On the basis of their atomic-like electronic structures semiconductor quantum dots (QD) are essential materials for applications such as single photon emitter and quantum dot cellular-automata logic devices [1,2]. A single semiconductor QD contains a hundred to a thousand atoms, and thus can tightly confine electrons and electron-hole pairs (excitons) in all three dimensions [1,2].

The droplet epitaxy (DE) growth technique is based on forming metallic droplets on a semiconductor surface [3–6]. One of the advantages of this technique is that it can form QDs in lattice-matching hetero-structures such as GaAs/AlGaAs, which is unattainable in the conventional Stranski-Krastanov growth mode [3]. However, the lowtemperature growth (LTG) can cause the formation of arsenic clusters and anti-species defects in the interface layer, and the quality of the capping layer consequently deteriorates with decreasing temperature [4]. In this study, we investigated the annealing temperature effects of LTG GaAs/AlGaAs QDs by DE. We explained that postannealing could decrease the defects. A post-annealing process is thus deemed essential to activate the transition and quality optically.

The samples were grown by molecular DE mode. For the growth of GaAs QDs, a 200 nm GaAs buffer and a 100 nm Al_0.3Ga_0.7As barrier were grown at a temperature of 580 °C on a semi-insulator GaAs (001) substrate. The GaAs buffer and Al_0.3Ga_0.7As barrier layer were grown with a growth rate of 0.5 ML/s, 0.71 ML/s, respectively. The arsenic valve was then closed.

To form a Ga droplet, 4 ML of Ga was deposited on the Al_0.3Ga_0.7As surface with a deposition rate of 0.5 ML/s at a temperature of 300 °C. The deposition rate was confirmed by oscillation of the reflection highenergy electron diffraction [3]. To fabricate GaAs QDs from the Ga droplet, the substrate temperature was subsequently decreased to 200 °C. During the crystallization process with As4, the temperature was kept at 200 °C with As4 beam equivalent pressure of 2 × 10⁻⁵ Torr. After crystallization, the GaAs QDs were embedded in the Al_0.3Ga_0.7As barrier layer. First, a 10 nm thick Al_0.3Ga_0.7As layer was grown by migration-enhanced epitaxy to cap the GaAs QDs and maintain the geometric structure at 200 °C. Second, a 90 nm Al_0.3Ga_0.7As layer and a 10 nm GaAs cap layer were deposited at 580 °C. Finally, to increase the quality of the GaAs QDs, the samples were processed by rapid thermal annealing.

Low-temperature processes at around 200 °C can cause defects from the ununiform arrangement. Annealing is therefore essential to improve the optical properties of GaAs/AlGaAs QD grown by DE using molecular beam epitaxy [4,7]. However, annealing the samples at high temperatures led to interdiffusion between the GaAs buffer and AlGaAs barrier layer and between the GaAs QD and AlGaAs. If the interdiffusion occurs, the Al composition will be changed, and this can affect the QD signal [5,8]. In order to determine the optimal annealing temperature, the samples were annealed at 650 °C (A0), 700 °C (A1), and 750 °C (A2) for 4 min.

Figure 1 shows the normalized photoluminescence (PL) spectra of three samples. Every sample was measured with a 532 nm laser (I = 4,000 mW/cm²) at 20 K. All samples show GaAs bulk signals with a sharp peak at around 1.50 eV, but the GaAs QD signals of the three samples are different. In contrast with A1 and A2, there is no QD signal in A0. However, A1 has a PL transition at 1.60 eV with an full width at half maximum (FWHM) of 80 meV. In the case of A2, the QDs emit energy at 1.65 eV (A2-L) with an FWHM of 50 meV and 1.75 eV (A2-H) with an FWHM of 120 meV.

Figure 1. Normalized PL spectra for the three annealed samples with annealing temperatures of 650 °C (A0), 700 °C (A1), and 750 °C (A2) at 20 K.

As theannealing temperature increases, the quantum states emit higher energy in Fig. 1. Due to the quantum confinement effect, the quantum state of QDs depends on their size. To compare the intensity of the QDs exactly, we set the GaAs bulk signal as a reference. The intensity of A2 QDs increased 23-fold based on A1. When the density of defects is high, the carriers should be trapped in defects. Therefore, the small size QDs, which have higher energy than the other QDs, cannot emit the transition energy. However, following annealing, the defects could be decreased [7,9]. As a result, the QDs of A2 emit more transition energy than the others.

Figure 2 depicts the integrated intensities of A1, A2-L, and A2-H QDs as follows Eq. (1) at T = 20 K. They are increased linearly by increasing power. We analyze the slope of the logarithm of PL intensity (I_PL) with the power of the excitation laser (P^k), where k is the emission coefficient [10,11].

Figure 2. Emission coefficient of A1, A2-L, and A2-H.

It depends on the height of the barrier. Due to the quantum confinement effect, QDs have an excitonic transition. The exciton transition gave 1 < k < 2 for the excitation power. Also, the emission from defects gave k < 1. The k of QDs with high barrier heights gave k = 1 [12,13].

A1, which emits high barrier QDs, gave k = 1.03. A2-L and A2- H gave k = 1.10 and k = 1.17, respectively, higher than A1. We can conclude that QDs of A2 have a lower barrier. Therefore, the carriers more easily escape for recombination than in the case of A1.

