Thermal-Electric Transient analysis for Metal Line under High Frequency Pulse Direct Current

Abstract

Temperature is one of the most sensitive factors for device and interconnects reliability, especially for Electromigration (EM). A 5°C temperature rise in metal line will induce a 30% EM lifetime decrease [1]. In order to achieve good EM lifetime, Root Mean Square of current (Irms) rule was designed to limit interconnects temperature rise induced by self-heating. Peak current (Ipeak) rule was also designed to prevent sudden temperature rise caused by instantaneous high current. Previous study reported [2] a high frequency pulse current (PDC) resulted in lower joule heating (JH) compared to an equivalent steady state condition. However, the effect of very high frequency (1GHz~1THz) with various duty ratios is still unclear. In this paper, both experimental measurement and finite element method (FEM) simulation approach were used to investigate the impact of temperature rise due to JH by high frequency PDC with various duty ratios. Special thermal test macros using 64nm pitch double patterning LELE technology have been implemented to study frequency and duty ratio effects on JH. Metal width effect was investigated as well. A waveform generator measurement unit was used to measure the resistance profile under different frequency waves. Temperature change was estimated using the temperature coefficient of resistance (TCR). Finite Element Model (FEM) was built based on process assumption, metal width and via profile which were verified by cross section measurement. The FEM model was validated by experimental data in intermediate frequency range, and then used to study very high frequency situation, which cannot be handled by experiment. It was found that high frequency can suppressed Joule heating in metal line. But it also limited metal line to cooling down when power is off. For very high frequency PDC, peak/bottom temperatures approach constant temperature, which is frequency independent. This constant temperature can be determined from steady state thermal model. Reducing duty ratio can control device turn on time thereby reducing peak and average temperature.