1. INTRODUCTION

Cavity-enhanced nano- and microlasers have become objects of high scientific interest. Due to their high-quality ($Q$) factors and low mode volumes on the order of the cubic wavelength, they usually operate in the regime of cavity quantum electrodynamics (cQED) and offer a rich spectrum of exciting physics [1–6] with potential applications such as, e.g., coherent light sources in the field of photonic quantum technologies [7]. Advances in epitaxial growth and fabrication of semiconductor micro- and nanolasers have paved the way to approach the limit where a few quantum dots (QDs) can drive the device to lasing [2,8–11]. Moreover, cQED effects result in high spontaneous emission coupling factors $\beta$, which leads to devices showing ultra-low threshold powers and even thresholdless lasing [12–14]. Up until now, QD microlasers have been exclusively based on standard self-assembled QDs, which exhibit excellent optical quality in terms of quantum efficiency, oscillator strength, and coherence times [15–17] but suffer from their random spatial and spectral position relative to the cavity mode. To go beyond existing work, it is thus highly desirable to apply deterministic fabrication technologies, which have been developed for the development of single-QD quantum devices and have been applied very successfully for the fabrication of state-of-the-art single-photon sources [18–21], and for few-QD microlasers. In this regard, the site-controlled integration of a few self-assembled QDs into a high $Q$-factor or microcavity is very beneficial in order to better control the light–matter coupling behavior and to tailor and maximize the gain provided by the QDs. Popular deterministic fabrication technologies usually allow for the integration of single QDs into microcavities by means of in situ lithography [22] or by the site-controlled growth of QDs on the nanopatterned surfaces [23,24]. Another interesting approach is based on vertically stacked disk-like QDs integrated into nanowires that show lasing oscillations up to room temperature [25]. While the QD number can precisely be controlled by this method via the number of stacks, the QD emission band suffers from a rather large inhomogeneous broadening of more than 30 meV and is thus incompatible with microcavity lasers based on an in-plane gain medium. In this regard, the buried-stressor approach stands aside because it not only enables the site-controlled growth of self-assembled QDs aligned to an oxide aperture but also exhibits additional control of the number of QDs at the desired location [26] and small inhomogenous broadening of the QD emission band. Controlling the number of such site-controlled QDs (SCQDs) is achieved by fine-tuning the aperture diameter and is very advantageous for precise control of the optical gain provided by these emitters in microcavity lasers. Utilizing this approach, single-photon sources [27,28] as well as high-$Q$ multi-SCQD micropillar structures [29] have already been realized.

In this work, we go beyond existing work by realizing and quantum-optically characterizing microlasers with a controlled number of SCQDs in the active region. The devices are fabricated by the advanced buried-stressor growth technique in conjunction with nanoprocessing of high-$Q$ micropillar cavities. Controlled by the aperture diameter, the fabricated devices demonstrate a few-QD lasing action proven by a characteristic s-shaped input–output curve and characteristic linewidth narrowing at lasing threshold. Furthermore, we perform measurements of the second-order autocorrelation function $g^{(2)}(\tau )$, which is essential to unambiguously proof lasing in high-$\beta$ microlasers [11]. Additionally, the influence of the aperture diameter, and thereby the number of SCQDs, on the lasing threshold is systematically investigated and explained by means of the aperture-dependent modulation of the $Q$-factor and the confinement factor ($\mathit{\Gamma }$).

