Site-controlled and advanced epitaxial Ge/Si quantum dots: fabrication, properties, and applications

In this chapter, we will provide a short review of methods for obtaining ordered epitaxial QDs. In general two pre-growth fabrication steps are necessary for the fabrication of site-controlled epitaxial QDs: initial pattern formation on a mask material covering the substrate surface and subsequent pattern transfer into the substrate by various selective dry and wet etching techniques. On the ex situ cleaned, patterned substrate the epi-layers are deposited by molecular beam epitaxy (MBE) or chemical vapor deposition (CVD) techniques and QDs nucleate preferentially on well-defined locations of the patterned substrate.

Some methods based on site-selective growth e.g. growth in windows fabricated in an oxide layer on top of the substrate [60–64] are omitting one of the two steps for substrate patterning. Additionally, there exist several site-control techniques that are not based on substrate pre-structuring. One example where the ordering and QD formation is achieved only after growth involves hydrogen incorporation on masked regions of GaAs_1−xN_x layers [65]. There, the mask-controlled local hydrogen treatment transforms the GaAs_1−xN_x regions into GaAs QDs that can be utilized as efficient single photon sources [66]. Other examples of fabrication of QD-ordering without the use of substrate templates include (i) reverse epitaxy [67, 68] where ion irradiation of a crystalline surface under normal incidence and elevated temperatures leads to natural self-organization based on the interplay between surface roughening and surface-diffusion induced smoothening; (ii) ordering of QDs through vertical growth of multilayer structures [38, 69–76], (iii) strain engineering [77, 78] and (iv) by assembly of Ge micro-and nanocrystals and QDs on SiO₂ via stress-induced de-wetting [79, 80].

The most successful approaches in terms of uniformity and reproducibility make use of templated self-assembly, which means that the host substrate is modified before growth. During epitaxial growth, the QD nucleation happens on predefined places of the pattern resulting in an ordered array of QDs.

For the initial pattern formation in the mask material covering the substrate different lithographic methods have been employed, such as electron-beam lithography (EBL) [22, 81–84], holographic [39, 40, 85] and extreme ultraviolet interference lithography (EUVIL) [41, 54, 56], UV-nano-imprint-lithography (UV-NIL) [46, 86], focused ion beam lithography [55, 57, 87, 88] and lithography using polystyrene nanospheres [89]. Pattern formation can be achieved using atomic force microscopy (AFM) and local oxidation [90–93] and different mask materials such as e-beam- and photo-resists, but also by using porous alumina membranes to pattern the Si substrate before growing Ge dots [94]. Certainly, all these methods have their advantages and disadvantages. Lithography using EBL- and FIB-methods are flexible with respect to pattern parameters, but time-consuming due to serial writing. On the other extreme, holographic lithography, EUVIL, and UV-NIL are methods with higher sample throughput but considerably lower flexibility for pattern adaptation. Thus, for most basic research needs, EBL is a suitable tool for pattern formation as possible substrate damage, as in the case of FIB processing, is avoided. The following discussion will, therefore, concentrate on EBL patterning.

After the pattern was defined in the mask material it has to be transferred into the substrate by dry or wet etching techniques. The former have the advantage of highly anisotropic etching rates while for the latter plasma-etching-induced defects in the substrate can be excluded² and pits with clear defined side-facets can be obtained [49, 82, 95–97]. The influence of etching depth, pit-shape and–size on the QD growth will be discussed in section 2.2.

Before growth, the samples have to be cleaned ex situ. For the growth on Si substrates, this cleaning typically includes Caro's etch [98] (piranha etch) and RCA cleaning [99], to remove residual organic and metallic impurities at the sample surface. The native oxide is removed from the sample surface by hydrofluoric acid. Before growth, the samples are degassed in situ at about 750 °C to desorb hydrogen before the Si buffer layer growth. The degassing temperature <750 °C prevents silicon-carbide formation and changes of the pit-shape [82]. If the SiO₂ is not removed before growth, it induces a large atom mobility of the Si underneath, smearing out the Si pits during the degassing step [100].

The growth of epitaxial semiconductor QDs can be divided into the two main deposition techniques, CVD [101] and MBE [102, 103]. In CVD, gaseous sources like Germane and Silane are used, hence epitaxial growth involves decomposition of the molecules and desorption of hydrogen. MBE, on the other hand, is an ultra-high vacuum technique (base pressures ∼10⁻¹⁰–10⁻¹² mbar) in which the elements are deposited onto the substrate in the form of atomic and/or molecular beams. These beams usually originate from elementary pure sources that are thermally evaporated in effusion cells or by electron beam evaporators. Main advantages of MBE include the low growth rates, precise control over deposition thickness and composition, independent tunability of different growth rates and substrate temperature T_G and abrupt doping profiles.

MBE growth is evidently not a method used in mass production, but it is indispensable in basic research [104] as demonstrated by a number of Nobel prizes, closely linked to MBE-grown samples: 2007 for Albert Fert and Peter Grünberg for 'The Discovery of Giant Magnetoresistance'; 2000 for Zhores Alferov and Herbert Kroemer for 'developing semiconductor heterostructures used in high-speed- and optoelectronics' and 1998 for Robert B Laughlin, Horst L Störmer and Daniel C Tsui for 'their discovery of a new form of quantum fluid with fractionally charged excitations'.

While plenty of group-IV QD related samples were grown by CVD techniques [25, 30, 60–62, 69, 105–107] we will in the following focus on MBE-growth of ordered QDs.

