# Fileset

[draft01.pdf](https://mdr.nims.go.jp/filesets/1818f2b2-e3e9-4905-9032-ac0073777383/download)

## Creator

[Nobuyuki Ishida](https://orcid.org/0000-0003-0161-0583), [Takaaki Mano](https://orcid.org/0000-0002-6955-260X)

## Rights

This is the version of the article before peer review or editing, as submitted by an author to Nanotechnology .  IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.  The Version of Record is available online at https://doi.org/10.1088/1361-6528/ad0b5e.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Quantitative characterization of built-in potential profile across GaAs p–n junctions using Kelvin probe force microscopy with qPlus sensor AFM](https://mdr.nims.go.jp/datasets/2c3884a5-3f26-4d78-9d44-5a6792738065)

## Fulltext

Quantitative characterization of built-in potentialprofile across GaAs p-n junctions using Kelvinprobe force microscopy with qPlus sensor AFMNobuyuki IshidaNational Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047,JapanE-mail: ishida.nobuyuki@nims.go.jpTakaaki ManoNational Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047,JapanAugust 2017Abstract. The electrostatic potential distribution in materials and devices playsan important role in controlling the behaviors of charge carriers. Kelvin probe forcemicroscopy (KPFM) is a powerful technique for measuring the surface potential ata high spatial resolution. However, the measured surface potential often deviatesfrom the potential deep in the bulk owing to certain factors. Here, we performedKPFM measurements across the p-n junction, in which such factors were eliminatedas much as possible by selecting the sample, force sensor, and measurement mode. Themeasured surface potential distribution agrees well with the line shape of the simulatedbulk potential. Our results demonstrate that KPFM is capable of quantitativelycharacterizing potential distributions whose changes occur on the order of 10 nm.1. BackgroundKelvin probe force microscopy (KPFM) is a technique for measuring the work functionand electrostatic potential of a surface by detecting the contact potential difference(CPD) between the tip and the sample [1, 2, 3, 4]. Since its invention, KPFM hasbeen used to evaluate various electronic [3, 5, 6, 7, 8, 9, 10, 11, 12, 13] and ionic devices[14, 15, 16, 17, 18, 19]. In particular, several reports have focused on the characterizationof the built-in potential profiles in p-n junctions [5, 20, 8, 21, 22, 9, 11, 12], which are thekey components of semiconductor devices. However, the magnitudes of the measuredbuilt-in potentials are smaller than those expected from the actual band structure.There are two primary reasons for this discrepancy. The first is related to the factthat KPFM measures the surface potential. In general, the surface potential is differentfrom the potential deep in the bulk owing to surface band bending arising from surface2reconstruction, defects, surface oxidation, etc. [23, 24] The other is the tip-averagingeffect [25, 26, 27, 28]. The CPD measured by KPFM is a weighted average of the surfacepotential underneath the tip apex because of the long-range nature of the electrostaticforce acting between the tip and sample. It is generally difficult to compensate for theseeffects for arbitrary samples. These issues have prohibited the direct comparison ofCPD profiles with the simulated bulk potentials of specimens with continuously varyingpotential distributions on the nanometer-scale, such as p-n junctions in semiconductordevices.KPFM is a derivative of atomic force microscopy (AFM). Most of the devicecharacterizations using KPFM use the cantilever-based optical lever method [5, 20, 6, 7,8, 21, 29, 30, 9, 10, 11, 13]. When a cantilever is used, the averaging effect is caused notonly by the tip apex and cone but also by the metal film coated on the cantilever [27]. Incontrast, in AFM using a tuning fork type force sensor (qPlus sensor) [31, 32], no largemetallic part comes closer to the surface except for a relatively long sharp metal tip.Thus, the tip-averaging effect is expected to be smaller than when using cantilever-typeAFM.In this study, we performed KPFM using a qPlus sensor AFM to measure the well-defined potential distribution formed across the GaAs p-n junction, where most of thepotential change occurs within the range of approximately 