understanding the boron-oxygen defect: properties ... · the boron-oxygen defect time b o light...

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School of Photovoltaic & Renewable Energy Engineering SPREE Seminar University of New South Wales Sydney, Australia 9 November 2017 Nitin Nampalli Supervisors: Malcolm Abbott, Stuart Wenham, Matthew Edwards Faculty of Engineering \ School of Photovoltaic and Renewable Energy Engineering Advanced Hydrogenation Group Understanding the boron-oxygen defect: properties, kinetics and deactivation mechanisms

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Page 1: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

School of Photovoltaic & Renewable Energy Engineering

SPREE Seminar

University of New South Wales

Sydney, Australia

9 November 2017

Nitin Nampalli

Supervisors: Malcolm Abbott, Stuart Wenham,

Matthew Edwards

Faculty of Engineering \ School of Photovoltaic and Renewable Energy Engineering

Advanced Hydrogenation Group

Understanding the boron-oxygen defect: properties,

kinetics and deactivation mechanisms

Page 2: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Motivation

• p-type silicon dominant for forseeable future

• PERC cells seeing an increasing market share

• Surface passivation quality is improving

• “Reliable kWh” is increasingly important

Strong imperative to:

(a) Improve bulk quality

(b) Minimise cell degradation

International Technology Roadmap for Photovoltaics, 8th Edition, 2017.

Page 3: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Motivation

• p-type silicon dominant for forseeable future

• PERC cells seeing an increasing market share

• Surface passivation quality is improving

• “Reliable kWh” is increasingly important

Strong imperative to:

(a) Improve bulk quality

(b) Minimise cell degradation

International Technology Roadmap for Photovoltaics, 8th Edition, 2017.

Page 4: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Motivation

• p-type silicon dominant for forseeable future

• PERC cells seeing an increasing market share

• Surface passivation quality is improving

• “Reliable kWh” is increasingly important

Strong imperative to:

(a) Improve bulk quality

(b) Minimise cell degradation

International Technology Roadmap for Photovoltaics, 8th Edition, 2017.

Page 5: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Motivation

• p-type silicon dominant for forseeable future

• PERC cells seeing an increasing market share

• Surface passivation quality is improving

• “Reliable kWh” is increasingly important

Strong imperative to:

(a) Improve bulk quality

(b) Minimise cell degradation

International Technology Roadmap for Photovoltaics, 8th Edition, 2017.

Page 6: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Motivation

• Boron-oxygen defects are the most important

source of LID in commercial Cz solar cells

• Cell efficiency loss:

– PERC: 1-12%rel

– Al-BSF: 1-6%rel

– For a cell manufacturer producing 1,000 MWp/year:

• 60-120 MWp/year in lost production

• USD $12-24 million/year in lost savings

Mitigation of BO

defects is of vital

importance

Page 7: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

The boron-oxygen defect

Time

B O Light Induced

Degradation

causes

but can be…

Temporarily

Deactivated

Permanently

Deactivated

“Dark Annealing”

(200 °C)

Illuminated Annealing

“Regeneration”

(~1 sun, >85 °C)

Deactivation is unstable!

Light Soaking

(1 sun, 25 °C)

Time

Op

en

Cir

cu

it V

olt

ag

e

Stable Deactivation

(Passivation)

Time

Light Soaking

(1 sun, 25 °C)

Page 8: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

State A

State B

State C

Regeneration

Destabilisation Degradation

Annihilation

Direct stabilisation

Direct destabilisation

The boron-oxygen defect

• Behaviour described

by 3-state model

• Focus of this work:

1. Recombination

properties

2. Reaction kinetics

3. Deactivation

mechanisms

1

2

3

Page 9: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Recombination properties of

the boron-oxygen defect

Page 10: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

𝜏𝑝0 =1

𝑁𝑡𝑟𝑎𝑝 ∙ 𝜎𝑝 ∙ 𝑣𝑡ℎ,ℎ

Recombination properties of BO

DA

LS BO 1

𝜏𝑒𝑓𝑓,𝐿𝑆=

1

𝜏𝑠𝑢𝑟𝑓+

1

𝜏𝑏𝑢𝑙𝑘,𝑛𝑜𝑛−𝐵𝑂+

1

𝜏𝑆𝑅𝐻,𝐵𝑂

Si wafer BO? 1

𝜏𝑒𝑓𝑓,𝐷𝐴=

1

𝜏𝑠𝑢𝑟𝑓+

1

𝜏𝑏𝑢𝑙𝑘,𝑛𝑜𝑛−𝐵𝑂

1

𝜏𝑆𝑅𝐻=

𝑛𝑝 − 𝑛𝑖2

∆𝑛 ∙ 𝝉𝒑𝟎 𝑛 + 𝒏𝟏 + 𝝉𝒏𝟎 𝑝 + 𝒑𝟏

𝑘 =𝜎𝑛𝜎𝑝

𝑝1 = 𝑛𝑖,𝑒𝑓𝑓 × 𝑒𝐸𝑖−𝐸𝑡𝑟𝑎𝑝

𝑘𝐵𝑇

𝜏𝑛0 =1

𝑁𝑡𝑟𝑎𝑝 ∙ 𝜎𝑛 ∙ 𝑣𝑡ℎ,𝑒

Page 11: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

kBO = 14

IDLS

TDLS

Ntrap Ntrap

Recombination properties of BO

S. Rein and S. Glunz, Applied Physics Letters 82(7), pp.1054-1056, 2003.

X. Wang et al., Energy Procedia 55, pp.169-178, 2014.

Etrap

k

kBO = 9.3

Is the value of Etrap,BO correct?

