Large-Scale Electromigration Statistics for Cu Interconnects

2009 ◽  
Vol 1156 ◽  
Author(s):  
Meike Hauschildt ◽  
Martin Gall ◽  
Richard Hernandez
Keyword(s):  
Activation Energy ◽  
Large Scale ◽  
Dielectric Material ◽  
Flow Direction ◽  
Stress Gradient ◽  
Wheatstone Bridge ◽  
Operating Conditions ◽  
Early Failure ◽  
Single Digit ◽  
Cu Interconnects

AbstractEven after the successful introduction of Cu-based metallization, the electromigration failure risk has remained one of the important reliability concerns for advanced process technologies. The observation of strong bimodality for the electron up-flow direction in dual-inlaid Cu interconnects has added complexity, but is now widely accepted. More recently, bimodality has been reported also in down-flow electromigration, leading to very short lifetimes due to small, slit-shaped voids under vias. For a more thorough investigation of these early failure phenomena, specific test structures were designed based on the Wheatstone Bridge technique. The use of these structures enabled an increase of the tested sample size past 1.1 million, allowing a direct analysis of electromigration failure mechanisms at the single-digit ppm regime. Results indicate that down-flow electromigration exhibits bimodality at very small percentage levels, not readily identifiable with standard testing methods. The activation energy for the down-flow early failure mechanism was determined to be 0.83 ± 0.01 eV. Within the small error bounds of this large-scale statistical experiment, this value is deemed to be significantly lower than the usually reported activation energy of 0.90 eV for electromigration-induced diffusion along Cu/SiCN interfaces. Due to the advantages of the Wheatstone Bridge technique, we were also able to expand the experimental temperature range down to 150 °C, coming quite close to typical operating conditions up to 125 °C. As a result of the lowered activation energy, we conclude that the down-flow early failure mode may control the chip lifetime at operating conditions. The slit-like character of the early failure void morphology also raises concerns about the validity of the Blech-effect for this mechanism. A very small amount of Cu depletion may cause failure even before a stress gradient is established. We therefore conducted large-scale statistical experiments close to the critical current density-length product (jL)*. The results indicate that even at very small failure percentages, this critical product seems to extrapolate to about 2900 ± 400 A/cm for SiCOH-based dielectrics, close to previously determined (jL)* products of about 3000 ± 500 A/cm for the same technology node and dielectric material, acquired with single link interconnects. More detailed studies are currently ongoing to verify the extrapolation methods at small percentages. Furthermore, the scaling behavior of the early failure population was investigated.

scholarly journals Heat Transfer in Rotating Serpentine Passages With Trips Normal to the Flow

1992 ◽  
Vol 114 (4) ◽  
pp. 847-857 ◽  
Author(s):  
J. H. Wagner ◽  
B. V. Johnson ◽  
R. A. Graziani ◽  
F. C. Yeh
Keyword(s):  
Heat Transfer ◽  
Turbine Blade ◽  
Large Scale ◽  
Flow Direction ◽  
Operating Conditions ◽  
Transfer Model ◽  
Transfer Coefficients ◽  
Flow Equations ◽  
Turbine Blade Cooling ◽  
Heat Transfer Coefficients

Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large-scale, multipass, heat transfer model with both radially inward and outward flow. Trip strips on the leading and trailing surfaces of the radial coolant passages were used to produce the rough walls. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature ratio, Rossby number, Reynolds number, and radius-to-passage hydraulic diameter ratio. The first three of these four parameters were varied over ranges that are typical of advanced gas turbine engine operating conditions. Results were correlated and compared to previous results from stationary and rotating similar models with trip strips. The heat transfer coefficients on surfaces, where the heat transfer increased with rotation and buoyancy, varied by as much as a factor of four. Maximum values of the heat transfer coefficients with high rotation were only slightly above the highest levels obtained with the smooth wall model. The heat transfer coefficients on surfaces where the heat transfer decreased with rotation, varied by as much as a factor of three due to rotation and buoyancy. It was concluded that both Coriolis and buoyancy effects must be considered in turbine blade cooling designs with trip strips and that the effects of rotation were markedly different depending upon the flow direction.

