dIdV

dIdV is commonly used to denote the differential conductance of an electronic system, defined as the derivative of current I with respect to the applied voltage V (dI/dV). It describes how the current changes in response to small variations in voltage and is a key quantity in nonlinear and mesoscopic transport. In the linear response regime at a fixed temperature and near zero bias, dI/dV at V ≈ 0 equals the conductance G, with G = dI/dV|V=0. At finite bias, dI/dV provides a voltage-dependent measure of the device’s conductance.

In tunneling and spectroscopic contexts, dI/dV spectra are often interpreted as reflecting the electronic structure of a sample. In scanning tunneling microscopy and spectroscopy, the differential conductance is measured to map the local density of states, with dI/dV ∝ ρs(eV) under common approximations. More generally, dI/dV can be described by transport theories such as the Landauer formalism, where the differential conductance involves the transmission function and the energy derivative of the Fermi-Dirac distribution, especially at finite temperature.

Experimentally, dI/dV is typically obtained by applying a small alternating current modulation to the bias and using lock-in detection to measure the in-phase signal. This approach enhances sensitivity to the slope of the I–V curve and enables energy-resolved studies of materials, molecules, and nanoelectronic devices.

Interpreting dI/dV requires consideration of temperature, bias range, and instrumental nonidealities, as these factors can affect its relationship to the density of states and to intrinsic transport properties.