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LUH
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
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