3.7 Interconnect Reliability

To estimate the life time of electronic products, several different characteristic quantities have to be extracted. However, the estimation has still a considerable variance because this measure evaluates the worst case only. The goal is to obtain the mean time to failure (MTTF) for standard operation conditions by extrapolations based on data of MTTF for elevated temperatures. To enforce a change of material properties, it requires a certain amount of external energy to cause harm to the device structure, if the energy exceeds a critical level.

The worst case for interconnect lines is a direct current, where the maximum of the electrical current density $J_{\mathrm{PEAK}}$ of a certain interconnect element is given by the approximation

$$\mathop{\mathrm{sup}}\big(\displaystyle J(\partial \mathcal{V})\big) {=} J_{\mathrm{PEAK}} \approx \frac{I_{\mathrm{PEAK}}}{A}.$$ (3.27)

Here, the maximum current density is estimated as the maximum of the expected current $I_{\mathrm{PEAK}}$ through the interconnect divided by the local area $A$ of the interconnect. The advantage of this approximation is that the peak value of the electrical current can be measured and verified for worst-case considerations. Other characteristic quantities are the mean value and the root mean square value of the current density $J$

$${\mathbf{{J}}}_{\mathrm{AVG}} {=}{\langle{{\mathbf{{J}}}}\rangle} {=}{\frac{1}{T}} \displaystyle \int^{T}_0{{\mathbf{{J}}}(t)} dt,$$ (3.28)

$$J_{\mathrm{RMS}} {=}\sqrt{{\langle{\vert{\mathbf{{J}}}\vert^2}\ra... ...sqrt{{\frac{1}{T}} \displaystyle \int^{T}_0{\vert{\mathbf{{J}}}(t)\vert^2} dt},$$ (3.29)

respectively. Here, the values are averaged over a characteristic time span, for instance a full period for oscillating signals.

There exist several additional constraints which affect the reliability of interconnect structures, such as the maximum allowed electric field for dielectric break down or the minium resistivity of the dielectric to limit leakage currents between different interconnect structures. However, these constraints are currently not of high interest because these requirements are just certain constraints of process technology nodes and can be taken into account in advance during the design phase.