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What is the most common way of extracting the flatband and threshold voltage of a MOS capacitor in Silvaco? (Either using the C-V measurement capability or not)
You can extract a CV curve using ATLAS and sweeping the voltage and defining the steps. You could then consider plotting 1/C^2 vs voltage to extract the threshold voltage.
Alternatively both ATLAS and ATHENA allow you to extract the VT voltage directly, which you could also conduct for comparison.
Finally, I assume you have calculated the analytical value for VT to check all three are in close agreement.
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