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Understanding the fill factor by means of characterisation and simulation

Pietro P. Altermatt

Leinbiz University of Hannover, Germany

SPREE Seminar @ UNSW, 19th March 2015

1

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Which parameters influence the

fill factor?

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…the lumped series resistance Rs

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… the Voc

M.A. Green, Solar Cells, 1992, (ISBN 0 85823 580 3), p. 96 M.A. Green, Solar Cells 7, 337 (1982)

n = 1.0 Rs = 0

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… der ideality factor n

M.A. Green, Solar Cells, 1992, (ISBN 0 85823 580 3), p. 96 M.A. Green, Solar Cells 7, 337 (1982)

Rs = 0

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Analytical approximation using Voc, n and Rs

Jsc = 39 mA/cm2

Detailed overview of analytical equations for FF: E. Sanchez and G.L. Araujo, Solar Cells 20, 1 (1987)

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Do we here have a „FF problem“ ?

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No

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FF in relation to Voc

It is advantageous to consider FF

in relation to Voc

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FF depends on n

The idality factor may influence FF as strongly as Rs.

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Contents

(Loss)-analysis using simulations

Characterization using I-V measurements

1 2

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Contents

1 Characterization using I-V measurements

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Measurement of I-V curves

Measurement

Dark 1-sun 1.1-sun 0.9 sun (Jsc-Voc)

1-sun

Jsc-Voc

dark

Voc

Vmpp

Bias [V]

C

urr

ent-

den

sity

[m

A/c

m2]

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I-V curves – logarithmic

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I-V curves – logarithmic

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I-V curves – logarithmic

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I-V curves – logarithmic

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I-V curves – logarithmic

Jsc-Voc

Voc

Vmpp

1-sun

dark

Bias [V]

C

urr

ent-

de

nsi

ty

[mA

/cm

2]

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Extraction of Rs

Measurement Extraction of Rs

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Rs extraction from I-V curves

Overview: P.P. Altermatt et al, Prog. PV 4, 399 (1996)

1-sun

Jsc-Voc

dark

Voc

Vmpp

Jsc-Voc

DLL

Bias [V]

Cu

rren

t d

en

sity

[m

A/c

m2]

Seri

es r

esis

tan

ce [

cm2]

Bias [V]

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Tripple light-level (TLL) method

K. F. Fong, K. R. McIntosh, A. W. Blakers, Prog. PV 21, 490 (2013)

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Tripple light-level (TLL) method

K. F. Fong, K. R. McIntosh, A. W. Blakers, Prog. PV 21, 490 (2013)

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Large J0 → I-V curve is higher

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Large J0 → I-V curve is higher

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Rs extraction from I-V curves

K. F. Fong, K. R. McIntosh, A. W. Blakers, Prog. PV 21, 490 (2013)

1-sun

Jsc-Voc

dark

Voc

Vmpp

Jsc-Voc

DLL

If possible, use the tripple light-level method to measure Rs

Bias [V]

Cu

rren

t-d

en

sity

[m

A/c

m2]

Seri

es r

esis

tan

ce [

cm2]

Bias [V]

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Simulation of the metallised parts

Y. Yang et al, Prog. PV 20, 490 (2012)

Device

simulation

Circuit

simulation

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Simulation of the metallized parts

Device

simulation

Internal Rs

Jsc-Voc

DLL.

Bias [V]

Seri

es r

esis

tan

ce [

cm2]

Circuit

simulation

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Parametrization of Rs

Measurement Extraction of Rs

Parametrization of Rs(V)

If simulation: internal Rs

Proper distinction between Rs- and

recombination losses

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Rs(V) as polynome 2nd degree

Jsc-Voc

where V0 is offen Voc

Internal Rs

DLL.

Bias [V]

Seri

es r

esis

tan

ce [

cm2]

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Rs-corrected I-V curves

Measurement Extraction of Rs

Parametrization of Rs(V)

Rs(V)-free I-V curves

If simulation: internal Rs

Proper distinction between Rs- and

recombination losses

Rs(V) polynome

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Rs-corrected I-V curves

10-1

100

101

Cu

rre

nt d

en

sity [m

A/c

m2]

0.650.600.550.500.450.40

External bias [V]

Exp

Rs(V)

Rs(Vmpp)

FF Exp = 78.52 FF Rs(V) = 83.18

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Rs-corrected I-V curves show recombination losses

10-1

100

101

Cu

rre

nt d

en

sity [m

A/c

m2]

0.650.600.550.500.450.40

External bias [V]

Exp

Rs(V)

Rs(Vmpp)

