The amazing world of self‑organized Ge quantum dots for Si photonics on SiN platforms

Beginning with our exciting discovery of germanium (Ge) spherical quantum-dot (QD) formation via the peculiar and symbiotic interactions of Si, Ge, and O interstitials, we have embarked on a journey of vigorous exploration, creating unique configurations of self-organized Ge-QDs/Si-containing layers. Our aim is to generate advanced Ge-QD photonic devices, while using standard, mainstream Si processing techniques. This paper summarizes our portfolio of innovative Ge-QD configurations. With emphasis on both controllability and repeatability, we have fabricated size-tunable, spherical Ge-QDs that are placed at predetermined spatial locations within Si-containing layers (SiO 2 , Si 3 N 4 , and Si) using a coordinated combination of lithographic patterning and self-assembled growth. We have successfully exploited the multi-dimensional, parameter spaces of process conditions in combination with layout designs to achieve exquisite control available through the thermal oxidation of lithographically patterned, poly-Si 1 − x Ge x structures in close proximity with Si 3 N 4 /Si layers. In so doing, we have gained insight into the growth kinetics and formation mechanisms of self-organized, Ge spherical QDs embedded within SiO 2 , Si 3 N 4 , and Si layers, respectively. Our Ge-QD configurations have opened up a myriad of process/integration possibilities including top-to-bottom evanescent-wave coupling structures for SiN-waveguided Ge-QD photodetectors and Ge-QD light emitters for Si photonics within Si 3 N 4 integrated photonics platforms for on-chip interconnects and sensing.


Introduction
Since the inception of the first transistors in the 1940s, the enormous investment and immense body of research on Group IV semiconductors, including silicon (Si) and germanium (Ge), have spearheaded spectacular and rapid advances in ultra-large-scale integrated circuits' (ULSI) technology enabling a vast landscape of applications including logic, memory, computing, and sensing, etc. Although Ge was the initial semiconductor of choice for both research and industry, it was quickly superseded by Si as the active-layer material of choice for both bipolar junction transistors (BJTs) and metal-oxide-semiconductor field-effect transistors (MOS-FETs). However, more recently, Ge-based nanoelectronics is making a comeback. In particular, Ge nanophotonics is breaking new ground as the enabling technology for Si photonic applications.
To date, relentless miniaturization of MOSFET's feature sizes to nanometer scales has been pursued to achieve desired increases in device performance and speed. However, such transistor-level performance gains have been offset by significant increases in power consumption and latency arising primarily from electrical interconnects. Densely routed metal nanowires result in considerable increases in the overall resistance and parasitic capacitance, limiting the performance and power efficiency of the integrated circuits [1]. Therefore, new materials, new device structures, and even new device design and fabrication paradigms are being aggressively investigated for Si-CMOS ULSI technology while expanding its versatility and functionality. On-chip optical interconnects appear to be one of the most promising solutions for addressing the power consumption and latency Po-Yu Hong and Chin-Hsuan Lin have contributed equally as the first author.

Fabrication-related challenges for Si/Ge-QDs
The generation of Si-or Ge-QDs with controllable size tunability and arrangement has been the subject of considerable research starting in the 1990s [7,8]. Several approaches have been proposed for the formation of Si-and Ge-QDs, including chemical synthesis, [9] epitaxial growth, [10] deposition followed by post-annealing, [11] lithographic patterning [12], and electrostatic-gate definition based on two-dimensional electron-gas (2DEG) heterostructures [13]. The key to implementing QD devices for practical applications lies in having an unprecedentedly high degree of control over the crystallinity, size, shape, density or number, and spatial location of QDs, all of which are essentially important for optimizing device performance. However, the growth and fabrication of the desired QDs with tunable sizes, shapes, and spatial arrangements face difficult technical challenges no matter whether bottom-up or top-down approaches are used.
The Holy Grail for device manufacturing is to achieve controllable generation of QDs embedded within desired host matrices with predictable electronic structure and optical properties. Both Si-and Ge-QDs have been created largely using "self-assembled" techniques, i.e., through random, non-lithographically controlled nucleation and growth. In general, self-assembled QDs exhibit anisotropic crystalline morphologies (shapes) with favored crystal facets as well as size fluctuations. Detailed knowledge of how the QDs are created and especially their interactions with their local environments are therefore essential to achieve the high level of control within an otherwise random growth process. From a device fabrication perspective, making electrical contacts to specific nanoscale QDs within a large ensemble of randomly distributed QDs is very challenging. In contrast to having a random distribution of self-assembled QDs, lithographically patterned QDs allow better control over positioning at designated spatial locations via layout design. Still, it is relatively difficult to produce very small QDs with good surface passivation even using advanced lithography/etching processes. In view of the above-mentioned fabrication-related challenges for the control of the QD sizes and positions, a "hybrid" approach appears to be the most promising wherein self-assembled QDs are grown within or on pre-patterned structures.

