Si/SiGe heterointerfaces in one-, two-, and three-dimensional nanostructures: their impact on SiGe light emission

Fast optical interconnects together with an associated light emitter that are both compatible with conventional Si-based complementary metal-oxide-semiconductor (CMOS) integrated circuit technology is an unavoidable requirement for the next-generation microprocessors and computers. Self-assembled Si/Si − x Ge x nanostructures (NSs), which can emit light at wavelengths within the important optical communication wavelength range of m, technology.

iNTRODUCTiON he group IV semiconductors silicon and germanium continue to be important materials for optoelectronic and electronic applications (Mangolini, 2013;Ray et al., 2013;Pavesi and Lockwood, 2016). Silicon, which has an indirect band gap of 1.1 eV, is used extensively in the microelectronics industry partly because of the stability of its oxide and this has allowed the development of reliable devices with nanoscale dimensions (Zwanenburg et al., 2013) even though the precise nature of the silicon-silicon oxide interface, even ater decades of research, is still not completely understood (Omura et al., 2013). Germanium has a room temperature direct bandgap of 0.8 eV (~1.55 μm), and it is separated by only 0.14 eV from the indirect band gap of 0.66 eV. hese properties make Ge one of the most promising materials for complementary metal-oxide-semiconductor (CMOS) compatible photonic components, including near-infra-red photodetectors (Ahn et al., 2007;Yin et al., 2007;Assefa et al., 2010;Michel et al., 2010) and, possibly, lasers (Liu et al., 2009Camacho-Aguilera et al., 2012;Grydlik et al., 2016) in the desired wavelength region of 1.3-1.6 μm. However, it is well known that conventional Ge hetero-epitaxy on Si is complicated by the 4.2% diference in Ge and Si lattice constants (Paul, 2004;Shiraki and Sakai, 2005). Various techniques for building quality Si/Ge planar heterojunctions (HJs) include multi-step annealing to relax Ge layers and reduce the density of strain-induced dislocations (Saraswat et al., 2006;Ye and Yu, 2014), growth of ultra-thin Ge ilms and superlattices using Si1−xGex alloy transition layers with graded Ge composition x (Iyer et al., 1989;Nayak et al., 1996;Paul, 2004;Saraswat et al., 2006;Shah et al., 2010) and, alternatively, employ three-dimensional (3D) growth in the form of SiGe clusters and cluster multilayers using the Stranski-Krastanov (S-K) growth mode (Mo et al., 1990;Schmidt et al., 1999a;Shin et al., 2000;Baribeau et al., 2006). Another promising approach is to use one-dimensional (1D) growth in the form of nanowires (NWs) produced by the vapor-liquid-solid (VLS) growth mode or similar techniques (Wagner, 1970;Kamins et al., 2004;Hannon et al., 2006;Zakharov et al., 2006). With regard to interfacial properties, it should be noted that axial Si/Ge NW HJs, where the heterointerface is perpendicular to the NW axis, have a reduced heterointerface area compared to radial or "core-shell" NW HJs, where the Si/Ge heterointerface is parallel to the NW axis (Lauhon et al., 2002;Xiang et al., 2006;Zakharov et al., 2006). In such applications, one of the deining parameters afecting the application of a Si or Ge nanostructure (NS) is, thus, its interfacial structure with its surroundings. he introduction of an interface modiies bulk material parameters (Barbagiovanni et al., 2012(Barbagiovanni et al., , 2014 and introduces new phenomena. Dangling bonds, stress, and defect states elicit the degree to which the interface potential conines charge carriers (Barbagiovanni et al., 2014). Any termination with atomic impurities, such as hydrogen or oxygen, at the interface inluences the oscillator strength (Guerra and Ossicini, 2010) and creates polarization efects at the interface (Guerra et al., 2011). Sub-oxide interface states give rise to defectinduced carrier recombination efects that can dominate quantum coninement (QC) efects (Barbagiovanni et al., 2014(Barbagiovanni et al., , 2015. However, with careful control over the fabrication conditions (Lockwood et al., 2013a) and with appropriate interface characterization (Cosentino et al., 2014), Ge NSs can be produced that clearly exhibit QC efects (Barbagiovanni et al., 2015).
he development of a Si-based light emitter compatible with CMOS integrated circuit technology and the desired fast optical interconnects is essential for the upcoming generation of high-speed microprocessors and computers. Self-assembled Si/ Si1−xGex NSs that can emit light in the optical communication wavelength range of 1.3-1.55 μm are presently well suited for use in CMOS foundries. However, the long carrier radiative lifetimes observed in such Si/Si1−xGex NSs hinder the development of eicient light-emitting devices and, thereby, the construction of lasers (Sturm et al., 1991;Zheng et al., 1994;Lu et al., 1995;Lockwood, 1998;Pavesi et al., 2000;Tsybeskov and Lockwood, 2009). he usual model for radiative recombination in Si/Si1−xGex NSs is based on a type II heterointerface energy band alignment (see Figure 1) (Kamenev et al., 2006;Mala et al., 2013). In type II band alignment, the electrons and holes are spatially separated, with in this case the electrons localized in Si and the holes located in the SiGe NS, which explains the experimentally observed long lifetime of the photoluminescence (PL) in Si/SiGe NSs (Kamenev et al., 2005(Kamenev et al., , 2006Tsybeskov and Lockwood, 2009;Mala et al., 2013). he SiGe NS PL saturates quickly, as the slow radiative recombination cannot compete with the faster Auger recombination even for modest carrier concentrations (Kamenev et al., 2005(Kamenev et al., , 2006Tsybeskov and Lockwood, 2009;Mala et al., 2013). For these reasons, it is necessary to produce Si/Si1−xGex heterostructures with good control over their composition and interface abruptness to enable the production of the sought ater fast and eicient PL at 0.8-0.9 eV.
