The name is absent

silicon optimization necessary. When there is no variation or variations are
very small, the designer can predict the behavior of the circuit with small
uncertainty. However, in the modern fabrication process, even considering
statistical characteristics of the process variation might not be enough. Op-
timizations after manufacturing (post-silicon) can improve efficiency of the
IC dramatically [34,52,70,71].

Tschanz et al. [71] used bidirectional adaptive body bias to mitigate effects
of the intra-die and inter-die variations on the circuits. They have consid-
ered frequency-leakage optimization in which the designer should optimize
the circuit for the maximum frequency while it meets a number of leakage
constraints. They vary the body bias to change the threshold voltage of
the transistors in the circuit. If variations reduce the operating frequency
then the threshold voltage should be decreased. If variations increase the
leakage current then the threshold voltage should be increased. Thus, by
increasing or decreasing the body bias, one can adjust the manufactured
ICs to meet the frequency and leakage constraints. To mitigate the inter-die
variation, they suggest optimizing the supply voltage based on the variation
realization in each IC. Intra-die variations can be also handled using differ-
ent reference voltages in different parts of the IC. They need an estimation
of variations to optimize each circuit separately. Our method can efficiently
provide them the estimation.

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