design of silicon solar cells - nanohub.org
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Design of Silicon Solar Cells
Mark Lundstrom
Electrical and Computer Engineering Purdue University
West Lafayette, Indiana USA lundstro at purdue dot edu
Lundstrom 2019
Purdue University, Spring 2019
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Objective
Lundstrom 2019
In this lecture, we will consider the optical and electrical design of a modern, high-efficiency, crystalline silicon solar cell.
The general principles discussed here are broadly applicable, but for thin-film, polycrystalline solar cells, there are some special considerations (which will be discussed later).
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The PERL cell
“Passivated Emiitter Rear Locally diffused”
Martin Green Group, University of New South Wales 3
Zhou, et al., Solar Energy Materials and Solar Cells, 41/42,87-99, 1996.
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Evolution of Si solar cells
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Martin A. Green, “The Path to 25% Silicon Solar Cell Efficiency: History of Silicon Cell Evolution,” Prog. In Photovoltaics: Research and Applications, 17, 183-189, 2009.
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Outline
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1) Introduction 2) Optical design 3) Principles of electrical design 4) Electrical design of the PERL cell 5) Series resistance 6) Discussion 7) Summary
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Maximizing light absorption / generation
solar cell
1) Maximize the number of phonons that get into the solar cell (AR coating, texturizing).
2) Maximize the “effective”
thickness of the absorber (light trapping).
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Anti-reflection coatings
7 Lundstrom 2019
¼ wavelength thick
λ̂ = 483 nm
Si
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Dual-level AR coatings (DLAR)
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Si
e.g. MgF2/ZnS
thin layer of SiO2 for electrical passivation
https://www.pveducation.org/pvcdrom/design-of-silicon-cells/double-layer-anti-reflection-coatings
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Dual-level AR coatings (DLAR)
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David D. Smith, et al., “Towards the practical limits of solar cells,” IEEE J. Photovoltaics, 4, 1465-1469, 2014.
approximate peak of solar spectrum
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Light absorption vs. semiconductor thickness
Si (indirect) CIGS (direct)
The direct bandgap of CIGS allows it to absorb light much faster than Silicon. A layer of silicon must be thousands of microns thick to absorb ~100% of the light, while CIGS need only be about 2 microns thick.
> 1000 microns of Si needed
α λ( ) GIGS >>α λ( ) Si
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What determines alpha?
p = !k
Econduction
band
valence band
EG
Direct gap: strong absorption (high alpha)
p
E conduction band
valence band
EGneed
phonon
Indirect gap: weaker absorption lower alpha)
E =p2
2m
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Current collection
The absorbing layer must be electrically thin, Wp << Ln, and optically thick, Wp >> 1/α
Generated carriers are only useful if they are collected before they recombine.
Electron diffusion length:
Wp << LnGenerated e-
N+ P
Ln = Dnτ n
Wp
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Light trapping
Near-perfect mirror
little reflection at top
texturized surface
13 Lundstrom 2019
½ wavelength reflection coating
index of refraction,
n
Probability of escaping from top surface = 1/4n2
(~2%)
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Random vs. patterned sufaces
1) Absorption enhanced by 4n2 (Yablonovitch limit) E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am.
A, 72, 899-907 (1982). 2) Similar enhancements possible with patterned surfaces.
P. Campbell, M.A. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62, 243-249 (1987).
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PERL cell optical design
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reflection coating back metal contact
front metal contact patterned top surface
(111) planes are exposed by anisotropic etching
M. A. Green, Prog. In Photovoltaics: Research and Applications, 17, 183-189, 2009.
anti-reflection coating
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Outline
1) Introduction 2) Optical design 3) Principles of electrical design 4) Electrical design of the PERL cell 5) Series resistance 6) Discussion 7) Summary
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The semiconductor equations
∇•D = ρ
∇•Jn −q( ) = G − R( )
∇•J p q( ) = G − R( )
3 coupled, nonlinear, second order PDE’s for the 3 unknowns:
ψ (!r ) n(!r ) p(!r )
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steady-state
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A continuity equation
Rate of increase of water level in lake = (in flow - outflow) + rain - evaporation
Wabash River
∂p∂t
−∇•!J p q( ) + G − R=
generation recombination
in-flow
out-flow
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Solar cells and recombination-generation
JD
N P
x 0 L
JD VD( ) = q RTOT VD( )−GTOT( )
RTOT = R x( )
0
L
∫ dx + RF + RB
GTOT = Gop x( )
0
L
∫ dx
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RF = J px 0( )
RB = Jnx L( )
J px 0( )
Jnx L( )
By integrating the continuity equations, we can relate the diode current to R and G. (see Appendix 1)
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Solar cell design
• The goal is to maximize optical generation and minimize minority carrier recombination.
• Recombination lowers the short-circuit current (i.e. the
collection efficiency) and reduces the open-circuit voltage. • To optimize solar cell performance, we need a clear
understanding where minority carriers are recombining.
