Development of hyperspectral CL imaging systems for the characterization of

semiconducting materials

P.R. Edwards, K.J. Lethy, J. Bruckbauer, N. Kumar,M. Wallace, F. Luckert, F. Sweeney, C. Trager-Cowan,

K.P. O’Donnell and R.W. Martin

Department of Physics

University of Strathclyde

Glasgow, Scotland

MAS Topical ConferenceCathodoluminescence 2011

2

Talk outline• Introduction

– to our research group & nitride semiconductors

• CL hyperspectral imaging– what it is & why we need it

– optical design considerations

– combining with

• WDX

• electron diffraction techniques(EBSD/ECCI)

• Data analysis– peak fitting

– multivariate statistical analysis

• Where next?

all illustrated with examples from our work

2.90

2.85

2.80

2.75

eV

1 µm

0 200 400 600 800 1000

distance (nm)

0

200

400

600

800

dist

ance

(nm

)

2.95

3.00

3.05

3.10

3.15

centroid (eV)

100 nm

6 kV

100 nm

6 kV

0.0 0.1 0.2 0.3 0.4 0.5 0.6

distance (µm)

2.76

2.78

2.80

2.82

2.84

centre (eV)

2.54

2.56

2.58

2.60

centre (eV)

0.0 0.2 0.4 0.6 0.8 1.0Distance (inches)

3

Introduction

• Semiconductor Spectroscopy and Devices group– Interested in light-emitting semiconductor materials– Particular focus on group III nitrides: GaN, InN, AlN and their alloys– Spectroscopic characterization techniques include:

• Photoluminescence (PL)• PL excitation (PLE)• Electroluminescence (EL)• CL (of course!)

– E-beam diffraction techniques(EBSD, ECCI)

– Theory & modeling

Past and present group members at recent ICNS-9, Glasgow

4

Our CL timeline

1999 2012

New variable-pressure SEM to arrive.

We use a geologist’s EPMA to measure InxGa1-xN composition.We want one.

2001

Cameca SX100 EPMA installed.CL spectrograph added.

B.C.

Previously focus on PL, PLE and CL spectroscopy

2005

Field emission SEM arrives.CL hyperspectral imaging immediately added

CL hyperspectral imaging software evolves

We are here

5

Group III nitrides

AlN

GaN

InN

• Emission wavelength dependent on bandgap

• Band gap energies of: 6.2 eV (AlN)3.4 eV (GaN)0.7 eV (InN)

• Alloys (e.g. InxGa1-xN) can be tailored toemit across the visible region and beyond

• Extremely bright CL at room temperature

Lattice constant (Å)

3.0 3.2 3.4 3.6

Ban

dgap

ene

rgy

(eV

)

0

1

2

3

4

5

6

7

GaN

InN

AlN

White/blue

LEDs

Blue laser

diodes

6

Hyperspectral imaging

• “Hyperspectral image”– a.k.a. “spectrum image”, “spectral map” etc.– Term borrowed from remote sensing– 20+ contiguous wavelength bands

• Acquisition modes:– Image at a time

(e.g. using tuneable filter)– Line at a time

(“push broom” method)– Spectrum at a time

� Christen et al. J. Vac. Sci. Technol. B 9, 2358 (1991)

e-λ

I

λ

I

λ

I

x

y

λ

“Data cube”

7

Why hyperspectral imaging?• More data! • No need to choose particular points or wavelength bands

beforehand• The only way to map wavelength shifts

Among many other factors causing wavelength shifts are:-

• Composition• Temperature• Elastic strain• Carrier concentrations• Magnetic and electric fields• Measurement geometry

– Self-absorption– Optical modes

All lead to continuous variability in the band-gap energy

e-λ

Iλ

Iλ

I

x

y

λ

“Data

cube”

8

Moving peaks• Changing alloy fractions:

(e.g. x varies in InxGa1-xN)

λ

Compressive strain

Blue shift

Tensile strain

Red shift

Em

issi

on

Pure GaNIn0.4Ga0.6N

Photon Energy (eV)1.0 1.5 2.0 2.5 3.0 3.5Lo

w t

em

pe

ratu

re P

L E

mis

sio

n (

a.u

.)