Material-related QCEs for Si/Ge-QDs
Ge-QDs exhibit much stronger QCEs than their counterpart Si QDs, because Ge has an inherently larger exciton Bohr radius (α B,Ge ~ 25 nm) than Si (α B,Si ~ 5 nm) [5]) thanks to the higher dielectric constant and lower carrier effective mass in Ge. Thus, Ge-QDs have discrete energy levels with larger energy-level separations than Si QDs at the same QD sizes. That is, in principle, the electronic band structures in proximity of the band gap of Ge-QDs should be more easily modified than for Si QDs, making Ge-QDs more attractive for use in advanced photonic devices. However, it is a known fact that Ge is less thermally stable than Si due to a lower melting point (T melt, Ge ~ 930 °C vs T melt, Si ~ 1410 °C). Additionally, Ge is susceptible to interface traps or surface recombination centers due to the lack of robust and defectfree Ge/Ge oxide interface. Hence, thermal stability and surface passivation of Ge-QDs for practical photonic device applications remain as issues to be addressed from device design and reliability perspectives.

Compatibility relationships of Ge and Si
From a device fabrication point of view, the material compatibility and mutual inter-miscibility [14] between elemental Ge and Si are a significant advantage. Binary alloys of SiGe can be formed across the entire chemical composition range from 100% Si (0% Ge) to 0% Si (100% Ge). In particular, binary alloys of Si x Ge 1−x with continuously variable Ge and Si compositions can be fabricated using CMOS-based approaches for generating high-density/high-speed ICs and novel photonics using novel band-gap engineering and strain engineering techniques. While the material compatibility and miscibility properties are well known, the fundamental nature of Si/Ge interactions and the extent of their attraction for each remain a topic to be explored further. For instance, a clear example of the disparity between Si and Ge chemical reactivities is demonstrated by the high-temperature thermal-oxidation behavior of SiGe alloys. In this case, preferential oxidation of Si occurs concurrently with the segregation and precipitation of Ge within the newly grown SiO 2 matrix [15,16]. Ge precipitation at the interface between the unoxidized SiGe and the newly grown SiO 2 layer results in a high concentration of dangling bonds and interfacial traps, which have prevented the formation of high-quality, stoichiometric gate-oxide layers on top of SiGe channels required for high-performance MOSFETs. Several approaches have been proposed to improve the electronic properties of the SiGe/ SiO 2 interface, including the insertion of a thin-Si capping layer over the SiGe channel [17] to prevent direct oxidation of SiGe as well as low-temperature plasma oxidation [18] to suppress Ge segregation.
An opposite, creative approach, namely exploiting the nominally bad outcome of Ge precipitation arising from the preferential oxidation of Si within SiGe alloys, has been employed for the fabrication of Ge-on-insulator (GOI) substrates via complete oxidation of SiGe layers grown on silicon-on-insulator (SOI) substrates [14,19]. Essentially, the thermal oxidation of SiGe-on-SOI is carried out to completion whereby the concentration of Ge within the oxidizing SiGe layer keeps increasing until only a Ge layer is left behind over an underlying SiO 2 layer.
These examples suggest that a deep understanding of the thermal/chemical behavior of the SiGe alloy system is absolutely essential, especially for high-temperature oxidation processes that are a vital part of Si processing. As shown by our own work below, great opportunities exist to create new and innovative Ge-QD configurations that cannot be predicted from a study of the Si/Ge equilibrium phase diagram alone. Thus, we have reported a novel and rather curious interplay between Ge and Si interstitials that occurs in an H 2 O oxidizing ambient at high temperature (800-900 °C), in particular, with Si 3 N 4 buffer layers in close proximity [20][21][22][23][24]. The complex interactions of Ge, Si, and O interstitials facilitate counter-intuitive reactions when simply based on knowledge of the equilibrium phase diagram. Our experimental work clearly demonstrated that we were able to successfully exploit these never-before-observed effects to controllably create size-tunable Ge spherical QDs within Si 3 N 4 , SiO 2 , and Si layers in a combined lithographically patterned and also self-organized approach [20][21][22][23][24]. Our unique capability of growing self-assembled Ge-QDs at designated spatial locations has allowed us to fabricate advanced Ge-QD photonic devices, including Ge-QD PIN photodiodes and Ge-QD microdisk light emitters on Si 3 N 4 platform using standard Si processing.

