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Nanoscale imaging of mobile carriers and trapped charges in delta doped silicon p–n junctions


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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Fig. 1: bb-EFM for 3D dopant profiling.
Fig. 2: Patterned B and P δ-layer structure buried h= 15 nm below the surface.
Fig. 3: Quantitative dopant profiling of a P patterned sample.
Fig. 4: Dynamics and interface traps.

Data availability

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


  1. Yang, K. H. M., Dong, Q., Austin, T. & Sylvester, D. Analog malicious hardware. In Proc. 2016 IEEE Symposium on Security and Privacy 18–37 (IEEE, 2016).

  2. Orji, N. G. et al. Metrology for the next generation of semiconductor devices. Nat. Electron. 1, 532–547 (2018).

    Article  Google Scholar 

  3. Holler, M. et al. Three-dimensional imaging of integrated circuits with macro- to nanoscale zoom. Nat. Electron. 2, 464–470 (2019).

    Article  Google Scholar 

  4. Holler, M. et al. High-resolution non-destructive three-dimensional imaging of integrated circuits. Nature 543, 402–406 (2017).

    Article  Google Scholar 

  5. Zschech, E. & Diebold, A. Metrology and failure analysis for 3D IC integration. AIP Conf. Proc. 1395, 233–239 (2011).

    Article  Google Scholar 

  6. Hill, C. D. et al. A surface code quantum computer in silicon. Sci. Adv. 1, e1500707 (2015).

    Article  Google Scholar 

  7. Škereň, T., Köster, S., Douhard, B., Fleischmann, C. & Fuhrer, A. Bipolar device fabrication using a scanning tunneling microscope. Nat. Electron. (2020).

  8. Stock, T. J. Z. et al. Atomic-scale patterning of arsenic in silicon by scanning tunneling microscopy. ACS Nano 14, 3316–3327 (2020).

    Article  Google Scholar 

  9. Goh, K. E. J., Oberbeck, L., Simmons, M. Y., Hamilton, A. R. & Butcher, M. J. Influence of doping density on electronic transport in degenerate Si:P δ-doped layers. Phys. Rev. B 73, 035401 (2006).

    Article  Google Scholar 

  10. Ruess, F. J. et al. Toward atomic-scale device fabrication in silicon using scanning probe microscopy. Nano Lett. 4, 1969–1973 (2004).

    Article  Google Scholar 

  11. Buech, H., Fuechsle, M., Baker, W., House, M. G. & Simmons, M. Y. Quantum dot spectroscopy using a single phosphorus donor. Phys. Rev. B 92, 235309 (2015).

    Article  Google Scholar 

  12. Koch, M. et al. Spin read-out in atomic qubits in an all-epitaxial three-dimensional transistor. Nat. Nanotechnol. 14, 137–140 (2019).

    Article  Google Scholar 

  13. International Technology Roadmap for Semiconductors—ITRS 2.0 (ITRS, 2015);

  14. Oberbeck, L. et al. Imaging of buried phosphorus nanostructures in silicon using scanning tunneling microscopy. Appl. Phys. Lett. 104, 253102 (2014).

    Article  Google Scholar 

  15. Gramse, G. et al. Nondestructive imaging of atomically thin nanostructures buried in silicon. Sci. Adv. 3, e1602586 (2017).

    Article  Google Scholar 

  16. Cheng, B., Roy, S., Roy, G., Adamu-Lema, F. & Asenov, A. Impact of intrinsic parameter fluctuations in decanano MOSFETs on yield and functionality of SRAM cells. Solid State Electron. 49, 740–746 (2005).

    Article  Google Scholar 

  17. Holmberg, V. C., Helps, J. R., Mkhoyan, K. A. & Norris, D. J. Imaging impurities in semiconductor nanostructures. Chem. Mater. 25, 1332–1350 (2013).

