Light emitting or light absorbing elements

Abstract

The present invention relates to a light emitting element comprising a light emitting portion composed of a Hex-Si 1‑x Ge x compound material, said Hex-Si 1‑x Ge x compound material having a direct band gap for emitting light. The present invention also relates to a light absorbing element comprising a light absorbing portion composed of a Hex-Si 1‑x Ge x compound material, said Hex-Si 1‑x Ge x compound material having a direct band gap for absorbing light.

Description

Technical Field

[0001] The present invention relates to devices or optoelectronic components for achieving efficient light emission from Group IV materials.

[0002] In particular, the present invention relates to a light-emitting element or a light-absorbing element including a light-emitting portion or a light-absorbing portion of a hexagonal Ge and SiGe alloy. Background Art

[0003] Achieving efficient light emission from Group IV materials has been the "holy grail" of silicon technology for decades, and despite significant effort, it remains elusive. Silicon is the backbone of the semiconductor industry because of its many advantageous properties. Unfortunately, due to its indirect band gap, Si cannot emit light efficiently. As early as 1973, it was predicted that hexagonal Ge (Ge) would have a direct band gap and therefore could emit light. However, hexagonal Ge was believed to have a small matrix element and therefore would not emit light efficiently.

[0004] It is therefore an object of the present invention to provide a method for producing optoelectronic applications and / or optoelectronic products comprising Si- and Ge-based emitters or components. Summary of the Invention

[0005] According to one aspect of the present invention, a light-emitting element is provided, wherein the element comprises a light-emitting portion, wherein the light-emitting portion comprises Hex-Si 1-x Ge x Compound material, the Hex-Si 1-x Ge x The compound material has a direct band gap for emitting light.

[0006] In particular, the Hex-Si 1-x Ge x The compound material is constructed to emit radiation at 300K with a B coefficient of 0.7×10 -10 cm 3 / s<B rad <11×10 -10 cm 3 / s, and more particularly, the radiation emission B coefficient at 300K satisfies 0.7×10 -10 cm 3 / s<B rad <8.3×10 -10 cm 3 / s of light.

[0007] In an advantageous embodiment, the Hex-Si 1-x Ge xThe compound material is configured to emit light between 1.8 μm (for x=0.65) and 3.5 μm (for x=1.0).

[0008] The light-emitting element according to any one of the preceding claims, wherein the Hex-Si 1-x Ge x The compound material includes the hexagonal Si structured to emit light between 1.5 μm and 7.0 μm. 1-x Ge x Strained quantum well structures of different compositions of compound materials.

[0009] In another embodiment of the present invention, the Hex-Si 1-x Ge x The compound materials exhibit direct bandgap emission with sub-nanosecond recombination lifetime.

[0010] In another embodiment, the Hex-Si 1-x Ge x The compound material shows a linear dependence of the photoluminescence intensity on the excitation power.

[0011] According to another aspect of the present invention, a light absorbing element is provided, wherein the light absorbing element comprises a light absorbing portion, wherein the light absorbing portion comprises Hex-Si 1-x Ge x Compound material, the Hex-Si 1-x Ge x The compound material has a direct band gap for absorbing light.

[0012] According to a preferred embodiment of the light emitting element or light absorbing element of the present invention, the Hex-Si x Ge 1-x The x of the compound material is defined as 0.2<x<1.0, or 0.6<x<1.0, or 0.2<x<0.99, or 0.2<x<0.9, or 0.6<x<0.9, or 0.6<x<0.99.

[0013] In another advantageous embodiment, the light emitting element or light absorbing element according to the present invention is defined as comprising an integral structure comprising the Hex-Si 1-x Ge x Cub-Si substrate of compound material.

[0014] According to the present invention, different types of light-emitting elements are obtained, which exhibit efficient light emission from direct-bandgap hexagonal Ge and SiGe alloys. Hexagonal SiGe realizes an ideal material system that fully combines electronic and optoelectronic functions on a single chip, thus opening the way to new device concepts and information processing technologies.

[0015] In particular, Si in the light-emitting or light-absorbing part 1-x Ge x The compound material can be a quantum dot, a quantum well or a bulk semiconductor light emitting / absorbing body or part.

[0016] In addition, the present invention relates to a method for manufacturing a light-emitting element, the method comprising the following steps: providing a substrate composed of a Group III-V compound semiconductor; depositing a Group 11 element catalyst in the form of one or more nano-disk-shaped seeds on the substrate; growing one or more Group III-V compound semiconductor nanowires; removing the one or more Group 11 element catalyst seeds; and epitaxially growing Si on the one or more Group III-V compound semiconductor nanowires. x Ge 1-x shell.

[0017] In particular, the step of growing one or more Group III-V compound semiconductor nanowires is performed using a Group 11 element catalyst-assisted chemical vapor deposition process.

[0018] Specifically, the depositing step includes annealing a Group 11 element catalyst seed crystal at a temperature higher than a eutectic temperature at which an alloy is formed between the catalyst seed crystal and the substrate, and forming an alloy between the seed crystal and the substrate.

[0019] More specifically, the growing step includes the steps of introducing trimethylgallium (TMGa) and arsine (AsH3) as material precursors, and more specifically, growing the nanostructured carbon nanotubes at a set temperature of 650°C and with a temperature of χ TMGa =1.9×10 -5 mol, The mole fraction is carried out.

[0020] In addition, Si is epitaxially grown on one or more III-V compound semiconductor nanowires. x Ge 1-x The step of shelling comprises the steps of introducing gaseous precursors GeH4 and Si2H6 at a temperature of 550-750°C, more particularly at a temperature of 600-700°C.

[0021] Next, the Group 11 element catalyst-assisted chemical vapor deposition process is a metal organic vapor phase epitaxy (MOVPE) process.

[0022] In addition, in the method according to the present invention, Si x Ge 1-x The x of the shell is limited to 0.2<x<1.0, or 0.6<x<1.0, or 0.2<x<0.99, or 0.2<x<0.9, or 0.6<x<0.9, or 0.6<x<0.99. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Although any other forms may fall within the scope of the method and apparatus described in this summary, specific embodiments of the method and apparatus will now be described by way of example and with reference to the accompanying drawings, in which:

[0025] Figure 1 Depicts the hexagonal Si 1-x Ge x The calculated band structure of

[0026] Figure 2 Depicts Hex-Si 1-x Ge x Overview of the material system;

[0027] Figure 3 Depicted are Hex-Ge and Hex-Si 0.2 Ge 0.8 the launch of

[0028] Figure 4 Depicts a single Hex-Si 0.2 Ge 0.8 Time-resolved photoluminescence measurements of nanowires;

[0029] Figure 5 Depicts Hex-Si 1-x Ge x Tunability of the direct band gap of the alloy;

[0030] Figure 6 Schematic diagram depicting the nanowire growth process;

[0031] Figure 7 Depicts the crystal quality of the WZ GaAs nanowire core;

[0032] Figure 8 A representative SEM of Hex-Ge sample is depicted;

[0033] Figure 9 Depicts Hex-Si 0.25 Ge 0.75 Atom probe tomography characterization of

[0034] Figure 10 Depicts Hex-Si 1-x Gex Full range of symmetrical (0008) reflections;

[0035] Figure 11 Depicts the comparison between Hex-Ge samples of different generations;

[0036] Figure 12 Depicts Hex-Si with different qualities 0.2 Ge 0.8 Arrhenius diagram;

[0037] Figure 13 The calculated band structure of hexagonal Ge is depicted;

[0038] Figure 14 Describes the Si 0.78 Ge 0.22 Experimental observation of efficient light emission;

[0039] Figure 15 shows a schematic diagram of the entire growth process according to the present invention;

[0040] Figure 16 Depicted are images of representative GaP / Si / SiGe core / multishell nanowires;

[0041] Figure 17 An example of a hexagonal GaP / Si / SiGe core / multishell nanowire is depicted;

[0042] Figure 18 Depicts a cross-sectional study of GaP / Si / SiGe core / multi-shell nanowires;

[0043] Figure 19 Depicts the incorporation of Ge into SiGe layers or shells and the growth pattern;

[0044] Figure 20 The linear dependence of SiGe thickness on growth time is depicted;

[0045] Figure 21 Depicts atomic bilayer stacking in the lonsdaleite (2H) and diamond structure (3C) phases of Ge, where the crystal structure has been generated using VESTA;

[0046] Figure 22 The band structure of 3C-Ge calculated using the HSE06 and MBJLDA functionals is depicted (a). The irreducible representation of the relevant high-symmetry states in the bandgap region is given in two-group notation with VBM set to zero.

[0047] Figure 23The band structure of 2H-Ge calculated using the HSE06 and MBJLDA functionals is depicted, where the irreducible representation of the relevant high-symmetry states in the bandgap region is given in two-group notation, and VBM is set to zero.

[0048] Figure 24 The optical transition matrix elements |p| for the lowest interband transitions in 2H-Ge along high-symmetry lines near Γ are plotted, where the matrix elements have been calculated for ordinary (E⊥c) and extraordinary (E||c) polarizations using the HSE06 and MBJLDA functionals, respectively.

