How to Simulate and Optimize Solar Cells. Lumerical Solutions, Inc.

Transcription

1 How to Simulate and Optimize Solar Cells Lumerical Solutions, Inc.

2 Outline Introduction About Lumerical Solar cell efficiency, simulation challenges and FDTD Simulation methodology Examples Organic solar cells with photonic crystal Plasmonic solar cells Moth-eye anti-reflection coating Demonstration Parameter sweep and optimization using concurrent computation Simulation tips Questions and Answers

3 Introduction Our technology MODE Solutions 20 mm FDTD Solutions 12 mm 6 mm INTERCONNECT DEVICE 2 mm

4 Introduction Solar cells and efficiency trends Lawrence Kazmerski, National Renewable Energy Laboratory (NREL)

5 Introduction Why simulate solar cells Complicated sub-wavelength patterning is used to enhance the efficiencies. Textured surface Moth-eye surface Nano particles Photonic crystal Simulations are essential to predict the performance of such devices because we cannot obtain accurate results using analytic methods Simulations give the opportunity to cheaply and quickly test ideas, optimize designs and solve problems Expensive and time-consuming to build prototypes Design optimization is challenging and results are not always intuitive

6 Introduction Combined optical and electrical simulation Optical Efficiency FDTD Solutions Electrical Efficiency DEVICE Quantum efficiency and power conversion efficiency

7 Introduction What do we want to simulate? Quantum efficiency Optical Efficiency (OE): The fraction of photons absorbed in the solar cells Electrical Efficiency (EE): The fraction of electrons that reach the electrode Quantum Efficiency (QE) = OE*EE We can then calculate the power conversion efficiency We can determine the maximum power point Note that not all the energy in all photons can be collected in a single cell Photons below the bandgap are not collected at all High energy photons are converted to electrons but much of the energy is lost A quantum efficiency of 100% does not mean a power conversion efficiency of 100%!

8 Introduction Optical simulation to solve Maxwell s equations Electric and magnetic fields E( r, ), H( r, ) Loss/absorption per unit volume at each wavelength Absorption rate per unit volume under solar illumination G( r) Optical efficiency OE 1 L( r, ) E( r, ) 2 L( r, ) ( ) 1 i Re( E ( ) H 2 N p AM 1.5 i* Number of absorped photon Number of incident photon d ( )) V AM 1.5 N 2 G( r) dv p Im[ ( r, )] N p ; Incident photon flux density E i (H i ) ; Incident electric (magnetic) field ( ) d S FDTD Solutions

9 Introduction Electrical simulation to solve Poisson and Continuity Equation Absorption rate per unit volume from the optical simulation is included in the Continuity Equation G(r) Solve for the potential, electron and hole density ( r), p( r), n( r) Calculate the electrical efficiency Number of electron reaching electrode EE Number of absorped photon Calculate the quantum efficiency and J-V curve QE OE EE Lumerical DEVICE coming soon

10 Introduction Simulation Challenges Complicated simulation methodology Complex device geometry with many small wavelength-scale features Broadband Material dispersion Source modeling Optical and electrical simulations Large simulations, long simulation times

11 Introduction FDTD Finite Difference Time Domain (FDTD) is a state-of-the-art method for solving Maxwell s equations in complex geometries Few inherent approximations = accurate A very general technique that can deal with many types of problems Arbitrarily complex geometries One simulation gives broadband results Can be used to study the effects of micro and nanoscale patterning and its impact on the absorption efficiency of the solar cells.

12 Simulation example of solar cell using FDTD Plasmonic solar cells E(t) E() 2 Fourier transform K. R. Catchpole and A. Polman, "Design principles for particle plasmon enhanced solar cells", APL 93, (2008). S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, "Photocurrent spectroscopy of optical absorption enhancement via scattering from surface plasmon polaritons in gold nanoparticles," J. Appl. Phys. 101, (2007).

13 Simulation example of solar cell using FDTD Moth-eye anti reflection Chih-Hung Sun et al., "Broadband moth-eye antireflection coatings on silicon", APL 92, (2008).

14 Methodology for the Optical Simulation

15 Simulation methodology Design parameterization Material properties Multi-coefficient model Simulation region Boundary condition Source modeling Unpolarized light Result analysis Optical absorption calculation

16 Design parameterization Parameterize the Solar cells design Create properties appropriate for your device Use the scripted parameterization

17 Design parameterization Parameterization can include position of sources and monitors Any group can set properties of the children

18 Design parameterization Essential for Reproducibility Easy parameter sweeps Optimization Lumerical s hierarchical group layout and script based parameterization makes almost anything possible It is worth the initial investment!

