Quantitative measurement of the charge carrier concentration using dielectric force microscopy

The charge carrier concentration profile is a critical factor that determines semiconducting material properties and device performance. Dielectric force microscopy (DFM) has been previously developed to map charge carrier concentrations with nanometer-scale spatial resolution. However, it is challenging to quantitatively obtain the charge carrier concentration, since the dielectric force is also affected by the mobility. Here, we quantitative measured the charge carrier concentration at the saturation mobility regime via the rectification effect-dependent gating ratio of DFM. By measuring a series of n-type GaAs and GaN thin films with mobility in the saturation regime, we confirmed the decreased DFM-measured gating ratio with increasing electron concentration. Combined with numerical simulation to calibrate the tip-sample geometry-induced systematic error, the quantitative correlation between the DFM-measured gating ratio and the electron concentration has been established, where the extracted electron concentration presents high accuracy in the range of 4 x 10(16) - 1 x 10(18) cm(-3). We expect the quantitative DFM to find broad applications in characterizing the charge carrier transport properties of various semiconducting materials and devices.