[0049] Figure 25 The radiative lifetimes t of 3C-Ge and 2H-Ge versus temperature, calculated only at the Γ point (dashed lines) or integrated over the entire BZ (solid lines), are shown, where the results of the HSE06 and MBJLDA functionals are given.

[0050] Detailed Description of the Figures

[0051] The smooth merging of the fields of integrated electronics and photonics using a single material family and CMOS-compatible process flows is a major goal of distributed information technology. Silicon (Si) crystallized in its usual cubic (diamond) structure has dominated the electronics industry for more than half a century. However, cubic silicon (Cub-Si), germanium (Cub-Ge), and Si 1-x Ge x Alloys are indirect bandgap semiconductors that cannot emit light efficiently.

[0052] Figure 1 Depicts the hexagonal Si 1-x Ge x The calculated band structure of: In particular, Figure 1 A-1B-1C-1D show the DFT calculation results of the band structures of Cub- and Hex-Si and Ge. Figure 1 E depicts the same as Hex-Si 1-x Ge x A parabolic fit as a function of the Ge content in the alloys is consistent with the energy of the emission band minimum. Figure 1 F plots the radiative lifetime of a GaAs with a 10 19 / cm 3 Different n-doped Hex-Si 1-x Ge x The radiation lifetime of the composition.

[0053] Figure 1The band structure of Cub-Si presented in A is well known, with the lowest conduction band (CB) minimum close to the X point and the second lowest minimum at the L point. As such, it is a typical example of an indirect bandgap semiconductor that, despite much effort, has not been used for efficient light emission. By changing the crystal structure from cubic to hexagonal, the band gap along the <111> Due to the symmetry of the crystal direction, the energy band at point L folds back to point Γ.

[0054] like Figure 1 As shown in Figure B, for hexagonal Si (Hex-Si), this leads to a local conduction band minimum at the Γ point, whose energy is close to 1.7 eV. Obviously, Hex-Si is still indirect because the lowest energy conduction band minimum is at the M point, close to 1.1 eV. Figure 1 As shown in C, Cub-Ge also has an indirect band gap, but unlike Si, the lowest conduction band minimum is located at the L point. As a result, for Hex-Ge, Figure 1 As shown in the calculated band structure in D, the band folding effect leads to a direct band gap at the Γ point, which is close to 0.3 eV.

[0055] To investigate how the direct band gap energy can be tuned by alloying Ge with Si, the Hex-Si ions were calculated using ab initio density functional theory (DFT) and the group expansion method for isostructural hexagonal binary alloys using so-called ab initio calculations detailed in the following paragraphs. 1-x Ge x (for 0<x<1) band structure. Figure 1 Selected results presented in E indicate that random Hex-Si 1-x Ge x The alloy's emission band gap at high symmetry points in the Brillouin zone is composition-dependent. Notably, for x > 0.65 (curve labeled M), a direct band gap is predicted at the Γ point, with its size tunable over an energy range of 0.3–0.7 eV. This spectral region is technologically significant for many potential applications, including optical interconnects in computing, silicon quantum photonic circuits, and optical sensing.

[0056] With respect to the ab initio calculations, it should be noted that all calculations were performed with the projected augmented wave method using density functional theory (DFT) as employed in the Vienna Ab Initio Simulation Package (VASP) A according to the present invention. A plane wave cutoff of 500 eV was used, and Ge 3d electrons were included as valence electrons. Brillouin zone integration was performed using a 12×12×6Γ centered k-point grid for hexagonal diamond Ge, and a 12×6×6Γ centered k-point grid for Si-Ge, ensuring convergence to the total energy of 1 meV / atom. For the structural calculations, the PBEsol exchange-correlation potential was used together with the Hellmann-Feynman force. The convergence threshold of . The modified Becke-Johnson exchange potential combined with the local density approximation (MBJLDA) is preferred for the electronic structure and optical properties because it ensures that the band gap is in good agreement with the experimental data available in the state of the art. Spin-orbit coupling is included in all calculations.

[0057] The alloys were studied using the cluster expansion method for isostructural hexagonal diamond binary alloys. For cluster expansion, the macroalloy was divided into clusters of 8 atoms obtained from the original wurtzite (WZ) unit cell. In this way, 46 different structures ranging from pure Ge to pure Si could be studied. As the cluster size increases, the method becomes more accurate, and calculations with clusters of 16 atoms confirmed that the changes in the thermodynamic mean are not significant. The radiative lifetime (τ) at temperature (T) was calculated using the following formula rad ):

[0058]

[0059] Among them A cvk represents the radiative recombination rate for the vertical optical transition between the conducting state |ck> and the valence state |vk>, where the single particle energy is ε ck and ε vk , the Fermi occupation function is f ck and f vk , and w k is the k-point weight. To reproduce the experimental conditions, n = 10 due to n-doping in the conduction band 19 cm -3 Charge carriers are included and the chemical potential of the electrons is modified accordingly. The radiative recombination rate is given by:

[0060]

[0061] where n eff is the refractive index of the effective medium (approximately set to the experimental value of cubic Ge, so n eff=5). The squares of the momentum matrix elements can be averaged over all directions corresponding to unpolarized light emission, as in Equation (A2), or for light polarized perpendicular to the linear axis, only the in-plane component is considered. A denser k-point grid is required to calculate the lifetime (72x72x36 for hexagonal diamond Ge and 24x12x12 for Si-Ge).

[0062] Figure 1 F shows that for different compositions, for polarization perpendicular to the c-axis, 10 19 / cm 3 n-doped Hex-Si 1- x Ge x Calculated radiation lifetime of alloy. Obviously, Hex-Si 1-x Ge x The radiative lifetime of the alloy is significantly lower than that of pure Hex-Ge, so the lowest energy transition is dipole-forbidden at the Γ point. This observation can be traced back to the fact that the random Hex-Si 1-x Ge x The symmetry in the alloy is reduced, which leads to the mixing of Ge s-states into the lowest conduction band wave function.

[0063] It has been found that Hex-Si 1-x Ge x The calculated lifetime of the alloy is close to that of III-V semiconductors such as GaAs.

[0064] Regarding the comparison with III-V semiconductors, Hex-Si 0.2 Ge 0.8 The measured lifetime at low temperatures is very similar to the recombination lifetimes reported in the prior art literature for III-V compound semiconductors, which are typically of the order of 1 ns. The prior art literature reports a temperature-dependent lifetime of 1 ns in core / shell GaAs / AlGaAs nanowires, which is very similar to that of the unpassivated Hex-Si nanowires according to the present invention. 0.2 Ge 0.8 The comparison of the quenching rate of the integrated photoluminescence intensity when increasing the temperature from 4K to 300K is quite favorable for Hex-SiGe, where Figure 3 As shown in C, this ratio varies between 15 and 100. 5 Prior art literature has observed quenching rates of approximately 200 for GaAsSbN / GaAs quantum wells. Prior art literature has also observed quenching rates higher than 100 for undoped GaN and up to 1000 for Mg-doped GaN.

[0065] The embodiment according to the present invention relates to Hex-Si 1-x Ge x Ge-rich alloys are attractive because they combine direct band gaps, strong optical transitions, and wavelength tunability. 1-x Ge x The Ge-rich alloy is indeed a direct-bandgap semiconductor, with strong emission and temperature-dependent nanosecond radiative lifetimes observed. The results show remarkable quantitative agreement with theoretical predictions.

[0066] exist Figure 2 In the figure, Hex-Si 1-x Ge x An overview of the material system. In particular, Figure 2 A shows a schematic diagram of hexagonal GaAs / Ge core / shell nanowires. Figure 2 B depicts the GaAs(111) B Tilt-view scanning electron micrograph of an epitaxial GaAs / Ge nanowire array grown along the

[0001] orientation on a substrate. Figure 2 C shows an overlay of HAADF-STEM and EDX images of a cross-sectional lamella of a representative GaAs / Ge core / shell nanowire, while Figure 2 D depicts the Aberration-corrected HAADF-STEM image of the GaAs / Ge structure obtained along the zone axis shows ABAB stacking along the

[0001] of the hexagonal crystal structure. Figure 2 E shows the hexagonal Reciprocal space diagram around the nanowire reflection. Figure 2 F plots Hex-Si as a function of Ge content 1-x Ge x Plots of in-plane lattice parameters (a) and out-of-plane lattice parameters (c) with errors less than the data notation used in the plots according to Table S1 below (lower and upper series of points):

[0067]

[0068]

[0069] Table S1. Hex-Si 1-x Ge x Extracted lattice parameters of samples: All measured Hex-Si with corresponding error values ​​extracted from XRD measurements 1-x Ge x Wurtzite lattice parameters of the samples.

[0070] In one embodiment of the method according to the present invention, Figure 2As shown in Figure A, a Ge-rich Si lattice-matched to Ge is grown around a thin (~35 nm diameter) WZ gallium arsenide (GaAs) core. 1-x Ge x alloy. A thin GaAs core is used to further reduce lattice strain and strain-induced defects. Figure 6 As outlined in the detailed description of , the Au catalytic particles used to grow the WZ GaAs nanowire template have been removed by wet chemical etching, and a thick (200-400 nm) Ge shell has been epitaxially grown on the WZ-GaAs. Figure 2 The overview scanning electron microscopy (SEM) image provided in B demonstrates the formation of arrays of Hex-GaAs / Ge-core / shell nanowires on the growth substrate. These nanowires are uniform in length and diameter and have smooth, well-defined {1100} side facets indicating single-crystalline nature.

