... In the classical ^-^ the solute distribution is governed by Boltzmann statistics, ie, * DM Ba... more ... In the classical ^-^ the solute distribution is governed by Boltzmann statistics, ie, * DM Barnett and WD Nix are Professors in the . , _ r r.; wi.'n ii Department of Materials Science and Engineering at c^ - Co expL CW/KI J, (i) stanford, -,. ... McGraw-Hill, New York (1968). ...
International Journal of Solids and Structures, 1988
... 9. Hardness variation as a function of depth of indentation for silicon.?888 AK BHATTACHARYA ... more ... 9. Hardness variation as a function of depth of indentation for silicon.?888 AK BHATTACHARYA and WD NIXmaterial that exhibits a large amount of elastic recovery, the best estimate of the true,relaxed indentation depth is the depth at zero load, just before separation between ...
ABSTRACT Creep crack growth in Cu and Cu + 1 wt% Sb has been studied at temperatures near 773 K u... more ABSTRACT Creep crack growth in Cu and Cu + 1 wt% Sb has been studied at temperatures near 773 K under various loading conditions. The presence of Sb in Cu facilitates brittle intergranular fracture at low temperatures and permits a study of cavitation at the crack tip using SEM techniques. Steep gradients in cavitation damage are observed under constant load conditions wherein the crack accelerates in the course of growth. With a constant stress intensity factor, the crack decelerates during growth and the cavitation spreads evenly over the ligament ahead of the crack tip. The crack growth rate is compared with the stress intensity factor and C*, which have been determined for different loading conditions. Results similar to those of Landes and Begley were obtained, indicating that C*, evaluated experimentally, correlates with crack growth rate under constant displacement rate conditions. Crack growth under constant displacement rate conditions can be described by a simple steady state model.
An unexpected mode of plastic deformation was observed in damascene Cu interconnect test structur... more An unexpected mode of plastic deformation was observed in damascene Cu interconnect test structure during an in-situ electromigration experiment and before the onset of visible microstructural damages (void, hillock formation). We show here, using a synchrotron technique of white beam X-ray microdiffraction, that the extent of this electromigration-induced plasticity is dependent on the line width. The grain texture of the line might also play an important role. In wide lines, plastic deformation manifests itself as grain bending and the formation of subgrain structures, while only grain rotation is observed in the narrower lines. This early stage behavior can have a direct bearing on the final failure stage of electromigration.
Obtaining quantitative electrical information with scanning probe microscopy techniques poses a s... more Obtaining quantitative electrical information with scanning probe microscopy techniques poses a significant challenge since the nature of the probe/sample contact is frequently unkown. For example, obtaining quantitative kinetic data from the recently developed atomic force microscopy (AFM) impedance technique requires normalization by the probe/sample contact area. In this paper, a methodology is proposed that enables the extraction of quantitative information from the AFM impedance technique. This methodology applies results from nanoindentation experiments and contact mechanics theory to characterize AFM probe contacts. Using these results, probe/sample contact forces (which can be accurately measured in the AFM) may be converted into probe/sample contact area estimates. These contact area estimates, when included in model of the probe/sample contact, enable the extraction of quantitative data. This methodology is applied to the recently developed AFM impedance measurement techni...
For a Cu single crystal, we find that indentation hardness increases with decreasing indentation ... more For a Cu single crystal, we find that indentation hardness increases with decreasing indentation depth, a phenomenon widely observed before and called the indentation size effect (ISE). To understand the underlying mechanism, we measure the lattice rotations in indentations of different sizes using white beam x-ray microdiffraction (μXRD); the indentation-induced lattice rotations are directly measured by the streaking of x-ray Laue spots associated with the indentations. The magnitude of the lattice rotations is found to be independent of indentation size, which is consistent with the basic tenets of the ISE model. Using the μXRD data together with an ISE model, we can estimate the effective radius of the indentation plastic zone, and the estimate is consistent with the value predicted by a finite element analysis. Using these results, an estimate of the average dislocation densities within the plastic zones has been made; the findings are consistent with the ISE arising from a dep...
