1. Introduction

Driven by the rapid growth of the demand in data centers, silicon-based photonic integrated circuits (PICs) have recently witnessed rapid development. They have reached a level of maturity that allowed the implementation of foundry-type fabrication processes [1,2]. This swift progress was leveraged by utilizing extremely reproducible process steps, originally developed over decades for silicon complementary metal-oxide semiconductor (CMOS) integrated electric circuits to the emerging field of PICs. While for most building blocks of a PIC standard layout libraries are offered by numerous commercial foundries [2], an efficient, Si-based electrically driven light emitter is still missing, mostly due to silicon indirect bandgap. To overcome this hurdle, several methods of heterogeneous integration of III-V semiconductor lasers have been developed [3]. Still, a monolithically integrated emitter would be desirable in terms of production costs and thermal stability. In this respect, promising results on laser emission from strained Ge [4–6], GeSn [7,8] and SiGe QDs [9] have been reported.

Due to the versatile toolbox available, Si PICs are also highly attractive for possible applications in quantum photonics [10–12]. Complex quantum optical devices integrated on a Si chip have been demonstrated [13]. Similar to classical integrated photonics, also in the quantum domain the indirect bandgaps of Si and Ge pose a major obstacle for the realization of deterministically emitting, monolithically integrated sources of quantum states of electromagnetic radiation. Hybrid integration of highly optimized III-V QD single photon sources [14] on a Si based integrated quantum optical platform is thus a long standing goal, albeit the most advanced III-V QDs do not emit in the Si transparent wavelength region [11]. Also, defect centers in Si have gained recent attention as single photon sources in the telecom wavelength region [15]. However, site controlled integration of these defects into a PIC platform would be required for prospective scalability but has not been demonstrated, yet.

Thus, despite the spatial separation of electrons and holes confined to SiGe QDs [16], single SiGe QDs as photon emitters remain an active area of research, mainly owing to their anticipated compatibility with CMOS technology [17], to their natural emission in the telecom wavelength band and, crucially for CMOS compatibility and scalability, to the possibility of perfectly controlling their nucleation site ([18] and references therein). Several routes to increase the photon emission efficiency of SiGe QDs have been developed, including Ge implantation during QD growth in an MBE reactor [19,20], annealing and hydrogen diffusion for passivation of recombination centers [21,22] and radiative lifetime reduction by the Purcell effect [23] in photonic crystal resonators (PhCR) [24–26].

In this work, we concentrate on the enhancement of the emission efficiency by site controlled integration of SiGe QDs into an advanced type of PhCR, providing a large Q-factor via simple design rules [27]. Unlike in previous approaches, in which either more than one QDs were present in the photonic structure [24,25] or all except one QD were removed from the PhCR by etching [26], here we additionally employ a SiGe QD growth regime, in which a priori exactly one QD is nucleating at the center of the PhCR. As a result, we achieve record Q-factor values for PhCR cavities coupled to a QD emitter monolithically fabricated on a Si integrated optical platform. The cavity coupled single QD emission occurs in the telecom wavelength region and is clearly observable up to room temperature.

2. Experiments

2.1 Photonic crystal cavities design and layout

In this work, we use a bichromatic-type PhCR [27] to enhance the emission efficiency of SiGe QDs via the Purcell effect [23]. This effect becomes increasingly efficient for PhCRs with decreasing mode volume ($V$) and increasing Q-factor ($Q$), ultimately scaling as the ratio $Q/V$[28]. In bichromatic PhCRs, both of these requisites can be effectively controlled by straightforward design rules [27,29]. As outlined in Ref. [27], the term bichromatic refers to the superposition of two photonic crystal structures with different periods $a$, $a'$, which only in cooperation result in localized optical modes. A scanning electron micrograph (SEM) of such a bichromatic PhCR typically used in this work is shown in Fig. 1(b). The aforementioned two photonic crystal structures are formed i) by a triangular lattice with hole radius $R$ and period $a$, and ii) by a line defect made of a row of holes with radius $r$ and period $a'<a$. In Fig. 1(b), these four design elements are indicated by white labels. As shown in Ref. [27], the ratio $\beta =\frac {a'}{a}$ most significantly determines the $Q$-factor of this type of PhCR. The closer $\beta$ approaches 1 from below, the more the effective confinement for optical modes resembles a parabolic potential. It is well known, that for such a potential the fundamental mode shows a Gaussian envelope in real and reciprocal space, and, thus, a minimal scattering into propagating modes, resulting in large Q-factors [27]. Since the line defect row has to end with holes centered at positions belonging to the underlying triangular lattice, $\beta$ can be expressed as $\beta =\frac {N}{N+1}$, where $N a$ is the center-to-center distance of outermost holes of the line defect. This distance is then subdivided into $N+1$ periods of length $a'$, i.e $N a=(N+1)a'$. In simulations, $Q>10^9$ has been predicted for an ideal Si-membrane PhCR with $\beta =0.96\ (N=24)$ [27,29]. However, due to technological deviations from the ideal design, reported experimental values for such a PhCR were limited to $Q \sim 1.2\times 10^6$ in previous reports [29,30].

