Physica A 302 (2001) 328–334www.elsevier.com/locate/physa

Junction symmetry e ects in resonant tunnelingthrough InAs nanocrystal quantum dotsDavid Katza , Shi-Hai Kanb , Uri Baninb , Oded Milloa ;∗aRacah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel

bDepartment of Physical Chemistry, The Hebrew University, Jerusalem 91904, Israel

Abstract

Tunneling spectra of InAs nanocrystals anchored to gold via linker molecules or deposited ontographite were measured using scanning tunneling microscopy, in a double-barrier tunnel-junctioncon5guration. The e ects of the junction symmetry on the tunneling spectra, due to both thevoltage division and the tunneling rates, are studied experimentally and modeled theoretically. Weobserve resonant tunneling through nanocrystal states without charging when the tip is retractedfrom nanocrystals deposited on graphite. Charging is regained upon reducing the tip-nanocrystaldistance, making the junctions more symmetric. In contrast, charging-free resonant tunneling wasnot achieved for the nanocrystal=linker-molecule=Au system. c© 2001 Elsevier Science B.V. Allrights reserved.

PACS: 74.50.+r; 74.70.Ad

Keywords: Scanning tunneling microscopy (or STM); Tunneling spectroscopy;Semiconductor nanocrystals; Quantum dots; Single electron tunneling

Tunneling spectroscopy of single semiconductor nanocrystal quantum dots (QDs) isof interest from both fundamental and applied aspects. On the one hand, the tunnelingspectra provide information on the QD discrete electronic level structure [1–4], whileon the other hand, semiconductor QDs are potential building-blocks in future electronicand opto-electronic nanodevices [5,6]. The tunneling spectroscopy experiments are com-monly performed in the double-barrier tunnel-junction (DBTJ) con5guration, where theQD is placed between two macroscopic electrodes [7]. In this geometry, in addition tothe QD level structure, the parameters of both junctions, in particular the capacitanceand tunneling rate, strongly a ect the I–V or dI=dV vs. V tunneling characteristics.

∗ Corresponding author. Tel.: +972-2-658-5670; fax: +972-2-658-4437.E-mail address: milode@vms.huji.ac.il (O. Millo).

0378-4371/01/$ - see front matter c© 2001 Elsevier Science B.V. All rights reserved.PII: S 0378 -4371(01)00450 -2

D. Katz et al. / Physica A 302 (2001) 328–334 329

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Fig. 1. (a) I–V tunneling characteristics and (b) corresponding tunneling spectra acquired at 4:2 K on an InAsQD∼ 2 nm in radius, showing the e ects of voltage division. The lower curves were taken with Vs =1:5 Vand at Is =0:04 nA, while the upper curves with Is =0:12 nA, moving the tip closer to the QD. The spectraare o set for clarity. A schematic of the tip-QD=DT=Au tunneling geometry is shown in the lower inset, andthe equivalent circuit is depicted at the upper inset.

Therefore, a detailed understanding of the role played by the DBTJ geometryand the ability to control it are essential for the correct interpretation of tunneling char-acteristics of semiconductor QDs, as demonstrated for semiconductor quantum wells [8].In a scanning tunneling microscopy (STM) experiment [1–3,9], a DBTJ is realized

by positioning the STM tip over the QD, as portrayed by the insets in Fig. 1. Thecapacitance and tunneling resistance of the tip-QD junction (C1 and R1) can be easilymodi5ed by changing the tip-QD distance, usually through the control over the STMbias and current settings (Vs and Is). On the other hand, the QD-substrate junctionparameters (C2 and R2) are practically stable for a speci5c measurement of a QD. Byvarying C1 one can modify the single electron charging energy, Ec, which depends onthe capacitance values, as well as the voltage distribution between the two junctions,determined by the capacitance ratio, V1=V2 =C2=C1 (see Fig. 1) [1,7]. The ratio between

330 D. Katz et al. / Physica A 302 (2001) 328–334

the tunneling resistances may a ect the degree of QD charging during the tunnelingprocess through the DBTJ [8].Previously, we have performed tunneling spectroscopy measurements on InAs nano-

crystals linked to gold by hexane–dithiol molecules, realizing a capacitively highlyasymmetric DBTJ (C2=C1 ∼ 10), where conduction band (valance band) [CB (VB)]states appeared at positive (negative) bias [1,9]. Single electron charging peaks were ob-served, from which two and up to six-fold degenerate s and p-like levels were identi5ed(denoted 1Se and 1Pe states, respectively), as depicted by the lower tunneling spectrumin Fig. 1(b). These states were directly imaged in a subsequent work on InAs=ZnSecore=shell QDs [10]. The observation of QD charging indicated that the tunneling rate�2˙ 1=R2 was smaller than (or on the order of) �1 ˙ 1=R1. Otherwise, for positivesample bias, an electron tunneling from the tip to the QD would escape to the substratebefore the next electron could tunnel into the QD (and an equivalent process wouldoccur for negative bias). Consequently, merely resonant tunneling through the QD stateswould take place, without charging. By increasing the tip-QD distance, we were ableto modify the voltage division between junctions, but could not achieve charging-freetunneling before losing the ability to obtain meaningful (well above the noise level)tunneling spectra. Recently, Bakkers and Vanmaekelbergh reported an STM study ofCdS and CdSe QDs, focusing on the role of voltage division [3]. In this paper, we dis-cuss the e ects of both the voltage division and tunneling rates on the tunneling spectra.In particular, we show that upon reducing R2, by working without linker molecules,charging-free resonant tunneling, as well as a transition back to tunneling accompaniedby QD charging, can be achieved for a single QD by controlling �1.InAs nanocrystals capped by organic ligands were prepared using colloidal chem-

