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edfas.org 13 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 19 NO. 4 The natural progression and general interest in the user community is to extend the sMIM capabilities to quantitative measurements. This article presents recent analytical and finite-element modeling developments of tip-bias-dependent depletion-layer geometry and impedance. These are compared to experimental results on reference samples for both silicon- and GaN-doped staircases to systematically validate the response of the sMIM-C channel to the doping concentration. INTRODUCTION In a standard sMIM experiment, microwaves are coupled through a customAFMcantilever to the probe tip, where they interact as evanescent waves with the portion of the sample immediately under the tip. A fraction of the microwaves is reflected, and the amplitude and phase (or equivalently, the real and imaginaryparts) of the reflection are determined by the local electrical properties of the sample. For a linear sample (e.g., a dielectric or metallic material), the permittivity and conductivity determine the reflection, while for a nonlinear sample (e.g., a doped semiconductor), the tip-bias-dependent depletion-layer structure contributes significantly. As a result, sMIMmea- surements can provide valuable nanoscale information about semiconductor devices, processes, and defects. A customAFMprobe ismounted in a specializedholder so that there is a coaxial connection from the microwave source to the AFMprobe tip. The specializedprobemodule with matching circuit is then fitted to a standard AFM. The AFM typically operates in contact mode for imaging but can also be used in intermittent and tapping modes. The sMIM probes contain a multilayer cantilever with a shielded signal line connecting a contact pad on the carrier chip to themetallic tip at the end of the cantilever. The holder connects to the contact pad and couples 3 GHz microwaves from the sMIM measurement electron- ics to the AFM probe carrier chip, where they propagate along the signal line in the cantilever to the conductive tip. [15] The reflected signal retraces the same path. This configuration is illustrated schematically in Fig. 1. The probes, probe interfacemodule, andelectronics arepart of a commercial ScanWave sMIMmodule (PrimeNano, Inc.). The sMIM is adapted to the most common commercial AFM platforms. [4,5] The sMIM-C measured on various bulk dielectrics shows a clear linear relationship between sMIM-C and the log of the permittivity. [4,5,16] The red squares shown in Fig. 2 are from a model that originates with a finite- element calculation of the tip-sample admittance for the conical geometry of the sMIM probe. The origins of the log( ε ) dependence can be seen in analytical models for spherically terminated conical tips above and in contact with linear materials, documenting the origin of the log dependence published by other researchers. [17] For sMIMmeasurements on nonlinear materials, such as a doped semiconductor, the tip-sample bias influences the tip-sample impedance, or, more conveniently, the reciprocal of the tip-sample impedance, the tip-sample admittance, Y T-S . As with linear samples, the sMIM signals are still proportional to the imaginary and real parts of Y T-S , the capacitance and conductance below the tip-sample interface, but the capacitance and conductance now dependnot only on the local permittivity and conductivity of the sample under the tip but also on the geometry of Fig. 1 Schematic of the PrimeNano ScanWave electronicswith amatching circuit and shielded coaxial line to the probe-sample interface Fig. 2 Graph of the numericallymodeled admittance versus the dielectric value (in red) with the experimentally measured sMIM versus the dielectric value (in blue) from a group of bulk crystal dielectric samples