 

Fig. 1. (a) $30\times 15\,\mu$m$^2$ AFM image of an uncapped sample with a single SiGe QD nucleated at the position predefined by a pit on a SOI substrate. No QDs outside the pits are observed. The inset shows a QD in a pit on larger scale. The red rectangular frame indicates the scan area shown in (b). (b) SEM image of an uncapped sample after aligned processing of the bichromatic resonator. The row of small holes is parallel to a [100] direction. The depicted resonator and QD are in virtually perfect registry in horizontal direction and in vertical direction with a deviation of less than 25 nm. Yellow dashed circles indicate air holes with radius enlarged by $\Delta r = +3$ nm with respect to the unmarked ones outside the line defect. They form a second-order grating and allow precise control of the outcoupling of radiation and its far-field distribution. The relevant design parameters of the PhCR as described in the text are indicated by white lines and labels. (c) Cross-sectional sketch along the center of a bichromatic PhCR’s line defect. The SiO$_2$ below the resonator was removed during HF etching through the PhCR holes as described in the text. (d) Cross-sectional sketch of the PhCR membrane’s center. The QD indicated in red is vertically centered with respect to the membrane. Broken lines indicate approximate shapes of the sample surface after pit etch (dotted line), buffer layer growth (dashed line), and temperature-graded cap layer growth (dash-dotted line). The inset indicates the temperature profile employed during layer growth as described in the text.

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On our chip, we fix $N=24$ and $R=100$ nm for all PhCRs. The remaining design parameters were varied, resulting in a series of implemented PhCRs with lattice periods covering the range between 330 nm and 430 nm in 10 nm steps. For each $a$, a subset of PhCRs with varying hole radii $r$ of the line defect with $r= 40,\,50,\,60,\,70$ nm was fabricated. The vertical outcoupling efficiency was controlled by a so-called far-field optimization (ff) structure based on the second-order Bragg grating effect [31,32]. For this purpose, the radius of each second hole around the main cavity [marked in yellow in Fig. 1(b)] was slightly increased by $\Delta r= 0$, 3 or 6 nm, labeled ff0, ff3, and ff6 in the following. Thus, in total, 132 bichromatic PhCRs, each with a different combination of $a$, $r$ and $\Delta r$ were implemented on one chip. However, since strong optical signals could be observed in our setups already with ff3 PhCRs, including ff6 PhCRs in the experiments reported here turned out to be not required.

2.2 Sample growth and fabrication

In order to maximize the radiative transition rate between electrons and holes confined into a QD via the Purcell effect, a PhCR has to be fabricated in exact registry with the QD, such that the latter occupies the position of maximum electric field amplitude of the PhCR’s electromagnetic fundamental mode. To achieve this alignment, we follow the route described in Ref. [26]. In brief, a custom-made silicon-on-insulator (SOI) substrate with reduced background emission in the wavelength range relevant for this work (1.3-1.6 $\mu$m) and a 70 nm Si device layer on top of a 2 $\mu$m thick buried oxide layer (BOX) was employed as an initial substrate for further growth and PhCR processing. Background emission as described above has recently been observed for commercial SOI substrates even at room temperature [33,34] and was ascribed to remnants of the hydrogen implantation for the SOI smart-cut process [35]. By a bonding/splitting/thinning/annealing process sequence [36] any potential optical active defects were removed in a similar way as reported in [33]. In addition, thinning of the device layer to just 70 nm allowed us to vertically center the Ge QDs in the designed slab thickness of 220 nm.

