Probing resistivity and doping concentration of semiconductors at the nanoscale using scanning microwave microscopy

We present a new method to extract resistivity and doping concentration of semiconductor materials from Scanning Microwave Microscopy (SMM) S11 reflection measurements. Using a three error parameters de-embedding workflow, the S11 raw data are converted into calibrated capacitance and resistance images where no calibration sample is required. The SMM capacitance and resistance values were measured at 18 GHz and ranged from 0 to 100 aF and from 0 to 1 MΩ, respectively. A tip-sample analytical model that includes tip radius, microwave penetration skin depth, and semiconductor depletion layer width has been applied to extract resistivity and doping concentration from the calibrated SMM resistance. The method has been tested on two doped silicon samples and in both cases the resistivity and doping concentration are in quantitative agreement with the data-sheet values over a range of 10(-3)Ω cm to 10(1)Ω cm, and 10(14) atoms per cm(3) to 10(20) atoms per cm(3), respectively. The measured dopant density values, with related uncertainties, are [1.1 ± 0.6] × 10(18) atoms per cm(3), [2.2 ± 0.4] × 10(17) atoms per cm(3), [4.5 ± 0.2] × 10(16) atoms per cm(3), [4.5 ± 1.3] × 10(15) atoms per cm(3), [4.5 ± 1.7] × 10(14) atoms per cm(3). The method does not require sample treatment like cleavage and cross-sectioning, and high contact imaging forces are not necessary, thus it is easily applicable to various semiconductor and materials science investigations.