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Short-circuit current Photo-generated carriers should diffuse to the junction and be collected.
EF
Some may recombine in the base.
And some may diffuse to the contact and recombine.
“base”
“emitter”
(absorbing layer)
“collection efficiency”
CE ≡ JSCqGTOT
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Wp << Ln
qVbi
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Open-circuit voltage
Fn
Some may recombine in the base.
“base”
“emitter”
Lundstrom 2019 22
Wp << Ln
Fp
q Vbi −VOC( )
And some may diffuse to the contact and recombine.
injected minority electron profile, n(x)
The same thing occurs on the P-side.
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Minority carrier profiles
JD
Wp
What are the minority carrier profiles in the quasi-neutral N and P regions?
N P
Δp x( ) = p x( )− p0 Δn x( ) = n x( )− p0
R x( ) = Δp
τ p R x( ) = Δn x( )
τ n
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RBC = SnΔn Wp( )
Wn
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MCDE
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To answer this question, we must solve the minority carrier diffusion equation (MCDE), a simplification of the general continuity equation (see Appendix 2).
d 2Δndx2 = 0 Δn x( ) = n x( )− p0On the P-side:
(assumes little recombination in the
P-region)
Δn x( ) = Ax + BSolution:
Wp << Ln
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FB N+P diode in the dark
Δn ′0( )
Δn x( )
′x Wp ′0
Δn Wp( ) = Δn ′0( )
1+ SnWp Dn
0 < Sn <107 cm/s
Δn ′0( ) = ni
2
N A
eqVD kBT −1( ) Δn Wp( )
Minority carrier electrons recombine in the P-base or at the back contact. (Same for holes in the N-emitter and front contact.)
Sn → 0
Sn →107
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FB N+P diode in the dark
Jn =
qWp
2τ n
Δn ′0( ) + Δn Wp( )⎡⎣
⎤⎦ +
qDn
Wp
Δn ′0( )− Δn Wp( )⎡⎣
⎤⎦
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recombination in the P-layer
recombination at the back
contact
J0 = J0n p-Si( ) + J0n b-c( )⎡⎣ ⎤⎦ + J0 p n-Si( ) + J0 p f-c( )⎡⎣ ⎤⎦
JD = J0 eqVD kBT −1( )
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Dark current components
→ 0 as Sp → 0
front contact → 0 as Sn → 0
back contact
→ 0 as τ p →∞
N-bulk → 0 as τ n →∞
P-bulk
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J0 = J0 p n-Si( ) + J0 p f-c( )⎡⎣ ⎤⎦ + J0n p-Si( ) + J0n b-c( )⎡⎣ ⎤⎦
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Model NP solar cell
lightly doped for long minority carrier lifetime
more heavily doped to suppress hole injection
Δp 0( ) = ni2
N D
eqVD kBT −1( )
bare surface has high
Sp
N+ P MS contact Sn≈ 107 cm/s
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Minimizing the dark current
lightly doped for long minority carrier lifetime
“emitter” “base”
heavily doped P-type
“back surface field” BSF “minority carrier
mirror” Lundstrom 2019
≈200 A SiO2 has low Sp
passivated front surface
N+ P
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Back surface field (BSF)
EC
EI
EF
EV
Sn ≈υth
! 1×107 cm s
Sn ≈υthe−ΔE kBT
<1×107 cm s
Sn ≈υthe−ΔE kBT
! 0.5 ×107 cm s
ΔE = kBT lnNA
++
NA
⎛⎝⎜
⎞⎠⎟
EC
EI
EF
EV
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Outline
1) Introduction 2) Optical design 3) Principles of electrical design 4) Electrical design of the PERL cell 5) Series resistance 6) Discussion 7) Summary
Lundstrom 2019
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PERL cell electrical design
Electrically passivated back surface
M. A. Green, Prog. In Photovoltaics: Research and Applications, 17, 183-189, 2009.
Reduced M-Si contact area
BSF
Electrically passivated front surface
Reduced contact area and FSF
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Passivated Emiitter Rear Locally diffused
Martin Green Group, University of New South Wales
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Zhou, et al., Solar Energy Materials and Solar Cells, 41/42,87-99, 1996.
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Typical PERL device parameters
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≈200 A SiO2
N+ P
400− 450 µm
N A ≈1.5×1016 cm-3
x j ≈1.33µm
800 µm
N D ≈ 4×1018 cm-3
ni 25 C( ) = 0.86×1010 cm-3
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Best PERL cell parameters
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JSC = 42.7 mA/cm2
VOC = 706 mV
FF = 82.8 %
η = 25.0 %
Jmax = 44.8 mA/cm2
JSC Jmax = 95.3 %
(3.5% shadowing, + reflection/absorption, ~100% CE)
qVOC = EG − 0.4 eV
Martin A. Green, “The Path to 25% Silicon Solar Cell Efficiency: History of Silicon Cell Evolution,” Prog. In Photovoltaics: Research and Applications, 17, 183-189, 2009.