    Article  Google Scholar 

  18. Lenk, A., Lichte, H. & Muehle, U. 2D-mapping of dopant distribution in deep sub micron CMOS devices by electron holography using adapted FIB-preparation. J. Electron Microsc. 54, 351–359 (2005).

    Google Scholar 

  19. Zalm, P. C. Ultra-shallow doping profiling with SIMS. Rep. Prog. Phys. 58, 1321–1374 (1995).

    Article  Google Scholar 

  20. De Wolf, P., Snauwaert, J., Clarysse, T., Vandervorst, W. & Hellemans, L. Characterization of a point-contact on silicon using force microscopy-supported resistance measurements. Appl. Phys. Lett. 66, 1530–1532 (1995).

    Article  Google Scholar 

  21. Gramse, G., Edwards, M. A., Fumagalli, L. & Gomila, G. Theory of amplitude modulated electrostatic force microscopy for dielectric measurements in liquids at MHz frequencies. Nanotechnology 24, 415709 (2013).

    Article  Google Scholar 

  22. Fumagalli, L. et al. Nanoscale capacitance imaging with attofarad resolution using a.c. current sensing atomic force microscopy. Nanotechnology 17, 4581–4587 (2006).

    Article  Google Scholar 

  23. Shao, R., Kalinin, S. V. & Bonnell, D. A. Local impedance imaging and spectroscopy of polycrystalline ZnO using contact atomic force microscopy. Appl. Phys. Lett. 82, 1869–1871 (2003).

    Article  Google Scholar 

  24. Lányi, S. & Hruskovic, M. The resolution limit of scanning capacitance microscopes. J. Phys. D 36, 598 (2003).

    Article  Google Scholar 

  25. Cho, Y. et al. Scanning nonlinear dielectric microscopy with nanometer resolution. Appl. Phys. Lett. 75, 2833–2855 (1999).

    Article  Google Scholar 

  26. Gramse, G. et al. Quantitative sub-surface and non-contact imaging using scanning microwave microscopy. Nanotechnology 26, 135701 (2015).

    Article  Google Scholar 

  27. Gil, A., Colchero, J., Gomez-Herrero, J. & Baro, A. M. Electrostatic force gradient signal: resolution enhancement in electrostatic force microscopy and improved kelvin probe microscopy. Nanotechnology 14, 332–340 (2003).

    Article  Google Scholar 

  28. Girard, P. & Titkov, A. N. Applied Scanning Probe Methods II: Scanning Probe Microscopy Techniques Ch. 9.4.3 (Springer, 2006).

  29. Girard, P. Electrostatic force microscopy: principles and some applications to semiconductors. Nanotechnology 12, 485–490 (2001).

    Article  Google Scholar 

  30. Sze, S. M. & Ng, K. K. Physics of Semiconductor Devices 3rd edn (Wiley, 2006)

  31. Niranjan, M. K., Zollner, S., Kleinman, L. & Demkov, A. A. Theoretical investigation of PtSi surface energies and work functions. Phys. Rev. B 73, 195332 (2006).

    Article  Google Scholar 

  32. Oberbeck, L. et al. Encapsulation of phosphorus dopants in silicon for the fabrication of a quantum computer. Appl. Phys. Lett. 81, 3197–3199 (2002).

    Article  Google Scholar 

  33. Polley, C. M. et al. Exploring the limits of n-type ultra-shallow junction formation. ACS Nano 7, 5499–5505 (2013).

    Article  Google Scholar 

  34. Schmidt, V., Wittemann, J. V., Senz, S. & Gösele, U. Silicon nanowires: a review on aspects of their growth and their electrical properties. Adv. Mater. 21, 2681–2702 (2009).

    Article  Google Scholar 

  35. Castagné, R. & Vapaille, A. Description of the SiO2:Si interface properties by means of very low frequency MOS capacitance measurements. Surf. Sci. 28, 157–193 (1971).

    Article  Google Scholar 

  36. Mizsei, J. Determination of SiO2–Si interface trap level density (Dit) by vibrating capacitor method. Solid State Electron. 44, 1825–1831 (2000).

