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If the probes are calibrated, you can measure anything that does not generate much heat (because the wafer has no heat sink).
What is measured is wide open. One thing that is done is to check for functionality. If some errors were made in the processing that generated shorts or that made the small signal parameters way off, it is not economical to continue with the manufacturing process of the parts on the wafer being put into packages.
-- Typically measuring S-parameters at several bias conditions to see how the amp performs (gain, VSWR). On-wafer testing is sometimes tricky due to the lack of optimum DC bias decoupling circuits required for stable operation of MMIC. Typically, on-wafer testing of high-power MMICs do not show MMICs best performance due to channel temperatures increasing b/c of the lack of a proper heat sink (not a good thermal conduction path to the prober chuck).
DC Characterization --
-- simply recording ID vs VG in some cases at several input power levels AND across a temperature range.
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