19 Material properties broadband simulations Absorption bandwidth of typical solar cell materials is large c-si 350nm<λ<1100nm GaAs 350nm<λ<870nm P3HT:PCBM 350nm<λ<700nm Material properties must be accurately modeled over a broad bandwidth Sun light spectrum. (AM1.5)

20 Material properties broadband simulations Finite Difference Time domain (FDTD) simulation gives broadband result Solar cell devices utilize many dispersive materials Well-known frequency domain relationship D( ) ( ) E( ) Users can define their own model, or import from experimental data (real and imaginary ɛ(ω)) FDTD is a time domain technique: relationship? D( t) ( t) E( t) E( t) ( t t 0 t) dt

21 Material properties broadband simulations Common solutions are Lorentz or Drude models Often insufficient for real materials Lumerical s Multi-Coefficient Model (MCM) can solve for materials with arbitrary dispersion such as Si, GaAs, P3HT:PCBM, ITO etc Si GaAs P3HT:PCBM ITO

22 Boundary conditions In many cases, periodic boundaries can be used e.g. 2D Hexagonal lattice PCOSC Sun light PML Periodic or Bloch Periodic or Bloch Periodic or Bloch PML Periodic or Bloch If we can further assume normal incidence, Anti- Symmetry Symmetry

23 Sources Sun light is modeled by a plane wave source Results for incoherent, unpolarized light can be obtained from sum of two orthogonal polarization simulation ) sin( ) cos( 2 1 ) ( 2 1 E E E E d E d E d unpolarize

24 Sources How do we incorporate the complicated spectrum of sun light into simulation result? 1. Calculate absorption rate as a function of wavelength for a flat spectrum. This is automatically done using CW normalization in FDTD Solutions. 2. Multiply the absorption with the solar spectrum as a post processing step.

25 Optical absorption calculation (1) Planar or sandwiched by lossless material We use 2 planar power monitors. Script function transmission 1 2 s real( P) ds P FDTD source Power monitor A()=transmission( top ) -transmission( bottom ) Absorption region top bottom P abs ()=A() (solar irradiance) [W/m 2 /nm] Lossless material top Absorption region Lossless material bottom

26 Optical absorption calculation (2) Loss material Absorption region Loss material P abs ( ) Non planar structure sandwiched by loss material. We use an Analysis group pabs Electric field distribution => field profile monitor Permittivity distribution => index monitor Calculate the normalized loss profile per unit volume p abs [1/m 3 ]. p abs ( r, ) 1 2 E( r, ) P( ) imag( ( r, )) FDTD source Integrate p abs over the absorption region and multiply by the solar irradiance 2 p ( r, ) dv solar irradiance [W/m /nm ] V abs 2

27 Solar cell optical simulation examples

28 Simulation examples Si Plasmonic solar cells Metal nanoparticles Nano particle (Au, Ag, Cu, ) on Si p Si n Si Al Z K. R. Catchpole and A. Polman, "Design principles for particle plasmon enhanced solar cells", APL 93, (2008) S. H. Lim, W. Mar, P. Matheu, D. Derkacs, and E. T. Yu, "Photocurrent spectroscopy of optical absorption enhancement via scattering from surface plasmon polaritons in gold nanoparticles," J. Appl. Phys. 101, (2007).

29 Plasmonic solar cells c-si 300nm<λ<1100nm EXCELLENT BROADBAND MATERIAL MODELS EASILY GENERATED Silicon Gold Silver Aluminum

30 Plasmonic solar cells E(t) E() 2

31 Plasmonic solar cells Enhancement of absorption A g( ) A particle bare ( ) ( )

32 Plasmonic solar cell Optimization of 2 parameters, period and diameter. FOM = OE plasmonic /OE bare OE plasmonic /OE bare Enhancement Period (nm) Enhancements of 15% are possible Diameter (nm)

33 Organic solar cell with photonic crystal 1D PCOSC Sun light 2D hexagonal lattice PCOSC Sun light PC Organic Solar Cell (PCOSC) John R. Tumbleston et al., "Electrophotonic enhancement of bulk heterojunction organic solar cells through photonic crystal photoactive layer." Appl. Phys. Lett. 94, , 2009