• These shifts cannot be mapped using conventional CL (monochromatic images and point spectra) ⇒⇒⇒⇒ Need for CL HSI

• Elastic strain:

9

However, for any optical system these parameters are linked through the invariant quantity, étendue or Lagrange Invariant:

Optical design and “étendue”

• Some basics:– Aim to get light from sample to detector– Do this using some optical system:

u'uh

h'object: scan area

image at spectrometer

slitcollection

optics

marginal ray

chief ray

want angle u to be as large as possible for maximum collection

want image size h' to be small enough for detector entrance

want object hto be as large as possible for maximum field of view

want angle u' to be small enough to match detector f-number

nh sin u = n'h' sin u'

10

Optical design

• Same principle of étendue holds irrespective of collector geometry(e.g. parabolic, ellipsoidal, etc.)

• No problem for panchromatic imaging– detector size and acceptance angle both large

• Not a major problem for monochromatic imaging or spectroscopy– can open spectrometer slit wider– loss of spectral resolution can be compensated by using grating of higher ruling density

• Big problem for hyperspectral imaging– widening slits results in loss of spectral resolution– higher density grating results in loss of bandwidth

u'uh

h'object: scan area

image at spectrometer

slitcollection

optics

marginal ray

chief ray

11

Optical design

• Calculate FOV vs. collection– Assume Lambertian emission profile

(intensity varies as cosθ)– Integrate over collection cone:

• Some typical numbers:– f/4 spectrometer (i.e. a high

acceptance angle)– 25 µm slit (matched to 1"

CCD with 1000 pixels)

• 90% collection limits you to 1 µm FOV• 10 µm FOV limits you to 9% collection

emission angle θ

∫ ∫= =

==u

udd

0

22

0

sinsincoscollection

θ

π

φ

θφθθ

0.1 1 10 1000.0

0.2

0.4

0.6

0.8

1.0

Col

lect

ion

effic

ienc

y

Field of view (µm)

× 250 × 25 × 2.5 × 0.25

0.000

0.447

0.632

0.775

0.894

1.000

Optical magnification

Collection N

.A.

12

CL systems at Strathclyde

• We get around the FOV vs. collection problem by developing two CL systems:1. High resolution system based on FEI Sirion field emission SEM

(where large field of view not required)2. Large field of view system based on Cameca SX100 electron

microprobe (where the stage is scanned rather than the beam)

13

CL system 1: High resolution

0.1 1 10 1000.0

0.2

0.4

0.6

0.8

1.0

Col

lect

ion

effic

ienc

y

Field of view (µm)

× 250 × 25 × 2.5 × 0.25

0.000

0.447

0.632

0.775

0.894

1.000

Optical magnification

Collection N

.A.

N.A. 0.28

• Use reflecting objective– Long working distance – Out of the way of the electron

beam and the other detectors (including in-lens SE detector)

– Zero chromatic aberration (especially important for UV)

– ×2.5 optical magnification allows, e.g.:

• 10 µm field of view with 0.2 nm spectral resolution and 85 nm bandpass

• 40 µm field of view with 4 nm spectral resolution and 570 nm bandpass

with 25 µm slit

14

• Collection at 90°to the beam

• Sample tilted to ~45°

• All-reflecting design

• Electron multiplying CCD allows on-chip electron amplification for improved signal:noise

• 1 MHz readout – spectral acquisition times down to 2 ms

• Control and analysis using home-grown software package “CHIMP”

CL system 1: High resolution

NA 0.28 reflectingobjective

quartz vacuum window

parabolic mirror

spectrograph

tilted sample

EMCCD

e-beam

15

Collection geometry dependence

InGaN/GaNQW cavity

CL collection cone

Direct collection Collection through mirror

Eucentricsample rotation

45°angled

stub

e-beam

2.9 3 3.1 3.2 3.3 3.4 3.5

energy (eV)

CL

inte

nsity

(a.

u.)

direct collection

collectionthrough mirror

A B A B

λ

emission

absorption

Plan view, collection from above

Same spectrum at A and B

Tilted sample, collection from side

Light from A absorbed more than light from B

Can lead to apparent red shift

light collection

lightcollection

16

CL system 2: Large field of view• Uses built-in optical

microscope of Cameca SX100 to collect emission

• Output directly coupled to f/number-matched CCD spectrograph

• This gives optical magnification of ~×3

• EPMA controls scan (moving beam or stage)