A review of the light-emitting properties of SiGe NSs in general, including quantum wells (QWs), wires, and dots, has been given elsewhere . In this paper, which also summarizes some older work, we assess how the nature of the interfaces between SiGe NSs and Si in heterostructures strongly afects carrier mobility and recombination for physical coninement in one-, two-, or three-dimensions corresponding to the cases of QWs, quantum wires, and quantum dots, respectively.
FiGURe 2 | Schematic representation of the Brillouin zone-folding concept in Si resulting from the new superlattice periodicity in the growth direction. Here, the conduction band minimum along the X direction is folded back into the Г point when the superlattice period is about 10 monolayers of Si (Kasper and Schäfler, 1991

QUANTUM weLLS
he planar epitaxial growth of 100% Ge on Si is made diicult by their 4% lattice mismatch (Paul, 2004). However, the formation of structural defects, such as dislocations, which can give rise to a large number of undesirable non-radiative recombination centers, can be circumvented by the use of controlled-composition Si1−xGex alloys with 0.1 < x < 0.2, which can be grown with techniques, such as molecular beam epitaxy (MBE) or ultra-high vacuum (UHV) chemical vapor deposition (CVD). he resulting heterostructures display a low defect density at the Si/SiGe interfaces. Such Si/Si1−xGex multilayer NSs with 0.1 < x < 0.2 have been intensively studied in the past as a likely method to conine electron-hole pairs in double HJ, or QW, conigurations and to reduce the thermal quenching of the luminescence at higher temperatures. So far, intense luminescence has been observed only at low temperatures in Si1−xGex in single and multiple QWs for x ≤ 0.2 [see Robbins et al. (1992)]. here have been several studies of the energy band alignment (i.e., to determine whether it is type I or type II; see Figure 1) in these NSs, but no inal conclusions have yet been reached (Houghton et al., 1995;hewalt et al., 1997;Shiraki and Sakai, 2005). Si and Ge interdifusion during the growth of Si/Si1−xGex QWs broadens the heterointerfaces, but this interdifusion can be reduced by using moderately low growth temperatures (less than 550°C). However, it should be noted that SiGe epitaxial growth at temperatures below 500°C usually produces a signiicantly high density of undesirable dislocations (Baribeau et al., 1990;Savage et al., 1999;Shiraki and Sakai, 2005). By staying within this fairly narrow growth "window, " high-quality Si/Si1−xGex QWs with x < 0.2 can be produced. Nevertheless, the thermal quenching of the PL quantum eiciency remains an unresolved problem in such QWs for the production of useful light emitters at wavelengths in the range of 1.3-1.5 μm.
Band Structure engineering via Brillouin Zone Folding in Atomic Layer Superlattices Gnutzman and Clausecker (1974) postulated that Brillouin zone folding within superlattices where the individual layer thicknesses were multiples of the Si or Ge unit cell dimensions would create a new artiicial unit cell along the growth direction that could result in the formation of a direct band gap material. Subsequently, high-quality (SimGen)p atomic layer superlattices, where m and n are the number of monolayers of Si and Ge, respectively, in each superlattice period and p is the number of periods, were grown in the 1980s by MBE (Kasper and Schäler, 1991), which stimulated further this idea. he theoretical aspects were reconsidered by Jackson and People (1986) in 1986 and, thereater, by other investigators. he essence of the zone-folding concept is demonstrated in Figure 2, where it can be seen that the new superlattice periodicity (d) creates a smaller Brillouin zone extending to ±π/d in contrast to that of the original material, which extends to ±2π/a where a is the lattice constant. he superlattice electronic band structure is then simply obtained by folding back the original band structure into this new reduced Brillouin zone. It is apparent from Figure 2 that for bulk Si the minimum in the conduction band, and thus a direct gap, can be obtained at the Brillouin zone center for d = 5a/2, which corresponds to 10 monolayers of Si. Given that the zone folding occurs only along the superlattice growth direction and that strains will appear to varying extents within the SimGen superlattice layers, together with modiications to the band ofsets at the heterointerfaces, this somewhat naive picture will be modiied [see, for example, Kasper and Schäler (1991), Brey and Tejedor (1987), Froyen et al. (1987), Hybertsen and Schlüter (1987), and People and Jackson (1987)]. heoretical work has shown that for strained layers of Si and appropriate superlattice periods a direct energy gap can be expected in these SimGen superlattices, but the calculated optical transition probability is still well below that of GaAs as the band-edge electronic states are inappropriately modiied by the zone folding. hus, the expected direct gap obtained by zone folding is now termed a quasi-direct band gap. Electrorelectance measurements of Si4Ge4 superlattices grown on (001)-oriented Si substrates (Pearsall et al., 1987) provided the irst experimental evidence of the anticipated modiications to the Si and Ge band structures in such superlattices. It was not until later, when strain-symmetrized SimGen superlattices were irst grown on strain-relaxed thick Si1−xGex alloy bufer layers on Si, that indications of the expected enhancement of the PL intensity and a smaller energy gap were obtained (Zachai et al., 1990;Kasper and Schäler, 1991). Further improvements in the crystal growth conditions led to a positive identiication of both of these novel features (Menczigar et al., 1993). Additional information on the research work on both the modiied band structure and light emission in SimGen atomic layer structures is provided in the extensive review by Abstreiter (1998). Si/SiGe Heterointerfaces in Nanostructures Frontiers in Materials | www.frontiersin.org At low temperatures, infrared light emission at energies useful for iber-optic transmission can easily be obtained from such SimGen superlattices. However, both the PL and the electroluminescence (EL) from such structures is basically quenched at room temperature primarily due to dissociation of the excitons and subsequent recombination of carriers at heterointerfaces or defects (Menczigar et al., 1992;Presting et al., 1992a). EL structures operating at room temperature have been reported (Engvall et al., 1993(Engvall et al., , 1995, but all the same, the infrared light emission is still quite weak. Results obtained more recently for a p-i-n diode based on a Si/Ge wavy superlattice quote an internal quantum eiciency of just ~10 −5 at 300 K . Hence, it was thought that light sources based on the zone-folding concept were unlikely to produce useful devices. It was predicted that these atomic layer superlattices would be more likely to ind ultimate use as infrared detectors instead of as light emitters (Presting et al., 1992b;Pearsall, 1994).