[0071] Figure 2 C shows a cross-sectional electron scattered X-ray (EDX) spectrum, confirming the expected core / shell geometry. Figure 2 The high-resolution high-angle annular dark field (HAADF) transmission electron microscopy (TEM) image provided in D confirms the high-quality epitaxial growth of the Ge shell on the GaAs core and shows ABAB stacking along the

[0001] crystal direction; this is a characteristic of the hexagonal crystal structure. These observations clearly confirm the single-crystalline nature of the nanowires and their hexagonal crystal structure. 1-x Ge x The crystal quality and lattice parameters of samples of core / shell wires (where x>0.5) were investigated by X-ray diffraction (XRD) measurements using synchrotron radiation.

[0072] For all measured samples, at least three separate hexagonal reflections have been measured. For pure Hex-Ge samples, the azimuthal angles were varied to improve the fidelity of the extracted lattice parameters. Additionally, the cubic GaAs substrate reflection was always used as an anchor point in reciprocal space to correct for any possible alignment offsets. Based on the measured symmetric reflections, such as Figure 10 As shown in the full series in , the tilt of the lattice planes (

[111] ,

[0001] ) relative to the sample surface can be calculated and corrected. In addition, the Q of the WZ(0008) reflection 面外 The position enables calculation of the c-lattice parameter, which corresponds to the

[0001] -crystal direction. For certain Ge concentrations, the (0008) nanowire reflections coincide with the cubic (444) substrate reflections (cf. Figure 10), which complicates the systematic evaluation of symmetric RSMs, so asymmetric spatial maps have also been measured around reflections allowed only in the hexagonal lattice. The positions of the asymmetric reflections in reciprocal space enable the extraction of the in-plane as well as out-of-plane lattice parameters (a, c). Figure 2 A series of Ge concentrations for all measurements is shown. The peak positions of the reflections are significantly sensitive to the amount of Ge present in the alloy, with lower Ge concentrations resulting in lower lattice parameters (a and c) that are closer to the native lattice parameters of Hex-Si. For all shown RSMs, Q 面外 direction corresponds to the crystal

[0001] direction, and Q 面内 The direction corresponds to directions, both in the hexagonal system, represented by the four Miller-Bravais indices.

[0073] In order to accurately determine the peak position, all RSMs were corrected according to the peak position of the cubic GaAs substrate reflection to eliminate any angular alignment offset. A 2D Gaussian fit was then performed on the data set in q space before gridding to reduce the influence of possible artifacts from the gridding procedure. For plotting the data set, the irregularly spaced q coordinates (measured and converted from angular space) were gridded into a regularly spaced q coordinate system.

[0074] The overall results from the XRD measurements can be found in Table S1, where the measured lattice parameters are given for each measured Ge concentration. For all samples, the thin GaAs core (approximately 35 nm) is surrounded by a thick (several 100 nm) Si x Ge 1-x Shell surrounded, so the WZ-GaAs core material is x Ge 1-x The influence of lattice parameters can be ignored. x Ge 1-x The crystalline nature of the shell dominates the overall structure. Furthermore, Hex-Ge and WZ-GaAs are nearly lattice matched (see lattice parameters of WZ-GaAs), which means that for samples with high Ge concentrations (>60%), essentially no strain in the shell is expected, which is also confirmed by FEM simulations. This is an important aspect as it confirms the high fidelity of the obtained lattice parameters, especially for pure Hex-Ge. The errors given in Table S1 take into account the accuracy of the peak positions defined by the 2D fits described, as well as the scatter of the individual lattice parameter values ​​extracted from the evaluation of multiple peaks. For the error estimates, the instrumental resolution can be neglected as its contribution to the given errors is much smaller than the total error value.

[0075] XRD measurements have been performed at the German Electron Synchrotron (DESY) in Hamburg at the high-resolution diffraction beamline P08. For the diffraction experiments, a high-precision 6-circle diffractometer was used with a photon energy of 15 keV and a corresponding wavelength of The energy was carefully chosen to ensure a high photon flux while still being able to obtain a higher index of reflection, which is required for accurate measurements of the lattice parameters. The X-ray beam was shaped by a slit system and the resulting spot size on the sample was 200 μm (horizontally) × 100 μm (vertically), which is sufficient to irradiate several thousand nanowires at a time. For measuring the scattered signal from the wires, a Dectris-"Mythen" 1D X-ray detector was used; this detector provides a high dynamic range and, due to the small pixel size (50 μm), an increased angular resolution in 2θ compared to most 2D detectors. For converting the measured angular coordinates into reciprocal space coordinates and for all further data processing, such as 2D peak fitting and post-processing for mapping, the freely available software library "Xrayutilities" in combination with Python 3.6 was used.

[0076] Figure 2 E shows a Si 1-x Ge x A set of asymmetric reciprocal space maps (RSM) of shell samples, the Si 1-x Ge x The shells have nominal Si compositions x = 1, 0.92, 0.86, 0.75 and x = 0.63, respectively. The RSM shows that as a function of Ge concentration, only the hexagonal phase allows The higher the Ge concentration, the lower the Q 面外 and Q 面内 The more the hexagonal reflection shifts, the greater the value, which indicates that the out-of-plane lattice parameter (c) and the in-plane lattice parameter (a) increase. 面外 The narrow peak width of α leads to the conclusion that the overall crystal quality is very high, with an estimated stacking fault (SF) density of 2-4 SFs / μm along the crystal

[0001] direction.

[0077] These results are consistent with Figure 7 The TEM measurements performed on the same sample are in good agreement. Figure 10 The a-lattice parameter and c-lattice parameter as a function of Ge composition were determined from a set of symmetric and asymmetric RSMs as shown in Table S1. The results of these experiments are given in Figure 2 The data points for x>0.7 are located on the linear interpolation line between Hex-Si and Ge (according to Vegard's rule), which indicates that Si1-x Ge x The lattice strain in the shell is negligible.

[0078] The structural quality of the crystals was investigated by transmission electron microscopy (TEM). Two different sample preparation methods were used. In the standard axial analysis, the nanowires were mechanically transferred to a porous carbon TEM grid. For the cross-sectional TEM studies, a focused ion beam (FIB) was used to prepare the nanowires. In both cases, a JEMARM200F probe-calibrated TEM operating at 200 kV was used for high-resolution TEM and scanning TEM analysis. For the chemical analysis, a 100 mm TEM equipped with a microscope was used. 2 Electron scattered X-ray (EDX) energy spectrum measurement was performed using the same microscope with an EDX silicon drift detector. TEM thin sections were prepared in a FEI NovaNanolab 600i dual beam system. To this end, the nanowires were initially transferred from the growth substrate to a Si sheet using a Kleindiek nanomanipulator and then arranged parallel to each other. These nanowires were covered with metal deposition induced by electron beams and ion beams to protect them during the procedure. The thin layer was cut by milling with 30 kV Ga ions and continued to be thinned using subsequent steps of 30, 16 and 5 kV ion milling to minimize the damage caused by Ga in the area imaged with TEM.

[0079] like Figure 3 As shown in A and 3B, the Hex-Si 1-x Ge x The optical properties of the nanowires show further advantageous examples according to the present invention. In a first advantageous embodiment, pure Hex-Ge is used as the Hex-Si 1-x Ge x The binary endpoints of the alloy, and Si 0.20 Ge 0.80 is representative of binary alloys within the composition range where a direct band gap is expected.

[0080] Figure 3 Depicted are Hex-Ge and Hex-Si 0.2 Ge 0.8 The launch: Figure 3 A shows Hex-Ge (from 5.0 kW / cm 2 to 9.1kW / cm 2 peak on the left) and Hex-Si 0.2 Ge 0.8 (from 5.0kW / cm 2 to 9.1kW / cm 2Excitation density-dependent photoluminescence (PL) spectra of a sample grown at 4K (peak on the right side of the graph), measured at 4K. All spectra are normalized to their own maximum. A Lasher-Stern-Würfel (LSW) model fit of the Ge spectrum is included as a dashed line. The vertical black dotted line highlights the shift and broadening of the peak, indicating BtB emission. Figure 3 B shows the temperature dependence of the PL spectrum normalized to its own maximum value at 1.9 kW / cm 2 The excitation density was measured. A clear red shift and broadening are observed for both the left and right peaks with increasing temperature, indicating BtB recombination. Fits using the Lasher-Stern-Würfel (LSW) model are shown as dashed lines. Open circles show the PL maximum plotted in (B), while closed circles represent the band gap determined by fitting using the LSW model.