2. SAMPLE TECHNOLOGY

The work-flow for the fabrication of micropillars with SCQDs has already been described in detail in a previous work of the authors [29]. In summary, this fabrication process is based on the buried-stressor SCQD growth technique and includes two-step metal-organic chemical vapor deposition (MOCVD) epitaxial growth with an intermediate partial oxidation of an AlAs aperture. The latter leads to nucleation of QDs over the non-oxidized material, where the number and position of the SCQDs are controlled by the diameter of the aperture. The layer of InGaAs SCQDs is located in the center of a $\lambda$-thick GaAs cavity integrated into 30/27 pairs of $\lambda /4$-thick ${\mathrm{Al}}_{0.90}{\mathrm{Ga}}_{0.10}\mathrm{As}/\mathrm{GaAs}$ layers representing the bottom/top distributed Bragg reflector (DBR). The fabrication is finalized by electron-beam lithography to define micropillars with a diameter of 5.2 μm and varying aperture diameters in a range of 700–1400 nm. These particular structure parameters ensure sufficiently high $Q$-factors as well as a suitable positioning and a controlled number of SCQDs in the micropillar. We would like to note that the aperture diameters mentioned in this work are nominal values based on structural sizes defined by UV lithography in the buried-stressor growth process. Since the oxidation of the apertures cannot be controlled with nm accuracy, there might be a constant offset of up to $\sim 100\mathrm{nm}$between the nominal and real diameters of the apertures. This issue could be solved in future work by an improved in situ control of the oxidation process. The micropillars are dry etched down to the 22nd pair of the bottom DBR [cf. schematic drawing and electron micrograph in Fig. 1(b)]. We would like to note that we slightly increased the number of DBR pairs compared to our previous work [29] (from 27/23 to 30/27) in order to achieve higher $Q$-factors, and thus lower optical losses, to overcome the laser threshold in our micropillars. Moreover, the design and growth of the planar microresonator was comprehensively optimized in order to maximize the spectral matching between SCQDs and micropillar fundamental modes and to minimize optical losses of the latter (cf. Fig. 1).

 

Fig. 1. (a) Top side: spectra at low (black trace) and higher (red trace) excitation powers of the micropillar with a diameter of 5.2 μm and an aperture diameter of 1400 nm. Bottom part: derivative (only positive values) of the low-power spectrum. The noise band is marked by a blue line, and identified SCQD lines are marked by red arrows. (b) Number of SCQDs as a function of the aperture diameter of micropillars with a diameter of 5.2 μm. Two excitonic emission lines (i.e., exciton and biexciton) per SCQD are assumed. Insets: schematic illustration of a micropillar structure (top) and scanning electron microscope (SEM) image of a fully fabricated micropillar (bottom). (c) Spectral distribution of the SCQD emission lines for all investigated micropillars. For the sake of clarity, the corresponding aperture diameters are subdivided into three groups: 700–950 nm (black bars), 950–1200 nm (red bars), and 1200–1400 nm (blue bars). Inset: wavelength of the fundamental pillar mode as a function of the aperture diameter. The fundamental mode experiences lower lateral light confinement and red-shifts with increasing aperture diameter [29]. (d) Number of the SCQD emission lines as a function of spectral detuning from the fundamental cavity mode for micropillars with an aperture diameter of 975 nm (pillar 2, blue bars) and 1250 nm (pillar 4, red bars).

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The fabricated micropillar structures are investigated via micro-photoluminescence (μPL) spectroscopy at a temperature of $\approx 18\mathrm{K}$. The sample is mounted inside a He-flow cryostat (Janis, ST500), and the investigated micropillars are optically excited by a continuous-wave laser (Omicron, LuxX 785-200) emitting at a wavelength of 785 nm. The resulting PL is collected via an aspheric lens with a numerical aperture of 0.5, spectrally dispersed by a spectrometer (Princeton Instruments, Acton SpectraPro SP-2750) including a Si-based charge-coupled device (CCD) camera (Princeton Instruments PIXIS 400 BR-SF) with an overall spectral resolution of $\simeq 25\mathrm{\mu eV}$. For autocorrelation measurements, the emitted light is spectrally filtered by means of a bandpass filter (590 pm bandwidth at half maximum) and coupled via single-mode optical fibers into superconducting nanowire single-photon detectors (SNSPDs, Scontel, TCORPS-001-SW50) in a Hanbury Brown and Twiss configuration with an overall temporal resolution of 60 ps.

