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We present experimental demonstration of photocarrier dynamics in InAs quantum dots (QDs) via terahertz (THz) time-domain spectroscopy (TDS) using two excitation wavelengths and observing the magnetic field polarity characteristics of the THz signal. The InAs QDs was grown using standard Stranski-Krastanow technique on semi-insulating GaAs substrate. Excitation pump at 800 nm- and 910 nm-wavelength were used to distinguish THz emission from the InAs/GaAs matrix and InAs respectively. THz-TDS at 800 nm pump revealed intense THz emission comparable to a bulk p-InAs. For 910 nm pump, the THz emission generally weakened and upon applying external magnetic field of opposite polarities, the THz time-domain plot exhibited anomalous phase-shifting. This was attributed to the possible current-surge associated with the permanent dipole in the QD.
© 2015 Optical Society of America
1. Introduction
The Stranski-Krastanow (SK) growth technique has long been employed in fabricating quantum dots (QDs) for various optoelectronic applications. The complex yet remarkable dynamics associated with the SK growth has been proven effective for QD-based photodetectors [1, 2] and lasers [3, 4]. Recently, QDs grown via the SK growth have become more popular since it has been found suitable for terahertz (THz) applications [5–10]. InAs QDs embedded on GaAs bulk (InAs/GaAs), in particular, have carrier lifetimes in the picosecond regime and average carrier mobility comparable to known semiconducting THz materials [9–11].
For excitation energy greater than the bandgap of the GaAs spacer in InAs/GaAs QD structures, carriers usually thermalize to the conduction band minimum in the GaAs spacer after excitation. It is then captured in the InAs wetting layer before it relaxes and recombines into the InAs QD [11]. THz emission thus follows two main mechanisms. First, the QD can act as a fast recombination site for carriers generated at the GaAs spacer resulting to carrier lifetimes in the picosecond range [9]. Interfacial strain caused by the lattice mismatch between InAs and GaAs, in addition, increases the acceleration of carriers towards the QD thus enhancing the THz emission [5]. Second, the QD can be suitable for intraband population inversion, that is, it can have long carrier relaxation yet fast carrier recombination. For energy difference of ≤40 meV, between two subband levels, intraband THz emission occurs [6–8].
Previously, we have reported enhanced THz emission from InAs/GaAs QDs due to current-surge from the acceleration of GaAs carriers brought about by interfacial strain field [5]. The results were deduced with the absence of detectable THz emission for excitation energy less than the GaAs bandgap. In this work, we report on a possible current-surge from the photo-carrier drift associated with the permanent dipole in the QD thus demonstrating THz emission exclusively from InAs QDs. We use two excitation wavelengths (800 nm and 910 nm) and we observe the magnetic field polarity variation of the THz signal. The 910 nm excitation wavelength probes only the InAs layers while a 180°-phase shifting in the THz signal at any excitation wavelength, upon the reversal of the external B-field direction, lends proof to the presence of Lorentz force-driven carriers [12, 13]. The results suggest that THz time-domain spectroscopy (TDS) may be utilized as an effective tool to unambiguously observe photocarrier transport in pyramidal InAs QDs.
2. Experimental details
The InAs QD sample was grown via molecular beam epitaxy (MBE) on semi-insulating (SI)-GaAs substrate. As in Fig. 1(a), 500 nm GaAs buffer was first grown followed by 500 nm AlAs sacrificial layer for epitaxial lift-off purposes. Another 800 nm GaAs buffer was then deposited before initiating the growth of the InAs QDs. The InAs QDs were grown at substrate temperature of 520°C with growth rate of 0.136 MLs−1 and In:As flux ratio of 1:261. To confine the QDs, 9 nm GaAs spacer was deposited on top. The growth was terminated after growing 20 nm Silicon-doped GaAs (n-GaAs) cap. Figure 1(b) shows the reflection high energy electron diffraction pattern during the formation of the InAs QDs. A well-defined chevron pattern was observed.
