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A method for determining the parameters of a layered semiconductor structure, using the data obtained by near-field microwave probing with a micron-size lateral resolution, was developed and tested experimentally. We have measured a frequency spectrum of the impedance of a coaxial antenna formed on a test structure surface. The corresponding inverse problem has been solved based on the quasistatic theory for the impedance of a monopole antenna interacting with a layered medium, which was proposed earlier [A. N. Reznik and S. A. Korolyov, J. Appl. Phys. 119, 094504 (2016)]. This method was applied to a low-barrier Mott diode structure with a nearly 100 nm thick undoped layer grown on a conducting substrate GaAs. Computer simulation allowed us to establish the optimal frequency intervals and estimate the accuracy of determining the structure parameters. Measurements were taken in the frequency range of 0.1–67 GHz on commercially available equipment. Three antennas with a radius of the central conductor of 5.5, 11, and 25 μm, respectively, were used. The accuracy of the experimental evaluation of the layer thickness d and conductivity σ was ∼1–3%, and for the substrate conductivity, it came to about 15%. As an example, we also present the parameters σ and d in four points of the sample surface image. These data show strong lateral inhomogeneity of the structure under study.

Using a drift-diffusion approximation, we obtain an analytical solution to the problem of charge-carrier injection into an insulating i layer of finite thickness with account of self-consistent boundary conditions. The main assumption is that the self-doping of the i layer is neglected. The solution makes it possible to calculate the potential, electric field, and current-voltage characteristics of a variety of structures such as metal-i layer-n+ (or p+) semiconductor, metal-i layer-metal, and n+(p+)-i-n+(p+) structures. The solution admits a generalization for structures having heterobarriers at the interface of the semiconductor layers. The proposed approach allows for the contact phenomena and bulk effects related to that the current is space charge-limited in the i layer. The solution is valid for both the limiting cases and the transient regimes.