An Analytical Transient Joule Heating Model for an Interconnect in a Modern IC: Material Selection (Cu, Co, Ru) and Cooling Strategies
2019 IEEE International Reliability Physics Symposium (IRPS)(2019)
摘要
Front- and backend self-heating have become an important barrier to the sustained increase in processor speed. Indeed, the severity of backend Joule heating with shrinking BEOL features has emerged as a crucial issue for the ICs reliability. In this work, we introduce an analytical transient Joule heating
$\Delta T_{\mathrm{J}}(t))$
model to calculate the self-heating of any wire located at any interconnect level within an IC. Specifically, we (i) propose a closed-form analytical formula to describe
$\Delta T_{\mathrm{J}}(t)$
of an interconnect; (ii) use this formula to develop a SPICE-compatible compact model to predict the temperature distribution for any given circuits/systems; (iii) validate the model by experiments as well as finite element method (FEM) simulation; (iv) compare and validate
$\Delta T_{\mathrm{J}}$
of different interconnect materials (e.g., Cu, Co, and Ru) as well as effectiveness of various cooling strategies (e.g., dummy vias, and larger wires), and finally (v) predict reliability of interconnects under various operating conditions. Our work demonstrates that Co can replace Cu for the lower BEOL levels (e.g., M1-M3) due to its superior reliability. However, excessive self-heating in Co makes Cu still a preferred option for the higher BEOL levels (M5-M10).
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关键词
closed form analytical model,compact transient thermal modeling,Joule-heating modeling,finite element method simulation,reliability,electromigration
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