Efficient Process Variation Characterization by Virtual Probe
In this chapter, we propose a new technique, referred to as virtual probe (VP), to efficiently measure, characterize, and monitor spatially correlated inter-die and/or intra-die variations in nanoscale manufacturing process. VP exploits recent breakthroughs in compressed sensing to accurately predict spatial variations from an exceptionally small set of measurement data, thereby reducing the cost of silicon characterization. By exploring the underlying sparse pattern in spatial frequency domain, VP achieves substantially lower sampling frequency than the well-known Nyquist rate. In addition, VP is formulated as a linear programming problem and, therefore, can be solved both robustly and efficiently. Our industrial measurement data demonstrate the superior accuracy of VP over several traditional methods including two-dimensional interpolation, Kriging prediction, and k-LSE estimation.
