Table Of ContentDetection of Single Electron Charging in an Individual InAs Quantum Dot by
Noncontact Atomic Force Microscopy
∗
Romain Stomp, Yoichi Miyahara, Sacha Schaer, Qingfeng Sun, Hong Guo, and Peter Grutter
Department of Physics, McGill University, 3600 rue University, Montreal, H3A2T8, Canada
5 Sergei Studenikin, Philip Poole, Andy Sachrajda
0 Institute for Microstructural Science, National Research Council of Canada, Ottawa, K1AOR6, Canada
0
(Dated: February 2, 2008)
2
Single electron charging in an individual InAs quantum dot was observed by electrostatic force
n
measurementswith anatomicforce microscope (AFM).Theresonant frequencyshift andthedissi-
a
J patedenergyofanoscillatingAFMcantileverweremeasuredasafunctionofthetip-backelectrode
voltage and the resulting spectra show distinct jumps when the tip was positioned above the dot.
1
The observed jumps in the frequency shift, with corresponding peaks in dissipation, are attributed
1
to a single electron tunneling between the dot and theback electrode governed by Coulomb block-
ade effect, and are consistent with a model based on the free energy of the system. The observed
]
i phenomenon may be regarded as the“force version” of theCoulomb blockadeeffect.
c
s
-
rl Self-assembled semiconductor quantum dots (SAQDs)
t grown by lattice mismatched heteroepitaxy have at-
m
tracted much attention as a promising system for many
.
t applications such as lasers, information storage devices
a
m and quantum computation. There have been a consider-
ablenumberofstudiesonthesingleelectronchargingef-
-
d fects on SAQDs locatedin field-effect structures because
n they enable the control of the charging state in the QDs
o
byexternalelectricfields. Thesestatescanbeprobedby
c
capacitance spectroscopy [1] which provides information
[
on the energy level structure as well as the charging en-
1
ergy of the QDs [2]. However, capacitance spectroscopy
v
2 probes an ensemble of dots and cannot be applied to an FIG. 1: (a) Schematic diagram of the sample structure and
7 individualQD.AccesstoindividualQDsisconsideredto the experimental setup, (b) equivalent electrical circuit, q is
2 beakeytechniquenotonlyforthefurtherunderstanding the charge in the QD, Ctip, Csub are the tip-QD and QD-
1 of the physics of QDs, but also for some practical appli- backelectrode capacitances, respectively.
0
cations such as information storage and qubit read-out
5
in quantum computation.
0
/ Scanning tunneling spectroscopy (STS) has been em- plainsthemainfeaturesoftheexperimentalresults. Asa
t
a ployed to investigate a single QD [3, 4]. However, appli- consequence,optimalsamplegeometriescanbe designed
m cationofSTS islimited to uncappedQDs onconducting and expected signal levels predicted for the experimen-
- substrates since a tunneling current greater than 1 pA tal detection of single charging events. In addition we
d is usually required. Electrostatic force measurement by observestrongvariationsintheAFMforcesensordamp-
n
o atomic force microscopy (AFM) is known to have sin- ing,whichdemonstratethepotentialofthis techniqueto
c gle electron sensitivity [5, 6, 7]. In these experiments, investigatethefascinatinginteractionsbetweenmicrome-
v: the observation of single electrons is based on the obser- chanicaloscillatorsandsingleelectronsystems[9,10,11].
i vation of quantized jumps in the force signal. Recently
X
spectacular results on a QD incorporated in a carbon The samples were prepared on a semi-insulating InP
r
nanotube (CNT) were reported [8]. To determine sin- wafer by chemical beam epitaxy [12]. The schematic of
a
gle charging effects in these experiments, corroborating the sample structure is depicted in Fig. 1. The SAQDs
transport measurement through the QD via the CNT spontaneouslyformduetolatticemismatchedheteroepi-
leads were necessary. This is unfortunately limiting for taxy. A two dimensional electron gas (2DEG) formed
many interesting systems such as SAQDs or suspected in the InGaAs quantum well was used as a back elec-
charge traps leading to 1/f noise in mesoscopic devices, trode located 20 nm underneath the InAs SAQDs layer.