In figure 2 we summarize the most crucial growth parameters for site-controlled Ge QD formation on pit-patterned Si(001) substrates. Those parameters are directly linked to the designed structural and optoelectronic QD properties. The nucleation position of the QDs can be shifted from in the pit center to positions at the pit rim via adjustment of the pit-depth, -diameter and -shape as well as the growth of the Si buffer layer. Furthermore, QD-distance, composition of the grown alloy, growth temperature (T_G), as well as deposition-rate and -volume need to be optimized. Additional preconditions include the substrate type and orientation [108], and elimination of contaminations or crystalline defects during template fabrication.

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Before the growth of the epitaxial Ge QD layer, a Si buffer layer has to be deposited [22, 83, 85, 109]. This layer serves the following two purposes. First, the QDs are not in direct contact with the initial substrate surface, and hence electronically and optically separated from possible residual impurities at the substrate/buffer layer interface. Second, the Si buffer layer growth already decorates the initially cylinder-shaped or pyramidal shaped pits with low-energy {11n}-facets [22], driven by capillary forces [110]. The pit depth decreases while the pit-diameter and -volume increases upon Si buffer layer deposition. A likely reason for the success of forming site-controlled Ge QDs on pit-patterned Si(001) substrates is that strained Ge develops the low-energy facet {105}, 11.3° inclined to the substrate surface. This angle is close to those of {117} to {1 1 10} facets formed during Si buffer layer growth in pits [22, 83, 85, 109].

In [22] it was found that for identical pits the inter-pit-distance d_pit has no significant influence on the pit-shape after Si buffer layer growth. In [22] we ascribed this finding to the lower surface mobility of Si as compared to Ge [111] caused by the larger Si–Si than Ge–Ge adatom binding energy. Notably, the independence of the Si buffer growth on d_pit is in distinct contrast to the strong dependence of the QD pattern on d_pit and the Ge deposition volume [22, 81, 112].

Since the contact angle of the pits after Si buffer layer and Ge WL growth critically influences the QD nucleation position, Ge growth as a function of the local substrate inclination was studied intensively [22, 57, 78, 84, 113–119]. Recently, we have demonstrated that the sidewall angle of the pit (α_pit) has to be less than 30° so that QD formation in the pit is energetically favorable [84]. For α_pit > 30°, substrate strain- and WL-relaxation favor QD formation at the pit-rim [84, 120, 121]. Such rim-bound QDs evolve through pre-pyramid-, pyramid-, and dome-stages [119] for which additional tweezers-like facets were found [120, 122].

Figures 3(a)–(c) depict AFM surface angle images and figures 3(d) and (e) the line scans through the pit-center pit in [109]-direction. All the facets of the wet-etched, differently sized pits were of {111}-type before growth. After Si buffer and Ge WL growth, we obtained pits with increasing sidewall inclination angles from 2° to 54.7°. In [22] we found that QD formation only occurs if α_pit is larger than 5°. For lower α_pit, it is energetically favorable to smooth very shallow pits. From previous work, it seems that the optimum angle α_pit for nucleation of upright QDs in the center of pits is between 5° and about 18°.

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For steeper pit angles but with α_pit < 30° the QDs flatten and exhibit asymmetric shape [22]. For increasing α_pit from 18° to 30 °C, the nucleation position of the QDs in the pit center becomes decreasingly favorable [84] and further increase of α_pit > 30° leads to QD formation around the pits (figures 3(b) and (c)).

Summarizing, perfect site-control of QDs in the pit-center requires: (i) α_pit after Ge WL deposition to be between 5° and 18° and (ii) the ratio between the QD base length and the pit opening size after Ge deposition should be about 1:2 which was verified for very small QDs of 3 nm height in about 35 nm wide pits [56] and for very large coherent QDs (∼300 nm base length) grown into pits with 500 nm diameter [123].

A particular case for QD nucleation is given, if the pit-angle is steeper than 30° and the pits are touching each other, i.e. there is no space for QDs to nucleate at the rim of the pits. This was shown in [82] for patterned areas with {111}-faceted pits, wet-etched into the substrate. In this case, Ge accumulation at the very bottom of the pits is forming inverted {111}-shaped pyramids. In contrast to the III–V material system, where similar 'inverted' QDs can be used as a source of single photons [49, 95], the optical properties of 'inverted Ge pyramids' were not superior to QDs grown on a flat substrate. Such {111}-pits can, however, be used for dislocation engineering during Si–Ge hetero-epitaxy as the 60° line dislocations can be efficiently confined to the pits [96, 97].

A critical and too often neglected role for uniform QD nucleation is played by the rate of Ge deposition. Local differences in the chemical potential lead to Ge adatom migration to the pits via surface diffusion. For a high Ge growth rate, the mobile Ge on the sample surface is quickly covered by the next impinging Ge atoms. For typical Ge growth rates (∼0.05 Å s⁻¹) it was found that Ge atoms diffuse tens of microns on the substrate and the WL surface before being captured by QDs [112, 124]. Those QDs as well as empty pits incorporate the mobile surface atoms with a capture rate that is related to the QD facet-types [112]. For QDs with fully developed faceting, such as pyramids, or, even more pronounced, domes the capture rates are much lower than for QDs with unfinished and thus not perfect crystal facets, such as pre-pyramids of transition-domes [112]. This directly hints to two points: First, there is a trend for QDs with unfinished facets to incorporate additional atoms that are used to form perfect crystal facets. Thus, this increased Ge incorporation lowers the surface energy of the system. Second, for QDs with already finished faceting, QD-stability against size-increase seems to exist.