What is the real value of kBO?

Statistical uncertainty?

Is kBO temperature-dependent?

Page 12: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Recombination properties of BO

Etrap

Ntrap

k

At low injection (Δn = 0.1×NA):

𝑁𝑡𝑟𝑎𝑝 ∝1

𝜏𝑆𝑅𝐻,𝐵𝑂

∝1

𝜏𝐿𝑆−

1

𝜏𝐷𝐴= 𝑁𝐷𝐷

𝑁𝑡𝑟𝑎𝑝 =1

𝜏𝑛0 ∙ 𝜎𝑛 ∙ 𝑣𝑡ℎ,𝑒

(Normalised Defect Density)

NDDmax NDD(t)

Page 13: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

ºº

Recombination properties of BO

K. Bothe et al., Solid State Phenomena 95-96, p. 223-228 (2004)

D. Walter et al., Solar Energy Materials and Solar Cells 131, p. 51-57 (2014)

Etrap

Ntrap

k

Firing What is the impact of firing on NDD?

Could k also be affected by firing?

Page 14: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Recombination properties of BO

• SRH properties of the BO defect ( k , Etrap )

• Impact of firing on k

• Impact of firing on defect density

Page 15: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Recombination properties of BO

• SRH properties of the BO defect ( k , Etrap )

• Impact of firing on k

• Impact of firing on defect density

Page 16: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

SRH Recombination Properties

Methods for determining recombination properties: – IDLS: Injection-Dependent Lifetime Spectroscopy

• A common characterization method

• Good sensitivity to k (if Etrap is known)

• Low sensitivity to Etrap (for mid-gap defects)

– TDLS: Temperature-Dependent Lifetime Spectroscopy

• Good sensitivity to Etrap, k

• Analysis at single injection level (Δn)

– TIDLS: Temperature- and Injection-Dependent Lifetime Spectroscopy

• Best sensitivity to Etrap, k

• Analysis over full range of Δn

Page 17: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

GOF

QDA = 1.60

QLS = 2.93

Qglobal = 2.22

k1 = 12.98

J0e,DA = J0e,LS = 84.7 fA/cm2

1013 1014 1015 1016 1017

5

10

15

20

25

30

GOF

QDA = 1.60

QLS = 1.02

Qglobal = 1.32

k1 = 11.74

J0e,LS = 80.8 fA/cm2

J0e,DA = 84.7 fA/cm2

1013 1014 1015 1016 1017

Inve

rse L

ifeti

me (

ms

-1)

Excess Carrier Density, n (cm-3)

Method B

(Constrained)

Method D

(Free J0e)

GOF

QDA = 1.60

QLS = 2.93

Qglobal = 2.22

k1 = 12.98

J0e,DA = J0e,LS = 84.7 fA/cm2

1013 1014 1015 1016 1017

5

10

15

20

25

30

GOF

QDA = 1.60

QLS = 1.02

Qglobal = 1.32

k1 = 11.74

J0e,LS = 80.8 fA/cm2

J0e,DA = 84.7 fA/cm2

1013 1014 1015 1016 1017

Inve

rse L

ifeti

me (

ms

-1)

Excess Carrier Density, n (cm-3)

Method B

(Constrained)

Method D

(Free J0e)

GOF

QDA = 1.60

QLS = 2.93

Qglobal = 2.22

k1 = 12.98

J0e,DA = J0e,LS = 84.7 fA/cm2

1013 1014 1015 1016 1017

5

10

15

20

25

30

GOF

QDA = 1.60

QLS = 1.02

Qglobal = 1.32

k1 = 11.74

J0e,LS = 80.8 fA/cm2

J0e,DA = 84.7 fA/cm2

1013 1014 1015 1016 1017

Inve

rse L

ifeti

me (

ms

-1)

Excess Carrier Density, n (cm-3)

Method B

(Constrained)

Method D

(Free J0e)

GOF

QDA = 1.60

QLS = 2.93

Qglobal = 2.22

k1 = 12.98

J0e,DA = J0e,LS = 84.7 fA/cm2

1013 1014 1015 1016 1017

5

10

15

20

25

30

GOF

QDA = 1.60

QLS = 1.02

Qglobal = 1.32

k1 = 11.74

J0e,LS = 80.8 fA/cm2

J0e,DA = 84.7 fA/cm2

1013 1014 1015 1016 1017

Inve

rse L

ifeti

me (

ms

-1)

