Local Variability Evaluation on Effective Channel Length Extracted With Shift-and-Ratio Method

In this study, the local variation of the effective channel reduction parameter (ΔL = L
_m
- L
_eff
) of a MOSFET is extracted by means of the traditional shift-and-ratio (SAR) method. AL is then correlated with the threshold voltage difference (AVTH) between the device under test (DUT) and the reference device. It is demonstrated that there exists an optimal VG range for extracting reliable values of AL through the SAR method. Statistical data analysis shows that for R ≈ (L
_long
/L
_short
) ≈ 25, better results are achieved since the value of σ (ΔL) varies typically as the reciprocal 1/√( W). The test structure used in this work is a Kelvin-based 2-D addressable MOSFET matrix implemented in 180-nm bulk CMOS technology. The sample space is of 2304 devices divided into nine subgroups of 256 same size closely placed nMOSFETs.