In order to avoid satellite QDs growing between the pits, the growth rate has to be low enough to allow atom migration towards the pits and to prevent that the mobile atoms are buried by subsequently deposited atoms before reaching their energetic minimum position. When mobile atoms are trapped between the pits they contribute to WL thickening. If the WL between pits reaches a critical thickness of about 4.2 ML, satellite QDs nucleate between the pits [125]. In figure 4 this subtle balance between incorporation (red arrows) and deposition rate (green arrows) is depicted. If the incorporation rate is larger than the deposition rate, QDs nucleate only in the pits (figure 4(a)). For large pit-periods, i.e. low density of material sinks (figure 4(b)), the incorporation rate is lower than the deposition rate leading to an increase of the WL thickness and QD formation between pits. Consequently, if the number of material sinks approaches zero (i.e. very large pit-periods of several microns) even at very low growth rates QD formation between pits cannot be avoided if the amount of deposited Ge is larger than the critical WL thickness for QD formation (4.2 ML for T_Ge = 700 °C, [125]).

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In [112, 124] the effect of long diffusion lengths for Ge ad-atoms on a Ge WL was exploited to map out the evolution of strictly ordered Ge QDs from pre-pyramids via pyramids and transition domes into domes by AFM and PL-spectroscopy. The dependence of the QD volume on the distance between the interface of the planar/patterned substrate is depicted in figure 5(a), and AFM micrographs of the respective QD shapes are shown in figures 5(b)–(g). Based on a one-dimensional diffusion model, a quantitative determination of the Ge surface diffusion constant and the rates at which Ge atoms are incorporated into the growing QDs was obtained, see figure 5(a) and [112].

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To quantitatively address the amount of Ge transferred at the border between planar and patterned area, we focus on the PL-signal from QDs, WL, and pit-WL. In figure 5(h) a 2D-representation of the change of the WL- and QD-related PL is shown as a function of the distance x between the planar and the patterned part of the substrate. The spectra were recorded starting from the planar part, approximately 70 μm outside the field and ending directly in the center of the patterned field at x = 100 μm [124]. The planar WL-PL undergoes a pronounced blue shift towards the border of the patterned field which is explained by increasing quantum confinement energy of the thinner WL near the border. The WL emission energy for x = −70 μm is at 1028.8 meV, which corresponds to a WL thickness of 3 ML [124], whereas the WL-emission energy at the border (at x = 0 μm) is 1056.6 meV, corresponding to a WL thickness of 2.57 ML [124]. Thus, the change in quantum confinement corresponds to a material transfer of about half a monolayer of Ge from the planar to the patterned part of the substrate over a distance of several tens of micrometers.

Upon increasing Ge deposition, steeper and larger QDs are formed on both, pit-patterned and planar substrates. Those larger QDs exhibit shapes of partially plastically relaxed superdomes or mainly elastically relaxed barns. On pit-patterned substrates, the latter evolve through cyclic growth mediated by collective shape oscillations between barn-shaped and dome-shaped QDs [123]. For optical applications such large QDs are not ideal since carrier quantum confinement and electron- and hole wavefunction overlap is diminished by the extended QD dimension. Additionally, dislocations in ordered QDs [126] lead to strong quenching of the QD related PL [81], similar to the case of randomly nucleated QDs [107]. Consequently, we will focus on the optical properties of smaller site-controlled QDs, pyramids and domes.

The main advantages of site-controlled QDs over randomly nucleated ones are their inherent addressability and enhanced size- and composition uniformity. In this section, we will discuss how these features influence the QD-PL as well as parameters that are detrimental for the PL from ordered SiGe QDs.

This will guide us to the exciting perspectives of combining GIB-QDs and site-control by templated self-assembly. In [40, 127] it was shown that for randomly nucleated SiGe/Si(001) QDs (figure 6(b)), a significantly stronger blue-shift of the QD-related PL emission peaks is observed as a function of the excitation intensity (P_exc) when compared to site-controlled QDs (figure 6(a)). These PL shifts are plotted in figure 6(c). The PL emission shifts by more than 90 meV when increasing P_exc from ∼30 mW cm⁻² to 245 W cm⁻² in the case of the QDs on the planar substrate (figure 6(c)), whereas it virtually does not shift with P_exc for ordered QDs. In the samples investigated, we observe for domes on a planar sample (94% of all QDs, height: 20.1 ± 0.1 nm) a similar size distribution as the ones on a patterned sample. Thus, it can be safely expected that domes contribute most to the QD PL spectra. In the light of a similar QD size distribution of QDs grown on patterned and planar substrates, this different PL behavior was attributed to the much larger inhomogeneity of the Ge distribution in QDs on planar substrates [40]. Three-dimensional band-structure calculations revealed that Ge-rich inclusions of approximately 5 nm diameter at the apex of the QDs can account for the observed differences in the PL spectra. The existence of such inclusions can be regarded as a truly zero-dimensional QD within the host dot [40]. This finding is in agreement with recent nano-tomography experiments [43].

