1.
Introduction

Epitaxial of Ge on Si is one of the most mature material systems in hetero growth of semiconductors. Two or three dimensional (3D) confined structures including Ge quantum dots (QDs), nanorings (NRs) and nanowires (NWs) can be readily obtained by using self-assembly growth techniques. As nonpolar semiconductor materials, GeSi nanostructures are particularly suitable for studying the fundamental crystallography phenomena in the heteroepitaxial growth process, as well as novel quantum mechanical phenomena. In these low-dimensional structures, carriers (electrons and holes) are confined in nanometer-sized regions in one, two or three spatial directions, leading to quantized energy states therein. Such quantum effects have offered a new freedom in exploring the relevant optoelectronic or electrical device applications based on these nanostructures. Moreover, by manipulating the composition, the strain as well as the carrier interaction in GeSi nanostructures, the electronic band structure and the carrier density of states (DOS) can be dramatically modified, which is expected to give rise to enhanced electrical and optical properties^[1].



Since Ge nanostructures are naturally compatible with the Si micro- and nano-complementary metal–oxide–semiconductor (CMOS) technology, enhancing the properties of Si by incorporation of Ge nanostructures has been desirable for a long time. Tremendous attempts have been made in this direction. Novel optoelectronic and electrical devices with Ge nanostructures have already been demonstrated, e.g. infrared photodetectors based on Ge QDs^[2], single electron transistors (SET) based on Ge NWs^[3] or Ge QDs^[4], photonic crystal (Phc) devices in cavity quantum electrodynamics (CQED) based on Ge QDs^{[5, 6]}, and channel electron mobility enhanced Si transistors based on Ge QDs^[7]. Particularly noteworthy is that a direct bandgap light-emitting in Ge has recently been realized via strain manipulation in tensile-strained nanomembranes^[8], showing significantly enhanced quantum efficiency and potential in lasing applications.



Ge QDs, NRs and NWs discussed in this article are obtained by self-assembly growth on Si (001) substrates, that is, by the Stranski-Krastanow (SK) growth mode in molecular beam epitaxy (MBE) or metal organic vapor phase epitaxy (MOVPE). By optimizing the growth parameters, the shape of the Ge nanostructures can be controlled to a certain degree. For example, the shape of Ge islands grown on Si show hut clusters, pyramids, domes, barns and super-domes^[9–13], depending on the growth temperature and Ge deposition amount. However, those obtained Ge nanostructures are generally distributed randomly on the Si substrate surfaces with large size and composition fluctuations. For device applications, high nanostructure uniformity is generally desirable. In particular, the ordering and addressable sites of Ge QDs are the key issue in applications based on the coupling between photonic crystal cavity and Ge QDs. To realize a more robust control of the Ge nanostructures, considerable efforts have been devoted to explore new growth approaches. Various effective techniques have been demonstrated to control the growth of Ge nanostructures, e.g. seed induced self-assembly^[14], pattern template substrate assisted self-assembly^[15], specific crystallographic plane^[16] and post-growth techniques^[17]. Ordered Ge QDs^[18], NRs^[19] and NWs^[20] have been realized. Benefiting from the progress made in controllable growth, other advanced nanostructure systems can also be realized, e.g. the QD molecules (QDM)^[21] (also named the QD posts) and the QD crystals^[22]. The inter-QD interaction and electronic state coupling provide another freedom in exploring new physical features in nanostructures. Therefore, controllable growth of Ge nanostructures opens a path to control the Ge material’s physical properties and to extend its application potentiality.



In this article, we briefly outline recent progresses achieved in controllable epitaxial growth of GeSi alloy nanostructures. The associated growth theories as well as experimental results will be discussed. This review is organized as follows: in the next section, three prevailing growth mechanism models that are generally employed in interpreting the site-selective nucleation and growth of Ge nanostructures on patterned or inclined Si surfaces are discussed. In Section 3, very recent results on the preferential growth of Ge islands on patterned Si substrates, including ordered Ge nanoislands (NIs), three-dimensional Ge QD crystals (QDCs), ordered Ge NRs, and coupled Ge QD molecules, will be discussed. In Section 4, Ge nanostructures grown on inclined Si surfaces are depicted, to be specific, ordered Ge nanowires and high density Ge islands. In Section 5, Ge nanostructures with readily tunable spatial geometries gown on Si nanopillars are also discussed. In addition, we also address optical microcavity device applications of site-selective growth of a single Ge QD in Section 6 to highlight the importance of the controlled growth techniques. Finally, a summary and the outlook of future development trends and application challenges for controllable Ge nanostructures are also given in Section 7.

2.
Theories for controlled growth of Ge nanostructures

Ge has shown a site-selective nucleation nature when grown on nano- or microstructure patterned Si (001) surfaces, which results in an effective route to control the QD morphology via substrate patterning. In general, GeSi NIs grown on patterned Si substrates were found to have a lower nucleation energy barrier and a smaller critical size^[23], less misfit strain and large volumes with respect to those grown on flat substrates^[18]. Several growth models have been proposed to understand such ordered and site-selective NI growth nature on the patterned substrate, i.e. the diffusion length model^[24], the nucleation model on inclined surfaces^[23] and the surface chemical potential (SCP) model on curved surfaces^[15]. In the following those models will be discussed respectively.

2.1
Diffusion length model

The diffusion length model typically applies to explain the ordering growth nature of GeSi islands grown on patterned substrate in a small period regime^[24–26]. It is proposed that the 2D QD ordering is kinetically determined by the mismatch between the Ge adatom surface diffusion length (L_d) and the pattern period (P) at different growth temperatures. Ge atoms move by exchange diffusion with adsorbed monomer or dimmers^{[27, 28]} when Ge atoms are deposited on a clean Si (001) surface. The surface L_d of Ge adatoms or addimmers can be simply expressed by

$${L_{ m d}}={(Dtau )^{1/2}},$$

(1)

where D denotes the diffusion constant, and τ is the time interval for adatom diffusion.

$$D={a^2}vexp ( - E/{k_{ m B}}T),$$

(2)

where a is the lateral motion (3.84 ?/s) corresponding to each hop of an adatom, v is a prefactor (about 10¹³), E is the effective diffusion barrier for adatoms or addimmers on patterned substrate, k_B is the Boltzmann constant, and T denotes growth temperature. In this model, the dominant part of adatom diffusion length is the effective barrier of E, which is closely related to the microstructures on the substrate surface.