Part of the diiculty in reproducing the theoretical structures arises from the practical problem of producing the atomically abrupt interfaces required in these heterostructures. here have been considerable eforts made in trying to grow such atomically abrupt layered structures, but even with the best attempts using MBE there have been problems, such as atomic difusion across interfaces (Lockwood et al., 1993), interface undulations (Lu et al., 1994), and surface segregation (Baribeau et al., 1996) that even ater two decades of research have not been fully overcome.

Band Structure engineering via Alloying
Alloying Si with Ge and/or C also permits electronic band structure engineering, where the energy gap may be varied in this case by altering the alloy composition and/or strain (People and Jackson, 1990;Pearsall, 1994). When designing such heterostructures, the Si1−xGex layer thickness must be kept below the critical thickness, which is deined as the maximum thickness for defect-free strained growth of the layer. his implies that layers having larger thicknesses exhibit partial or total relaxation of the layer together with the formation of lattice defects, such as dislocations. he Si1−xGex critical thickness drops rapidly with increasing Ge concentration (Pearsall, 1994) and, hence, the emitting/absorbing regions in infrared emitters/detectors are necessarily quite thin. However, it is possible that wavy Si1−xGex/ Si superlattice structures, which deviate from planar growth (see below), may alleviate this restriction (Baribeau et al., 1999). Moreover, and most signiicantly, it has been found that the alloy band gap remains indirect. hese conditions place severe limits on the device structure. Nonetheless, considerable research has been undertaken on determining the optical properties of Si/ Si1−xGex heterostructures (Pearsall, 1994), which exhibit type I band alignment (People and Jackson, 1990;Houghton et al., 1995) (see Figure 1), and, to a lesser extent, on Si/Si1−xCx or even Si/Si1−x−yGex Cy (St Amour et al., 1995;Orner et al., 1996;Soref et al., 1996;Sturm, 1998).
Photoluminescence and EL have both been detected from Si1−xGex alloy layers produced in both single epilayer and superlattice form with a higher intensity than that observed from bulk Si. he alloy layer luminescence energy exhibits the same dependence on x as the bulk energy gap, but it is at an overall lower energy Rowell et al., 1990;Sturm et al., 1991;Lenchyshyn et al., 1992). he recombination mechanism can vary depending on the alloy layer thickness, its crystalline quality, and the heterointerface sharpness and can give rise to near band-edge light emission and/or excitonic luminescence (Noël et al., 1992;Lenchyshyn et al., 1993;Rowell et al., 1993). In early work, it was found that the EL from Si1−xGex/Si p-i-n diodes was quenched when the temperature was increased above 80 K , but EL was later reported at higher temperatures (up to 220 K) in p-i-n diode structures (Robbins et al., 1991). here has been a continual improvement in materials quality and this, coupled with changes in device design, has continued to advance EL device performance [see, for example, Fukatsu et al. (1992), Mi et al. (1992), Kato et al. (1995), Förster et al. (1996, and Presting et al. (1996)] to the point that EL has been obtained at wavelengths near 1.3 μm at room temperature (Mi et al., 1992;Presting et al., 1996). From a practical point of view, one major problem with such devices at present is their low eiciency at room temperature, which results from thermal dissociation of the exciton (Mi et al., 1992;Presting et al., 1996). For example, Si1−xGex/Si p-i-n diodes that had been grown on patterned substrates to optimize the unrelaxed alloy layer thickness  had an EL internal quantum eiciency of only ~10 −4 at 300 K . Again, as for SimGen heterostructures, interface sharpness, or more-pointedly a lack thereof, is a critical factor in the diode performance.
Since Ge has a larger lattice constant (5.658 Å) compared to Si (5.431 Å), it has been proposed that for axial Si/Ge NW HJs the strain created through the 4% lattice mismatch between Si and Ge can be relieved in part at the heterointerfaces via the lateral expansion of the Ge segment of the NW (Kästner and Gösele, 2004;Ertekin et al., 2005). hus, investigations of axial Si/Ge NW HJs can open new and interesting prospects for constructing low defect-density NSs for applications in CMOS compatible photonic components. We have investigated such axial structures and summarize our indings below (Wang et al., 2015).

Nanowire Heterojunctions
For this study, axial Si/Ge NW HJs were grown using the VLS technique and Au nanoparticles as a precursor in a lampheated reduced-pressure CVD reactor (Chang et al., 2009). he samples were characterized with a transmission electron microscope (TEM) equipped with a ield emission source and an

Si Ge
FiGURe 5 | High-resolution TeM image of the Si/Ge Nw HJ interface close to the Nw surface with clearly observed distortion of the lattice fringes (see box). An amorphous layer of ~ 1 nm thickness at the NW surface is indicated by an arrow (Wang et al., 2015).
