variation sparsity in the power framework.
3.3.2 Regular grid tomography
First, we assume that the logic gates are located on a regular T × R grid on
the chip. The matrix of process variation on the regular grid is denoted by
H = {hStt}s=i...T,t=i...R, where hs,t is variation of the gate located in the (s, t)-th
point of the grid. We stack all the elements of the matrix H in a long column
vector d. Assume W is the transformation matrix for a wavelet in which variation
vector d is sparse. Let
s = Wd; (3.6)
then, s is a sparse vector.
Using the wavelet basis to model the spatial correlation of the process varia-
tion, Equation 3.4 becomes
p = Ad + e = AW1s + e. (3.7)
The sparse s can be recovered using the optimization in Equation 2.4:
min ∣∣s∣∣ι + Λ∣∣AW1s — y∣∣2∙ (3.8)
The process variation d is then recovered using d = Ws.
32
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