strain, stress and cracks - u.s. pvmc module lifetime... · ... the key to combine ... undisturbed...

1 BROOKHAVEN SCIENCE ASSOCIATES

Strain, Stress and Cracks

Klaus Attenkofer PV Reliability Workshop (Orlando)

April 7-8, 2015


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


Material’s Response to Applied Forces σ

= F/

A

ε = dl/l Strain:

Stre

ss:

Stress: Force per area (pressure)

Strain: Deformation due to stress

Elastic regime: Following Hooks law

Plastic regime: Not applicable to brittle materials

Strain hardening regime

http://www.mscsoftware.com/training_videos/patran/Reverb_help/index.html#page/Fatigue%2520Users%2520Guide/fat_theory.15.4.html


The Microscopic World

ε = dl/l σ

= F/

A

Time averaged stress field

Compressing lattice constant

Expansion due to force


Materials Changes and Hysteresis

•  Materials properties –  Defect density –  Doping profile –  Surface coatings

•  “External” factors –  Temperature –  Electric fields –  cracking allowing

chemical penetration –  Stress caused by

compound material –  External stress

Influence factors:

http://www.mscsoftware.com/training_videos/patran/Reverb_help/index.html#page/Fatigue%2520Users%2520Guide/fat_theory.15.4.html


External Strain

Facility level

Module level

Cell level

Finite Element Analysis is the key to combine environmental impacts to the microscopic world

Total strain= External strain factors & Internal factors

Damage depend on the combination: Opportunity to improve

http://www.predictiveengineering.com/consulting/fea

http://www.comsol.com/blogs/efficient-solar-panel-design-improves-pv-industry/

https://summerofhpc.prace-ri.eu/slovenia-ulfme-wind-loading-on-a-solar-tracker/


Fracture: What to Measure

Crack Development

Curvature of wafer

Fracture

http://www.predictiveengineering.com/consulting/fea

lx

ε = dl/l

σ =

F/A

FEA σ = F/A

dl/l l of Reference/Standard

Mechanical properties

External force to bend


Lifetime Model / Performance

Distribution function of environmental stress factors

Mechanical response of panel

Crack development

Electrical performance at given time

Field data

FEA + ε = dl/l + Curvature of wafer

FEA + Spice-model


X-rays and Matter Scattering (photon in – photon out)

Photo-absorption (spectroscopy) Coherent scattering (Thomson)

Incoherent Scattering (Compton)

XAFS EXAFS


Rocking Curve & Bragg Reflection

Crystal monochromators

)(4.12)()sin()(2

keVEnnd ΈΈ OT

ș șd㩷

dsinș dsinș

TTOO cot'

'

'EE

d: Latiice (d)-spacing,㱔: glancing angle, 㱗: X-ray wavelength10 keV : 1.24 Å, 1 Å : 12.4 keV

Energy (wavelength) resolution

Higher harmonics

E1 = 10 keV (n = 1)

E2 = 20 keV (n = 2)

E3 = 30 keV (n = 3)

Bragg’s law of difraction

E1,E2,E3, 䊶䊶䊶䊶

X-ray diffraction by a single crystal

Kinematical diffraction

(imperfect crystal,

small crystal)

Dynamical diffraction

(nearly perfect crystal)

Single scattering

X-rays are scattered only once in the crystal.

Multiple scattering

Silicon

Germanium

Quartz

Diamond

gallium arsenide

stationary wave field

angleangle

Silicon single crystal, E = 10 keV

hkl 㪙㫉㪸㫈㪾㪸㫅㪾㫃㪼㩿㪻㪼㪾㫉㪼㪼㪀

Z(arc sec)

� Z�� (Prad)

㪈㪈㪈㪈㪈㪅㪋㪇㪊㪌㪅㪋㪎㪍㪉㪍㪅㪌㪌

㪉㪉㪇㪈㪏㪅㪏㪊㪍㪊㪅㪐㪏㪋㪈㪐㪅㪊㪉

㪊㪈㪈㪉㪉㪅㪉㪋㪍㪉㪅㪉㪎㪊㪈㪈㪅㪇㪉

㪋㪇㪇㪉㪎㪅㪈㪍㪎㪉㪅㪋㪐㪌㪈㪉㪅㪈㪇

㪋㪉㪉㪊㪋㪅㪇㪇㪈㪈㪅㪏㪏㪍㪐㪅㪈㪋㪉

㪊㪊㪊㪊㪍㪅㪊㪎㪐㪈㪅㪉㪉㪏㪌㪅㪐㪌㪉

㪋㪋㪇㪋㪇㪅㪉㪉㪈㪅㪌㪋㪊㪎㪅㪋㪎㪐

F0h on the web!!!

