Letterpubs.acs.org/NanoLett

Excited-State Spectroscopy on an Individual Quantum Dot Using
Atomic Force Microscopy
Lynda Cockins, Yoichi Miyahara,* Steven D. Bennett,† Aashish A. Clerk, and Peter Grutter
Department of Physics, McGill University, 3600 rue University, Montreal, Quebec H3A2T8, Canada
S Supporting Information*

ABSTRACT: We present a new charge sensing technique forthe excited-state spectroscopy of individual quantum dots,
which requires no patterned electrodes. An oscillating atomic
force microscope cantilever is used as a movable charge sensor
as well as gate to measure the single-electron tunnelingbetween an individual self-assembled InAs quantum dot andback electrode. A set of cantilever dissipation versus bias
voltage curves measured at different cantilever oscillation
amplitudes forms a diagram analogous to the Coulomb diamond usually measured with transport measurements. The excitedstate levels as well as the electron addition spectrum can be obtained from the diagram. In addition, a signature which can result
from inelastic tunneling by phonon emission or a peak in the density of states of the electrode is also observed, which
demonstrates the versatility of the technique.
KEYWORDS: Quantum dot, Coulomb blockade, single-electron tunneling, atomic force microscopy, excited-state spectroscopy,
charge sensing

T

In this manuscript, we present a new and extremely versatiletechnique for measuring excited QD states using the dissipationof an atomic force microscope (AFM) cantilever. Previous
experiments have shown that the ground state energy
spectrum,12−15 electron tunneling rate,12,14,15 and shellstructure (even without requiring a magnetic field)16 of single
dots and multidot complexes can all be measured, in addition to
imaging the dot topography in situ by using an AFM cantilever
as a movable charge sensor and gate. For a system consisting of
a QD tunnel coupled to a charge reservoir and capacitively
coupled to a conductive AFM cantilever, a bias voltage applied
between the charge reservoir and cantilever tip can induce
electrons to tunnel between the dot and reservoir (Figure 1).

he excited state spectrum is a measure of the energy levelsof a system associated with a fixed number of electrons.
Experimental techniques capable of accessing this spectrum
provide a useful tool for investigating quantum systems. This isespecially true when the system is a quantum dot (QD), a
promising potential quantum bit.1 Here, excited states can bedirectly exploited for a variety of tasks. For example, when amagnetic field lifts the spin degeneracy of a discrete energy level
due to the Zeeman effect, access to the excited level allows anelectron to be loaded into the QD with either spin up or downorientation.2 The excited state spectrum of a single QD can bemeasured optically by photoluminescence3 or by interband
optical absorption spectroscopy4,5 with confocal microscopy,
however such experiments always measure electron−holeexcitations which are subject to the Coulomb interaction
between electrons and holes. Although electrical transportmeasurements in single-electron transistor devices6 can provide
pure electronic excitation spectrum, other electrical techniques
which use fewer electrodes that are spatially separated from the
QD are highly valuable. They not only increase the flexibility inthe types of QDs studied (since fewer strict fabrication criteria
need to be met) but also reduce the invasiveness of themeasurement.7 An example is provided by charge sensing
techniques, which use a highly sensitive electrometer, such as aquantum point contact8 or single-electron transistor,9 to probe
the dot energy levels without passing an electrical current
through the QD. Such techniques have recently been used tomeasure QD excited states: first by using a quantum point
contact nearby a lateral QD2,10 and then by using a singleelectron transistor for a QD formed in a carbon nanotube.11© 2011 American Chemical Society

Figure 1. (a) Schematic of the setup. (b) Equivalent circuit diagram.

Since the AFM cantilever is acting as a scanning charge sensor
as well as gate, conveniently any dot can be spatially accessed
without the need for patterned electrodes anywhere on thesample. This allows for the measurement of a wide variety ofReceived: October 13, 2011
Revised: December 21, 2011
Published: December 26, 2011709

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LetterFigure 2. Oscillating cantilever tip (symbolized by the red curve), modulates the QD levels around. The levels are shown at three separate times, t0 is
the initial position of the levels, at t1 and electron tunnels into the dot, and at t2 an electron tunnels out of the dot. The density of states of the 2DEG
are shown in yellow. The dot and 2DEG are separated by a tunnel junction. (a) A small oscillation amplitude opens an energy window that justallows tunneling into the ground state (GS). (b) The larger oscillation amplitude opens an energy window that allows tunneling into the first excitedstate (ES) as well as GS (Δ: energy level spacing). (c) The energy window touches a region where the density of states of the 2DEG is not uniform,
affecting the tunneling rate of the tunneling-out electron. (d) Inelastic tunneling process involving photon/phonon emission.

