Thin film solar cell simulations with FDTD

Transcription

1 Thin film solar cell simulations with FDTD Matthew Mishrikey, Prof. Ch. Hafner (IFH) Dr. P. Losio (Oerlikon Solar) 5 th Workshop on Numerical Methods for Optical Nano Structures July 7 th, 2009

2 Problem Description Thin film solar cell design Trial and error manufacture vs. computer simulation 2

3 Problem Description Goals - Estimate potential of new ZnO morphologies by simulation - Optimize Si layer thicknesses (current matching condition) - Whole day optimization (angular incidence) - Determine if simulation is an alternative to cost-intensive manual optimization 3

4 Methods Boundary discretization methods + Excellent for 2D geometries - Accuracy convergence breakdown for noisy, singular surfaces - Large, dense matrices in 3D FEM + Gridding + Higher order convergence (hp-fem) - Matrices get difficult with Nonlinear materials +/- Modular, but difficult to implement FDTD + Broadband results with high frequency resolution + Simple methods are more extensible - Material modeling - Gridding problems (staircasing), grid refinement + Free (meep) 4

5 Material properties Use a 5 order Lorentzian model to fit available data (data provided by O.S.) 5

6 Material properties 6

7 Accuracy test Compare FDTD with analytical result for 1D layered structure, using fitted material models, normal incidence energy 5% 23% 68% 3% FDTD: resolution of 600 cells per micrometer 7

8 Absorption Rate Polarization field P P evolves with E according to D.E. absorption rate Meep lets you keep track of absorption (or gain) energies (only in a box now) Lossy rotten egg scatterer: Easy to compute loss in egg, less easy to integrate loss in yolk or egg white nested scatterer illumination Computes abs. rate within this box 8

9 Simplified 2D Geometry Triangular roughness with 2 geometric parameters Brute force analysis of optimal absorption rate α in { } sx in { } We can use a mirror symmetry reduce the domain by a factor of 2 9

10 Simplified 2D Geometry Absorption rate plotted for each geometry best worst Strong dependence of absorption rate on roughness angle α Weaker dependence on lattice size Sample timing info: Lattice width sx = 250 nm sx = 650 nm sx = 850 nm decay = 1e min 50 min 74 min decay = 1e min 166 min 115 min 10

11 Simplified 2D Geometry Reflectivity spectra for best and worst geometries Absorption strongest at shorter lambda, as can be surmised from material data 11

12 Simplified 2D Geometry Angle α evolution of reflectivity spectra for a fixed lattice constant Peaks are trackable, and generally shrinking As seen by crossover in previous plots, it s possible for a larger angle α to have a worse overall absorption rate 12

13 Semi-periodic Roughness Geometry We can obtain more realistic reflection spectra with a more random surface Also, we can check if absorption increases with more structure variation (surface shift and scaling) γ = 105 Progressive shift and/or Scaled back-reflector 2.2 μm 13

14 Semi-periodic Roughness Geometry Quad core: ~ 12.5 hours per polarization, field decay 1e-10 γ = 100 grating lobes improved absorption 14

15 Semi-periodic Roughness Geometry In the case of offset, mcsi/zno interface is shifted right by 300 nm, and back reflector by 450 nm yscale factor of back reflector is not entirely intuitive! best performance with matched back reflector 15

16 Preliminary Conclusions We can characterize cell performance as a function of surface morphology. Know behaviors are confirmable, e.g. more ZnO roughness yields more absorption. Lattice constant for triangular gratings is not as critical as roughness angle α. More lattice constant simulations will resolve absorption resonance patterns. Offset roughness geometries have little effect on reflectance spectra, and a similarly contoured back reflected appears optimal (more sample points needed!). 16

17 Future work 1. Charge transport simulations extract and match currents of p-i-n layers Compare with simulations including material properties for doped layers 2. Obtain better material data for shorter wavelengths, compare peak absorption with peak quantum efficiency of published result [Krc, 2002] 3. Non-normal incidence characterization (Whole-day optimization) -> nonlinear effects? 4. Further investigation of roughness/randomness; fourier decomposition of AFM surfaces 17

18 References [Krc 2002] J. Krc, F. Smole, M. Topic, Analysis of Light Scattering in Amorphous Si:H Solar Cells by a One-Dimensional Semi-coherent Optical Model, Prog. Photovolt: Res. Appl. 2003; 11: