Conductance matrix of multiterminal semiconductor devices with edge channels

A method for determining the conductance matrix of multiterminal semiconductor structures with edge channels is proposed. The method is based on the solution of a system of linear algebraic equations based on Kirchhoff equations, made up of potential differences $U_{ij}$ measured at stabilized currents $I_{kl}$, where $i$, $j$, $k$, $l$ are terminal numbers. The matrix obtained by solving the system of equations completely describes the structure under study, reflecting its configuration and homogeneity. This method can find wide application when using the known Landauer–Buttiker formalism to analyze carrier transport in the quantum Hall effect and quantum spin Hall effect modes. Within the proposed method, the contribution of the contact area resistances $R_c$ to the formation of conductance matrix elements is taken into account. The possibilities of practical application of the results obtained in developing analog cryptographic devices are considered.