Samples were patterned by electron beam lithography using a Raith eline plus system. A three-mask-level process allows the aligned exposure of the QD positioning mask and the PhCR mask with respect to alignment marks defined in the first lithographic step. At each lithographic level, the sample surface was cleaned and dipped in 10% HF for 30 s. The HF dip promotes the adhesion of the positive polymethyl methacrylate (PMMA) resist (Allresist 679.04) applied to the sample surface by spin-coating. The alignment marks were plasma-etched into the SOI substrate to a depth of $\sim 110$ nm in an Oxford Plasmalab 100 inductively coupled reactive ion etcher (ICP-RIE). In the second lithographic step, a single pit (SP) per PhCR was exposed at a defined position with respect to the alignment marks. This is distinctly different from our previous work [24,26], where a pit array was defined with all but the center pit in registry with air holes of the PhCR to be defined in the final lithographic layer. The improvements resulting from this modification will be discussed below.

These pits were transferred into the SOI substrate by ICP-RIE etching at $-90^\circ$C in a SF₆/O₂ plasma to a depth of 35 $\pm$ 5 nm as measured by atomic force microscopy (AFM, Digital Instruments Veeco Dimension 3100 with Nanoscope IV controller). The cross-section of the device layer after pit-etching is schematically indicated by the dotted line in Fig. 1(d). At this point, the SP pre-patterned SOI substrate was ready for the QD growth process.

After cleaning in piranha solution [37] as well as by a RCA sequence [38], and finally by a dip in 5%- hydrofluoric acid (HF) to remove the native oxide, the pre-patterned substrate was transferred into a solid-source MBE (Riber Siva 45) chamber for site-controlled SiGe QD growth in the etched pits [18,39]. After performing an in-situ degassing at 650$^\circ$C for 15 minutes, a 34 nm thick Si buffer was grown at a growth rate of 0.7 Å/s while ramping the substrate temperature from 450$^\circ$C to 550$^\circ$C. The buffer layer buries potential surface defects and remaining contaminations and flattens the pit sidewalls by exposing $\{1,1,n>7\}$ low-surface-energy Si facets that enable site-controlled Ge QD nucleation [18] at the pit center. A sketch of the surface profile after the buffer deposition is shown in Fig. 1(d) by the dashed line.

Next, $\sim 4$ monolayers (ML) Ge corresponding to $\sim 5.69$ Å were deposited at a growth rate of 0.04 Å/s while the substrate temperature was maintained constant at 650$^\circ$C. Since the total Ge coverage stays below the critical one for spontaneous Ge QD formation on flat substrate areas (4.2-4.9 ML at 650$^\circ$C), a two dimensional Ge WL without QDs forms there [18]. On the other hand, QD formation in the pit sets in already at a Ge coverage much smaller than 4 MLs. In addition, at this Ge coverage and the employed growth temperature, the Ge surface diffusion length is much larger than $30\,\mu$m [18,40] so that sufficient Ge for the formation of a QD in a pit reaches one of these sparse pits [18]. We want to emphasize that a pit spacing of 100 $\mu$m, corresponding to the center-to-center PhCR distance in the chip layout of this work, is the largest for perfectly site-controlled QD formation ever reported. It exceeds previously reported ones by at least a factor $\sim 6$ [18,25,41,42]. As predicted in [18,40], no fundamental limit on the distance of site-controlled SiGe QDs seems to exist under suitable growth conditions.

Finally, samples intended for QD emission experiments were capped by a 115 nm thick Si layer. As indicated in the inset of Fig. 1(d), the first $\sim 38$ nm of this cap were grown while ramping the substrate temperature from 500-700$^\circ$C to minimize Si/Ge intermixing [43]. The elevated growth temperature in the late state of the ramp is beneficial both to achieving low defect densities in and a planarization of the Si capping layer. The remaining 77 nm capping layer were then grown at 700$^\circ$C as well. As a result, the total thickness of grown layers plus original device layer is $\sim$220 nm, with a QD positioned in its center. Note that this total thickness is widely accepted as standard for the SOI integrated optical platform [3], allowing for a straightforward combination of the QD layer stack with device layouts readily available in PIC design libraries. Samples intended for structural characterization by surface scanning methods were grown without the Si cap.