FF Exp = 78.52 FF Rs(V) = 83.18 FF Rs(Vmpp) = 83.09

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Comparison of pseudo-FF with 1FF

n = 1.0 Rs = 0

M.A. Green, Solar Cells, 1992, (ISBN 0 85823 580 3), p. 96 M.A. Green, Solar Cells 7, 337 (1982)

pFF is often smaller than 1FF

FF Exp = 78.52 FF Rs(V) = 83.18 FF Rs(Vmpp) = 83.09 FF n=1 = 83.28

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Loss analysis

If simulation: internal Rs

Proper distinction between Rs- and

recombination losses

Rs(V) polynome

Recombination losses

pFF

Loss analysis Predictions

Measurement Extraction of Rs

Parametrization of Rs(V)

Rs(V)-free I-V curves

1FF

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Content

(Loss)-Analysis using simulations

2

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Domain & discretization

Domain 2D

Entire cell

Finger

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Reproduction of the ideality factor

Ultimate test

S. Steingrube et al. Energy Procedia 8, 263 (2011)

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Which is the most likely current-path?

V

dark

applied forward bias

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Exponentially increasing recombination rates

39

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Dark I-V curve = recombination rate

40

30

20

10

0

Str

om

dic

hte

[m

A/c

m2]

7006005004003002001000-100

Spannung [mV]

many few

Number of defects

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Illuminated I-V curve is shifted to 4th quadrant

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Think of G – R

G

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J(V) = G – R(V)

R(V)

G

J(V) = G – R(V)

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Losses in the various cell regions

R(V)

Rec

om

bin

atio

n c

urr

ent

[m

A/c

m2]

Voltage [V]

Total

Emitter Base

Al-BSF

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Predictions

Loss analysis Predictions

Measurement Extraction of Rs

Parametrization of Rs(V)

Rs(V)-free I-V curves

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After improvement of the emitter in a PERC cell R

eco

mb

inat

ion

cu

rren

t [

mA

/cm

2]

Bias [V]

Total

Emitter Base

Al-BSF

Voc = 614 mV Voc = 633 mV

FF = 75.4 FF = 76.3

Bias [V]

Standard cell Improved emitter

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Losses in the p-type Cz base

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Ladungsträgerkonzentration n [cm-3

]

1012 1013 1014 1015 1016 1017

Lebensdauer e

ff [µ

s]

10-5

10-4

B-dotiertes Cz-Si

Ndop=5.11015

cm-3

nach Beleuctung (1Sonne 60 Stunden)

nach Tempern(200°C 10 min)

Injection dependent lifetime in the p-type base

p/n=10

n

pn

0 1 0 1

SRH

0 0

( ) ( )( )

p nn n n p p nn

n p n

Injection density n [cm-3]

B-O complex

Ndop=5.1x1015 cm-3

Eff

ecti

ve li

feti

me

J. Schmidt, A. Cuevas, J. Appl. Phys. 86 (1999) 3175

S. Rein, S.W. Glunz, Appl. Phys. Lett. 82 (2003) 1054

K. Bothe R. Sinton, J. Schmidt, Prog. PV 13 (2005) 287

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Deactivated B-doped Cz wafers

49

D. Waler et al, Appl. Phys. Lett. 104, 042111 (2014)

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Improved emitter → smaller FF because of base! R

eco

mb

inat

ion

cu

rren

t [

mA

/cm

2]

Bias [V]

Total

Emitter Base

Al-BSF

Voc = 614 mV Voc = 633 mV

FF = 75.4 FF = 76.3

Bias [V]

Standard cell Improved emitter

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FF, pFF und 1FF

Two cells with low FF 1) Mainly due to Rs pFF is close to 1FF 2) Mainly due to n pFF is far from1FF

Determine FF and pFF, if possible using Rs(V), and 1FF

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More recent progress of PERC cells (1)

52

Inital Improved emitter

79.69 80.38

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More recent progress of PERC cells (2)

53

Improved base and rear Improved emitter

80.80 80.38

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More recent progress of PERC cells (3)

54

Improved base Improved base and rear

81.46 80.80

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Emitter losses increase…

55

Inital Improved emitter… …base …base and rear

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…because Vmpp increases

56

Inital Improved emitter… …base …base and rear

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Main points

• Extraction of Rs(V) from three I-V curves (TLL method)

• Clear distinction between Rs(V) and recombination losses

•Rs(V)-corrected I-V curve

→ pFF < 1FF ?

• Further analysis and prediction with simulations

FF is not only determined by Rs, but also by the ideality factor, i.e.by recombination, especially in good cells (where the base or the rear surface dominates)

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Thank you!

altermatt@solar.uni-hannover.de