3 Example_3_SiNx_on_Si.dat

Start from Cauchy to get a

Gen-Osc for SiNx layer.

Minimize number of Genosc

parameters.


Out-of-range oscillators,

Correlation & sensitivity

– Fit with 2 Gaussian Oscillators

Photon Energy (eV)

4 6 8 10 12

Ima

g(D

iele

ctr

ic C

on

sta

nt)

, e 2

0.0

0.5

1.0

1.5

2.0

3) sion_pbpgaussian near bandgapout-of-range gaussian

Measured spectral

range


Out-of-range oscillators,

correlation & sensitivity – Note that 3 different oscillators, all fit the measured spectral range equally

well !!

– The Gen-Osc function insensitive to the out-of-range Gaussian parameters

– The amplitude, center energy & broadening are correlated !!

Photon Energy (eV)

4 6 8 10 12 14Im

ag

(Die

lectr

ic C

on

sta

nt)

, e 2

0

2

4

6

8

10

3) sion_pbpout-of-range gaussian, eo=9p4evout-of-range gaussian, eo=11evout-of-range gaussian, eo=12evgaussian near bandgap

Measured spectral

range

Photon Energy (eV)

4 6 8 10 12 14

Ima

g(D

iele

ctr

ic C

on

sta

nt)

, e 2

0

2

4

6

8

10

3) sion_pbpout-of-range gaussian, eo=9p4evout-of-range gaussian, eo=11evout-of-range gaussian, eo=12evgaussian near bandgap

Measured

spectral range


4 Example_4_Resist_on_Si.dat

Use si_vuv.mat for substrate

Cauchy PBP Gen-Osc

Gaussians work well to match

absorptions from organic film, such

as this photoresist.


GENOSC Process Overview

Use Oscillator

To Fit DATA

Create

Oscillator Model

Existing

Oscillator Model

Tabulated

Optical Constants

Pt-by-Pt Fit

Reference

optical constants

itera

te


Using Genosc to Fit Data

Starting with Existing Genosc Layer

Cauchy Point-by-Point GENOSC

Choosing the correct oscillators

Fitting out-of-range oscillators

Parameter correlation


Advanced Genosc

When the pt-by-pt fit fails?


5 Example_5_Organic_on_Si.dat

Use si_vuv.mat for substrate

Is the PBP result KK consistent?

– Use Gen-Osc to check


What to do when Pt-by-Pt Fails?

1. Ask why did it fail?

Abrupt n,k changes (try # Pts. To Avg. = 2)

Starting model inaccurate (Roughness, Grading, Depolarization?)

2. Match e2 with oscillators (Gaussians) and match e1 at long-l. Fit. Go to #4 if needed.

3. Slowly move into absorbing region with Genosc, adding oscillators as needed. Go to # 4 if needed.

4. After oscillators come close to solution, do Normal Fit for n,k to develop a “reference” material file.

5. E-mail to us! ([email protected])


Example 5

Previous point-by-point fit is not KK consistent.

However, we can match e2 at all wavelengths,

and e1 at longer wavelengths to get “starting

point”.


Example 5, continued

Allowing all fit

parameters to vary,

we get: Generated and Experimental

Wavelength (nm)

0 300 600 900 1200 1500 1800

Y i

n d

eg

ree

s

0

20

40

60

80

100



Wavelength (nm)

0 300 600 900 1200 1500 1800

D i

n d

eg

ree

s

-100

0

100

200

300


Watch for oscillators that get lost.


6 Example_6_Organic_on_Si.dat

Is the Point-by-Point Fit KK consistent?

Try # Pts. To Avg. for next guess = 2

Extra Credit, Alternatively Try: – Match e2 with oscillators (Gaussians) and match

e1 at long-l. Fit.

– After oscillators come close to solution, do

Normal Fit for n,k to develop a “reference”

material file.


