3.4.2 Material Interfaces

Using the same concept to that described above for the grain boundary model, one can derive a similar expression for the source function for the material interfaces of a dual-damascene interconnect. A schematic representation of a material interface is shown in Figure 3.4.

Figure 3.4: Interface model.

Since the copper/capping layer and the copper/barrier layer interface act as blocking boundaries for copper diffusion, the flux $\JV_{,2}$ vanishes, so that (3.44) becomes

$$\G = \frac{\JV_{,1}}{\symIntThickness}.$$ (3.55)

Applying (3.46) in the above equation yields an expression similar to (3.52),

$$\G = \ensuremath{\ensuremath{\frac{\partial \Cim}{\partial t}}} =... ...\symIntRelTime}\left[\Ceq-\Cim\left(1+\frac{\symOmR}{\symOmT\CV}\right)\right],$$ (3.56)

but the characteristic generation/annihilation time is now given by

$$\frac{1}{\symIntRelTime} = \frac{\symOmT\CV}{\symIntThickness}.$$ (3.57)

The grain boundary and material interface model presented here is quite general and can be used for every interface of an interconnect structure.