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Abstract
The photocarrier dynamics in molecular beam epitaxy (MBE)-grown single- (SLQD) and multi-layered (MLQD) InAs/GaAs quantum dots were studied. Photoluminescence (PL) spectroscopy has shown that the MLQD has more uniform QD size distribution as compared to the bimodal SLQD. Correlation between PL and THz-TDS has shown that photocarrier transport is more favored in the MLQD owing to this uniform QD size distribution, resulting to higher THz emission. The THz emission from the QD samples were found to be proportional to temperature. A drift-related photocarrier transport mechanism is proposed, wherein photocarriers generated in the QDs are accelerated by an interface electric field.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
InAs/GaAs quantum dots (QDs) are zero-dimensional artificial heterostructures that have found applications as far-infrared emitters and detectors [1,2]. These QDs have been attractive due to their relative ease-of-integration with the well-established GaAs device fabrication technology. In order to design and optimize the optoelectronic device, the optical and luminescence properties of the QD structure are usually studied. Among various optical characterization techniques, photoluminescence (PL) spectroscopy is very popular since it is contactless and non-destructive [3]. In InAs/GaAs QDs, the origin of these PL emissions can be due to ground state (GS), excited state (ES), or defect-related transitions [4–6]. Similarly, terahertz time-domain spectroscopy (THz-TDS) is becoming a valuable optical characterization technique for investigating carrier dynamics and transport in semiconductor heterostructures [7]. The ultrafast photoexcitation of semiconductors via illumination of femtosecond laser pulses creates a transient photocurrent, resulting in the generation of THz radiation [8]. The measured THz radiation can provide information on different semiconductor material properties such as doping type, surface electric field, band offset, and dipole orientation [9–12]. Moreover, semiconductor heterostructures such as quantum wells (QWs) and QDs have the potential to serve as viable active components of THz-TDS systems [13,14]. The development of QD photoconductive antenna (PCA) devices would also result in cheaper and compact THz-TDS systems since it is compatible with the telecommunication wavelength technology [14]. The incorporation of nanoparticles and nanostructures have also been previously reported to enhance THz emission in semiconductor devices [15]. These reports primarily attribute the enhancement to plasmonics effects. In this work, the QD structures, themselves, are the THz emitters owing to transient photocurrent generation . PL spectroscopy was performed to investigate the photocarrier recombination and optical properties of MBE-grown single - (SLQD) and multi-layered (MLQD) InAs/GaAs QD samples. Temperature- and excitation power-dependent PL spectroscopy were used to distinguish between the possible origins of the PL transitions. THz-TDS was done to study photocarrier dynamics and transport in the QD samples in comparison with bare semiconductor surfaces such as p-InAs and SI-GaAs. Using temperature-dependent THz-TDS spectroscopy, we elucidate the THz radiation mechanism from the QD samples. We also studied the correlation between PL and THz to assess recombination versus photocarrier transport. These results could provide insights in the design and optimization of future QD-based THz optoelectronic devices.
2. Experimental details
The InAs/GaAs SLQD and MLQD samples were grown via Stranski-Krastanov (SK) Growth Technique using a Riber 32P molecular beam epitaxy (MBE) facility. A semi-insulating gallium arsenide (SI-GaAs) wafer was used as the substrate. Initially, a 1 µm undoped GaAs buffer was deposited on the substrate at $T_s =$ 640 °C. It was then followed by the deposition of three pairs of GaAs/AlAs superlattice and a 300 Å undoped GaAs layer. For the SLQD sample, the growth of the InAs/GaAs QD layer was initiated by the deposition of a single InAs wetting layer. After a certain critical thickness, island formation resulted to the formation of pyramidal QD structures. Then, a 300 Å undoped GaAs layer was grown on top of the QD layer. For the MLQD, similar steps were taken using eight InAs/GaAs QD layers, with each QD layer separated by a 330 Å undoped GaAs layer. Lastly, a 300 Å n-GaAs cap was deposited on top. Based from previous AFM measurements, the dimensions of our MBE-grown QD samples have a typical height of 6 nm-9 nm, diameter of 20 nm-40 nm, and density of $1-3\times 10^{10}\mu m^{-2}$ [16–18].
Photoluminescence spectroscopy was performed using an 808 nm Mai Tai laser as the excitation source. The samples were loaded on the cold finger of a closed-cycle helium (He) cryostat. The PL signal was collected and focused into the entrance slits of a Triax 550 spectrometer equipped with a silicon (Si) photodiode. Temperature-dependent PL spectroscopy was performed from 14 K to 300 K at a fixed laser power of 105 mW. The excitation dependent PL spectroscopy was performed from 0.1 mW to 175 mW at a fixed temperature of 14 K.