Zhong et al. have studied the temperature dependent growth of ordered Ge QDs on patterned Si substrates with submicron periods^{[29, 24]} and found that only at an intermediate temperature range around 700 °C could the growth of ordered Ge QDs be achieved. Ge adatom L_d of 160–1100 nm were estimated at the temperature range of 600–800 °C using anE of ~1.5 eV. The ordered QD growth at around 700 °C was attributed to the comparable Ge adatom L_d to P, while the stochastic growth at higher (or lower) growth temperatures was attributed to a larger (or smaller) L_d in comparison with P.

2.2
Nucleation model on inclined surfaces

This model shows that the island nucleation position is determined by the interplay between the strain relaxation energy and the surface energy on different surface areas. The strain relaxation lowers local energy and benefits the QD nucleation. In contrast, the surface energy increases the local energy and suppresses the nucleation of QDs on the local site. The competing results of two energies determine where a QD nucleates.



As shown in Fig. 1(a), the Ge was deposited on a site with local groove-shaped micro- or nanostructures on Si (001) surfaces^[23]. The inclined micro- or nano surface of the groove has an inclination angle of $varphi $. The angle between the Ge island surface and the Si (001) surface is $theta $ ($theta geqslant varphi $). The width of the Ge island is 2l. Accordingly, the total energy E on a surface site is expressed by:

$$begin{aligned}E=&{E_{ m e}} + {E_{ m s}} =& - {varepsilon _0}S(tan theta - tan varphi ) + 2varGamma {S^{1/2}}{(tan theta - tan varphi )^{1/2}},end{aligned}$$

(3)

where ${E_{
m e}}$ is the strain relaxation energy, and ${E_{
m s}}$ is the surface energy. ${varepsilon _0}=(2ln 2){sigma ^2}(1 - {v^2})/pi Y$ is the elastic energy density per unit area. $sigma $ is the internal strain in the Ge island. $v$ is the Poisson ratio and $Y$ is the Young modulus of elasticity. $S={l^2}(tan theta - tan varphi )$ is the surface area of the Ge island.

$$varGamma =({gamma _{ m f}}sec theta - {gamma _{ m w}}sec varphi ){(tan theta - tan varphi )^{ - 1}},$$

(4)

where ${gamma _{
m f}}$ and ${gamma _{
m w}}$ are the surface energy of the Ge island and the GeSi alloy WL. ${gamma _{
m w}}={gamma _0}(1 - alpha cos (nvarphi ))$, $alpha $ defines the surface energy anisotropy and $n$ defines the angle of low-energy facets. Fig. 1(b) shows the calculated nucleation barrier of Ge islands as a function of the angles. One crucial calculation result of this model is that Ge islands grown on patterned Si surfaces have smaller critical size and lower nucleation barrier compared with that grown on flat Si surfaces as shown in Fig. 1(b), which coincides well with experimental results^{[18, 30]}. Another crucial result of this calculation shows that the Ge island nucleation site critically depends on the competition between the local strain relaxation energy and the surface energy. More specifically, the island would nucleate on the bottom area of the groove when the strain relaxation energy dominates. When the surface energy dominates, the island would nucleate on the bottom or the tip areas of the groove. Such theoretical results also agree well with the experimental results^{[26, 31]}.






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Figure1.
(Color online) (a) Schematic growth of Ge islands on the groove-shaped Si surfaces in the nucleation barrier model. (b) The calculated Ge island nucleation barrier as a function of the inclination angles. Adopted from Ref. [23].

2.3
Surface chemical potential model on curved surfaces

This model attributes the prior nucleation sites of Ge islands on the patterned Si surface to the local SCP minimum^[15]. It indicates that the control of dot ordering in heteroepitaxy is realized by a local SCP, which is closely related to the spatially non-uniform relaxation of the strained energy and the variation of the surface energy due to the surface fluctuation of the epilayer. The SCP is closely related to the local surface curvature, the surface free energy and the strain energy, and is simply introduced as follows.



The SCP, μ, can be written as

$$mu ={mu _0} + Omega gamma kappa + Omega {E_{ m{s}}},$$

(5)

where ${mu _0}$ is the chemical potential for the flat surface. The second and the third terms are the surface energy and the strain energy, respectively. $Omega $ is the atomic volume, and $gamma $ is the surface free energy per unit area. $kappa $ is the local surface curvature, and ${E_{
m s}}$ is the local strain relaxation energy.



The curvature $kappa $ is given by

$$kappa=- z''{[1 + {(z')^2}]^{ - 3/2}},$$

(6)

with z being the height of the surface along the normal direction to the surface plane, z' and z" being the first and second derivatives with respect to X, respectively, and X being the position along the surface plane. The change of local chemical potential due to morphology comprises the surface energy $Omega gamma kappa $ and the strain energy $Omega {E_{
m s}}$. The local strain relaxation energy in respect to a flat film, ${E_{
m s}}$, can be formulated by

$${E_{ m{s}}}= - frac{C}{2}left( {frac{kappa }{{left| kappa ight|}}{{[kappa ({z_{ m s}} - {z_0})]}^2} - {varepsilon ^2}} ight),$$

(7)

where C is the elastic constant, ${z_{
m{s}}}$ is the position of the top surface, ${z_0}$ is the position of the neutral plane of the bent film, and $varepsilon $ is the misfit strain between QDs and the WL. The quantity $({z_{
m{s}}} - {z_0})$ represents the average displacement of the bent film and is treated as a fitting parameter, which is chosen to give a minimum μ in a selective area and correct QD positions. Benefitting from the involvement of the local surface curvature, it is much more convenient to link the SCP with the substrate surface morphology. By using 1D or 2D curvature, this model can give the 1D or 2D calculation results of local SCP distribution. In this model, for a curved surface, convex regions with a positive $kappa $ have a higher chemical potential than concave regions with a negative $kappa $. Ge adatoms diffuse from convex regions to concave regions.