Fig. 1 (a) Cross-section of the MBE-grown InAs QDs. (b) The chevron pattern observed during the formation of the InAs QDs. (c) THz-TDS applied B-field orientation.
To determine the average height and diameter of the InAs QDs, atomic force microscopy (AFM) measurement was performed on another InAs QD sample grown without an n-GaAs cap. Photoluminescence (PL) spectroscopy was also conducted at room temperature (300K) to observe the optical emission of the InAs QDs. A standard lock-in technique was employed using 488 nm Argon laser excitation source with power density set to 5 W/cm2. The PL signal was detected using a photomultiplier tube.
The THz emission of the grown sample was probed via standard THz-TDS measurement in reflection geometry [14]. The excitation source was a p-polarized mode-locked Ti:Sapphire with 100 fs laser pulse width and 80 MHz repetition rate. The excitation wavelength was tuned at 800 nm and 910 nm while keeping the average power constant at 100 mW. The pump beam was incident on the sample at 45° angle and was mechanically chopped at 2 kHz. The detector was an optically gated low-temperature-grown GaAs photoconductive dipole antenna. Dependence of the THz radiation in the polarity of an applied magnetic field (B-field) was determined using a 650 mT permanent magnet with the B-field oriented as in Fig. 1(c). The same THz-TDS scan was performed on two other reference samples, an SI-GaAs substrate and a bulk p-InAs, for comparison.
3. Results and discussion
The AFM image of the InAs QDs is shown in the inset of Fig. 2(a). The density of the QDs was approximately 3.8 × 1010 cm−2 with average height and diameter of 8 nm and 40 nm respectively before capping. Figure 2(a) shows the corresponding room temperature PL spectrum of the InAs QDs. There were two distinct peaks, A and B. Curve fitting showed that peak A was at 1.014 eV while peak B was at 1.066 eV resulting to a separation of approximately 52 meV. Peaks A and B were attributed to optical transitions from ground state and first excited state respectively [15]. The 52 meV separation can be a good approximation of the difference between the two subband levels in the conduction band [8]. Given that energy difference, intraband THz emission was not likely to occur. It has been shown by Omambac et. al. [15] that with the same InAs QD growth parameters and energy transition, the carrier relaxation time was long thus an energy difference between two subband levels below 40 meV was unlikely. Accordingly, the THz emission of the grown sample cannot be attributed straightforwardly from the InAs QDs. As in Fig. 1(a), there were other epitaxial layers such as the GaAs spacer and buffer, and the InAs wetting layer that may have also contributed to the THz emission of the sample. It is worth mentioning however, that there was no detectable PL emission from the InAs wetting layer at room temperature suggesting a highly dominant photocarrier capture mechanism in the InAs QD structures.
Fig. 2 (a) Room temperature PL spectrum of the InAs QD. Peaks A and B are at 1.014 eV and 1.066 eV respectively. The QD density (from the AFM inset) is approximately 3.8 × 1010 cm−2. THz waveforms of the p-InAs, SI-GaAs and InAs QD using (b) 800 nm pump and (c) 910 nm pump. The insets show the corresponding power spectra of the THz waveforms.
