Modeling the Tensile Strength and Crack Length of Wire-Sawn Silicon Wafers

2009 ◽  
Vol 131 (1) ◽  
Author(s):  
Claudia Funke ◽  
Susann Wolf ◽  
Dietrich Stoyan

Solar silicon wafers are mainly produced through multiwire-sawing. This sawing implies microcracks on the wafer surface, which are responsible for brittle fracture. In order to reduce the sawing-induced cracks, the wafers are damage etched after sawing. This paper develops a model for the impact of crack length manipulation on fracture stress distribution. It investigates the effect of damage-etching on the mechanical properties of solar silicon wafers. The main idea is to transform the fracture stress distribution into a crack length intensity function and to model the effect of etching in terms of crack lengths. The fracture stress distribution is determined statistically by fracture tests of wire-sawn and sawn and etched wafers. The Griffith criterion then enables the transition to crack lengths and crack length intensity functions. Two numerical parameters, called truncation parameter and scaling parameter, determine this relationship and enable a quantitative description of the effect of etching. They turn out to be dependent on etchant and geometry of load and thus tested crack population.

Author(s):  
Hao Wu ◽  
Shreyes N. Melkote

Breakage of thin solar silicon wafers during handling and transport depends on the stresses imposed on the wafer by the handling/transport device. In this paper, the stresses generated in solar silicon wafers by a rigid vacuum gripper are analyzed via a combination of experiments and numerical modeling. Specifically, stresses produced in monocrystalline (Cz) and multicrystalline (Cast) silicon wafers of different thicknesses when handled by a vacuum gripper are analyzed using the finite element (FE) method. With the measured surface profiles of the wafer and the gripper as input, the handling process is simulated using FE modeling and the stress distribution obtained. The FE modeling results are validated by experimental data of wafer surface profile during handling. The results show that while the vacuum level does not have significant impact on the stress distribution, the initial surface profiles of the thin wafer and gripper play a dominant role in producing regions of high stress in the wafer.


2013 ◽  
Vol 136 (2) ◽  
Author(s):  
S. Saffar ◽  
S. Gouttebroze ◽  
Z. L. Zhang

Solar silicon wafers are mainly produced through multiwire sawing. The sawing process induces micro cracks on the wafer surface, which are responsible for brittle fracture. Hence, it is important to scrutinize the crack geometries most commonly generated in silicon wafer sawing or handling process and link the surface crack to the fracture of wafers. The fracture of a large number of multicrystalline silicon wafers has been investigated by means of 4-point bending and twisting tests and a failure probability function is presented. By neglecting the material property variation and assuming that one surface crack is dominating the wafer breakage, 3D finite element models with various crack sizes (depth, length, and orientation) have been analyzed to identify the distribution of surface crack geometries by fitting the failure probability from the experiments. With respect to the 63% probability, the existing surface cracks in the wafers studied appear to have depth and length ratios less than 0.042 and 0.19, respectively. Furthermore, it has been shown that the surface cracks with depth in the range from 10 to 20 μm, length up to 10 mm and angles in the range of 30 deg–60 deg, can be considered as the most common crack geometries in wafers we tested. Finally, it has been found that the mechanical strength of the wafers tested parallel to the sawing direction is approximately 15 MPa smaller than those tested perpendicular to the sawing direction.


2001 ◽  
Vol 38 (04) ◽  
pp. 1033-1054 ◽  
Author(s):  
Liudas Giraitis ◽  
Piotr Kokoszka ◽  
Remigijus Leipus

The paper studies the impact of a broadly understood trend, which includes a change point in mean and monotonic trends studied by Bhattacharyaet al.(1983), on the asymptotic behaviour of a class of tests designed to detect long memory in a stationary sequence. Our results pertain to a family of tests which are similar to Lo's (1991) modifiedR/Stest. We show that both long memory and nonstationarity (presence of trend or change points) can lead to rejection of the null hypothesis of short memory, so that further testing is needed to discriminate between long memory and some forms of nonstationarity. We provide quantitative description of trends which do or do not fool theR/S-type long memory tests. We show, in particular, that a shift in mean of a magnitude larger thanN-½, whereNis the sample size, affects the asymptotic size of the tests, whereas smaller shifts do not do so.


2021 ◽  
Vol 1 (2) ◽  
Author(s):  
Manh Tung BUI ◽  
Tien Dung LE ◽  
Trong Hung VO

Quang Ninh underground coal mines are currently in the phase of finishing up the mineralreserves located near the surface. Also, in this phase, a number of coal mines have opened and preparednew mine sites for the extraction of the reserves at greater depth. Several mines have mined at -350 mdepth and are driving opening excavations at -500 m depth below sea level. The mining at greater depthfaces many difficulties, such as a significant increase in support and excavation pressures. The longwallface pressure is mostly manifested in great magnitude that causes support overloaded and jumped andface spall/roof fall. This paper, based on the geological condition of the Seam 11 Ha Lam coal mine,uses the numerical program UDEC for studying the impact of mining depth on stress distribution aroundthe longwall face. The results show that the deeper the mining is, the greater the plastic deformationzone is. The peak front abutment stress moves closer to the coal wall, mainly concentrating on theimmediate roof and top coal. The top coal is greatly broken, and its bearing capacity is decreased. Somesolutions to the stability of roof strata are proposed, and a proper working resistance of support isdetermined. Additionally, the paper suggests that the starting depth for deep mining in Quang Ninhunderground coal mines should be -350 m below sea level.