3. RESULTS AND DISCUSSION

In order to determine the number of SCQDs as a function of the aperture diameter, we performed μPL measurements at low excitation powers well below threshold power. Thereby, the emission of higher excitonic states beyond the biexciton as well as too strong contributions by micropillar modes are avoided. Figure 1(a) shows two spectra of a micropillar with a diameter of 5.2 μm and an aperture diameter of 1400 nm recorded at a very low excitation power (few nW, black trace) and at a higher excitation (few μW, red trace). In order to estimate the number of QD lines, we calculated the derivative of the low-power spectrum and counted all SCQD-related lines above a carefully selected noise level [cf. bottom panel of Fig. 1(a) where the noise level is marked by a blue line]. Using this method, the number of SCQDs is determined for each aperture diameter under the assumption that each SCQD emits two emission lines (biexciton and exciton), which was verified independently by statistical reference measurements on a SCQD sample without upper DBR. Figure 1(b) presents the determined number of SCQDs as a function of the aperture diameter. We observe a linear increase in the number of SCQDs with the aperture diameter, starting with $\sim 10\mathrm{SCQDs}$ for the aperture with a diameter of 700 nm and ending in $\sim 20\mathrm{SCQDs}$ for the largest aperture diameter of 1400 nm. We would like to note that also single SCQD structures can be achieved by the buried-stressor approach by further decreasing the aperture diameter [30]. In the present work, we focus on structures with 10–20 SCQDs to overcome the laser threshold. In Fig. 1(c), a spectral distribution of the SCQD emission lines is presented. Most of the SCQD emission lines are observed between 918 nm and 922 nm, which indicates a very small inhomogeneous distribution with 50% of the SCQD emission lines in a spectral window of only $\approx 4\mathrm{nm}$. This value is comparable to [31,32] or even smaller than the inhomogeneous broadening of SCQD arrays achieved with other SCQD techniques [33]. Given that the wavelength of the fundamental cavity mode (FM) shifts red with increasing aperture diameters [cf. inset in Fig. 1(c)] while the QD emission is not significantly influenced by the aperture diameter, we expect optimum spectral matching between SCQD emission lines and the FM for the structures with smallest apertures. Figure 1(d) depicts the comparison between the spectral matching of the SCQDs and the FM for two micropillars (pillar diameter: 5.2 μm) with aperture diameters of 975 nm and 1250 nm, respectively [cf. pillars 2 and 4 in Fig. 1(b)]. It shows a better matching for the former one resulting in an averaged spectral detuning of QD lines relative to the FM of 0.8 nm and 2.6 nm for pillars 2 and 4, respectively. The findings on the SCQD number evaluation and the inhomogeneous distribution of SCQDs are additionally confirmed by reference measurements under lateral detection (not shown here) on micropillars with a diameter of 4.5 μm located close to the edge of the sample. These studies confirm both the SCQD number for a particular aperture diameter and the good spectral overlap between the narrow SCQD emission band and the FM.