as contact leads cannot easily be attached. In this Let- The electricalcontactto the 2DEGwasmade by indium
ter, we reportthe observationofsingle electroncharging diffusion and low resistance Ohmic characteristics were
events of a single SAQD by electrostatic force measure- confirmedbetweentwosuchcontactsat4.2K.The sam-
ment and present a simple theoretical model which ex- pleusedinthisexperimenthasasinglelayerofuncapped
2
characterizedby a parabolawhichreflects the capacitive
force between the tip and the back electrode. Since this
force is attractive, the resonant frequency shift is nega-
tive. For clarity, the negative frequency shift is plotted
inallthefollowingfigures. Theminimumfrequencyshift
atnon-zerobiasaccountsforthecontactpotentialdiffer-
ence between the tip and the sample. In addition to the
parabolic background, some jumps are found in the fre-
quency shift at variousbias voltages. We attribute them
tothediscretechangeintheelectrostaticforceduetose-
quentialchargingofasingleQDbyasingleelectrontun-
nelingbetweenthe QDandthebackelectrode(Coulomb
blockade). TheseCoulombblockade(CB)jumpsarealso
observed in the dissipation signal as peaks at the same
bias voltages. The increase in dissipation is obviously
FIG.2: Resonant frequencyshift, ∆f and dissipated energy
of the AFM cantilever as a function of the tip-sample bias related to the dissipated energy in the electron tunnel-
voltage. The arrows points the sudden increases in the ∆f ing process. This correspondence is helpful to identify
causedbyasingleelectroncharginginaQDandtheyappear the CB jumps at a lower bias voltage whose frequency
asapeakinthedissipationatthecorrespondingbiasvoltage. shift counterpart tends to be identified with difficulty.
Theinsetsshowthemagnifiedspectrumaroundthestructure
No structure like those mentioned above were observed
A- and A+. Here, a fitted parabola to the spectrum around
on the sample without the QD.
theminimum is subtracted.
We consider a simple model based on the free energy
of the system as depicted in Fig. 1(b) to calculate the
InAs SAQDs with a small dot density (5 µm−2 ). The force acting on the AFM tip. The free energy consists of
typicaldotis50±10nmindiameterand12nminheight. the electrostatic charging energy and the work done by
InordertoprobeindividualQD,weusedanAFMinthe the voltage source and can be expressed as [17]:
frequency modulation mode [13]. In this technique, the
q2 C 1C C
AFM cantilever is self-oscillated at its mechanical reso- W = − tipqV − sub tipV2. (1)
2C C B 2 C B
nance frequency f by a positive feedback circuit with Σ Σ Σ
0
a phase shifter and the resonance frequency shift ∆f Here q is the charge residing in the QD. C and C
sub tip
caused by the tip-sample interaction is measured by a arethe QD-substrate,the tip-QD capacitanceand C =
Σ
phase locked loop [14]. The oscillation amplitude, A, C +C , respectively. The force acting on the tip F
tip sub
of the tip is held constant at 5 nm with an automatic can be obtained by F =−∂W/∂z where z is the tip-QD
gain controller (AGC). This enables the measurementof distance. Then we get
dissipationinthe cantileveroscillationsimultaneouslyto
∆f. Our home-made cryogenic AFM [15] uses a fiber- F = 1 ∂Ctip q2 −C qV + 1C2 V2 (2a)
interferometricdeflectionsensorandhasbeenpreviously C2 ∂z (cid:18) 2 sub B 2 sub B(cid:19)
Σ
used for successful imaging of vortices on Nb [16]. The 2
1∂C q
experiments were performed at 4.2 K in high vacuum of = series VB− , (2b)
2 ∂z (cid:18) C (cid:19)
1×10−4 mbar. The cantilever used in our experiment sub
had a resonance frequency, f0, of 150 kHz with a spring where Cseries = CtipCsub/(Ctip +Csub). The first term
constant,k,of15N/m. Thetipwascoatedwitha10nm accounts for the interaction between the charge in the
Ti/20nmPttoensuregoodelectricalconductivityat4.2 QD and its image charge in the tip but it is negligibly
K. After identifying a single QD by AFM by noncontact smallunderourexperimentalconditions. Thethirdterm
imaging, we performed series of electrostatic force spec- showsthe parabolicbackgroundandaccountsfor the in-
troscopy (EFS) over the QD as a function of tip-sample teraction between the polarized charges in the tip and
separation. This spectroscopy records the change in the the back electrode. The interaction between the charge
resonancefrequencyof the cantilever,∆f,causedby the in the QD and the polarizedcharge in the tip is actually
tip-sample interaction as a function of the bias voltage included in the second term and is responsible for the
betweenthetipandthebackelectrodewhilethedistance detection of the charge in the QD. It should be noticed
regulation is turned off. The average tip-QD distance is from Eq. (2b) that the expression reduces to a simple
typicallymorethan10nmsothatthetunnelingbetween parabola when q is independent of V .