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Figures 7(a)–(d) presents perfectly site-controlled QDs for d_pit varying from 425 nm (figure 7(a)) to 3.4 μm (figure 7(d)). These fields were located on one and the same sample, grown in the same MBE-growth run: 3 ML of Ge were grown at T_Ge = 700 °C and at a growth rate of 0.03 Å s⁻¹. Figure 7(e) presents PL-spectra containing emission contributions from QDs, the WL between QDs and Si bulk. With increasing sample temperature during PL investigations, thermal quenching of the WL-related PL signal is concomitant with a transition of carriers into the QDs. A schematic illustration of the related carrier diffusion paths is shown in the upper inset of figure 7(e). This carrier transfer is associated with an activation barrier E_A2 of about 25 meV induced by a thinner WL around the pits in the vicinity of the QDs. Since almost all generated holes diffuse into the WL quantum well, they become trapped because the activation barrier prevents diffusion into the QDs. Thus, for very low temperatures efficient PL emission from the QDs is unlikely and PL spectroscopy on single epitaxial Ge QDs on Si substrates should be conducted at elevated temperatures. Figure 7(e) depicts spectra recorded at a sample temperature of 40 K. In contrast to the 10K-PL spectra (see [128]), where QD signals are barely detectable, some of the holes trapped in the WL can now overcome E_A2 and diffuse into the QD. Simultaneously, the integrated PL signal decreases because of the low exciton binding energy E_A1 and phonon-induced thermal PL-quenching. Overall, the relative contribution of carrier recombination in the QDs increases [128].

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In order to minimize line broadening of the QD related PL peaks, the PL spectra of individual QDs at extremely low excitation powers between 0.1 μW < P_exc < 1.4 μW were investigated. When decreasing P_exc from about 30 to 0.1 μW we observed that the line-width of the QD-related NP-peak at 920 meV decreases to a full-width-at-half-maximum of about 16 meV, following the empirical power law ${\rm{FWHM}}\,={A}\cdot {{{P}}_{{\rm{exc}}}}^{{m}}$ with A = 0.02006 and m = 0.11025.

These widths are significantly sharper than PL-lines from any SiGe QD ensembles published till then [54, 129]. This spectral linewidth is comparable to the ones of individual Si nanocrystals at 70 K for particles with functionalized ligands [130]. However, they are still broader than the ones observed from top-down fabricated Si QDs [131–133] and Si nanocrystals encapsulated in an oxide matrix (∼200 μeV) [130], and substantially broader than those of QDs made from CdSe (∼1.6 μeV) [134], CuCl (∼1 μeV) [135], InGaAs (∼2 μeV) [136] and ordered InAs QDs (∼500 μeV) [47], even though we employed comparable excitation power densities in [128] as in the last case.

In [128], several mechanisms were discussed that contribute to the relatively broad Ge QD-PL signals even at low P_exc. The indirect bandgap and the type-II band alignment in SiGe QDs lead to carrier lifetimes in the μs range [137, 138] that are substantially longer than, e.g., in type-I InAs QDs. Thus, even at our lowest P_exc, which is within the limits of experimental feasibility, filling effects are expected to be important [128]. Such a state filling becomes in particular important for site-controlled Ge QDs, because their rather homogeneous composition [43] causes spreading of the hole-wave-functions over most of the QD [40].

In addition, the strain distribution leads to a splitting of the six-fold degenerate conduction band (CB) of the Si matrix near the apex and the four base corners of pyramids, where the electrons are located [40, 45] adding to the complex and dense system of energy levels [139]. Another major contribution to line broadening in long-time averaged spectra comes from spectral diffusion which is caused by charge fluctuations in the vicinity of the QDs [140, 141]. Such fluctuations can, for instance, be associated with growth defects, e.g. in the low-temperature Si cap layer. Moreover, thermally induced charge fluctuations of the weakly bound electrons of our type-II excitons (inset in figure 7(e)) would lead to differently charged excitonic complexes [142]. Their energy shifts with respect to the neutral exciton level were predicted to be enhanced in type-II heterostructures [143]. Since the SiGe/Si heterosystem is indirect both in real and k-space, phonon broadening at T_PL is another expected contribution to the observed line width. In [130] it was demonstrated that the mechanical coupling of a nanocrystal to its matrix largely influences the luminescence linewidth due to exciton–phonon interaction.

Thus, two strategies appear feasible to further reduce the linewidths of SiGe QDs for CMOS-based single photon emission applications. Firstly, lower growth temperature, T_G could suppress interdiffusion and should thus allow smaller QDs with well-separated hole-confinement levels. It would also sharpen the interface between Ge QD and Si matrix and might, therefore, reduce exciton–phonon interaction. Secondly, locating a single QD in a photonic crystal cavity [144] will lead to reduced radiative lifetimes due to the Purcell effect, which would also reduce level filling effects. Under these conditions, time-resolved experiments should allow us to separate the aforementioned transition mechanism and to gain access to the intrinsic linewidths of individual transitions.

Both of the aforementioned strategies will also need to be applied to the recently developed GIB-QDs that will be discussed in the following. In these QDs defect-based electron states that are similar to color centers in diamond, contribute to the greatly enhanced PL intensities even at room temperature, and might, therefore, be well suited for Si-based single photon sources.

In the following, we will describe the fabrication procedure of ion bombarded Ge QDs, focusing on Ge ion implantation and emphasizing the crucial parameters that have to be taken into account to optimize the yield of radiative recombination.

We deposit crystalline Ge and SiGe QDs on Si (or silicon-on-insulator, SOI) substrates using a solid source SIVA45 MBE system from Riber. We want to stress, however, that even though in [6, 37, 38] the samples were grown by MBE in combination with in situ low energy GIB, all fabrication steps can in principle be performed with fabrication methods that are compatible with Si integration technology. In a large part of the literature about Ge-on-Si QDs (see e.g. [25, 30, 60–62, 69, 105–107]), the samples were grown by CVD and also ion-implantation and annealing are standard procedures in Si technology.