Si/SiGe Heterointerfaces in Nanostructures Frontiers in Materials | www.frontiersin.org energy-dispersive X-ray spectrometer (EDX) with a probe size of 0.2 nm, Raman scattering spectroscopy, and PL spectroscopy. Figure 3 shows a TEM image at moderate resolution of a single axial Si/Ge NW HJ with a clearly visible Si/Ge heterointerface and smooth NW surface. he diameter of the Si segment of the NW is ~105 nm and it is nearly constant. he Ge segment of the NW diameter gradually increases from ~105 to 115 nm within ~100 nm from the Si/Ge heterointerface and then remains constant. Figure 4 presents a high-resolution TEM image of the Si/Ge NW heterointerface close to the NW center. A lattice fringe spacing fast Fourier transform (FFT) of the central heterointerface area indicated a nearly ideal crystallinity of the NW center. Figure 5 shows a TEM micrograph at high resolution of the same Si/Ge NW HJ with attention on the area close to the NW surface where a ~1-nm-thick amorphous oxide layer can be seen (marked by an arrow) and structural imperfections (see area marked by a box) are conirmed by a FFT analysis. No other structural defects are observed in the vicinity of the Si/Ge NW HJ.
Results of compositional EDX microanalysis of the Si/Ge NW HJs are shown in Figure 6. he Si/Ge NW HJ is comprised of Si and Ge NW segments with a clearly observed ~8-nm-thick SiGe transition layer produced by spontaneous SiGe intermixing. he EDX data indicate that a 2-nm-thick Si0.8Ge0.2 layer is formed close to the Si segment of the NW, and this is known to be a stable SiGe alloy composition produced by spontaneous intermixing (Brunner, 2002;Kamenev et al., 2004). Figure 7A shows Raman spectra of Si/Ge NW HJs measured using lasers with diferent wavelengths. Under 515 nm excitation, we observe three distinct Raman peaks associated with the Si-Si (~520 cm −1 ), Si-Ge (~400 cm −1 ), and Ge-Ge (~300 cm −1 ) types of vibrations with the main Raman peak at 300 cm −1 . Under 458 nm 250 300 350 400 450 500 550   (Wang et al., 2015). Note that the second Raman peak around 270 cm −1 under 458 nm excitation is, most likely, associated with a laser plasma line. Frontiers in Materials | www.frontiersin.org excitation, we observe the same peaks but with the main Raman peak now at ~520 cm −1 . his diference is due to a strong spectral dependence of the Raman scattering cross-section (Cerdeira et al., 1972). A Raman peak at ~500 cm −1 is better observed using 458 nm excitation and is associated with the Si-Si vibration in the presence of a neighboring Ge atom denoted as Si-Si(Ge) (Alonso and Winer, 1989). he Raman spectra are also sensitive to the excitation intensity (see Figure 7B). As the excitation intensity increases, the major Raman peak at ~520 cm −1 broadens and shits toward lower wavenumbers (similar behavior is observed for the Si-Ge and Ge-Ge Raman peaks, not shown). However, with increasing excitation intensity the Raman peak at 500 cm −1 shits in the opposite direction. Figure 8A shows the Si/Ge NW PL spectrum measured at low temperature. he PL spectrum clearly reveals at least two peaks: a narrower PL peak at ~1.08 eV (PL1) and a broader PL peak at ~1.03 eV (PL2). No signiicant PL at photon energies close to the bulk c-Si transverse optical (TO) phonon-replica PL peak at ~1.1 eV is found. he spectral positions and relative intensities of these two PL peaks are found to be temperature dependent (see Figure 8B): both PL peaks change their positions signiicantly with temperature and exhibit the lowest photon energy at ~60 K. he PL1 peak is detectable even at room temperature and exhibits an asymmetric broadening, which [in agreement with Tsybeskov et al. (1996)] can be itted by employing Boltzmann thermal broadening on the high energy side of this feature.
High-resolution TEM studies, analyses of lattice fringes, and EDX measurements (Figures 3-6) indicate that close to the center of the NW in the vicinity of the Si/Ge HJ the latticemismatch-induced strain is partially relaxed via spontaneous intermixing and the formation of a ~8-nm-thick SiGe transition layer. Additional structural relaxation occurs by gradual (within ~100 nm from the Si/Ge heterointerface) lateral expansion (i.e., increase in diameter) of the Ge segment of the NW (Figure 3). Close to the NW surface, we ind a distortion in the lattice fringe patterns, which is easily detected by FFT analysis (Figure 5 box). hese structural imperfections are located within a 2-3-nm-thick interface layer between the NW core and an oxide layer at the NW surface and they are slightly extended (up to 0.80 .9 11 .1 1.2 5-6 nm) toward the NW core in the vicinity of the Si/Ge NW HJs (Figure 5). We conclude that the Si/Ge NW HJs with a diameter approaching 70-100 nm can have a nearly perfect crystalline core and overall smaller density of structural defects (due to a lesser surface-to-volume ratio) compared to thinner NW HJs. he observation of an easily detectable PL signal (Figure 8) supports this conclusion and indicates that non-radiative recombination centers associated with the NW surface states do not fully control carrier recombination in Si/Ge NW HJs with diameters greater than 50 nm (which is the average diameter of NWs in our samples). Also, the PL1 peak is red-shited by ~20 meV and considerably broadened compared to the c-Si PL spectrum, suggesting that the Si segment of the NW close to the Si/Ge HJ is non-uniformly strained. he PL associated with this segment of the Si/Ge NW HJ exhibits a peak shit toward higher photon energy as the temperature increases from 20 K to above room temperature, indicating that there is compressive stress due to the mismatch in Si and Ge CTEs and, possibly, NW bending. he PL peak at 1.03 eV (PL2) is even more broadened, and it disappears at T > 80K. We attributed PL2 to radiative carrier recombination within the SiGe alloy layer at the Si/Ge heterointerface (Chang et al., 2009). he PL2 peak position, signiicant PL2 intensity temperature dependence, and the PL signal disappearance at T > 80 K are consistent with exciton localization on compositional luctuations in SiGe alloys (Kamenev et al., 2004). hus, the structure of the interface region strongly afects carrier recombination in Si/Ge NW HJs.
