5.1 Material and Simulation Parameters

The following simulations are focused on contemporary copper dual-damascene interconnect structures of the 65 nm and 45 nm technology nodes. The typical materials used in such interconnects are: copper (Cu) as conductor metal, tantalum based (TaN/Ta) barrier layers at the bottom and sides of the lines, silicon nitride based (SiN/SiCN) capping layers, and low-k interlevel dielectrics, such as SiCOH.

The tables below present the materials' parameters for the electro-thermal, vacancy dynamics and mechanical deformation problem. These parameters were chosen from the recent literature, where they were obtained either by experimental or theoretical studies. Since electromigration just takes place in the conductor line, the parameters related to the material transport equations are presented for copper only.

Electromigration experiments are carried out under accelerated test conditions, which means that the interconnect lines are normally tested at a higher current density and at a higher temperature than that found at use conditions. Therefore, the simulation results presented in the following sections follow this trend, and were obtained for a current density of 2 MA/cm$^2$ and temperature of 300 $^\circ$C, unless otherwise stated.

Table 5.1: Parameters of the electro-thermal equations.

Parameter	Cu	Ta	SiN	SiCOH	Reference
$\gamma_{E0}$ ($\Omega$m)	$4.0\times10^7$	$3.3\times10^5$	-	-	[81]
$\alpha_{E}$ (K$^{-1}$)	0.0043	0	0	0	[157]
$\beta_{E}$ (K$^{-2}$)	0	0	0	0	-
$\gamma_{T0}$ (W/mK)	379	53.65	0.8	0.35	[158,12]
$\alpha_{T}$ (K$^{-1}$)	0	0	0	0	-
$\beta_{T}$ (K$^{-2}$)	0	0	0	0	-
$\symMatDens$ (kg/m$^3$)	8920	16690	3100	2200	[158,12]
$\symSpecHeat$ (J/kgK)	385	140.15	170	1000	[158,12]

Table 5.2: Parameters of the mechanical equations.

Parameter	Cu	Ta	SiN	SiCOH	Reference
$\symYoungMod$ (GPa)	130	186	265	9.2	[97,12]
$\symPoissonRatio$	0.34	0.35	0.27	0.16	[158]
$\symThermExp$ (K$^{-1}$)	$16.5\times10^{-6}$	$6.50\times10^{-6}$	$1.50\times10^{-6}$	$0.68\times10^{-6}$	[158]

Table 5.3: Parameters of the vacancy dynamics equations.

Parameter	Cu	Reference
$\DVo$ (cm$^2$/s)	0.52	[97]
$\Ea$ (eV)	0.89	[159]
$\Z$	-5.0	[67]
$\Q$ (J)	$1.2\times 10^{-20}$	-
$\symVacRelFactor$	0.4	-
$\symAtomVol$ (cm$^{3}$)	$1.18\times 10^{-23}$	-
$\Co$ (cm$^{-3}$)	$1.0\times 10^{16}$	-
$\symVacRelTime$ (s)	1.0	[97]

Table 5.4: Simulation conditions.

Parameter	Value
$\symCurrDens$ (MA/cm$^2$)	2.0
$\T$ ($^\circ$C)	300