After MBE growth, the samples were prepared for the PhCR mask layer in the same way as for the previous lithographic steps. Due to the large etch depth of the alignment marks, a large fraction of them still shows sufficient contrast for automatized alignment by the e-beam system after the growth of $\sim 150$ nm Si on top of them. With good alignment marks in place, individual PhCRs could be aligned with $\sim 25$ nm accuracy relative to the SQD positions [see Fig. 1(b)]. Once again, the PhCRs were transferred into the sample by dry etching as described above. The etch time was adjusted for etching all the way down to the BOX. Compared to our previous work [24,26], here, no QDs are present at the positions of the PhCRs’ air holes, i.e. in the etch volume. Therefore, a more homogeneous etch rate can be expected, resulting in a tighter etch time control and steeper air hole sidewalls.

Finally, free-standing PhCR membranes as sketched in Fig. 1(c) are implemented by lateral under-etching through the PhCR air holes during a $\sim 24$ minutes wet chemical etch in 10%-HF. After this etch, the 2$\mu$m thick BOX below the PhCRs is removed. Identically processed, uncapped samples were used to confirm the alignment accuracy by scanning electron microscopy (SEM, LEO Supra 35 from Zeiss).

In addition to SQD samples, reference samples grown on unpatterned SOI substrates were investigated (see Table 1). These reference samples contain the same layer sequence as the SQD samples, including a cap layer. Each layer was grown under nominally identical conditions as its counterpart in the SQD samples. As discussed above, in the absence of pits the deposited Ge forms a homogeneous two-dimensional layer of constant thickness without QDs. In the following, we refer to this type of reference sample as a wetting layer (WL) sample. To fabricate reference PhCRs on the WL samples, only the third level electron beam lithography step described above and the HF etch step are required.

Table 1. List of SQD and reference samples onto which sets of PhCRs with systematically varying design parameters as described in the text were processed.

View Table

3. Results and discussion

3.1 Post-processing characterization

Figure 1(a) shows the morphology of a SQD that is nucleated on a SP pre-patterned substrate. The SQD is surrounded by a flat area free from randomly nucleated QDs as shown by a $30\times 15\ \mu$m$^2$ AFM image in Fig. 1(a). This perfect site control for QD nucleation is achieved by adjusting the Ge surface coverage to stay below the supersaturation regime of $\sim 4.5$ ML [44]. The area shown in Fig. 1(b) corresponds to the area within the red rectangle in Fig. 1(a). Figure 1(b) shows a SEM image of a bichromatic PhCR fabricated to be accurately aligned with the QD, in order to maximize the dipole interaction of the QD with the electric field of the PhCR fundamental mode. The image was taken on an uncapped control sample, for which the QD is not hidden by the capping layer that is required for optically active QDs. The PhCR and QD are in virtually perfect registry in horizontal direction and in vertical direction with deviation of less than 25 nm. The remaining misalignment is much smaller than typical QD dimensions. It indicates limitations imposed by the employed fabrication technology in a similar range, as previously reported [25]. The yellow dashed circles in Fig. 1(b) mark photonic crystal air holes with radii slightly modified by $\Delta$r. By these holes we are able to control the trade-off between highest $Q$-factor and ff-coupling efficiency.

We want to emphasize, that the QD-free area covers the whole $100\times 100\,\mu \text {m}^2$ unit cell of the pit array outside the pit. Therefore, no secondary QD emitters are present to contribute to the resonant emission (RE) from PhCRs. Such a configuration is in contrast to the work of Zeng et al. [25], where PhCRs overlapping with more than one QD separated by 2 $\mu$m are reported.

3.2 Optical characterization

The emission properties of the cavity coupled QDs were studied by micro-photoluminescence ($\mu$-PL) spectroscopy in a setup described in details elsewhere [45]. For optical excitation, a continuous-wave (CW) diode laser emitting at a wavelength of 442 nm was focused via a microscope objective with numerical aperture (NA) 0.7 to a PhCR. The sample was mounted on the cold finger of a liquid He cryostat, allowing to cool the sample to less than 10 K. Via x-y translation stages mounted in the isolation vacuum chamber of the cryostat, cold finger and sample can be positioned with $\sim \!\!100$ nm accuracy over $\sim \!\!1$ cm traveling range. The PL emission was collected through the same objective and coupled to either a single- or a multi-mode fiber after filtering out the excitation laser. The multi-mode fiber was connected to a grating spectrometer with 300 mm focal length, NA=0.25, equipped with 300 or 600 grooves/mm gratings at blaze wavelengths of 1 or 1.6 $\mu$m, respectively. We detect the dispersed signal with a liquid-N₂-cooled InGaAs line detector, containing 1024 pixels at 25 $\mu$m pitch. A single-mode fiber and a superconducting single photon detector (SSPD) operated in time-correlated photon counting (TCSPC) mode [46] were used for time-resolved PL decay experiments. In theses experiments, the same diode laser operated in pulsed mode with a pulse length of $\sim \!\!130$ ps was used.

