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edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 19 NO. 4 16 curve (Fig. 5c) as the calibration to convert sMIM-C mea- sured on a device sample to log doping. [10] Figure 6(a) presents the results of nano-C-V curves from the IMEC staircase, verifying that the nanoscale response matches the theory discussed in the introduction of this article. This “image” is frommultiple sMIM scans over the same 8-µm-length line on the sample, collected as the bias voltage scans from 0 to 2.5 V. The demarcations of the doped regions are marked with vertical white lines, separated by exactly the widths of the regions published by IMEC for this sample. The data for the six C-V curves in Fig. 6(b) were taken from the vertical dashed black lines, which are placed exactlymidway between thewhite lines. The C-V curveswere shifted so they all have the same sMIM value at the most positive voltage, quite deep into accu- mulation. These empirical C-V curves for n -type silicon closely resemble the mirror images of the theoretical C-V curves for a p -type silicon, as they should. (The sMIM-C is proportional to the admittance at the tip/sample interface and therefore to the capacitance.) Figure 6(c) shows the sMIM-C values from the C-V curves in Fig. 6(b) at the tip- sample voltage with the highest doping sensitivity (0.96 V), and they vary linearly with log doping density over approximately 4 orders of magnitude. The derived linear calibration has the formula log(ND) = 1.83 × sMIM-C + 19.9, with a correlation coefficient of 0.972. sMIM REFERENCE APPLIED TO A GaN DEVICE This section extends themethods discussedpreviously ondoped silicon systems to III-V semiconductormaterials. An n -type GaN staircase reference sample was prepared using an n -type GaN subtrate and growing four epitaxial layers with varying doping levels. Two of the steps, 2 and 5, have the same doping concentration, as shown in Fig. 7(b). The samplewas independentlymeasured using sec- ondary ionmass spectrometry (SIMS) to verify the doped step values, and these values were used for calibration. Figure 7(a) shows the sMIM-C image, with roughly verti- cal regions representing the individual steps. Using the technique described previously, an average profile of the steps is used to extract the sMIM step value (Fig. 7b), which is then plotted versus log doping to establish the calibration curve (Fig. 7c). After calculating the calibration curve on the calibra- tion sample, it can nowbe applied on an “unknown” GaN device to convert the sMIM to units of log doping concen- tration. The test device is amultilayer structurewith both n - and p -type doped regions. This article concentrates on the n -type regions, because the calibration staircase is n -type only. Figure 8(a) shows a cross-sectional schematic of the “unknown” device. The schematic identifies three regions of interest on the sample that are n -type doped regions: Fig. 6 (a) Image of an 8 µm line scanned repeatedly while the bias voltage swept from 0 to 2.5 V. The vertical white lines demarcate the doped regions in this cross-sectional sample. The vertical dotted black lines indicatewhere valueswere extracted to give C-V curves. (b) C-V curves extracted from (a). The curves have been shifted vertically so they meet at bias = 2.5 V, deep into accumulation. (c) Calibration from sMIM-C to log(ND) at bias = 0.96 V, where sMIM-C has the most doping contrast (a) (b) (c)