scholarly journals Analytical modeling of reservoir effect on electromigration in Cu interconnects

2007 ◽  
Vol 22 (1) ◽  
pp. 152-156 ◽  
Author(s):  
Zhenghao Gan ◽  
A.M. Gusak ◽  
W. Shao ◽  
Zhong Chen ◽  
S.G. Mhaisalkar ◽  
...  
Keyword(s):  
Analytical Model ◽  
Analytical Modeling ◽  
Interface Energy ◽  
Design Guidelines ◽  
Void Size ◽  
Electrical Field ◽  
Electrical Field Gradient ◽  
Damascene Interconnects ◽  
Extension Length ◽  
Electron Wind

Electromigration (EM) in Cu dual-damascene interconnects with extensions (also described as overhangs or reservoirs) ranging from 0 to 120 nm in the upper metal (M2) was investigated by an analytical model considering the work of electron wind and surface/interface energy. It was found that there exists a critical extension length beyond which increasing extension lengths ceases to prolong electromigration lifetimes. The critical extension length is a function of void size and electrical field gradient. The analytical model agrees very well with existing experimental results. Some design guidelines for electromigration-resistant circuits could be generated by the model.

scholarly journals Cheating at Craps

2021 ◽  
Vol 48 (4) ◽  
pp. 53-61
Author(s):  
Andrea Marin ◽  
Carey Williamson
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Modeling And Simulation ◽  
Analytical Model ◽  
Quantitative Evaluation ◽  
Mathematical Analysis ◽  
Simulation Modeling ◽  
Analytical Modeling ◽  
The World ◽  
Simulation Results

Craps is a simple dice game that is popular in casinos around the world. While the rules for Craps, and its mathematical analysis, are reasonably straightforward, this paper instead focuses on the best ways to cheat at Craps, by using loaded (biased) dice. We use both analytical modeling and simulation modeling to study this intriguing dice game. Our modeling results show that biasing a die away from the value 1 or towards the value 5 lead to the best (and least detectable) cheating strategies, and that modest bias on two loaded dice can increase the winning probability above 50%. Our Monte Carlo simulation results provide validation for our analytical model, and also facilitate the quantitative evaluation of other scenarios, such as heterogeneous or correlated dice.

scholarly journals Fatal Void Size Comparisons in Via-Below and Via-Above Cu Dual-Damascene Interconnects

2004 ◽  
Vol 812 ◽  
Author(s):  
Z. -S. Choi ◽  
C. L. Gan ◽  
F. Wei ◽  
C. V. Thompson ◽  
J. H. Lee ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Failure Mechanisms ◽  
Simulation Tool ◽  
Void Size ◽  
Dual Damascene ◽  
Preferential Nucleation ◽  
Failure Correlation ◽  
Void Volumes ◽  
Damascene Interconnects ◽  
Critical Void

AbstractThe median-times-to-failure (t50's) for straight dual-damascene via-terminated copper interconnect structures, tested under the same conditions, depend on whether the vias connect down to underlaying leads (metal 2, M2, or via-below structures) or connect up to overlaying leads (metal 1, M1, or via-above structures). Experimental results for a variety of line lengths, widths, and numbers of vias show higher t50's for M2 structures than for analogous M1 structures. It has been shown that despite this asymmetry in lifetimes, the electromigration drift velocity is the same for these two types of structures, suggesting that fatal void volumes are different in these two cases. A numerical simulation tool based on the Korhonen model has been developed and used to simulate the conditions for void growth and correlate fatal void sizes with lifetimes. These simulations suggest that the average fatal void size for M2 structures is more than twice the size of that of M1 structures. This result supports an earlier suggestion that preferential nucleation at the Cu/Si3N4 interface in both M1 and M2 structures leads to different fatal void sizes, because larger voids are required to span the line thickness in M2 structures while smaller voids below the base of vias can cause failures in M1 structures. However, it is also found that the fatal void sizes corresponding to the shortest-times-to-failure (STTF's) are similar for M1 and M2, suggesting that the voids that lead to the shortest lifetimes occur at or in the vias in both cases, where a void need only span the via to cause failure. Correlation of lifetimes and critical void volumes provides a useful tool for distinguishing failure mechanisms.

scholarly journals Laboratory-Scale Evidence for Lightning-Mediated Gene Transfer in Soil