In Fig. 2, we compare the emission of a SQD at the center of a $N24$ bichromatic PhCR with results from reference PhCRs fabricated on a WL sample. As a typical example, the emission spectrum of a QD in a PhCR with $a=360$ nm (a360) $r=70$ nm (r70) and second order out-coupling grating formed by air holes with nominal radius of 103 nm ($\Delta r = +3$ nm, ff3) is shown in Fig. 2 by the blue line. The emission spectrum is dominated by sharp resonances corresponding to the modes of the photonic structure. At 4 K, the dominant peak (labelled $M_0$) is observed at $\sim \!\!1336$ nm wavelength ($\sim \!0.9281$ eV photon energy). As shown by the dotted line in Fig. 2, increasing the temperature to 290 K results in a $\sim \!\!11$ nm red-shift of the $M_0$-resonance as a consequence of the Si refractive index’s increase with temperature. We attribute the $M_0$ resonance in Fig. 2 to the emission of the SQD amplified in weak coupling regime by the fundamental mode of the PhCR according to the Purcell effect [23]. As shown in Supplement 1 (Fig. S2), the mode $M_0$ can be tuned in the wavelength range between $\sim \!\!1304$ nm and $\sim \!\!1339$ nm by selecting a PhCR period in the range 350 nm $\leq a \leq$ 370 nm. For all these different PhCR lattice constants, a strong SQD emission coupled to mode $M_0$ is observed, indicating a broad emission spectrum of a single SiGe QD, in agreement with the the results reported in [41], and, thus, no experimental issues with respect to spectrally overlapping the QD emission with the PhCR resonances [47]. As discussed in Supplement 1, the dominating processes resulting in such a broad emission spectrum have not been identified up to now. Their identification is beyond the scope of the current publication and will be addressed in future work.

 

Fig. 2. Resonantly enhanced PL emission spectrum of the SQD centered in a N24 bichromatic PhCR with parameters a360 r70 ff3 (blue line) measured at 4K. $M_{0}$ indicates the fundamental mode of the PhCR and $M_{3}$ indicates the third excited mode in resonance with optical wetting layer transitions. For comparison, the emission spectrum of this PhCR is shown for a temperature of 290 K by the dotted line on a scale expanded by a factor 3 (labeled $\times 3$). The $\sim$11 nm red-shift of the $M_0$-resonance wavelength is due to the increase of the Si refractive index with temperature. The red line shows the emissions from the Ge WL reference sample measured for a PhCR with nominally the same parameters as the one containing the QD (blue line). The intensity scale for this spectrum is three-fold expanded (indicated by label $\times 3$). The gray line shows the emissions from the same Ge WL reference sample coupled to a cavity with different parameters (a350 r70 ff3), expanded by a factor 2 (labeled $\times 2$). For this cavity layout, the spectral features, in particular the fundamental mode labeled $M_0^\text {ref}$, are more similar to the blue spectrum as compared to the spectrum shown in red. A more detailed discussion of the spectral features shown by the full lines is provided in the text. The shaded wavelength range indicates the width of the ensemble QD emission observed before PhCR fabrication (see Fig. S1 in Supplement 1). The PL traces are vertically offset for clarity by 80, 180, 280 cps for the red, blue and doted lines, respectively. The inset shows the resonant scattering result obtained at room temperature for the SQD - PhCR system with PL emission shown in blue. A Q-factor of 53605 is determined. The resonance frequency coincides with the PL emission peak measured at 290 K.

