With the solid state nanopores supplied by ZP we see that we are measuring ionic current, where the size of the current is determined by the applied voltage, the ionic strength of the buffer and the dimensions of the nanopore. The current is constant (the open pore current) and as objects move through the pore, they will influence the current (usually a temporary reduction - a blockade or event - but could also be an increase). The theoretical value for the open pore current arising for a particular pore size in a specific buffer and at a certain voltage is in excellent agreement with the measured values. Blockades are also in excellent agreement with the size and charge density of the molecule under analysis.
Tunnelling currents may also be involved but we would assume that their effects are negligible under most conditions with our chips (with 2D materials things might be different). Capacitance variation would be a source of increased electrical noise.