50 nm. The measurementswere performed on a step-free GaAs(110) surface with a flat band from the bulk to thesurface [23, 33]. This enabled us to analyze the bulk potential distribution via surfacepotential measurements. Under these ideal conditions, we verified the quantitativityof the KPFM measurements. We show that the use of higher-order polynomialsinstead of a 2nd-order polynomial (a quadratic function) in the fitting procedure duringCPD derivation improves the accuracy of the CPD measurements. The CPD profilesobtained by the fittings coincided well with the line shape of the simulated potentialdistribution. Our results demonstrate that KPFM can quantitatively measure thepotential distribution as long as the change in the potential distribution occurs onthe order of 10 nm. We also show that the use of one-dimensional (1D) tunnelingspectroscopy together with KPFM is a powerful way to characterize band structures insemiconductor devices in detail.2. Methods2.1. Sample preparation and characterizationWe fabricated GaAs p-n junctions on n-type GaAs(001) substrates using solid-sourcemolecular beam epitaxy. First, we grew a 300 nm thick n-GaAs (Si doped, ND = 1×1018cm−3) buffer layer at a substrate temperature of 580 ◦C. Subsequently, p-n junctionlayers consisting of 600 nm thick n-GaAs (Si doped, ND = 5× 1017 cm−3) and 600 nmthick p-GaAs (Be doped, NA = 5× 1017 cm−3) were deposited. Finally, we grew a 300nm thick p+-GaAs (Be doped, NA = 2 × 1019 cm−3) layer. An alloyed AuGe/Ni/Au3electrode was fabricated on the substrate side for the ohmic contact. For the surface,the ohmic behavior was obtained by contacting the surface with the metal part of thesample holder due to the high doping concentration of the p+-GaAs layer.The diode properties of the device and its open-circuit voltage (OCV) wereevaluated by measuring the current-voltage characteristics in dark and under lightirradiation conditions, respectively. The measurements were performed using a sourcemeasure unit (ADCMT, 6241A) at 78 K under the ultrahigh vacuum (UHV) conditions.A laser diode (635 nm) was used as the light source. The total power of the laser was0.95 mW, and the roughly estimated diameter of the laser spot was 2 mm. The laserlight was introduced into the UHV chamber through a viewing port. The theoreticalpotential profile across the p-n junction was calculated using SEMITIP software version6 developed by Feenstra [34].2.2. STM and AFM measurements. Scanning tunneling microscopy (STM) and AFM measurements were performedat 78 K under UHV conditions (< 1 × 10−8 Pa) using a low-temperature scanningprobe microscopy (SPM) system (Unisoku USM-1400). The qPlus sensors withelectrochemically etched tungsten (W) tips were used. The typical resonance frequencyof the sensor ranged from 24 to 31 kHz. The surface oxide layers on the W tips wereremoved by Ar+-ion sputtering (1.5 kV) for 20 min, and the tip apex was conditioned onclean Au(111) surfaces prior to the experiments. The forces acting between the tip andsample were acquired in the frequency modulation (FM) mode [35] with an oscillationamplitude of 4 nm. A bias voltage was applied to the sample with respect to the tip.An n-type GaAs(001) wafer with a p-n junction layer on top was cut into pieces withthe size of approximately 8 mm × 3 mm. Each piece was fixed between two metal plateson a sample holder. A voltage can be applied to each metal plate individually. Thesample was cleaved at room temperature to obtain a clean GaAs(110) surface and wasimmediately transferred to the low-temperature SPM head. In the scanning tunnelingspectroscopy measurements, the variable tip-sample separation technique was used toensure a large dynamic range of current detection. The obtained spectra were convertedto a constant tip-sample separation by multiplying the measured current by exp(2κ∆z),where κ is the decay constant and ∆z is the offset of the tip-sample separation [36].The value of κ was determined experimentally by measuring the tip-sample distancedependence of the tunneling current [36, 37]. A value of 11 nm−1 was used for the datapresented in this study.3. Results and discussionFirst, STM was performed across the p-n junction to observe the surface propertiesusing a qPlus sensor with a W tip. The measurements were performed on a GaAs(110)surface prepared via cleavage. Figure 