Thin film solar cell simulations with FDTD

Matthew Mishrikey, Prof. Ch. Hafner (IFH) Dr. P. Losio

(Oerlikon

Solar)

5th

Workshop on Numerical Methods for Optical Nano

Structures

July 7th, 2009

2

Problem Description

Thin film solar cell designTrial and error manufacture vs. computer simulation

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

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)

5

Material properties

Use a 5 order Lorentzian

model to fit available data (data provided by O.S.)

6

Material properties

7

Accuracy test

Compare FDTD with analytical result for 1D layered structure, using fitted material models, normal incidence

FDTD: resolution of 600 cells per micrometer

energy

5%23%68%3%

8

Absorption Rate

Polarization field P

P evolves with E according to D.E.

Meep

lets you keep track of absorption (or gain) energies (only in a

box now)

absorption rate

nestedscatterer

Computes abs. rate within this box

Lossy ‘rotten egg’

scatterer: Easy to compute loss in egg, less easy to integrate loss in yolk or egg white

illumination

9

Simplified 2D Geometry

Triangular roughness with 2 geometric parameters

Brute force analysis of optimal absorption rate

α

in {10 20 30 40 50 60}sx

in {0.25 0.35 …

0.85}

We can use a mirror symmetry reduce the domain by a factor of 2

10

Simplified 2D Geometry

Absorption rate plotted for each geometry

Strong dependence of absorption rate on roughness angle αWeaker dependence on lattice size

Sample timing info:

Lattice width sx

= 250 nm sx

= 650 nm sx

= 850 nm

decay = 1e-07 18 min 50 min 74 min

decay = 1e-12 25 min 166 min 115 min

best

worst

11

Reflectivity spectra for best and worst geometries

Simplified 2D Geometry

Absorption strongest at shorter lambda, as can be surmised from material data

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

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)

2.2 μm

Progressive shiftand/or

Scaled back-reflector

γ

= 105°

14

Semi-periodic Roughness Geometry

Quad core: ~ 12.5 hours per polarization, field decay 1e-10

grating lobes

improved absorption

γ

= 100°

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

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!).

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

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; 11:15-26