In Fig. 2(b) are the THz emissions of the SI-GaAs, p-InAs and InAs QD using the 800 nm pump. The THz emission of the InAs QD was higher than the SI-GaAs and was comparable to the p-InAs. It should be noted that for the InAs QD, the 800 nm pump could excite not only the InAs QDs but also the GaAs spacer and buffer, and the InAs wetting layer. By tuning the pump to 910 nm, excitation in GaAs layers was eliminated. It can be clearly seen in Fig. 2(c) that there was no THz emission from the SI-GaAs. Generally, the THz emission of the InAs QD and the p-InAs weakened using the 910 nm pump. This was due to the decreased electron excess energy at 910 nm excitation. The photo-Dember voltage was directly proportional to the temperature of photoexcited electrons which, in turn, was directly proportional to the electron excess energy [16, 17]. The inset in Figs. 2(b) and 2(c) shows the corresponding power spectra of the THz waveforms. The frequency bandwidth of the p-InAs (under 2 THz) did not vary much with the excitation wavelengths as compared with the SI-GaAs and the InAs QD. Using the 910 nm pump, there was no observed THz emission in the SI-GaAs. Consequently, the elimination of the THz emission from the GaAs layers of the InAs QD resulted to a lower frequency bandwidth (under 1 THz) at 910 nm pump. The high frequency component of the THz emission (at 800 nm pump) was due to the shorter capture time of carriers from the GaAs spacer to the InAs QD relative to the relaxation time of carriers within the QD. The change in bandwidth of the InAs QD (at 910 nm pump) can be approximately modeled by the generated photocurrent of a biased photoconductive antenna which is proportional to the THz electric field ETHz by:
where EDC, μe, Iopt, τp and τc are the DC bias field, electron mobility, optical pulse, optical pulse duration and carrier lifetime respectively with the assumption that the charged particles approaches drift velocity [18]. Equation (1) explicitly indicates that the peak THz frequency is inversely proportional with the carrier lifetime. Only carriers in the InAs layers were excited at 910 nm pump, thus lower frequency bandwidth was expected [19]. The power spectrum of the InAs QD THz waveform correspondingly had peak frequency of about 0.5 THz. If intraband THz emission was the dominant mechanism, the energy separation of the two peaks in the room temperature PL should have been approximately 2 meV. This was certainly not the case based on the curve fitting of the PL spectrum.In Fig. 3 are the THz waveforms of the SI-GaAs, p-InAs and InAs QD using the 800 nm pump and considering no-B, B+y and B−y cases. There was an observed enhancement in the THz emission in all samples upon the application of B-field. This was due to the increased THz emission efficiency. In the Drude-Lorentz model, the acceleration of carriers upon the application of external magnetic field (B+y or B−y) is given by the expression:
where e, E, m*, τ and ωc = eB/m* are the charge, electric field, effective mass, mean scattering time and cyclotron frequency respectively [20]. Although the application of B-field perpendicular to the plane of incidence changes the direction of the current transients, it does not change the magnitude of acceleration of the carriers. It rather bends the direction of current transients parallel to the surface wherein THz emission is more efficient [20, 21]. The insets in Fig. 3 show the THz waveforms obtained by subtracting the B+y and B−y data with the no-B data. As expected, there was an observed 180° flipping in the THz signal of the SI-GaAs and the p-InAs due to the reversed direction of the drift current. GaAs and InAs layers would result to a complete reversal of the THz waveforms upon changing the direction of the applied B-field [12,13]. Accordingly, the observed 180° flipping in the InAs QD was mainly due to its GaAs buffer and spacer, and InAs wetting layer.Fig. 3 THz waveforms of the (a) SI-GaAs, (b) p-InAs, and (c) InAs QD using 800 nm pump with and without applied B-field. The insets show the corresponding THz waveforms after subtracting B+y and B−y data with no-B data.
Similar response was observed in the p-InAs using the 910 nm pump and considering no-B, B+y and B−y cases. As in Fig. 4(a), there was a THz enhancement upon the application of B-field and there was a 180° flipping in the THz signal upon subtracting the B+y and B−y data with the no-B data. For the InAs QD however, there was no apparent flipping in the THz signal as the B-field direction was varied [Fig. 4(b)]. Partial flipping in the THz signal was observed only after subtracting the B+y and B−y data with the no-B data as in the inset of Fig. 4(b). The distinct response of the sample with the applied B-field was attributed exclusively from the InAs QDs. Although InAs wetting layer was also excited at 910 nm pump, its contribution to THz radiation due to transient photocurrent was negligible. The PL spectrum exhibited no detectable signal from the InAs wetting layer at room temperature evident of highly dominant photocarrier capture in the InAs QD structures. This was due to the slower carrier relaxation in the InAs QD compared to the capture time from InAs wetting layer to InAs QD.
