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edfas.org 15 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 19 NO. 4 doping level under the tip (or electrode, in the case of patterned sampleswith electrodes present). This is similar to capacitance-versus-voltage curves from macroscopic samples commonly used to characterize semiconductor materials and test structures. Figure 3(b) presents the classical solution to the parallel-platemodel, numerically generated here for a range of doping concentration levels. Thismodel is incomplete for describing the geometries for AFM probe-sample interactions. Similar to what was observed in themeasurements of linear dielectrics shown in Fig. 2, where the sMIM signal is proportional to log( ε ), experimental data from doped semiconductors show sMIM signals varying linearly with log([doping concentration]). To confirm the origins of the log([doping concentration]) behavior, finite-elementmod- elingwas used to assess the depletion-layer geometry for a conical tip and how this geometry varies for both doping and applied gate (i.e., tip) voltage. Figure 4(a) shows the results for one doping level. The finite-element models also allow calculation of the tip-sample capacitance for each doping level and gate voltage, resulting in capacitance-voltage (C-V) curves for the geometry of an sMIM probe on an oxide-coated semiconductor (Fig. 4e). Experimental data presented subsequently in this article resemble the model results, indicating that most critical physics are accounted for by the models. Figure 4(f) shows that the capacitance seen andmeasured by sMIM is linear in log doping over several orders of magnitude for dopings of practical importance, enabling thepossibilityof calibrating sMIMresults to invert for doping density. EXAMPLES OF sMIM AND C-V ON SILICON SAMPLES It has been shown in previous work [4,5] that sMIM-C is linear with the log N A . Results presented in this section show application of sMIM-C’s linear relationship to log N A for quantification of sMIM-C doping concentration in log units. An IMEC n -type doped staircase was used as a calibration sample. The IMEC staircase is measured using ScanWave sMIM to determine a calibration curve that can then be applied to an unknown sample to convert sMIM-C to units of doping concentration. Figure 5(a) shows the sMIM-C image of the IMEC staircase doping standard. The sample was measured using a two-pass method with no applied bias. The data are collected line by line; the first line is in contact mode, and the second pass is at a height 100 nmabove the sample surface. The difference image is shown in Fig. 5(a). An average profile is shown in Fig. 5(b). The resulting profile shows excellent correlation to the IMEC published doping concentration data. The average profile graph (Fig. 5b) highlightswhere the average sMIM-C valuewas calculated for the graph in Fig. 5(c), plotting the measured sMIM-C versus known doping concentration. Due to the very linear response of the sMIM-C versus log doping concentration, one can use the corresponding Fig. 5 (a) Processed sMIM-C image of an n -type IMEC staircase. (b) Average profile with “calibration samples” highlighted in green. (c) Plot of sMIM-C calibration values versus published values of log doping. The linear fit is a calibration that can be applied to subsequent unknown doped samples. (a) (b) (c)