MSEG 667
Nanophotonics: Materials and Devices
10: Photovoltaics
Prof. Juejun (JJ) Hu
hujuejun@udel.edu
References
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“$1 per W Photovoltaic Systems,” DOE ARPA-E white paper to explore a
grand challenge for electricity from solar (2011).
M. Green, “Solar Cells: Operating Principles, Technology, and System
Applications,” Prentice Hall (1981).
M. Green et al., “Solar cell efficiency tables (version 39),” Prog. Photovolt:
Res. Appl. 20, 12-20 (2012).
W. Shockley and H. Queisser, “Detailed Balance Limit of Efficiency of p‐n
Junction Solar Cells,” J. Appl. Phys. 32, 510-519 (1961).
E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72, 899-907
(1982).
T. Tiedje et al., “Limiting Efficiency of Silicon Solar Cells,” IEEE Trans.
Electron Devices 31, 711-716 (1984).
Z. Yu et al., "Fundamental limit of light trapping in grating structures," Opt.
Express 18, A366-A380 (2010).
H. Atwater and A. Polman, “Plasmonics for improved photovoltaic
devices,” Nat. Mater. 9, 205-213 (2010).
Photovoltaics

The average power incident upon the continental United
States is ~ 500 times the national consumption


Broadband light
source
Cost, cost & cost
Basic solar cell structure
I
0
VOC
I SC

 eV
I  I s   exp 
 k BT

 
  1  I SC
 
ISC : short circuit current
Is : diode saturation current
V
Other types of solar cells designs

All-back-contact c-Si cell


Eliminates front contact
shading
Single-side contacts
simplify cell stringing

CuInSe2
Thin film polycrystalline cells


Substrate
!
Superstrate configuration
Substrate configuration

CuInxGa1-xSe
(CIGS)
CdTe
CuZnSnSe/S
(CZTS)
Efficiencies of different solar cells
“$1 per W
Photovoltaic
Systems,”
DOE ARPA-E
white paper
Key performance metrics

I
Short circuit current: number
of absorbed photons
I SC  eA  
g
0
 Ee   
d 

Ee    : solar spectral irradiance
0
V
I SC
 : quantum efficiency
A : solar cell area

Saturation current: semiconductor material quality
 1
2
I s  eAni  
 NA

Dn
n
1

ND
Dp 

 p 
 n , p : electron/hole lifetime
Dn , p : diffusion coefficients
ni : intrinsic carrier density
Key performance metrics (cont’d)

VOC 

I
Open circuit voltage: split of
quasi-Fermi levels
EFn  EFp
e

I

kBT
 ln  SC  1
e
 Is

Energy conversion efficiency
and Fill Factor (FF)

 eV
P  VI  VI 0  exp 
 k BT

0
I SC
V
Pm  Vm I m
 
  1  VI SC
 
Differentiate with respect to voltage to obtain the maximum power:
dP
 0  Vm
dV
VOC 
kBT  eVm 
ln 1 

e
k
T
B


FF 
Pm
V I
 m m
VOC I SC VOC I SC
Shockley-Queisser limit in single-junction cells

Energy loss mechanisms
1) Sub-bandgap photon loss
1) and 2)
only
2) Carrier thermal relaxation
3) Voltage VOC loss (eVOC < Eg)
4) FF < 1
2)
conduction band
EFn

3)  Eg
1)   Eg
E Fp
2)
valence band
Mitigate VOC loss: non-radiative
recombination suppression
W. Shockley and H. Queisser, J.
Appl. Phys. 32, 510-519 (1961).
Other efficiency limiting factors and mitigation


Carrier recombination

Radiative recombination: photon recycling

Non-radiative recombination: material quality improvement
Poor band edge absorption



Light trapping
Shunt resistance and series resistance

Contact resistance reduction

Processing optimization
Surface reflection

Surface texturing

Anti-reflection coatings
Impact of shunt and series resistance
Simulation results quoted from Pveducation.org
Beyond the S-Q limit: spectrum splitting &
tandem cells
Dichroic mirrors
Cell 1
Cell 2
Cell 3
Cells with band gap matched
to the reflected bands
Eg1 > Eg2 > Eg3
Current matching:
X. Wang et al., Prog. Photovolt:
Res. Appl. 20, 149-165 (2012).
J. McCambridge et al., Prog.
Photovolt: Res. Appl. 19, 352360 (2011).

