Regarding surface potential, read the scholarly books for MOS transistors. The surface potential ϕs for MOS structures is the deviation of the potential of the semiconductor at the gate insulator interface from the flat-band voltage Vfb (potential) in the semiconductor in free space. The determination of the value of surface potential ϕs is from the solution of the Poisson equation in the semiconductor depth under the gate of the MOS structure at boundary conditions ϕ=0 in the semiconductor depth and equal electric fields in the gate dielectric (Vg−Vch−Vfb−ϕs)/ti and semiconductor at the interface between them. Here, Vg is the potential of the gate, Vch is the potential of channel (Vch=Vs≈0V the bias at source side and Vch=Vd the bias at the drain side the MOS transistor channel) and ti is the thickness of the gate dielectric.

The solution of the Poisson equation is a transcendental equation, without closed analytical form in the general case, because it depends on distributions of charges, density of states, traps, their occupation, etc. Nevertheless, omitting traps, assuming rectangular density of states in the charge transport band of the semiconductor (e.g., conduction band for electrons) and Boltzmann statistics for charge occupation, the solution of the Poisson equation tends to the form of

(Vg−Vch−Vfb−ϕs)²≈contant×[exp(±ϕs/ϕt)-1]+(omitted terms)

where ϕt = kT/q ≈ 26 mV at room temperature is the thermal voltage, the latter is the product kT of the Boltzmann constant k by the absolute temperature T over the magnitude of the electronic charge q. Take ±=+ for nMOS and ±=− for pMOS, because the gate bias potential and the surface potential are with negative polarity for biasing of the pMOS transistors in the strong inversion regimes. The equation above is for strong invention of the MOS structure, with gate biasing “above” the threshold voltage (VT) of the MOS transistor/structure, that is, ±(Vg-VT)>(2−3)×ϕt, taking again ±=+ for nMOS and ±=− for pMOS.

Here, I do not go in more details, first, because all the above is embedded in the Silvaco ATLAS TCAD simulator (one still has to properly setup the structure and material parameters - refer to documentation of the software and literature for values of material parameters), and second, the objective of the works of the person question is likely related to other things. In particular, the question goes to how to determine the gate biasing potential Vg without and with presence of biomolecules. For the latter, the type of the simulator is quite irrelevant, al long as one knows how much change ΔVg causes the presence of the biomolecules.

In principle, the Nernst equation should be able to be used do demine ΔVg, and this is well explored in the literature related to ISFETs (Ion Selective Field Effect Transistors) circa 1980s. However, there are also other electro-chemical effects related to attachment of molecules from liquids to surfaces, e.g., the so-called “double layers”. I recommend the person questioning to inspect the works of Mohammad Waleed Shinwari (https://scholar.google.com/citations?user=_Ik4Q9gAAAAJ&hl=en), who has researched in depth the sensing of biomolecules by MOSFET structures, transistors, arrays of them and theory and methods for this kind of sensing.

Finally, prepare sample immersible in buffer solution, contact the buffer solution with reference electrode and get the DC transfer current-voltage (I-V) curves of your sample, applying gate voltage to the reference electrode and measuring the current trough the counter and working electrodes. Any electrochemical potentiostat can do this test. Use the simulator to replicate the measured I-V curves, assuming short circuit between the reference electrode and gates of the sample. Then, repeat the same test with biomolecules dissolved and replicate again the measured I-V curves, using the model from the previous experiment, but this time adding voltage (and may be impedance) between the reference electrode and the gates of the sample. Whatever you have added between the reference electrode and the gates of the sample is the sensing effect for the presence of the biomolecules. I expect change of gate voltage for same current, which can be attributed to a shift of threshold voltage of the MOS transistors in the sample by presence of the biomolecules. Finally compare your findings to the literature (e.g., the publications of M. W. Shinwari and other researchers) and prepare reports, manuscripts for publication and other items, as you need to accomplish the objectives of your works.

In conclusion, I do not think that you need to determine surface potential in MOS transistor/structure, because it is not an experimentally measurable quantity. I think you need to determine qualitatively and quantitatively what electrically measurable quantity from your sensor changes with what of the of the biomolecules.