http://sergey.gmca.aps.anl.gov/x0h.html

Photon Energy E=10 keV

Crystal monochromators

)(4.12)()sin()(2

keVEnnd ΈΈ OT

ș șd㩷

dsinș dsinș

TTOO cot'

'

'EE

d: Latiice (d)-spacing,㱔: glancing angle, 㱗: X-ray wavelength10 keV : 1.24 Å, 1 Å : 12.4 keV

Energy (wavelength) resolution

Higher harmonics

E1 = 10 keV (n = 1)

E2 = 20 keV (n = 2)

E3 = 30 keV (n = 3)

Bragg’s law of difraction

E1,E2,E3, 䊶䊶䊶䊶

For Silicon:

Typical Angular Resolutions:

http://cheiron2009.spring8.or.jp/images/PDF/Lecture/X-ray_Monochromator_T_Matsushita.pdf


Crystalline and Non-Crystalline Materials

Silicon 400 reflectivity: ~ 80% in 10µrad

X-ray diffraction by a single crystal

Kinematical diffraction

(imperfect crystal,

small crystal)

Dynamical diffraction

(nearly perfect crystal)

Single scattering

X-rays are scattered only once in the crystal.

Multiple scattering

Silicon

Germanium

Quartz

Diamond

gallium arsenide

stationary wave field

angleangle

Bragg-condition

Diffuse scattering (PDF) of glass and plastic: > 1% in large solid angle

X-ray absorption of total encapsulated cell:

In %-range for energies above 20 keV


The Experimental Setup

Various information can be extracted:

http://www.phy.ncu.edu.tw/~CondensedLab/HRXRD.html

4-crystal setup provides monochromatic beam and “angular slit”

Sample can be measured in reflectivity (Bragg) or transmission mode (Laue)

Slit and detector can be replaced by area-detector (spatial resolution ~5µm)

•  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:

Slit can be replaced by analyzer crystal to achieve high resolution with large (in scattering plane) beam

http://www.anka-cos.kit.edu/100.php


Crack Growth in Silicon

tilted platelets cleaved by the 50 N load. By measuring theaverage width of the X-ray image associated with the length ofcrack C2 into ½011" and comparing it with the calculatedtheoretical values for the crack widths from the differentdiffraction planes, it can be concluded that the crack runs fromdifferent (11l) planes into a predominantly ð112Þ plane. Someirregularities indicate conchoidal fracture. Since the criticalcrack lengths even for the narrowest images are greater thanthe wafer thickness, the cracks penetrate through to both sidesof the wafer, except the last 2.3 mm of the tip. This ending partof the tip is not visible either at the surface by NIC or in thebulk by infrared transmission light and therefore cannot beindexed, but {110} and {111} can be excluded. We thenexpected them to be visible in reflection XRDI as well as intransmission, and careful X-ray experiments on both sides ofthe wafer confirmed this to be the case. The crack C3 inFig. 2(b) appeared at relatively low temperature in the brittleregime of silicon in the perpendicular ½011" direction (compareFig. 1b). This crack starts again through complex high-indexedplanes capable of consuming much of the strain energy. Thenit deflects for a long distance into the low-energy ð011Þ planeuntil it ends in another more complicated plane which cannotbe indexed any more.