scholarly journals Heat Transfer in Rotating Serpentine Passages With Trips Normal to the Flow

1991 ◽  
Author(s):  
J. H. Wagner ◽  
B. V. Johnson ◽  
R. A. Graziani ◽  
F. C. Yeh
Keyword(s):  
Heat Transfer ◽  
Turbine Blade ◽  
Large Scale ◽  
Flow Direction ◽  
Operating Conditions ◽  
Transfer Model ◽  
Transfer Coefficients ◽  
Flow Equations ◽  
Turbine Blade Cooling ◽  
Heat Transfer Coefficients

Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large scale, multi–pass, heat transfer model with both radially inward and outward flow. Trip strips on the leading and trailing surfaces of the radial coolant passages were used to produce the rough walls. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant–to–wall temperature ratio, Rossby number, Reynolds number and radius–to–passage hydraulic diameter ratio. The first three of these four parameters were varied over ranges which are typical of advanced gas turbine engine operating conditions. Results were correlated and compared to previous results from stationary and rotating similar models with trip strips. The heat transfer coefficients on surfaces, where the heat transfer increased with rotation and buoyancy, varied by as much as a factor of four. Maximum values of the heat transfer coefficients with high rotation were only slightly above the highest levels obtained with the smooth wall model. The heat transfer coefficients on surfaces, where the heat transfer decreased with rotation, varied by as much as a factor of three due to rotation and buoyancy. It was concluded that both Coriolis and buoyancy effects must be considered in turbine blade cooling designs with trip strips and that the effects of rotation were markedly different depending upon the flow direction.

scholarly journals Heat Transfer in Rotating Serpentine Passages With Trips Skewed to the Flow

1994 ◽  
Vol 116 (1) ◽  
pp. 113-123 ◽  
Author(s):  
B. V. Johnson ◽  
J. H. Wagner ◽  
G. D. Steuber ◽  
F. C. Yeh
Keyword(s):  
Heat Transfer ◽  
Turbine Blade ◽  
Large Scale ◽  
Flow Direction ◽  
Operating Conditions ◽  
Transfer Model ◽  
Transfer Coefficients ◽  
Flow Equations ◽  
Turbine Blade Cooling ◽  
Heat Transfer Coefficients

Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large-scale, multipass, heat transfer model with both radially inward and outward flow. Trip strips, skewed at 45 deg to the flow direction, were machined on the leading and trailing surfaces of the radial coolant passages. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature ratio, rotation number, Reynolds number, and radius-to-passage hydraulic diameter ratio. The first three of these four parameters were varied over ranges that are typical of advanced gas turbine engine operating conditions. Results were correlated and compared to previous results from similar stationary and rotating models with smooth walls and with trip strips normal to the flow direction. The heat transfer coefficients on surfaces, where the heat transfer decreased with rotation and buoyancy, decreased to as low as 40 percent of the value without rotation. However, the maximum values of the heat transfer coefficients with high rotation were only slightly above the highest levels previously obtained with the smooth wall model. It was concluded that (1) both Coriolis and buoyancy effects must be considered in turbine blade cooling designs with trip strips, (2) the effects of rotation are markedly different depending upon the flow direction, and (3) the heat transfer with skewed trip strips is less sensitive to buoyancy than the heat transfer in models with either smooth walls or normal trips. Therefore, skewed trip strips rather than normal trip strips are recommended and geometry-specific tests will be required for accurate design information.

scholarly journals Rotating Heat Transfer Experiments With Turbine Airfoil Internal Flow Passages

1986 ◽  
Author(s):  
Joel H. Wagner ◽  
Jay C. Kim ◽  
Bruce V. Johnson
Keyword(s):  
Heat Transfer ◽  
Gas Turbine ◽  
Large Scale ◽  
Flow Direction ◽  
Internal Flow ◽  
Operating Conditions ◽  
Coolant Temperature ◽  
Rossby Number ◽  
Transfer Coefficients ◽  
Bulk Fluid