Excess Carrier Density, n (cm-3)

Method B

(Constrained)

Method D

(Free J0e)

GOF

QDA = 1.60

QLS = 2.93

Qglobal = 2.22

k1 = 12.98

J0e,DA = J0e,LS = 84.7 fA/cm2

1013 1014 1015 1016 1017

5

10

15

20

25

30

GOF

QDA = 1.60

QLS = 1.02

Qglobal = 1.32

k1 = 11.74

J0e,LS = 80.8 fA/cm2

J0e,DA = 84.7 fA/cm2

1013 1014 1015 1016 1017

Inve

rse L

ifeti

me (

ms

-1)

Excess Carrier Density, n (cm-3)

Method B

(Constrained)

Method D

(Free J0e)

GOF

QDA = 1.60

QLS = 2.93

Qglobal = 2.22

k1 = 12.98

J0e,DA = J0e,LS = 84.7 fA/cm2

1013 1014 1015 1016 1017

5

10

15

20

25

30

GOF

QDA = 1.60

QLS = 1.02

Qglobal = 1.32

k1 = 11.74

J0e,LS = 80.8 fA/cm2

J0e,DA = 84.7 fA/cm2

1013 1014 1015 1016 1017

Inve

rse L

ifeti

me (

ms

-1)

Excess Carrier Density, n (cm-3)

Method B

(Constrained)

Method D

(Free J0e)

SRH Recombination Properties

IDLS analysis

N. Nampalli et al., Frontiers in Energy 11(1), 2017.

𝟏

𝝉𝑫𝑨=

1

𝜏𝑠𝑢𝑟𝑓+

1

𝜏𝑏𝑢𝑙𝑘,𝑓𝑖𝑥𝑒𝑑+

1

𝜏𝑆𝑅𝐻,𝑛𝑜𝑛−𝐵𝑂

𝟏

𝝉𝑳𝑺=

1

𝜏𝑠𝑢𝑟𝑓+

1

𝜏𝑏𝑢𝑙𝑘,𝑓𝑖𝑥𝑒𝑑+

1

𝜏𝑆𝑅𝐻,𝑛𝑜𝑛−𝐵𝑂+

1

𝜏𝑆𝑅𝐻,𝐵𝑂

Page 18: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

SRH Recombination Properties

IDLS analysis

N. Nampalli et al., Frontiers in Energy 11(1), 2017.

𝟏

𝝉𝑫𝑨=

1

𝜏𝑠𝑢𝑟𝑓+

1

𝜏𝑏𝑢𝑙𝑘,𝑓𝑖𝑥𝑒𝑑+

1

𝜏𝑆𝑅𝐻,𝑛𝑜𝑛−𝐵𝑂

𝟏

𝝉𝑳𝑺=

1

𝜏𝑠𝑢𝑟𝑓+

1

𝜏𝑏𝑢𝑙𝑘,𝑓𝑖𝑥𝑒𝑑+

1

𝜏𝑆𝑅𝐻,𝑛𝑜𝑛−𝐵𝑂+

1

𝜏𝑆𝑅𝐻,𝐵𝑂

A B C D E F G H I J

Constrained Partially unconstrained Free

B C E F G H J

11.89 11.96 11.94 11.96 12.24 12.12 13.15 12.38 14.55 14.72

0.68 0.74 0.66 0.55 0.98 1.51 1.01 0.85 1.20 1.51

A D I

4

6

8

10

12

14

16

18

20

22

24

26

Be

st

Fit

Ca

ptu

re C

ros

s S

ec

tio

n R

ati

o, k

1

klit= 9.3

MAD

Median

kBO > 9.3

Not all fitting methods

are accurate kBO > 9.3

kBO = 11.9 ± 0.45

Page 19: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

SRH Recombination Properties

TIDLS analysis

1015 1016 1017

0

5

10

15

20

25

Elevated T (K)

298

323

344

364

374

395

420

444

464

Inve

rse lif

eti

me a

t ele

vate

d T

, D

A(T

)-1 (

s-1

)

Excess Carrier Density, n (cm-3)

Increasing T

1014 1015 1016 1017

0

5

10

15

20

25

30 Elevated T (K)

298

326

344

364

373

394

420

445

463

Inve

rse lif

eti

me a

t ele

vate

d T

, L

S(T

)-1 (

s-1

)

Excess Carrier Density, n (cm-3)

Increasing T

Page 20: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

SRH Recombination Properties

TIDLS analysis

– Determine Etrap , k

EC – Etrap = 0.41 ± 0.10

kBO = 11.5 ± 1.00

Page 21: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

SRH Recombination Properties

TIDLS analysis

– Determine Etrap , k

– T-dependence of τSRH,BO

EC – Etrap = 0.41 ± 0.10

kBO = 11.5 ± 1.00

𝜎𝑛 𝑇 = 𝜎𝑛 300𝐾 ∙𝑇

300

𝜶𝒏

Assumption: αn = αp = αBO

𝜏𝑛0 𝑇 = 𝑁𝑡𝑟𝑎𝑝 ∙ 𝝈𝒏 𝑻 ∙ 𝑣𝑡ℎ,𝑒 𝑇−1

αBO = –2.3

𝝈𝒏/𝒑 𝑻 ∝ 𝑻−𝟐.𝟑

Page 22: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Recombination properties of BO

