Blech [75,76,77] designed an experiment where conductor islands were deposited onto a titanium nitride (TiN) film and stressed at a high current density. As the conductor resistivity was much lower than that of the TiN layer, the conductor stripe would carry most of the current and the resulting movement of the ends of the stripe could be measured. In this way, the electromigration induced drift velocity is determined by
Blech observed that only the upstream end (in relation to the electron flow) of the line moved according to (2.22), and that the upstream end stopped moving, when the stripe was reduced to a certain length. Also, he observed that no drift could be detected below a threshold current density.
These observations can be explained by considering the flux due to electromigration and the gradient of the chemical potential via a gradient of mechanical stress [75,76,77,78] according to
Integrating (2.24) over the length of the interconnect line yields
Given that the maximum stress the conductor line can withstand is , a critical product for electromigration failure can be stated as
From the above expression, for a given current density, , a critical line length can be determined, so that shorter lines will not fail due to electromigration. This is known as ``Blech Length'', given by
An important consequence of the Blech effect is that the product during electromigration tests has to be significantly higher than the critical product for the corresponding test structure. Otherwise, the test structure might fail at a later time than it would normally do, giving a false sense of safety . Another point to be mentioned is that the presence of residual stresses from the fabrication process reduces the stress which has to be produced by electromigration in order to reach the maximum value a line can withstand. This results in smaller values for the Blech length and for the maximum operating current density than that given by (2.27) and (2.28), respectively .