• WDX acquisition unaffected

• Separate CL control synchronises spectrum acquisition – again using “CHIMP”

xyz scanning stage

1/8 mspectrograph

cooled CCD

electroncolumn

to WDX spectrometers

mirror

lens

optical reflecting objective

electron objective

PC

17

CL system 2

f/3.7spectrograph

cooled CCD

lens and folding mirror

Hg calibration lamp

WDX spectrometer

18

“CHIMP” software• Controls hyperspectral

image acquisition

• Allows analysis, e.g.– Individual or mean

spectra– Maps of intensity, peak

position, FWHM, real colour

– Linescans– Line spectra– Correlation plots– Multiple peak fitting– Principal component

analysis– Importing images files

(e.g. *.tif, Cameca *.img)

Cathodoluminescence Hyperspectral Imaging & Manipulation Program

19

Peak fitting• Typical acquisition times of 10’s of ms - spectra tend to be noisy

• Many emission peaks from semiconductors can be approximated by simple functions (e.g. Gaussian, Lorentzian, Voigt, Pekarian)

• We use a Levenberg-Marquardt non-linear least squares (NLLS) optimization algorithm to fit functions to each spectrum in the hyperspectral image

• This results in much reduced noise in images of peak intensity, wavelength, widths etc.

Pixel (138,191)

1.5 2.0 2.5 3.0 3.5

energy (eV)

0

500

1000

1500

corr

ecte

d si

gnal

(co

unts

) • Example of a 3-peak fit to a CL spectrum from a GaN/InGaN LED structure

• The fitting is repeated independently for each of the 1000s of spectra in the dataset

20

Wafer mapping using CL HSI

2.54

2.56

2.58

2.60

centre (eV)

0

2000

4000

6000

8000 height (counts)

125

130

135

140

145 FWH

M (m

eV)

0.0 0.2 0.4 0.6 0.8 1.0Distance (inches)

Peak energy Peak width Peak height

Pixel (138,191)

1.5 2.0 2.5 3.0 3.5

energy (eV)

0

500

1000

1500

corr

ecte

d si

gnal

(co

unts

)

2" diameter wafer

yellow band (defects)

InGaN/GaN quantum well

GaN near-band-edge

• GaN/InGaN blue LED structure• 100’s of 1mm2 LEDs with metal contacts• Focus here on the QW peak• Fitting allows it to be easily deconvolved

from overlapping defect band• Long-range variation could be due to

change in InGaN composition• No variation within each 1 mm2 LED

21

Electric field-induced peak shifts

GaN

InGaN

CB

VB

CB

VB

ener

gy

GaN Quantum well structure

Ideal band diagram- electron and hole wavefunctions overlap

In certain crystal directions, heterojunctions lead to polarization fields being induced- electron and hole wavefunctions separated- emission intensity reduced- red-shift in emission wavelength- compounded by piezoelectric field

“Quantum-Confined Stark Effect”

22

Effect of electric field E on CLBlue-shifted, narrower, lower intensity - correlates with higher SE signal

2.54

2.56

2.58

2.60

centre (eV)

CB

VB

CB

VB

energy

voltage

Higher SE signal implies lower (more negative) potential at surface

This results from injection of excess carriers into p-n junction

Open circuit, so results in p-type becoming more negative (c.f. photovoltaic effect)

Higher electric field counteracts QCSE (blue shift narrowing) but reduces radiative recombination

CL peak position Secondary electron signal

substratetop surface

top surface

substrate

small E large E

23

CL and WDX• The EPMA-based system allows CL hyperspectral imaging and WDX

mapping to be carried out simultaneously

• E.g. the quaternary alloy AlxInyGa1-x-yN

• Grown using MBE: complex interplay between elemental concentrations

� P.R. Edwards, R.W. Martin, et al. (2009) Superlattices and Microstructures 45, 151-155

incr

easi

ng T

24

Correlations

2-dimensional histograms

4 5 6 7 8 9

% InN

3.16

3.17

3.18

3.19

3.20

3.21

cent

re (

eV)

0

5

10

15

20

25

30

pixel frequency

Ga vs. In Al vs. In CL energy vs. InN fraction

Pearson product-moment correlation coefficients:+(-) 1: perfect +ve (-ve) linear correlation0: no linear correlation

-0.40 -0.08 -0.75

25

CL and EBSD

-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0 5 10 15 20 25

wingseed wing wingseed

distance (µm)

In plane strain

referencepoint

[1210]

3.413 eV

3.408 eV

• Previous work collaborating with Angus Wilkinson (University of Oxford)

• GaN sample with periodic strain variation

• Electron backscatter diffraction (EBSD) used to map strain tensor variation

• Good agreement with strain calculated from CL wavelength image (measured ex-situ)

