SPP Workshop Jena 2010 0 Measuring Procedure for the In- Process-Characterization of Optically Produced Sub-100-nm- Structures M. Zimmermann Dr. M. Z. Shaikh A. Tausendfreund S. Kieß Prof. G. Goch T. Bringewat Prof. S. Simon Bremen Institute for Metrology, Institute of Parallel and Automation and Quality Science Distributet Systems Stuttgart
Outlook 1 • 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
Introduction 2 Example for typical nano-defect: ZnO nano-grass structure (applications: LED-displays, thin layer solar-cells) Ideal structure, reference: incomplete rod coverage insufficient rod growth no rod creation Institute of Solid State Physics Bremen
Introduction 3 Example for typical nano-defect: ZnO nano-grass structure (applications: LED-displays, thin layer solar-cells) areas of short circuits Ideal structure, reference: incomplete rod coverage insufficient rod growth no rod creation Institute of Solid State Physics Bremen
Introduction 4 Example for typical nano-defect: ZnO nano-grass structure (applications: LED-displays, thin layer solar-cells) areas of short circuits Ideal structure, reference: incomplete rod coverage insufficient rod growth no rod creation Institute of Solid State Physics Bremen typical light scattering pattern: How do the defects effect the scattering pattern?
Strategy to Characterize Nano-Defects 5 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
Discrete Dipole Approximation (DDA) 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 . ⇒ Scattering body ~ 10 � m 2 Computation Time ~ 5 Days Nanostructured Scattering body is replaced (CPU : Intel Core i7 @ 2.67 GHz, 12GB Ram) Surface by N interacting dipoles Simulation for a variety of large surface scattering bodies is a problem.
Discrete Dipole Approximation (DDA) 7 •Scattering target as a cuboidal DDA Fundamental Equation grid of N dipoles. •State of each dipole is represented by a polarization vector (P j ) which is the unknown quantity. •Mutual interaction between Interaction Interaction Incident beam electric field Incident beam electric field matrix matrix dipoles (A ij ) is established due to the incident beam (E inc ) . Polarization Polarization vectors vectors •The polarization vectors (P j ) are then used for calculating various scattering properties.
Discrete Dipole Approximation (DDA) 8 DDA Implementation The interaction matrix term ( A ij ) depends only on the distance vector between the dipoles i and j. Ʃ A’ i-j P j A ij = A’ i-j FFT (Convolution) N 2 Operations DDA Algorithm Iterative Solver Matrix-Vector Product reduces to FFT Matrix Transposition N log N Operations Iterative solvers spend most of the computational time calculating the matrix vector product
Hardware Acceleration of DDA 9 Graphics Processing Unit (GPU) • 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.
Hardware Acceleration of DDA (Data Reordering) 10 GPU global memory ( source ) GPU global memory ( destination ) 1 2 3 1 4 2 4 5 5 Thread Thread Thread 3, 4, 5, 6, 7, 8 1 2 Thread Thread Thread 3, 4, 5, 6, 7, 8 3 1 2 shared memory After each iteration of matrix transposition, CUFFT (FFT for CUDA) is used for fourier analysis.
Hardware Acceleration of DDA 11 DDA computation time comparison (CPU vs GPU) CPU single bicgstab Computation time in min CPU double bicgstab CPU double qmr GPU double bicgstab GPU single bicgstab GPU double qmr Sphere diameter in dipoles Computation Time reduces from 5 days to less than 1 day.
Surface Model for DDA-Input 12 defect-free defective Reference: Real ZnO- Institute of Solid State surfaces Physics Bremen 4 µm 4 µm Surface model for DDA- input generated by numerical algorithm rods are statistically distributed Defect parameter: • Rod dimensions • Rod density • Rod orientation Discrete dipole positions in cuboidal grid
Simulations and Comparison with Measurements 13 Simulations with DDA dimensionless dimensionless scattered light scattered light intensity intensity defective surface defect-free surface 4 µm DDA-Code DDA-Code
Simulations and Comparison with Measurements 14 Simulations with DDA dimensionless scattered light scattered light intensity defective surface defect-free surface 4 µm laser Planed Measurement Setup illuminated nano- structures rotary table
Simulations and Comparison with Measurements 15 Simulations with DDA dimensionless scattered light scattered light intensity defective surface defect-free surface 4 µm laser Planed Evalanche Measurement photodiode Setup illuminated nano- structures stepper motor positioning control rotary table
Simulations and Comparison with Measurements 16 Simulations with DDA dimensionless scattered light scattered light intensity defective surface defect-free surface 4 µm Planed Measurement Setup
Simulations and Comparison with Measurements 17 Simulations with DDA dimensionless scattered light scattered light intensity defective surface defect-free surface 4 µm Planed Measurement Setup
Simulations and Comparison with Measurements 18 Simulations with DDA dimensionless scattered light scattered light intensity defective surface defect-free surface 4 µm Laser First Real Measurements ZnO-sample on CCD-Chip glass-substrate For light transmitting media scattered light can distance ~ 2 mm be measured by using a CCD-chip CCD-chip (3mm*4mm)
Simulations and Comparison with Measurements 19 Simulations with DDA dimensionless scattered light scattered light intensity defective surface defect-free surface 4 µm First Real Measurements on CCD-Chip Intensity-distribution indicates surface defect
Surface Model of Optically Produced Nano-Structures 20 Laser-induced ZnO ripple-structures REM-image: surface model for DDA-input: zoom: → 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
Conclusion 21 • 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
Acknowledgement 22 Thank you for your attention The authors gratefully acknowledge the support provided by the German Research Foundation (DFG) within the framework of the Priority Program 1327.
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