Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2021 / Paper 2 / Section A(ii) / 15 / ii / Solution

Assume the usual one-lead-biased measurement, $V_s=V_{sd}$ with drain grounded and the gate referred to that ground; the printed map does not separately specify the wiring. This assumption is needed to assign individual source/drain capacitances. In this Coulomb diamond capacitance extraction, the smaller zero-bias gate intervals are 5 mV wide. In the constant interaction model with no orbital gap between those additions,An upper diamond tip lies at gate 123.75 mV between the zero-bias vertices 120 and 125 mV and at bias 2.50 mV. Its positive and negative edge slopes are therefore $s_{+}=2.50/3.75=2/3$ and $s_{-}=-2.50/1.25=-2$. Reservoir alignment givesThe gate capacitance is not negligible in the second denominator. ConsequentlyThe consistency check is $e^2/C_{\Sigma }=2.50\mathrm{meV}$, matching the smaller tip's bias energy. The conventional electrostatic charging energy $E_C=e^2/(2C_{\Sigma })$ is 1.25 meV; it is half the charging energy contribution to the addition energy. A different applied-bias convention changes the slope formulas, so the convention must accompany the extraction.