1(a) presents a large-scale STM image. The4(a)(b)[001]Growth direction0 pm200 pm0 pm150 pmFigure 1. (a) Large-scale (200 nm × 40 nm) constant current topographic images ofthe GaAs(110) surface obtained across the p-n junction with STM mode. The terminalof the p-n junction is short-circuited. Excitation of the qPlus sensor is turned off duringthe measurements. Bias voltage and tunneling current are set to −2.2 V and 10 pA,respectively. The dashed line represents the position where the KPFM measurementsshown in Fig. 2 were performed. (b) High-resolution topographic images (50 nm × 20nm) around the p-n junction interface in (a). The arrow indicates the position of thep-n junction interface estimated from the KPFM measurement.surface was atomically flat, and no steps were observed over a distance of more than 1µm. Therefore, the surface was considered to have no surface states within the bandgap;thus, the band near the surface was flat [23, 33]. In the middle of the image, a sharpcontrast change was observed; however, this position did not coincide with the positionof the interface between the p- and n-type layers. The position of the contrast changevaries depending on the bias voltage. Figure 1(b) shows a magnified STM image of thep-n junction interface. The p- and n-type layers were continuously connected withoutany strain or defects. Therefore, estimating the position of the interface using onlytopographic images was challenging. The arrow above the image indicates the positionof the p-n junction interface estimated from the CPD profile described below.Next, we performed KPFM to characterize the electrostatic potential distributionacross the p-n junctions. The qPlus sensor was oscillated with an amplitude of 4.0 nm,and the forces acting between the tip and sample were detected using the shift in theresonance frequency (∆f) of the sensor [35]. Tip-sample separation was controlled usingthe STM mode. For the KPFM measurements, ∆f was measured as a function of thebias voltage (U) at 1024 points on a 180 nm line along the [001] direction, as indicatedin Fig. 1(a) (dashed line). Each ∆f–U spectrum was fitted with a 2nd-order polynomial(a quadratic function) to derive the bias voltage (UCPD) at which the electrostatic forcebetween the tip and sample was minimized [1]. This method of CPD detection is calledKelvin probe force spectroscopy [38, 39, 40]. This method is equivalent to FM-KPFM[41] and is known to have a smaller tip-averaging effect than amplitude-modulationKPFM [41]. The CPD profile derived by the fitting is shown in Fig. 2(a) (solid blueline). The simulated potential profile is also displayed (dashed black line). The width ofthe space-charge layer estimated from the CPD profile was in reasonable agreement with5that of the simulation. However, the magnitude of the built-in potential (the potentialdifference between the p- and n-type layers) was smaller than that in the simulation.To determine the cause of the discrepancy between the experiment and theory, weanalyzed each ∆f–U spectrum and the fitting curve. In Fig. 2(b), we show the ∆f–Uspectrum (gray solid line) obtained at the left end of the 1D measurement line (n-typelayer) and the fitting curve (blue dashed line). The discrepancy between the spectrumand fitting was relatively large on the left side of the inflection point. Consequently,the CPD derived from the fitting shifted to the right (higher bias voltage) comparedwith the bias voltage at which the electrostatic force was minimized. The data obtainedin the p-type layer also exhibited a similar shift, although the shift was smaller thanthat in the n-type layer (see Supplementary Fig. S1). These shifts in the CPD valuesarising from fitting errors led to a smaller magnitude of the built-in potential than thetheoretical value.Errors in the fitting arise from bias-dependent changes in the tip-samplecapacitance. The electrostatic force gradient (F ′ts) between the tip and the samplemeasured by FM-AFM can be expressed as follows [3, 38]:F ′ts =12d2C(z, U)dz2(U − UCPD)2, (1)where z is the tip-sample separation and C(z, U) is the tip-sample capacitance. Whenthe tip and sample are metallic, the C(z, U) generally does not depend on U . Therefore,fitting the ∆f–U spectrum to a 2nd-order polynomial is physically reasonable fordetermining the minimum electrostatic force. However, this