= Top-gate density tuning
{title2=$\Delta n_s=\epsilon\Delta V_g/(ed)$}
A gate separated by <dielectric> thickness $d$ has geometric <capacitance> per area $C/A=\epsilon/d$ in the parallel-plate approximation. An electron-density change is $\Delta n_s=(\epsilon/ed)\Delta V_g$ with the stated polarity/reference convention. Fringing, trapped charge, depletion and finite <quantum capacitance> can modify the relation. An absolute gate voltage additionally requires the zero-density offset or another calibration.
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