Integrated circuits and certain silicon-based quantum devices require the precise positioning of dopant nanostructures, and hydrogen resist lithography can be used to fabricate such structures at the atomic-scale limit. However, there is no single technique capable of measuring the three-dimensional location and electrical characteristics of these dopant nanostructures, as well as the charge dynamics of carriers and trapped charges in their vicinity. Here, we show that broadband electrostatic force microscopy can be used for non-destructive carrier profiling of atomically thin n-type (phosphorus) and p-type (boron) dopant layers in silicon, and their resulting p–n junctions. The probe has a lateral resolution of 10 nm and a vertical resolution of 0.5 nm, and detects the capacitive signature of subsurface charges in a broad 1 kHz to 10 GHz frequency range. This allows the bias-dependent charge dynamics of free electrons in conducting channels and trapped charges in oxide–silicon interfaces to be investigated.
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All data needed to evaluate the conclusions in this paper are present in the paper and/or the Supplementary Information. Additional data related to this paper can be requested from the authors. The data created during this research are available at https://doi.org/10.5281/zenodo.3899692.
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Technical discussions with I. Alic are acknowledged. This work has been supported by FWF project no. P28018-B27, EFRE project no. IWB 2018 98292, NMBP project no. MMAMA 761036 and UKRI EPSRC project no. EP/M009564/1.
The authors declare no competing interests.
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STM images of patterned Si surface prior to coverage with Si. a, Layout of patterns at which hydrogen is desorbed on the Si surface. b, c, Zoom and overview STM image of boron pattern imaged before coverage with Si. Actual width of stripes appears to be 6 nm, 10 nm, 19 nm, 35 nm, with a pitch of 9 nm. The error between design and measured width is due to finite desorption width of the hydrogen.
EFM image after 2 h of continuous scanning with the PtSi tip and tip calibration. a, Zoom onto the stripes separated by 100 nm, 70 nm and 30 nm, b, corresponding line profile as indicated. PtSi-FM tips from Nanonsensors (Germany) with nominal tip radius 20–30 nm were used. At the end of the measurement the tip was calibrated by approach curve c, C’(z) approach curve for tip calibration as detailed in the methods section. Black dots for fresh tip. Red dots after prolonged scanning. Blue line represents simulated curve that fits best to the experimental data with a tip radius of ra = 26.4 ± 0.2 nm and ra = 31.2 ± 0.3 nm for fresh and worn tip, respectively.
Comparison of SMM and EFM lateral resolution. a, EFM C’ image of P δ-layer stripes buried 15 nm below the surface and b, corresponding line profile as indicated in the image. A fresh PtSi-FM tip from Nanonsensors (Germany) with calibrated tip radius of ra,EFM = 26.4 ± 0.2 nm was used. Peaks were fitted with two double logistic functions (solid lines) giving a lateral resolution of 13 ± 2 nm and 10 ± 1 nm for first and second peak, respectively. c, SMM capacitance image and d, corresponding profile line as reported in Gramse et al15. Solid Pt tips from (RMN, US) were used and tip radius was calibrated to be ra,SMM = 20 nm). The scan-rate in both images was identical with 0.4 lines per second.
Comparison of lateral resolution in current and force-sensing techniques and impact of measurement parameters. Dashed lines represent modelled C(z) scan line and solid lines C’(z) scan line over a 500 nm wide stripe of phosphorus. Effect of tip radius, tip–sample distance and carrier frequency are studied as indicated, while the other parameters are fixed to R = 16 nm, z = 21 nm, f = 1 MHz.
Extended Data Fig. 5 Experimental comparison of EFM lateral resolution and electrical contrast at different frequencies.
Experimental comparison of EFM lateral resolution and electrical contrast on dopant test sample measured at different frequencies. Histograms are shown as black insets. We found best contrast at measurement frequencies of 10–100 MHz as can be seen in the insets.
Simulated carrier profile and capacitance bias curve. a, Calculated carrier concentration (phosphorus doping) below the tip (along the symmetry axis) for various applied voltages for dopant concentration 3×1021cm-3 (orange) and 3×1018cm-3 (red). b, Corresponding simulated C’(V) curve.
Sensitivity analysis to amount of dopants and lateral resolution. a, Solid line represents calculated contrast of acceptor dopant delta layer with radius r = 20 µm at 15 nm below the surface as a function of dopant density. Dashed lines show the same for donor doping and varying delta layer radii. The EFM electrical sensitivity is ~1zF/nm for the here used tips (area is marked), it can be improved to 0.3zF/nm using softer tips. b, Lateral resolution as a function of delta layer dopant concentration (other parameters are fixed to h = 15 nm, R = 16 nm, z = 21 nm, f = 1 MHz).
2D Finite element model for estimation of the measurement parameters on the lateral resolution. Shown is the electron concentration in the substrate. A 500 nm wide stripe of highly doped phosphorus (3×1020 cm−3) at a depth of 15 nm is moved below the probe. Capacitance and Maxwell-Stress Tensor are calculated.
Simulated capacitance bias curve for different doping profiles. a, Simulated doping profile below the tip for P, B and mixed P + B doping layers as indicated in the plot b, Corresponding simulated C’(V) curve.
Single C’(V) spectra that were averaged Fig. 4c). Curves show good reproducibility as long as the tip is not modified.
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Gramse, G., Kölker, A., Škereň, T. et al. Nanoscale imaging of mobile carriers and trapped charges in delta doped silicon p–n junctions. Nat Electron 3, 531–538 (2020). https://doi.org/10.1038/s41928-020-0450-8