Temperature-Dependent Resistance Model for Cu-Alloy Wires

N. Lu, R. Wachnik
IBM,
United States

Keywords: interconnect, wire resistance model, modeling of temperature coefficient of resistance, CuMn

Summary:

To improve the reliability (electromigration lifetime, etc.) of interconnect in advanced nodes of semiconductor technology, doping Cu wires with impurities (e.g., Mn, Al, Ag, or Ti) using an alloy seed layer has been introduced into BEOL in semiconductor technologies since 32nm technology node. While dramatically improving the reliability of Cu wires, there is a modest increase in Cu wire resistance with the addition of an alloy seed layer when compared with pure Cu with a same cross-sectional area (i.e., at a same wire capacitance). The room temperature behavior of Cu wires with an alloy seed layer has been extensively studied and reported. In general, the more the amount of alloy in a Cu wire, the larger the resistance increase. On the other hand, the temperature coefficient of resistance for Cu wires with an alloy seed layer has been less reported. The modeling of the temperature coefficient of resistance for Cu wires with an alloy seed layer has received even less attention in the literature. In SPICE models and parasitic extraction (PEX) tools from semiconductor foundries, there is a tendency to naturally combine (a) an existing resistance mode for pure Cu wires at all temperatures and (b) a characterization of Cu-alloy wire resistance at a room temperature to arrive at a resistance model for Cu-alloy at all temperatures. Such a natural generalization, unfortunately, may not yield a highly accurate resistance model for Cu-alloy wires. In this paper, we study the temperature coefficient of resistance for Cu wires with an alloy seed layer. We report both measured silicon data for CuMn wires ranging from -35C to 115C and a more accurate resistance model for Cu-alloy wires for all temperatures. Our new resistance model for Cu-alloy wires improves the accuracy of the model when compared to measured hardware data. The degree of improvement is obvious when the amount of Mn used is relatively large. It is worth noting that our new Cu-alloy wire resistance model also naturally combines (a) the same resistance mode for pure Cu wires at all temperatures and (b) the same characterization of Cu-alloy wire resistance at the room temperature but to arrive at a different model for Cu-alloy resistance at all temperatures. Also, our new Cu-alloy resistance model do not introduce any new fitting parameters.