2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Bui MANH TUNG ◽  
Nguyen VAN QUANG ◽  
Nguyen PHI HUNG ◽  
Vo NGOC DUNG ◽  
Do HOANG HIEP

The extraction with higher cutting height for extra-thick seam is the new research orientation in longwall caving technology. Due to the increase of top coal thickness and of cutting height which leads to the change of cutting/caving height ratio, the rule of roof failure (including top coal caving) and the distribution of stress around the face alter correspondingly. This paper is based on the geological conditions of face 8102 of Tashan-DaTong mine, employing the numerical model by UDEC2D code, analysing the effect of cutting/caving height ratio on the law of stress distribution ahead of the face. When the ratio of cutting/caving height decreases and the cutting height increases, the results of the research have shown that: (i)- peak stress redistributes further ahead of the face and its value manifestly drops; (ii)- the plastic deformation ahead of face significant increases and the zone of plastic strain also expands. It is therefore concluded that the variation of cutting/caving height ratio results in the redistribution of roof pressure, which contributes to the control of roof failure and face stability.


F1000Research ◽  
2021 ◽  
Vol 8 ◽  
pp. 1020
Author(s):  
Omnia Nabil ◽  
Carl Hany Halim ◽  
Ashraf Hassan Mokhtar

Background: The flat occlusal preparation design (FOD) of posterior teeth offers promising results of fracture resistance and stress distribution, but its application in vital teeth is limited as there may be a danger of pulp injury. Although this danger is omitted in endodontically treated teeth, there is no research work assessing the impact of FOD on the fracture resistance and distribution of stresses among these teeth. The aim of this study was to assess the impact of FOD of endodontically treated molars on the fracture resistance and distribution of stresses among a ceramic crown-molar structure when compared to the two planes occlusal preparation design (TOD). Methods: 20 human mandibular molars were endodontically treated and distributed equally to two groups: Group I (TOD) and Group II (FOD). Ceramic CAD/CAM milled lithium disilicate (IPS e.max CAD) crowns were produced for all preparations and adhered using self-adhesive resin cement. Using a universal testing machine, the fracture resistance test was performed. The fractured samples were examined using a stereomicroscope and scanning electron microscope to determine modes of failure. Stress distribution was evaluated by 3D finite element analysis, which was performed on digital models of endodontically treated mandibular molars (one model for each design). Results: Group II recorded statistically non-significant higher fracture resistance mean values (3107.2± 604.9 N) than Group I mean values (2962.6 ±524.27 N) as indicated by Student’s t-test (t=0.55, p= 0.57). Also, Group II resulted in more favorable failure mode as compared to Group I. Both preparation designs yielded low von-Mises stresses within the factor of safety. However, the stress distribution among different layers of the model differed. Conclusions: FOD having comparable fracture strength to TOD and a more favorable fracture behavior can be used for the preparation of endodontically treated molars.


2005 ◽  
Vol 867 ◽  
Author(s):  
Gregory P. Muldowney

AbstractMaterial removal in CMP occurs during intervals of pad-wafer contact separated by intervals of non-contact. One predictable sequence of non-contact intervals for a fixed point on the wafer is the traverse of the pad grooves, during which the wafer surface is renewed with fresh chemistry and heat is conveyed away. It is well understood that good uniformity requires machine kinematics that expose all points on the wafer to the same total contact time, mean slurry concentration, and temperature. Less widely known is that coherent structures tens to hundreds of nanometers high and matching the pitch of the pad groove pattern may be formed on an otherwise planar wafer despite multiple rotary motions. This unexpected phenomena is of interest not only because it manifests the impact of grooves and transport at scales not easily studied, but also because shrinking device architectures will ultimately disqualify even nanoscale departures from planarity. Wafer polish experiments are conducted alternately using circular, Cartesian grid, and spiral groove patterns using specialized pad conditioning and CMP recipes to amplify groove-induced nanotopography. Polish results illustrate sharp patterns in finished wafers (visible to the naked eye) that should not survive dual-axis tool kinematics. Computational 3-D model results are then presented for transient slurry mixing in the pad-wafer gap of a 200-mm polisher using the same groove patterns. A direct correspondence is found between observed wafer nanotopography and predicted groove-scale slurry mixing dynamics. In particular, the surface structures are underpolished areas traceable to intervals of non-contact protracted by depleted polish chemistry that prevails in groove segments when oriented relative to the local pad and wafer motion in a way that suspends transverse mixing in the groove crosssection. The study conclusively defines the features required in a groove pattern and polish recipe to form coherent structures matching the groove pitch. As validation of the theory, a groove pattern expected to form no surface topography is defined, experimentally tested, and shown to perform as predicted. Findings are discussed in the context of next-generation pad grooving and texturing as required for progressively more demanding applications of CMP.


