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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

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Problem Description

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

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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

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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)

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Material properties

Use a 5 order Lorentzian

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

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Material properties

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Accuracy test

Compare FDTD withanalytical result for

1D layered structure,

using fitted material

models, normalincidence

FDTD: resolution of

600 cells per

micrometer

energy

5%23%68%

3%

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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

nested

scattererComputes 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

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Simplified 2D Geometry

Triangular roughness with 2geometric parameters

Brute force analysis of optimal

absorption rate

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

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Simplified 2D Geometry

Absorption rate plotted for each geometry

Strong dependence of absorption rate on roughness angle

Weaker 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

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Reflectivity spectra for best and worst geometries

Simplified 2D Geometry

Absorption strongest

at shorter lambda,

as can be surmisedfrom material data

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Simplified 2D Geometry

Angle

evolution of reflectivity spectra for a fixed lattice constant

Peaks are trackable,

and generally

shrinking

As seen by crossover

in previous plots, its

possible for a larger

angle

to have a

worse overall

absorption rate

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Semi-periodic Roughness Geometry

We can obtain morerealistic reflection

spectra with a more

random surface

Also, we can check if

absorption increases

with more structure

variation (surface shiftand scaling)

2.2 m

Progressive shift

and/or

Scaled back-reflector

= 105

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Semi-periodic Roughness Geometry

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

grating lobes

improved absorption

= 100

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Semi-periodic Roughness Geometry

In the case of offset,

mcSi/ZnO

interface

is shifted right by300 nm, and back

reflector by 450 nm

yscale

factor of back

reflector is notentirely intuitive!

best performance with

matched back reflector

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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 .

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!).

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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

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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