Considering the Raman measurements, we anticipate that under the applied laser excitation intensity of 10 2 -10 3 W/cm 2 , the sample temperature increases signiicantly. he Si-Si Raman peak position in Si/Ge NW HJs is in full agreement with the bulk c-Si Raman temperature dependence, but under 700 W/cm 2 incident power density, the sample temperature is estimated to be ~680 K. his signiicant laser heating of our samples is due to a reduced thermal conductivity of the Si/Ge NW HJs and results in the behavior observed with increasing excitation power density described above. he temperature increase produces a strong shit of the Raman peak associated with the Si-Si(Ge) vibration mode toward higher wavenumbers, indicating strong (2-3 GPa) compressive strain, as also found from the PL data. his conclusion is supported by the Raman polarization dependence in Si/Ge axial NW HJs (Wang et al., 2015).

QUANTUM DOTS
"By the 1990s, a diferent type of SiGe NS, namely the 3D self-assembled system produced by the well-known Stranski-Krastanov, or cluster-layer, growth mode in lattice-mismatched materials, had been demonstrated (Eaglesham and Cerullo, 1990;Mo et al., 1990;Jesson et al., 1993;Kamins et al., 1997;Baribeau et al., 2006). It has been shown that dislocation-free SiGe growth can be achieved using a higher temperature (≥600°C), and that the non-planar geometry is mainly responsible for the signiicant increase of the SiGe critical layer thickness. It has also been found that, compared to two-dimensional (2D) Si/SiGe NSs, the PL and EL quantum eiciency in 3D Si/SiGe NSs is higher (up to 1%), especially for T > 50 K (Cerdeira et al., 1972;Apetz et al., 1995;Schittenhelm et al., 1995;Schmidt et al., 1999b). Despite many successful demonstrations of PL and EL in the spectral range of 1.3-1.6 μm, which is important for optical iber communications, the proposed further development of 3D Si/SiGe-based light emitters was discouraged by several studies, indicating a type II energy band alignment at Si/SiGe heterointerfaces (Van de Walle and Martin, 1986;hewalt et al., 1997;Schittenhelm et al., 1998;El Kurdi et al., 2006), where the spatial separation of electrons (located in Si) and holes (localized in SiGe) (see

Lockwood et al. Si/SiGe Heterointerfaces in Nanostructures
Frontiers in Materials | www.frontiersin.org Figure 1) was thought to make carrier radiative recombination very ineicient. Later, it was also shown that 3D Si/SiGe NSs exhibit an extremely long (of the order of 10 −2 s) luminescence lifetime (Kamenev et al., 2005), which is of the order of a million times longer than in III-V semiconductors and their NSs. hus, according to this analysis, 3D Si/SiGe NSs cannot be used to achieve eicient and commercially valuable light-emitting devices. Recently, however, it has been shown that despite the fact that the Si/SiGe heterointerface most likely exhibits type II energy band alignment, it is still possible to obtain conditions favorable for an eicient carrier radiative recombination. " For further details of this early work, see the additional review material given in Lockwood and Tsybeskov (2013). With 3D coninement, the role of the dot surface and its interface with its surroundings becomes even more critical in determining the physical properties of SiGe NSs. In this section, we provide a summary of the latest time-resolved and continuous-wave (CW) PL investigations of the recombination dynamics of 3D Si/Si1−xGex multilayer NSs grown by MBE (Modi et al., 2012a,b;Lockwood et al., 2013b;Mala et al., 2013). Signiicantly, the Si/Si1−xGex NSs comprised a single Si1−xGex nanometer-thick layer (NL) integrated into Si/Si0.6Ge0.4 cluster multilayers (CMs).

Photoluminescence from SiGe Nanostructures
he PL spectra typically observed in 3D Si/SiGe NSs is similar to that found for III-V QWs with type II energy band alignment, as the PL exhibits a blue shit on increasing the excitation intensity (Lockwood and Tsybeskov, 2010). his efect is found in samples grown by both MBE and CVD. Figure 9A shows PL spectra in a CVD grown sample measured for diferent excitation intensities. At the lowest excitation intensity shown, the PL feature that is shown resolved into two components (see Figure 9A) peaks at ~0.8 eV. On increasing the excitation intensity, an unbroken PL blue shit of 30-40 meV for each decade of excitation intensity increase is observed (see Figure 9B). Under much higher photoexcitation intensity (1-10 kW/cm 2 ), the low energy part of the PL spectrum does not shit any further, while the high energy part continues shiting toward higher energy. A modiied Arrhenius plot of the normalized integrated PL intensity as a function of temperature for the diferent excitation intensities can be itted with two thermal quenching activation energies, E1 and E2 (Lockwood and Tsybeskov, 2010). Activation energy E1 is found to be ~15 meV and is independent of the excitation intensity for all samples. Activation energy E2, however, depends considerably on the excitation intensity: it increases drastically from ~120 to 340 meV when the excitation intensity increases from 0.1 to 10 W/cm 2 . his high value for E2 implies that such PL can easily be observed at room temperature.