In following, we demonstrate lasing in micropillars with a controlled number of SCQDs and discuss the influence of the oxide aperture on lasing behavior. Noteworthy, the investigated micropillars exhibit two orthogonally polarized modes resulting from the lifted twofold degeneracy of the FM by means of a slightly elliptical cross section of the pillars. As discussed in [34], this ellipticity is most probably related to a slight asymmetry in the electron-beam lithography process. Figure 2(a) shows input–output curves for the strong (black squares) and weak modes (red circles) of a micropillar with an aperture diameter of 975 nm [cf. pillar 2 in Fig. 1(b)]. The weak and strong modes are spectrally separated by 230 pm and located at 922.90 nm and 923.13 nm, respectively. As a result of gain competition, the strong mode exhibits the expected s-shape in the input–output curve with a super-linear increase indicating the transition to coherent emission related to lasing threshold. In contrast, the weak mode shows only linear increase and saturation of emission intensity at high input powers. Additionally, spectra of both modes are shown in the inset in Fig. 2(a) at an input power of 5.2 mW, where the transition to lasing starts. We would like to note that the high input power required to achieve lasing is attributed to high absorption of light in GaAs of the upper DBR. Considering the absorption law $P_{\mathrm{eff}}=P_0{e}^{-\alpha d}$ and an absorption coefficient of GaAs $\alpha =1.4\times {10}^4/\mathrm{cm}$ at the laser wavelength (785 nm) [36] as well as the total GaAs layer thickness $d=1934\mathrm{nm}$, we calculated an effective threshold input power of 0.34 mW reaching the active layer (in Figs. 2, 3, and 4, raw power values are presented). The lasing behavior of the strong mode is supported by a reduction in its linewidth with increasing input power, limited by the spectral resolution of the spectrometer at high excitation powers. Meanwhile, the linewidth of the non-lasing weak mode fluctuates around 50 pm in the whole power range [cf. Fig. 2(b)]. Most importantly, to prove the transition from thermal to coherent emission in our micropillar with SCQDs, we performed power-dependent measurements of the second-order autocorrelation function $g^{(2)}(\tau )$. In Fig. 2(c) $g^{(2)}(\tau =0)$ is presented for the strong mode and the weak mode as a function of the pump power. For the strong mode of the studied micropillar the transition to lasing occurs in the pump range between 5 mW and 6 mW, resulting in a drop of $g^{(2)}(\tau =0)$ from 1.6 to 1.0. The inset in Fig. 2(c) shows two auto-correlation histograms recorded from the strong mode under excitation power of 5.1/6.2 mW (blue/black curves) resulting in a pronounced bunching at zero time delay and a flat behavior, respectively. $g^{(2)}(\tau =0)$ below the threshold does not reach the expected value of 2.0 for thermal light because of the finite time resolution of the detectors ${\tau }_{\mathrm{res}}$ that exceeds the coherence time of light in this power range (${\tau }_{\mathrm{coh}}<{\tau }_{\mathrm{res}}=60\mathrm{ps}$) [37]. In contrast, $g^{(2)}(\tau =0)$ of the weak mode remains around 1.6 in the transition region supporting the non-lasing character of the emitted light. Due to the observed transition to coherent light as well as the clear bunching behavior above the threshold for the strong and weak modes, respectively, further measurements at lower excitation powers, and thus lower count rates, were not performed.

 

Fig. 2. (a) Input–output curves of the strong mode and the weak mode of a micropillar with an oxide aperture diameter of 975 nm. The input–output curve of the strong mode is approximated using the rate equations model from [35]. Inset: spectra of both modes taken at a pump power of 5.2 mW. (b) Linewidth of the strong mode and the weak mode as a function of the input power. The spectral resolution limit is indicated with a dashed horizontal line. (c) Excitation power-dependent autocorrelation values $g^{(2)}(\tau =0)$ for the strong mode and for the weak mode. Inset: autocorrelation histograms recorded from the strong mode at 5.1 mW (blue, below threshold) and 6.2 mW (black, above threshold), respectively. The corresponding working points are marked with arrows. Black squares and red circles in (a)–(c) correspond to the strong mode and the weak mode, respectively.

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Fig. 3. (a) Input–output curves, (b) power-dependent emission linewidth, and (c) $g^{(2)}(\tau =0)$ for the micropillars 1–4 with respective oxide aperture diameters of 780 nm (black), 975 nm (blue), 1115 nm (olive), and 1250 nm (red). The threshold power for each micropillar is marked with a dashed line of its respective color.