... In the classical ^-^ the solute distribution is governed by Boltzmann statistics, ie, * DM Ba... more ... In the classical ^-^ the solute distribution is governed by Boltzmann statistics, ie, * DM Barnett and WD Nix are Professors in the . , _ r r.; wi.'n ii Department of Materials Science and Engineering at c^ - Co expL CW/KI J, (i) stanford, -,. ... McGraw-Hill, New York (1968). ...
International Journal of Solids and Structures, 1988
... 9. Hardness variation as a function of depth of indentation for silicon.?888 AK BHATTACHARYA ... more ... 9. Hardness variation as a function of depth of indentation for silicon.?888 AK BHATTACHARYA and WD NIXmaterial that exhibits a large amount of elastic recovery, the best estimate of the true,relaxed indentation depth is the depth at zero load, just before separation between ...
ABSTRACT Creep crack growth in Cu and Cu + 1 wt% Sb has been studied at temperatures near 773 K u... more ABSTRACT Creep crack growth in Cu and Cu + 1 wt% Sb has been studied at temperatures near 773 K under various loading conditions. The presence of Sb in Cu facilitates brittle intergranular fracture at low temperatures and permits a study of cavitation at the crack tip using SEM techniques. Steep gradients in cavitation damage are observed under constant load conditions wherein the crack accelerates in the course of growth. With a constant stress intensity factor, the crack decelerates during growth and the cavitation spreads evenly over the ligament ahead of the crack tip. The crack growth rate is compared with the stress intensity factor and C*, which have been determined for different loading conditions. Results similar to those of Landes and Begley were obtained, indicating that C*, evaluated experimentally, correlates with crack growth rate under constant displacement rate conditions. Crack growth under constant displacement rate conditions can be described by a simple steady state model.
An unexpected mode of plastic deformation was observed in damascene Cu interconnect test structur... more An unexpected mode of plastic deformation was observed in damascene Cu interconnect test structure during an in-situ electromigration experiment and before the onset of visible microstructural damages (void, hillock formation). We show here, using a synchrotron technique of white beam X-ray microdiffraction, that the extent of this electromigration-induced plasticity is dependent on the line width. The grain texture of the line might also play an important role. In wide lines, plastic deformation manifests itself as grain bending and the formation of subgrain structures, while only grain rotation is observed in the narrower lines. This early stage behavior can have a direct bearing on the final failure stage of electromigration.
Obtaining quantitative electrical information with scanning probe microscopy techniques poses a s... more Obtaining quantitative electrical information with scanning probe microscopy techniques poses a significant challenge since the nature of the probe/sample contact is frequently unkown. For example, obtaining quantitative kinetic data from the recently developed atomic force microscopy (AFM) impedance technique requires normalization by the probe/sample contact area. In this paper, a methodology is proposed that enables the extraction of quantitative information from the AFM impedance technique. This methodology applies results from nanoindentation experiments and contact mechanics theory to characterize AFM probe contacts. Using these results, probe/sample contact forces (which can be accurately measured in the AFM) may be converted into probe/sample contact area estimates. These contact area estimates, when included in model of the probe/sample contact, enable the extraction of quantitative data. This methodology is applied to the recently developed AFM impedance measurement techni...
For a Cu single crystal, we find that indentation hardness increases with decreasing indentation ... more For a Cu single crystal, we find that indentation hardness increases with decreasing indentation depth, a phenomenon widely observed before and called the indentation size effect (ISE). To understand the underlying mechanism, we measure the lattice rotations in indentations of different sizes using white beam x-ray microdiffraction (μXRD); the indentation-induced lattice rotations are directly measured by the streaking of x-ray Laue spots associated with the indentations. The magnitude of the lattice rotations is found to be independent of indentation size, which is consistent with the basic tenets of the ISE model. Using the μXRD data together with an ISE model, we can estimate the effective radius of the indentation plastic zone, and the estimate is consistent with the value predicted by a finite element analysis. Using these results, an estimate of the average dislocation densities within the plastic zones has been made; the findings are consistent with the ISE arising from a dep...
Uploads