[0081] Regarding the fitting using the Lasher-Stern-Würfel (LSW) model, the observed photoluminescence spectra of Hex-Ge and Hex-SiGe are both composed of a single peak. The observation of a single photoluminescence peak is attributed to band-to-band (BtB) recombination. The absence of exciton effects at low temperatures is due to the presence of a single peak. Figure 9 The As doping level inferred by atom probe tomography is shown to be 9·10 18 cm -3 At this doping level, the shallow individual As dopants in small-bandgap semiconductors are expected to merge into a doping band, which in turn is expected to merge with the conduction band. GaAs nanowires with similar doping levels also exhibit a single-peak photoluminescence spectrum that is very similar to that found in Hex-SiGe.

[0082] To accurately determine whether the observed photoluminescence is due to BtB recombination, the experimental spectrum was fitted using the Lasher-Stern-Würfel (LSW) model. This model, which predicts the shape of the photoluminescence peak, is derived from the Planck-Einstein radiation law and is given by the following equation:

[0083]

[0084] In this formula, Δμ is the splitting of the quasi-Fermi level, and a(E) is the absorption coefficient. Parabolic bands have been used to model the absorption coefficient. Corrections for Urbach band tails and excitation-related Burstein-Moss shifts have been performed similarly to the prior art. Figure 3 A shows the fitting of photoluminescence measurements that are both temperature-dependent and excitation power-dependent.

[0085] The high-quality fit of the LSW model clearly demonstrates that the observed photoluminescence is due solely to BtB recombination. Crucial to the analysis is that the measured recombination lifetime is due to BtB recombination and not to, for example, impurity- or defect-related optical transitions. In accordance with the advantageous effects of the present invention, it should be noted that the derived carrier temperature exceeds 700 K at the highest excitation density.

[0086] Figure 3 C depicts the shrinkage of the band gap with temperature, which was fitted using Vina's equation as listed below.

[0087] Regarding the temperature dependence of the fundamental band gap, although the temperature dependence of the fundamental band gap is most commonly described by the Varshni equation, the Vina equation provides a more accurate description for high temperatures.

[0088]

[0089] Where a is a constant, b represents the electron-phonon interaction, and θ is the Debye temperature of the material. For the band gap of Hex-Ge, Figure 3 The Vina equation was fitted in C, where the following values ​​were obtained; a = 0.36 eV, b = 9.2 meV, and the Debye temperature was θ = 66 K.

[0090] Figure 3 Si shown in C 0.20 Ge 0.80 The contraction of the band gap follows a different behavior due to compositional fluctuations in the crystal. The initial rapid shift of the apparent band gap is likely due to carrier thermalization towards compositional pockets with lower band gaps, while the apparent deviation from Vina's law at high temperatures is most likely due to the fact that the spectrum should be interpreted as a convolution of the Fermi-Dirac distribution with a Gaussian broadening function due to compositional fluctuations, the details of which are beyond the scope of this paper.

[0091] Figure 3 Figure A presents power-dependent photoluminescence spectra recorded at a temperature of 4 K. The spectrum obtained for the Hex-Ge sample exhibits a narrow emission peak at the lowest excitation level studied. As the excitation density increases, the emission peak broadens towards higher energies and the peak blue-shifts by 19 meV. In order to understand the recombination mechanism, the data, which are both excitation-dependent and temperature-dependent, have been fitted with the Lasher-Stern-Würfel (LSW) model, which describes band-to-band (BtB) recombination in semiconductors. The model fit is included in Figure 3A and 3B, and confirmed that the observed spectrum of Hex-Ge can be explained by the BtB recombination process. Based on the fitting, it can be concluded that the high energy broadening is due to the increase in electron temperature, while the observed blue shift is due to the Burstein-Moss effect. Compared with the pure Hex-Ge sample, the Hex-Si 0.20 Ge 0.80 The line width of the sample is large (60 meV at the lowest excitation density compared to 14 meV for Hex-Ge), so it can not be fitted by the LSW model. 0.20 Ge 0.80 Only a slight blue shift caused by 6 meV excitation was observed in the sample.

[0092] Figure 3 B shows the composition of Hex-Ge and -Si 0.20 Ge 0.80 Temperature-dependent photoluminescence spectra of the sample were recorded. A clear asymmetric broadening was observed at high temperature, which can be attributed to the broadening of the tail of the Fermi-Dirac distribution according to the LSW model fitting, which supports the identification that the observed emission peak is due to the BtB recombination process. The band gap of Hex-Ge shifts from 3.5μm (0.353eV) at low temperature to 4.4μm (0.28eV) at room temperature, confirming that Figure 3 The expected band gap contraction for the BtB transition is depicted in Figure C. The temperature dependence of the fundamental band gap was discussed above for Si 0.20 Ge 0.80 The shrinkage of the band gap and a detailed fit to the Hex-Ge data yield a Debye temperature of 66 K.

[0093] Figure 3 D shows Hex-Ge (two light-colored dotted lines on the top) and Hex-Si 0.2 Ge 0.8 Temperature dependence of the sample integrated emission intensity (as a function of the inverse temperature) on the Arrhenius plot of PL intensity (two dark dotted lines at the bottom). All intensities are normalized relative to their corresponding intensities at 4K. The reduced temperature dependence at higher excitation densities indicates an approach to the radiation limit. A decrease in the integrated emission intensity (15-100 times) is observed when increasing the lattice temperature. As described above for Hex-Si 0.2 Ge 0.8 As depicted by the measured lifetime at low temperatures, the ratio of the photoluminescence emission intensities at 4K and 300K compares favorably with many well-developed III-V semiconductors. Figure 3As shown in Figure D, the decrease in intensity with increasing temperature is suppressed for higher excitation powers due to saturation of non-radiative processes. The fact that emission decreases with increasing temperature provides the first indication that Hex-Ge is a direct-bandgap semiconductor. In contrast, for indirect-bandgap semiconductors at low temperatures, excited carriers accumulate in the indirect minimum and therefore do not emit light efficiently. As the lattice temperature increases, the photoluminescence intensity is expected to increase as carriers are thermally excited to higher-energy direct minima where they can recombine with higher quantum efficiency.

[0094] Derived Hex-Si 0.20 Ge 0.80 Radiative lifetime and radiative emission efficiency. It is important to note that the measured decay lifetime is determined by the fastest recombination process, which can be radiative or non-radiative in nature. Therefore, it is crucial to choose experimental conditions where the measured recombination lifetime is dominated by pure radiative recombination. This can be achieved at low temperatures, as non-radiative processes are typically thermally activated and therefore negligible.

[0095] Regarding the temperature dependence of the integrated photoluminescence intensity, Figure 4 C presents a detailed Arrhenius analysis of the temperature dependence of the integrated PL. The goal is to provide quantitative information about the ratio between radiative and nonradiative recombination rates. To explain the temperature dependence of the photoluminescence emission intensity, we must first establish an appropriate recombination rate equation model. Because the donor is already incorporated into the donor band, which moves into the conduction band, we do not incorporate the donor energy level into the recombination rate equation model.

[0096] Based on the LSW analysis described above, it was concluded that the photoluminescence spectrum can be explained by band-to-band (BtB) recombination, with acceptor-related transitions having only a minor influence. Therefore, the recombination rate equation model is limited to a three-level system consisting of the conduction band, the valence band, and a "killer defect" characterized by the activated non-radiative recombination lifetime. The single-center model in the Reshchikov classification is then used, which is explained in more detail using a structural coordinate diagram. In this single-center model, the internal quantum efficiency (η) of the radiative emission is int ) According to The ratio of the radiative recombination rate to the total recombination rate varies with temperature. Figure 3 D shows the 68W / cm 2 Low excitation data collected under this condition can be used to calculate the non-radiative recombination rate using the equation by assuming that the non-radiative recombination rate is similar to that of III-V materials. Thermal activation was performed for fitting.

[0097] The excellent quality of the Arrhenius fit provides evidence that nonradiative recombination into an as yet unknown killer defect can indeed be explained by activated nonradiative recombination rates.

[0098] Therefore, the temperature dependence of the photoluminescence intensity can be expressed as

[0099]

[0100] where the photoluminescence quenching rate to the non-radiative center is given by In most semiconductors, there are different non-radiative recombination centers characterized by, for example, activation energies E A , E B and quenching rate R A , R B ,get

[0101]

[0102] For the samples indicated in Table S2 and whose Arrhenius plots are Figure 12 It is helpful to perform this analysis on three different generations of Hex-SiGe samples as shown in Figure 2. In sample C, an activation energy of E A =16±1meV and the quenching efficiency is R A =3±1, and the first quenching mechanism is at least partially due to surface recombination. B =91±2meV and R B =6·10 2 ±1 second quenching mechanism. These recombination rates imply that when both non-radiative channels are fully activated (room temperature) The first quenching mechanism appears to have disappeared in sample B grown at a higher temperature. In sample B, we only observed photoluminescence quenching at temperatures above 100 K, which was again tentatively attributed at least in part to surface recombination. B = 34 ± 5 ​​meV is tentatively explained by detrapping from localized states due to alloy fluctuations in the Hex-SiGe nanowire shell. Once the carriers are detrapped, they diffuse rapidly to the nanowire surface where they recombine non-radiatively. In sample A, because at 36 kW / cm 2 At the excitation density and So both quenching mechanisms have vanished, indicating that sample A remains within the radiative bounds out to 220 K. Sample A is likely of higher quality due to its thick hex-SiGe shell, which reduces the amount of surface recombination, and its length, which reduces the effects of re-evaporated arsenic (As) and gallium (Ga) from unwanted growth on the substrate. To be completely sure, we have regrown sample A and obtained the same temperature dependence as the first grown sample.

