Lundstrom ECE 305 S16
ECE-305: Spring 2016
Solar Cell Fundamentals
Professor Mark Lundstrom Electrical and Computer Engineering
Purdue University, West Lafayette, IN USA [email protected]
3/22/16
Pierret, Semiconductor Device Fundamentals (SDF) pp. 356-361
Solar cells
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modern Si solar cell
Chapin, Pearson, Fuller, 1954
http://www.bell-labs.com/org/physicalsciences/timeline/span10.html#
solar cells today
3 SunPower http://us.sunpower.com
recombination and dark current
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minority carriers injected across junction
Fn FPqVA
− VA +
ID
Lundstrom ECE 305 S16 Every time a minority electron recombines on the p-side, one electron flows in the external current.
generation and current
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minority carriers collected by junction
Fn FPqVA
IL < 0
hf > EG
Lundstrom ECE 305 S16
Every time a minority electron is generated and collected by the PN junction, one electron flows in the external current.
light and dark current
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VD
I mA( )ID = I0 e
qVA /kBT −1( )
≈ 0.7V
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IL < 0photocurrent
dark current
hf > EG
solar cell operation
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1) Light generates e-h pairs
EF
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solar cell operation
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2) PN junction collects e-h pairs
EF
3) Current flows through load IL < 0
RL
VL +−
forward bias across PN junction develops
ID > 0
Lundstrom ECE 305 S16
solar cell operation
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4) Forward bias reduces current
FpFn qVD
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5) IV characteristic is a superposition
ITOT = I0 eqVD kBT −1( )− ISC
light-generated current
diode (dark) current
IV characteristic
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PD = ITOTVD < 0
VD
ID
ITOT = I0 eqVD kBT −1( )− ISC
−ISC
Pout = −ISCVD = 0
VOC
Pout = ITOTVOC = 0
Pout = ImpVmp = −ISCVOCFF
η = PoutPin
= ISCVOCFFPin
ID = I0 eqVD kBT −1( )
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solar cell efficiency
η = PoutPin
= ISCVOCFFPin
1) Short circuit current 2) Open-circuit voltage 3) Fill factor
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1) Maximum short circuit current
Example: Silicon Eg = 1.1eV. Only photons with a wavelength < 1.13 µm will be absorbed.
solar spectrum (AM1.5G)
Pin = 100 mW cm2
λ < hcEG
JSC max = 44 mA cm2
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2) Open-circuit voltage
ITOT = I0 eqV /kBT −1( )− ISC
Lundstrom ECE 305 S16
ITOT = 0 = I0 eqVOC /kBT −1( )− ISC
I0 eqVOC /kBT −1( ) = ISC
VOC ≈ 0.7 V
VOC = kBTqln ISC
I0
⎛⎝⎜
⎞⎠⎟
Δn 0( ) = ni2 NA( ) eqVA kBT −1( )
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Increasing VOC
0
Δn x( )
Wp << Ln
WP
n+
p-Si
I0 = qADn
WP
ni2
NA
⎛⎝⎜
⎞⎠⎟
Δn x( )
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3) Efficiency
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η = PoutPin
= ISCVOCFFPin
η ≈44 ×10−3A/cm2( )× 0.7 V× 0.8
100 ×10−3 V/cm2
≈ 25%
VD
ID
−ISC
VOC
ID = I0 eqVD kBT −1( )
High efficiency Si solar cell
Martin Green Group UNSW – Zhao, et al., 1998 (24.5% at 1 sun) 16
370 − 400 µm
η = PoutPin
= ISCVOCFFPin
VOC = kBTqln ISC
I0
⎛⎝⎜
⎞⎠⎟
FF = 0.81
JSC = 41.5 mA/cm2 94%( )VOC = 0.703
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JSC – VOC Trade-off
1) Smaller bandgaps give higher short circuit current
2) Larger bandgaps give higher open-circuit voltage
3) For the given solar spectrum, an optimum bandgap exists. EG
ηJSC ↓VOC ↓
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“Shockley-Queisser Limit”
η ≈ 34%
VOC = kBTqln ISC
I0
⎛⎝⎜
⎞⎠⎟
I0 ∝ ni2
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solar cell summary
1) Light is absorbed and produces e-h pairs 2) PN junctions separate e-h pairs and collect the carriers. 3) Current flow in external circuit produces a FB voltage and
the FB diode current reduces the total current. 4) Power out is ISCVOC FF. 5) Unlike integrated circuit chips, where the value added
comes from the design/system, manufacturing costs are critical in PV.
Lundstrom ECE 305 S16