Figure 3 shows normalized photoreflectance (PR) spectra with increasing annealing temperature at 260 K with I_ex of 8 mW/cm². The GaAs transition is shown in Fig. 3(a), and the AlGaAs transition is shown in Fig. 3(b). The GaAs transition energy of all cases starts at 1.41 eV (A0), 1.418 eV (A1), and 1.415 eV (A2). The AlGaAs transition energy appears at 1.908 eV (A0), 1.907 eV (A1), and 1.916 eV (A2). They have more than one oscillation below the transition energy. The broadening of oscillations is changed by the thermal process.

Figure 3. Normalized PR spectra of A0, A1, and A2 at T = 260 K. (a) GaAs and (b) AlGaAs.

The regions below the E_g of GaAs and AlGaAs are caused by interference between the reflected beam and the surface. The reflected beam can change the charge distribution of the GaAs and AlGaAs interface [14]. This phenomenon is defined as Franz-Keldysh oscillations (FKO) by Aspnes [15]. Generally, the FKO signal is constructed with a few period functions. Each period has its own frequency. They can be distinguished with fast Fourier transform (FFT). With the frequency, we can calculate the electric field of the surface. This will be explained in detail below.

Table I shows the frequency and electric field of GaAs and AlGaAs fitted with a FFT analysis at 260 K. Equation (2) is the FKO equation defined by Aspnes [16]. E_g is the bandgap energy of the material and χ is the phase of the signal.

Table 1 . Frequency and electric field of GaAs at 260 K..

T = 260 K	A0	GaAs A1	A2	A0	AlGaAs A1	A2
f [${(eV)}^{-\frac{3}{2}}$]	35.90	33.02	28.25	38.00	36.27	31.42
F [kV/cm]	71.66	77.91	91.07	78.68	82.43	95.64

This equation can be defined with a FFT. To distinguish the periods, we need to simplify Eq. (2). We put $x={\left(E-E_g\right)}^{3/2}$ and $2\pi f=\frac{2}{3}\frac{1}{{\left(\hslash \Theta \right)}^{3/2}}$

$\hslash \Theta$ is the photoelectric energy, and we define ${\left(\hslash \Theta \right)}^{3/2}={\left(\frac{e^2{F}^2{\hslash }^2}{8\mu }\right)}^{-1/2}$. Therefore, the frequency can be defined as given in Eq. (4).

where F is the electric field and µ is the effective mass of the electrons and holes. In this paper, we used µ = 0.056m₀ for GaAs and µ = 0.076m₀ for AlGaAs.

Table I shows the frequency and electric field of three samples with Eq. (5). With increasing annealing temperature, the frequency decreased and the electric field increased.

Figure 4 shows the average value of the electric fields for GaAs and AlGaAs as a function of temperature. At 300 K, the electric field is 84.4 (A0), 90.27 (A1), and 99.31(A2) kV/cm, and then decreases linearly by decreasing temperature. Due to the thermal expansion, the electron distribution changes to higher energy, and the bandgap is reduced. As a result, the photo-generated excess carriers can increase more easily. This is known as the photovoltage effect. Because of this effect, the electric fields of the three samples decreased at the following temperature.

Figure 4. Average values of GaAs and AlGaAs electric fields of three samples from 200 to 300 K.

In the LTG of compound semiconductors such as GaAs, atoms can be occupied at the wrong lattice point; these are called anti-site defects. The anti-site defects can cause GaAs to create carrier traps and lower carrier mobilities. Prabhu showed that carrier lifetimes increased with increasing annealing temperature [17]. The Shockley–Read–Hall recombination theory shows that the carrier lifetime is inversely proportional to the density of trap states [18]. Therefore, the density of trap states can decrease by increasing the annealing temperature. The results in Table I and Fig. 4 show the increased electric field with increasing annealing temperature. As the trap density decreased, more excess carriers diffused to surface states, and more electric fields occurred in A2.

To confirm the origin of the electric field, we analyzed the A2 electric fields according to the laser power [Fig. 5(a)] and temperature [Fig. 5(b)]. Figure 5(a) shows the electric fields of A2 with decreasing excitation power at 300 K. With increasing excitation power, the electric fields of GaAs and AlGaAs decreased. When the laser power is increased, the number of carriers increases [19]. Due to the screening effect, the probe-beam causes a repulsive force between electrons partially cancels the attraction between the nucleus and the electrons. As a result, the recombination between surface states decreases with increasing laser power. Figure 5(b) shows that the electric field increases with increasing temperature because of photovoltaic effects [20]. Figures 5(a) and 5(b) show that the electric field of GaAs and AlGaAs surface have similar values within the margin of error (± 5kV/cm). We conclude that the electric field forms between GaAs and AlGaAs cap layer above the LTG GaAs QD and AlGaAs.

Figure 5. The electric field of GaAs as functions of (a) excitation power and (b) temperature.

We investigated the effects of a post-thermal annealing process on improving the crystal quality for LTG GaAs/AlGaAs QDs by DE. With increasing post-annealing temperature, the QD transition energy was blue-shifted, and the emission intensity of PL for QDs was increased. From the results, we found that the density of defects decreased. In PR, the amplitude of FKO becomes stronger with increasing annealing temperature. The interface electric field strength also increases due to the lowering of the defect density. As a result, we found that the defect density decreased as the annealing temperature increased.

This research was supported by National Research Foundation of Korea (NRF) grants funded by the Government of Korea (NRF-2022M-3H4A1A0208533911, NRF-2021R1I1A305996311, and NRF-2018M3-A7B406999621).

The authors declare no conflicts of interest.