2019 ◽  
Vol 40 (Supplement_1) ◽  
Author(s):  
E Tenekecioglu ◽  
R Torii ◽  
Y Katagiri ◽  
J Dijkstra ◽  
R Modolo ◽  
...  

Abstract Background and aim Scaffold design and plaque characteristics influence implantation outcomes and local flow dynamics in treated coronary segments. Our aim is to assess the impact of strut embedment/protrusion of bioresorbable scaffold on local shear stress distribution in different atherosclerotic plaque types. Method Fifteen Absorb everolimus-eluting Bioresorbable Vascular Scaffolds were implanted in human epicardial coronary arteries. Optical coherence tomography (OCT) was performed post-scaffold implantation and strut embedment/protrusion were analyzed using a dedicated software. OCT data was fused with angiography to reconstruct three-dimensional coronary anatomy. Blood flow simulation was performed and wall shear stress (WSS) was estimated in each scaffolded surface and the relationship between strut embedment/protrusion and WSS was evaluated. Results There were 9083 struts analysed. Ninety-seven percent of the struts (n=8840) were well apposed and 243 (3%) were malapposed. At cross-section level (n=1289), strut embedment was significantly increased in fibroatheromatous plaques (76±48μm) and decreased in fibro-calcific plaques (35±52 μm). Compatible with strut embedment, WSS was significantly higher in lipid-rich fibroatheromatous plaques (1.50±0.81Pa), whereas significantly decreased in fibro-calcified plaques (1.05±0.91Pa). After categorization of WSS as low (<1.0 Pa) and normal/high WSS (≥1.0 Pa), the percent of low-WSS in the plaque subgroups were 30.1%, 31.1%, 25.4% and 36.2% for non-diseased vessel wall, fibrous plaque, fibro-atheromatous plaque and fibro-calcific plaque, respectively (p-overall<0.001). Table 1. Cross-section level Embedment/Protrusion and WSS according to the plaque type Plaque type Embedment depth (μm) Protrusion distance (μm) WSS (Pa) Non-atherosclerotic intimal thickening/normal vessel wall (n=2275) 47±34*Δ¥ 123±34¶Ξπ 1.44±0.9解 Fibrous (n=4191) 53±40*#& 118±38¶Ψ‡ 1.24±0.78αθ∞ Fibroatheromatous (n=2027) 76±48#ΦΔ 94.6±46Ω†Ψπ 1.50±0.81Σ§α Fibro-calcific (n=590) 35±52&Φ¥ 139±50‡†Ξ 1.05±0.91∞£Σ For embedment: *p=0.09, #p<0.001, &p<0.001, Φp<0.0001, Δp<0.0001, ¥p<0.0001. For protrusion: ¶p=0.74, Ξp<0.0001, πp<0.0001, Ψp<0.0001, ‡p<0.0001, †p<0.0001. For WSS: θp<0.001, §p=0.06, £p<0.0001, αp<0.0001, ∞p<0.0001, Ωp<0.0001. n=total strut number in each plaque type, p-values come from mixed-effects regression analysis. Conclusion The composition of the underlying plaque influences strut embedment which seems to have effect on WSS. The struts deeply embedded in lipid-rich fibroatheromas plaques resulted in higher WSS compared to the other plaque types.


2018 ◽  
Vol 16 (3) ◽  
pp. 78-93
Author(s):  
Yongtao Peng ◽  
Yaya Li ◽  
Meiling He

For the realization, a qualitative and quantitative description of matching degree between the elements for logistics supply network and demand network, logistics super network models are constructed by the theory of super network. Faced with the problems of diverse demand and massive circulation for commodities, this article studies the structure of the logistics super network of multi-commodity circulation and establishes the continuous cost function of the logistics demand and supply, reflecting the logistics cost of different commodities in different phrases. This article aims to establish the optimization model of logistics supernetwork by aiming to maximize the matching of supply and demand of multi-commodity. The model is transformed into the variational inequality problem, and proves the existence and uniqueness of the equivalence solution. Use the case of the logistics supernetwork of coal, a modified projection algorithm is adopted and the fact is revealed that improving the supply capacity of the network matching may have the original 81.3% increase to 90.5%, improving the impact of the relationship between trades, matching degree can be increased to 90.1%.


2019 ◽  
Vol 963 ◽  
pp. 530-533
Author(s):  
Kevin Moeggenborg ◽  
Ian Manning ◽  
Jon Searson ◽  
Gil Yong Chung

The impact of surface stress due to polish and grind processes on wafer bow was studied as a function of abrasive size. Results indicate that sub-surface damage from these processes can introduce significant surface stress. For polishing processes, this stress is proportional to mean abrasive size. The study also investigates stress as a function of depth below the wafer surface and finds that most stress is concentrated near the wafer surface.


Sign in / Sign up

Export Citation Format

Share Document