Figs. 2(a) and (b) show the scanning electron microscopy (SEM) image of the growth result of Ge islands on a patterned Si substrate and the corresponding 1D SCP distribution along the blue dash line in (a), respectively^[15]. It is clearly seen that in Fig. 2(b) three SCP minima coexist in both the top and the bottom areas of the microridge. The positions of those SCP minima correspond precisely to the nucleation sites of the Ge islands. This model also applies well in 2D SCP calculation and has shown good agreement between the calculated position of 2D SCP minima and the experimental growth results^{[32, 33]}.






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Figure2.
(Color online) (a) SEM image of the Ge island growth results on square-grid micropit patterned Si (001) substrate. (b) The calculated 1D SCP distribution along the blue dash line shown in (a). The corresponding height profile is also indicated. Adopted from Ref. [15].

3.
Preferential growth of Ge islands on patterned Si substrates

The self-assembly growth of Ge on nanoscale patterned Si surfaces is one of the most promising approaches to realize site-controllable Ge islands in various geometries^[15–46]. Considerable efforts have been devoted to investigate the growth behavior of semiconductor nanostructures using substrate with pre-patterned micro- or nanostructures (also namely template assisted self-assembly), e.g. micro holes^[15], nanoridges^[34], nanogrooves^[35] and nanopits^[36]. Taking advantage of such selectively nucleation nature of Ge islands on patterned Si substrate, Ge NIs distributed in an ordered manner in one or two dimensions can be achieved^{[34, 18]}. In addition, the Ge NIs grown on patterned Si substrates show dramatically improved size, shape and composition uniformity compared to that grown on flat Si surfaces^{[37, 38]}. The crystal and optical quality of the ordered QDs obtained on patterned substrates is also better than random QDs grown on flat Si substrate^{[39, 40]}. Growth of Ge on patterned Si surfaces is also highly flexible in fabricating versatile Ge nanostructures with attractive features. By using the strain effect induced vertical alignment growth nature of Ge islands, multilayer ordered Ge QDs with perfect 3D ordering could be achieved, e.g. the 3D Ge QDCs^[22]. Besides, by carefully tailoring the pattern features and optimizing the growth parameters, very low density site-controllable single Ge NIs^[41] and QDM^[42] can both be realized.



Various kinds of substrate patterning techniques have been demonstrated to be effective in fabricating nanostructure patterns on Si surfaces for site-selective growth of Ge, e.g. nanoimprint lithography^[40], extreme ultraviolet (EUV) interference lithography^[1], electron-beam lithography (EBL)^[36], X-ray holographic lithography^{[43, 26]} and nanosphere lithography (NSL)^[44]. Controllable growth of nanostructures using pre-patterned substrate is also effective for group III–V semiconductors^{[45, 46]}, and thus is a widely applicable and feasible approach in this area. In this section, the recent progress achieved in controllable growth of Ge Nis on patterned Si surfaces is reviewed.

3.1
Ordered Ge nanoislands

Our group has done extensive studies on the controllable growth of Ge islands on periodic patterned Si surfaces, achieving a number of ordered Ge NIs in various geometries^{[41, 44, 47, 52–55]}. Ordered Ge NIs on Si surfaces with areal densities ranging from 4 × 10⁵ to 1 × 10¹⁰ cm^?3 have been realized via pattern-assisted growth.



A new scalable chemical approach to fabricate an ordered pit-pattern on Si (001) surfaces with tunable pit period and size, namely NSL^[44], in a hexagonal geometry was developed. 2D ordered Ge NIs are realized by MBE growth on such NSL-pit-patterned Si (001) substrates^{[44, 47]}. Fig. 3(a) shows the AFM image of Ge NIs grown on such pit-patterned Si substrates by depositing Ge of nominally 8 MLs at a growth rate of 0.06 ?/s at 550 °C. A 120-nm-thick Si buffer layer was firstly deposited at a growth rate of 0.5 ?/s while ramping the substrate temperature from 450 to 550 °C before Ge deposition. It is clearly seen that hexagonally ordered dome-shaped Ge NIs with a period of 220 nm were successfully achieved. Those NIs show high size uniformity, as shown by the size statistical results in Fig. 3(b). A height dispersion of 4.1% was achieved^[47].






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Figure3.
AFM images (1 × 1 μm²) of (a) a pit pattern with a periodicity of 200 nm, (b) a pit pattern after Si buffer layer growth, (c) ordered Ge NIs after deposition of 10 ML of Ge on a pit-patterned Si substrate, and (d) randomly distributed Ge NIs grown under the same conditions on a plane substrate. The unit of the height bar is nm. Adopted from Ref. [44].




3D ordered Ge NIs can also be fabricated by using multilayer self-assembly on pit-patterned Si (001) substrates by MBE^[47]. The lateral ordering of Ge NIs results in remarkably improved size uniformity in comparison with random NIs on flat substrates. A much stronger and narrower photoluminescence (PL) peak was observed from ordered NIs than from random ones. Such an enhanced PL signal is attributed to the high density of states and the uniform distribution of excitons in the ordered and uniform NIs, which can efficiently suppress the Auger effect and the Coulomb screening effect.



High density and 3D ordered Ge QD arrays are referred to as QDCs^[22]. A perfectly regimented QDC can be formed given that the QDs are 3D ordered, the QDs are small and homogeneous, and the interdot spacing is small enough for strong overlap of carrier wave-functions. In 3D artificial QDCs, the discrete energy levels of a single QD will split into extended states and emerge as 3D minibands^{[48, 49]}. Moreover, coupling within QDCs leads to a drastic increased density of state of carriers, compared to single dots or quantum well superlattices^{[50, 51]}.