Formation of self-organized Ge-QD/SiO / SiGe sheets within Si 3 N 4 and Si layers
Our previous reports have already demonstrated a CMOScompatible fabrication approach for the controllable placement of self-organized Ge-QDs/SiO 2 shells within Si 3 N 4 ( Fig. 1a) [20] and self-aligned Ge-QDs/SiO 2 /SiGe nanosheets on Si (Fig. 1b) layers [21] within a single-step thermal-oxidation process (Fig. 1). The Ge-QDs were created using the selective oxidation of poly-Si 1 − x Ge x lithographically patterned structures (for instance, pillars and islands) with specifically designed Si 3 N 4 layers on top [22][23][24] or at the sidewalls [25][26][27][28] of Si patterned structures. The proximal Si 3 N 4 layer is one of the key enablers for the formation of Ge spherical QDs and responsible for a unique phenomenon, namely, activating Ge-QD migration in the solid state within the already-formed SiO 2 layers during the thermal-oxidation process. We have conducted a series of experiments to exploit the multi-dimensional process parameter spaces (including Si 3 N 4 thickness as well as the process temperature and time of thermal oxidation) for controllably growing size-tunable Ge spherical QDs at specific, designated spatial locations [22][23][24]. Our experimental observations also elucidated the fundamental mechanisms responsible for the Ge-QD migration. At high temperature and in an oxidizing ambient, a number of counter-intuitive and symbiotic phenomena occur simultaneously to facilitate the coalescence and migration of spherical Ge-QDs. First, Ge catalyzes the release of Si interstitials through selective oxidation of the proximal Si 3 N 4 . Second, silicon interstitials facilitate the coalescence of Ge nanocrystals through Ostwald Ripening. Third, Si interstitials also "make room" for the coalescing and migrating Ge-QD through a unique destruction/construction mechanism whereby the Si interstitials catalyze the decomposition of the SiO 2 matrix surrounding the Ge-QD, and in the direction of the Si interstitial gradient, thereby promoting the migration of the Ge-QD toward the source of Si interstitials namely either the Si 3 N 4 layer or the Si substrate [31]. In an oxidizing ambient, these silicon interstitials combine with O interstitials and re-form the oxide matrix in the wake of the moving Ge-QD! [31]. Thus, in effect, the symbiotic cooperation between Ge, Si and O interstitials is responsible for the never-before-seen phenomenon of migration of the Ge-QDs in the solid state through a SiO 2 matrix. Fourth, the discovery by Stekolnikov et al. [40] that in the stress-free state, Ge crystals assume a spherical habit because of the miniscule differences in surface-free energy of the various Ge crystalline facets leads ultimately into the creation of spherical Ge-QDs via Ostwald ripening facilitated by mechanical decoupling from the surrounding SiO 2 matrix through the oxide destruction and migration of the spherical Ge-QDs [22].