Internal convective cooling is used to maintain acceptable gas turbine rotor blade temperatures. The heat transfer from the blade coolant passage walls is governed by forced convection, Coriolis forces and buoyance due to wall and coolant temperature differences. Currently little data is available to designers regarding the combined effects of these three parameters. To obtain required data, a rotating heat transfer facility was developed for experiments with large scale models and run at rotation and flow parameters typical of current gas turbine operating conditions. Analysis of the equations of motion showed that the perinent nondimensional parameters were Reynolds number, Rossby number, the difference in wall fluid and bulk fluid density and geometric ratios. The models were instrumented to measure average heat transfer rates on the coolant passage wall elements, and with pressure taps for friction data. An initial set of experiments have been conducted with rough wall geometries, typical of those used in blades. Results from the rotating experiments showed large heat transfer coefficient increases and decreases on the coolant passage leading and trailing surfaces compared to nonrotating heat transfer coefficients. The heat transfer was shown to be a function of inward or outward flow direction and Rossby number for the experiments conducted.

Heat Transfer in Rotating Serpentine Passages With Smooth Walls

1991 ◽  
Vol 113 (3) ◽  
pp. 321-330 ◽  
Author(s):  
J. H. Wagner ◽  
B. V. Johnson ◽  
F. C. Kopper
Keyword(s):  
Heat Transfer ◽  
Turbine Blade ◽  
Large Scale ◽  
Flow Direction ◽  
Vertical Tube ◽  
Operating Conditions ◽  
Transfer Model ◽  
Transfer Coefficients ◽  
Flow Equations ◽  
Heat Transfer Coefficients

Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large-scale, multipass, smooth-wall heat transfer model with both radially inward and outward flow. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature ratio, Rossby number, Reynolds number, and radius-to-passage hydraulic diameter ratio. These four parameters were varied over ranges that are typical of advanced gas turbine engine operating conditions. It was found that both Coriolis and buoyancy effects must be considered in turbine blade cooling designs and that the effect of rotation on the heat transfer coefficients was markedly different depending on the flow direction. Local heat transfer coefficients were found to decrease by as much as 60 percent and increase by 250 percent from no-rotation levels. Comparisons with a pioneering stationary vertical tube buoyancy experiment showed reasonably good agreement. Correlation of the data is achieved employing dimensionless parameters derived from the governing flow equations.

scholarly journals Heat Transfer in Rotating Serpentine Passages With Trips Skewed to the Flow

1992 ◽  
Author(s):  
B. V. Johnson ◽  
J. H. Wagner ◽  
G. D. Steuber ◽  
F. C. Yeh
Keyword(s):  
Heat Transfer ◽  
Turbine Blade ◽  
Large Scale ◽  
Flow Direction ◽  
Operating Conditions ◽  
Transfer Model ◽  
Transfer Coefficients ◽  
Flow Equations ◽  
Turbine Blade Cooling ◽  
Heat Transfer Coefficients

Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large scale, multi-pass, heat transfer model with both radially inward and outward flow. Trip strips, skewed at 45 degrees to the flow direction, were machined on the leading and trailing surfaces of the radial coolant passages. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature ratio, rotation number, Reynolds number and radius-to-passage hydraulic diameter ratio. The first three of these four parameters were varied over ranges which are typical of advanced gas turbine engine operating conditions. Results were correlated and compared to previous results from similar stationary and rotating models with smooth walls and with trip strips normal to the flow direction. The heat transfer coefficients on surfaces, where the heat transfer decreased with rotation and buoyancy, decreased to as low as 40 percent of the value without rotation. However, the maximum values of the heat transfer coefficients with high rotation were only slightly above the highest levels previously obtained with the smooth wall model. It was concluded that (1) both Coriolis and buoyancy effects must be considered in turbine blade cooling designs with trip strips, (2) the effects of rotation are markedly different depending upon the flow direction and (3) the heat transfer with skewed trip strips is less sensitivity to buoyancy than the heat transfer in models with either smooth walls or normal trips. Therefore, skewed trip strips rather than normal trip strips are recommended and geometry-specific tests will be required for accurate design information.

