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Statistical Experimental Design and Analysis<br />

Example of Experiment Design<br />

.PARAMDEX<br />

+ DL NOISE/SIG=2.5<br />

+ DW NOISE/SIG=2.5<br />

+ TOX NOISE/SIG=2.5<br />

+ VFB NOISE/SIG=2.5<br />

Note that these statements are equivalent to the following:<br />

.PARAMDEX<br />

+ P(DL) NOISE/SIG=2.5<br />

+ P(DW) NOISE/SIG=2.5<br />

+ P(VFB) NOISE/SIG=2.5<br />

+ P(TOX) NOISE/SIG=2.5<br />

Specifying Model Parameter Selectors<br />

The following example illustrates the use of the constructs M(.,.) and EM(.,.) with the inter and<br />

intra variations. The use of M(.,) is not very useful in this case but we will assume that the<br />

statistical variations were stated as follows:<br />

.PARAM TOX=0.015<br />

.MCMOD NCH TOX LOT/GAUSS=0.0003<br />

.MCMOD PCH TOX LOT/GAUSS=0.0003<br />

There are two independent random variables TOX associated with the PMOS and NMOS<br />

transistor. Two PMOS, or respectively two NMOS, transistors are assumed to be perfectly<br />

tracking each other, but the PMOS and NMOS transistors have independent variations. This is a<br />

very hypothetical situation, since the Oxide Thickness should affect the PMOS and NMOS<br />

transistors in the same way. The associated .PARAMDEX command would be as follows:<br />

.PARAMDEX<br />

+ M(PCH,TOX) SIG=2.5<br />

+ M(NCH,TOX) SIG=2.5<br />

Suppose now we are interested in intra-die variations. The statistical variations can be defined<br />

as follows:<br />

.PARAM TOX=0.015<br />

.MCMOD NCH TOX DEV/GAUSS=0.0003<br />

.MCMOD PCH TOX DEV/GAUSS=0.0003<br />

It follows that the associated .PARAMDEX statements are:<br />

578<br />

Eldo® User's Manual, 15.3

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