Fig. 3 shows a series of six topographs around the tip of thecrack C2. These images were taken from a movie of the wholeheating process, then image processed to improve the contrastand converted into false colours for improved visibility of the

contrast related to the strain fields. In Fig. 3(a), at roomtemperature before heating, a higher strain is visible at thecrack tip, indicated by the blue colours. This part of the crackbelow position P1 is inside the bulk of the wafer and notvisible at the surfaces (compare Figs. 4b and 4c). Directly afterheating, crack C2 opens and stops at position P1, about2.3 mm away from the visible sharp crack tip (Fig. 3b), whichcan be seen in images 0038–0048 on the video of the crackdevelopment. Obviously the opening of the crack appears onlyfor this part of the crack where the cleavage plane makes theconnection between the front and back side of the wafer. Inthe part of the crack that remains invisible below the surfaces,a long internal boundary line between the crack and theundisturbed crystal with a length of at least 4.6 mm results.Much more energy would be needed to elongate such a buriedcrack than the shortest direct connection, which would be, forexample, a straight h110i line with a length of only about1.0 mm between the wafers surfaces. Between images 0049 and0104 (corresponding to a temperature rise from 635 to 893 K)the opened crack remains at this position. During this period,for which the crack remains sessile, a substantial long-rangestrain field below P1 gradually builds up, visible as the dark-blue colours in Figs. 3(b)–3(e). Above P1 in parallel a muchhigher strain piles up in a very small volume S1, like a hot spotand into the ½001" direction, visible as the green–red colours.Another hot spot of strain S2 near the tip remains withoutconsequences during the experiment.

X-ray diffraction and imaging

852 Andreas Danilewsky et al. % Crack propagation and fracture in silicon wafers J. Appl. Cryst. (2013). 46, 849–855

Figure 2Transmission topographs of two cracks introduced from a 50 Nindentation at the wafer edge, 90& from the notch: Tc indicates theshadow of a thermocouple, P1 the position where crack C3 originates(room temperature, view from the back side through the sample). (a)Before the first heating sequence. The left crack C1 is short and shows asubstantial strain field at the tip of the crack for which ! = 20. The moredangerous crack C2 is almost four times longer and has a sharp contrast atthe tip; no strain field is visible which results in ! = 167. (b) After the firstheat treatment. The new horizontal crack C3 is generated. Around thecrack tips dense dislocations and slip bands were produced, visible fromthe black contrasts.

Figure 3False-coloured X-ray diffraction images around the tip of crack C2 (detailfrom Fig. 2a). (a) Image 0037 at room temperature before heating of thecrack C2. P1 marks the position where the opening of the crack isimpeded. (b) Image 0045 at '598 K (!T ’ 155 K). The image shows theopening crack which produces a huge strain field below P1 and a smallone S1 directly above. (c) Image 0049 at 689 K shows increasing strainfields, the upper one into the [001] direction. A small-sized strained areaS2 builds up near the tip. (d) Image 0060 at 788 K shows increasing strainat S1 above P1. (e) Image 0104 at 893 K. The strain fields below andabove P1 have both increased in size and intensity. The thermal stressexceeds 24.8 MPa. ( f ) Image 0105 at 895 K. The crack C3 has developedto the left into the [011] direction in less than 0.72 s and the strain fieldshave significantly decreased in size and intensity.

Before Heating After Thermal Cycling

tilted platelets cleaved by the 50 N load. By measuring theaverage width of the X-ray image associated with the length ofcrack C2 into ½011" and comparing it with the calculatedtheoretical values for the crack widths from the differentdiffraction planes, it can be concluded that the crack runs fromdifferent (11l) planes into a predominantly ð112Þ plane. Someirregularities indicate conchoidal fracture. Since the criticalcrack lengths even for the narrowest images are greater thanthe wafer thickness, the cracks penetrate through to both sidesof the wafer, except the last 2.3 mm of the tip. This ending partof the tip is not visible either at the surface by NIC or in thebulk by infrared transmission light and therefore cannot beindexed, but {110} and {111} can be excluded. We thenexpected them to be visible in reflection XRDI as well as intransmission, and careful X-ray experiments on both sides ofthe wafer confirmed this to be the case. The crack C3 inFig. 2(b) appeared at relatively low temperature in the brittleregime of silicon in the perpendicular ½011" direction (compareFig. 1b). This crack starts again through complex high-indexedplanes capable of consuming much of the strain energy. Thenit deflects for a long distance into the low-energy ð011Þ planeuntil it ends in another more complicated plane which cannotbe indexed any more.

