Measuring Procedure for the In- Process-Characterization of - - PowerPoint PPT Presentation

Measuring Procedure for the In- Process-Characterization of Optically Produced Sub-100-nm- Structures

SPP Workshop Jena 2010

• M. Zimmermann
• A. Tausendfreund
• Prof. G. Goch
• Dr. M. Z. Shaikh
• S. Kieß
• T. Bringewat
• Prof. S. Simon

Institute of Parallel and Distributet Systems Stuttgart Bremen Institute for Metrology, Automation and Quality Science

1

Outlook

• Introduction
• Strategy to Characterize Nano-Defects
• Discrete Dipole Approximation (DDA)
• Hardware Acceleration of DDA
• Surface Model for DDA-Input
• Simulations and Comparison with Measurements
• Surface Model of Optically Produced Nano-Structures
• Conclusion

2

Introduction

Example for typical nano-defect: ZnO nano-grass structure (applications: LED-displays, thin layer solar-cells)

Ideal structure, reference: Institute of Solid State Physics Bremen insufficient rod growth no rod creation incomplete rod coverage

3

Introduction

Example for typical nano-defect: ZnO nano-grass structure (applications: LED-displays, thin layer solar-cells)

Ideal structure, reference: Institute of Solid State Physics Bremen insufficient rod growth no rod creation incomplete rod coverage

areas of short circuits

4

Introduction

Example for typical nano-defect: ZnO nano-grass structure (applications: LED-displays, thin layer solar-cells)

Ideal structure, reference: Institute of Solid State Physics Bremen insufficient rod growth no rod creation incomplete rod coverage

areas of short circuits

How do the defects effect the scattering pattern?

typical light scattering pattern:

5

Strategy to Characterize Nano-Defects

Example for typical nano-defect: ZnO nano-grass structure (applications: LED-displays, thin layer solar-cells) areas of short circuits

• Simulate the light scattering process for a multitude of samples (need fast

numerical algorithm)

• Find regularities in the light scattering pattern characterizing the defect
• Compare measured light pattern with the simulations
• Optimize the light scattering measurement system by the simulation results

for in-process applications

Recognition of defects should be possible

6

For computing scattering radiation and absorption properties of arbitrary shaped particles.

• Developed for the field of astrophysics.
• Applicable to any shape of inhomogeneous particles.
• Consideration of material properties.
• Dipole size down to less than λ.

Nanostructured Surface Scattering body is replaced by N interacting dipoles Scattering body ~ 10 m2 Computation Time ~ 5 Days

Simulation for a variety of large surface scattering bodies is a problem.

(CPU : Intel Core i7 @ 2.67 GHz, 12GB Ram)

Discrete Dipole Approximation (DDA)

⇒

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Discrete Dipole Approximation (DDA)

Interaction matrix Interaction matrix Polarization vectors Polarization vectors Incident beam electric field Incident beam electric field

• Scattering target as a cuboidal

grid of N dipoles.

• State of each dipole is

represented by a polarization vector (Pj) which is the unknown quantity.

• Mutual interaction between

dipoles (Aij) is established due to the incident beam (Einc) .

• The polarization vectors (Pj) are

then used for calculating various scattering properties.

DDA Fundamental Equation

8

Discrete Dipole Approximation (DDA)

N2 Operations reduces to N log N Operations

DDA Algorithm Iterative Solver Matrix-Vector Product FFT Matrix Transposition

Iterative solvers spend most of the computational time calculating the matrix vector product

Aij = A’i-j Ʃ A’i-j Pj

(Convolution)

FFT

The interaction matrix term (Aij) depends only on the distance vector between the dipoles i and j.

DDA Implementation

9

Hardware Acceleration of DDA

• PROGRAMMING MODEL
• A kernel is executed as a grid of thread blocks.
• A thread block is a batch of threads
• Partition data into data subsets that can be

handled by thread blocks in parallel.

