You've left out a lot of detail needed to help answer your question.

I'm assuming you are doing thermal oxide in silicon over a doped region
as the conductor. In this case, the surrounding silicon to the doped
region will have a substantial effect, depending on how highly doped it
is in the first place. There will be charge leakage through that
silicon, unless you form a p-n diode and reverse bias it - in which case
bipolar operation is out.

You don't indicate where the membrane is in relation to all this and how
it is driven.

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Tom Rust
Nanochip Inc