Fig. 3 shows a series of six topographs around the tip of thecrack C2. These images were taken from a movie of the wholeheating process, then image processed to improve the contrastand converted into false colours for improved visibility of the

contrast related to the strain fields. In Fig. 3(a), at roomtemperature before heating, a higher strain is visible at thecrack tip, indicated by the blue colours. This part of the crackbelow position P1 is inside the bulk of the wafer and notvisible at the surfaces (compare Figs. 4b and 4c). Directly afterheating, crack C2 opens and stops at position P1, about2.3 mm away from the visible sharp crack tip (Fig. 3b), whichcan be seen in images 0038–0048 on the video of the crackdevelopment. Obviously the opening of the crack appears onlyfor this part of the crack where the cleavage plane makes theconnection between the front and back side of the wafer. Inthe part of the crack that remains invisible below the surfaces,a long internal boundary line between the crack and theundisturbed crystal with a length of at least 4.6 mm results.Much more energy would be needed to elongate such a buriedcrack than the shortest direct connection, which would be, forexample, a straight h110i line with a length of only about1.0 mm between the wafers surfaces. Between images 0049 and0104 (corresponding to a temperature rise from 635 to 893 K)the opened crack remains at this position. During this period,for which the crack remains sessile, a substantial long-rangestrain field below P1 gradually builds up, visible as the dark-blue colours in Figs. 3(b)–3(e). Above P1 in parallel a muchhigher strain piles up in a very small volume S1, like a hot spotand into the ½001" direction, visible as the green–red colours.Another hot spot of strain S2 near the tip remains withoutconsequences during the experiment.

X-ray diffraction and imaging

852 Andreas Danilewsky et al. % Crack propagation and fracture in silicon wafers J. Appl. Cryst. (2013). 46, 849–855

Figure 2Transmission topographs of two cracks introduced from a 50 Nindentation at the wafer edge, 90& from the notch: Tc indicates theshadow of a thermocouple, P1 the position where crack C3 originates(room temperature, view from the back side through the sample). (a)Before the first heating sequence. The left crack C1 is short and shows asubstantial strain field at the tip of the crack for which ! = 20. The moredangerous crack C2 is almost four times longer and has a sharp contrast atthe tip; no strain field is visible which results in ! = 167. (b) After the firstheat treatment. The new horizontal crack C3 is generated. Around thecrack tips dense dislocations and slip bands were produced, visible fromthe black contrasts.

Figure 3False-coloured X-ray diffraction images around the tip of crack C2 (detailfrom Fig. 2a). (a) Image 0037 at room temperature before heating of thecrack C2. P1 marks the position where the opening of the crack isimpeded. (b) Image 0045 at '598 K (!T ’ 155 K). The image shows theopening crack which produces a huge strain field below P1 and a smallone S1 directly above. (c) Image 0049 at 689 K shows increasing strainfields, the upper one into the [001] direction. A small-sized strained areaS2 builds up near the tip. (d) Image 0060 at 788 K shows increasing strainat S1 above P1. (e) Image 0104 at 893 K. The strain fields below andabove P1 have both increased in size and intensity. The thermal stressexceeds 24.8 MPa. ( f ) Image 0105 at 895 K. The crack C3 has developedto the left into the [011] direction in less than 0.72 s and the strain fieldshave significantly decreased in size and intensity.

Strain map during thermal cycling

RT 155C 400C

500C 600C

600C

Crack formation and relaxation of strain

J. Appl. Cryst. (2013). 46, 849–855


First Experiments at XPD (23ID)

7mm

5mm

Reflected beam in Laue geometry @ 34.5keV

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)


Proposed Setup at NSLS-II: 8-ID

Damping Wiggler Si-111 Si-220

Solar panel

Optional analyzer crystal

Area detector

•  Beam parameters: •  Photon energy: 20keV-36keV •  Flux: 1013 Photon/s •  Beam size: 80mm x 3mm

•  Available beam time: 3x7days per week + x

IR-Camera

•  Required time: •  ~20min-25min per cell with 5-10µm

resolution •  Detector readout determines time

•  Number of cells per quarter year: ~2000

About: 3TB/hour!


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

strain, stress and cracks - u.s. pvmc module lifetime... · ... the key to combine ... undisturbed...

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