34 Organic solar cell with photonic crystal P3HT:PCBM 300nm<λ<700nm P3HT:PCBM EXCELLENT BROADBAND MATERIAL MODELS EASILY GENERATED PEDOT:PSS ITO nc_zno

35 Organic solar cell with photonic crystal Absorption of 1D PCOSC P 3 A( ) P in ( ) ( ) HT:PCBM Leaky (Quasi- waveguide) Modes 616nm 657nm Absorbed power in P3HT:PCBM Incident plane wave power 637nm Absorption vs. wavelength ITO (n=1.45) and PEDOT:PSS (n=1.8) => lossless P=400nm, w=300nm, h=300nm, t=70nm Γ X Band-diagram of the 1DPCOSC Planar Organic Solar Cell (PLOSC)

36 Organic solar cell with photonic crystal TM polarization A B C P=400nm, w=300nm, h=300nm, t=70nm PC(ITO/PEDOT:PSS with loss) A B C ITO PEDOT:PSS P3HT:PCBM nc-zno Absorption distribution

37 Parameter sweep demo Thickness t from 0.1 to 0.2um Measure number of photons absorbed in P3HT:PCBM over 400nm and 700nm

38 Parameter sweep demo Number of absorbed photons as a function of thickness t.

39 Concurrent computing Optimization and parameter sweep require many simulations Send them to many different workstations Each workstation can run in distributed computing mode, using all cores N computers means you can get your optimization or parameter sweep results N times faster!

40 Optimization demo 4 parameters (P, w, hf, t) optimization Figure of Merit (FOM) = OE PC /OE flat, OE PC = (OE PC,TE +OE PC,TM )/2

41 Optimization demo Nearly 15% absorption enhancement FOM=OE PC /OE FLAT

42 Simulation tips Use a coarse mesh (large values of dx) Use conformal meshing Use mesh grading if a fine mesh is required in a particular region Always make any fine mesh simulations the last step! Multi-wavelength calculations Check material fits! Reduce memory and simulation time Store only necessary data to keep file sizes smaller Remove movie monitors for faster simulations

43 Tip: Use a coarse mesh Memory scales as dx 3 Simulation time scales as dx 4 Example convergence tests from silicon absorption in CMOS image sensors

44 Tip: Conformal meshing Potential problems with finite sized mesh Devices can be extremely sensitive to certain dimensions Can we define dimensions to better than the mesh size? Yes Conformal meshing

45 Electrical simulation With some simple assumptions the J-V curve is analytic Assume no recombination ev E qv/ kbt g J( V ) J0( e 1) J ph Aexp( ) J ph e OE( )IAM1.5( )d charge on electron number of absoebed photon hc kt J ph 2 Eg e( n 1) kt A 2 4 c

46 Electrical simulation Beyond simple assumptions to accurate results We need to solve Poisson and Continuity Equation numerically Lumerical DEVICE, coming soon...

47 Challenges and solutions Challenge Wavelength scale microscopic patterning Complex 3D geometries Solutions and best practices Full vectorial 3D Maxwell solver can capture all physical effects Parameterize designs Simulation time Broadband simulation Optimization and parameter sweeps Opto-electronic modeling 3D simulations are often necessary for realistic results Take advantage of symmetry and periodicity to reduce the size of simulations Store only necessary field data Use coarse mesh size where possible Always for initial simulations Do convergence testing of mesh size last! Use distributed parallel computation to take advantage of modern hardware Time domain gives broadband results Highly dispersive materials require multi-pole material models Check the material fit before running the simulation! Using a global search algorithm that significantly reduces the number of simulations required Use concurrent computing to use all your available computer resources optimally Combine optical and electrical modeling Bring optical generation rate into electrical models Lumerical DEVICE coming soon!

48 Question and Answer Dr. James Pond CTO Chris Kopetski Director of Technical Services Dr. Guilin Sun Senior R&D Scientist Dr. Mitsunori Kawano Technical Sales Engineer Sales inquiries Sales representatives (other regions) Free, 30 day trial at

49 Appendix Poisson and Continuity Equation Poisson equation ( ) q[ p n N D N Continuity equation 1 J n ( G n U n ) q 1 J p G p U p q J n J p A ] qnm qd n n qpm qd p p Drift current n p Inputs from the optical simulation