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PERL: Dark current components
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Martin A. Green, “The Passivated Emitter and Rear Cell (PERC): From Conception to mass production,” Solar Energy Materials and Solar Cells, 143, 190-197, 2015.
Zhou, et al., Solar Energy Materials and Solar Cells, 41/42,87-99, 1996.
J0 = J0n p-Si( ) + J0n b-c( )⎡⎣ ⎤⎦+ J0 p n-Si( ) + J0 p f-c( )⎡⎣ ⎤⎦
JD = J0 eqVD kBT −1( )
J0 = 50 fA cm2
J0 p n-Si( ) + J0 p f-c( ) = 15 fA cm2
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Outline
1) Introduction 2) Optical design 3) Principles of electrical design 4) Electrical design of the PERL cell 5) Series resistance 6) Discussion 7) Summary
Lundstrom 2019
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2D effects
ID I x( )
VD V x( ) <VD
Wn
dR = ρS
dxWn
ρS =
ρx j
=1
N Dqµnx j
distributed series resistance
N ρS ≈150Ω ! (PERL)
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Series resistance
0 < ID− VA +
ID = I0 eqVD kBT −1( )
−VD + RS
ID = I0 eq ′VD−IDRS( ) kBT −1( )
′VD =VD + IDRS
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Effect on dark and illuminated IV
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FF0.840.790.74
Fill Factor is reduced
IDRS
dark illuminated
Larger VD to reach the same current
RS ≈ 0.5Ω-cm2 PERL
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Outline
1) Introduction 2) Optical design 3) Principles of electrical design 4) Electrical design of the PERL cell 5) Series resistance 6) Discussion 7) Summary
Lundstrom 2019
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Limits
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The solar spectrum and bandgap set the upper limit for the short-circuit current.
What sets the limit for the open-circuit voltage?
VOC < EG q
Why?
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Voc and QFLs
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Fn
Fp
EFM1
EFM 2Fn − Fp( ) = qVOC
EFM1 − EFM 2 = qVOC = Fn − Fp
See Appendix 3
q Vbi −VOC( )
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What determines Fn – Fp?
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np = ni2e Fn−Fp( ) kBT
ΔnNA = ni2e Fn−Fp( ) kBT
Fn − Fp( ) = kBTq ln Δnni2 NA( ) =
kBTqln Δnnp0
Fn − Fp( ) = kBTq ln Δnnp0
⎛
⎝⎜⎞
⎠⎟
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What determines Δn?
Lundstrom 2019
R VOC( ) = GTOT ≈ JSC q
R VOC( ) = Δn VOC( )Wp
tn
R VOC( ) = GTOT →Δn VOC( )
Δn VOC( ) = JSC q( )Wp
tn
Higher lifetime gives higher Δn, which give more QFL splitting and a higher VOC
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What determines the lifetime?
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• Defects at the surfaces
• Contacts
• Defects in the p-bulk
• Defects in the n-bulk
In practice Fundamental
Band-to-band radiative recombination (Shockley-Queisser)
But for Si, Auger recombination
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VOC and bandgap
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qVOC = Fn − Fp( )
Fn − Fp( ) = kBTq ln Δnnp0
⎛
⎝⎜⎞
⎠⎟
Δn VOC( ) = JSC q( )Wp
tn
np0 = ni2 NA
ni2 = NCNVe
−EG kBT
VOC = EG − 0.3− 0.4( )eV
VOC = EG −kBTqln
WpNCNV NA
JSC q( )tn⎛
⎝⎜⎞
⎠⎟
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Estimating the efficiency of a solar cell
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1) Maximum JSC from the bandgap
VOC = EG
q− 0.3− 0.4( )2)
4) Efficiency η = JSCVOCFFPin
3) FF assuming low series resistance: FF ≈VOC kBT q( )
4.7 +VOC kBT q( )
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Outline
1) Introduction 2) Optical design 3) Principles of electrical design 4) Electrical design of the PERL cell 5) Series resistance 6) Discussion 7) Summary
Lundstrom 2019
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Summary
1) Optical design should ensure that all phonons with energies above the bandgap are absorbed. For indirect gap semiconductors, light-trapping makes physically thin layers optically thick.
2) Recombination must be minimized to maximize the
collection efficiency (JSC) and open-circuit voltage (VOC). 3) Series resistance lowers the fill factor (FF). 4) The short-circuit current can be close to the maximum
possible, but the open-circuit voltage is still significantly less than the bandgap.
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Questions
Lundstrom 2019
1) Introduction 2) Optical design 3) Principles of electrical design 4) Electrical design of the PERL cell 5) Series resistance 6) Discussion 7) Summary