A Two-Dimensional Electron Gas as a Sensitive Detector for Time-Resolved Tunneling Measurements on Self-Assembled Quantum Dots
© The Author(s) 2010
Received: 15 December 2009
Accepted: 25 February 2010
Published: 10 March 2010
A two-dimensional electron gas (2DEG) situated nearby a single layer of self-assembled quantum dots (QDs) in an inverted high electron mobility transistor (HEMT) structure is used as a detector for time-resolved tunneling measurements. We demonstrate a strong influence of charged QDs on the conductance of the 2DEG which allows us to probe the tunneling dynamics between the 2DEG and the QDs time resolved. Measurements of hysteresis curves with different sweep times and real-time conductance measurements in combination with an boxcar-like evaluation method enables us to unambiguously identify the transients as tunneling events between the s- and p-electron QD states and the 2DEG and rule out defect-related transients.
Studies on single or double (lithographically defined) QDs in a two-dimensional electron gas (2DEG) were enormously successful using time-resolved single charge read-out by an adjacent quantum point contact [1–3]. However, these measurements are limited to low temperatures (<300 mK) in a dilution refrigerator since the weak spatial confinement results in an orbital level spacing of typically smaller than 1 meV and a Coulomb charging energy which is a few meV. In contrast, self-assembled QDs can exhibit strong confinement and localization energy , resulting in an orbital level spacing energy of up to 80 meV and Coulomb charging energy of about 20 meV. Therefore, self-assembled QDs could enable to study these transport phenomena at higher temperature. However, no corresponding read-out scheme—like a quantum point contact—was demonstrated yet which would enable us to scale the size of a QD device down to a single self-assembled QD. Up to now, the charge carrier dynamics is mainly observed in time-resolved capacitance measurements of large ensembles of self-assembled QDs [6–9]; a measurement method which is very unlikely to scale down to a single dot. Using a 2DEG as a sensitive charge detector in the vicinity of self-assembled QDs could enable to scale down the QD number to probe single electron tunneling and/or hole dynamics in a time-resolved manner. It is also of basic importance to understand the carrier dynamics and read-out scheme in a future QD-based Flash memories , where single charge-carrier read-out is desired.
In this paper, we show that a 2DEG can be used as an efficient and sensitive detector to study the charge tunneling dynamics in an ensemble of self-assembled InAs QDs. Measurements of hysteresis curves of the transconductance of the 2DEG with different sweep times and real-time conductance measurements in combination with a boxcar-like evaluation method enable us to unambiguously identify the transients as tunneling events of the QD states and rule out defect-related transients. The developed evaluation methods and the favorable scaling laws of a 2DEG give us confidence to predict a time-resolved charge read-out of a single self-assembled QDs even up to room temperature in the future.
The investigated samples are inverted high electron mobility transistor (HEMT) structures with embedded self-assembled InAs QDs which were grown in a molecular beam epitaxy (MBE) system. The QDs are separated by a tunneling barrier from a 2DEG, which consists of a 10-nm-thick Al0.34Ga0.66As and a 20-nm-thick GaAs layer (total thickness of tunneling barrier d t = 30 nm). The sample growth sequence can be found in Ref. [11, 12]. We have prepared Hall bar devices with a metallic top gate in order to control the charge state of the dots and the 2DEG. Hall measurements yield a charge carrier density and a mobility of the 2DEG of about 7.4 × 1011 cm−2 and 9,340 cm2/Vs, respectively. The dot density of the sample is about 8.3 × 109 cm−2. The conductance of the 2DEG is measured in a two-terminal geometry at a fixed source-drain voltage between VSD = 30 and 50 mV. All measurements have been taken in a He cryostat at 4.2 K.
A major problem in hysteresis measurements on QDs—including laterally defined QDs in a 2DEG—may be the existence of defect states inside or nearby the QDs. If the charge carrier storage time inside the defect states is longer than the scan time, these deep levels will also cause a hysteresis effect in the transfer characteristic. Balocco et al.  have already observed a hysteresis effect on similar devices at room temperature and could relate the hysteresis to charge storage in such deep levels. Other groups require a light illumination to discharge the QDs [14–16] or measured hysteresis on laterally patterned electron channels [17, 18], however, could not rule out defect-related charge storage. We present here a simple evaluation method to rule out defect-related storage within the hysteresis measurement on QDs.
