Modeling Wide-Eg InGaP PV Cells for Conversion Efficiencies Up to 16.5%
Yubo Sun1, Kyle Montgomery2, Xufeng Wang1, Stephanie Tomasulo4, Minjoo Larry Lee3 and Peter Bermel1
1Purdue University 2University of California, Davis 3Yale University 4U.S. Naval Research Lab
Why consider wide-Eg InGaP (2.19 eV)?
Theoretical Efficiency Limit of wide-Eg cells
Modeling Flow Diagram
• Shockley-Queisser solar cell
efficiency limit varies with Eg
Wide bandgap In0.24Ga0.76P
• Theoretical PV cell efficiency over
16.5% at 2.19 eV
•
•
τ: minority carrier lifetime
µ: electron/hole mobility
: surface recombination velocity
• Only recombination losses
considered here are radiative (this
excludes SRH, Auger, and
surface/interface recombination)
Fig. State-of-the-art record efficiency triple junction cell
structure and absorbed spectrum http://spie.org/x41195.xml
Wide-Eg InGaP could convert highenergy solar photons more efficiently
It could serve as the top cell for
proposed ultra-high efficiency spectrumsplitting modules
Spectrum-splitting holographic
concentrator for ultra-high
efficiencies over 50% [1]
from n-p to n-i-p
Detailed balance calculation of single junction
solar cell efficiency as a function of Eg, accounting
for various loss mechanisms [2]
Benchmark
measured
EQE, light
I-V
Fitting EQE
Fitting I-V
RS, RSH, n
• Layers were deposited using MBE
growth technology
10-16
layers
In0.24Ga0.76P (2.19eV)
Extrapolation of InGaP absorption Curve
• In0.25Ga0.75P absorption data is
extracted from the extrapolation
of InP and In0.5Ga0.5P absorption
file
AlInP (2.4eV)
Cross-sectional view of modeled
InyGa1-yP solar cell
~360 nm
Δλ1
• The ratio of the wavelength
difference at the band edge is equal
to ΔEg between In0.5Ga0.5P and InP,
In0.25Ga0.75P respectively
Δλ2
• Urbach tail absorption beyond
band edge wavelength is neglected
GaP substrate enables high
transmittance of unabsorbed solar
photons
Bandgap energy (and corresponding wavelength)
versus lattice constant for III-V alloys at 300K [4]
4
Fitting EQE for Recombination Parameters
Rs : series resistance
Rsh : shunting resistance
ideality factor
3
• Indium fraction y modulated to
bridge lattice mismatch between
p-n junction and GaP substrate
Fig. Cross-sectional view of metamorphic InyGa1-yP solar
cell presented in the experiment for measurement[3]
Energy Band Diagram,
EQE, light I-V etc.
2
Modeled Structure & III-V Grower Diagram
• Graded buffer has 10-16 steps of
~360 nm each, with y increasing
by ~2% at each step
ADEPT 2.1
Numerical
Simulation
Optimum ŋ
1
InGaP Cross-section Cell Structure
extrapolated InyGa1-yP
absorption curve
In0.25Ga0.75P
In0.5Ga0.5P
InP
566nm
656nm
925nm
5
Light I-V Fitting and Parameter Extraction
6
Optimization of InGaP Cell Emitter Design
• Interface recombination between
window layer and emitter is
controlled by surface recombination
velocity (sf = 0 cm/s for minority
carriers to ignore the loss)
• Bulk recombination is quantified by
minority carrier lifetime (
EQE can be accurately modeled by
considering both bulk and interface
recombination losses
The optimum ŋ = 5.16%, when
t = 0.6 µm and ND = 3×1014/cm3
• “Ideal” EQE accounts for parasitic
absorption from window layer, while
eliminating interface and bulk
recombination
Measured and simulated I-V of 2.19eV InGaP PV
cell with extracted ideality factors, Rs, and Rsh [5]
7
Results and Optimization for n-i-p InGaP
30 nm
2 µm
Voc (V)
Jsc (mA/cm2)
FF
ŋ (%)
Measurement [3]
1.42
3.11
0.71
3.13
Simulation
1.43
3.16
0.706
3.19
Including lateral transport in
explicit 2D model would be
important for verification
8
Conclusions and Future Work
Conclusions
• Mobility did not include doping density dependence, due to the shortage of
mobility data at various doping levels for wide-Eg InGaP. Mobility should
follow the general form:
• Wide-Eg In0.24Ga0.76P were modeled. Both IV and EQE curves showed
excellent agreement with experiment, yielding surface and bulk
recombination parameters
• A modification to the experimental design (an n-i-p structure) was
proposed, which could double the cell efficiency (from 3.13 to 6.3%)
• Contact resistance increases due to lightly doped emitters were not modeled.