Formation of Ge-QDs/SiO 2 shell
Previous reports have already discovered that high-temperature thermal oxidation (> 800 °C) of Si 1 − x Ge x results in the preferential oxidation of its Si content to SiO 2 with concurrent Ge segregation. The thermodynamic explanation for this phenomenon is based on the large difference in the heats of formation of SiO 2 (− 911 kJ/mol) and GeO 2 (− 477 kJ/mol) [29]. The resultant SiO 2 matrices therefore contain a combination of precipitated Ge nanocrystals in equilibrium with Ge interstitials. The concentration gradient of Ge interstitials is highest at the SiO 2 /SiGe interface [15,16]. Among the first interesting and counter-intuitive findings made by us was the fact that following the complete thermal oxidation of poly-Si 1 − x Ge x lithographically patterned structures over the specially designed Si 3 N 4 layers, the Ge nanocrystals and their associated Ge interstitials surprisingly catalyze the local decomposition and oxidation of the proximal Si 3 N 4 layer [20]. It is a well-known fact that Si 3 N 4 has a much lower oxidation rate than that for pure Si substrates. This effect has been practically exploited in CMOS processing using Si 3 N 4 layers as "hard masks" for the local oxidation of lithographically uncovered Si in CMOS isolation technology [30]. As described above, our extensive transmission-electron microscopy (TEM) observations show that Ge nanocrystals are indeed able to decompose the proximal solid layers of Si 3 N 4 and even migrate through them in the solid state! We discovered that this unique and localized Si 3 N 4 decomposition process releases Si interstitials which, in turn, promote migration of Ge nanocrystals through their surrounding SiO 2 matrix along the Si interstitial concentration gradient toward the Si 3 N 4 layer. Concurrent with the migration process, the Ge nanocrystals grow in size by Ostwald Ripening culminating in complete coalescence [31] and ultimately resulting in the formation of spherical Ge-QDs with both high chemical purity (Fig. 2) and high degree of crystallinity (Fig. 3) [20].

Ge-QDs-mediated Si 3 N 4 oxidation
Our second experimental observation supporting the Ge catalytically enhancing local oxidation of Si 3 N 4 is that Ostwald-ripened, spherical Ge-QDs are able to penetrate an entire layer of Si 3 N 4 through a solid-state migration process and reach the underlying Si substrate [21], leaving behind a trail of re-formed SiO 2 in its wake [31]. Our design of experiments and extensive observations allowed us to propose a dynamic SiO 2 destruction-construction mechanism in proximity of the migrating Ge-QD surface providing an explanation for the unique migration and penetration behaviors of Ge-QDs [22,23]. In brief, in the presence of oxygen interstitials supplied by the thermal-oxidation ambient, the migrating Ge-QD causes the SiO 2 ahead of it to decompose and subsequently re-form in its wake, as evidenced by a trail of SiO 2 re-formed behind the migrating Ge-QD [22]. Also, the Ge-QD is accompanied with a ~ 1 nm-thick conformal interlayer of SiO 2 between the Ge-QD and surrounding LPCVD-Si 3 N 4 (Fig. 2) as it penetrates the LPCVD-Si 3 N 4 layer. The thickness of SiO 2 interlayers is essentially determined by a dynamic equilibrium existing between the local concentrations of O and Si interstitials near the Ge-QD/ Si 3 N 4 interface supplied by the external oxygen ambient and the Si interstitials released from the locally decomposing Si 3 N 4 layer [32].
We have also experimentally observed a large increase in the local thickness of this conformal SiO 2 interlayer when the nature of the proximal Si 3 N 4 layer changes from a low-pressure chemical-vapor deposited (LPCVD)-Si 3 N 4 layer to plasma-enhanced chemical-vapor deposited (PECVD)-Si x N y : H layer [33]. This is because the significantly higher temperature (780 °C) deposition for LPCVD-Si 3 N 4 layers results in a much denser Si 3 N 4 film with lower hydrogen incorporation as compared to the PECVD-Si x N y : H layers which are nominally deposited

