Biosensors based on a method for determining the conductance matrix of multiterminal semiconductor nanostructures

A method for determining the conductance matrix is analyzed to study the properties of silicon nanostructures fabricated within Hall geometry on an $n$-type Si(100) surface as ultra-narrow $p$-type silicon quantum wells bounded by $\delta$ barriers heavily doped with boron. Within the proposed approach, the total current flowing through the multiterminal silicon nanostructure is written in the matrix form as $\mathbf{I}=\mathbf{G}\cdot\mathbf{V}$, where $\mathbf{I}$ and $\mathbf{V}$ are the columns of currents and voltages for each of the $N$ terminals, $\mathbf{G}$ is the $N\times N$ conductance matrix uniquely describing the conductance of the structure under study, taking into account the contribution of contact-area resistances. The high sensitivity of matrix elements to changes in the state of the silicon nanostructure surface under conditions of the precipitation of sodium-acetate solution containing single-strand synthetic oligonucleotides is demonstrated. The prospects of practical application of the results obtained in developing modern biosensors based on determining the conductance matrix of multiterminal semiconductor nanostructures are discussed.