The THz emission from the samples was measured using a standard THz-TDS setup in conjunction with a cryostat. A mode-locked Ti:Sapphire femtosecond laser with a central wavelength of 870 nm, pulse width of 100 fs, and repetition rate of 80 MHz was used as the excitation source. The central wavelength at $\lambda =$ 870 nm with full width at half maximum $\Delta \lambda =$ 12 nm was chosen to avoid photo-excitation of the GaAs layers. The laser beam was split into pump and probe arms. The pump beam was mechanically chopped using an optical chopper and hits the samples at an excitation power of 70 mW. The estimated beam spot size at the focal point is 55 µm and the corresponding excitation fluence is 20 µJ/cm2. The THz emission from the samples was collected using a pair of off-axis paraboloids (f = 75 mm) and redirected into the dipole gap of an LT-GaAs PCA and the probe beam ($\lambda =$ 870 nm) was used to optically gate the PCA. To avoid photoexcitation of the GaAs layers, the temperature-dependence measurements of the THz emission were performed at a range having a maximum of 200 K; wherein the bandgap of GaAs would still be higher than the 870 nm wavelength of the fs laser excitation.
3. Results and discussion
Figure 1(a) and 1(b) show the temperature-dependent PL spectra for the SLQD and MLQD, respectively. Two prominent energy peaks can be observed for both spectra. At $T =$ 14 K a peak at 1.240 eV (Peak A) and 1.290 eV (Peak B) can be observed in the SLQD PL. Similarly, a peak at 1.305 eV (Peak C) and 1.390 eV (Peak D) can be observed in the MLQD PL. The PL signal from the MLQD is relatively weaker than the SLQD sample. A third peak near 1.424 (Peak G) can also be observed in the MLQD especially at 300 K, corresponding to bulk GaAs. No signal was observed from the wetting layer.
Fig. 1. (a) Temperature-dependent PL spectra of (a) SLQD and (b) MLQD. The PL spectra undergoes redshift as T increases. The PL peak intensity also decreases and the FWHM broadens at elevated T. Two peaks can be observed for both SLQD and MLQD PL. A 3rd peak corresponding to bulk GaAs only becomes evident in the MLQD sample at 300 K
In general, the PL intensity of the samples decreases as T increases. However, an anomalous behavior in this trend can be observed from $T=14~K$ to $30~K$. These results have been previously reported as due to (i) carrier redistribution between different QD sizes or (ii) competition between GS and ES transitions [4,19,20]. Additionally, multilayering is expected to result in a more uniform QD size distribution for the MLQD. This should yield narrower full width half maximum (FWHM) of the MLQD PL spectra, as compared to the SLQD. However, we observed comparable FWHM between the SLQD and MLQD samples. Using the absorption coefficient of $1.3 \times 10^{4}$ $cm^{-1}$ at 808 nm for GaAs, we have calculated the penetration depth to be $\approx$ 766 nm [21]. This suggest that all QD layers are possibly photoexcited, resulting in a broad FWHM of the MLQD PL. The PL spectra undergo a redshift as T is increased and thermal effects induce broadening. Peak B also becomes less prominent at higher T. The PL spectra were deconvolved and Gaussian curve fitting was performed in order to properly extract the energy values. The temperature-dependence of the bandgap $E_g (T)$ was then modelled using the Varshni Eq. [22]:
where $E_0$ is the bandgap at $T=0~K$, $\alpha$ and $\beta$ are constants, and $T$ is the temperature. Band-to-band transitions such as GS and ES transitions are known to obey Eq. (1) Meanwhile, defect-related transitions will not follow Eq. (1) and will thermalize at higher T [23]. Figure 2 shows the plot of the PL energy peak versus T. As it can be seen, all observed peaks follow the behavior dictated by Eq. (1). None of the peaks are possibly defect-related. Table 1 summarizes the results of Varshni fitting.Fig. 2. Temperature-dependence of the PL energy peaks for (a) SLQD and (b) MLQD. All peaks followed the behavior dictated by the Varshni equation, suggesting these are band-to-band transitions. None of the PL peak energies is possibly defect-related
Table 1. Varshni Fitting Parameter Values