Ge-QD-mediated Si 3 N 4 densification
Our next interesting finding is that the penetrating Ge-QD not only facilitates local decomposition of the proximal Si 3 N 4 layer, but also mediates local densification of the proximal Si 3 N 4 for a significantly reduced thermal budget. For instance, thanks to the catalytic action of Ge, Si 3 N 4 densification was now possible at 900 °C for 10 min as opposed to previously needing exposure to 1200 °C, for 3 h [36]. EELS mapping, Energy-Dispersive linescans, and spectral analysis (Fig. 4) showed that the densification of Si 3 N 4 is achieved by an increase in both Si and N concentrations with essentially no change in the stoichiometric ratios [35] as well as being accompanied by phase transition from the amorphous to the nanocrystalline state [27,28,35]. The latter phase transition effect was evidenced by the appearance of spotty diffraction rings within nanobeam diffraction (NBD) patterns and diffraction peaks corresponding to α-or β-phase states in X-ray diffraction (XRD) spectra [27,28]. Densified Si 3 N 4 is desired for the fabrication of Si 3 N 4 waveguides and related photonic devices due to the significant reduction in H-induced traps and the consequent reductions in absorption/propagation losses.

Ge-QD-mediated Si 1 − x Ge x -sheet formation
Yet, another discovery was the fact that when the Ge-QD ultimately penetrates the Si substrate, it enables the simultaneous formation of self-aligned, conformal heterostructures of Ge-QD/SiO 2 -shell/Si 1 − x Ge x nanosheets on the Si surface (Fig. 1a, d). The conformal, single-crystalline Si 1 − x Ge x nanosheet is generated by the Ge interstitials migrating from the penetrating Ge-QD through a thin SiO 2 -shell and dissolving within the Si surface. The Ge content and the corresponding compressive strain within the resulting single-crystalline Si 1 − x Ge x nanosheets are tunable by adjusting the process time of thermal oxidation and the contact size of the penetrating Ge-QDs. [32] Single-crystalline (100) Si 1 − x Ge x nanosheets with Ge content as high as x = 0.85 and a compressive strain of 3% were achievable on Si (100) substrates. [32] Similarly, by changing the crystal orientation of the Si substrate, (110) Si 1 − x Ge x shells with Ge content of x = 0.35 and corresponding compressive strain of 1.5% were created on top of Si (110) substrates. [32] The strain values of our Si 1 − x Ge x nanosheets are much higher than that for Si 1 − x Ge x channels described in the previous work using epitaxial growth, process stressors [37], and mechanical stress [38]. The so-formed, self-aligned stacking heterostructures of Ge-QD/SiO 2 /SiGe-nanosheet heterostructures are analogous to the commonly used poly-Si/SiO 2 / Si MOS structures and, thereby, indeed provide a core "building block" required for the fabrication of Ge-based MOS devices. the TEM high-contrast regions corresponding to significant enhancements in X-ray fluorescence (XRF) intensity for both nitrogen and silicon and accompanied by a corresponding decrease in the oxygen XRF intensity

Ge-QD-mediated deconstruction-construction of SiO 2 , Si 3 N 4 , and Si during thermal-oxidation process
Our extensive experimental observations show that the Ge-QDs appear to not only facilitate the decomposition of proximal Si-containing layers such as SiO 2 , Si 3 N 4 , and Si, but also in turn, mediate the regrowth of SiO 2 [22], densification of Si 3 N 4 [27,28], and the generation of SiGe nanosheets on Si [27,32,39]. Such deconstruction-construction processes dynamically occur as a result of the exquisite interplay between Ge, Si, and O interstitials during the thermal-oxidation process, pointing to ultimately achieving the ability to form self-organized heterostructures of Ge-QD/SiO 2 -shell on Si 3 N 4 and Ge-QD/SiO 2 -shell/SiGe-nanosheet on Si with precise control of the Ge-QD sizes and at the desired spatial locations.

Engineering advantages of Ge-QD/SiO 2
The key engineering advantages of our combined, lithographically patterned as well as self-organized Ge-QD/ SiO 2 approaches lie in controllably positioning size-tunable spherical Ge-QDs at desired locations [27,28,39]. In so doing, we have created a large parameter space for designing advanced photonic devices exploiting quantum electrodynamics effects. The strengths of our proposed Ge-QD fabrication approaches for practical device applications include: (1) spherical shape, (2) self-assembled Ge-QDs within selforganized SiO 2 shells, (3) size-tunable electronic structures with predictable optical properties, (4) scalable numbers of Ge-QDs, and (5) self-aligned Ge-QD/SiO 2 shell/SiGenanosheet heterostructures fabricated using (6) mainstream Si-CMOS manufacturing processes.

