Strain, Stress and Cracks Klaus Attenkofer PV Reliability Workshop (Orlando) April 7-8, 2015 1 BROOKHAVEN SCIENCE ASSOCIATES
Overview Material s response to applied forces or what to measure Definitions Hysteresis and the underlying material changes Life time calculation X-rays: A tool to measure atomic distances X-rays probing atomic spacing X-rays and compound materials The experiment: 2-D and 3-D images State-of-the-art: Some examples of stress & strain mapping First tests State-of-the-art Conclusion 2 BROOKHAVEN SCIENCE ASSOCIATES
Material s Response to Applied Forces Stress: Force per area (pressure) Strain: Deformation due to stress σ = F/A Stress: Plastic regime: Not applicable to brittle materials Strain hardening regime Strain: ε = dl/l Elastic regime: Following Hooks law http://www.mscsoftware.com/training_videos/patran/reverb_help/index.html#page/fatigue %2520Users%2520Guide/fat_theory.15.4.html 3 BROOKHAVEN SCIENCE ASSOCIATES
The Microscopic World Time averaged stress field σ = F/A Compressing lattice constant Expansion due to force 4 ε = dl/l BROOKHAVEN SCIENCE ASSOCIATES
Materials Changes and Hysteresis http://www.mscsoftware.com/training_videos/patran/reverb_help/index.html#page/fatigue %2520Users%2520Guide/fat_theory.15.4.html Influence factors: Materials properties Defect density Doping profile Surface coatings External factors Temperature Electric fields cracking allowing chemical penetration Stress caused by compound material External stress 5 BROOKHAVEN SCIENCE ASSOCIATES
External Strain http://www.comsol.com/blogs/efficientsolar-panel-design-improves-pvindustry/ Finite Element Analysis is the key to combine environmental impacts to the microscopic world Facility level https://summerofhpc.prace-ri.eu/ slovenia-ulfme-wind-loading-on-asolar-tracker/ Module level http://www.predictiveengineering.com/consulting/fea Total strain= External strain factors & Internal factors Cell level Damage depend on the combination: Opportunity to improve 6 BROOKHAVEN SCIENCE ASSOCIATES
Fracture: What to Measure Fracture http://www.predictiveengineering.com/consulting/fea σ = F/A Mechanical properties External force to bend ε = dl/l FEA l x Curvature of wafer l of Reference/Standard σ = F/A dl/l Crack Development 7 BROOKHAVEN SCIENCE ASSOCIATES
Lifetime Model / Performance Field data Distribution function of environmental stress factors FEA + ε = dl/l + Curvature of wafer Mechanical response of panel Crack development FEA + Spice-model Electrical performance at given time 8 BROOKHAVEN SCIENCE ASSOCIATES
X-rays and Matter Scattering (photon in photon out) Coherent scattering (Thomson) Photo-absorption (spectroscopy) Incoherent Scattering (Compton) XAFS 9 EXAFS BROOKHAVEN SCIENCE ASSOCIATES
Rocking Curve & Bragg Reflection Bragg s law of difraction 2d( )sin( ) n ( ) n d: Latiice(d)-spacing, : glancing angle, : X-ray wavelength 10 kev : 1.24 Å, 1 Å : 12.4 kev 12.4 E( kev ) d For Silicon: Dynamical diffraction (nearly perfect crystal) hkl Typical Angular Resolutions: Photon Energy E=10 kev (arc sec) ( rad) dsin dsin stationary wave field angle http://cheiron2009.spring8.or.jp/images/pdf/lecture/x-ray_monochromator_t_matsushita.pdf 10 BROOKHAVEN SCIENCE ASSOCIATES
Crystalline and Non-Crystalline Materials Bragg-condition Silicon 400 reflectivity: Diffuse scattering (PDF) of glass and plastic: ~ 80% in 10µrad > 1% in large solid angle M s X-ray absorption of total encapsulated cell: In %-range for energies above 20 kev 11 BROOKHAVEN SCIENCE ASSOCIATES
The Experimental Setup Sample can be measured in reflectivity (Bragg) or transmission mode (Laue) 4-crystal setup provides monochromatic beam and angular slit Slit and detector can be replaced by area-detector (spatial resolution ~5µm) Slit can be replaced by analyzer crystal to achieve high resolution with large (in scattering plane) beam Various information can be extracted: Orientation of the bragg-plane (curvature)in respect to x-ray beam: Rotation of sample to achieve bragg condition Lattice plane parameter l: angle of reflected beam Strain: http://www.anka-cos.kit.edu/100.php http://www.phy.ncu.edu.tw/~condensedlab/hrxrd.html 12 BROOKHAVEN SCIENCE ASSOCIATES
Crack Growth in Silicon Before Heating After Thermal Cycling Strain map during thermal cycling RT 155C 400C 500C 600C 600C Crack formation and relaxation of strain J. Appl. Cryst. (2013). 46, 849 855 13 BROOKHAVEN SCIENCE ASSOCIATES
5mm First Experiments at XPD (23ID) Reflected beam in Laue geometry @ 34.5keV 7mm Signal to Background: 26000/100 Mini-Module 0.02 degrees rotation between frames Results: Signal/Background ~300 Bend of cell in wafer is 0.2 degrees Setup needs to be improved to provide strain analysis (easy task) 14 BROOKHAVEN SCIENCE ASSOCIATES
Proposed Setup at NSLS-II: 8-ID IR-Camera Optional analyzer crystal Damping Wiggler Si-111 Si-220 Solar panel Area detector Beam parameters: Photon energy: 20keV-36keV Flux: 10 13 Photon/s Beam size: 80mm x 3mm Available beam time: 3x7days per week + x Required time: ~20min-25min per cell with 5-10µm resolution Detector readout determines time Number of cells per quarter year: ~2000 About: 3TB/hour! 15 BROOKHAVEN SCIENCE ASSOCIATES
Conclusion Modified topography provides: Curvature of PV cell within package Locally resolved strain map (5-10µm resolution) Signal/Background ratio is no problem Perfect tool to provide input for simulation tools Expected throughput for optimized system: About 20-30min per cell About 1 full panel per day 3 beamtimes with about (7+x) days available per year 16 BROOKHAVEN SCIENCE ASSOCIATES