An IC manufacturing yield model considering intra-die variations

Abstract

In deep submicron feature sizes continue to shrink aggressively beyond the natural capabilities of the 193 nm lithography used to produce those features thanks to all the innovations in the field of resolution enhancement techniques (RET). With reduced feature sizes and tighter pitches die level variations become an increasingly dominant factor in determining manufacturing yield. Thus a prediction of designspecific features that impact intra-die variability and correspondingly its yield is extremely valuable as it allows for altering such features in a manner that reduces intra-die variability and improves yield. In this paper, a manufacturing yield model which takes into account both physical layout features and manufacturing fluctuations is proposed. The intra-die systematic variations are evaluated using a physicsbased model as a function of a design's physical layout. The random variations and their across-die spatial correlations are obtained from data harvested from manufactured test structures. An efficient algorithm is proposed to reduce the order of the numerical integration in the yield model. The model can be used to (i) predict manufacturing yields at the design stage and (ii) enhance the layout of a design for higher manufacturing yield.

Handling partial correlations in yield prediction

“…Experiments are performed on large testcases, each of which has 360K variation locations. Compared to [2], which is the only previous work to the best of our knowledge, the OPCA based method can reduce the error on yield estimation from 17.1% − 21.1% to 1.3% − 2.8% with 4.6× speedup. The HAQ technique can reduce the error to 4.1% − 5.6% with 6 × −9.4× speedup.…”

“…The variation and yield models in this work are based on the case of metal thickness like in [2]. With small modifications, they can be applied to other cases, such as sequential timing yield.…”

“…This model is applicable to either manufacturing variations or parametric variations. For example, if the m random variables represent metal thickness, this model can predict CMP (Chemical-Mechanical Planarization) yield [2]. As pointed out by previous research works, after the CMP procedure, metal thickness may have systematic variations depending on layout patterns and random variations due to CMP process fluctuations [3].…”

“…For instance, [2] clustered the random variables according to spatial proximity and treat the variables within each cluster as perfectly correlated. Then, it managed to reduce the problem dimension to the number of clusters.…”

“…The first one is based on Orthogonal Principle Component Analysis (OPCA), which is a more formal treatment to partial correlations compared to the clustering based method [2]. The second one is a hierarchical adaptive quadrisection (HAQ) technique which can form heterogeneous cluster sizes according to systematic variations.…”