Since each sub-cell is connected in
series, suitable band gaps must be
chosen such that the design
spectrum will balance the current
generation in each of the sub-cells
Tandem cell design example
N. Yastrebova, technical white paper: ”High-efficiency multijunction solar cells: current status and future potential,” (2007).
Tandem cells mark the efficiency records
Beyond the S-Q limit: downconversion &
upconversion


One high energy photon → multiple electron-hole pairs

Multi-excitation generation: quantum dots

Fluorescent downconversion: quantum cutting in rare earth ions
Two low energy photons → one electron-hole pair

Upconversion: e.g. rare earth ions

Two photon absorption
T. Trupke et al., J. Appl. Phys. 92,
1668 (2002).
B. Richards, Sol. Energy Mater.
Sol. Cells 90, 1189-1207 (2006).
A. Shalav et al., Sol. Energy Mater.
Sol. Cells 91, 829 (2007).
Beyond the S-Q limit: thermophotovoltaics (TPV)
  Eg
  Eg
Thermal emitter
Spectral filter
DBR filter
J. Appl. Phys. 97,
033529 (2005).
Solar cell
Cell materials
Ge, InSb:
smaller band
gap to capture
photons from
thermal emitter
(T < 2000 K)
Concentrator photovoltaics (CPV)
 Reduced capital expense for solar cells
 Increased VOC with high photon flux
 Large carrier concentration increases
the quasi-Fermi level separation
 Fill factor boost
 Capital investment for additional optics
 Requires active tracking
 Aggravated heating issue
“III–V multijunction solar cells for
concentrating photovoltaics,” Energy
Environ. Sci. 2, 174-192 (2009).
"Planar micro-optic solar concentrator,"
Opt. Express 18, 1122-1133 (2010).
Micro-concentrators
Luminescent solar concentrators (LSC)
Leakage
LSC with fluorescent emitters
Small, efficient solar cells



LSC: transparent slab embedded with luminescent
emitters (organic dyes or quantum dots)
Luminescent light is waveguided in the LSC slab
and eventually collected by solar cells mounted
along the slab edge
Efficiency limiting factors: dye/QD re-absorption,
luminescence leakage out of the escape cone
Appl. Opt. 18, 3090 (1979).
Opt. Express 16, 21773 (2008).
Surface reflection mitigation

Reflectance on planar Si surface:
R

n1  n2
n1  n2
2
70.5°
3.5  1
~ 30%
3.5  1
2

Surface texturing by anisotropic wet etching: multiple
reflections increases absorption
Random texture on c-Si
Inverted pyramid texture
Light trapping: the Lambertian (4n2) limit


The upper limit for absorption enhancement factor in a
thin film solar cell (with respect to single pass absorption)
is given by 4n2
Isotropic
Assumptions




Ergodicity
Isotropic radiation
Weak absorption limit
scattering
d
Inadequacies


The ergodicity condition
is violated in periodic
grating structures
Solar radiation has
a small divergence
angle of 0.534°
Maximum absorption 4n2 × ad
E. Yablonovitch, J. Opt. Soc.
Am. 72, 899-907 (1982).
Z. Yu et al., Appl. Phys.
Lett. 98, 011106 (2011) .
Z. Yu et al., Opt. Express 18,
A366-A380 (2010).
Understanding light trapping using wave optics
k0
Absorption occurs during
mode propagation
Cell
kslab

Diffraction couples light
into waveguided modes
in the solar cell slab

kout
x
Waveguided modes leak back
to free space when the phase
matching condition is met
Consider a 1-D grating light trapping structure
2
k slab  k0  G  k slab , x  k0, x  N1 

kout  k slab  G  kout , x  kslab , x  N 2 
2

 k0, x   N1  N 2  
2

Understanding light trapping using wave optics

Consider normal incidence: k0, x  0
2
kout , x  k0, x  N 
 N  N1  N2  Z 

 k0  kout , x  k0

To reduce phase-matched leakage channels back to free
space, the number of N’s satisfying the above condition
should be minimized
2



2
N

 k0



 k0
2
 
 0
k0
Only one leakage channel N = 0
To achieve maximal light trapping enhancement at 0, the
grating period should be smaller than 0