Due to the non-uniform growth of the InAs/GaAs QD, it is possible to obtain uneven size distributions. Depending on their relative size, smaller QDs will emit at higher energies while larger QDs will emit at lower energy. Hence, in the case of SLQD, the presence of two observed PL peaks do not necessarily suggest GS and ES transitions. It is also possible to observe PL emission from the MLQD sample due to GS transitions from different InAs/GaAs QD layers due to the deep penetration of the excitation laser. In order to further investigate the origin of the PL transitions, excitation power-dependent PL spectroscopy was performed. Figures 3(a) and 3(b) show the PL spectra of the samples for the lowest four excitation powers (0.1 to 20 mW). For the SLQD sample, Peak A and Peak B continuously increase and no observable change in the PL lineshape can be observed as the excitation power is increased. Meanwhile, for the MLQD sample, Peak D becomes higher than Peak C starting at $\approx$ 1 mW. Peak C also increases at a slower rate as compared to peak D. For a more qualitative description, plots of the PL intensity vs excitation power are shown in Fig. 3(c) and 3(d). In the SLQD sample, Peak A and Peak B have equal slopes and a linear increase in PL intensity can be observed. We conclude that Peaks A and B are GS due to two possible QD size distribution and the SLQD sample is bimodal [24]. However, in the case of the MLQD sample, a cross-over can be observed $\approx$ 1 mW due to the change in the relative PL intensities of Peaks C and D. The observations in Fig. 3(b) and 3(d) for the MLQD are consistent with state filling [17,25]. We can surmise that peak C is the GS and peak D is the ES. It also shows that the incorporation of multilayers in the MLQD sample has resulted to a more uniform QD size distribution [26,27]. The effect of multilayering growth in the QD size distribution is as follows:in S-K growth, the growth starts as a 2D planar growth until eventually the strain in the growth surface would be high enough to cause dislocations resulting to QD island formation. The lowest QD layer will have a random size distribution. Upon deposition of the GaAs spacer layer, there will be undulations that will be preferable nucleation sites for the next QD layers. The succeeding QD layers will have wider base and greater height as compared the the QDs below. As the number of QD layers is increased, the topmost QDs will have a more uniform QD size distribution [16].
Fig. 3. Normalized excitation power-dependent PL spectra of the (a) SLQD ad (b) MLQD. The plot of PL intensity vs excitation power was fitted with a linear trendline for the (c) SLQD and (d) MLQD. Peak A and B continuously increase as the excitation power is increased. Meanwhile, Peak C becomes saturated at 1 mW and Peak D eventually becomes higher as excitation power is increased, consistent with state-filling
The photocarrier dynamics and transport in the InAs/GaAs QD samples were also studied using THz-TDS. Figure 4 shows the THz-TDS waveforms and corresponding FFT spectra for p-InAs, SLQD, MLQD, and SI-GaAs at $T =$ 200 K. Using Eq. (1), the energy gap of GaAs was estimated to be 1.465 eV at this temperature. The excitation laser wavelength was set to 870 nm, corresponding to a photon energy of 1.425 eV, in order to avoid photoexcitation of the GaAs layers. In addition, the FWHM, $\Delta \lambda$ of the excitation laser was only 12 nm, thus the possible photon energy ranges only from 1.415 - 1.435 eV. This further assures that no GaAs layer is being photoexcited. The strongest THz emission was obtained from p-InAs, followed by the MLQD and the SLQD. No significant THz emission was measured from SI-GaAs. The THz emission from the MLQD and SLQD samples are about $30\%$ and $6\%$ of p-InAs, respectively. The higher THz emission from the MLQD sample has been previously attributed to the higher number of QD emitters participating in the THz generation process as compared to the SLQD. Possible effects of multilayering resulting to less scattering and smoother interfaces, as in the PL result might have also contributed to the THz emission enhancement [28].
Fig. 4. (a) THz-TDS waveforms for p-InAs, SLQD, MLQD, and SI-GaAs (b) Corresponding FFT spectra of the THz-TDS waveforms. The highest THz signal was obtained from p-InAs. The THz emission from the MLQD sample is about $30\%$ and the SLQD is $6\%$ as compared to p-InAs.
Recombination and transport are competing processes affecting both luminescence and THz emission [29,30]. The relative PL intensity of the MLQD sample is lower than the SLQD sample, suggesting less efficient recombination dynamics. Moreover, temperature- and excitation power-dependent PL spectroscopy have also shown that the MLQD sample has a more uniform QD size distribution. A uniform QD size distribution would result to less scattering and smoother interface [28]. If other non-competing processes are excluded, it can be inferred that photocarriers in the MLQD will undergo transport as compared to the SLQD where recombination process is more likely to proceed. This scenario should explain why the THz emission is higher in the MLQD as compared to the SLQD.