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Fig. 4. (a) Measured (black triangles) and simulated (blue rhombuses) $Q$-factor as a function of the aperture diameter. Inset: simulated $Q$-factor in a wider aperture range. (b) $\mathit{\Gamma }$-factor (black squares) and the threshold pump power (red circles) as a function of the aperture diameter. The horizontal dashed line refers to the $\mathit{\Gamma }$-factor of a micropillar with a diameter of 5.2 μm randomly distributed QDs with a density of ${10}^9/{\mathrm{cm}}^2$. The vertical dashed line separates the micropillars exhibiting transition to lasing (aperture diameters from 700 nm to 1200 nm) from the non-lasing ones.

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Using the rate equation model from [35] and a transparency carrier concentration of $3.0\times {10}^{18}/{\mathrm{cm}}^3$, a volume of the active material of $0.12\times {10}^{-15}{\mathrm{cm}}^3$, a photon lifetime in the cavity of 10 ps, and a spontaneous emission lifetime of 0.2 ns, we approximated the input–output characteristic of the strong mode [cf. Fig. 2(a)] and estimated a $\beta$-factor of 0.014. Though this value is higher compared to conventional vertical cavity surface emitting lasers (VCSELs), it is still lower than 1 required for thresholdless lasing due to a rather high mode volume of the micropillars with a diameter of 5.2 μm. Nevertheless, reducing the diameter of micropillars below 2 μm while maintaining high $Q$-factors should allow to systematically approach the ultimate $\beta =1$ limit.

In order to more systematically investigate the influence of the oxide aperture on the lasing in micropillars with SCQDs, we performed the set of measurements already presented in Fig. 2 for SCQD micropillars with different aperture diameters ranging from 700 nm to 1400 nm. The results for the micropillars 1, 3, and 4 [cf. Fig. 1(b)] together with already introduced pillar 2 (Fig. 2) are presented exemplary in Fig. 3. Interestingly, pillars 1–3 show a clear threshold to lasing in terms of the s-shape of the input–output curve, the linewidth narrowing down to the spectral resolution limit, and a clear reduction in $g^{(2)}(\tau =0)$ (black, blue, and olive bullets in Fig. 3). In contrast, pillar 4 with the largest aperture diameter of 1250 nm does not exhibit any lasing signatures (red bullets in Fig. 3). To better understand this rather unexpected feature (in light of the larger number of SCQDs for pillar 4), the $Q$-factor of the micropillars is investigated and indicates an aperture-diameter dependence with a minimum at about 1300 nm as presented in Fig. 4(a). The experimental result (black triangles) is supported by the numerical simulations [38] (blue rhombuses) predicting a decrease in the $Q$-factor of nearly a factor 2 with increasing aperture diameter in a range from 700 nm to 1300 nm. As reported by us previously [29], this decrease in the $Q$-factor is attributed to enhanced light scattering induced by the partially oxidized aperture. Compared to a structure without aperture and with the same mode volume, the predicted minimum $Q$-factor at an aperture diameter of 1350 nm is reduced by a factor of 2.3. The increase in the $Q$-factor for aperture diameters above 1400 nm is explained by reduced light scattering in the large diameter regime [cf. inset of Fig. 4(a)]. Another important laser parameter that can be uniquely controlled in our concept by the design of the aperture and the resulting nucleation of SCQDs is the optical confinement factor $\mathit{\Gamma }$ defined as the ratio of the mode energy in the active region (represented by the SCQDs in our case) to the total mode energy and can be calculated via [39]

