A Graphene Quantum-Dot Electrometer Array for Sub-Micrometre Imaging of Interfacial Charge Layers in Cryofixed Cells: A Design Analysis

We analyse, as a design study, a cryogenic sensor that images the electrostatic stray field of a vitrified biological cell with an array of gate-defined quantum dots in gapped bilayer graphene. No device has been fabricated and no transport data are reported. The sensor is a Coulomb-blockade electrometer: each dot converts the offset charge induced on it by the sample into a shift in its resonance, and the steepness of that resonance—a property of the discrete density of states rather than of the device area—sets the gain, so that sensitivity is not lost as the element is made smaller. For a 50 nm dot at 4.2 K we estimate a charge sensitivity of order 10−2 e/√Hz for a charge 50 nm away, limited by an assumed 1/f offset-charge noise; this is a calculated, not a measured, figure. Because a vitrified sample is electroneutral beyond the Debye length, the sensor does not see net charge but the frozen interfacial dipole layers, whose dipole density equals the permittivity times the potential step across each layer. The measured quantity is therefore a band-limited map of lateral variations in the interfacial potential within about 100 nm of the sensor; a laterally uniform layer is invisible. In this map the membrane potential enters with a weight β = Cmt/εwε0 ≈ 0.07 relative to the surface potential of the glycocalyx, so the sensor is primarily a surface-potential imager and only secondarily, through a calibration we specify, a membrane-potential probe. A 10 mV surface-potential contrast at a period of 250 nm exceeds the 1 ms detection limit by a factor of about 4–13, and the 8 × 8 array at 250 nm pitch resolves periods of 250–300 nm. We give the device geometry, the plunge-freezing protocol, the controls and the inversion procedure, and list what remains to be measured.