[0103] Figure 4 Depicted is a representation of a single Hex-Si 0.2Ge 0.8 A plot of the time-resolved photoluminescence measurements of the nanowires: Figure 4 A shows the Hex-Si crystals at different temperatures recorded from a single line of sample A according to the properties shown in Table S2 below. 0.2 Ge 0.8 Photoluminescence lifetime measurements of . All decay traces show single exponential decay and are vertically shifted for clarity.

[0104]

[0105] Table S2. Growth parameters for improved quality Hex-SiGe samples: The input temperature of the MOVPE reactor for SiGe-shell growth is listed here, as well as Figure 4 The resulting nanowire geometries are presented in B and 4B.

[0106] Figure 4 B shows three Hex-Si 0.2 Ge 0.8 Temperature dependence of wire lifetimes, represented by the upper, middle, and lower series of points, designated A, B, and C, for samples of progressively lower quality. As emphasized by the dashed lines, the onset of lifetime degradation due to non-radiative recombination shifts to higher temperatures for higher-quality wires. The inset shows a representative SEM image of a single nanowire from sample A used for lifetime measurements.

[0107] Figure 4 C depicts the Figure 4 The integrated photoluminescence intensity (as a function of temperature) of the same lines in B shows a nearly temperature-independent radiative efficiency for the best sample (A, upper series). The inset shows the excitation power dependence of the integrated photoluminescence intensity, which exhibits a slope very close to unity.

[0108] Figure 4 D shows a comparison of the low temperature (lighter set of dots) and room temperature (dark set of dots) lifetimes for a set of ~60 lines from sample A. The average lifetime shows a small decrease from 0.98 ns at 4K to 0.46 ns at 300K. Figure 4 E shows Figure 4 Comparison of the integrated photoluminescence intensity of the same line measured at 4 K and 300 K in D, which again shows a nearly temperature-independent radiative efficiency.

[0109] Regarding the temperature dependence of the radiation lifetime, such as Figure 4 As shown in Figure B, a temperature-independent recombination lifetime is observed in sample A. In this section, it is shown that such a T-independent recombination lifetime can only be explained by radiative recombination in a degenerately doped semiconductor.

[0110] The non-radiative recombination is characterized by activation behavior at low temperatures, as explained by the temperature dependence of the integrated photoluminescence intensity, which is affected by By analyzing the expression of the well-known Shockley-Read-Hall (SRH) non-radiative recombination mechanism of intrinsic materials, the SRH lifetime can be expressed as Among them E t To capture the energy level, E i is the intrinsic Fermi level, and τ p，0 is the SRH lifetime of the minority holes. At higher temperatures, due to τ n0 and τ p0 The fact that both are inversely proportional to the thermal velocity, the expected SRH life decreases with T -1 / 2 The following conclusions are drawn: It is clearly impossible to explain the observed temperature-independent recombination lifetime as being due to non-radiative recombination.

[0111] Auger recombination is discussed, which can be expected to be due to the high n-doping through unintentional arsenic (As) incorporation during growth. The Auger rate includes two different processes, the nnp-Auger process, in which the excess energy is transferred to electrons, and the npp-Auger process, in which the excess energy is transferred to holes. For the present invention, there is a high n-doping due to As incorporation during growth, resulting in a doping concentration n0. It is expected that the nnp-Auger process will be the most important in n-doped Hex-SiGe samples. However, the Auger coefficient is temperature dependent, which leads to a T-dependent recombination lifetime, which is inconsistent with the observations. Most importantly, as Figure 4 A linear relationship was observed between the integrated photoluminescence intensity and the excitation power, as shown in the inset of C. No decrease in PL intensity was observed at high excitation, which strongly suggests that the Auger process was still weak under the experimental conditions.

[0112] Regarding the possibility of radiative recombination, the radiative lifetime of an intrinsic semiconductor varies with T 3 / 2 As the radiative lifetime increases, it exhibits a sub-nanosecond radiative lifetime at low temperatures, which increases to over 1 microsecond at room temperature. For degenerately doped semiconductors, the radiative lifetime is expected to be independent of temperature because the B coefficient of radiative recombination is related to is proportional to, where L is the spontaneous radiative recombination rate. It can be easily seen that for degenerate semiconductors, p∝T 3 / 2 , L∝T 3 / 2 , and n becomes independent of temperature. It is expected that both the B coefficient of the radiative recombination rate and the radiative lifetime are independent of temperature.

[0113] The photoluminescence lifetime measurements of all three samples were Figure 4 Provided by B. Figure 4C recalls that samples C, B, and A are within the radiation limits up to 40K, 100K, and >220K. This behavior is Figure 4 The results are fully reproduced in samples B, where the lifetime remains unchanged up to 40K, 90K, and >220K, which is indeed within the expected lifetime for a degenerate semiconductor. In samples C and B, non-radiative recombination becomes the dominant recombination mechanism above 40K and 90K, respectively, as evident by the observed slope close to -0.50, as expected for non-radiative SRH recombination at high temperatures. Non-radiative recombination at high temperatures is believed to be due to recombination at the nanowire surface.

[0114] In order to again obtain appropriate statistics, photoluminescence lifetime measurements were performed on more than 60 different nanowires obtained from sample A at 4 K and at 300 K. The data are Figure 4 Shown in D. A scatter in the recombination lifetime at 4 K is observed, which is attributed to variations in the local density around each individual wire.

[0115] Furthermore, the measurements were performed at high excitation densities to saturate the non-radiative processes and maintain them up to the radiative limit at elevated temperatures. 0.20 Ge 0.80 Typical results of time-resolved luminescence measurements of a single line of the sample as a function of temperature at Figure 4 A. A clear monoexponential decay transient is observed, which is characteristic of a single dominant decay channel. 1-x Ge x Nanowires, the characteristic recombination lifetime is about 1 ns, very similar to direct bandgap semiconductors such as GaAs or InP with similar doping levels at low temperatures, as described above for Hex-Si 0.2 Ge 0.8 The lifetimes measured at low temperatures are described. It was also observed that the experimentally obtained lifetimes were an order of magnitude smaller than the theoretically calculated lifetimes, suggesting that the perfect crystal symmetry is also violated by other factors.

[0116] Figure 4 B and 4C show the temperature dependence of both the recombination lifetime and the integrated emission intensity (as a function of temperature) of single lines from three different samples grown under different conditions, resulting in different qualities, see Table S2. The lines show comparable lifetimes at low temperatures, but for sample C ( Figure 4 B), both the intensity and lifetime begin to decrease at approximately 40K (100K), which is a low (medium) quality line. For higher quality samples, the integrated photoluminescence intensity and lifetime (as a function of temperature) are observed to be constant up to 220K, which decisively indicates the absence of unsaturated thermally activated non-radiative recombination processes and provides strong evidence for pure radiative recombination, as described above for the temperature dependence of the radiative lifetime.

[0117] To ensure that the data for individual wires were representative, more than 60 individual wires were analyzed from high crystal quality sample A. Figure 4 D and 4E. This analysis shows that the photoluminescence efficiency and lifetime are almost independent of temperature up to 300K. Figure 4 Excitation power dependence of the emitted photoluminescence intensity in the inset of C. Importantly, this figure shows that the photoluminescence intensity increases linearly with a slope very close to unity, which is consistent with a purely radiative decay mechanism.

[0118] Regarding the excitation power dependence of the integrated photoluminescence intensity, it should be noted that at low excitation densities, Δn < n0, non-radiative, radiative, and Auger processes all produce a linear dependence of the PL intensity on the excitation power with a slope of unity. However, this simplified analysis assumes that the non-radiative recombination centers are not saturated.

[0119] Because no deviations from linear behavior were observed, the data indicate that even if nonradiative recombination centers exist, they can be saturated with the excitation power. This indicates that there are no nonradiative recombination centers in the bulk of the material, meaning that the radiative limit has been reached. Note that this argument applies to both Δn < n0 and Δn > n0.

[0120] At high excitation density, Δn>n0, using existing technical analysis, according to the analysis, the total carrier generation rate G should be equal to the total carrier recombination rate through the following formula

[0121] G=An+Bn 2 +Cn 3 (A7)

[0122] Where An is the Shockley-Read-Hall non-radiative recombination rate, Bn 2 is the radiative recombination rate, and Cn 3 is the Auger non-radiative rate. At high excitation densities (for Hex-Ge it is higher than 500W / cm 2 , as by Figure 3 A), when the photoinjected carrier density Δn, Δp is greater than the electron concentration due to unintentional As doping (see Figure 9 APT measurement in ).

[0123]

[0124] In a plot of integrated photoluminescence intensity versus excitation density, Equation A6 yields a slope of two for non-radiative recombination (provided the non-radiative recombination centers are unsaturated, see above), a slope of one for radiative recombination, and a slope of 2 / 3 for Auger recombination. Note that no decrease in PL intensity is observed at the highest excitation power, providing the first indication that Auger recombination losses are not yet dominant in this material.

