Morphological evolution of voids by surface drift diffusion driven by capillary, electromigration, and thermal-stress gradients induced by steady-state heat flow in passivated metallic thin films and flip chip solder joints. I. Theory

2008 ◽  
Vol 104 (2) ◽  
pp. 023521 ◽  
Author(s):  
Tarik Omer Ogurtani ◽  
Oncu Akyildiz
Keyword(s):  
Thin Films ◽  
Thermal Stress ◽  
Steady State ◽  
Heat Flow ◽  
Flip Chip ◽  
Morphological Evolution ◽  
Metallic Thin Films ◽  
Drift Diffusion ◽  
Steady State Heat ◽  
Surface Drift

Morphological Evolution of Intragranular Void under the Thermal-Stress Gradient Generated by the Steady State Heat Flow in Encapsulated Metallic Films: Special Reference to Flip Chip Solder Joints

2008 ◽  
Vol 139 ◽  
pp. 151-156
Author(s):  
Tarik Omer Ogurtani ◽  
Oncu Akyildiz
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Heat Flow ◽  
Thermal Stresses ◽  
Morphological Evolution ◽  
Stress Gradient ◽  
Lateral Spreading ◽  
Windward Side ◽  
State Heat ◽  
Steady State Heat

The morphological evolution of intragranular voids induced by the surface drift-diffusion under the action of capillary forces, electromigration (EM) forces, and thermal stress gradients (TSG) associated with steady state heat flow is investigated in passivated metallic thin films via computer simulation using the front-tracking method. As far as the device reliability is concerned, the most critical configuration for interconnect failure occurs even when thermal stresses are low if the normalized ratio of interconnect width to void radius is less than certain range of values (which indicates the onset of heat flux crowding). This regime manifests itself by the formation of two symmetrically disposed finger shape extrusions (pitchfork shape slits) on the upper and lower shoulders of the void surface on the windward side. The void growth (associated with supersaturated vacancy condensation) on the other hand inhibits anode displacement but enhances cathode and shoulder slit velocities drastically, which causes lateral spreading.

Effect of Spatially Varying Porosity on Magnitude of Thermal Stress During Steady-State Heat Flow

1979 ◽  
Vol 62 (7-8) ◽  
pp. 431-432 ◽  
Author(s):  
K. SATYAMURTHY ◽  
J. P. SINGH ◽  
M. P. KAMAT ◽  
D. P. H. HASSELMAN
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Heat Flow ◽  
State Heat ◽  
Steady State Heat ◽  
Spatially Varying

Steady-State Thermal Stresses in Wedge-Shaped Cutting Tools

1975 ◽  
Vol 97 (3) ◽  
pp. 1060-1066
Author(s):  
P. F. Thomason
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Metal Cutting ◽  
Thermal Stresses ◽  
Heat Conduction Problem ◽  
Equivalent Stress ◽  
Cutting Tools ◽  
Thermoelastic Stress ◽  
Plastic State ◽  
Steady State Heat

Closed form expressions for the steady-state thermal stresses in a π/2 wedge, subject to constant-temperature heat sources on the rake and flank contact segments, are obtained from a conformal mapping solution to the steady-state heat conduction problem. It is shown, following a theorem of Muskhelishvili, that the only nonzero thermal stress in the plane-strain wedge is that acting normal to the wedge plane. The thermal stress solutions are superimposed on a previously published isothermal cutting-load solution, to give the complete thermoelastic stress distribution at the wedge surfaces. The thermoelastic stresses are then used to determine the distribution of the equivalent stress, and this gives an indication of the regions on a cutting tool which are likely to be in the plastic state. The results are discussed in relation to the problems of flank wear and rakeface crater wear in metal cutting tools.

scholarly journals Reconstructing bottom water temperatures from measurements of temperature and thermal diffusivity in marine sediments

2014 ◽  
Vol 11 (5) ◽  
pp. 2391-2422
Author(s):  
F. Miesner ◽  
A. Lechleiter ◽  
C. Müller
Keyword(s):  
Steady State ◽  
Heat Flow ◽  
Water Temperature ◽  
Marine Sediments ◽  
Bottom Water ◽  
Measured Data ◽  
Temperature History ◽  
Artificial Data ◽  
Bottom Water Temperature ◽  
Steady State Heat

Abstract. Temperature fields in marine sediments are studied for various purposes. Often, the target of research is the steady state heat flow as a (possible) source of energy but there are also studies attempting to reconstruct bottom water temperature variations to understand more about climate history. The bottom water temperature propagates into the sediment to different depths, depending on the amplitude and period of the deviation. The steady state heat flow can only be determined when the bottom water temperature is constant while the bottom water temperature history can only be reconstructed when the deviation has an amplitude large enough or the measurements are taken in great depths. In this work, the aim is to reconstruct recent bottom water temperature history such as the last two years. To this end, measurements to depths of up to 6 m shall be adequate and amplitudes smaller than 1 K should be reconstructable. First, a commonly used forward model is introduced and analyzed: knowing the bottom water temperature deviation in the last years and the thermal properties of the sediments, the forward model gives the sediment temperature field. Next, an inversion operator and two common inversion schemes are introduced. The analysis of the inversion operator and both algorithms is kept short, but sources for further reading are given. The algorithms are then tested for artificial data with different noise levels and for two example data sets, one from the German North Sea and one from the Davis Strait. Both algorithms show good and stable results for artificial data. The achieved results for measured data have low variances and match to the observed oceanographic settings. Lastly, the desired and obtained accuracy are discussed. For artificial data, the presented method yields satisfying results. However, for measured data the interpretation of the results is more difficult as the exact form of the bottom water deviation is not known. Nevertheless, the presented inversion method seems rather promising due to its accuracy and stability for artificial data. Continuing to work on the development of more sophisticated models for the bottom water temperature, we hope to cover more different oceanographic settings in the future.

Sign in / Sign up

Export Citation Format

Share Document