b) Give two reasons for this choice. [4 c)Which is more likely to be used for global interconnects? [2] d) Give two reasons for this choice. 4 2. a) Tungsten more likely for local or interlevel interconnects b) local interconnects lengths are short so higher resistivity of w is less of a problem, and high melting temperature of w means it can withstand subsequent processing steps c)Copper more likely used for global interconnects d) lower resisitivity, it cannot withstand higher temperatures of earlier steps but acceptable later in processing 3. Two global interconnects are fabricated to be 0.25 microns in both thickness and width. They are made of a metal having a resistivity of 2 micro-Ohm-cm. They are parallel to each other over a length of 5 mm and their nearest sides are separated by 0.5 microns filled with SiO, (relative dielectric constant, K=4).[13 a) What is the resistance of each of these two independent lines? [5] b) What is their relative capacitance ( ignore interactions with other lines)?[41 c) what is the resulting rc time constant? 4 3.a)R=pLA=5x103/{0.252x101}=160092 b)C=kEAd=0.25X10°X5X10/{0.5×10°}=885X104F )RC=1.42×10 Reliability [15] 4. a) Your company has developed a new chip fab line having 20 independent processes: 10 of them with a yield of 97%o each and 10 with a yield of 96% each. Your estimated break-even yield is 60%. If you were to go into production now, would you expect to make a profit? [31 b)Would electromigration be more of a problem with tungsten or aluminum interconnects? Why? 31 c)You need to double the current density in a given interconnect. Would your problems with electromigration double or could things be much worse? Explain. [4] d) Briefly explain how grain boundaries play a role in hillock and/or void formation in interconnects. 5 4. a)No profit. Your yield will be about 44%(0.97 x0.95) b) Electromigration is more of a problem with Al because of its smaller mass relative W, even though W may have a higher resistivity c)Doubling the current density would result in a very large increase in electromigration by increasing the temperature, which is in the exponential of the grain boundary diffusion term. Increasing resistivity with increasing temperature is also a valid factor d) Hillocks and voids form at point along a conductor where electromigration flux converges or diverges. respectively. Hence hillocks are more likely where more grain2 b) Give two reasons for this choice. [4] c) Which is more likely to be used for global interconnects? [2] d) Give two reasons for this choice. [4] 2. a) Tungsten more likely for local or interlevel interconnects. b) local interconnects lengths are short so higher resistivity of W is less of a problem, and high melting temperature of W means it can withstand subsequent processing steps. c) Copper more likely used for global interconnects. d) lower resisitivity, it cannot withstand higher temperatures of earlier steps but is acceptable later in processing. 3. Two global interconnects are fabricated to be 0.25 microns in both thickness and width. They are made of a metal having a resistivity of 2 micro-Ohm-cm. They are parallel to each other over a length of 5 mm and their nearest sides are separated by 0.5 microns filled with SiO2 (relative dielectric constant, k = 4). [13] a) What is the resistance of each of these two independent lines? [5] b) What is their relative capacitance (ignore interactions with other lines)? [4] c) What is the resulting RC time constant? [4] 3. a) R = rL/A =5 x 10-3/{0.252 x 10-12} = 1600 W. b) C = ke0A/d =0.25 x 10-6 x 5 x 10-3/{0.5 x 10-6} = 8.85 x 10-14 F c) RC = 1.42 x 10-10 s. Reliability [15] 4. a) Your company has developed a new chip fab line having 20 independent processes; 10 of them with a yield of 97% each and 10 with a yield of 96% each. Your estimated break-even yield is 60%. If you were to go into production now, would you expect to make a profit? [3] b) Would electromigration be more of a problem with tungsten or aluminum interconnects? Why? [3] c) You need to double the current density in a given interconnect. Would your problems with electromigration double or could things be much worse? Explain. [4] d) Briefly explain how grain boundaries play a role in hillock and/or void formation in interconnects. [5] 4. a) No profit. Your yield will be about 44% (0.9710 x 0.9510). b) Electromigration is more of a problem with Al because of its smaller mass relative to W, even though W may have a higher resistivity. c) Doubling the current density would result in a very large increase in electromigration by increasing the temperature, which is in the exponential of the grain boundary diffusion term. Increasing resistivity with increasing temperature is also a valid factor. d) Hillocks and voids form at point along a conductor where electromigration flux converges or diverges, respectively. Hence hillocks are more likely where more grain