The QDs evolve in the strain-driven Stranski–Krastanow growth mode [13] on a Ge WL, once an overcritical thickness of Ge (∼4 monolayers, ML) is exceeded [16, 125]. Strain-driven plastic relaxation of the QDs does not occur for the amount of deposited Ge generally used in this work, which is typically ∼6 ML. This is important since the introduction of, e.g. 60° line dislocations in the Ge QDs due to elastic relaxation [126, 147] would quench the QD PL almost completely [81, 107]. Due to the relatively low Ge T_G of 500 °C used in [6, 37, 38], the height of the Ge-rich and hut-shaped QDs is only about 2–3 nm, and the QD-density can be conveniently tuned by varying the Ge coverage [6]. GIB-QDs and DEQDs differ from conventional, epitaxial Ge-on-Si QDs by ion bombardment. For this purpose, positively charged ions are accelerated towards the sample. For GIB-QDs, low-energy Ge-ions (≤3 keV) are employed. A Ge ion undergoes collisions with Ge atoms in the QD causing a displacement cascade since the ion is rather heavy and its energy (≤3 keV) much larger than the about 14 eV displacement energy of crystalline Ge. The displaced Ge atoms in the QD, called recoil atoms, still have enough energy to displace further atoms, leading to a collision cascade of ellipsoidal shape. Importantly, the cascade of a single Ge-ion (≤3 keV) produces a single, few nm wide amorphous zone. According to TRIM simulations [148], the energy that is dissipated by the Ge ion itself through ionization, vacancy formation and the creation of phonons ranges from 14.5% to 11.5% for an acceleration voltage V_GIB between 0.3 and 3 kV. The rest of the energy dissipates through the recoil atoms. Thereby, phonon formation and atom ionization in the QD due to the recoil atoms account for the main energy loss mechanisms during the GIB-process with approximately 60% and 20%, respectively [148].

The values of V_GIB and the ion dose have to be chosen carefully with respect to the QD height since V_GIB directly determines the penetration depth and the amount of amorphization in the sample. For ion energies smaller than 3 keV the ion becomes stopped within the height of the QD. For the thermal stability of the GIB-QDs, it is essential that GIB leads to a situation where one extra Ge atom (N + 1 atoms) is present in the volume of a QD for which N atoms would make a perfect crystal. Therefore, if V_GIB is chosen too high, the ion penetrates the QD and stops only in the Si substrate where it does not contribute to the PL enhancement associated with the GIB-process [37].

Already during Ge-deposition and ramp-down to T_G of the Si capping layer, partial recrystallization of the amorphized zone takes place via solid-phase epitaxial regrowth (SPER) [149, 150], in which amorphized Ge is recrystallized if the sample temperature is above about half of the melting temperature of the crystal [149, 151]. The driving force for the recrystallization process is the lower energy configuration of crystalline as compared to amorphous material, mainly due to the lack of dangling bonds (DBs) and bond-angle-distortions [149–151]. The surface diffusion-driven recrystallization starts from the surface of the crystalline parts of the QD that were not amorphized during GIB. This immediately explains the importance of choosing a not too high ion dose, i.e. not to amorphise the QD completely. For the GIB-QD fabrication presented in [6, 37], we used a dose of about 10⁴ ions per μm², i.e. only one to two ions hit a QD leaving enough crystalline regions from which recrystallization can commence. Full recrystallization of the partly amorphized QD is, however, inhibited by the aforementioned presence of one or two extra Ge atoms in the otherwise perfect crystal lattice. If enough thermal budget is available, e.g. through post-growth annealing or a high-enough T_G of the Si capping layer, a minimum energy configuration for the bond arrangement of a QD supersaturated with an extra atom can be obtained. In [37] we found by Monte Carlo and density functional theory calculations used to crystallize amorphous Ge, containing one excess in a perfect crystal of the same volume that the system reaches an energetic minimum configuration of a split-[110] self-interstitial with concomitant displacement of the surrounding ∼40 Ge atoms, depicted in figure 8(b). The core atoms of the split-[110] interstitial are shown in black while the surrounding displaced Ge atoms appear gray. In [−110]-direction, an undisturbed Ge crystal lattice would be seen as hexagonal lattice where atoms, located in different lattice planes in [−110]-direction would not be visible.

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After SPER, on top of the recrystallized Ge QD surface, a crystalline Si capping layer can be grown. Avoiding non-radiative recombination centers in the Si matrix is essential with respect to the optical or optoelectronic properties and the application-potential of the QDs. In [37] we found, that there exists an optimum T_G-window around 475 °C, for which the PL yield of GIB-QDs at room temperature is maximized. If the capping layer growth temperature (T_CAP) is too low (<400 °C), the recrystallization process of the GIB-QD surface via SPER is disturbed, leading to imperfect overgrowth and the formation of non-radiative recombination centers in the Si capping layer. On the other hand, if T_CAP is too high (>600 °C) the defect structure can migrate out of the QD by overcoming an activation energy of about 3.2 eV [37].

In [37] we have demonstrated that post-growth thermal annealing at a temperature between 500 °C and 600 °C improves the RT PL properties of GIB-QD. In this case, the minimum energy configuration of a point defect with a surrounding distorted lattice can be reached, and unwanted non-radiative recombination centers that might be introduced in the Si substrate during the GIB process can be healed out. Annealing at higher temperatures (>600 °C) leads to quenching of the GIB-QD PL at RT, caused again by migration of the defect out of the QD [37]. This activation energy for migration of the defect was found to be ∼3.2 eV, which is in agreement with the activation energy for diffusion found for extended defects in Ge in [152].