    Article  Google Scholar 

  37. Bussmann, E. et al. Scanning capacitance microscopy registration of buried atomic-precision donor devices. Nanotechnology 26, 085701 (2015).

    Article  Google Scholar 

  38. Keizer, K. G., Koelling, S., Koenraad, P. M. & Simmons, M. Y. Suppressing segregation in highly phosphorus doped silicon monolayers. ACS Nano 9, 12537–12541 (2015).

    Article  Google Scholar 

  39. Becker, G. T., Regazzoni, F., Paar, C. & Burleson, W. P. Stealthy dopant-level hardware Trojans: extended version. J. Cryptographic Eng. 4, 19–31 (2014).

    Article  Google Scholar 

  40. O’Brien, J. L. et al. Towards the fabrication of phosphorus qubits for a silicon quantum computer. Phys. Rev. B 64, 161401 (2001).

    Article  Google Scholar 

  41. Shen, T. C. et al. Ultradense phosphorous δ-layers grown into silicon from PH3 molecular precursors. Appl. Phys. Lett. 80, 1580–1582 (2002).

    Article  Google Scholar 

  42. Adams, D. P., Mayer, T. M. & Swartzentruber, B. S. Nanometer-scale lithography on Si(001) using adsorbed H as an atomic layer resist. J. Vac. Sci. Technol. B 14, 1642–1649 (1996).

    Article  Google Scholar 

  43. McKibbin, S. R., Clarke, W. R., Fuhrer, A., Reusch, T. C. G. & Simmons, M. Y. Investigating the regrowth surface of Si:P δ-layers toward vertically stacked three dimensional devices. Appl. Phys. Lett. 95, 233111 (2009).

    Article  Google Scholar 

  44. Gramse, G., Schönhals, A. & Kienberger, F. Nanoscale dipole dynamics of protein membranes studied by broadband dielectric microscopy. Nanoscale 11, 4303–4309 (2019).

    Article  Google Scholar 

  45. Fumagalli, L., Gramse, G., Esteban-Ferrer, D., Edwards, M. A. & Gomila, G. Quantifying the dielectric constant of thick insulators using electrostatic force microscopy. Appl. Phys. Lett. 96, 183107 (2010).

    Article  Google Scholar 

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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.

Author information

Authors and Affiliations



G.G. conceived and designed the experiments, performed the experiments, analysed the data and wrote the paper. A.K. performed the experiments, contributed materials/analysis tools and wrote the paper. T.S. contributed materials/analysis tools. T.J.Z.S. contributed materials/analysis tools and wrote the paper. G.A. conceived and designed the experiments and wrote the paper. F.K. conceived and designed the experiments. A.F. contributed materials/analysis tools, conceived and designed the experiments and wrote the paper. N.J.C. conceived and designed the experiments and wrote the paper.

Corresponding author

Correspondence to Georg Gramse.

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Extended data

Extended Data Fig. 1 STM images of patterned Si surface.

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.

Extended Data Fig. 2 EFM image after 2 h of continuous scanning and tip calibration.

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.

Extended Data Fig. 3 Comparison of SMM and EFM lateral resolution.

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.

Extended Data Fig. 4 Comparison of lateral resolution in current and force-sensing techniques.

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.

Extended Data Fig. 6 Simulated carrier profile and capacitance bias curve.

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.

Extended Data Fig. 7 Sensitivity analysis to amount of dopants and lateral resolution.

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).

Extended Data Fig. 8 2D Finite element model for estimation of the measurement parameters.

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.

Extended Data Fig. 9 Simulated capacitance bias curve for different doping profiles.

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.

Extended Data Fig. 10 Single C’(V) spectra from Fig. 4c.

Single C’(V) spectra that were averaged Fig. 4c). Curves show good reproducibility as long as the tip is not modified.

Supplementary information

Supplementary Information

Supplementary discussion and Figs. 1 and 2.

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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).

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