• SRH properties of the BO defect ( k , Etrap )

• Impact of firing on k

• Impact of firing on defect density

Page 23: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Measure Normalised Defect Density (NDD)

Dark Anneal: 200 oC, 15 min

Light Soak: 35 oC 0.77 suns, 48 hr

Impact of firing – Experiment details

PECVD SiNx:H

NDD Meas. 1

Page 24: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Impact of firing – Experiment details

PECVD SiNx:H

NDD Meas. 1

Fired

Not Fired

NDD Meas. 2

Relative change

due to firing

Varying Tpeak

0 10 20 30 40 50 60 700

100

200

300

400

500

600

700

800 Tpeak

= 827 C

Tpeak

= 790 C

Tpeak

= 735 C

Tpeak

= 686 C

Tpeak

= 632 C

Tpeak

= 580 C

Tpeak

= 518 C

Tpeak

= 463 C

Tem

pera

ture

,

(C

)

Time, t (s)

350

Nfire = 1, 2, 3

Page 25: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

0 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

0 463 518 580 632 686 735 790 827

4

8

12

16

20

24

28

32

Bes

t F

it C

ap

ture

Cro

ss S

ecti

on

Rati

o, k

1

Tpeak

(C)

Nfire

Impact of firing on kBO

kBO

Before Firing

After Firing

New, non-BO

CID defect

Page 26: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Impact of firing on NDDBO

0 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

0 463 518 580 632 686 735 790 827

10

100

Norm

alis

ed D

efe

ct D

ensity, N

DD

aft

er (m

s-1)

Tpeak

(C)

Nfire

Before Firing After Firing

New, non-BO

CID defect

Page 27: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Summary – Properties of the BO defect

• SRH properties of BO: – Determined kBO = 11.9 (> 9.3)

– Confirmed that Etrap = EC – 0.41 eV

– Determined that σn/p(T) ∝ T–2.3

• Impact of firing on BO properties: – Confirmed that kBO is not affected by firing

– Demonstrated that firing reduces NDDBO

– Firing can induce other (non-BO) CID defects in Cz silicon

Page 28: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Transition kinetics of the BO

system

Page 29: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

0 50 100 150 200 250 30010-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

De

fec

t tr

an

sit

ion

ra

te c

on

sta

nt,

ij (

s-1

)

Temperature, T ( C)

AB

BA

BC

CB

0 50 100 150 200 250 30010-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

De

fec

t tr

an

sit

ion

ra

te c

on

sta

nt,

ij (

s-1

)

Temperature, T ( C)

AB

BA

BC

CB

0 50 100 150 200 250 30010-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

De

fec

t tr

an

sit

ion

ra

te c

on

sta

nt,

ij (

s-1

)

Temperature, T ( C)

AB

BA

BC

CB

Transition kinetics of the BO system

κBA

κAB

κBC

κCB

Dependence of transition rates

on T and illumination (Δn) are

of vital importance!

Page 30: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

• Degradation:

– 𝜅𝐴𝐵 appears to be independent

of illumination intensity (>0.1

suns)

– Other studies show 𝜅𝑑𝑒𝑔 ∝

𝑝02

Transition kinetics of the BO system

J. Schmidt and K. Bothe, Physical Review B 69, p.024107, 2004.

K. Bothe and J. Schmidt, Journal of Applied Physics 99, p. 013701, 2006.

Which is true?

𝜿𝑨𝑩 ∝ 𝒑𝟎𝟐

𝜿𝑨𝑩 ∝ 𝒑 ∙ 𝒑𝟎

𝜿𝑨𝑩 ∝ 𝒑 𝟐

Page 31: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

• Annealing:

– Known to occur in dark (no

carrier dependence

assumed)

– But…one study showed

𝜅𝐵𝐴 ∝1

𝑝0 for compensated Si

Transition kinetics of the BO system

B. Lim et al., Applied Physics Letters 98, p.162104, 2011.

Does 𝜿𝑩𝑨 have a

carrier dependence?

Page 32: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Issue with reaction rate studies

• Process T ≠ Measurement T !

