The mask 3D effect on 2D pattern process window, positive focus shift, or negative focus shift? A simulation study

Mask 3D effect has been studied in the past and the main characteristic of it is that it will cause positive focus shift to the semi-dense patterns at pitches of 200 and 300 nm for as much as 20-30 nm when a 6% attenuated phase shifting mask (PSM) is used. This has been verified for quite some time until recently, we have found an evidence that it may not be true in case of more complicated two-dimensional (2D) structures, such as trench-end-to-trench patterns. In these structures, there is a perpendicularly oriented trench relative to an array of trench ends that are pointing toward it at each side, or there are two perpendicular arrays of trench ends pointing toward the single trench at each side. We have done a finite-difference time-domain (FD-TD) simulation study on the trench ends for a dense pitch of 90 nm through the semi-dense pitch of 200 nm; we found that the focus shift for the linewidth of the array trench ends is toward positive direction while the focus shift of the single perpendicularly oriented trench carries the negative sign. Such opposite best focus shift can impact common process window in the depth of focus for the already critical photolithographic process for both 28 nm, 20 nm, and the 14 nm technology nodes. The impact become less and less as the trench width increases and the pitch increases. We have compared our simulation results with wafer data and a good agreement is obtained. Though the mechanism is not understood at this moment, we will try to provide an explanation.