Low-temperature PL dynamics have been measured for a CVD grown sample using a ~6-ns excitation pulse at 2.33 eV (532 nm) (Lockwood and Tsybeskov, 2010). he initial PL decay is fast (< 20 ns), close to the resolution of the detection system. However, a slower PL component demonstrates a strong dependence on the PL photon energy: at photon energies below 0.8 eV, the PL lifetime is found to be ~20 μs and then it drastically decreases to ~200 ns for PL observed at 0.89 eV.

Single Nanometer-Thick SiGe Nanocluster Sample
A TEM micrograph of a specially fabricated sample containing a very thin Si1−xGex cluster layer above a regular stack of such cluster layers that was grown using Si/SiGe MBE is shown in Figure 10A (Modi et al., 2012a). he sample is grown on a Si substrate and comprises two SiGe cluster layers with a cluster height of ~6-8 nm separated by a Si layer of ~8 nm thickness between the SiGe clusters (i.e., there are two SiGe/Si pairs); a 30-nm-thick Si spacer layer; another ive SiGe/Si layer pairs to initiate 3D growth; a layer of SiGe clusters with a height of approximately 18 nm; a thinner separating Si layer; a inal SiGe cluster layer; and a thin Si cap. he SiGe alloy cluster layers are composed of up to 40 atomic percent (at.%) Ge, and induce considerable global and local strain, which is readily visible in dark-ield TEM imaging (see, for example, Figure 10B). Much of the strain is accommodated within a 60-70 nm depth of the Si substrate and within the 30-nm-thick Si spacer layer above it (see the bright regions in Figure 10B). he top two pairs of Si/SiGe layers, however, show a lower TEM contrast than the layers below them, primarily due to the much thinner (and strained) Si layer sandwiched between the two thicker SiGe cluster layers.
A dark-ield TEM image at greater magniication for the two Si/SiGe cluster layers closest to the Si substrate is presented in Figure 11 together with results from an EDX alloy-composition scan. As shown in Figure 10B, this region of the sample has a high strain and likely signiicant strain-induced Si/SiGe intermixing. he EDX analysis shows that the Ge atomic concentration at the Si/SiGe heterointerface increases from 0 to ~35 at.% within   Figure 11B). Figure 12 displays the corresponding information for the two topmost Si/SiGe clusters layers, where the Ge atomic concentration in the cluster reaches a maximum value of ~38 at.% within a much shorter distance d = 3 nm. he EDX scans, thus, reveal that the topmost Si/SiGe cluster layer has a much more abrupt Si/SiGe heterointerface compared to that found in the bottommost cluster layers. Photoluminescence measurements of this sample (see Figure 13A) reveal spectroscopic features that are consistent with the TEM and EDX data. Using photoexcitation at a wavelength of 405 nm, which has a penetration depth of ~0.1 μm, a PL peak is observed at 0.78 eV with a full-width at half maximum (FWHM) of ~130 meV. At an excitation wavelength of 325 nm with a penetration depth of only ~10 nm, the PL spectrum is shited slightly toward lower photon energy and has a signiicantly reduced FWHM (~100 meV). his result demonstrates that the cluster composition and Si/SiGe interface abruptness, as illustrated in Figures 11 and 12, are inluencing the PL behavior: the more abrupt the Si/SiGe interface, the smaller the FWHM of the PL peak, and, in the topmost SiGe layer, a higher Ge composition results in the PL peak being shited toward lower photon energy (Modi et al., 2012a). In other similar samples, it has been shown that continuous optical excitation at shorter wavelengths produces substantial PL fatigue ater a delay of about 10 min due to the accumulation of charge within the SiGe clusters (Modi et al., 2012b).
he PL lifetimes as a function of incident wavelength and PL intensity as a function of excitation energy density are shown in Figures 13B,C, respectively, both being measured under pulsed laser excitation with a pulse duration of ~6 ns. he PL excited at 532 nm and recorded at 0.78 eV, which originates predominantly from the lowermost Si/SiGe cluster layers, has a lifetime that is approximately 100 times longer than the same PL excited at 355 nm, which originates predominantly from the topmost Si/SiGe cluster layer. No changes in the PL lifetime are found under 355 nm excitation with energy densities varied from 10 −5 to 5 × 10 −2 J/cm 2 until the Auger limit has been reached, with the carrier concentration then approaching ~10 19 cm −3 [see Figure 13C and Kamenev et al. (2005)]. here is a dramatic diference in the PL intensity as a function of excitation energy density for excitation at the two diferent wavelengths: the PL intensity under 532 nm excitation quickly saturates, in agreement with the indings of Kamenev et al. (2005) and Cerdeira et al. (1972), while, most impressively, the PL intensity under 355 nm excitation is linear versus excitation intensity for many orders of magnitude (see Figure 13C). hese results clearly demonstrate that in Si/SiGe 3D NSs the PL peaked near 0.78 eV strongly depends on the Si/SiGe heterointerface abruptness. he EDX measurements show that in conventional MBE-grown 3D Si/SiGe NSs the transition from pure Si to Si1−xGex with x = 0.3-0.4 in the cluster can require an intermixed SiGe interface whose width is more than 5 nm. hese difused type II Si/SiGe heterointerfaces are responsible for a signiicant electron-hole spatial separation (d > 5 nm) and the observed slow PL, which cannot compete with Auger recombination even at low optical excitation intensities. However, by means of growth engineering, more abrupt Si/SiGe heterointerfaces with, for example, d = 3 nm, can be obtained. hese sharper heterointerfaces yield a PL lifetime of <20 ns, which remarkably is only a little slower than that found in direct band-gap III-V semiconductors. his extremely fast PL has a quite high quantum eiciency, which, in contrast to the previously reported results, remains constant over several orders of magnitude of optical excitation intensity.