We have successfully realized 3D Ge QDCs on pit-patterned Si (001) substrate^[52–54] by using a patterned substrate with a high density of NSL-pits and optimizing the growth parameters. We systematically investigated the influences of growth parameters on the growth of QDCs, including the Si buffer layer thickness, the Ge deposition amount for the first QD layer, the pit facet inclination angle, the Ge deposition amount in the subsequent QD layers, the Si spacer layer thickness and the growth temperatures. The optimized growth conditions were found^[53]. Figs. 4(a) and 4(b) show the AFM and TEM images of the 3D ordered ten-layer Ge QDCs. It is clearly seen that nearly perfect 3D ordering was achieved with the highest ever areal dot density of 1.2 × 10¹⁰ cm², and that the lateral and the vertical interdot spacings were ~10 and ~2.5 nm, respectively. The vertical and the in-plane periods are 7 and 100 nm, respectively, as illustrated in Fig. 4(c). The coupling effect and the formation of electron minibands are identified in the obtained 3D Ge QDCs by optical emission measurements^[53]. The PL intensity of the 3D Ge QDCs shows dramatic enhancement as compared with that of the random QDs grown on flat Si surfaces with the same conditions. The PL spectra show non-phonon (NP) recombination and its transverse-optical (TO) phonon replica of excitons in QDs. In addition, with increasing excitation power, peak energies of both the NP and TO peaks remain nearly constant and the width of the TO peak decreases. These anomalous features of the PL peaks are attributed to miniband formation due to strong coupling of the holes and the emergence of quasioptical phonon modes due to periodic scatters in ordered GeSi QDs.






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Figure4.
(a) Surface morphology of the 15 layer uncapped Ge QDCs. Inset shows the FFT image. (b) HRTEM of a Ge QD column in 10 layer QDCs. (c) Schematic 3D structure of the Ge QDCs. Adopted from Ref. [54].




Ordered Ge NIs with very low areal density can also be obtained by MBE growth on nanohole patterned Si (001) substrate^[41]. Periods in the order of microns were realized, the record largest period being 15 μm. Figs. 5(a)–5(f) show the AFM images of the low density ordered Ge NIs with periods of 0.6, 1, 3, 5, 10 and 15 μm, respectively. It is clearly seen that no redundant islands exist on the flat regions between nanoholes. Only one island nucleates in a nanohole on the patterned surfaces. Those low density and site-controllable Ge NIs are beneficial for versatile novel optoelectronic application, e.g. single electron transistors (SETs) and cavity integrated optical devices. From the height-profile evolution of the NI with Ge deposition, it was found that the nanohole filling started at the initial Ge deposition, indicating an immediate nucleation and growth of NIs inside the nanoholes. Such a phenomenon is explained by a lower SCP inside the nanoholes. The optical properties of the Ge NIs are found to be improved remarkably after a post-growth rapid thermal annealing treatment, showing a high quality of the ordered NIs after thermal treatment.






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Figure5.
(Color online) Surface morphology of the ordered low-density Ge NIs grown on the patterned Si substrate with a period of (a) 0.6, (b) 1, (c) 3, (d) 5, (e) 10 and (f) 15 μm, respectively. The insets in (d)–(f) are enlarged AFM micrographs of a single Ge NI in corresponding periods. The white arrows in (f) indicate the NI positions for a better view. Adopted from Ref. [41].

3.2
Ordered Ge nanorings

Long-range ordered Ge NRs on patterned Si (001) substrate are realized on pit-patterned Si (001) substrate by MBE^[19]. A modified approach was developed to fabricate an ordered pit-pattern on Si (001) surfaces with a large period but a small pit-size using NSL and reactive ion etching (RIE) technology. The pit size and period were readily tunable by varying the diameter of the polystyrene spheres (PS), the RIE parameters and the wet chemical etching time. With proper etching time, ordered inverted pyramid-like pits with four {111} facets were formed. The pit-pattern has a relatively large period of 430 nm (the same as that of the PS pattern) and a small pit-size. The average side length and the depth of the square pits were 90 and 40 nm, respectively.



The ordered Ge NRs are transformed from ordered Ge NIs by capping of Si at high temperatures. The growth procedure contains two steps. First, ordered Ge NIs are grown by sequentially deposition of the Si buffer layer and Ge island seed layer. Then a Si spacer layer is deposited followed by the growth of a second Ge island layer. After that, a Si capping layer is deposited at 640 °C to evolve the NIs to ring-shaped structures. Figs. 6(a) and 6(b) show the 3D surface morphologies at the first Ge island seed layer and the final Ge NRs, respectively. Both ordered Ge NIs and NRs were successfully realized with the same period of 430 nm. The mechanism behind the shape transformation from Ge NIs to NRs on patterned substrate is the Ge out-diffusion and Ge-Si interdiffusion during the Si capping process at high temperatures, which is similar to that on flat Si substrate^[55]. The formation of ordered Ge NRs was found to critically depend on the pattern period. A smaller period leads to the formation of a GeSi alloy network between NIs, and the NIs can scarcely transform into NRs^[56]. The Si capping layer thickness is found to play an important role in the shape transformation of Ge islands. Si capping layer thickness less than 3 nm and larger than 3.5 nm lead to incomplete and over transformation, respectively. The optimized Si capping layer thickness is ~3 nm. A post-growth annealing treatment at 610 °C for 30 min in a high vacuum improves the size uniformity of the ordered Ge NRs. The size dispersion obtained from the statistical size distribution of the NR width for the annealed 3 nm-thick-Si capped NR sample is fitted to be ~10% using a Gaussian function. Experimental results also indicate that the high growth temperature and the long-period of annealing time can improve the NR uniformity.






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Figure6.
(Color online) 3D AFM images of (a) ordered Ge NIs and (b) ordered Ge NRs. Adopted from Ref. [19].

3.3
Coupled Ge quantum dot molecules

QDMs are complex nanostructures consisting of several coupled QDs in close proximity. Localized electrons or holes may transfer between adjacent QDs via quantum tunneling, leading to the formation of delocalized states that are truly molecular in nature, with bonding and antibonding orbital states^[58]. A number of unique and fascinating properties have been discovered in QDMs, e.g. the formation of delocalized states of single holes leads to tunable g factors for the holes^[59], reversal of the orbital character of the ground state^[60], novel spin-flip tunneling^[61] and exciton spin memory^[62]. QDMs have been demonstrated in various semiconductor material systems, e.g. InAs QDMs^{[59, 61, 63]}, PbSe QDMs^{[64, 65]} and SiGe QDMs^{[66, 67]}. Changes to the structure of the QDM can lead to surprising properties, which are pretty suitable for studying the quantum charge or spin physics in interacting QDs.