scholarly journals Heat Transfer in Rotating Serpentine Passages With Smooth Walls

1990 ◽  
Author(s):  
J. H. Wagner ◽  
B. V. Johnson ◽  
F. C. Kopper
Keyword(s):  
Heat Transfer ◽  
Turbine Blade ◽  
Large Scale ◽  
Flow Direction ◽  
Vertical Tube ◽  
Operating Conditions ◽  
Transfer Model ◽  
Transfer Coefficients ◽  
Flow Equations ◽  
Heat Transfer Coefficients

Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large scale, multi–pass, smooth–wall heat transfer model with both radially inward and outward flow. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages (coolant–to–wall temperature ratio, Rossby number, Reynolds number and radius–to–passage hydraulic diameter ratio). These four parameters were varied over ranges which are typical of advanced gas turbine engine operating conditions. It was found that both Coriolis and buoyancy effects must be considered in turbine blade cooling designs and that the effect of rotation on the heat transfer coefficients was markedly different depending on the flow direction. Local heat transfer coefficients were found to decrease by as much as 60 percent and increase by 250 percent from no rotation levels. Comparisons with a pioneering stationary vertical tube buoyancy experiment showed reasonably good agreement. Correlation of the data is achieved employing dimensionless parameters derived from the governing flow equations.

Adsorption Isotherm Predictions for Multiple Molecules in MOFs Using the Same Deep Learning Model

2019 ◽  
Author(s):  
Ryther Anderson ◽  
Achay Biong ◽  
Diego Gómez-Gualdrón
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Molecular Simulation ◽  
Large Scale ◽  
Learning Model ◽  
Operating Conditions ◽  
Small Subset ◽  
Screening Methods ◽  
Large Set ◽  
Metal Organic

<div>Tailoring the structure and chemistry of metal-organic frameworks (MOFs) enables the manipulation of their adsorption properties to suit specific energy and environmental applications. As there are millions of possible MOFs (with tens of thousands already synthesized), molecular simulation, such as grand canonical Monte Carlo (GCMC), has frequently been used to rapidly evaluate the adsorption performance of a large set of MOFs. This allows subsequent experiments to focus only on a small subset of the most promising MOFs. In many instances, however, even molecular simulation becomes prohibitively time consuming, underscoring the need for alternative screening methods, such as machine learning, to precede molecular simulation efforts. In this study, as a proof of concept, we trained a neural network as the first example of a machine learning model capable of predicting full adsorption isotherms of different molecules not included in the training of the model. To achieve this, we trained our neural network only on alchemical species, represented only by their geometry and force field parameters, and used this neural network to predict the loadings of real adsorbates. We focused on predicting room temperature adsorption of small (one- and two-atom) molecules relevant to chemical separations. Namely, argon, krypton, xenon, methane, ethane, and nitrogen. However, we also observed surprisingly promising predictions for more complex molecules, whose properties are outside the range spanned by the alchemical adsorbates. Prediction accuracies suitable for large-scale screening were achieved using simple MOF (e.g. geometric properties and chemical moieties), and adsorbate (e.g. forcefield parameters and geometry) descriptors. Our results illustrate a new philosophy of training that opens the path towards development of machine learning models that can predict the adsorption loading of any new adsorbate at any new operating conditions in any new MOF.</div>

scholarly journals Tagasaste, leucaena and paulownia: three industrial crops for energy and hemicelluloses production