is not the case forsemiconductors, where C(z, U) depends on U because the width of the surface-charginglayer near the surface varies depending on the bias voltage [42]. For example, the widthof the accumulation layer (formed by the accumulation of charge carriers) is generallysmaller than that of the space-charge layer (formed by the depletion of charge carriersand the resultant charging of dopant atoms). The physically important aspect of CPDdetection is finding the bias voltage at which the electrostatic force is minimized; fittingwith a 2nd-order polynomial is not essential.To more accurately trace the curvatures near the inflection points of the ∆f–Uspectra, we attempted fittings using higher-order polynomials. The fitting curve usinga 9th-order polynomial is shown in Fig. 2(b) (red dashed line). The errors observedin the 2nd-order polynomial fitting were reduced, particularly on the left side of theinflection point. Consequently, the derived CPD shifted to the left (smaller value) thanthat derived from the 2nd-order polynomial fitting. The CPD profile obtained fromthe 9th-order polynomial fittings is shown in Fig. 2(a) (red solid line). The profilewas weakly smoothed using a three-point moving average filter to remove the noisediscussed below (the raw CPD profile is shown in Supplementary Fig. S2(h)). Themagnitude of the built-in potential was in reasonable agreement with the theoreticalvalue. Furthermore, the CPD variation across the space-charge layer reproduced theline shape of the simulated potential well.Supplementary Fig. S2 shows the dependence of the CPD profile on the order of the62 4 6 8Order of polynomial10 16 18 2012 141.50Bult-in potential (eV)1.451.401.351.302nd-order poly. fit9th-order poly. fitSimulation0 40 80Distance (nm)120 1600.00.2-0.20.4-0.40.6-0.60.81.0CPD (V)(a)(b)(c)-2.0 -1.0 0.0 1.0 2.0Bias voltage (V)-0.3-0.8-0.9-0.6-0.7-0.4-0.5-0.2Frequency shift (Hz)2nd-order poly. fit9th-order poly. fitExperimentFigure 2. (a) CPD profiles obtained across the p-n junction indicated in Fig. 1(a).The bias voltage and tunneling current were set to −2.4 V and 10 pA, respectively, forSTM feedback control. During the ∆f–U measurements, the tip was lifted by 100 pmfrom the set point separation. Blue and red solid lines indicate the CPD profiles derivedfrom 2nd- and 9th-order polynomials, respectively. The dashed black line displays thesimulated potential profile, which is offset for comparison with the CPD profiles. (b)∆f–U curve obtained at the left end of the 1D measurement line (gray solid line). Blueand red solid lines show the fitting curves using the 2nd- and 9th-order polynomials,respectively. Vertical lines indicate the inflection points of each polynomial. (c) CPDdifference between p-type and n-type layers (built-in potential) plotted as a functionof the order of polynomial. The dashed horizontal line indicates the theoretical valueof the built-in potential.7polynomial used for fitting. The magnitudes of the built-in potential in the CPD profileswere substantially smaller than the simulated values up to 3rd-order polynomial fitting.For the 4th- and higher-order polynomials, the line shape did not change noticeably andshowed reasonable agreement with the simulations. The noise level of the CPD profileincreased with increasing fitting order, probably because the increased accuracy of CPDdetection made the actual measurement noise more visible.To evaluate the quantitativity of the CPD measurements in detail, we measuredthe magnitude of the built-in potential from the CPD difference between the p- andn-type layers. In Fig. 2(c), the magnitude is plotted as a function of the polynomialorder from 2 to 20. The CPD difference increases steeply between the 2nd- and 4th-order fitting. Subsequently, it increased gradually up to the 10th-order fitting, when itsaturated near the theoretical value. After the 9th-order fitting, the difference from thetheoretical value was less than 10 mV. This finding indicates that the decrease in thebuilt-in potential due to the tip-averaging effect is negligible (less than 1 %) and thatKPFM using a qPlus sensor AFM can quantitatively measure the potential distributionsthat vary on the order of 10 nm.We also measured the changes in the potential distribution induced by lightirradiation at the p-n junction. In this measurement, the