istry [11]. The QDs were either anchored to a gold substrate via hexane–dithiol (DT)molecules (hereby, the QD=DT=Au geometry) or deposited onto freshly cleaved highlyoriented pyrolitic graphite (hereby, the QD=HOPG geometry). The tunneling spectrawere obtained either directly using lock-in technique or by numerical di erentiation ofmeasured I–V curves, yielding similar results. The data presented in this paper wereacquired at 4:2 K.Two tunneling spectra measured on the same InAs QD in the QD=DT=Au geometry

are presented in Fig. 1(b), showing the e ect of voltage division. The lower curve wasobtained with the tip retracted from the QD (using Is=0:04 nA and Vs=1:5 V), whilethe upper curve was obtained after bringing the tip closer to the QD (Is=0:12 nA).The apparent gap in the density of states around zero bias is larger for the spectrummeasured with the tip closer to the QD (LV =2:53 V), as compare to LV =1:61 Vwhen the tip retracted. This can also be clearly seen in Fig. 1(a), where the tunnelingcurrent is onset, for both positive and negative bias, at larger bias values in the uppercurve. This behavior is attributed to the e ect of voltage division between the twojunctions. In our measurements C1 is smaller than C2, therefore the applied voltage VBmainly drops on the tip-QD junction and tunneling through the discrete QD levels isonset in this junction. The real QD level spacings should thus correspond to spacings inV1, which is not directly measured. Hence, the apparent level spacings in the tunneling

D. Katz et al. / Physica A 302 (2001) 328–334 331

Fig. 2. A 20 nm× 15 nm topographic STM showing a single InAs QD ∼ 2:7 nm in radius on a bare HOPGsurface. The tip-QD=HOPG tunneling con5guration is shown schematically in the inset.

spectra are larger than the real level spacings by a factor of VB=V1 = (1 + C1=C2).Therefore, upon reducing the tip-QD distance, C1 increases and so does the measuredgap. Another consequence of reducing the tip-QD distance (i.e., making the junctionmore capacitive-symmetric) is that now tunneling can occur simultaneously through theCB and VB states even for a relatively small positive bias. This e ect manifests itselfin the upper curve of Fig. 1(b) by the appearance of an extra peak (and possibly peakbroadening) within the original s-like state doublet seen in the lower curve. Obviously,moving the tip closer to the QD can only increase the ratio of �1=�2, so QD chargingwas not be eliminated. This may be achieved only by retracting the tip further awayfrom the nanocrystal. However, as noted above, we did not enter the regime of resonanttunneling without QD charging in the QD=DT=Au geometry, possibly due to the low�2 value resulting from the linker molecules.In order to achieve charging-free resonant tunneling, R2 had to be reduced. To

this end, we deposited the InAs QDs on freshly cleaved HOPG. HOPG surfaces areatomically Mat as compared to the Au 5lms, facilitating the STM detection of the InAsnanocrystals. As illustrated in Fig. 2, a single nanocrystal is indeed clearly observedon the HOPG surface. However, the unlinked QDs were very mobile on the surfaceeven at 4:2 K. This imposed some problems in the spectroscopic measurements, sincein many cases the QDs could di use away from the tip before establishing optimal Isand Vs values.In Fig. 3(a), we plot a tunneling spectrum (solid curve) measured on an InAs QD,

∼ 2 nm in radius, using the QD=HOPG geometry portrayed in the inset of Fig. 2.For comparison, we also plot a representative spectrum measured on a QD of similarradius in the QD=DT=Au con5guration (dashed line). Both spectra exhibit a gap in thedensity of states around zero bias, associated with the QD energy band gap, and peaksat positive (negative) bias reMecting the CB (VB) states. However, there is a profounddi erence between these two spectra. In the spectrum measured in the QD=DT=Au

332 D. Katz et al. / Physica A 302 (2001) 328–334

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Fig. 3. (a) Tunneling spectra measured on InAs QDs ∼ 2 nm in radius. The solid curve was measured in theQD=HOPG geometry, and the dashed curve in the QD=DT=Au geometry. (b) Calculated spectra showing thee ect of tunneling rate ratio. The dashed and solid curves were calculated with �2=�1 = 1 and 10, respectively.