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To corroborate our conjecture, we note that in the spectra displayed by the full gray and red lines of Fig. 2 the intense cavity-coupled SQD emission is absent and only faint lines are observed instead in the corresponding spectral region. These two spectra were measured on the WL sample, that contains no QDs. The red spectrum was observed for a PhCR nominally identical to the one corresponding to the spectrum for the SQD sample (blue line in Fig. 2). However, the spectral features of both resonators show distinct differences too large to be attributed to limitations of chip-to-chip PhCR reproducibility. Instead, we rather ascribed to them to unequal Ge distributions within the PhCR for the SQD and the WL samples, and thus, to different effective refractive indices for these two nominally identical PhCRs. This effect can be compensated by a slight spectral tuning of the resonance wavelengths via the PhCR lattice constant $a$. As shown by the full gray line in Fig. 2, reducing the PhCR period $a$ from 360 nm to 350 nm results in resonance wavelengths resembling, up to a small blue-shift, those observed for the SQD sample. Most importantly, also for the spectrally tuned resonator on the WL sample, only a small peak (labelled $M_0^\text {ref}$ in Fig. 2 ) is observed within the spectral range of resonance-coupled SQD emission shown in Fig. S2 of Supplement 1. Therefore, the strong resonance $M_0$ is clearly due to the presence of a QD in the PhCR. More evidence for assigning the emission coupled to the $M_0$ mode to the SQD is obtained from its temperature- and excitation-power-dependence as discussed in upcoming paragraphs.

The origin of the faint resonances that are observed also in the absence of QDs in the spectral wavelength range above 1300 nm is attributed to residual WL emisson and/or emission associated with defects either in the SOI substrate [48], or in the MBE grown Si. The main contribution of the WL sets in at wavelengths shorter than 1290 nm, indicated by the broad background emission originating from photonic crystal regions outside the actual PhCR with superimposed resonances from WL regions inside the PhCR shown in Fig. 2. In this broad spectral region, for all PhCRs compared in Fig. 2 rather similar mode intensities are observed (note the different scaling factors for the blue, red, and gray spectra). This is especially true for the two PhCRs with different lattice constants $a$ on the WL sample, where the residual intensity differences are tentatively assigned to different Q-factors and outcoupling efficiencies of the various modes. For the SQD sample, the WL is thinner, since Ge from the WL is consumed during QD formation [40,49], thus, more dissimilarity to the WL-only samples can be expected.

The inset in Fig. 2 shows the spectral profile of the $M_0$ resonance as observed at room temperature in a cross-polarized resonant scattering (RS) experiment [50]. A tunable laser with a spectral resolution better than 1 pm provided by a fiber-based reference Fabry-Perot cavity [29] was scanned through the resonance of the PhCR (blue dots). The peak position of the RS signal is in agreement with the emission maximum of the $M_0$ mode observed at $T=290$ K. The RS signal is fitted to a Fano-resonance as described in [50] (red line in inset) and a very high Q-factor close to 53500 is obtained. We want to emphasize, that this value is limited by the effects of out-coupling structure (ff3) included in the respective PhCR layout. Omitting this structure (ff0) while leaving all other parameters of the PhCR unchanged (a=360 nm, r=70 nm, N=24) results in an even larger Q-factor as shown in the inset of Fig. 3 by the blue dots and the fitted Fano-resonance (red line). In this case, we observe $Q\sim 104,000$, which is the largest Q-factor so far reported for a SOI based PhCR loaded with a QD emitter [25,26,51–54]. We ascribe this huge improvement of the Q-factor as compared to previous works [25,26,51–54] mainly to our novel pit-pattern layout, together with the perfectly site-controlled QD growth technique, that allows restricting the number of QDs per PhCR to exactly the one centered within the cavity. With this layout, we avoid Q-factor degradation as a consequence of secondary QDs in the cavity that possibly act as photon scatterers or absorbers. In addition, via the differences in the etch rates of Si and SiGe for the employed plasma etching recipe, secondary QDs degrade the etch homogeneity and induce additional structural deviations from the ideal PhC structure. Also in this respect, exactly one QD per PhCR area is highly beneficial for achieving a high degree of structural homogeneity across the PhCR. Again, we observe the RS resonance shifted to a larger wavelength by $\sim \!\!11$ nm due to the different temperatures for PL and RS experiments. It is interesting to note that for the ff0-design the $M_0$ resonance is observed at 5 nm longer wavelength as compared to the ff3-design. This finding is in agreement with a slightly smaller effective index of refraction in the ff3-design due to its smaller Si volume as a consequence of the enlarged air holes forming the ff3 structure.