Fourfold symmetric GeSi QDMs have been realized using a self-limiting growth of Si_0.7Ge_0.3/Si (001) films^[67] or strain-relieving effect^{[66, 68]}. The obtained QDs in QDMs show the size selection effect arises from efficient adatom trapping inside the central pit of the QDM. However, the controllability of the QDM morphology was still poor. In contrast, pattern-assisted MBE growth is a more feasible and robust route to obtain desired Ge QDMs. GeSi QDMs in various configurations were achieved on patterned Si (001) substrates, including the double QD (DQD), and the fourfold symmetric QDs.



Fig. 7 shows a specific QDM configuration consisting of one Ge QD at the center and four surrounding Ge QDs are obtained on pit-patterned Si (001) substrate^[57]. A periodic Si dot-pattern was firstly fabricated in a large area using a modified NSL approach and RIE. The Si dots show a dome shape in a hexagonal distribution with a mean height of ~22 nm. After cleaning and desorption, a Si buffer layer was then grown, leading to a drastic change of the morphology of the Si dots into a truncated pyramid with sidewalls of {11n} facets via material redistribution driven by energy. The height of the Si dots was also considerably reduced to ~5 nm. Fig. 7(a) shows the growth results after depositing of 5 MLs Ge at a growth rate of 0.05 ?/s with the substrate temperature increasing from 400 to 480 °C. It is found that Ge QDMs are formed with a small mount-like dot in the center and four dome-like dots at the edge. Fig. 7(b) shows the enlarged 3D AFM micrograph of the Ge QDM. The height profiles for the Si dot, the dot after buffer layer growth and the Ge QDM are shown in Fig. 7(c). For comparison, the AFM image of the Ge QDs under the same growth parameters is also given in Fig. 7(d). Those results clearly indicate that the preferential growth of Ge QDs on patterned substrates is significantly affected by the geometrical profiles of the pattern. The 2D SCP calculation shows four SCP minima located at the four {11n} facet edges that coexist around the Si dot, which exactly correspond to the GeSi dot nucleation positions. This result again verifies that the site-selective nucleation nature of Ge on patterned Si surfaces is essentially driven by the SCP difference. Ge atoms tend to nucleate preferentially in sites where the SCPs are lowest.






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Figure7.
(Color online) (a) AFM image (1 × 1 μm²) of the Ge QDMs after deposition of 5 ML Ge on Si dot-patterned substrate. (b) An enlarged single Ge QDM. (c) The height profiles along the dashed lines in (a). (d) AFM image (1 × 1 μm²) of the Ge QDs after deposition of 5 ML Ge on a flat substrate. Adopted from Ref. [57].




Ge double quantum dot (DQD) molecule structure is also realized on patterned Si surfaces with nanopits elongated along Si <110>. Elongated nanopits along Si <110> with different elongation ratios are first fabricated by combing EBL and RIE. After chemical cleaning, such patterned Si substrates are loaded into the MBE growth chamber. By optimizing the growth parameters, including the Ge deposition amount, growth rate, and substrate temperature, we successfully realized the growth of Ge DQD molecules, as shown in Figs. 8(a)–8(d)^[69]. It is clearly seen that two pyramid- or dome-shaped dots in close proximity to each other aligned along the nanohole elongation direction were formed in the nanohole. The interdot spacing could have a continuous increase with increasing the nanohole elongation ratio, as shown in Fig. 8(e). The DQD growth evolution as well as the Ge elemental distribution in the DQDs were both investigated in detail^[69]. The two dots in a DQD show unsymmetrical features in both size and composition due to the asymmetric nanohole profiles after Si buffer layer growth. Moreover, whether a single or a double QD formed in a given nanohole was found to be determined by the growth temperature of the Si buffer layer, SCP calculation results show that there are two SCP minima in close proximity to each other inside the elongated nanohole, which are the kinetic reason for the nucleation and growth of a DQD inside the nanohole.






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Figure8.
(Color online) AFM micrographs of a Ge DQD unit-cell grown in nanoholes with elongation ratios of (a) 3, (b) 4, (c) 5 and (d) 6. (e) The interdot spacing as a function of r. Image size: 500 × 500 nm². Adopted from Ref. [69].

4.
Ge nanowires grown on vicinal Si surfaces

The vicinal substrate is a naturally patterned substrate, hereafter named Si (001)/θ, where periodic atomic steps are perpendicular to the miscut direction. The shapes of the Ge nanostructures can be modified by the miscut angle, which exhibit asymmetrical shapes and can even become NWs on a specific crystallographic plane^[70–72]. Although the shapes of Ge nanostructures are different, these structures are naturally bordered by {105} facets due to the energetic stability^[70]. Further, the steps on vicinal substrates essentially affect the thermodynamics and growth kinetics of self-assembled Ge nanostructures, which make the nucleation and the evolution more complex than on normal Si (001) substrate. The fourfold symmetry of the elastic field is broken by the substrate miscut, producing the direction of low elastic interaction between the Ge nanostructures^[73].



We have done extensive investigations on the growth of Ge nanowires grown on vicinal Si surfaces^{[20, 75–77]}. The atomic nucleation and nanostructure formation behaviors and the associated growth kinetics are systematically studied. The nucleation of the Ge islands is greatly affected by the degree of the miscut angle. By slightly changing the miscut angle, the density of the Ge islands is significantly enhanced, because the formation energy of the Ge island decreases substantially with the increase of miscut angle^[20]. Meanwhile, highly dense Ge QDs are obtained on the high miscut due to the existence of an additional energy barrier for adatoms diffusing over steps^[20]. For the substrate with a miscut angle of 8°, the specific crystallographic plane can result in horizontally elongated NWs^[72]. The growth mode and evolution transition of the NWs are markedly different from those on the flat Si (001) substrate^{[72, 74]}.

