Nonlinear effects

You can account for nonlinear effects when assessing the value of scan compression.

Chris Allsup, Synopsys -- Test & Measurement World, 6/1/2006

The linear relation for area A(x) described by equation 6 in the accompanying article ('Limits of test time reduction') is accurate if the number of gates added per scan chain remains constant with increasing compression. The silicon area overhead for some compression architectures, however, may increase disproportionately with higher compression levels. In addition, increasing the number of scan chains tends to increase the amount of wire routing congestion in designs, which may contribute to a further increase in area at higher compression levels.

This nonlinear increase in compression area is illustrated in Figure A, where A(x) is represented by:

     (a)

where æ is a second-order area scaling coefficient.

Figure A. Effect of nonlinear increase in compression area is illustrated here.

The nonlinear increase in silicon area tends to offset the benefits of higher compression. Figure B compares ë for different die areas based on the linear relation for area (equation 6) and the nonlinear relation (equation a).

Figure B. Shown here are the effects of a nonlinear increase in compression area on optimal compression level for different die areas A0.

Initial compression area overhead

The linear relation for compression area does not describe some compression architectures that require an initial fixed amount of circuitry even for very small compression levels. All other factors being equal, the effect of this fixed area overhead is an increase in total cost across all compression levels. In this situation, it is useful to modify equation 6 to include this fixed area overhead A_F:

     (b)

In some architectures, the high initial area overhead for compression circuits can lead to a relatively lower unit increase in silicon area overhead as compression is increased, compared with implementations in which A_F = 0. Figure C compares two hypothetical scan compression types, SC₁ and SC₂, where A_F1 = 0.008 cm², A_F2 = 0, and ã₂/ã₁ = 1.25. The minimum total costs are measured at their optimal ë values. SC₂ has a net cost advantage over SC₁ that is greatest for A₀ = 2.0 cm².

Figure C. Cost difference per 1 million units for two compression types, SC1 and SC2, are illustrated here, where AF1 = 0.008cm2 and AF2 = 0.

Formulas for ë and Ä_cost that account for the effect of significant initial compression area overhead are obtained by replacing A₀ with A₀ + A_F in equations 16 and 17:

     (c)

     (d)

You can compare two different types of implementations as presented in Figure C—one with an initial fixed area overhead for compression, and one without—by comparing the total costs using equation 12 directly:

 (e)

The difference in total cost Ä_cost is determined by first substituting A_F1 and ã₁ into equation e to reflect the cost of the fixed area overhead implementation, then substituting A_F2 = 0 and ã₂ in equation e to reflect the cost of the second implementation. Ä_cost is obtained by subtracting the two total costs at the ë values calculated from equation c.

Back to "Limits of test time reduction."

Also see: "Optimizing compression in scan-based ATPG DFT implementations"