 

Fig. 3. Resonantly enhanced PL emission spectrum of the SQD centered in a N24 bichromatic PhCR with parameters a360 r70 without far-field optimization (ff0) as measured at 4K. The inset shows the resonant scattering spectrum of the same cavity measured at room temperature (blue symbols). The data were fitted to the Fano function [50] plotterd in red. From the fit, a resonance wavelength of 1350.95 nm, a FWHM of 13.0 pm, and thus, a Q-factor of $\sim 104,000$ were obtained for the $M_0$ resonance.

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For estimating the Purcell factor $F_p$, by which the radiative decay rate of the excited QD into the fundamental PhCR is enhanced with respect to the decay rate resulting from all allowed radiative decay channels into vacuum modes in the absence of a PhCR, we use [55]

Further evidence for the distinctly different nature of the emission sources coupled to the modes $M_0$, $M_3$ and $M_0^\text {ref}$ of the PhCRs shown in Fig. 2 is provided by their different quenching behavior as the temperature rises from cryogenic to room temperature. Figure 4(a) shows Arrhenius plots of observed mode intensities integrated over the line shapes for modes $M_0$ (blue symbols), $M_3$ (red symbols) of the PhCR aligned to a SQD and for mode $M_0^\text {ref}$ (green symbols) of the PhCR on the WL sample. The data were fitted to the simplest quenching function given by [56]

Fitting results and extracted activation energies, $E_a$, are shown as dotted lines and labels in Fig. 4(a). The largest activation energy ($E_a=119.6\pm 10.8$ meV) is obtained for the $M_0$ resonance that we assigned to be fed by the SQD emission. Again we observe a distinctly different behavior for the $M_0^\text {ref}$ mode, for which we observe a more than 10 times reduced value for the activation energy of only $E_a=12.9\pm 3.3$ meV. The difference in the activation energies can be naturally understood by presence and absence of a QD in the PhCR’s center on the SQD and WL sample, respectively.

 

Fig. 4. (a) Temperature dependence of the peak area of the three selected modes ($M_0$, $M_3$, and $M_0^\text {ref}$) as a function of reciprocal temperature. Arrhenius fits give thermal activation energies $E_a$ of each mode. (b) Peak area ($I_\text {mode}$) versus excitation power ($I_\text {exc}$) for modes $M_0$ and $M_3$ of the a360r70ff3 PhCR on the SQD sample (red an blue symbols, respectively). For mode $M_0^\text {ref}$ of the a350r70ff3 PhCR on the GeWL sample this dependence is shown by the green symbols. Dotted lines and $m$ values result from fits to $I_\text {mode} \propto (I_\text {exc})^m$ as described in the text.

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As shown in Fig. S3 of Supplement 1, for the $M_0$ mode intensity of the a360r70ff0 design, we observe an activation energy identically within experimental errors to the one assigned to the QD emission in the previous paragraph. Thus, we have strong evidence that a QD is present also in the center of the a360r70ff0 PhCR. Nevertheless, only a small PL intensity is detected for the $M_0$ mode of this PhCR as shown in the main panel of Fig. 3, as a consequence of a reduced coupling to radiating modes for to the ff0 design. In turn, this reduced coupling manifests itself also in the large Q-factor for this design discussed in a previous paragraph.

For the WL emission into mode $M_3$ of the PhCR on the SQD sample occurring at $\sim 1220$ nm in Fig. 2, we observe an activation energy ot $E_a=39.2\pm 3.9$ meV, intermediate to the values reported for modes $M_0$ and $M_0^\text {ref}$ in a previous paragraph. In the same spectral range, very similar $E_a$-values are obtained for the emission peaks of the WL reference sample, as shown in Fig. S4 of Supplement 1.