Figure 3. (a) Dissipation (contrast enhanced) over the dot. (b) Line profile of the dissipation at amplitudes represented with dashed lines in panel a.
Each spectrum consisted of 30 000 points, taken over 30 s. The spectra in parts a and b were subjected to a 201 point moving average.

Ctip + Csub, which is the sum of the capacitances of the tip-dot
and dot-2DEG (Figure 1b).
The bias voltage Vb is applied to the 2DEG layer (via an
Ohmic contact formed by indium diffusion), and the cantileveris electrically grounded (Figure 1b). Tunneling between tip anddot is negligible due to the much larger tunnel barrier height ofthe vacuum gap as compared to the dot-2DEG barrier. Since
the cantilever tip is electrostatically coupled to the dot by Ctip,
the oscillating cantilever tip leads to an effective ac-gating of theelectrochemical potential levels of the dot through themodulation of the lever-arm, α = Ctip(z(t))/[Ctip(z(t)) +Csub], about a mean value which is set by Vb and the mean tipdot separation. For small oscillation amplitudes (i.e., in the
weak coupling regime16), when Vb is tuned to a point of QD
charge degeneracy, single-electron tunneling from the 2DEG ispossible, causing the dot to fluctuate between its n and n + 1
electron ground states. Although n stochastically fluctuates dueto the tunneling, its average value follows the oscillating tip
motion, subjecting the cantilever tip to an oscillating electrostatic force.16 The finite average time between tunnel events
causes a 90° out-of-phase as well as in-phase component of theoscillating force with respect to the cantilever motion. These
two components lead to increased cantilever dissipation and ashift in the cantilever resonance frequency, respectively.12,14,15
Increasing the cantilever oscillation amplitude will eventually
modulate the energy levels of the dot so much that an electron
can tunnel between n electron ground state and n + 1 electron
excited states. This is demonstrated by the schematic in Figure
2. The new tunneling processes involving excited states also
contribute to the dot-induced cantilever dissipation, causing it
to increase.16 By taking the derivative of the dissipation withrespect to Vb we can detect these small changes, and thereby

dots randomly distributed over the sample surface, such as
epitaxially grown self-assembled QDs or colloidal nanoparticles,
which are difficult to couple to patterned electrodes forconventional transport or charge sensing measurements. Here
we provide the first measurement of the excited states of a QD
by using an AFM cantilever as a charge sensor.
The experiment was performed in a home-built cryogenic
AFM,17 operated at 4.7 K. A Nanosensors PPP-NCLR
cantilever, with a resonance frequency of approximately 160
kHz and nominal spring constant of 48 N/m, was used. At 4.7
K, the cantilever quality-factor was approximately 150 000. The
tip-side of the cantilever was coated with a 10 nm titanium
adhesion layer and a 20 nm platinum layer to ensure electricalconductivity at low temperature. A Nanosurf easyPLL was usedin the self-oscillation mode for frequency detection andoscillation amplitude control. In self-oscillation mode, thecantilever is oscillated at its resonance frequency, and theoscillation amplitude of the cantilever is held constant by anautomatic gain controller.18 This allows us to simultaneously
measure the shift in resonance frequency (due to conservative
tip−sample interactions) and the damping (referred to as thedissipation) of the cantilever.19 Cantilever deflection is detectedby a fiber optic interferometer,20 operating with an RFmodulated 1550 nm wavelength laser diode. As depicted in
Figure 1a, the sample studied consists of uncapped InAs selfassembled QDs separated by a 20 nm InP tunneling barrier
from a two-dimensional electron gas (2DEG) backelectrodeformed in In0.47Ga0.53As quantum well.21 The dots typicallyhave charging energies greater than 15 meV, and so at 4.7 K weare in the Coulomb blockade regime for these dots. The
charging energy of the dot is defined as EC = e2/2CΣ where CΣ =710