𝑮 𝑻 =∆𝑛 𝑇

𝝉𝒆𝒇𝒇 𝑻, ∆𝒏

p(T) = p0(T) + Δp(T) p(300K) = p0(300K) + Δp(300K)

𝑮 𝟑𝟎𝟎𝑲 =∆𝑛 300𝐾

𝝉𝒆𝒇𝒇 𝟑𝟎𝟎𝑲, ∆𝒏

Need a method to determine ∆𝒏 𝑻

from 𝝉𝒆𝒇𝒇 𝟑𝟎𝟎𝑲 and 𝑮 𝟑𝟎𝟎𝑲

Page 33: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Reaction kinetics of the BO system

• Model to obtain τeff(T) from τeff(300 K)

• Temporary deactivation (annealing) kinetics

• Degradation kinetics

Page 34: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Temperature dependence of lifetime

280 300 320 340 360 380 400 420 440 460 480 500

0.98

1.00

1.02

1.04

1.06 Data

Fit

Ge

ne

rati

on

ra

te c

orr

ecti

on

fac

tor,

fc

orr(T

)

Measurement temperature, T (K)

𝐺 𝑇 =∆𝑛 𝑇

𝜏𝑒𝑓𝑓 𝑇, ∆𝑛

Page 35: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Temperature dependence of lifetime

𝟏

𝝉𝑫𝑨 𝑻, 𝜟𝒏=

1

𝜏𝑠𝑢𝑟𝑓 𝑇, 𝛥𝑛+

1

𝜏𝑏𝑢𝑙𝑘,𝑓𝑖𝑥𝑒𝑑 𝑇+

1

𝜏𝑆𝑅𝐻,𝑛𝑜𝑛−𝐵𝑂 𝑇

𝟏

𝝉𝑳𝑺 𝑻, 𝜟𝒏=

1

𝜏𝑠𝑢𝑟𝑓 𝑇, 𝛥𝑛+

1

𝜏𝑏𝑢𝑙𝑘,𝑓𝑖𝑥𝑒𝑑 𝑇+

1

𝜏𝑆𝑅𝐻,𝑛𝑜𝑛−𝐵𝑂 𝑇+

1

𝜏𝑆𝑅𝐻,𝐵𝑂 𝑇, 𝛥𝑛

𝝉𝑫𝑨 𝑻, 𝜟𝒏 𝝉𝑳𝑺 𝑻, 𝜟𝒏

𝐺 𝑇 =∆𝑛 𝑇

𝜏𝑒𝑓𝑓 𝑇, ∆𝑛

Page 36: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

𝑷𝒂𝒓𝒂𝒎 𝑻 = 𝑷𝒂𝒓𝒂𝒎 𝟑𝟎𝟎𝑲 ×𝑻

𝟑𝟎𝟎

𝜶𝒑𝒂𝒓𝒂𝒎

Temperature dependence of lifetime

𝜏𝑛0,𝐵𝑂 𝑇 = 𝝉𝒏𝟎,𝑩𝑶 𝟑𝟎𝟎 𝑲 ∙𝑻

𝟑𝟎𝟎

𝜶𝒏𝟎,𝑩𝑶

𝜏𝑛0,𝑛𝑜𝑛−𝐵𝑂 𝑇 = 𝝉𝒏𝟎,𝒏𝒐𝒏−𝑩𝑶 𝟑𝟎𝟎 𝑲 ∙𝑻

𝟑𝟎𝟎

𝜶𝒏𝟎,𝒏𝒐𝒏−𝑩𝑶

1

𝜏𝑠𝑢𝑟𝑓 𝑇, 𝛥𝑛= 2 ∙

𝑺𝒆𝒇𝒇(𝟑𝟎𝟎 𝑲

𝑊∙

𝑻

𝟑𝟎𝟎

𝜶𝑺𝒆𝒇𝒇

∙ 1 +𝛥𝑛

𝑝0

𝟏

𝝉𝑫𝑨 𝑻, 𝜟𝒏=

1

𝜏𝑠𝑢𝑟𝑓 𝑇, 𝛥𝑛+

1

𝜏𝑏𝑢𝑙𝑘,𝑓𝑖𝑥𝑒𝑑 𝑇+

1

𝜏𝑆𝑅𝐻,𝑛𝑜𝑛−𝐵𝑂 𝑇

𝟏

𝝉𝑳𝑺 𝑻, 𝜟𝒏=

1

𝜏𝑠𝑢𝑟𝑓 𝑇, 𝛥𝑛+

1

𝜏𝑏𝑢𝑙𝑘,𝑓𝑖𝑥𝑒𝑑 𝑇+

1

𝜏𝑆𝑅𝐻,𝑛𝑜𝑛−𝐵𝑂 𝑇+

1

𝜏𝑆𝑅𝐻,𝐵𝑂 𝑇, 𝛥𝑛

𝜏𝑏𝑢𝑙𝑘,𝑓𝑖𝑥𝑒𝑑 𝑇 = 𝝉𝒃𝒖𝒍𝒌,𝒇𝒊𝒙𝒆𝒅 𝟑𝟎𝟎 𝑲 ∙𝑻

𝟑𝟎𝟎

𝜶𝑏𝑢𝑙𝑘,𝑓𝑖𝑥𝑒𝑑

1

𝜏𝑠𝑢𝑟𝑓 𝑇, 𝛥𝑛=

2 ∙ 𝑝0 + 𝛥𝑛

𝑞 ∙ 𝑊∙ 𝑱𝟎𝒆 𝟑𝟎𝟎𝑲 ∙

𝑻

𝟑𝟎𝟎

𝜶𝑱𝟎𝒆

𝐺 𝑇 =∆𝑛 𝑇

𝜏𝑒𝑓𝑓 𝑇, ∆𝑛

Page 37: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Temperature dependence of lifetime