p-n junction was an opencircuit, and the bias voltage was applied to the substrate side (n-type layer side)electrode. The sample and the tip were prepared separately from those used to obtainthe data shown in Fig. 2. Figure 3 shows the CPD profiles obtained under dark- andlight-irradiation conditions. Light irradiation significantly altered the CPD profiles.The OCV estimated from the CPD change was 535 mV, which was consistent with theOCV (539 mV) obtained from the current-voltage characteristics of the p-n diode (seeSupplementary Fig. S3). This result confirmed that the potential distribution could alsobe quantitatively measured under the device operating conditions.To further verify the accuracy of our CPD measurements, we performed 1Dtunneling spectroscopy across the p-n junction. As the GaAs(110) has no surface stateswithin the band gap, the band edge positions can be estimated by analyzing the onsetof the tunneling current (It) in It–U spectra [36]. For the It–U measurement, thevariable tip-sample separation technique was used to obtain a large dynamic range ofthe tunneling current [36]. After the measurement, the It–U spectra were converted toa constant tip-sample separation (see the Methods section for the detailed procedure).The applied variation in the tip-sample separation is shown in Supplementary Fig. S4.It–U spectra were acquired at 1024 points on a 180 nm line along the [001] direction. InFig. 4(a), we present a two-dimensional (2D) color map of the absolute tunneling currentas a function of the distance (X-axis) and bias voltage (Y-axis). The valence band edge(EV) and conduction band edge (EC) calculated in the simulation are indicated by theyellow dashed lines.As seen in Fig. 4(a), the onsets of the valence and conduction band components(tunneling out of the valence band states and tunneling into the conduction band states)approximately reproduce the positions of EV and EC, which visualizes the band structure80 40 80Distance (nm)120 1600.00.2-0.20.4-0.40.6-0.60.8-0.8CPD (V)DarkLight 535 mVFigure 3. (a) CPD profiles obtained in the open-circuit configuration in the darkand under light-irradiation conditions. A bias voltage was applied to the substrate (n-type layer) side electrode. For the fitting procedures in CPD derivation, the 9th-orderpolynomial was used. The OCV estimated from the CPD change at the p-type layerwas 535 mV.across the p-n junction. However, some discrepancies were observed. In the regionsoutside the space-charge layer, the onset of the valence (conduction) band componentin the n-type (p-type) layer deviated slightly from the band edges by 50-100 mV (see alsoIt–U spectra shown in Supplementary Fig. S4). This was induced by the relatively smallcurrent component, called the dopant-induced component (D-component), observed inthe bandgap region [43], as explained in Supplementary Fig. S4. In the space-charge-layer region, the onset of the conduction (valence) band component agrees well withEC (EV) around the n-type (p-type) layer side edge. However, the deviations fromthe theoretical line shape increased toward the p-type (n-type) layer side. Becauseof these deviations, the apparent bandgap derived from the It–U spectra was largerthan the actual bandgap. These findings suggest that 1D tunneling spectroscopy canqualitatively visualize the band structure, but is less quantitative than CPD analysis.Despite its relatively low quantitativity, 1D tunneling spectroscopy providesessential information about the potential reference, that is, the band edge positionsrelative to the Fermi level. Note that KPFM measurements do not provide a potentialreference unless the work function of the tip is determined accurately. Considering thesefacts, the combined use of 1D tunneling spectroscopy and KPFM is a powerful methodfor characterizing the quantum semiconductor devices based on III-V materials. Insuch devices, precise controls and characterizations of some local physical properties,including the electric field, the doping condition, and the Fermi level position, arerequired for extracting the best device performance [44, 45].The 2D color map shown in Fig. 4(a) suggests that the D-component is highlysensitive to band bending. The D-component rapidly decreased as soon as the bandbegan to bend near the space-charge layer for both the n-type and p-type layers