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Lettermeasure the energy separations of the excited states (Δ1, Δ2,etc.).
In order to measure the excited states, the cantilever tip wasplaced over the center of an isolated dot (see the Supporting
Information, Figure S1) with a mean tip−sample separation of
20 nm and the Vb was swept for different oscillation amplitudes
while the distance-regulating feedback was shut off. Figure 3a
consists of 67 dissipation versus Vb spectra taken with different
cantilever oscillation amplitudes and the three representative
spectra are shown in Figure 3b. Such a spectrum taken at small
amplitude resembles Coulomb oscillation peaks observed intransport spectroscopy and is indeed an electron addition
spectrum (i.e., it measures the transition between n-electronand (n + 1)-electron ground states). The shift marked by thewhite curly bracket in Figure 3a is caused by a charge
rearrangement somewhere near the dot.
As clearly observed in Figure 3b, the height of the dissipation
peaks decreases with increasing cantilever oscillation amplitude.
The decrease and broadening of the peaks result from thechange of the probability distribution of the position of theoscillating cantilever tip: the cantilever is spending less of its
cycle near the position that leads to maximal tunneling, but it ishitting this condition over a larger range of voltages. As
described in ref 16, the highly asymmetric peak shape (mostnoticeable for the 1.9 nm oscillation amplitude spectrum in
Figure 3b) occurs because of degenerate energy levels within
the dot: the first half of the peaks within a set of degeneratelevels will always be skewed in the same direction along theenergy axis, while the latter half will be skewed in the opposite
direction. Figure 3a,b clearly shows that the first two peaks are
skewed away from each other, meaning that these peaks belong
to a single spin-degenerate orbital level. Although the third
peak is clearly skewed to the right, the directionality of the
fourth peak is difficult to discern. Included in the Supporting
Information is a single-electron addition spectrum (Figure S2)
which clearly shows that the fourth peak is skewed in the
opposite direction to the third peak, to the left, and therefore
these two peaks belong to another spin-degenerate orbital level
which is not degenerate with the next orbital level.
Figure 4 shows the dissipation derivative with respect to Vb,
with a zoom on the first two rightmost peaks. The derivative of
the broadened dissipation peaks look like down-pointing
triangles. As one increases the magnitude of Vb (i.e., moves
right to left), the rightmost bright white line of each triangle
corresponds to the transition from Coulomb blockade to where
the number of electrons on the dot can fluctuate between n andn + 1 by single-electron tunneling, and the dark line
corresponds to the transition from this fluctuating region to
the Coulomb blockade state with n + 1 electrons on the dot.
The feature shown in A−A′ in Figure 4a results from the singleelectron tunneling between the ground state level of the QD
and 2DEG and the process is depicted in Figure 2a.
The main features of interest in Figure 4 are the lines thatrun parallel to the rightmost triangle edges (e.g., B−B′). The
parallel lines result from the opening of additional tunnelingpaths once excited states become accessible within the energy
window set by the top and bottom swing of the cantilever
oscillation (Figure 2b). In Figure 4b, showing only the first(right) and second (left) peaks, two lines are visible on the firstpeak (the first marked B−B′) and two are visible on the second.
At larger oscillation amplitudes, more lines corresponding to
the higher excited states are resolved as can be seen in Figure
4a. While these features are consistent with excited state

Figure 4. (a) Derivative of dissipation data in Figure 3a (subjected to a
151 point moving average). (b) Close up of the first (right) andsecond (left) peaks in (a). Lines are overlaid to guide the eyes.

tunneling, they could also be due to other, more extrinsic,
effects (e.g., photon/phonon assisted inelastic tunneling andfeatures in the density of states of the reservoir). While all theseeffects are of great interest, the unambiguous identification of
their roles in our system requires more detailed study, as
discussed extensively in a recent review.22 We, however, stressthat our main result is to show that the present technique iscapable of resolving such features, regardless of their origin.
Here we discuss a possible scenario based on the assumptionthat the observed features (B−B′) originate from the orbital
excited states of the dot. Using the measured lever arm (α =0.042 ± 0.003: the detail found in Supporting Information), thedissipation spectrum acquired with the smallest oscillation
amplitude directly provides an energy spacing between the firstn=2
two Coulomb blockade peaks Eadd
= 2EC n=2 = 40 meV, andn=3
between the second and third peaks, Eadd
= 2EC n=3 + ΔE = 62
meV (Figure 3b). Here, ΔE is the orbital level spacing obtained
from the addition spectra, and we have allowed for the effective
charging energy EC (i.e., the interaction contribution to theaddition energy) to be n dependent. In the commonly used
constant interaction model (CI),23 EC is independent of n (i.e.,
ECn=2 = ECn=3), and thus our addition-spectrum measurement
would directly yield ΔE = 22 meV. This value for the levelspacing obtained from the addition spectrum is inconsistent
with what we measure from the excited-state spectra (via thelarge-oscillation cantilever dissipation spectra, Figure 4). Fromthese spectra, we found the level spacings of the first two orbital
excited states are: Δ1 = Δ2 = 11 meV for n = 1 and Δ1 = Δ2 =12 meV for n = 2.
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Letteremission, it will not change as a function of magnetic field,
while if due to the density of states of the 2DEG then a Zeeman
splitting of C−C′ would occur which reflected the g-factor of
the 2DEG.22 The capability of detecting inelastic tunnelingprocesses offers the prospect of inelastic tunneling spectroscopy30 in nano/atomic scale tunnel junctions.
In conclusion, we have demonstrated that an AFM can beused to not only measure the addition energy spectrum but also
the excited states of a quantum dot. In addition an interesting
feature was observed, resulting from a change in electron
tunneling rate, which could be attributed to the detection of aphonon mode or change in the density of states of thereservoir. The high spatial resolution of the AFM in
combination with the ability to measure the energy levels ofconfined electronic systems allows for the ability to study
systems which are difficult to contact with electrodes. Potential
examples of other such systems would be impurity or donor
atoms, or molecules on insulating surfaces.