Post-growth hydrogen passivation can further enhance the RT PL properties of GIB-QDs [37]. Weber et al have shown [153–156] that DBs in Ge exhibit different electronic properties as compared to DBs in Si. In Ge, the DBs create states below the VB edge that are negatively charged. Thus, interstitial hydrogen cannot efficiently passivate DB defects and electrons will not be localized at DB sites [153–156]. Therefore, optically active GIB-defects are not negatively affected by hydrogen passivation. In contrast, if the H-passivation properties are chosen correctly [37, 157], the PL yield of GIB-QDs can be increased upon H-implantation since residual crystalline defects induced by GIB in the Si substrate can be cured by H passivation. This reduces the number of non-radiative recombination channels in the GIB-QD-Si matrix system and therefore increases the PL yield from GIB-QDs.

Figure 8(a) schematically depicts a GIB-QD (gray), embedded in a crystalline Si matrix (tan color) containing a split-[110] self-interstitial (red color) with surrounding lattice deformation (dark gray color). At this interstitial site, the electrons are highly localized (see color map in figure 8(b)), creating states well below the CB edge of crystalline Ge [37]. Due to the strong spatial confinement, the electrons exhibit wave-function contributions at the Γ-point, as displayed by red color in the electronic orbital iso-surface cross-sections presented in figure 8(b). Figure 8(c) presents a band alignment scheme that describes possible optical recombination paths in GIB-QDs. Upon optical excitation, electrons diffuse to local energy minima in the CB, introduced by the strain fields around the QDs (open red circles in figure 8(c)). From there they can tunnel through a barrier caused by ∼1 nm of recrystallized Ge to the localized states below the CB gap introduced by the GIB-process (red arrow in figure 8(c)). Hence, electrons can directly recombine with holes confined in still crystalline regions of the QD.

Excitation of an ensemble of GIB-QDs with different sizes, the filling of the different defect induced levels and the filling of the first excited hole states at higher excitation power lead to the observed broad range of transition wavelengths in the GIB-QD PL, ranging from 1250 to ∼1650 nm [6, 38]. The energy level scheme [37] presented in figure 8(c) is consistent with the observed emission wavelength of GIB-QDs. It becomes clear that the high activation energies for thermal quenching of the GIB-QD PL of about 350 meV are consistent with the escape of holes from the confining QD potential. Importantly, this high activation energy prevents quenching of the GIB-QD related PL intensity in a temperature window from 10 K to above RT. In [6], we observed that with increasing P_exc, the integrated PL intensity (I_PL) of the GIB-QDs increases with a power coefficient of m = 1 according to ${{I}}_{{\rm{PL}}}({{P}}_{{\rm{exc}}})\sim {{{P}}_{{\rm{exc}}}}^{{m}}.$ This, in combination with the short observed carrier lifetimes of about 1 ns, and the efficient PL from GIB-QDs at RT and above are indications for optically direct electron–hole recombination in real and reciprocal space caused by the presence of the GIB-induced defect site in this epitaxial system [6, 37].

Finally, we want to stress that having both, the GIB-induced defect and a QD are necessary pre-requisites for obtaining high PL yields at RT and above. In contrast to PL emission from GIB-QDs, the PL signal from quantum wells (QW) that underwent the same GIB-treatment as the QDs is almost completely suppressed at RT, as can be seen in figure 9.

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While the holes are efficiently trapped in the GIB-QDs, in the GIB-QW samples and also in Ge bulk samples that underwent GIB-treatment, the holes can diffuse away from the extended split-[110] self-interstitial into regions without crystal distortions between two such defects. This is schematically depicted in figure 9 by the blue arrows and the letter 'H' in the inset. The resulting charge carrier separation reduces the overlap of the electron and hole wave function and thus the transition matrix element for optical transitions. Therefore, QDs are a necessary precondition for direct optical transitions in Si/Ge heterostructures treated by GIB [6, 37] or implantation of other isolated ions (DEQDs). In contrast, enhanced PL yields can neither be observed in GIB treated quantum well structures (figure 9), nor in bulk Ge, where the split-[110]-self-interstitial is known for almost twenty years [158–161].

In [6] we have grown a single layer of GIB-QDs on a SOI substrate and fabricated a microdisk resonator with a diameter of about 1.8 μm (scheme in the inset of figure 10). The emission wavelength (λ_PL) of the GIB-QDs is in the near infrared telecommunication O-band around 1330 nm. Upon increased optical excitation, the PL response at 10 K from the GIB-QDs in the microdisk increases super-linearly, showing a clear threshold behavior, as well as linewidth narrowing of the emission modes above a threshold. These are two clear indicators for lasing from such structures. On a double logarithmic plot of the Integrated PL intensity (I_PL) versus the optical excitation power P_exc the curve shows a characteristic S-shaped behavior, typical for light amplification by stimulated emission of radiation [6].

