# Area and Delay Penalties in Restructurable Wafer-Scale Arrays

## Abstract

The penalties for restructuring wafer-scale arrays for yield enhancement are assessed. Each element of the fabricated array is assumed to be defective with independent probability *p*. A fixed fraction *R* of the elements are to be connected into a prespecified defect-free configuration by means of switched interconnections. The area penalty is determined by the required number of tracks per wiring channel *t*. Propagation delay is determined by the required maximum connection length *d*. It is shown that: Connection of *RN* fixed I/O ports to distinct nondefective elements from an *N*-element linear array requires *d*, *t* =θ(log*N*); Connection of *RN* pairs of elements from two *N*-element linear arrays requires only constant *d* and *t*; Connection of a chain of *RN* ^{2} elements from an *N*×*N* array also requires only constant *d* and *t*; Connection of a \(\sqrt R N \times \sqrt R N\) lattice from an *N*×*N* array requires \(d = \Omega (\sqrt {\log N} )\). Constant *t* suffices to connect a lattice if *d*=θ(log*N*). Algorithms are presented that connect any fraction *R* < l-*p* of the elements with probability approaching one as *N* increases. It appears that these results hold even under actual defect distributions.

### Keywords

Hexagonal Expense Tral Percolate Active Element## Preview

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