2001 ◽  
Vol 67 (8) ◽  
pp. 3440-3444 ◽  
Author(s):  
Sandrine Demanèche ◽  
Franck Bertolla ◽  
François Buret ◽  
Renaud Nalin ◽  
Alain Sailland ◽  
...  
Keyword(s):  
Escherichia Coli ◽  
Laboratory Scale ◽  
Electrical Field ◽  
Antibiotic Resistant ◽  
Electrical Fields ◽  
Bacterial Membranes ◽  
Naked Dna ◽  
Electrical Field Gradient ◽  
Lightning Discharges ◽  
Storm Cloud

ABSTRACT Electrical fields and current can permeabilize bacterial membranes, allowing for the penetration of naked DNA. Given that the environment is subjected to regular thunderstorms and lightning discharges that induce enormous electrical perturbations, the possibility of natural electrotransformation of bacteria was investigated. We demonstrated with soil microcosm experiments that the transformation of added bacteria could be increased locally via lightning-mediated current injection. The incorporation of three genes coding for antibiotic resistance (plasmid pBR328) into the Escherichia coli strain DH10B recipient previously added to soil was observed only after the soil had been subjected to laboratory-scale lightning. Laboratory-scale lightning had an electrical field gradient (700 versus 600 kV m−1) and current density (2.5 versus 12.6 kA m−2) similar to those of full-scale lightning. Controls handled identically except for not being subjected to lightning produced no detectable antibiotic-resistant clones. In addition, simulated storm cloud electrical fields (in the absence of current) did not produce detectable clones (transformation detection limit, 10−9). Natural electrotransformation might be a mechanism involved in bacterial evolution.

scholarly journals Natural Electrotransformation of Lightning-Competent Pseudomonas sp. Strain N3 in Artificial Soil Microcosms

2006 ◽  
Vol 72 (4) ◽  
pp. 2385-2389 ◽  
Author(s):  
Hélène Cérémonie ◽  
François Buret ◽  
Pascal Simonet ◽  
Timothy M. Vogel
Keyword(s):  
Gene Transfer ◽  
Horizontal Gene Transfer ◽  
Residence Time ◽  
Lightning Strike ◽  
Pseudomonas Sp ◽  
Electrical Field ◽  
Soil Microcosms ◽  
Electrical Fields ◽  
Cell Lysate ◽  
Electrical Field Gradient

ABSTRACT The lightning-competent Pseudomonas sp. strain N3, recently isolated from soil, has been used to study the extent of natural electrotransformation (NET) or lightning transformation as a horizontal gene transfer mechanism in soil. The variation of electrical fields applied to the soil with a laboratory-scale lightning system provides an estimate of the volume of soil affected by NET. Based on the range of the electric field that induces NET of Pseudomonas strain N3, the volume of soil, where NET could occur, ranges from 2 to 950 m3 per lightning strike. The influence of DNA parameters (amount, size, and purity) and DNA soil residence time were also investigated. NET frequencies (electrotransformants/recipient cells) ranged from 10−8 for cell lysate after 1 day of residence in soil to 4 × 10−7 with a purified plasmid added immediately before the lightning. The electrical field gradient (in kilovolts per cm) also played a role as NET frequencies ranging from 1 × 10−5 at 2.3 kV/cm to 1.7 × 10−4 at 6.5 kV/cm.

Characterization of Photochemically or Electrochemically Reduced Blue Titanium Dioxide

1990 ◽  
Vol 45 (6) ◽  
pp. 864-870 ◽  
Author(s):  
R. P. Muller ◽  
J. Steinle ◽  
H. P. Boehm
Keyword(s):  
Titanium Dioxide ◽  
Dynamic Equilibrium ◽  
Inert Gases ◽  
Blue Colour ◽  
Electrical Field ◽  
Trapped Electrons ◽  
Surface Sites ◽  
Electrical Field Gradient ◽  
Reduced Surface

Blue TiO2 which is formed under UV irradiation under inert gases in the presence of hole scavengers is characterized. The concentration of surface-trapped electrons which cause the blue colour was analytically determined after irradiation in the presence of methanol or other organic compounds. The saturation concentration is controlled by a dynamic equilibrium of photoreduction and reoxidation of the reduced surface sites which leads to H2 formation. The blue colour can also be produced by chemical or electrochemical reduction. Mobility of the surface-trapped electrons in an electrical field gradient is demonstrated. The reduced TiO2 is similar to a hydrogen titanium bronze.

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