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At RT, this S-shape of I_PL over P_exc is still present, however, less pronounced, as can be seen in figure 10. At the threshold, I_PL increases super-linearly with P_exc and eventually saturates at high P_exc > 1 mW to a value of m = 1 $({{I}}_{{\rm{PL}}}({{P}}_{{\rm{exc}}})\,\sim \,{{{P}}_{{\rm{exc}}}}^{{m}})$ The gray curve in figure 10 depicts a PL emission spectrum from a microdisk recorded at T_PL = 300 K. The pronounced maximum of the PL at about 1330 nm is the emission from the whispering gallery cavity mode TE(12, 1), running around the circumference of the microdisk.

This finding implies that strong RT light emission and even lasing is feasible using GIB-QDs as gain material. Moreover, this monolithic solution might be the long-awaited missing piece of Si photonics marking a major step towards optoelectronics integration on Si for high-performance optical communication and computing applications.

At this point, we want to stress that until now, microdisk resonators containing only single layers of GIB-QDs were fabricated. One straightforward way to further increase the PL yield of GIB-QDs and epitaxial QDs, in general, is by increasing their sheet density through vertical stacking. In such a way, the density of emission centers increases linearly with the number of layers. Over the last decades of QD-related research, a lot of research effort has been devoted to the growth of multilayer structures that are separated by a matrix material that typically has a similar composition as the host substrate [38, 69–76]. Concerning GIB-QDs as compared to fully crystalline QDs, the growth of stacked layers turns out to be more difficult, simply due to the intentionally induced amorphous zone in the GIB-QDs that has to be overgrown consistently by crystalline Si for every QD layer. In [38] we have shown that if only a single GIB-QD cannot be overgrown in a crystalline way, this will lead to a full breakdown of the growth in the following layers above the GIB-QD, as can be seen in figure 11(b). This can be avoided if the growth temperature of the Si spacer layer is chosen to be about 500 °C, the optimum temperature for the overgrowth of GIB-QDs [37]. Figure 11(a) shows a high-angle annular dark field transmission electron microscopy image of an eleven-fold stack of GIB-QDs. For this successful stacking of GIB-QDs, the PL yield was found to increase by a factor of 7 (blue spectrum in figure 11(c)) as compared to the single layer samples (gray spectrum in figure 11(c)) for which lasing was demonstrated [6]. For the sample containing the large defect induced by non-successful solid phase epitaxial regrowth during the growth of the Si spacer layer, no PL was observed at RT, as can be seen in figure 11(c) by the red spectrum [38].

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Thus, PL enhancement from GIB-QD multilayers can be achieved, if the growth conditions of the Si spacer layer are chosen appropriately. For the formation of lasing devices using GIB-QD multilayers as gain material, the main challenge will be to achieve photonic structures with smooth sidewalls after the etching process as enhanced sidewall roughness caused by different etching rates of Si and Ge will lead to a decrease in the quality factors of the devices.

Up to now, only GIB-QDs and DEQDs in the form of randomly nucleated QDs have been investigated. The two main applications will employ GIB-QDs (i) as gain material for CMOS-compatible group-IV nanostructure lasers in optical interconnects and (ii) for quantum cryptography using single photon emitters based on Si technology. For both goals, two main conditions will have to be fulfilled. (i) For any kind of large scale integration, addressability of the QDs is a must, and (ii) the QDs will have to be embedded into optical resonators if possible located at positions where the cavity modes exhibit maxima. Both conditions can be fulfilled by the growth of QDs at predefined positions, e.g. by the growth of ordered QDs via templated self-assembly. The dominant material classes [162] for state-of-the-art solid-state single photon sources are (i) defects in bulk 3D crystals, such as nitrogen-vacancy [163] and Ge vacancy centers [164] in diamond, silicon carbide [165, 166], yttrium aluminum garnet [167] and zinc oxide [168]; (ii) self-assembled III-V QDs, such as InAs QDs grown on GaAs [11]; (iii) emitters from defects in two-dimensional hosts such as WSe₂ and MoSe₂ [169]; and (iv) localized oxygen-related defects in single-walled carbon nanotubes [170]. By using GIB-QDs and DEQDs we aim at merging topic (i) and (ii) by using defects within group-IV QDs.

For III–V QDs, single, self-assembled and randomly nucleated QD are chosen as single photon emitters. Strategies for the fabrication of large numbers of identical QD-cavity emitter units which are necessary to implement mass-produced integrated cryptography are missing thus far. This is a major advantage of the Si–Ge QD system (see chapter 2) over III–V QDs, for which spatial matching between cavity and QD can only be achieved with extremely low yield or under degraded QD performance. The possibility of CMOS-compatible parallel processing of cavity-enhanced single-QD emitters might ultimately tip the scale in the transition from purely academic single photon sources to mass-produced, integrated optoelectronic systems.

Figure 12(a) depicts a perspective view of an AFM image of ordered QDs (red color) grown on a substrate with regular arrays of pits (black color) with different pitch, ranging from 325 nm to 3.4 μm. In the Ge/Si system, growth of ordered and uniform QDs with different pit-spacing is possible even on one-and-the-same sample if the growth and substrate patterning parameters are carefully adjusted (chapter 2). Choosing a QD system with high inter-QD spacing provides access to a single QD as a possible emitter of single photons, as schematically indicated in figure 12(a), and to address several emitters in a controllable fashion. Furthermore, in combination with photonic resonators, the QDs can be intentionally placed into the maxima of the cavity modes, as shown in figure 12(b) and reported in [144, 171].

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As mentioned before, in [6, 37, 38] we investigated the optical properties with GIB-QDs of the shape of {105}-faceted hut-clusters. These Ge hut clusters were grown at a rather low Ge T_G of 500 °C. The growth of ordered QDs on patterned substrates is, however, easier to achieve at higher T_G as Ge ad-atoms can migrate more efficiently to the pre-determined material sinks on the substrate.

