$[3]$ Hall effect measurement can be applied to the semiconductors for determination of the sheet conductivity and extraction of the carrier types, concentrations, and mobility. $($a$)$ Do an extensive verification to explain if the Hall effect measurement can be applied to nanoscale devices with both major and minority carriers transport at near the surface in quantum well at atomic scale $?$ If$,$ yes, how to do $?($b$)$ Propose new methods other than Hall effect measurement to extract the carriers concentration and mobility for major carriers in accumulation layer and minority carriers in the inversion layer, which always exist simultaneously in the nanoscale CMOS devices with short channel and narrow width at below $100$ nm $(\backslash (\backslash$mathrm$\{$L$\}<mn>1</mn><mn>0</mn><mn>0</mn><mtext></mtext><mi>\backslash </mi>$mathrm$\{$~nm$\},\backslash$mathrm$\{$~W$\}<mn>1</mn><mn>0</mn><mn>0</mn><mtext></mtext><mi>\backslash </mi>$mathrm$\{$~nm$\}\backslash )).$ Describe the details of test structures design, measurement $($I$-$V$,$ C$-$V$,$ and high frequency$),$ extraction methods and fundamental theory $($cited references$).(30\backslash \%)$