• MEMORY ARCHITECTURE

Global Memory: R/W communication between Host (CPU) and Device (GPU).

• High latency
• Visible to all multiprocessors.

Shared Memory:

• Low Latency
• Visible only to threads within the block.

Graphics Processing Unit (GPU)

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Hardware Acceleration of DDA (Data Reordering)

After each iteration of matrix transposition, CUFFT (FFT for CUDA) is used for fourier analysis.

3 2 1

GPU global memory (source) GPU global memory (destination) shared memory

1 3 4 5 4 5

Thread 1 Thread 2 Thread 3, 4, 5, 6, 7, 8 Thread 1 Thread 2 Thread 3, 4, 5, 6, 7, 8

2

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Hardware Acceleration of DDA

DDA computation time comparison (CPU vs GPU) Sphere diameter in dipoles Computation time in min CPU single bicgstab CPU double bicgstab CPU double qmr GPU double bicgstab GPU single bicgstab GPU double qmr Computation Time reduces from 5 days to less than 1 day.

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Surface Model for DDA-Input

4 µm 4 µm

Real ZnO- surfaces Surface model for DDA- input generated by numerical algorithm

defect-free defective

Reference: Institute of Solid State Physics Bremen

Defect parameter:

• Rod dimensions
• Rod density
• Rod orientation

rods are statistically distributed Discrete dipole positions in cuboidal grid

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Simulations and Comparison with Measurements

defect-free surface defective surface

4 µm

scattered light scattered light

dimensionless intensity

DDA-Code DDA-Code

Simulations with DDA

dimensionless intensity

14

Simulations and Comparison with Measurements

4 µm

illuminated nano- structures rotary table laser

defect-free surface defective surface scattered light scattered light

dimensionless intensity

Simulations with DDA Planed Measurement Setup

15

Simulations and Comparison with Measurements

4 µm

illuminated nano- structures rotary table laser Evalanche photodiode stepper motor positioning control

defect-free surface defective surface scattered light scattered light

dimensionless intensity

Simulations with DDA Planed Measurement Setup

16

Simulations and Comparison with Measurements

4 µm

defect-free surface defective surface scattered light scattered light

dimensionless intensity

Simulations with DDA Planed Measurement Setup

17

Simulations and Comparison with Measurements

4 µm

defect-free surface defective surface scattered light scattered light

dimensionless intensity

Simulations with DDA Planed Measurement Setup

18

Simulations and Comparison with Measurements

4 µm

ZnO-sample glass-substrate CCD-chip (3mm*4mm) Laser distance ~ 2 mm For light transmitting media scattered light can be measured by using a CCD-chip

First Real Measurements

• n CCD-Chip

defect-free surface defective surface scattered light scattered light

dimensionless intensity

Simulations with DDA

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Simulations and Comparison with Measurements

4 µm

First Real Measurements

• n CCD-Chip

Intensity-distribution indicates surface defect

defect-free surface defective surface scattered light scattered light

dimensionless intensity

Simulations with DDA

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→ Perform simulations for a multitude of ripple structures → Find regularities in the scattering pattern for characterizing defects (e.g. change of grid constant, unstructured areas) → Develop evaluation algorithms to calculate specific parameters like the grid constant

Surface Model of Optically Produced Nano-Structures

REM-image: surface model for DDA-input: zoom:

Laser-induced ZnO ripple-structures

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Conclusion

• DDA-Algorithm could be accelerated by a factor of five
• Simulation results could be qualitatively verified for transparent ZnO-

Nanorod surfaces

• For opaque surfaces the mechanical part of the setup of a laboratory

measuring instrument was realized On-going work:

• Simulation of light scattered from laser-induced ripple structures
• Extension of laboratory measurement system and implementation of

light sensitive Evalanche-diode

• Development of in-process measurement system based on obtained

results

22

Acknowledgement

The authors gratefully acknowledge the support provided by the German Research Foundation (DFG) within the framework of the Priority Program 1327.

Thank you for your attention