4.1
Ordered Ge nanowires

Generally, self-assembled Ge NWs can be obtained on a vicinal Si (001) surface misoriented toward the [110] direction by 8 degrees^{[75, 76]}. The Ge NWs are compactly aligned on the surface and bordered by {1 0 5} facets. Here, we systemically studied the self-assembly of Ge on the miscut Si (001) surface misoriented toward the [100] direction (Si (001)/ [100]θ)^[77]. Fig. 9(a)–9(f) show the growth results after 5.4 ML Ge deposition at 515 °C on Si (001)/[110] θ (θ = 0°, 3°, 5°, 7°, 9° and 11°). On the normal Si (001) substrate, hut clusters bordered by {105} facets are obtained at the low growth temperature, as shown in Fig. 9(a). Laterally aligned Ge NWs can be obtained on the vicinal surfaces with miscut angle from 3° to 9°, as shown in Fig. 9(b)–9(e). The lateral NWs are also compactly arranged. However, the NWs orient perpendicular to the miscut direction, which is remarkably different from the case of NWs on Si (001)/[110] 8°. More interestingly, statistical analyses of the surface morphologies versus the substrate orientations reveal that the NWs on the Si (001)/[100]θ substrates are bordered by stable (001) and (105)






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Figure9.
(Color online) AFM images (0.5 × 0.5 μm²) of the surface morphologies after 5.4 ML Ge deposition at 515 °C on Si (001)/[100] θ with, (a) θ = 0°, (b) θ = 3°, (c) θ = 5°, (d) θ = 7°, (e) θ = 9°, (f) θ = 11°, respectively. The miscut direction of [100] is denoted by the arrow. The unit of color bar is nm. Adopted from Ref. [77].




facets rather than the two {105} facets. The width of NWs on different Si (001)/[100] θ substrates are almost constant. Meanwhile, the thickness of the wetting layer beneath the Ge NWs shows a peculiar behavior and has a minimum at around the 6° miscut angle. The theoretical analysis based on the ATG model is carried out to explain the behavior of Ge NWs growth, which shows a very good agreement with the experimental results.



Systematic studies on PL spectroscopy of Ge nanowires reveal a typical type-II band alignment of Ge nanowires^[76]. However, full width of half maximum (FWHM) of PL peaks is nearly constant, which is attributed to the formation of a mini-band due to strong coupling of holes in closely neighboring nanowires. The magnetoresistance measurements (MR) of Ge nanowires are also studied, which reveal an asymmetrical MR versus magnetic field B^[75]. The magnetic field B_min corresponding to the minimum MR increases with increasing temperature and has a much larger value in the case of current perpendicular to the NWs than one parallel. The anomalous MR behaviors can be explained by taking into account the spin orbit coupling of holes which depends on the band structure and morphology of Ge NWs.

4.2
High density Ge nanoislands

Self-assembled Ge islands on Si (001)/[110] θ miscut toward the [110] direction are systematically studied^[20]. Fig. 10(a)–10(d) shows the growth results after depositing 1.8 nm Ge_0.7Si_0.3 alloy on Si (001)/θ substrates with θ = 0.2°, 2°, 4°, and 6°, respectively. In addition to the shape of GeSi islands, the density of self-assembled GeSi islands on Si (001)/[110] θ also clearly depends sensitively on the miscut angle θ. With 1.8 nm Ge_0.7Si_0.3 alloy deposition, there are just a few Ge islands on Si (001)/[110] 0.2° substrate, as shown in Fig. 10(a). With the miscut angle increasing from 0.2° to 4°, the density of Ge islands is remarkably enhanced, as shown in Fig. 10(a) and 10(c). Particularly, for the growth on Si (001)/[110] 4° substrates, dense and small Ge islands are obtained. The Ge islands are next to each other and cover the whole surface compactly. Density loss occurs on Si (001)/[110] 6° substrates due to the coalescence of neighboring QDs induced by an excess amount of GeSi alloy. Systematic studies of the Ge islands density with the miscut angles and the amounts of deposited GeSi alloys are done. The results reveal that extremely high density (~2 × 10¹¹ cm^?2) can be obtained by optimizing the miscut angle and the growth condition. Moreover, there is essentially no wetting layer on higher miscut substrates, which means a transition occurs from SK to VW growth mode for self-assembled Ge islands on higher miscut Si substrates. Combining with the theoretical calculation, we reveal that the critical nucleation volume on miscut Si (001)/[110] θ (θ > ~4.5°) tends to 0, meaning that the nucleation on such substrates can take place at the beginning of heteroepitaxial growth. Superior optoelectronic properties are observed from the dense Ge islands obtained from higher miscut substrate due to the stronger hole confinement in the Ge islands without wetting layer.






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Figure10.
(Color online) AFM images (1 × 1 μm²) of surface morphology after 1.8 nm Ge_0.7Si_0.3 growth on miscut Si (001)/<110>θ substrates, (a) θ = 0.2°, (b) θ = 2°, (c) θ = 4°, (d) θ = 6°. The miscut direction of <110> and angle are denoted by the arrow and the number. The unit of color bar is nm. Adopted from Ref. [ 20].




Superior PL properties are observed in these dense Ge islands on miscut Si surfaces. Temperature-dependent PL measurements have been performed, revealing a rather strong PL peak persistent up to 300 K, which is attributed to the good confinement of excitons in the dense GeSi QDs due to the absence of the wetting layer on the miscut substrate^[20].

5.
GeSi nanostructures grown on Si nanopillars

The fabrication and characterization of ordered Ge nanostructures on pit-patterned Si substrates have been systematically studied. However, the Ge nanostructures on pillar-patterned Si substrates have rarely been studied in detail. Fig. 11 shows the controlled Ge nanostructures on periodic Si (001) sub-micro pillars (SMPs), which are obtained by EBL and inductive coupled plasma etching^[78]. The SMP with a period T and a diameter D is denoted by $p_T^D$. Quantum rings (QRs) are obtained at the edge of SMPs on $p_{600}^{550}$ at 580 °C, as shown in Fig. 11(a). Fourfold symmetric Ge QDMs can be obtained on $p_{600}^{450}$ at the same conditions, as shown in Fig. 11(b). The results suggest that the edge of the top terrace of SMPs is a preeminent position for Ge nanostructures nucleation. On the smallest SMP $p_{450}^{350}$, a single quantum dot is formed at the center of SMPs instead of the edge of the top terrace, as shown in Fig. 11(c). These results suggest that the evolution of the self-assembled Ge nanostructures depends on the diameter of the SMPs. Such growth behaviors of Ge nanostructures are explained by the distribution of surface chemical potential affected by the surface morphology of SMPs. For the chemical potential of $p_{600}^{550}$, the edge of the top terrace has a ring-like potential minimum, as shown in Fig. 11(d). For the chemical potential of $p_{600}^{450}$, the potential minima is also located at the edge of the top terrace as shown in Fig. 11(e). However, the distribution of the potential minima is in fourfold stripes, rather than a continuous stripe. The discontinuity of potential minima can be attributed to the formation of {113} facets near the top terrace of SMPs. The smaller the pillars, the larger the {113} facets. For the case of $p_{400}^{350}$, the area of the potential minima is quite small, so that a single Ge island is obtained in the center of the top terrace. A scalable fabrication method based on NSL and reactive ion etching of Si is also carried out to obtain the SMPs, on which QRs and QDMs can also be grown^[79]. The Ge surface diffusion and nucleation are also investigated via growing Ge QDs on top of Si pillars, from which the diffusion length of Ge adatoms can directly be measured and determined by the radius of the pillars below^[79]. Besides that, a scalable SMP is fabricated by NSL and metal assisted chemical etching, around which GeSi coaxial quantum wells are obtained^{[81, 82]}. The Si SMPs embedded with Ge nanostructures can have unique properties. By designing the period and diameter of the SMPs, the modification and enhancement of the PL can be realized.