Example 6 Results

0 si_jaw 1 mm

1 GenOsc 89.853 nmMSE = 2.5


Wavelength (nm)

0 200 400 600 800 1000

Y in d

egre

es

0

20

40

60

80

100

Model Fit Exp E 65°Exp E 70°Exp E 75°


Wavelength (nm)

0 200 400 600 800 1000

D in d

egre

es

-100

0

100

200

300



7 Example_7_Organic_on_Si

How do we get the answer without

reference material file?

Try:

– Slowly move into absorbing region

with Genosc, adding oscillators as

needed.

– After oscillators come close to

solution, do Normal Fit for n,k to

develop a “reference” material file.


Example 7

Point-by-Point Fit FAILS


Wavelength (nm)

200 400 600 800 1000 1200

Y in

degre

es

10

20

30

40

50

60

70

80



Cauchy to Sellmeier

Cauchy Fit up to 1.75eV

Then, convert to Genosc (Sellmeier)


Extend Data to 2eV

Range-select to 2eV (Generate),

don’t fit yet. Generated and Experimental

Photon Energy (eV)

1.2 1.4 1.6 1.8 2.0

Y in

de

gre

es

15

18

21

24

27

30

33


Must need absorption at 1.8eV and above


Add Gaussian, Fit and Repeat

Difficult, take small steps (.2eV)

After oscillators come close to solution, do Normal

Fit for n,k to develop a “reference” material file.

Build another Genosc with new “Ref.Mat” file.

0 si_jaw 1 mm

1 GenOsc 60.127 nm


Photon Energy (eV)

1.0 1.5 2.0 2.5 3.0 3.5 4.0

Y in

de

gre

es

D in

de

gre

es

10

20

30

40

50

60

70

80

-100

-50

0

50

100

150

Model Fit Exp Y-E 65°Exp Y-E 70°Exp Y-E 75°Model Fit Exp D-E 65°Exp D-E 70°Exp D-E 75°

GenOsc Optical Constants

Photon Energy (eV)

1.0 1.5 2.0 2.5 3.0 3.5 4.0

Ind

ex o

f R

efr

actio

n '

n'

Extin

ctio

n C

oe

fficie

nt '

k'

1.2

1.4

1.6

1.8

2.0

2.2

0.0

0.2

0.4

0.6

0.8

nk

MSE = 12


EXTRA CREDIT - Depolarization

Film was non-uniform and this is

required to fit data better.


Photon Energy (eV)

1.0 1.5 2.0 2.5 3.0 3.5 4.0

Y in

de

gre

es

D in

de

gre

es

10

20

30

40

50

60

70

80

-100

-50

0

50

100

150

Model Fit Exp Y-E 65°Exp Y-E 70°Exp Y-E 75°Model Fit Exp D-E 65°Exp D-E 70°Exp D-E 75°

0 si_jaw 1 mm

1 genosc 59.191 nm

MSE = 3.9


Photon Energy (eV)

1.0 1.5 2.0 2.5 3.0 3.5 4.0%

Depola

rization

0

3

6

9

12

15

18

Model Fit Exp -dpolE 65°Exp -dpolE 70°Exp -dpolE 75°


Extra Slides

The following slides provide an

additional Example.


p-semi Oscillator

The Genosc psemi has 9 main

variable parameters (11 total*):

1. E Center energy

2. A Amplitude

3. B Broadening

4. WL Left end point

5. WR Right end point

6. PL position left control point

7. AL amplitude left control point

8. PR position right control point

9. AR amplitude right control point.

eV

e 2

PL=0.75

(fixed)

A & E1

(variable)

WL WR

PR=0.5

(fixed)

AR:(variable)

B (variable)

O2R = 0

(fixed)

O2L = 1

(fixed)

Psemi-M1

AL:(variable)


Psemi-Triangle oscillator

Psemi-TRI

eV

e 2

A, Ec (variable)

WL

(variable)

PR=0.5

(fixed)

AR:(variable)

PL=0.5

(fixed)

AL:(variable)

B (variable)

AL = 0.3, AR = 0.5

WR

(variable)


Psemi-M0 oscillator

AR (variable) = 0.8

A

B = 0.05eV

O2R = 0

(all variable)

eV

e 2

PR=0.5

PR=0.6

AR = 0.5

AR = 0.3

Eo

(variable)

WR (variable)

PR (variable)

Psemi-M0


8 Example_8_Direct_gap_film_on_SiC.dat

Use SiC_4H_o_g.mat for substrate

Try to match with Gaussians. How many

does it require?