The above discrepancy between the level spacing extracted
from the addition spectrum (ΔE) and from the large-oscillation
dissipation (Δ1) could result from two different causes. First,
adding a single electron to the dot could change the dot
confinement potential and hence the level spacing; similareffects have been seen in other QD systems.23,24 Second,
interaction effects beyond the CI model could be significant. A
Hartree−Fock treatment25 of a few-electron QD shows that theeffective charging energy for adding the third electron [ECn=3]
should be less than that for adding the second [ECn=2]; this is theresult of exchange interactions, as well as the difference
between interorbital and intraorbital direct interactions. In
contrast, if we assume ΔE = Δ1, our addition energies are
consistent with ECn=3 > ECn=2. Although this could be explained bya large antiferromagnetic exchange interaction, such aninteraction is inconsistent with microscopic calculations.25 We
thus believe that the first mechanism mentioned above is themore plausible explanation. In either of the above scenarios, theadvantage of being able to directly measure the excited state
spectrum at fixed n is clear: it provides a direct method formeasuring the level spectrum, without needing to make any
assumption about whether EC or the dot potential aredependent on the number of dot electrons. We note that
excited-state spectroscopy of an ensemble of self-assembled
InAs QDs grown on a GaAs substrate has previously beenreported. This was done by combining capacitance spectroscopy and far-infrared transmission spectroscopy which probes
intraband absorption.26,27 Reference 27 obtained the ndependent charging energy and observed ECn=3 < ECn=2. Thisapparent discrepancy might point to the different electronic
structure of uncapped versus capped QDs, a topic which
deserves more detailed investigation. We stress that, unlike thetechnique of ref 27, our approach allows one to directly probe
the excitation of a single QD without optical measurement.
Another feature of interest is the resonant line marked C−C′
in Figure 4a which occurs ∼40−50 meV from the n = 1 groundstate; it cannot be explained by the tunneling electron accessing
higher energy levels of the dot. The slope of C−C′ indicatesthat the mechanism involves a tunneling-out process.22 We
however confirmed that the dot is empty prior to the first peak
as no more peaks are observed in the frequency shift ordissipation for −6 V< Vb <+ 5 V, meaning that C-C′ cannot becaused by an electron tunneling out of lower lying energy levelsof the dot. Possible causes of C−C′ are thus a peak in thedensity of states of the 2DEG, or an inelastic tunneling
pathway. A peak in the density of states of the 2DEG affects theelectron tunneling rate, and can lead to abrupt changes in thedissipation which are enhanced in the dissipation derivative.
This commonly observed feature,6,28 which provides an avenue
for probing the density of states of the reservoir itself,22 is
depicted in Figure 2c.
Alternatively the C−C′ feature may be caused by a newtunneling pathway where inelastic tunneling is enabled by theemission of a phonon (the slope of C−C′ is indicative ofemission). The process is depicted in Figure 2d. The energy of
C−C′ (40−50 meV) is similar to that of the longitudinal optical(LO) phonon modes of InAs QDs grown on InP measured by
Raman spectroscopy.29 Here, the phonon energy corresponds
most closely to the LO phonon in the InP tunneling barrier asreported by ref 29, with the other possibilities being the InAs
dot, the 2DEG, or one of the interfaces between them. We
remark that the origin of C−C′ could be resolved by measuring
C−C′ as a function of magnetic field: if caused by phonon■

ASSOCIATED CONTENT

S Supporting Information*

Atomic force microscope images of quantum dot; determining
the dot level degeneracies from the dissipation peaks
asymmetry; and dissipation spectrum over quantum dot at 28
K: determining the tunneling rate and lever arm. This material
is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author*E-mail: yoichi.miyahara@mcgill.ca.
Present Address†

Department of Physics, Harvard University, 17 Oxford Street,
Cambridge, Massachusetts 02138, United States.

■

ACKNOWLEDGMENTS
We thank P. Poole, S. Studenikin, and A. Sachrajda at the
National Research Council of Canada for supplying us with the
InAs quantum dot samples and for helpful discussions. Funding
was provided by the Natural Sciences and Engineering
Research Council of Canada, le Fonds Québécois de leRecherche sur la Nature et les Technologies, the Carl Reinhardt
Fellowship, and the Canadian Institute for Advanced Research.

■

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