andcompletely vanished in the space-charge layer. This is because the charge carriers90 40 80(A)It(A)ItBias voltage (V)Distance (nm)16010-1010-1210-1410-1610-1010-1110-1210-130.01.02.0(a)(b)-2.0-1.0Bias voltage (V)1200 40 80Distance (nm)CPD1601200.01.02.0-2.0-1.0Figure 4. (a) 2D map of 1D tunneling spectroscopy data. The X-axis corresponds tothe distance, and the Y-axis corresponds to bias voltage. Excitation of the qPlus sensoris turned off during the measurement. To obtain comparable tunneling current valuesin both p- and n-type layers, the tip-sample separation at the initial bias point was keptconstant along the 1D measurement line. To do this, the tip was moved in the constantheight mode without feedback control. The current values below the noise level (20fA) in the raw data before distance compensation are mapped in white. The positionsof EV and EC from the simulation are indicated by yellow dashed lines. (b) 2D mapof 1D tunneling spectroscopy data obtained with the constant tip-sample separationmode and CPD profile (orange solid line) derived from simultaneously obtained ∆f–Uspectra. Tip-sample separation was regulated using the STM mode with a bias voltageof −2.2 V and tunneling current of 10 pA.(electrons or holes) that contribute to the D-component are depleted because of bandbending [46]. We also observed fluctuations in the onset positions of the D-componentdepending on its location in both the p- and n-type regions outside the space-chargelayer. This fluctuation can be explained by slight local potential fluctuations due to thepresence of impurities. These findings indicate that analyzing the spatial dependenceof the D-component provides strong insights into local band bending and local carrierconcentration.The qPlus sensor AFM enables simultaneous detection of tunneling current andelectrostatic forces. Thus, we can directly compare the band structures estimated from101D tunneling spectroscopy and the CPD profiles at the same location. Figure 4(b) showsa 2D color map of the It–U spectra and CPD profile (orange solid line) simultaneouslyobtained across the p-n junction. For this experiment, the variable tip-sample separationtechnique could not be used because ∆f signals cannot be converted for constant tip-sample separation. Therefore, the apparent bandgap in the 2D color map appears to belarger than the actual bandgap in all regions across the p-n junction. Nevertheless,the shapes of the band edges approximately reproduce the line shapes of EC andEV. Importantly, the line shapes varied almost parallel to the CPD profile. Thisresult also supports the fact that KPFM accurately measured the electrostatic potentialdistribution across the p-n junction.4. SummaryIn summary, our results demonstrate the effectiveness of KPFM measurements usingqPlus sensor AFM for characterizing the electrostatic potential distributions formed insemiconductor devices. We demonstrated that, for a semiconductor surface, the use of ahigher-order polynomial instead of a 2nd-order one (a quadratic function) in the fittingprocedure improves the accuracy of CPD detection. The CPD profile obtained by thefittings across the p-n junction reproduced well not only the magnitude of the built-inpotential but also the change in the potential across the space-charge layer. We alsosucceeded in measuring the open-circuit voltage of the p-n diode by detecting changesin the CPD profiles upon light irradiation. In addition to the KPFM measurements, wedemonstrated that 1D tunneling spectroscopy using the variable tip-sample separationtechnique could visualize the band structure across the p-n junction. The simultaneous1D tunneling spectroscopy and KPFM measurements provided evidence that the bandedge position and CPD profile varied similarly. All these measurements demonstratethat the KPFM measurements using qPlus sensor AFM can quantitatively measure thepotential distribution, whose change occurs on the order of 10 nm. Our results alsoprovide a basis for the future evaluation of quantum semiconductor devices based onIII-V semiconductors using STM, AFM, and KPFM.AcknowledgmentsWe would like to thank T. Noda for valuable discussions. This work was partiallysupported by JSPS KAKENHI Grant Numbers JP17K06366 and JP21H01818.References[1] Nonnenmacher M, O’Boyle M P and Wickramasinghe H K 1991 Applied Physics Letters 