Spherical-shaped Ge-QDs
The unique migration and Ostwald ripening of our Ge-QDs within Si-containing layers assume their perfectly spherical shape as predicted by Stekolnikov et al. [40]. In their calculations [40], a stress-free Ge nanocrystal in free space tends to assume a spherical shape after surface reconstruction due to the surface energies of the major {111}, {311}, and {100} facets being practically equal (0.99-1.01 J/m 2 ). Although our Ge-QDs are indeed embedded within Si-containing matrices, we attribute the destruction/construction mechanism [31] for mechanically decoupling the interfacial bonds between the growing, Ostwald-ripened Ge-QD and the various host materials, namely SiO 2 , Si 3 N 4 , and Si during the thermal-oxidation processes. The dynamic SiO 2 destruction-construction mechanisms near the Ge-QD surface [22,23] mechanically decouple the Ge-QD from its surrounding layers of Si 3 N 4 and Si, which not only enable the unique solid-state migration behavior of Ge-QDs, but also facilitate the surface reconstruction of the migrating Ge-QD into assuming a perfectly spherical shape. Spherical QDs are highly desirable for quantum-electronic and photonic devices, because their three-dimensional, radially symmetric quantum confinement gives rise to atomic-like discrete orbitals (1s, 2s, 2p, 3s, 3p, …) with a high degree of isotropy and predictable optoelectronic properties.

3-D placement of Ge-QDs
Precise placement of our spherical Ge-QDs at pre-designated, nano-spatial locations both laterally and vertically is achievable via controlled heterogeneous nucleation and growth within or at the sidewall edges of lithographically patterned structures. Pattern-dependent oxidation combined with Ostwald ripening offers additional nanofabrication tools for controlling the QD locations [41]. We have also confirmed using extensive plan-view/cross-sectional view TEM examinations that following thermal oxidation, Ge nanocrystals tend to nucleate either at the process-induced defects or geometrically induced highly stressed sites. Representative examples are the formation of Ge-QDs at specially designed included-angle locations of polygonal cavities [41] and sidewall spacer corners [27,28,42]. Figure 5 shows the spatial locations of Ge-QDs formed by the thermal oxidation of poly-SiGe spacer layers at the sidewall edges of lithographically patterned Si/Si 3 N 4 structures and at concave corners. EDX maps of Ge-QD distribution for the letters of alphabet: G, E, Q, and D in Fig. 5 show that the QDs prefer to nucleate at the concave corners (higher stress regions) rather than at convex corners. Therefore, the striking advantage of our Ge-QD nanofabrication approach lies in the exquisite control in three dimensions of Ge-QD arrays using an ingenious combination of layout design and thermal oxidation of SiGe spacer islands located at the sidewalls of lithographically patterned, stacked heterostructures of Si 3 N 4 /Si. Figure 6a and b shows a pair of Ge double QDs (DQDs) and two vertically stacked, paired Ge DQDs formed using a single-step thermal oxidation both of a stack and two stacks of Si/Si 3 N 4 ridges, respectively, with a spacer island of poly-SiGe located at each sidewall.

Process-controlled tunability of QD size and photoluminescence wavelength
Our Ge-QDs are formed by Ostwald Ripening via the coalescence of separate Ge nanocrystals formed within the original, thermally oxidized Si 1 − x Ge x layer. The resulting Ge-QD size is essentially determined by the total Ge content with the original Si 1 − x Ge x island and is adjustable by controlling both the geometric dimensions and chemical composition of the island. Thus, a continuously tunable range of nanofabrication controlled QD diameters from 5 to 100 nm has been achieved [27,39]. The high degree of scalability and uniformity in the QD sizes have allowed us to demonstrate size-tunable photoluminescence (PL) peak energies ranging from 0.8 to 3.5 eV. [27] A systematic blue-shift in the PL peak energies occurs when Ge-QD diameters are reduced below 30 nm, presenting strong evidence for QCE. PL peak energy was shown to be inversely proportional to the diameter (D QD ) of the Ge-QDs, following a power law proportionality of (1/D QD ) 2 [27,43,44].