Single Nanometer-Thick SiGe Quantum Well Sample he specially prepared MBE-grown single QW sample is depicted in Figure 14A. he sample structure comprises a Si substrate (not visible in the TEM micrograph); a Si1−xGex bufer layer with x = 10 at.% (partly visible at the bottom of the micrograph); eight repeats of combined Si1−xGex cluster (reaching 10 nm thickness in the center) and Si layer pairs; a single 4-5 nm thick Si1−xGex NL followed by a thin Si layer; and a inal Si1−xGex cluster layer capped with Si (Mala et al., 2013). he EDX scan of the sample shown in Figure 14B reveals that the Si1−xGex NL composition is relatively uniform (x = 8 at.%) while in the Si1−xGex clusters x monotonically increases from ~5 at.% at the Si/SiGe-cluster interface to up to 40 at.% at the cluster center.
Two quite diferent PL spectra obtained using diferent excitation wavelengths but with approximately the same excitation intensities are compared in Figure 15A. he PL obtained under CW 325 nm excitation is peaked near 0.9 eV; whereas under 365 nm excitation, it is now peaked around 0.8 eV. PL spectra obtained with pulsed photoexcitation at 355 nm from a Nd:YAG laser are shown in Figure 15B. he time-integrated measurements were performed using a lock-in ampliier synchronized with the laser pulse; the accumulation time was in the range of 10 −3 -10 −2 s. he PL peak intensity was measured at diferent wavelengths using a digital oscilloscope with an adjustable time window and employing a much shorter (~0.1 μs) accumulation time. As for the case of CW excitation at two diferent wavelengths, the two diferent techniques, although using the same excitation wavelength in this case, produced quite diferent PL results: the time-integrated spectrum exhibits a peak near 0.8 eV, while the maximum of the peak-intensity spectrum is at ~ 0.92 eV. Such diferences in the PL spectra can be explained by a substantial diference in the lifetimes of the respective PL constituents. Earlier work has shown that the PL lifetime is indeed expected to be much shorter for the 0.92 eV peak compared with the 0.8 eV peak (Kamenev et al., 2005).
he intensity of the 0.92 eV PL peak is linearly dependent on the excitation energy density with no saturation evident until an energy density of at least ~50 mJ/cm 2 , while the 0.8 eV PL peak intensity varies with excitation energy density as the square root (Mala et al., 2014). Also, the rise time of this Frontiers in Materials | www.frontiersin.org latter PL peak decreases with both increasing excitation energy density and temperature. he PL dynamics associated with the SiGe NL and the SiGe clusters using pulsed laser excitation at a wavelength of 355 nm and 6-ns long in duration are illustrated in Figure 16A. he 0.92 eV PL peak rises even faster than the system time resolution, while the 0.8 eV PL peak has a rise time of 2-3 μs. he former PL peak decays considerably faster compared to the latter PL peak. Non-exponential decays are exhibited by both kinds of PL bands. his suggests that in both cases the carrier recombination processes are characterized by a time-dependent recombination rate, Ri, and Figure 16B presents these rates that have been extracted from the PL decay data as a function of time. he recombination rate thus obtained is in the range of 10 6 -10 7 s −1 for the 0.92 eV PL peak and is ~10 5 -10 4 s −1 for the 0.8 eV peak PL.

interpretation Based on interfacial Recombination
At low temperatures, carrier difusion is known to be negligible in Si/SiGe NSs (Modi et al., 2012a). Hence, to account for the difference between the PL spectra obtained using shorter (325 nm) and longer (365 nm) wavelength excitation (see Figure 15A), one must allow for the diference in photoexcitation penetration depth, which is ~10 −6 cm at 325 nm and ~10 −5 cm at 365 nm (Paul, 2004;Modi et al., 2012a). hus, the PL at ~ 0.9 eV is mostly associated with the 4-5-nm-thick Si1−xGex NL with x = 8 at.%, while the PL at ~ 0.8 eV is related to SiGe CMs with x reaching a maximum of 40 at.%. he PL in Si1−xGex CMs is shited toward lower photon energies compared to that in bulk Si1−xGex alloys having a similar composition (Weber and Alonso, 1989), which is most likely due to the presence of strain and strain-induced Si/Si1−xGex interfacial mixing (Cerdeira et al., 1972;Schmidt and Eberl, 2000).
With pulsed laser excitation at 355 nm, the PL arising from both the SiGe NL and the SiGe CMs can be observed. he time-integrated PL signal shown in Figure 15B shows predominantly the PL peak at ~0.8 eV with a weak shoulder at ~0.9 eV, while the PL peak maximum intensity is now at ~0.92 eV (see Figure 15B). his indicates that the PL at 0.92 eV decays much faster than the 0.8 eV PL (Kamenev et al., 2005). It is noteworthy from the crystal quality point of view that in both the CW and time-resolved experiments no PL associated with crystallographic dislocations (Fukatsu et al., 1996) was found.