[0125] For Hex-Si 0.20 Ge 0.80 samples, a clear boundary between the Δn<n0 and Δn>n0 states cannot be determined due to the additional complexity of alloy broadening. Most likely, Si 0.20 Ge 0.80 The alloy will consist of composition pockets where either Δn < n0 or Δn > n0 applies. Figure 4 The observation that the slope is exactly one, shown in the inset of C, means that both types of pockets are within the radiation limit.

[0126] Regarding Hex-SiGe's radiative efficiency and B-factor, to compare Hex-SiGe's radiative emission intensity with other well-known direct-bandgap semiconductors, such as GaAs or InP, the radiative emission rate at room temperature is most relevant for device applications. By comparing at 300K, exciton effects and the effects due to carrier localization in the Hex-SiGe alloy are no longer relevant. A key parameter for comparing semiconductor radiative efficiency is the B-factor, which is the recombination rate corrected for doping density.

[0127] The radiation rate R per unit volume of the semiconductor rad It can be expressed in terms of the B coefficient, the n-type and p-type doping concentrations n0 and p0, and the number of excited electron-hole pairs Δn=Δp. For highly n-doped semiconductors with n0>>Δn, R rad It can be expressed as:

[0128] R rad =B rad (n0+Δn)(p0+Δp)≈B rad n0Δp (A9)

[0129] Experimentally observed radiative lifetime τ rad The recombination rate R per unit volume rad and the number of excited electron-hole pairs Δn=Δp is determined so that τ rad =Δp / R rad Combining this result with Equation A9 yields the following definition of the B coefficient:

[0130]

[0131] where τ rad is the radiation lifetime at 300K, and n0 is the activated donor density. In order to determine B rad Coefficient, about τ rad and doping density n0 are evaluated for the determined values.

[0132] like Figure 4 As shown in D, the measured photoluminescence lifetime shows a spread over the different lines. This spread is attributed to the variation in the optical density of states of each individual line. Using the decay time ( Figure 4 D) and extrapolating them to 300 K assuming temperature independence, we deduce an upper limit of 1.6 ns, while the lower limit is close to 0.4 ns, as given by Figure 4 The 300K measurement is shown in D.

[0133] There is controversy over whether the measured photoluminescence decay at 300K is equal to the radiative lifetime. The main arguments in favor are given by Figure 4 E is provided, which shows that the photoluminescence intensity at 300 K is almost equal to the photoluminescence intensity at 4 K. Since Hex-SiGe is known to be within the radiative limit at 4 K, and nearly the same emission intensity is observed at 300 K, it is clear that Hex-SiGe should remain very close to the radiative limit at 300 K.

[0134] A second point of interest may be that the degeneracy bound Δn<n0 is still valid. The main evidence for this is that for most lines, Figure 4 In the same excitation range as in the inset of C, the excitation power is measured to be independent of the photoluminescence decay time. In addition, combined with the above comments on the excitation power dependence of the integrated photoluminescence intensity, Figure 4 In B, the temperature-independent photoluminescence lifetime was measured, which can only be understood for semiconductors with degenerate doping.

[0135] Because the measurements were performed within the radiation limit and the carriers accumulated in the direct minimum at low temperatures, the observation of direct bandgap emission with sub-nanosecond recombination lifetimes was inferred. 1-x Ge x (0.65<x<1) is decisive evidence for a new type of direct bandgap semiconductor with large optical matrix elements.

[0136] The radiative transition rate of Hex-SiGe is then compared with other direct bandgap semiconductors. rad By R rad =B rad ·n·p, where n and p are the electron and hole densities, and B radis the coefficient of radiative recombination, which is directly related to the transition dipole moment. rad The radiation lifetime τ rad The measurement results of It is deduced that n0 is the activated donor density.

[0137] The donor density n0 is estimated using two techniques, the first of which is Figure 9 The atom probe tomography shown in FIG, where the donor concentration n0 = 9·10 18 cm -3 . However, this number may be different from the number of active dopants. The active dopant concentration can be calculated from the electron quasi-Fermi level (eQFL) and the density of states in the conduction band. Regarding the fit using the Lasher-Stern-Würfel (LSW) model, the results of the LSW fit model as described above yielded an eQFL of 35 meV, and the density of states was calculated using the effective mass according to DFT calculations. Using these values, the following doping levels were obtained: n0 = 2.3 10 18 cm -3 .

[0138] Now, the 9.10 18 cm -3 The upper bound of the donor density is combined with the upper bound of the radiation lifetime of 1.6 ns, giving 0.7·10 -10 cm 3 The lower bound of the B coefficient of / s is about half of the B coefficient of InP. Using n0 and τ rad The lower limit of the B coefficient is 11·10 -10 cm 3 The upper limit of / s is 9 times the B coefficient of InP. The following table S3 is used to analyze the different III-V materials Cub-Si and Hex-Si. 0.2 Ge 0.8 Extracting the B-coefficients and hence the transition matrix elements is very important for possible device applications of Hex-SiGe such as lasers, modulators, detectors and LEDs, which all rely heavily on the strength of the light-matter interaction.

[0139] Regarding the radiation efficiency and B coefficient of Hex-SiGe, we obtain a value of 0.7·10 at 300K. -10 cm 3 / s<B rad <11.10 -10 cm 3 / s, which is comparable in size to GaAs and InP, and almost 5 orders of magnitude larger than Cub-Si shown in Table S3 below. 1-x Gex It is a fully silicon-compatible semiconductor with radiation emission intensity comparable to that of direct-bandgap III-V semiconductors.

[0140]

[0141] Table S3. Hex-Si 0.2 Ge 0.8 , GaAs, InP and Cubic-Si radiation coefficients: The listed are the Hex-Si as calculated and described in S8 above regarding the radiation efficiency and B coefficient of Hex-SiGe 0.2 Ge 0.8 The B coefficient of GaAs, InP and Cub-Si are known in the art.

[0142] Figure 5 Depicts Hex-Si 1-x Ge x Tunability of the direct band gap of the alloy: Figure 5 A shows the tunability of the PL spectra of different compositions. The spectra were obtained at 4K at 1.9 kW / cm 2 The Hex-Si was measured using time-correlated single photon counting measurements outlined in the next paragraph on lines dispersed onto a silicon substrate capped with a gold (Au) layer. 0.3 Ge 0.7 and Hex-Si 0.35 Ge 0.65 spectrum. Figure 5 B shows the comparison of the measured peak energy and the calculated emission band minimum as a function of Ge content.

[0143] In this regard, for a single Si 0.2 Ge 0.8 The wire was mechanically transferred to a substrate with chromium (15 nm), gold (300 nm) and SiO as black mirror. x This method improves the measurement intensity and avoids possible optical signals emitted by the wafer. 0.2 Ge 0.8The sample of the wire was mounted in an Oxford Instruments HiRes2 helium flow cryostat and excited with a 1030 nm, NKT ONEFIVE Origami femtosecond pulsed laser at a 40 MHz repetition rate. The photoluminescence signal was measured in a backscattering geometry using a 36X gold-coated Cassegrain objective that focused the excitation laser into a spot of ~3 μm. A 1350 nm long-pass filter was used to filter out the laser light from the PL signal. The PL signal was then focused onto an SM2000 single-mode fiber using an achromatic lens and fed to a Single Quantum superconducting nanowire single-photon detector optimized for a quantum efficiency of >35% at 1800 nm and >15% at 2000 nm. The 1350 nm long-pass filter in combination with the SM2000 fiber defined a spectral interval from 1350 nm to ~2300 nm over which the PL was integrated. The temporal correlation between the laser pulses and the detection events was measured and counted using a PicoQuant PicoHarp 300 module. The overall instrument response function (IRF) showed a FWHM of 96 ps, and τ IRF = 21 ps, which is the minimum observable decay time of the system. Figure 4 In addition to the illustrations of C, Figure 4 All measurements presented in this paper were performed with 125 pJ pulses, giving a value of ∼0.4 mJ / cm 2 The excitation density of the photoluminescence spectra was obtained. All lifetime measurements were baseline corrected and fitted with a single exponential decay transient. Spectrally resolved photoluminescence experiments with accurate temperature control were performed on grown samples mounted in an Oxford Instruments HiRes2 helium flow cryostat. The samples were illuminated with a 976 nm continuous wave laser tuned to a frequency of 35 kHz and focused to a 45 μm spot on the sample using an off-axis parabolic Au mirror with a focal length of 2.1 cm. The photoluminescence signal was calibrated using the same off-axis parabolic mirror and coupled to a Si CMOS instrument equipped for x > 0.8. 1-x Ge x The FTIR was performed on a ThermoScientific Nicolet IS50r FTIR system with an MCT detector for the samples and an extended InGaAs detector for samples with x ≤ 0.8. The FTIR was operated in step-scan mode, which enabled the use of a lock-in technique to eliminate thermal background. To minimize parasitic absorption, the entire optical path was purged with nitrogen.