SiN-embedded Ge-QD microdisk light emitters
Our technique of embedding Ge-QDs within densified Si 3 N 4 is readily applicable for the fabrication of Si 3 N 4 -embedded Ge-QD microdisk light emitters. Microdisk light sources enable in-plane photonic integration thanks to the fact that radiation from the strongly confined whispering-gallery cavity modes (WGMs) around the microdisk resonators allows easy coupling of the emitted light with the bus waveguides. The process flow and schematic diagrams for the nanofabrication of Si 3 N 4 -embedded Ge-QDs microdisks are strates, d SiO 2 planarization followed by Si 3 N 4 deposition over the Ge-QDs/SiO 2 arrays, e lithographic patterning of Si 3 N 4 /Ge-QDs/SiO 2 microdisks, followed by Si 3 N 4 spacer deposition, and f Si 3 N 4 /Ge-QDs/SiO 2 microdisks released from the SOI substrates using TMAH wet etching to remove the underlying Si layers described in Fig. 7. Starting with SOI substrates with 200 nm-thick single-crystalline Si (c-Si) layers, bi-layers of 20 nm-thick Si 3 N 4 and 60 nm-thick poly-Si 0.85 Ge 0.15 were sequentially deposited using LPCVD (Figs. 7a, 8a). Poly-Si 0.85 Ge 0.15 pillars with pillar width/pitch of 100 nm/120 nm were lithographically patterned using electron-beam lithography (EBL) in combination with SF 6 /C 4 F 8 plasma etching (Figs. 7b, 8b). Subsequently, thermal oxidation at 900 °C within an H 2 O ambient converted the Si content of the poly-SiGe pillars to SiO 2 , and the released Ge ultimately coalesces into a single Ge-QD with a diameter of 50 nm per oxidized pillar (Figs. 7c, 8c). Following the formation of the self-organized Ge-QD/capping SiO 2 array, LPCVD-SiO 2 layers were deliberately deposited to fill in gaps between the oxidized pillars and then etched back for the planarization of QD array. A 50 nm-thick Si 3 N 4 layer was subsequently deposited over the entire Ge-QDs/SiO 2 array (Figs. 7d, 8d). Next, Si 3 N 4 -embedded Ge-QDs/SiO 2 microdisks with diameters of 3-7 μm and thickness of 200 nm were lithographically patterned using a combined process of EBL followed by CHF 3 plasma etching. A 20 nm-thick Si 3 N 4 layer was subsequently deposited and then directly etched back, so that Ge-QDs/SiO 2 microdisks were wrapped all around by the surrounding Si 3 N 4 layer (Figs. 7e, 8a). Finally, the underlying Si layers were partially etched within the SOI substrates by dipping in 2.38% tetramethyl ammonium hydroxide (TMAH, C 4 H 13 NO) solution at 85 °C for few minutes, thus forming Si pedestals supporting the Si 3 N 4 /Ge-QDs/SiO 2 / Si 3 N 4 microdisks (Figs. 7f, 8b).
Plan-view (Fig. 9a) and cross-sectional (Fig. 9b, c) SEM micrographs show that suspended, Si 3 N 4 -encapsulated Ge-QDs microdisks supported over SOI substrates by multifaceted Si pedestals. The faceted Si pedestals (Fig. 9a) were produced by TMAH etching that has highly anisotropic etch rates exposing slower etching crystal planes of Si. [30]. The resulting microdisk is partially released from the underlying SOI substrates with a 250 nm-thick, 2 μm-wide air gap (Fig. 9c). The upward-bending periphery of the cantilevered microdisk induces a large tensile stress within the Si 3 N 4 -embedded Ge-QDs. In this way, the excited Ge-QD luminescence is effectively confined within the high refractive-index contrast, Si 3 N 4 -embedded Ge-QDs/SiO 2 microdisk heterostructure. The geometrical dimensions of the microdisk structures such as their diameters and thicknesses are important parameters influencing the ultimate lasing characteristics, such as threshold, rate of increase of laser intensity, number of modes, and resonance positions. We analyzed the transverse electric-field (TE) profiles and polarized modes of suspended Ge-QDs/SiO 2 /Si 3 N 4 microdisks using the commercially available, two-dimensional simulation software, CMOSOL Multiphysics. Figure 10 shows the calculated TE distributions for microdisks with diameters of 3-7 μm and thickness of 200 nm. The circular distribution of TE spots suggests that the Ge-QD/Si 3 N 4 microdisks operate in the whispering-gallery mode (WGM) regime. It is clearly seen in Fig. 10a-d that larger disks increase the number of WGM cavity modes, TE m,n (the subscripts "m" and "n" are the azimuth and the radial number, respectively), along the disk edge. Also, photon leakage out of the disks is suppressed due to the strong optical confinement. Additionally, we see Fabry-Perot (FP) cavity modes in the center of large disks (Fig. 10d), resulting in a broad PL peak. On the other hand, smaller microdisks reduce the FP resonant-mode number due to their smaller sizes/mode volumes and considerable radiative loss via evanescent fields spreading to regions outside the smaller microdisks (Fig. 10a), degrading the Q factors. To improve light confinement within smaller microdisks, a geometric configuration of microdisk arrays has been proposed to facilitate near-field optical coupling and radiative transfer between neighboring microdisks [45,46].  10e-h shows that the TE spots for all 3 μm-diameter microdisks become sharper and more focused by decreasing the inter-disk spacing from 250 to 150 nm. Accordingly, we have developed the nanofabrication of 3 × 3 microdisk array to improve both light confinement and Q factors. Threshold powers of 35 W/cm 2 and ~ 100 W/cm 2 for optically pumped lasing are achievable within an array of 3 × 3 Si 3 N 4 -embedded Ge-QD microdisks as well as a single Si 3 N 4 -embedded Ge-QD microdisk, respectively. [47]