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Alberto Palma ◽  
Javier Mauricio Loaiza ◽  
Manuel J. Díaz ◽  
Juan Carlos García ◽  
Inmaculada Giráldez ◽  
...  
Keyword(s):  
Activation Energy ◽  
Acid Hydrolysis ◽  
Energy Production ◽  
Combustion Process ◽  
Operating Conditions ◽  
Raw Material ◽  
Energy Of Combustion ◽  
Increasing Temperature ◽  
Hydrolysis Of ◽  
Chamaecytisus Proliferus

Abstract Background Burning fast-growing trees for energy production can be an effective alternative to coal combustion. Thus, lignocellulosic material, which can be used to obtain chemicals with a high added value, is highly abundant, easily renewed and usually inexpensive. In this work, hemicellulose extraction by acid hydrolysis of plant biomass from three different crops (Chamaecytisus proliferus, Leucaena diversifolia and Paulownia trihybrid) was modelled and the resulting solid residues were used for energy production. Results The influence of the nature of the lignocellulosic raw material and the operating conditions used to extract the hemicellulose fraction on the heat capacity and activation energy of the subsequent combustion process was examined. The heat power and the activation energy of the combustion process were found to depend markedly on the hemicellulose content of the raw material. Thus, a low content in hemicelluloses resulted in a lower increased energy yield after acid hydrolysis stage. The process was also influenced by the operating conditions of the acid hydrolysis treatment, which increased the gross calorific value (GCV) of the solid residue by 0.6–9.7% relative to the starting material. In addition, the activation energy of combustion of the acid hydrolysis residues from Chamaecytisus proliferus (Tagasaste) and Paulownia trihybrid (Paulownia) was considerably lower than that for the starting materials, the difference increasing with increasing degree of conversion as well as with increasing temperature and acid concentration in the acid hydrolysis. The activation energy of combustion of the solid residues from acid hydrolysis of tagasaste and paulownia decreased markedly with increasing degree of conversion, and also with increasing temperature and acid concentration in the acid hydrolysis treatment. No similar trend was observed in Leucaena diversifolia (Leucaena) owing to its low content in hemicelluloses. Conclusions Acid hydrolysis of tagasaste, leucaena and paulownia provided a valorizable liquor containing a large amount of hemicelluloses and a solid residue with an increased heat power amenable to efficient valorization by combustion. There are many potential applications of the hemicelluloses-rich and lignin-rich fraction, for example as multi-components of bio-based feedstocks for 3D printing, for energy and other value-added chemicals.

scholarly journals Experimental Study on Backflow Patterns Induced by a Bilateral Groin Pair with Different Spacing

2021 ◽  
Vol 11 (4) ◽  
pp. 1486
Author(s):  
Cuiping Kuang ◽  
Yuhua Zheng ◽  
Jie Gu ◽  
Qingping Zou ◽  
Xuejian Han
Keyword(s):  
Cross Sections ◽  
Large Scale ◽  
Recirculation Zone ◽  
Flow Direction ◽  
Wake Flow ◽  
Zone Length ◽  
Array Configuration ◽  
Contraction Ratio ◽  
River Training ◽  
Spanwise Velocity

Groins are one of the popular manmade structures to modify the hydraulic flow and sediment response in river training. The spacing between groins is a critical consideration to balance the channel-depth and the cost of construction, which is generally determined by the backflow formed downstream from groins. A series of experiments were conducted using Particle Image Velocimetry (PIV) to observe the influence of groin spacing on the backflow pattern of two bilateral groins. The spacing between groins has significant effect on the behavior of the large-scale recirculation cell behind groins. The magnitude of the wake flow induced by a groin was similar to that induced by another groin on the other side, but the flow direction is opposite. The spanwise velocity near the groin tip dictates the recirculation zone width behind the groins due to the strong links between the spanwise velocity and the contraction ratio of channel cross-sections between groins. Based on previous studies and present experimental results, quantitative empirical relationships are proposed to calculate the recirculation zone length behind groins alternately placed at different spacing along riverbanks. This study provides better understanding and a robust formula to assess the backflow extent of alternate groins and identify the optimum groins array configuration.

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