B
the tip and the QD is negligible and the electrostatic In this system, unlike the double tunneling junction
force is the dominant interaction. which has been investigated by STS, only an electron
Figure 2 shows a typical EFS spectrum and the dis- tunnelingbetweenthe backelectrodeandtheQDispos-
sipation signal. The overall shape of the spectrum is sible because of the large tip-QD distance. For this tun-
3
neling to be possible, the final state must be energeti- jumpCisalsoduetothesmalleramplitude. Theshiftof
cally favorable. This requires W(n+1) < W(n) for an the jump due to this effect should be corrected in order
electron to tunnel onto the QD with n electrons, and to investigate the detail of the spectra, such as internal
W(n − 1) < W(n) for an electron to tunnel off the energy levels of the QD where the separations between
QD with n electrons. This determines the bias range neighboring jumps are of serious concern. Regardless,
(Coulomb blockade) in which the electron tunneling is wefocusonthe tip-QDdistancedependence ofthe jump
forbidden: B to demonstrate that the observedfeature is consistent
with the theory discussed above.
e 1 e 1
n− <VB < n+ . (3) Figure 4(a) shows a series of EFS spectra taken over
C (cid:18) 2(cid:19) C (cid:18) 2(cid:19)
tip tip a QD at various tip-QD distances. As expected from
This translates into the condition, −E /e < V < the theory, the jump shifts to the lower bias voltage as
c sub
the distance becomes smaller because of the larger C .
E /e = e/2C which relates the charging energy of the tip
c Σ
Assuming that the spacing between B+ and B- is equal
QD, E , to the applied voltage to the QD through the
c
relation, V =(C V −ne)/C . Eq. 3 leads to to 3∆, Ctip is found to range from 0.064 to 0.094 aF.
sub tip B Σ
This is one order of magnitude smaller than that in the
C V 1 STS experiment. In STS such a small value is not per-
q =−ne=−e Int tip B + (4)
missible because of associated low tunneling rate which
(cid:18) e 2(cid:19)
is far less than that equivalent to a current of 1 pA. In
where the function Int gives the nearest integer to the other words, the electrostatic force detection is sensitive
argument. By combining Eq. (2a) and Eq. (4), the force to evena single electronchargingeventunlike STS mea-
can be obtained as a function of the bias voltage. The surements which statistically average a large number of
calculatedF-V curvesareshowninFig.3(a)forvarious suchevents. Larger∆f intheexperimentthanthecalcu-
B
z . Step-like structures are found on the parabolic back- lated one is attributed to the electrostatic force between
0
ground. The distance between two neighbouring jumps the tip and the substrate around the QD which is not
isconstantandgivenby∆=e/C . Thestepheightin- taken into account in the calculation. It also accounts
tip
creases at higher bias voltages because it is proportional for less sharp jumps in the experimental spectra.
to the VB as can be seen in the second term of Eq. (2a). AsisshowninFig.4(b),thespacingbetweenthejumps
This means that the structure nearer the zero bias is
harder to observe. A closer look at Eq. (2a) shows that
decreasingC (increasingthedistancebetweentheQD
sub
and the back electrode)enhances the jumps and reduces
the parabolic background. Note that increasingthe QD-
back electrode separation decreases the tunneling rate.
The resonant frequency shift of the cantilever mea-
sured in EFS is related to the force through the rela-
tionship [18]:
f2 1/f0
∆f(z )= 0 F(z +A cos(2πf t))cos(2πf t)dt.
0 0 0 0
kAZ
0
(5)
Thefrequencyshiftisaweightedaverageoftheforceover
one oscillation period. The calculated ∆f-V curves are
B
shown in Fig. 3(b). Although the step in F-V curve
B
translatesinto broaderincreasein∆f becauseofthe av-
eraging,the onsetof the increasestill correspondsto the
step in F-V curve at the closest distance in one oscilla-
B
tionperiod. ThisallowsustodetermineC from∆f-V
tip B
curves using Eq. (3). When we look at Fig. 2 carefully,
the spacings between two neighboring jumps are not ex-
actly the same. One reasonis that the oscillation ampli-
tude decreases around the jumps due to feedback errors
of the AGC. The decrease in the amplitude leads to an
increase in the closest tip-QD distance which results in FIG.3: Calculated(a)electrostaticforceand(b)correspond-
the shift of the jumps to higher bias voltage. The sig- ingfrequencyshift asafunctionofz0 usingEq.(2a),(4)and
nificant decrease in amplitude was actually observed at (5). Aparallelplatecapacitormodelwithanareaof227nm2
(17 nm diameter disk) is assumed.
jump B and C, respectively. The sharper increase at
4
(in particular the back electrode to QD spacing). This
will enable experimental investigation of single charging
events in diverse systems such as SAQDs and charge
traps in mesoscopic systems. In contrast to STS, this
techniquecanbe usedtoinvestigatingaQDonlyweakly
coupled to an external electrode. Finally, we have ob-
served strong contrast in dissipation, which cannot be
explained by classical Joule dissipation. We currently
only speculate that this is due to back action effects of
single electron charging events on the micromechanical
AFM oscillator.
This research was supported by the Natural Science
andEngineeringResearchCouncil ofCanada,the Cana-
dian Institute of Advanced Research, and NanoQu´ebec.
FIG. 4: (a) Electrostatic Force Spectra as a function of the
tip-QD distance. The number on the righthand side is the
absolute tip-QD distance obtained from a linear fitting. (b) ∗ Corresponding author: [email protected]
Spacing of the jump B- and B+ versustip-QDdistance.
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