SiN-waveguided Ge-QD PIN photodiodes
The process flows and key processing modules for fabricating Ge-QDs/Si 3 N 4 /Si PIN photodiodes are described in Fig. 11. The fabrication processes for forming Ge-QD array are essentially the same as that for fabricating Ge-QD microdisks, as described in the previous section. Following the formation of Ge-QD arrays, lithographic definition is combined with ion implantation of BF 2 (2 × 10 15 cm −2 , SiGe-nanosheet arrays, d lithographic patterning followed by BF 2 ion implantation and e lithographic patterning followed by As ion implantation for forming P + -Si and N + -Si regions, respectively, and f contact/metallization for forming PIN contact electrodes Fig. 12 a I-V characteristics and b power-dependent photoresponsivity, and c frequency response of Ge PIN photodiodes measured in the dark and under 850 nm illumination 40 keV) and As (1 × 10 15 cm −2 , 40 keV) generating the p +and n + -regions required for PIN diode construction. Subsequently, rapid-thermal annealing (RTA) at 900 °C for 30 s activates the implanted dopants, forming the adjacent p + -Si and n + -Si regions that are self-aligned with the Ge-QD/ Si 3 N 4 /Si heterostructure. Figure 12 shows that our self-aligned Ge-QD PIN diodes exhibit extremely low dark current density (< 5 pA/μm 2 ) at operating voltages between 0 and 5 V and high photoresponsivity (ℜ = 20 mA/W at zero bias of V = 0 V). Our PIN diodes exhibit a wide-dynamic range for photocurrent linearity at incident optical powers (P IN ) ranging from 0.1 nW to 10 μW and 3 dB frequency (f 3dB ) of 10 GHz at E-field of 10 5 V/cm under 850 nm illumination.

Conclusion
An ingenious combination of lithography and self-assembled growth has allowed accurate control over the placement, shapes, and sizes of our "designer" Ge-QDs. This significant accomplishment has opened up the possibility of creating diverse photonic and sensing devices for practical applications.