Parameter Relevant lifetime

component

Exponent of temperature

dependence Value for αparam

τbulk,fixed* τbulk,fixed(T) αb 2.880 ± 0.032

Seff τsurf(T) αSeff -1.395 ± 0.030

J0e τsurf(T) αJ0e 41.449 ± 0.044

τn0,BO τSRH, BO(T) αn0,BO 1.870 ± 0.003

τn0,non-BO* τSRH,non-BO(T) αn0,non-BO -1.420 ± 0.006

* may be specific to wafers used in this study

1 1.1 1.2 1.3 1.4 1.5 1.6

0.1

1

10

J0e

bulk,fixed

n0,BO

n0,non-BO

Seff

T / 300 K

Para

me

ter

valu

e r

ela

tive t

o 3

00

K

10-9

10-7

10-5

10-3

10-1

101

103

105

107

109

J0e r

ela

tive t

o 3

00

K

25 50 75 100 125 150 175 200

Temperature, T ( C)

Page 38: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Reaction kinetics of the BO system

• Model to obtain τeff(T) from τeff(300 K)

• Temporary deactivation (annealing) kinetics

• Degradation kinetics

Page 39: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Annealing kinetics

0 1 10 100 1000

8

9

10

11

12

13

14

15

16 T = 478 K (205 C)

T = 448 K (175 C)

T = 438 K (165 C)

T = 433 K (160 C)

T = 428 K (155 C)

Inve

rse lif

eti

me

, T

(t,T

=3

00

K)

(ms

-1)

Anneal time, t (s)

Defect dissociation

(B A) 𝜅BA ∝1

𝑝(𝑇)

DA LS BO

Page 40: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Annealing kinetics

κBA κBA (p/NV)-1

𝜅BA = 𝜈𝐵𝐴′ ∙ 𝑒

−𝐸𝑎,𝐵𝐴𝑘𝐵𝑇 𝜅BA = 𝜈0,𝐵𝐴 ∙

𝑁𝐶(𝑇

𝑝(𝑇)∙ 𝑒

−𝐸𝑎,𝐵𝐴𝑘𝐵𝑇

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7

-14

-12

-10

-8

-6

-4

-2

0

Ea,BA = 1.26 0.14 eV

BA' = 1012.6 1.6 s-1

This work

Rein et al. (2001)

Schmidt et al. (2004)

Schmidt et al. (2002)

Lim et al. (2011)

Fit line to data in this work

ln(

BA [

s-1

] )

1000/T (K-1)

220 200 180 160 140 120 100

Dark anneal temperature (C)

Page 41: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Reaction kinetics of the BO system

• Model to obtain τeff(T) from τeff(300 K)

• Temporary deactivation (annealing) kinetics

• Degradation kinetics

Page 42: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Degradation kinetics

J. Schmidt and K. Bothe, Physical Review B 69, p.024107, 2004.

𝜅AB ∝ 𝑝 𝑇 2

DA LS BO

Page 43: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Degradation kinetics

K. Bothe and J. Schmidt, Journal of Applied Physics 99, p. 013701, 2006.

κAB κAB (p/NC)2

(This work)

𝜅AB = 𝜈𝐴𝐵′ ∙ 𝑒

−𝐸𝑎,𝐴𝐵𝑘𝐵𝑇 𝜅AB = 𝜈0,𝐴𝐵 ∙

𝑝(𝑇)

𝑁𝐶(𝑇)

2

∙ 𝑒−𝐸𝑎,𝐴𝐵𝑘𝐵𝑇

Page 44: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Implications of degradation kinetics

• Fast initial degradation (“FRC”)

– May be partially related to p2 dependence

K. Bothe and J. Schmidt, Journal of Applied Physics 99, p. 013701, 2006.

κAB is not constant

(due to p2 dependence)

Fast initial degradation

occurs in same time

scale as change in κAB

Page 45: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Implications of degradation kinetics

• Regeneration rates

– Regen (B C) occurs only after degradation (A B)

– κBC will be limited by κAB

A. Herguth et al., Progress in Photovoltaics: Research and applications 16, pp.135-140, 2008

P. Hamer et al., Solar Energy Materials and Solar Cells 145, pp.440-446, 2016

A: ~100%

B: ?% (<100%)

C: ~100%

Starting State: B

(fast recovery)

Starting State: A

(slow recovery)

B: 100%

C: ~100% κBC must be determined

starting from State B (LS),

not State A (DA)

Page 46: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Summary – Reaction Kinetics

• Developed parameterization to obtain

τeff(T) from τeff(300 K)