Figure 4(b) (black squares) depicts the $\mathit{\Gamma }$-factor as a function of the aperture diameter. This factor is calculated taking into account the numerically calculated field distribution in $x$, $y$, and $z$ directions in the micropillars and the lateral geometric distribution of the SCQDs (predominantly at the edge of the apertures [26]) as well as their averaged sizes (base length 50 nm, height 3 nm) measured with the atomic force microscope. For each particular aperture diameter, the electric field distribution $E_{x,y,z}$ was calculated and integrated over SCQDs by considering their number and lateral position in the cavity and by subsequently dividing the result by the integral of the electric field distribution of the FM. We would like to mention that we did not include the spectral overlap between SCQDs and the FM in the calculations, which, however, would not significantly change the estimated $\mathit{\Gamma }$-factors due to the contribution of all counted SCQDs from the spectrally narrow broadened QD ensemble (cf. Fig. 1) to lasing oscillations of the FM via the well-known off-resonant QD-cavity coupling in high-$Q$ microresonators, which is effective over a spectral range of typically a few nm [40–42]. In Fig. 4(b), we observe a decrease in $\mathit{\Gamma }$-factor by a factor of 3 starting with a value of $6·{10}^{-6}$ for the small aperture diameters between 700 nm and 900 nm and dropping to $\approx 2\hspace{0.17em}·{10}^{-6}$ for a diameter of 1500 nm. Because of the relationship $g_{\mathrm{mod}}\sim \mathit{\Gamma }·g_{\mathrm{opt}}$ between the modal gain and the optimum modal gain, which corresponds to a perfect spatial matching of QDs to the confined optical mode, the laser threshold scales inverse proportional with $\mathit{\Gamma }$-factor. This aspect together with the improved spectral matching and the higher $Q$-factors for the smaller aperture diameters discussed above results in a threshold behavior controlled by the diameter of the oxide aperture as presented in Fig. 4(b) (red circles). Noteworthy, the aperture-induced dependence of both $Q$- and $\mathit{\Gamma }$-factors is a fundamental characteristic of the investigated micropillars, so that spectral matching can be engineered accurately by means of the aperture and micropillar design for a particular region of aperture diameters where all lasing requirements are fulfilled. The microlasers with an aperture diameter $<1000\mathrm{nm}$ exhibit a reduced pump power at the threshold compared to the structures with the aperture diameters between 1000 and 1200 nm. Moreover, in the structures with the oxide aperture diameter $>1200\mathrm{nm}$ (e.g., Pillar 4) the insufficient spectral matching between SCQDs and the FM together with the reduced $Q$- and $\mathit{\Gamma }$-factors causes no lasing to be finally observed. Interestingly, the $\mathit{\Gamma }$-factor for our investigated micropillars with a rather small number of SCQDs exceeds that of a standard micropillar with an active medium based on randomly distributed QDs at a density as high as ${10}^9\mathrm{QDs}/{\mathrm{cm}}^2$ (corresponding to $>200\mathrm{QDs}$ in the active area) as marked with a horizontal dashed line in Fig. 4(b). This nicely highlights the advantage of our SCQD concept, where fewer than 20 emitters provide higher modal gain than 200 randomly distributed QDs in the conventional microlaser approach. As such, it has high potential to reduce the required number of QDs to sustain lasing in microlasers to a minimum in future developments.

4. SUMMARY AND CONCLUSION

In conclusion, we report on the fabrication of micropillar lasers with a controlled number of 10–20 SCQDs as active medium. The structures are realized by using the buried-stressor growth technique and exhibit clear lasing signatures in terms of s-shaped input–output characteristic, pronounced linewidth narrowing, and the second-order autocorrelation function ($g^{(2)}(\tau =0)$) approaching unity above lasing threshold. Moreover, we demonstrate that laser characteristics such as the threshold pump power depend on the number of SCQDs in the active layer, which can be controlled by the diameter of the oxide aperture in our growth process. Interestingly, for a given design of the micropillar cavity, the diameter of the oxide aperture controls the optical properties of the laser to a wide extent by determining not only the number of emitters in the gain medium but also by influencing the $Q$- and $\mathit{\Gamma }$-factors of the devices. In this context, it is important to note that the localized growth of a small ensemble of SCQDs aligned to the cavity mode can increase the modal gain by more than one order of magnitude compared to a conventional device based on standard randomly distributed QDs. As such, our results can revolutionize the development of low-threshold high-$\beta$ microlasers with precisely tailored operation properties that can simply be controlled by the diameter of the integrated oxide aperture.