How many PSEMI oscillators are required?

Count up the total number of “free”

parameters.


Poly-Silicon The dielectric function of silicon varies with crystallinity.

Amorphous films have broad UV absorption: no distinct electronic

transitions (E1, E2,…)

As crystallinity increases, individual peaks separate & become

narrower.

To quantify crystallinity, optical constants are compared to

“reference” measurements where a film with known crystallinity was measured.

Photon Energy (eV)

1.0 2.0 3.0 4.0 5.0 6.0

Ima

g(D

iele

ctr

ic C

on

sta

nt)

, e 2

0

10

20

30

40

50

a-Si70% Poly-Si85% Poly-Sic-Si

e2 for different

silicon films from

one “reference”

file.


Estimating Crystallinity

Ellipsometry can be used to estimate the amount of

crystallinity by comparing the measured optical constants

to the “reference” files. To improve accuracy, a new

“reference” file can be created for the particular deposition process.

Photon Energy (eV)

1.0 2.0 3.0 4.0 5.0 6.0

Ima

g(D

iele

ctr

ic C

on

sta

nt)

, e 2

0

10

20

30

40

50

75% Poly-Si80% Poly-Si90% Poly-SiCrystalline Si

For high crystalline %,

the peak is narrower

and eventually

separates into two

distinct regions.


Estimating Crystallinity - 2

For amorphous films and small-grain poly-Si,

the absorption peak is broad – but there is still

a shift of the optical constants as shown

below.

Photon Energy (eV)

1.0 2.0 3.0 4.0 5.0 6.0

Ima

g(D

iele

ctr

ic C

on

sta

nt)

, e 2

0

10

20

30

40

a-Si10% poly-Si20% poly-Si30% poly-Si


Estimating Bandgap

The ellipsometer is sensitive to optical constants of film. It will be most sensitive to the shape of absorbing region where e2 is larger. Although many models such as Tauc-Lorentz and Cody-Lorentz contain a bandgap term, the indirect gap of silicon films is not directly measurable. The bandgap can be estimated by plotting the decrease in a toward zero (log-scale).

Discussed in Woollam Newsletter article from year 2012

Photon Energy (eV)

0.0 1.0 2.0 3.0 4.0 5.0 6.0Lo

g(A

bso

rptio

n C

oe

ffic

ien

t in

1/c

m)

0

3

5

8

10


Tauc-Lorentz model matches

different a-Si and poly-Si films.

Blue area shows the level of

absorption that the SE can

detect. Values below are

extrapolated from T-L shape


Estimating Bandgap - 2 Cody-Lorentz provides more flexibility for amorphous

semiconductors. Similar to the Tauc-Lorentz, SE is sensitive to

shape primarily from the more absorbing UV region and the

bandgap region just shifts as the overall shape changes.

Lesson: T-L and C-L can provide a qualitative ‘bandgap’ value for comparison, but may not match actual physical

property of film.

Photon Energy (eV)

0.0 1.0 2.0 3.0 4.0 5.0 6.0Lo

g(A

bso

rptio

n C

oe

ffic

ien

t in

1/c

m)

2.0

3.0

4.0

5.0

6.0

7.0


Documents

Session 3B - Penn Engineeringnanosop/documents/... · Session 3B Using the Gen-Osc Layer to Fit Data UPenn, February 2014 ©2014 J.A. Woollam Co., Inc. 2 Using Gen-Osc to Fit Data