• Carrier dependence confirmed for

annealing (A B), degradation (B A)

• Carrier dependence explains other

observed kinetics phenomena

1 1.1 1.2 1.3 1.4 1.5 1.6

0.1

1

10

J0e

bulk,fixed

n0,BO

n0,non-BO

Seff

T / 300 K

Pa

ram

ete

r v

alu

e r

ela

tiv

e t

o 3

00

K

10-9

10-7

10-5

10-3

10-1

101

103

105

107

109

J0e r

ela

tiv

e t

o 3

00

K

25 50 75 100 125 150 175 200

Temperature, T ( C)

A,

B:

~0

%

C:

~1

00

%

Page 47: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Mechanisms for permanent

deactivation of BO defects

Page 48: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Permanent deactivation

D. Walter et al., Solar Energy Materials and Solar Cells 131, p. 51-57 (2014)

K. Bothe et al., Solid State Phenomena 95-96, p. 223-228 (2004)

V. Voronkov and R. Falster, Physica Status Solidi C 13(10-12), p. 712-717 (2016)

State A

State B

State C

Regeneration

Destabilisation Degradation

Annihilation

Direct stabilisation

Direct destabilisation

Defect precursors

Thermal formation

Thermal deactivation

BO defect

Firing

1

2

Why does permanent

deactivation occur?

Page 49: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Deactivation mechanisms

• Why does regeneration occur?

• Why does thermal deactivation occur?

• Are they related?

Page 50: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Measure Normalised Defect Density (NDD)

Dark Anneal: 200 oC, 15 min

Light Soak: 35 oC 0.77 suns, 48 hr

Experimental Details

PECVD SiNx:H

Bare

Thermal SiO2

NDD Meas. 1

Page 51: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Regeneration

PECVD SiNx:H (hydrogen)

Bare (no hydrogen)

Thermal SiO2

(no hydrogen)

NDD Meas. 1

Fired

Not Fired

NDD Meas. 2 NDD Meas. 3

Regeneration

Illuminated Anneal: 172 oC, 0.66 suns, 2 hr

Relative change

due to regeneration

Relative change

due to firing

Page 52: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Regeneration

D. Walter and J. Schmidt, Solar Energy Materials and Solar Cells 158, p.91-97 (2016)

Fired Non-fired Fired Non-fired Fired Non-fired

No dielectric SiNx:H SiO

2

0.00

0.25

0.50

0.75

1.00

1.25

Hydrogen-related reduction

in FDD due to regeneration

FD

D a

fter

regen.

(re

l. to

ND

Daft

er)

Rel.

ch

an

ge in

ND

D d

ue t

o r

eg

en

.

Some improvement in hydrogen-lean wafers

Regeneration observed in

hydrogen-lean samples

(very long time scales)

Page 53: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Deactivation mechanisms

• Why does regeneration occur?

• Why does thermal deactivation occur?

• Are they related?

Page 54: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Thermal deactivation

PECVD SiNx:H (hydrogen)

Bare (no hydrogen)

Thermal SiO2

(no hydrogen)

NDD Meas. 1

Fired

Not Fired

NDD Meas. 2 NDD Meas. 3

Regeneration

Illuminated Anneal: 172 oC, 0.66 suns, 2 hr

Relative change

due to firing

Varying Tpeak

0 10 20 30 40 50 60 700

100

200

300

400

500

600

700

800 Tpeak

= 827 C

Tpeak

= 790 C

Tpeak

= 735 C

Tpeak

= 686 C

Tpeak

= 632 C

Tpeak

= 580 C

Tpeak

= 518 C

Tpeak

= 463 C

Tem

pera

ture

,

(C

)

Time, t (s)

350

Nfire = 1, 2, 3

Page 55: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Thermal deactivation

0 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

0 463 518 580 632 686 735 790 827

10

100

Norm

alis

ed D

efe

ct D

ensity, N

DD

aft

er (m

s-1)

Tpeak

(C)

Nfire

Before Firing After Firing

New, non-BO

CID defect Wafers with SiNx:H dielectric

Page 56: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

0 450 500 550 600 650 700 7500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0Simple Arrhenius

model

Rela

tive N

DD

after

firing

Peak firing temperature, Tpeak

(C)

Data Model

Nfire

= 1

Nfire

= 2

Nfire

= 3

Increasing Nfire

Thermal deactivation

V. Voronkov and R. Falster, Physica Status Solidi C 13(10-12), p. 712-717 (2016)

0.9 1.0 1.1 1.2 1.3 1.4 1.5-4.0

-3.0

-2.0

-1.0

0.0

1.0

Nfire

= 1

Nfire

= 2

Nfire

= 3

Linear fit (Nfire

= 1 only)

Linear fit (all Nfire

)

ln [

-ln

(

ND

D%

,BO)

]

1000/T (K-1)

800 750 700 650 600 550 500 450 400

Peak Firing Temperature, Tpeak

(C)

Reaction: BO X

All Nfire

Ea,f

= 0.79 0.08 eV

(ft

step) = 10

4.19 ± 0.5

Nfire

= 1

Ea,f

= 0.77 0.1 eV

(ft

step) = 10

4.15 ± 0.6

Page 57: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Thermal deactivation

V. Voronkov and R. Falster, Physica Status Solidi C 13(10-12), p. 712-717 (2016)

0 450 500 550 600 650 700 750

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rela

tive N

DD

after

firing

Peak firing temperature, Tpeak

(C)

Data

Model - Freeze-in

Model - Freeze-in (adj.)