At a higher excitation energy density, the 0.8 eV peaked PL demonstrates a sub-linear dependence of the PL intensity on excitation energy density. However, the PL intensity of the 0.92 eV peak exhibits a linear dependence on the excitation energy density, indicating that the experimentally determined recombination rate of 10 6 -10 7 s −1 is mostly due to radiative recombination. Given that Auger recombination is competing with radiative recombination, it is expected that the long-lived PL would saturate sooner than the short-lived PL. he experimental data in Figure 16A conirm that the decay of the PL peaked at 0.8 eV is indeed signiicantly slower when compared to that of the 0.92 eV PL peak. Figure 16A also shows that the 0.8 eV PL rise time of ~2-3 μs is much longer than the exciting laser pulse duration of ~6 ns. his exceptionally long PL rise time could be associated with a special kind of Auger-assisted carrier spatial redistribution in the Si/SiGe NSs that is termed the Auger fountain (Ohnesorge et al., 1996;Lee et al., 2009).
Non-exponential PL decays have been observed before in Si/ SiGe NSs and analyzed by employing a stretched exponential function {exp[(-t/τ) β ]}, a power function {1/(1 + αt) m }, or multiple exponential decays (Zrenner et al., 1995;Fukatsu et al., 1996;Kamenev et al., 2005). he stretched exponential PL decay phenomenon has been observed in a wide variety of systems apart from Si/SiGe NSs and it provides a good empirical it to the data, although it most likely has no fundamental signiicance (Kuskovsky et al., 1998). Indeed, the underlying physical mechanism involved in non-exponential PL decay has yet to be  identiied. In a diferent approach to this issue, we extract the recombination rate directly from the PL decays without requiring any assumption or a speciic physical model. Figure 16B indicates that initially both of the PL bands have an almost time-independent recombination rate, exhibiting single-exponential decays of ~9 × 10 4 s −1 for the 0.8 eV PL band and ~3 × 10 7 s −1 for the 0.92 eV PL band. he recombination rate decreases with increasing time, and varies as Ri(t)~t −α with α = 0.67 for the 0.8 eV PL band and α = 0.82 for the PL band peaked at 0.92 eV.
In accordance with the donor-acceptor pair recombination model (homas et al., 1965), the electron-hole time-dependent recombination rate can be explained by assuming that it depends on the average distance separating electrons and holes, ae-h. Due to the previously discussed type II energy band alignment at the Si/SiGe heterointerfaces, it is assumed that the holes are localized within the SiGe and the electrons are located in the Si. he recombinationrate dependence on this distance can be expressed as where R0 is the maximum recombination rate (~10 8 s −1 , see Figure 11B) and a0 is the minimal radius of the localized exciton at the Si/SiGe heterointerface (~1.5 nm). For the Si1−xGex NL with x ~ 8 at.%, ae-h ≤ 5 nm (a value that is comparable to the SiGe NL thickness) while in the Si1−xGex CMs where 0 ≤ x ≤ 40 at.%, ae-h is in the range of 9 nm < ae-h < 14 nm (see Figure 17). hese results are consistent with the TEM and EDX data (see Figure 14). hus, we again see that carrier migration and recombination are both strongly inluenced by the NS interfacial characteristics.
CONCLUSiON he earlier studies and most recent investigations reported here of Si-Ge interfacial efects in SiGe NSs all demonstrate that for eicient carrier recombination and, hence, best device performance it is critical to ensure that the as-grown and possibly laterprocessed heterointerfaces are as sharp as possible. he sharpness is inluenced by many factors, such as growth conditions, strain, and thermal processing, which in practice can make it diicult to attain the ideal structures required. his is certainly the case for NS coninement in one dimension. However, we have demonstrated that axial Si/Ge NW HJs with good core crystallinity and fairly abrupt heterointerfaces can be fabricated using Au-catalyzed VLS growth. Spontaneous intermixing at the Si/Ge heterointerface and lateral expansion of the Ge segment of the nanowire partially relieves the lattice mismatch-induced strain. With a Si/Ge NW diameter in the range of 50-120 nm, surface-related structural defects and imperfections do not fully control carrier recombination in the Si/Ge NW HJs, and the PL signal associated with band-to-band electron-hole recombination at the Si/Ge NW HJ has readily been measured and attributed to a speciic interfacial SiGe alloy composition revealed by EDX.
For 3D coninement, the experiments outlined here have shown that two quite diferent Si1−xGex NLs when amalgamated with a special Si0.6Ge0.4 CM structure exhibit strong PL that can have a characteristic decay time as much as 1000 times shorter than that found for PL in regular Si/SiGe CMs. he non-exponential PL decay observed in Si/SiGe NSs has been ascribed to diferences in the distances separating electrons and holes across the Si/ SiGe heterointerface. he results demonstrate that sharp Si/SiGe heterointerfaces can signiicantly reduce the carrier radiative recombination lifetime and thereby increase the PL quantum eiciency. hese SiGe NL/CM combined NSs are now possible contenders for applications requiring light-emitting devices in CMOS compatible optoelectronics.

AUTHOR CONTRiBUTiONS
DL planned and prepared most of this paper as well as participated in the experiments and their interpretation. XHW performed the electron microscopy work. J-MB prepared most of the samples used in this study. SM carried out some of the photoluminescence studies of some samples. XLW carried out some of the photoluminescence and Raman studies of some samples. LT planned and supervised the experimental work in NJIT and provided interpretation of the results.

ACKNOwLeDGMeNTS
his work is supported in part by NSF grant ECCS-1027770, Hewlett-Packard Laboratories and he Foundation at NJIT. We would like to acknowledge the invaluable contributions over a number of years from our many collaborators on this work and whose names are given in the references to our work in this paper. We thank especially B. Kamenev, E.-K. Lee, H. Y. Chang, and N. Modi of New Jersey Institute of Technology, and T. Kamins of Hewlett Packard Laboratories.