• Our FE-SEM CL system has the geometry to allow electron diffraction and CL measurements simultaneously

26

CL and ECCI• Electron Channelling

Contrast Imaging(forescatter imaging)

• Contrast results from small changes in strain

• This occurs at threading dislocations (screw, edge, mixed) and also atomic steps

� C.Trager-Cowan et al. Phys. Rev. B 75 085301 (2007)

SEM pole piece

ECCI detectordiode

Channellingin electrons

Electrons out

27

CL/ECCI and defects• Apparent 1:1 correlation

between CL dark spots and ECCI spots

• These measurements will allow direct correlation between structural and optical properties (e.g. which dislocation types act as centres for non-radiative carrier recombination)

• Requires compromise between the contradictory demands of the two techniques: high kV for ECCI, low kV for CL

1 µm

ECCI

CL

28

Principal component analysis

The classic description in 2-D:

x

y

x'

y'

x'

y'

c1c2

Data varies in x and y Mean adjusted data Find new orthogonal axes, with most variance along first axis: this is first principal component

29

Principal component analysis

[ ] [ ] [ ]WH

RHWX

≈

+= mrrnmn ,,,

…

…

≈

m spatial data points

nsp

ectr

al c

hann

els

r spectram spatial data points

r images

m spatial data points

“scores” “loadings”original data

Principal components ranked in order of their contribution to the total data variance

Hyperspectral image now described not as sum of n monochromatic wavelengths, but as the sum of r (where r<m) spectra [See work by P. Kotula (Sandia) on EDX data]

original data

spectraimages

residual

30

PCA example: Eu-doped GaN• Example: Rare earth-doped semiconductors• Emission due to transitions within 4f shell of RE ions

– Largely independent of host material– Sharp emission lines with fixed spectral “signature”

• GaN implanted with Eu• Promising route to producing red LEDs from GaN

31

Eu-doped GaN

0 5 10 15 20

distance (mm)

0

1

2

3

4

5

6

dist

ance

(m

m)

400 500 600 700 800

w avelength (nm)

0

500

1000

1500

corr

ecte

d si

gnal

(co

unts

)

400 500 600 700 800

w avelength (nm)

0

500

1000

1500

2000

corr

ecte

d si

gnal

(co

unts

)

400 500 600 700 800

w avelength (nm)

0

20

40

60

corr

ecte

d si

gnal

(co

unts

)

Calculated “real” colour image from hyperspectral image (log scale)

Sample spectra: overlapping peaks, including Eu-related, GaN band edge and yellow band, and thickness fringes

32

PCA & overlapping peaksPCA results when taking first 6 components;

0 5 10 15 20

distance (mm)

0123456

dist

ance

(m

m)

0 5 10 15 20

distance (mm)

0123456

dist

ance

(m

m)

0 5 10 15 20

distance (mm)

0123456

dist

ance

(m

m)

0 5 10 15 20

distance (mm)

0123456

dist

ance

(m

m)

0 5 10 15 20

distance (mm)

0123456

dist

ance

(m

m)

0 5 10 15 20

distance (mm)

0123456

dist

ance

(m

m)

400 500 600 700 800

w avelength (nm)

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

raw

sig

nal

(cou

nts)

400 500 600 700 800

w avelength (nm)

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

raw

sig

nal

(cou

nts)

400 500 600 700 800

w avelength (nm)

0.0

0.1

0.2

0.3

0.4

0.5

raw

sig

nal

(cou

nts)

400 500 600 700 800

w avelength (nm)

-0.05

0.00

0.05

0.10

raw

sig

nal

(cou

nts)

400 500 600 700 800

w avelength (nm)

0.00

0.05

0.10

raw

sig

nal

(cou

nts)

400 500 600 700 800

w avelength (nm)

0.0

0.1

0.2

0.3

0.4

raw

sig

nal

(cou

nts)

33

0

200

400

600

800

1000

1200

1400

1600

1800

2000

3 3.5 4 4.5 5 5.5

Energy (eV)

CL

in

ten

sit

y

w urtzite

zincblende

PCA example with moving peaks

Zincblende AlxGa1-xN, x ≈ 0.6

• Growth requires Ga-rich conditions• Leads to Ga droplets forming on the

surface, which need to be removed

• Suspected wurtzite inclusions where droplets removed

0 20 40 60 80

distance (µm)

0

10

20

30

40

50

60

dist

ance

(µm

)

