Modeling electric-field-sensitive scanning probe measurements for a tip of arbitrary shape

Kuljanishvili, Irma; Chakraborty, Subhasish; Maasilta, I. J.; Tessmer, S. H.; Melloch, M. R.

doi:10.1016/j.ultramic.2004.07.004

Cited by 9 publications

(26 citation statements)

References 18 publications

(21 reference statements)

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“…2d implies an effective lever arm of α tip = 1/10.8. This is a reasonable value, consistent with the expected tip-sample mutual capacitance [25][26][27] .…”

Section: Methodssupporting

confidence: 86%

Scanning-probe spectroscopy of semiconductor donor molecules

et al. 2008

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Semiconductor devices continue to press into the nanoscale regime, and new applications have been proposed for which a single dopant atom acts as the functional part of the device 1-3 . Moreover, because shallow donors and acceptors are analogous to hydrogen atoms, experiments on small numbers of dopants have the potential to be a testing ground for fundamental questions of atomic and molecular physics 4,5 . Although dopant properties are well understood with respect to the bulk, the study of configurations of dopants in small numbers is an emerging field 6,7 . Here we present local capacitance measurements of electrons entering silicon donors in a gallium arsenide heterostructure. To the best of our knowledge, this study is the first example of single-electron capacitance spectroscopy carried out directly with a scanning probe tip 8 . The precise position with respect to tip voltage of the observed single-electron peaks varies with the location of the probe, reflecting a random distribution of silicon within the donor plane. In addition, three broad capacitance peaks are observed independent of the probe location, indicating clusters of electrons entering the system at approximately the same voltages. These broad peaks are consistent with the addition energy spectrum of donor molecules, effectively formed by nearest-neighbour pairs of silicon donors.Electron tunnelling spectroscopy through isolated dopants has been observed in transport studies 9,10 . In addition, Geim and coworkers identified resonances due to two closely spaced donors, effectively forming donor molecules 11 . Rather than measuring transport current, our scanning-probe method is essentially a capacitance technique 8,12 . In contrast to the work of Geim et al., the measurements show discernible peaks attributed to successive electrons entering the molecules.Our method is an extension of scanning charge accumulation imaging 12 . Figure 1a shows the experiment schematically. The key component is a metallic tip with an apex of radius ∼ 50 nm, connected directly to a charge sensor, which achieves a sensitivity of 0.01e/ √ H z (ref. 13). For the capacitance spectroscopy measurements reported here, the tip's position is fixed (that is, not scanned) at a distance of ∼1 nm from the sample surface. We then monitor the tip's a.c. charge q tip in response to an a.c. excitation voltage V exc applied to an underlying electrode, as a function of d.c. bias voltage V tip . As detailed in the Methods section, if the quantum system below the tip can accommodate additional charge, the excitation voltage causes it to resonate between the system and the underlying electrode-giving rise to an enhanced capacitance,The first observations of donor-layer capacitance peaks acquired with our method probed a gallium arsenide heterostructure sample grown by molecular beam epitaxy, for which the donor layer was bulk-doped with Si at a density of 10 24 m −3 . To achieve better characterized results that would be more conducive to analysis, we used a GaAs [001] heterostructure...

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“…2d implies an effective lever arm of α tip = 1/10.8. This is a reasonable value, consistent with the expected tip-sample mutual capacitance [25][26][27] .…”

Section: Methodssupporting

confidence: 86%

Scanning-probe spectroscopy of semiconductor donor molecules

et al. 2008

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“…This means the nanometer-scale radius of curvature of the tip is relevant for capacitance measurement techniques. To maximize the amplitude of the signal without compromising spatial resolution, the tip radius should be approximately equal to the depth of the dopant layer beneath the surface 8,9 .…”

Section: Discussionmentioning

confidence: 99%

“…At the most schematic level, this technique treats the scanned tip as one plate of a parallel-plate capacitor, although realistic analysis requires a more detailed description to account for the curvature of the tip 8,9 . The other plate in this model is a nanoscale region of the underlying conducting layer, as shown in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Scanning-probe Single-electron Capacitance Spectroscopy

Walsh

Romanowich

Gasseller

et al. 2013

JoVE

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The integration of low-temperature scanning-probe techniques and single-electron capacitance spectroscopy represents a powerful tool to study the electronic quantum structure of small systems -including individual atomic dopants in semiconductors. Here we present a capacitance-based method, known as Subsurface Charge Accumulation (SCA) imaging, which is capable of resolving single-electron charging while achieving sufficient spatial resolution to image individual atomic dopants. The use of a capacitance technique enables observation of subsurface features, such as dopants buried many nanometers beneath the surface of a semiconductor material 1,2,3 . In principle, this technique can be applied to any system to resolve electron motion below an insulating surface.As in other electric-field-sensitive scanned-probe techniques 4 , the lateral spatial resolution of the measurement depends in part on the radius of curvature of the probe tip. Using tips with a small radius of curvature can enable spatial resolution of a few tens of nanometers. This fine spatial resolution allows investigations of small numbers (down to one) of subsurface dopants 1,2 . The charge resolution depends greatly on the sensitivity of the charge detection circuitry; using high electron mobility transistors (HEMT) in such circuits at cryogenic temperatures enables a sensitivity of approximately 0.01 electrons/Hz ½ at 0.3 K 5. Video LinkThe video component of this article can be found at

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“…Eriksson et al and Kuljanishvilli et al [19] showed that w is equal to the depth of the layer below the exposed surface and that the accuracy of the expression holds to a few percent, if the depth of the layer is comparable to or greater than the radius of curvature of the tip's apex. To estimate of the radial dependence of the donor-layer potential P(r), we note that for our sample the donor layer is only 20 nm from the underlying 2D layer; the apex of the tip is three times farther away.…”

Section: Approximate Expressionsmentioning

confidence: 99%

“…(2) and (3), where we have used V trap 0 eP(0))=500 mV, V exc =15 mV and the bell-functions calculated in (c) For these parameters we find a charging peak of width HWHM(D)=32 mV, roughly double the width of a single-electron peak. [19]. Here we show the case for which both conductors i and k are part of the tip and k is a distance S from the sample dielectric surface.…”

Section: Numerical Approachmentioning

confidence: 99%