Also measurements of the emission intensity in the various PhCR modes $I_\text {mode}$ as functions of the excitation intensity $I_\text {exc}$ are in agreement with our source assignments. In the double logarithmic plot shown in Fig. 4(b), individual results for modes $M_0$, $M_3$ and $M_0^\text {ref}$ as labelled in Fig. 2 are shown by blue, red and green symbols, respectively. For a characterization, we use the exponent $m$ of the commonly employed empirical relation $I_\text {mode} \propto (I_\text {exc})^m$. As shown in Fig. 4(b), for $I_{M_0}$ we obtain $m\approx 1$ for low and $m\approx 2/3$ for intermediate excitation power, with a transition region between 30 $\mu$W and 70 $\mu$W. Such a behaviour is typically observed for QD emitters, with the $m=1$ region indicating dominant electron (e) hole (h) pair recombination and the $m=2/3$ region Auger-recombination involving three particles (for example two e and one h) [57,58]. At even higher excitation, additional e-h recombination paths result in a further decrease of $m$. On the other hand, for the $M_3$ mode we obtain $m\approx 1.9$, typically for WL emission [57], where the carrier lifetime is limited by Shockley-Read- Hall recombination over trap states. For this recombination process, $m=2$ is expected [59]. Due to e, h localization in QDs, the trap states do not influence the carrier lifetime in QDs as long as they are not close to a QD. Thus, they are much more efficient for extended QW states. For mode $M_0^\text {ref}$ of the a350r70ff3 PhCR on the WL reference sample, we observe $m=0.88$, indicating e-h pair as the dominant recombination channel in this spectral region of the WL emission.

The decay dynamics of the $M_0$ emission was characterized by TCSPC experiments [46]. The results of two measurements at different average laser power at a pulse width of $\sim \!\!130$ ps and a repetition rate of 5 MHz are shown in Fig. 5. For an average excitation power of 33.2 $\mu$W, an initial fast decay component with a decay time of $\tau \approx 0.65$ ns is observed, followed by a slower decay with a time constant $\tau \approx 3.9$ ns. For a lower average excitation power of 5 $\mu$W, a single exponential decay with a time constant $\sim \!3.7$ ns close to the slow component at larger excitation is measured. According to [58], the observed decay characteristics is expected for QDs excited to more than one e-h pair. In this case, more combinatorial recombination paths for e-h pair recombination as well as Auger processes become effective, resulting in a reduced life time of the e-h density in the QD. Eventually, after the rapid initial decay only one e-h pair will be present in the QD, resembling the situation after weak excitation. Therefore, the slowest decay constants are expected to be equal for intense and weak excitation, in agreement with the experimental results shown in Fig. 5.

 

Fig. 5. Semi-logarithmic plot of time-resolved $M_0$ mode emission of a PhCR with parameters a360 r70 ff3 measured at 10K and recorded under 5 MHz repetition rate with 130 ps laser pulses at 442 nm. At 33.2 $\mu$W average excitation power (red line) clearly a fast and a slow decay component are observed. At lower power (5 $\mu$W, blue line) the fast component is absent.

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4. Summary and conclusions

In this work we used CMOS compatible lithographic alignment to position single SiGe QDs at the electric field maxima of bichromatic PhCRs’ fundamental modes. Due to the high reproducibility of the alignment process, we were able to produce a large set of resonators with varying layouts, each one centered with respect to its single QD. By this lithographic tuning we could identify the cavity layout best matching the emission maximum of the coupled QD. The bichromatic cavity design provides very large Q-factors but requires extremely accurate alignment of QD and cavity, due to its narrow Si region at the cavity center. By reducing the amount of Ge within the resonator and the surrounding photonic crystal to a minimum of exactly one QD on its associated WL, we improve the resonators’ structural quality by improving the etching homogeneity for the fabrication process. In addition, by these measures we avoid light scattering out of the resonator due to secondary QDs. As a consequence, we were able to demonstrate a Q-factor in excess of $10^5$ for a QD-coupled resonator mode. This value represents the largest Q-factor reported so far for QD-loaded photonic crystal resonators realized in a SOI integrated optics platform [25,26,51–54]. The dependence of mode emission intensities on temperature, excitation power, and time after pulsed excitation was carefully analyzed and compared to results from cavities fabricated on samples containing a WL without QDs. By this analysis we were able to identify PhCRs for which the emission coupled to the high Q fundamental mode is associated with optical transitions within the SiGe QD. As these transitions occur in the relevant telecom wavelength band, the nano-optical system consisting of a single SiGe QD coupled to a high-Q PhCR as investigated in this work is of high relevance as a potential quantum optical source for a future SOI based integrated quantum photonic platform compatible with existing fiber networks. With respect to the latter aspect, the results of time resolved PL decay indicate that photon emission at a level of a single e-h pair is within reach.