[0144] According to one aspect of the present invention, it has been determined that Hex-Si 1-x Ge xThe direct nature of the band gap and the direct band gap can be adjusted by composition design. Figure 5 A shows photoluminescence measurements recorded at T = 4 K over a wavelength range of at least 1.8 μm up to 4 μm from a series of samples with x = 0.65-1.00. Bright emission is observed to red-shift with increasing Ge content from 0.67 eV (x = 0.65) to 0.35 eV (x = 1.00). Figure 5 The peak energy of the emission is compared with the calculated energy of the direct band gap (Γ) in B, showing excellent agreement. Therefore, as an example according to the present invention, a Hex-Si with a direct band gap of x>0.65 is obtained. 1-x Ge x .

[0145] Figure 5 C depicts the relative photoluminescence (PL) intensity between the compositions: where Figure 5 Relative PL intensity of the samples presented in A and 5B. Note that in cases where the same number of lines is probed, only the measurements of the entirety of the grown vertical lines are included, thus excluding the Si 0.35 Ge 0.65 For this comparison, the same MCT detector and the same KBr beam splitter were used at 4 K with a 5 kW / cm 2 All samples were excited with an excitation density of 1.5 Å. It was found that although the setup efficiency changed for the high-Si content sample, the total excitation volume changed due to thickness differences, and possible strain-induced non-radiative recombination centers, the samples were very similar in intensity. Due to these additional factors, it is impossible to make a conclusive experimental demonstration of whether the material becomes more efficient with higher Si content. In addition, it was confirmed that the PL spectrum was not measured from the line with x < 0.65, indicating that the direct-indirect transition is located near this point.

[0146] Figure 5 D depicts several compositions of Hex-Si with 0.4<x<1.0 1-x Ge x The relative photoluminescence (PL) intensity of the Hex-SiGe nanowires was measured using a time-correlated single photon counting setup sensitive at wavelengths below 2.3 μm as described previously. This setup only allows the measurement of the integrated photoluminescence intensity using a spectral filter. Importantly, the growth conditions were optimized for wires with x = 1 (pure Ge) and wires with x = 0.2, and the PL intensity can be further optimized for other compositions. The wires were mechanically transferred to a substrate with chromium (15 nm), gold (300 nm) and SiO as black mirrors. x (12nm) on the top layer of silicon wafer.

[0147] Direct bandgap Hex-Si1-x Ge x Opened the way to Hex-Si 1-x Ge x The present invention provides a path for the tight monolithic integration of light sources and passive cubic Si photonic circuits on the same chip. This will reduce stray capacitance, thereby improving performance and reducing energy consumption, which is important for green information and communication technologies. According to one aspect of the present invention, a Hex-Si substrate is provided on a conventional Cu-Si substrate for light emitting or light absorbing elements. 1-x Ge x The compound structure serves as the light emitting or light absorbing part. Possible integration pathways are Si 1-x Ge x The strain-induced transformation, for example, through the dielectric (i.e. SiO x or SiN x ) strain envelope, or through template-assisted selective area growth of the hexagonal phase.

[0148] According to another aspect of the present invention, a Hex-Si substrate for emitting light 1-x Ge x The wavelength range of compound materials can be extended to 1.4μm to 7.0μm by using strain. This includes: using different compositions of hexagonal Si in each layer of the quantum well structure. 1-x Ge x Compound materials are used to grow strained quantum well structures, thereby 1-x Ge x Apply strain to compound materials.

[0149] Figure 6 A schematic diagram of the nanowire growth process according to the present invention is depicted. Figure 6 As schematically shown in the figure, in a first method step, in a close-coupled showerhead (CCS) metal-organic vapor phase epitaxy (MOVPE) reactor, III-V compound semiconductor nanowires, in particular GaAs nanowires, are grown by catalyst-assisted growth according to the Vapor-Liquid-Solid (VLS) mechanism using Group 11 element catalyst seeds, in particular gold (Au) catalyst seeds.

[0150] According to the method steps of the present invention, the catalyst seeds of the group 11 element (here, Au catalyst seeds) are deposited in a nano-disk array arrangement on the III-V compound semiconductor substrate (here, GaAs (111)) by electron beam etching technology. B The growth was carried out at a reactor flow rate of 8.2 standard liters per minute (slm) and a reactor pressure of 50 mbar. For GaAs nanowires, the growth template was heated at a set thermocouple temperature of 635°C at a set molar fraction of Then, the annealing was performed under AsH3 flow. Then, the set temperature was set at 650℃ and the molar fraction was set to χ TMGa =1.9×10 -5 mol, The growth was carried out using trimethylgallium (TMGa) and arsine (AsH3) as material precursors to obtain a V / III ratio of 2.4.

[0151] After the growth of the GaAs core nanowires, in a further process step, the GaAs core nanowires are chemically treated with a cyanide-based solution to remove the Au catalyst particles and thus avoid gold contamination in the SiGe shell (see Figure 6 Finally, the GaAs nanowire core is used as a hexagonal material template and in the next method step, Si is grown thereon by introducing suitable gaseous precursors for shell growth. x Ge 1-x As one aspect of the method according to the present invention, the gas precursor is GeH4 and Si2H6, and the gas precursor is GeH4 and Si2H6. SiGe =1.55×10 -4 Mole fraction of mol Si growth 1-x Ge x Shell for a certain period of time.

[0152] Figure 7 A schematic diagram of the nanowire growth process according to an example of the method according to the present invention is shown. In the first method step, the core nanowire growth starts with (a) a substrate patterned with Au catalyst seeds is introduced into the MOVPE reactor and annealed at a temperature higher than the eutectic temperature to form an alloy between the catalyst seeds and the substrate. (b) Thereafter, GaAs gas precursors (TMGa and AsH3) are introduced to grow Au catalyzed GaAs core nanowires. To continue with the SiGe shell growth: (c) the Au seeds are chemically etched away from the GaAs core and (d) the sample is reintroduced into the MOVPE reactor. Hex-Si is epitaxially grown around the GaAs core from (Si2H6 and GeH4) precursors. 1-x Ge x Shell. (Molecules were drawn using freely available MolView software.) The 30-degree tilted SEM images in the bottom panel represent the results of the growth steps in the top panel.

[0153] Regarding the crystal quality of the WZ GaAs nanowire cores grown using one example of the method according to the invention, Figure 7A depicts bright-field TEM images recorded in the [11-20] zone axis of five (5) representative GaAs core nanowires of pure WZ crystal, where stacking faults are represented by thin upward lines, resulting in stacking fault densities of (0-6 SFs / μm). Figure 7 B shows a magnified bright-field TEM image of the top of one of the nanowires in (a) (highlighted by the box) to demonstrate the purity of the crystal structure. Figure 7 C depicts Figure 7 The HAADF-STEM image of the portion highlighted by the dashed box in B shows the ABAB stacking of GaAs atomic columns, a characteristic of the hexagonal crystal structure. The clearly visible gray line designated X7 highlights the stacking fault that forms a cubic layer in the hexagonal structure.

[0154] Figure 8 A representative SEM of a Hex-Ge sample according to the present invention is depicted. It shows a generalized scanning electron microscope (SEM) image of the Hex-Ge / GaAs core shell, which demonstrates the uniformity of growth across the sample, and a detailed inset showing a magnified image of the nanowire array.

[0155] Figure 9 Shown Hex-Si 0.25 Ge 0.75 Atom probe tomography characterization of: Figure 9 A shows Hex-Si with a thickness of 35nm / 46nm 0.25 Ge 0.75 3D volume reconstruction of a portion of a core / shell nanowire. For clarity, only a 40 nm thick slab is shown of the entire 1100 nm long analyte. The Ge and Si are clearly seen forming a shell around the hexagonal Ga and As core. Figure 9 B shows a plot of the atomic species concentration in the SiGe shell (as a function of radial distance across the core / shell structure) highlighted in the yellow rectangle in (a). Each data point in this plot represents a 2 nm slice taken along the entire length of the nanowire analyte (excluding the cubic top). Constant As incorporation at a level of approximately 200 ppm is observed throughout the shell, while Ga concentration rapidly decreases to a value close to the noise level of ~10 ppm.

[0156] Figure 9 C shows the radial profile of the SiGe core / shell structure from an APT measurement integrated over a 1.0 μm length of the structure shown, showing a Si content of approximately 25% as shown in (b). A nearest neighbor analysis of the Si atoms was performed on the highlighted dotted rectangular volume of (c), as previously used to evaluate random alloys of GeSn. The nearest neighbor analysis evaluates the distance between each Si atom pair and its nearest (to the fourth nearest) neighbor.

[0157] at last, Figure 9 D depicts a plot comparing nearest neighbor analysis of the measured data with a random data set. This provides no evidence of Si aggregation and is confirmed to be a reliable way to evaluate random alloys.

[0158] For APT measurements, individual nanowires (nanowires) were separated from the nanowire population using a Kleindiek nanomanipulator inside a FEI Nova Nanolab 600i dual beam as previously described. APT analysis was performed in a LEAP4000X-HR from Cameca. The system was equipped with a laser that produces picosecond pulses with a wavelength of 355 nm. Experimental data were collected at a laser or voltage pulse frequency of 65-125 kHz and a laser pulse energy of 5-10 pJ or a pulse fraction of 25-27.5%. Except for a slightly higher compression of the core in the laser pulse mode and a lower quality of the mass spectrum in the voltage pulse mode, no significant differences were seen between the laser and voltage pulses. During the analysis, the sample was pulsed at 2.10 -11 mbar vacuum maintained at a base temperature of 20 K.