Figure 5 shows the THz amplitudes at different temperatures for p-InAs, SLQD, and MLQD. For p-InAs, the THz emission decreases as temperatures increases. However, the THz emission for the QDs was found to increase as temperature increases. The observed temperature-dependence from the samples can be explained by investigating the origin of the THz generation mechanism. The generated THz electromagnetic radiation $E_{THz}$ is given by the expression [31]:
Fig. 5. Temperature-dependence of the THz emission from p-InAs, SLQD and MLQD. The THz amplitudes were normalized with respect to peak-to-peak amplitude of p-InAs at $T =$ 14 K. The THz emission from p-InAs decreases while the THz emission from the SLQD and MLQD increases as T is increased.
where $S$ is the illuminated area of the semiconductor, $c$ is the speed of light, $R$ is the distance from the emitter and observation point, $J$ is the transient photocurrent and $P$ is the nonlinear (NL) polarization. Various works have investigated the NL effect in semiconductor surfaces [32,33]. For the excitation fluence values used in the experiment, the NL effect is expected to be negligible [34]. Morever, the 100 orientation and excitation geometry of the layers further suppress THz emission from NL effects [9,35]. The linear process of THz radiation can be primarily attributed to the generation of a transient photocurrent that is described by the Drift-Diffusion Eq. [36]:
At low excitation fluence, the dominant THz radiation mechanism for low $E_g$ semiconductors such as InAs is carrier diffusion [36,37]. For intermediate $E_g$ semiconductors such as GaAs, the dominant THz radiation mechanism is carrier drift [38,39]. In the case of InAs/GaAs QDs, we also propose a drift-related carrier transport mechanism. Based on theoretical works, the photo-carriers in InAs/GaAs QDs are not confined in the center of the pyramidal QD [40]. In particular, electrons were found to be closer in the apex while holes are closer to the base, resulting to the creation of a permanent dipole. B-field dependent THz-TDS measurements have also shown that carrier drift is the origin of the THz emission from InAs/GaAs QDs [18]. For p-InAs, the diffusion current $\vec {J}_{diff}$ is given by:
and for a drift-type THz emitter such as QDs, the drift current $\vec {J}_{drift}$ is given by: Note that the electron mobility $\mu _e$, electric field $\vec {E}$, and carrier concentration $N_e$ have implicit temperature-dependence. We discuss the effects of T on these parameters since the resulting behavior of the THz emission will be a complex convolution of these effects. First, the change in excess energy $h\nu -E_g$ from $T=14K-200K$ is not significant to induce a temperature-dependence in $N_e$ or result to carrier repopulation between the $\Gamma -L$ valleys [41]. The change in $N_e$ due to the growth of thermal carriers is also expected to occur at a much higher T ($T\;>\;750$ K) [42]. Next, in general, scattering effects decreases $\mu _e$ at higher T. In particular, $\mu _e$ is related to scattering time $\tau _e$ via the relation $\mu _e = e \tau _e /m_e^*$ where $m_e^*$ is the electron effective mass [43]. Due to polar impurity scattering, the behavior of $\tau _e$ is known to increase from 0-100 K, then decreases as T is further increased [44]. However, correction using the carrier temperature $T_e$ would instead show a monotonic decrease of $\tau _e$ as T is increased resulting to decrease in $\mu _e$ [45]. The decrease in the THz emission in p-InAs as T increases can be primarily attributed to the decrease in $\mu _e$. Meanwhile, the THz emission from the QD samples was found to be proportional to T. Since $\mu \propto 1/T$, we surmise that the role of $\mu _e$ is not as significant as $\vec {E}$. Previous works have investigated the temperature-dependence of the THz emission from intermediate $E_g$ semiconductors such as InP and SI-GaAs at 800 nm [42,45]. It has been shown that the surface electric field $E_{surf}$ increases as T increases due to shifting of the Fermi level. In the case of QDs, the photocarriers are under the influence of an interface electric field $\vec {E}_{int}$ brought about at the InAs and GaAs interfaces instead of $E_{surf}$. For modulation-doped heterostructures (MDHs) wherein $E_{int}$ is very high, temperature-dependent photoreflectance measurements have confirmed that $\vec {E}_{int}$ increases as T increases [46]. The increase in the THz emission from the QD samples is possibly due to the increase in the $E_{int}$, thus validating the conjecture that the THz emission from the SLQD and the MLQD samples are drift-related.4. Summary and conclusions
In summary, we have investigated carrier dynamics and transport in MBE-grown InAs/GaAs QD structures. Temperature- and excitation power-dependent PL spectroscopy have shown that the SLQD sample has a bimodal size distribution. Multi-layering in the MLQD samples has also resulted to a more uniform QD size distribution. The uniform QD size distribution in the MLQD sample has resulted to more intense THz emission than the SLQD sample possibly due to less scattering and smoother interface quality. The temperature-dependence of the THz emission from QDs was found to increase as temperature increases, in contrast to a diffusion-type THz emitter such as p-InAs. A drift-related THz radiation mechanism is proposed in the QD samples wherein photocarriers generated in the QD structures are accelerated by the interface electric field.
Funding
CHED-PCARI (IIID-2015-13); DOST-PCIEERD-GIA (Project No. 04001); UP OVPAA (OVPAA-BPhD-2012-03).
Disclosures
The authors declare no conflicts of interest.
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