geometry, resonant tunneling accompanied by QD charging is clearly seen, exhibited(in the CB) by the doublet of peaks that is followed by a higher order multiplet. Asdiscussed above, the doublet corresponds to tunneling through the two-fold degenerates-like CB state with the spacing assigned to Ec, while the higher order multiplet isassigned to tunneling through the p-like state [1]. The charging multiplets are absentin the spectrum measured in the QD=HOPG system, and each multiplet is replaced bya single peak, indicating charging-free resonant tunneling through the s and p-like CBstates. Typically, the peaks observed in the QD=HOPG con5guration are broadened ascompared to those seen for the QD=DT=Au geometry, possibly due to small degeneracylifting within the s and p states. A similar behavior is seen also for the more complexVB. We attribute the di erence between the two spectra to the di erent ratios betweenthe tunneling rates (�2=�1) achieved in either of the DBTJs. A signi5cantly lower tunnelbarrier of the QD-substrate junction is expected in the QD=HOPG con5guration.To con5rm this interpretation, we performed theoretical simulations using the

“Orthodox Model” for single electron tunneling [7] modi5ed to account for the e ect ofa discrete QD level spectrum [9]. The solid and dashed theoretical curves presented inFig. 3(b) were calculated assuming the same two-fold and six-fold degenerate (s and p)CB levels, and two four-fold degenerate VB states [1,12,13]. The capacitance valueswere also kept the same for the two curves, C1 = 0:1 aF and C2 = 1:1 aF, resulting in

D. Katz et al. / Physica A 302 (2001) 328–334 333

a ∼ 90% voltage drop on the tip-QD junction and Ec ∼ 100 meV. The two curves dif-fer in the ratio between the tunneling rates: �2=�1 = 1 and 10 for the dashed and solidcurves, respectively (only the ratio is relevant for our discussion). The dashed curveshows strong charging multiplets, typical for resonant tunneling taking place along withQD charging. The solid curve, on the other hand, exhibits only a signature of charginge ect (e.g., one small charging peak in the p multiplet), which vanished for �2=�1larger than 100. It is evident that the curve for �2=�1 = 1 resembles the experimentalspectrum obtained for the QD=DT=Au system, while the �2=�1 = 10 curve better corre-sponds to the QD=HOPG con5guration, consistent with our interpretation above. Notealso that the apparent s–p level separation (both in theory and experiment) is smallerfor the QD=HOPG con5guration, due to the absence of charging contribution. The lackof charging implies that the relative peak areas of the s and p states should reMect thedi erent degeneracies of each level. However, experimentally, the peak areas are notas reproducible as peak positions. Theoretically, the treatment of peak shapes requiresa more elaborate description of the tunneling rates using overlap integrals between thetip and the QD states, and the e ect of degeneracy lifting.A transition from charging-free tunneling to resonant tunneling in the presence of

charging is demonstrated for the QD=HOPG system by Fig. 4. Here we plot twotunneling spectra acquired on the same QD of radius 2:5 nm, with di erent tip-QDseparations. The dashed curve was measured with Vs=1:5 V and Is=0:1 nA, whilethe solid curve was taken with Is=0:8 nA, moving the tip closer to the QD. Thereare two marked di erences between these two spectra. First, the apparent gap in thedensity of states around zero bias is larger for the curve measured with the tip closerto the QD. As explained in the discussion of Fig. 1, this is attributed to the e ectof voltage division between the two junctions. The second di erence is even moreprofound. In the solid curve, a doublet is observed at the onset of tunneling into the CB,in contrast to a corresponding single peak seen in the dashed curve. The second peak in

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Fig. 4. Tunneling spectra measured on a single QD (r ∼ 2:5 nm) with two di erent tip-QD separations,exhibiting the transition from charging-free resonant tunneling (dashed curve) to tunneling with QD charging(solid curve).

334 D. Katz et al. / Physica A 302 (2001) 328–334

the solid curve cannot be associated with the p state since the apparent s–p separationmust be larger here as compared to the dashed curve due to the e ect of voltagedivision, while the observed spacing is smaller. The peak spacing within this doubletis 170 meV, comparable to Ec values measured for InAs QDs of similar size [1].Hence, we attribute this doublet to single electron charging of the 1Se level. As thetip approaches the QD, �1 increases towards the value of �2 and thus the process ofresonant tunneling becomes accompanied by QD charging. Unfortunately, the tunnelingcurrent exceeded the saturation value of detection at a voltage that did not allow us tocheck whether single electron charging takes place also in the p level. We have alsoperformed size dependent spectroscopy of QDs on HOPG [14], yielding similar resultsfor the band gap and s–p level spacing to those reported in Ref. [1].In summary, we have demonstrated the e ect of varying the DBTJ parameters on

the measured tunneling spectra. The capacitance ratio between the junctions was foundto primarily a ect the apparent level spacing, whereas by varying the ratio between thetunneling rates, a control over the degree of QD charging during the tunneling processis achieved.

We thank Y.-M. Niquet for his helpful discussions. This work was supported by theIsrael Science Foundation founded by the Israel Academy of Science, the BIKURAfoundation, and by Intel-Israel.

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