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Figure11.
(Color online) AFM images of the surface morphologies of SMPs of (a) $p_{600}^{550}$, (b) $p_{600}^{450}$ and (c) $p_{450}^{350}$, after 10 MLs Ge deposition at 580 °C, (d)–(f) are the corresponding 2D surface chemical potentials. Adopted from Ref. [78].

6.
Device applications

One of the key advantages for the controlled growth of Ge nanostructures is the site-selective nucleation of a single Ge QD, which is an enabling technology that will enable access to new and interesting physics associated with the optical or electrical behaviors in confined zero dimension semiconducting systems, as coupling of photons and matter will be enhanced and the transport of carriers will be quantized due to confinement. A number of cutting edge applications based on a single solid state QD, such as the single electron transistors^[83], single photon sources^{[84, 85]}, on demand polarization-entangled photons source^[86], low threshold laser oscillation^[87–89] and strong coupling effect such as vacuum Rabi splitting^{[90, 91]}, will become much more technologically feasible with the ability of controlling the nucleation of a single Ge QD at a pre-defined position.



Another important advantage of the controlled growth of Ge QDs comes from the fact that Ge is compatible with Si technology and able to emit light in the telecom-band. However, the light emitted by Ge QDs between 1.3 and 1.6 μm generally exhibits poor spectral purity and low luminescence intensity due to the indirect band gap nature and relatively large dot size^{[44, 47]}. Various approaches have been introduced to enhance the Ge QD’s light emission efficiency and select the emission wavelength^{[5, 92–94]}. One of the most promising methods is using resonant enhancement between the QD emission and the optical modes inside a photonic crystal micro or nanocavity^[95]. Enhanced PL output has been observed due to the coupling of the random distributed multilayer Ge QD emitters to leaky modes of photonic crystal slabs^[96]. However, since the locations of self-assembled QDs grown on flat substrate are random, the difficulty of achieving site-controlled SQD in an optical nanocavity has partially hindered the research of SQD-cavity systems. A monolithically integrated cavity quantum electrodynamics system, consisting of a single site-controlled QD embedded in a nanocavity, could fix the emitter location with respect to the cavity mode electric field maximum and significantly enhance the emitter-cavity coupling by optical resonance in the cavity.



Based on our progresses achieved in the growth of site-controlled low density Ge QDs^{[41, 69]}, we have recently demonstrated an optical nanocavity emission device by integration of a single Ge QD at the cavity mode electric field maximum of an L3 nanocavity on a silicon-on insulator (SOI) platform, which represents a scalable fabrication method and is highly suitable for large-volume fabrication of Si nanocavities with precisely embedded Ge single QDs^[97]. Strong resonant luminescence at telecom wavelengths from Ge SQD embedded in a modified PhC L3 cavity is observed up to room temperature. The enhancement factor of the fundamental resonant mode is ~1300, with an estimated Purcell factor ~60.



Figs. 12(a) and 12(b) show an atomic force microscopy (AFM ) micrograph of the site-controlled Ge QDs grown on nanohole-patterned SOI substrate with a dot period of 2 μm and a scanning electron micrograph (SEM) of the fabricated modified L3-type PhC with a cavity period of 397 nm, respectively. Statistical analysis reveals that the mean overlay error between SQD and cavity center is ±22 nm, indicating high overlay accuracy. The simulated electric field intensity profile (|E|²) at the plane of z = 0 (the center of the membrane) for the fundamental mode of the L3 cavity and the corresponding far-field pattern using three-dimensional finite-difference time-domain (3D-FDTD) are shown in Figs. 12(c) and 12(d), respectively. A strong light field is confined within a small mode volume of V_c ~ 0.67(λ/n)³ ~ 0.0645 μm³, where λ is the resonance wavelength of light in a vacuum. The Q factor of this design is ~20000. The far-field pattern is concentrated along the vertical direction and will produce high collection efficiency for a limited objective numerical aperture (N_A). Fig. 12(e) shows the 3D schematic structure of the finished device.






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Figure12.
(Color online) (a) AFM micrograph of the Ge QDs grown on the nanohole patterns with a period of 2 μm. The dotted PhC cavity pattern schematically shows the relative position between cavity center and SQD. (b) The SEM image of fabricated PhC L3 cavity with embedded Ge SQD. The three holes adjacent to the cavity are laterally shifted by 0.2a, 0.025a, 0.2a, respectively, shown with orange arrows. (c) The simulated electric field intensity profile (|E|²) at the plane of z = 0 (the center of the membrane) for the fundamental mode of the L3 cavity. (d) The simulated far-field pattern (electric field intensity profile, |E|²) for the fundamental mode of the L3 cavity. White concentric circles correspond to θ = 30°, 45°, 60°, 90° from the inner one to the outer one, respectively. (e) Schematic structure of the finished device. The red dot represents the single Ge QD in the top Si/Ge layer. Adopted from Ref. [97].