6810121416182022

(counts)G

aLα

counts

340 2 4 6 8 10

distance (µm)

0

2

4

6

8

10

dist

ance

(µm

)

3.803.853.903.954.004.054.104.15

CL energy (eV

)PCA example with moving peaks

Emission energy map calculated from CL hyperspectral image

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

3 3.5 4 4.5 5

Photon energy (eV)

Nor

mal

ised

CL

inte

nsity

• First 4 principal components show closely-grouped peaks around band-edge

• Moving peak can be approximated by combination of these

• Can use this to calculate peak position• Shows inhomogeneity in zincblende material

as well as showing wutzite inclusions

35

Data analysis comparisonExample: GaN/InGaN mesa from work with Enyuan Xie

(University of Strathclyde, Institute of Photonics)

0 1 2 3 4

distance (µm)

0

1

2

3

4

5

dist

ance

(µm

)

1.5 2.0 2.5 3.0 3.5

energy (eV)

10

100

corr

ecte

d si

gnal

(co

unts

)

p-GaN

2nd order

n-GaN

red QW

blue QW

red quantum well near surface

GaN yellow band (defect related)

blue quantum well (from pits)

GaN band edge (NUV)

mean spectrum from entire hyperspectral image

real colour image

substrate

36

Extracting wavelength images

0 1 2 3 4

distance (µm)

0

1

2

3

4

5

dist

ance

(µm

)

0 1 2 3 4

distance (µm)

3.32

3.34

3.36

3.38

3.40

3.42

0 1 2 3 4

distance (µm)

0

1

2

3

4

5

dist

ance

(µm

)

0 1 2 3 4

distance (µm)

3.32

3.34

3.36

3.38

3.40

3.42

Pixel (57,5)

1.5 2.0 2.5 3.0 3.5

energy (eV)

200

400

600

800

corr

ecte

d si

gnal

(co

unts

)

This is not “smoothing” – none of these images has lost any spatial resolution

Peak intensity – simply find point in spectrum with highest intensity

Centroid – find “centre of mass” of the spectrum

NLLS fitting of peak function (in this case Gaussian + LO phonon replicas)

Centroid of principal components (in this case the first 5 PCs)

19.01% of variance2nd component

1.5 2.0 2.5 3.0 3.5

energy (eV)

0.0

0.1

0.2

0.3

0.4

raw

sig

nal

(cou

nts) 46.79% of variance1st component

1.5 2.0 2.5 3.0 3.5

energy (eV)

0.0

0.1

0.2

0.3

0.4

raw

sig

nal

(cou

nts) 5.74% of variance4th component

1.5 2.0 2.5 3.0 3.5

energy (eV)

-0.05

0.00

0.05

0.10

0.15

raw

sig

nal

(cou

nts)

Focusing on the GaN near-band-edge emission:

37

Summary• CL hyperspectral imaging of semiconductors allows mapping of

changes in peak energy and width, as well as the more usual intensity

• This allows variations in important material/device parameters to be probed, e.g. composition, strain and electric field

• We have developed CL hyperspectral imaging systems for measurements covering length scales from nm to cm

• The multidimensional nature of the datasets lends itself to analysis using– spectral peak fitting– multivariate statistical methods

38

Continuing work

• Simultaneous ECCI and CL imaging– Working to overcome the opposing requirements of the two techniques

• CL in variable-pressure SEM– Allowing CL measurement of less conductive materials (such as wider

bandgap semiconductors) without coating

• Integration of CL with electrical measurements– Bias-dependent CL to probe carrier dynamics within LED junctions

while maintaining high spatial resolution.– Electron Beam-Induced Current (EBIC) to complement the CL and

ECCI measurements on individual dislocations

• Keep pushing towards higher spatial resolution– See tomorrow’s talk…

39

Acknowledgments• Thanks to

– C. Liu, D. Allsopp, P. Shields and W. Wang (University of Bath)– T. Wang and co-workers (University of Sheffield)– R. Oliver and M. Kappers (University of Cambridge)– N. Grandjean (EPFL)– S. Fernandez-Garrido and E. Calleja (Universidad Politécnica de Madrid)– S. Novikov and T. Foxon (University of Nottingham)– E. Xie, E. Gu, I.M. Watson, and M.D. Dawson (University of Strathclyde,

Institute of Photonics)for providing samples.

• This research was supported by the UK Engineering and Physical Sciences Research Council.