582921–2923[2] Melitz W, Shen J, Kummel A C and Lee S 2011 Surface Science Reports 66 1–27[3] Sadewasser S and Glatzel T (eds) 2012 Kelvin Probe Force Microscopy: Measuring andCompensating Electrostatic Forces (Springer)11[4] Glatzel T, Gysin U and Meyer E 2022 Microscopy 71 i165–i173[5] Kikukawa A, Hosaka S and Imura R 1995 Applied Physics Letters 66 3510–3512[6] Shikler R, Meoded T, Fried N and Rosenwaks Y 1999 Applied Physics Letters 74 2972–2974[7] Robin F, Jacobs H, Homan O, Stemmer A and Bächtold W 2000 Applied Physics Letters 762907–2909[8] Glatzel T, Sadewasser S, Shikler R, Rosenwaks Y and Lux-Steiner M 2003 Materials Science andEngineering: B 102 138–142[9] Minj A, Cros A, Auzelle T, Pernot J and Daudin B 2016 Nanotechnology 27 385202[10] Cai M, Ishida N, Li X, Yang X, Noda T, Wu Y, Xie F, Naito H, Fujita D and Han L 2018 Joule2 296–306[11] Noda T, Ishida N, Mano T and Fujita D 2020 Applied Physics Letters 116 163501[12] Nakamura T, Ishida N, Sagisaka K and Koide Y 2020 AIP Advances 10 085010[13] Hiraoka M, Ishida N, Matsushita A, Uchida R, Sekimoto T, Yamamoto T, Matsui T, Kaneko Y,Miyano K, Yanagida M and Shirai Y 2022 ACS Applied Energy Materials 5 4232–4239[14] Zhu J, Zeng K and Lu L 2012 Journal of Applied Physics 111 063723[15] Luchkin S Y, Amanieu H Y, Rosato D and Kholkin A L 2014 Journal of Power Sources 268887–894[16] Masuda H, Ishida N, Ogata Y, Ito D and Fujita D 2017 Nanoscale 9(2) 893–898[17] Masuda H, Matsushita K, Ito D, Fujita D and Ishida N 2019 Communications Chemistry 2 140[18] Otoyama M, Yamaoka T, Ito H, Inagi Y, Sakuda A, Tatsumisago M and Hayashi A 2021 TheJournal of Physical Chemistry C 125 2841–2849[19] Ishida N 2022 Beilstein Journal of Nanotechnology 13 1558–1563[20] Chavez-Pirson A, Vatel O, Tanimoto M, Ando H, Iwamura H and Kanbe H 1995 Applied PhysicsLetters 67 3069–3071[21] Jiang C S, Moutinho H R, Friedman D J, Geisz J F and Al-Jassim M M 2003 Journal of AppliedPhysics 93 10035–10040[22] Gysin U, Glatzel T, Schmölzer T, Schöner A, Reshanov S, Bartolf H and Meyer E 2015 BeilsteinJournal of Nanotechnology 6 2485–2497[23] Mönch W 2001 Semiconductor Surfaces and Interfaces, Third edition (Springer)[24] Zhang Z and Yates J T J 2012 Chemical Reviews 112 5520–5551 pMID: 22783915[25] Fuller E J, Pan D, Corso B L, Tolga Gul O, Gomez J R and Collins P G 2013 Applied PhysicsLetters 102 083503[26] Panchal V, Pearce R, Yakimova R, Tzalenchuk A and Kazakova O 2013 Scientific Reports 3 2597[27] Wagner T, Beyer H, Reissner P, Mensch P, Riel H, Gotsmann B and Stemmer A 2015 BeilsteinJournal of Nanotechnology 6 2193–2206[28] Axt A, Hermes I M, Bergmann V W, Tausendpfund N and Weber S A L 2018 Beilstein Journalof Nanotechnology 9 1809–1819[29] Jiang C S, Friedman D J, Geisz J F, Moutinho H R, Romero M J and Al-Jassim M M 2003 AppliedPhysics Letters 83 1572–1574[30] Baumgart C, Helm M and Schmidt H 2009 Phys. Rev. B 80(8) 085305[31] Giessibl F J 2000 Applied Physics Letters 76 1470–1472[32] Giessibl F J 2019 Review of Scientific Instruments 90 011101[33] van Laar J, Huijser A and van Rooy T L 1977 Journal of Vacuum Science and Technology 14894–898[34] Semitip version 6, https://www.andrew.cmu.edu/user/feenstra/[35] Albrecht T R, Grütter P, Horne D and Rugar D 1991 Journal of Applied Physics 69 668–673[36] Feenstra R M 1994 Phys. Rev. B 50(7) 4561–4570[37] Ishida N, Sueoka K and Feenstra R M 2009 Phys. Rev. B 80(7) 075320[38] Vančura T, Kičin S, Ihn T, Ensslin K, Bichler M and Wegscheider W 2003 Applied Physics Letters83 2602–2604[39] Münnich G, Donarini A, Wenderoth M and Repp J 2013 Phys. Rev. Lett. 111(21) 21680212[40] Albrecht F, Fleischmann M, Scheer M, Gross L and Repp J 2015 Phys. Rev. B 92(23) 235443[41] Zerweck U, Loppacher C, Otto T, Grafström S and Eng L M 2005 Phys. Rev. B 71 125424[42] Schwarz A, Allers W, Schwarz U D and Wiesendanger R 2000 Phys. Rev. B 62(20) 13617–13622[43] Feenstra R M and Stroscio J A 1987 Journal of Vacuum Science and Technology B: MicroelectronicsProcessing and Phenomena 5 923–929[44] Otsubo K, Hatori N, Ishida M, Okumura S, Akiyama T, Nakata Y, Ebe H, Sugawara M andArakawa Y 2004 Japanese Journal of Applied Physics 43 L1124[45] Watanabe K, Asahi S, Zhu Y and Kita T 2021 Journal of Applied Physics 130 085701[46] Feenstra R M, Yu E T, Woodall J M, Kirchner P D, Lin C L and Pettit G D 1992 Applied PhysicsLetters 61 795–797