Tunneling through a multigrain system: Deducing sample topology from nonlinear conductance

We study a current transport through a system of a few grains connected with tunneling links. The exact solution is given for an arbitrarily connected double-grain system with a shared gate in the framework of the orthodox model. The result is generalized for multigrain systems with strongly different tunneling resistances. We analyze the large-scale nonlinear conductance and demonstrate how the sample topology can be unambiguously deduced from the spectroscopy pattern (differential conductance versus gate-bias plot). We present experimental data for a multigrain sample and reconstruct the sample topology. A simple selection rule is formulated to distinguish samples with spectral patterns free from spurious disturbance caused by recharging of some grains nearby. As an example, we demonstrate experimental data with additional peaks in the spectroscopy pattern, which cannot be attributed to coupling to additional grains. The approach can be used to judge the sample topology when it is not guaranteed by fabrication and direct imaging is not possible.