Strong Purcell enhancement of PL intensity is observed from the Ge QDs coupled to the PhC cavities. Fig. 13 shows the measured emission spectra of the Ge SQD-PhC cavity devices with a cavity period of 395 nm and a single Ge QD without cavity. Black and red curves represent the μ-PL spectrum of the L3 cavity and Si/Ge membrane with unprocessed Ge single QD array, respectively. Note that the PL spectrum of the unprocessed region is multiplied by a factor of 25 for better viewing. Several sharp resonant peaks are observed to dominate the spectrum over an almost flat and weak background emission in the μ-PL spectrum. These resonant peaks are identified as the PhC cavity modes, corresponding to the four theoretically predicted cavity modes noted as M0 to M3, respectively^[96]. The highest emission peak at 1498.8 nm represents luminescence from the fundamental cavity mode (M0 mode). Compared with the unprocessed region, the PL intensity is significantly enhanced. The enhancement factor, which is defined as the ratio of the resonant peak intensity to the PL intensity of the unprocessed Si/Ge membrane at the peak wavelength, is ~1318. Figs. 13(b) and 13(c) show the magnified graph of the PL spectrum for the emission peaks M0 and M3 in Fig. 13(a), respectively. The FWHM of peak M0 is fitted to be 349 pm using a Lorentz function. The corresponding Q factor is 4300. This experimental Q factor is reduced by the air holes’ fabrication errors and the free-carrier absorption of the photogenerated carriers. The peak M3 is located at 1334.1 nm with a FWHM of 1051 pm.






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Figure13.
(Color online) (a) PL spectra of a single Ge QD in an unprocessed membrane and an L3 nanocavity measured at T = 7 K with an excitation power of 460 μW. (b) and (c) Magnified graphs of the PL spectra for the emission peak labeled as “M0” and “M3” in (a), respectively.




PL emission spectra of such single Ge QD-Phc integrated devices with cavity periods ranging from 397 to 415 nm were also measured. The Ge QD-PhC cavity devices showed strong and sharp emission lines ranging from 1200 to 1600 nm, with the peak wavelength linearly redshifting with increasing the cavity period. A maximum Purcell factor of ~100 is obtained at a cavity period of 402 nm, which is attributed to the best coupling strength between the interband ground state transition of QD and the fundamental optical mode of cavity.

7.
Summary and outlook

The above results represent the state of the art nature in the topic of realization and application of controllable MBE growth of GeSi nanostructures. The diffusion length model as well as the surface chemical potential model have provided a good understanding on the growth kinetics of site-selective nucleation of GeSi nanostructures on patterned Si surfaces from the theoretical prospect, while the nucleation and growth of Ge islands or NWs on inclined surfaces are also well understood. The full control of the spatial geometry, periodicity, size, shape and strain of Ge NIs have been achieved on patterned Si substrates, showing the ability of realization of ordered Ge NIs, QDCs, ordered NRs, QDMs, etc. Growth of high density Ge NIs or ordered NWs has been realized on vicinal Si surfaces, while the associated growth kinetics and inclination angle dependences are also extensively investigated and well understood. Si pillars are also demonstrated to be an effective route to control the preferential nucleation of Ge and grow diverse Ge nanostructures, including NI rings, QD molecules, QWs etc. Optical microcavity device demonstrations using preferentially grown Ge nanoislands are also addressed, showing promising capability towards realization of single photon sources at 1550 nm. Besides that, several other groups have also made significant progresses in the fabrication, physical property characterization, and application of the controllable growth of GeSi nanostructures, such as Brehm et al. in Johannes Kepler University Linz^[98], Schmidt et al. in IFW Dresden^[3], Chen et al. in Shanghai Institute of Technical Physics CAS^[99], and Zhang in Institute of Physics CAS^[100]. These results help us to fully understand the physics of site-controllable growth on the one hand, and on the other hand build a solid base for both electrical and optical device applications of the controllable GeSi nanostructures.



In closing, further development trends in this topic rely on the exploration of diverse optoelectronic device applications by utilizing the abilities of controlled growth of GeSi nanostructures. (e.g. single electron transistors based on a single Ge island or NW, or electron-injected single photon emission devices using a single Ge island.) The dot ordering and alignment approach provides a scalable, low cost and CMOS compatible way to fabricate Si-based single QD-cavity systems, showing a promising candidate for Si-based non-classical devices. Further efforts are also necessary to realize telecom band Si single photon sources and Si-based integrated cavity QD emission systems. In addition, the electronic coupling effects of adjacent Ge nanostructures render the Ge 3D QDCs or QD molecules attractive for the exploration and understanding of novel quantum physics phenomena. However, the challenges remain the difficulty in realizing confined Ge nanostructures with true quantized energy levels, which could be limited by the relatively low barriers between the GeSi alloy nanostructures and the Si matrix. For instance, a true Ge QD could only be realized given the average Ge content inside the QD exceeds 90% and the dot size is in proximity to that of an InAs QD, especially in lateral directions. Exploration of further advanced growth techniques that can simultaneously realize the site-control of Ge nanostructures and the ultra-small sizes and ultra-high Ge contents is the next step towards attractive device applications of the controllable Ge nanostructures.



Even though some progresses have been made in enhancing the luminescence efficiency of GeSi nanostructures via tailoring their spatial distribution or electronic coupling, to date GeSi nanostructures have not been applied successfully in optoelectronic devices or systems compared with III-V nanostructures, which is limited by their low quantum efficiencies that are still 1–3 orders of magnitude lower compared with III-V nanostructures. The essential difficulty comes from the fact that their inherent indirect band gap nature remains unchanged. Indirect to direct band gap structure modification via tensile-strain or incorporation of Sn could be promising routes to circumvent the bottleneck of low quantum efficiency. Direct band gap structures have already been successfully realized in tensile-strained Ge^[101] or GeSn alloys^[102]. Prototype laser diodes^[103] and high quantum efficiency photo detectors^[104] using bulk GeSn or tensile-strained Ge films have also been demonstrated recently. These achievements highlight that introduction of tensile strain or incorporation of Sn in GeSi nanostructures could be effective to improve the quantum efficiency and to facilitate their applications in optoelectronic devices. However, several practical difficulties such as fabrication of highly reliable and scalable stressors for tensile-strain Ge, increasing the solubility of Sn in growth of GeSn, and suppression of the dislocation defect densities have to be further addressed prior to practical device applications.