2D simulation of lateral transport is required [6]
Future Work
• Piecewise mathematic model to reproduce and improve absorption data
of In0.24Ga0.76P (e.g., to capture the Urbach absorption tail)
• Address other limits of current approach with refined models
• Model other direct, wide-Eg InyGa1-yP (y=0.18-0.30) PV cells and
compare directly to experiment
• Realistic ion implantation doping profiles for heavily doped emitters covering
intrinsic layers upon shallow p-type substrates [7]
Cross-sectional view of modeled InyGa1-yP
solar cell with optimized n-i-p structure
Fig. Cell Efficiency as a function of intrinsic layer
thickness and emitter doping. The experimental design
point is in blue, and the optimized result is in red.
10
References: 9
Limitations of modeling and optimization
The optimum ŋ = 6.3%, when
t i= 2 µm and NA = 9×1017/cm3
[1] Eisler, C. N., E. D. Kosten, E. C. Warmann, and H. Atwater, "Spectrum spliCng photovoltaics: Polyhedral specular reflector design for ultra-­‐high efficiency modules." In 2013 IEEE 39th Photovoltaic Specialists Conference (PVSC), pp. 1848-­‐1851 (2013). [2] Hirst, L.C. and N. J. Ekins-­‐Daukes,, “Fundamental losses in solar cells.” Progress in Photovoltaics 19, 286–293 (2011). [3] Tomasulo, S., K. N. Yaung, J. Faucher, M. Vaisman, and M. L. Lee, "Metamorphic 2.1-­‐2.2 eV InGaP solar cells on GaP substrates." Applied Physics LeCers 104, 173903 (2014); S. Tomasulo, J. Faucher, J. R. Lang, K. N. Yaung, and M. L. Lee, “2.19 eV InGaP solar cells on GaP substrates,” in 2013 IEEE 39th Photovoltaic Specialists Conference (PVSC), pp. 3324–3328 (2013). [4] Schubert, E. Fred, Thomas Gessmann, and Jong Kyu Kim, Light emiEng diodes. John Wiley & Sons, Inc., 2005. [5] Bermel, P., M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, … and I. Celanovic, “Design and global opjmizajon of high-­‐efficiency thermophotovoltaic systems.” OpGcs Express 18, A314-­‐A334 (2010). [6] Van der Heide, A. S. H., A. Schönecker, G. P. Wyers, W. C. Sinke, and ECN Solar Energy, "Mapping of contact resistance and locajng shunts on solar cells using resistance analysis by mapping of potenjal (RAMP) techniques." In Proceedings of the 16th European Photovoltaic Solar Energy Conference, pp. 1438-­‐1442 (2000). [7] Tabatabaie-­‐Alavi, K., A. N. M. M. Choudhury, N. J. Slater, and C. G. Fonstad, "Ion implantajon of Be in In0. 53Ga0. 47As." Applied Physics LeCers 40, 517-­‐519 (1982). Cell Efficiency as a function of emitter thickness and
emitter doping. The experimental design point is in blue,
and the optimized result is in red.
11
12