The growth of site-controlled QDs at rather low T_G of 500 °C–550 °C was reported, however only for QD arrays with very small QD pitch of 35–150 nm [55–57, 172]. For the growth of ordered QDs with large inter-QD spacing which is needed for single photon emission applications, higher T_G of about 600 °C–700 °C have to be employed [22, 112].

Thus, we investigated the influence of the Ge T_G on the optical properties of GIB-QDs at RT. In epitaxial QD systems the form, i.e. the faceting and the size, as well as the chemical composition and, importantly, the composition distribution within a single QD strongly depend on T_G.

For rather low T_G < 400 °C, the surface diffusivity of the adatoms is low, which leads to the incorporation of Ge atoms before they can form three-dimensional (3D) clusters. The elastic energy stored in the two-dimensional film is mainly relaxed by the formation of misfit dislocations [173]. For higher T_G between 400 °C and 550 °C, rectangular {105}-faceted QDs develop, which are called hut clusters [19], figures 13(b), (c). Their elongated rectangular base is caused by kinetic barriers at the QD edges [146]. Those hut clusters induce strong hole-confinement, as their size is only a few nanometers in height and a few tens of nm in base width [6]. For higher T_G in the range of 600 °C–720 °C, the QDs evolve into square-based, {105}-faceted pyramids (P) [19] (figure 13(d)) and into multi-faceted domes (D) [105, 106], (figures 13(e)–(g)). The steepest side facets of the domes are inclined at an angle of 33.6° with respect to the (001) substrate surface, while the inclination angle for the {105} pyramid facets is only 11.3°. The pyramids and domes show a bimodal [105, 125], or a uniform, mono-modal [40, 125, 174] QD size distribution, depending on the Ge coverage and growth conditions. At high coverage, plastic relaxation sets in and dislocated QDs, so-called superdomes [106], form. These usually have similar side facets and aspect ratios as the coherent domes but have a significantly larger size. For even higher T_G of 720 °C–800 °C, barn-shaped QDs [175] develop along with domes and pyramids. Barns exhibit all facets of the domes, as well as additional steeper ones like the {111} facets, which are inclined by 54.7° toward (001). For T_G ∼ 900 °C, cupolas form [176] which exhibit very steep side facets, inclined by 68° to the (001) substrate.

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However, for the growth of GIB-QDs and, in particular, site-controlled GIB-QDs only hut-cluster-, pyramid- and dome-shaped QDs are of interest. The other QD architectures mentioned are simply too large, and in most cases too diluted with Si to provide efficient quantum confinement. Figure 13(a) shows PL spectra from such smaller QDs, indicating that GIB-QDs can be grown in the form of pyramids and domes as well. The inset in figure 13(a) shows that there exists an optimum T_G of ∼500 °C for which the GIB-QD related PL is maximized. However, for domes grown at 650 °C, the integrated PL intensity only drops by a factor of 2 and those domes can be conveniently grown on pit-patterned substrates [112]. This provides the potential upon introduction of a single defect, that such an isolated, site-controlled QD can be the fundament for future CMOS-compatible single photon sources or lasing applications in on-chip interconnects.

4.1.1. Optical gain increase from GIB-QD and DEQDs

4.1.2. Electrically driven GIB-QD and DEQD-lasers

4.1.3. Site-controlled GIBs and DEQDs in photonic cavities

4.1.4. Merging plasmonics and DEQDs

4.1.5. Additional strain engineering

In [6, 37, 38], we have focused on light emission enhancement of Ge QDs upon ion implantation of Ge atoms only. Based on theoretical evaluation we concluded that the implanted, additional atom leads to the formation of a split-[110] self-interstitial surrounding by a deformed crystal lattice. At the former, electrons are confined and efficiently recombine with holes confined in the QDs. That said, it is not clear that different implantation and annealing conditions, and the use of different ion species would not lead to different optically active defect. At this point, there is no reason to conclude that the aforementioned split-[110] self-interstitial configuration leads to optimum PL yield. Thus, it is very clear that ongoing studies will have to shed light on this new field of research. While there were plenty of studies conducted on defects in Si and Ge [155, 156, 192–210], most of them deal with defects in bulk materials. We have shown in section 3.2 and figure 9 that only in QDs both, electrons and holes are efficiently confined. The knowledge gained for the bulk material will, however, be highly beneficial when studying different defects in zero-dimensional QDs obtained by implantation of various atom species, such as Si, Sn, B, As, P, B, etc.

Such a radiation environment produces displacement damage in QDs where first the incident particles displace atoms, and the resulting defects give rise to new energy levels which, in turn, alter the material and electrical and optical device properties [155, 156, 192, 193]. Some of the known defects in bulk Si and Ge include E-centers which consist of a vacancy and group-V atom and also provide deep donor levels below the CB edge [194–197]. X and W centers are small clusters of Si interstitials containing tri- and tetra-interstitial defects (also known as I₃ and I₄ defects) [198–201]. Those interstitials are known to play a role during the initial stages of interstitial evolution of samples that were ion-implanted and annealed. Other defects include vacancies [202] and di-vacancies [203, 204], both in pure Si and Ge as well as in SiGe alloys [198, 205]. Additionally, knowledge gained on the thermal stability of defects in bulk semiconductors such as point-defect self-diffusion [152, 206–210] will need to be translated to nanostructure systems such as DEQDs.