A simple estimation can now clarify how many charge carriers on average are depleted inside the 2DEG if one charge carrier is added to the QDs. Taking the QD sheet density of 8.3 × 109 cm−2 times the maximum number of six electrons per QD yields a charge carrier difference of 5.0 × 1010 cm−2 for completely charged to completely uncharged QDs, which is 7 percent of the charge carrier density inside the 2DEG at zero bias. The band structure calculation before yielded a relative change of about 6 percent; hence, both values are in good agreement. This means, that—as expected—one charge carrier inside the QD roughly depletes one charge carrier in the 2DEG if no free charges are surrounding the QDs.
Comparing the estimated value of about 7 percent in the change of the electron concentration inside the 2DEG with the observed value of 13% for the total change of the measured conductance leads to a second conclusion: the conductance change of the 2DEG is only partly due to a change in the charge carrier concentration; about 50% seems to have the origin in the change of the charge carrier mobility μ. Our estimation of an additional decrease in the mobility after charging the QDs with electrons is in contrast to a previous publication by Zhukov et al. . They observed an increase in the electron mobility for charged QDs; however, they used a sample structure with Si segregation from the delta doping into the spacer layer. These Si donors produce a strong disorder potential inside the 2DEG which is screened again by the charged QDs. Screening the disorder potential results in an increase in the charge carrier mobility. Our results are more in qualitatively agreement with the investigation of Ribeiro et al. . They observed a decrease in the mobility for increasing QD area density, i.e., for increasing number of charge carriers per unit area.
The ratio between the number of charge carriers inside the QD (N QD) and the number of charge carrier in the 2DEG (N 2DEG)—which is the conductance change due to carrier depletion—is independent on the sample size and number of QDs involved. This estimation supports our conclusion that this technique could be used to study the carrier dynamics of single self-assembled QDs as successfully shown before for lithographically defined QDs even if the charge in charge carrier mobility is not temperature independent and not scalable to smaller sample sizes.
The charge carriers inside the QDs deplete the 2DEG. As a consequence, a decrease in the conductance can be observed time resolved in the first milliseconds in Fig. 4. At t = 600 ms, an emission bias of V e = −1 V is applied, which sets the Fermi level E F below the lowest (s-) states of the QDs (schematically depicted in the left inset), and tunneling from the QDs to the 2DEG takes place. Note here the different time scales for the emission and charging process, as the time window of charging transient is about 2 ms and of the emission transient 30 ms. The different time scales of the charging and emission transient can be explained as follows. By applying the charging pulses the Fermi level E F of the 2DEG is in resonance with the highest p-level of the QDs and charge tunneling into the highest p-shell occurs on a faster time scale of about 1 ms. Afterward, the charge carriers relax into the lower QD states, which is well known to be of the order of ps for electrons in self-assembled QDs . Due to this two-step process (tunneling and relaxation), only the tunneling time into the p-states is visible in the charging transients. In contrast, the emission transient is a multi-tunneling process, because electrons of every QD state tunnel out simultaneously with different tunneling times up to 30 ms. This maximum tunneling time is in good agreement with frequency-dependent capacitance–voltage (C–V) measurements on the same sample, which yield a tunneling time for the first s-electron of τ s1 = 6 ms.
In conclusion, we have demonstrated that a 2DEG can act as a very sensitive detector for hysteresis and time-resolved measurements on self-assembled QDs. In such transport measurements, the clear identification of the QD states and the possibility to rule out a defect-related influence is of central importance. We have demonstrated two different evaluation methods—one for the hysteresis and another of the time-resolved measurements—that enables us to identify the QD electron tunneling in the measured transients and the charge storage inside the QD states in the hysteresis measurements. In these hysteresis measurements, we could show that the conductance change is partly due to depletion of the 2DEG in present of the charged QDs. The relative change of the conductance due to this depletion is up to 7% and should be independent on sample size and temperature. This makes us confident that it is possible to study the charge carrier dynamics of a single QD even at room temperature in the future.
The authors gratefully acknowledge financial support by the DFG in the framework of the NanoSci-E+ project QD2D of the European Commission.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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