Model - Arrhenius

Page 58: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Deactivation mechanisms

• Why does regeneration occur?

• Why does thermal deactivation occur?

• Are they related?

Page 59: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

0 450 500 550 600 650 700 750 8000

2

4

6

8

10N

orm

alis

ed D

efe

ct D

ensity (

ms

-1)

Peak firing temperature, Tpeak

(C)

SiNx:H, NDD

before

SiNx:H, NDD

after

SiO2, NDD

after

Thermal reduction in NDD

due to firing

Fired Non-fired Fired Non-fired

SiNx:H SiO

2

0.00

0.25

0.50

0.75

1.00

1.25F

DD

aft

er

firin

g (

rel. to

ND

Db

efo

re)

Thermal reduction in FDD

due to firing

Rel.

ch

an

ge in

ND

D d

ue t

o f

irin

g

Thermal deactivation

N

Page 60: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Regeneration

Fired Non-fired Fired Non-fired Fired Non-fired

No dielectric SiNx:H SiO

2

0.00

0.25

0.50

0.75

1.00

1.25

Hydrogen-related reduction

in FDD due to regeneration

FD

D a

fter

regen.

(re

l. to

ND

Daft

er)

Rel.

ch

an

ge in

ND

D d

ue t

o r

eg

en

.

Page 61: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Revision to 3 state model?

Page 62: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

4 state model

State D

High temperature

Thermal effects

Hydrogenation

+ other minor effects

Page 63: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Summary – Permanent deactivation

• Effective regeneration requires sufficient

quantities of hydrogen. Regeneration could

involve other mechanisms (slower).

• Thermal deactivation occurs independent of

regeneration. Likely not hydrogen-related.

• Thermal deactivation is likely to be defect

dissociation

• 4-state model proposed to account for thermal

deactivation

Fired Non-fired Fired Non-fired

SiNx:H SiO

2

0.00

0.25

0.50

0.75

1.00

1.25

FD

D a

fte

r firin

g (

rel. to

ND

Dbefo

re)

Thermal reduction in FDD

due to firing

Page 64: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Implications of this work

Page 65: Understanding the boron-oxygen defect: properties ... · The boron-oxygen defect Time B O Light Induced Degradation causes but can be… Temporarily Deactivated Permanently Deactivated

Implications

1. Improved understanding of the BO defect

– Recombination properties

– Mechanism of permanent deactivation

– 4-state model

Fired Non-fired Fired Non-fired

SiNx:H SiO

2

0.00

0.25

0.50

0.75

1.00

1.25

FD

D a

fte

r firin

g (

rel. to

ND

Db

efo

re)

Thermal reduction in FDD

due to firing

Impact:

- Easier identification of the BO defect

- Multiple, tailored solutions to mitigate BO defect

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Implications

2. Accurate reaction kinetics modelling for BO

– 4-state model

– Conversion from τeff(300K) to τeff(T)

– Carrier dependence of reactions

1 1.1 1.2 1.3 1.4 1.5 1.6

0.1

1

10

J0e

bulk,fixed

n0,BO

n0,non-BO

Seff

T / 300 K

Para

me

ter

valu

e r

ela

tive t

o 3

00 K

10-9

10-7

10-5

10-3

10-1

101

103

105

107

109

J0e r

ela

tive t

o 3

00

K

25 50 75 100 125 150 175 200

Temperature, T ( C)

Impact:

- Better estimate of regeneration time-scales for

industrial wafers / solar cells

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Acknowledgements

• Funding sources – Australian Renewable Energy Agency (ARENA)

– Australian Center for Advanced Photovoltaics (ACAP)

– UK Institution of Engineering and Technology (IET) / A.F. Harvey Engineering Prize.

– Commercial partners (ARENA 1-A060)

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Acknowledgements

• Supervisors: Malcolm Abbott, Stuart Wenham, Matt Edwards

• Hydrogenation group

• Laboratory: – MAiA processing team

– LDOT team

– Others

• Admin staff: – TETB

– SPREE

• Friends and family

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Thank you for your attention

[email protected]

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Motivation

• p-type silicon dominant for forseeable future

• PERC cells seeing an increasing market share

• Surface passivation quality is improving

• “Reliable kWh” is increasingly important

Strong imperative to:

(a) Improve bulk quality

(b) Minimise cell degradation

International Technology Roadmap for Photovoltaics, 8th Edition, 2017.