Fig. 4 THz waveforms of the (a) p-InAs and (b) InAs QD using 910 nm pump with and without applied B-field. The insets show the corresponding THz waveforms after subtracting B+y and B−y data with no-B data. (c) Direction of the permanent dipole moment in the InAs QD. The electron (hole) is localized at the apex (base).
The THz emission of the InAs QD at 910 nm pump might arise from the photo-carrier drift in the InAs QD along the growth direction. This was an occurrence upon excitation but before carrier recombination which was possibly due to the InAs QD having a permanent dipole that spatially separates the electron and hole within the QD. Permanent dipole in a QD results from the induced strain and the difference between the effective mass of the hole and electron along the growth direction [22–25]. Localization of the hole and electron commonly occurs for QDs with pyramidal shapes such as the InAs QD sample. Fry et. al. had showed experimental evidences of a permanent dipole in an InAs QD [26]. However, their findings on the permanent dipole moment direction (p⃗) was in contradiction with the theoretical modeling made by Grundmann et. al [22]. From the theoretical model, the electron (hole) wave function was localized near the apex (base) of the QD as illustrated in Fig. 4(c).
Considering the THz-TDs performed in the InAs QD sample at 910 nm pump, the dipole moment direction followed the prediction of Grundmann. It can be seen from Figs. 3(a) and 4(b), in the no-B case, that the SI-GaAs and InAs QD samples had the same transient current direction. The SI-GaAs used in this study was characteristically p-type. For p-type semiconductors, Fermi-level pinning at the surface causes photoexcited electrons (holes) to be swept towards the surface (substrate) [14]. This corresponds to a dipole moment directed towards the substrate. The THz emission in SI-GaAs and InAs QD was both drift-related. Since the SI-GaAs and InAs QD samples had the same emitted THz waveform polarity in the no-B case, the dipole moment direction of the InAs QD was therefore assumed to be similar to the SI-GaAs which was towards the substrate.
Accordingly, the partial flipping of the THz signal with the applied B-field in opposite directions, shown in the inset of Fig. 4(b), proved the photo-carrier drift in the InAs QD. The partial flipping was due to the Lorentz force acting on the dipole. The flipping was not described by a 180°-phase shift in contrast to the bulk case reported by Migita et. al. [12]. Calculating the approximate cyclotron radius (Rc) of the electron for a B-field of B = 650 mT, an average builtin electric field of Ebi = 42 kV/cm [27] and using Eq. (2) to solve for the carrier velocity as a function of time, we get:
corresponding to Rc ∼ 500 nm – 2000 nm. These values were much larger than the dimension of the QD. For an InAs QD with 8 nm height and 40 nm diameter, the maximum inscribed circular radius was only 6 nm. The QD confinement hindered the complete circular revolution of the electron resulting to an incomplete reversal of the THz signal upon B-field polarity variation.4. Summary and conclusion
We have demonstrated THz emission exclusively coming from InAs QD associated with the possible current surge from the photo-carrier drift in the QD. The photo-carrier drift was believed to be due to the permanent dipole in the QD which was a result of the induced strain and the difference in effective mass of the hole and electron along the growth direction. This was supported by the partial flipping of the THz signal when the sample was immersed in opposite B-field polarities perpendicular to the plane of incidence of the 910 nm excitation laser. Complete reversal of the THz signal was not observed in this study owing to the much larger cyclotron radius as compared to the QD dimension. Even as the detected THz emission from the InAs QD may not be sufficiently intense, the anomalous B-field polarity characteristics establishes the underlying confined photocarrier transport from the apex to the base of the pyramidal QD.
5. Acknowledgements
The authors would like to acknowledge the support from the University of the Philippines (UP), Department of Science and Technology (DOST)-Philippine Council for Industry, Energy and Emerging Technology Research and Development, and DOST-Grants-In-Aid Program. E. Estacio also acknowledges the UP-Office of the Vice President for Academic Affairs for the Balik-PhD grant ( OVPAA-BPhD-2012-03).
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