[0159] Figure 10 Depicts Hex-Si 1-x Ge x Full range of symmetrical (0008) reflections: Figure 10 A shows the reciprocal space map (RSM) of the grown WZ GaAs nanowires on a Cub-GaAs substrate, which contains the WZ-GaAs (0008) reflection and the Cub-GaAs (444) reflection. Figure 10 B shows a thick Ge shell Figure 10 RSM of a similar sample in A, including Cub-GaAs (444) substrate reflection and Hex-Ge (0008) reflection. Figure 10 C(x=0.92), Figure 10 D(x=0.86), Figure 10 E(x=0.75), Figure 10 F(x=0.63) shows that there is Si 1-x Ge x Additional RSMs of the shell samples are also listed in Table S1. A clear increase in Q is observed for increasing Si content. 面外 displacement, which corresponds to a reduced lattice constant. Figure 10 In the RSMs in D and 10E, reflections from the parasitic epitaxial Cub-SiGe layer are also found.

[0160] Figure 11 A comparison between Hex-Ge samples of different generations is shown. Figure 11A shows the photoluminescence from the first Hex-Ge shell grown using a WZ-GaP core, thus generating many defects due to the large lattice mismatch between the core and the shell. Figure 11 The first Hex-Ge grown on a lattice-mismatched GaAs shell is shown in B, where the Hex-Ge is grown at a temperature of 600°C. Figure 11 C shows the spectrum of a Hex-Ge shell grown at a temperature of 650°C, further improving the optical quality.

[0161] Figure 12 Depicts Hex-Si with different qualities 0.2 Ge 0.8 This figure shows the Arrhenius diagram of Figure 4 The same data is provided for Sample C, but presented here as Arrhenius plots. For the lowest-quality sample, C, two nonradiative processes with activation energies of 16 meV and 91 meV were observed. For Sample B, only a single activation energy of 34 meV was observed, while Sample A showed no intensity decay over the entire measured temperature range. Details of the samples are given in Table S2.

[0162] The calculated band structure of hexagonal Ge is Figure 13 As shown in A. It is clear from this figure that hexagonal Ge has a direct band gap at the center of the Brillouin zone (Γ point). Figure 13 In B, as Si 1-x Ge x The conduction band minimum is calculated as a function of the composition. It is clear that for x>0.6, the material has a direct band gap. These calculations are done by Figure 13 The photoluminescence measurement shown in C was confirmed.

[0163] As the Si concentration increases, the emission blue shifts. The experimentally obtained emission energy as a function of composition is included in Figure 13 B, and the agreement with the calculation is obvious. The intensity of the optical process is determined by the matrix elements. 1-x Ge x The computational optical matrix elements of the compound are Figure 13 As shown in D. For 0.2<x<0.9, (actually 99-60% Ge), F9 v ->Γ8 c The element is much higher (almost 100 times) than pure Ge and / or Si materials. More specifically, the composition x>0.6 has a direct band gap, and a band gap energy of approximately 0.6-0.7 eV, which is close to the telecommunication wavelength.

[0164] In one aspect of the present invention, the optical device is characterized by a hexagonal Si 1-x Ge xCompounds. This material compound is important for the integration of photonic functions in the silicon industry. This material can be used to make light-emitting diodes (LEDs), lasers, and detectors, and can be integrated into Si technology or used as active components in passive optical circuits. Such devices have applications in logic chips, telecommunications, chemical sensing, IR imaging, and more.

[0165] Efficient light emission has been verified by performing time-resolved photoluminescence lifetime measurements, resulting in photoluminescence lifetimes of the order of 0.5-0.8 ns for detailed aspects of the optical device according to the present invention, characterized in that Si 0.78 Ge 0.22 .

[0166] Another aspect of the present invention relates to a structure comprising hexagonal Si 1-x Ge x Optoelectronic applications and / or optoelectronic products of emitters or components consisting of compounds which, more particularly, exhibit a direct band gap in the center of the Brillouin zone for 0.6<x<1.0.

[0167] In addition, according to another aspect of the present invention, for hexagonal Si with 0.2<x<1.0 1-x Ge x Compound, composed of hexagonal Si 1-x Ge x Optical emitters or elements composed of compounds can exhibit large matrix elements.

[0168] In particular, the hexagonal Si with a special range of 0.6<x<0.8 1-x Ge x The optical emission elements composed of the compounds exhibit large oscillator strength and a direct fundamental band gap of 0.6-0.8 eV, which corresponds to an emission wavelength of 1.5-2.0 μm.

[0169] The method or process according to the present invention enables the production or fabrication of hexagonal Si alloys over the entire stoichiometric range of the alloy. 1-x Ge x Crystal. Si 1-x Ge x The hexagonal phase of the crystal is achieved through the "crystal transformation" technology, in which Si 1-x Ge x The hexagonal crystal structure of the hexagonal material is taken from the hexagonal material template. According to one aspect of the method of the present invention, this is achieved by taking a non-tapered and single-crystalline wurtzite (hexagonal) GaAs nanowire (nanowire) as a template and then growing Si thereon using the metal organic vapor phase epitaxy (MOVPE) technique. 1-x Ge x epitaxial layer.

[0170] Experimental observations of efficient light emission of an example of the optoelectronic compound according to the present invention are shown in Figure 14 As shown in the figure, the photoelectron compound is composed of Si 0.78 Ge 0.22 composition, demonstrating a photoluminescence (PL) lifetime of 0.7 ns, while a schematic diagram of the complete growth process according to the present invention is shown in Figure 15 Shown in A-15J.

[0171] In one aspect of the method according to the present invention, GaAs nanowires are deposited in a nanodisk array arrangement on a GaAs (111) substrate by a vapor-liquid-solid (VLS) mechanism using electron beam lithography. B The gold (Au) catalyst seed crystals on the substrate are grown. Figure 15 The growth template in A is brought into the MOVPE reactor. Then, Figure 15 As shown in A, the gas precursors (trimethylgallium (TMGa) and arsine (A) required for growing GaAs core nanowires are s H3)) is introduced into the growth chamber. After the GaAs nanowires are grown (see Figure 15 B), they were chemically treated with a dilute potassium cyanide solution to remove Au droplets, thus avoiding gold contamination.

[0172] Finally, by introducing a suitable gaseous precursor for shell growth (germane (G e H4) and disilane (Si2H6)) to grow Si on GaAs nanowire cores 1-x Ge x Shell, see Figure 15 D. In Figure 15 FJ shows Si with x=0-0.5 1-x Ge x Experimental implementation of the shell.

[0173] In one embodiment of the method according to the present invention, the epitaxial process was carried out at a reactor flow rate of 8.2 standard liters per minute (slm). The growth template was heated at a surface temperature of 526° C. monitored by Argus at a temperature set to χ AsH3 =6.1×10 -3 The mole fraction of A s Annealing was performed under H3 flow. Then, the surface temperature was set at 546℃ with the values ​​of χ TMGa =1.9×10 -5 , χ AsH3 =4.55×10 -5 The mole fractions of TMGa and A s H3 was used as the material precursor to grow, and a V / III ratio of 2.4 was obtained. SiGe=1.55×10 -4 Mole fraction of Si growth 1-x Ge x crystal.

[0174] exist Figure 17 In A, a scanning electron microscope (SEM) image is depicted of an array of GaP / Si / SiGe core / multi-shell nanowires with a length of approximately 7 μm. A higher magnification cross-sectional SEM image ( Figure 17 Inset of A) shows that the nanowires are non-tapered and have smooth sidewalls. Figure 17 B shows a high-angle annular dark-field scanning transmission electron microscopy (HAADF STEM) image of a representative GaP / Si / SiGe core / multi-shell nanowire, where the SiGe shell has been deposited at 600°C. HAADF high-resolution STEM image of the SiGe / Si / GaP interface viewed along the [11-20] zone axis ( Figure 17 C) along with the fast Fourier transform (FFT) (see inset) shows the hexagonal phase characteristics of the system and the perfect epitaxy between the layers. The composition of GaP / Si / SiGe core / multi-shell nanowires is analyzed by energy dispersive X-ray (EDX) spectroscopy ( Figure 17 D) and the composition line distribution extracted from the graph ( Figure 17 For this nanowire, the Ge content measured in atomic % was found to be 60.0 ± 0.5 atomic % in the outer shell.

[0175] Figure 18 Depicted is a cross-sectional study of GaP / Si / SiGe core / multi-shell nanowires. Figure 18 A shows a bright-field TEM cross-sectional image of a representative nanowire, and Figure 18 B depicts the Figure 18 The FFT corresponding to A. Figure 18 C shows an EDX chemical analysis of the same cross section, where the Ge content in each facet is averaged and the results in each facet are represented by a different symbol.

[0176] To better understand the gas-solid shell growth mechanism and for future optical characterization experiments, it is important to evaluate the uniformity of the Ge distribution along the entire shell. Therefore, the Ge content in the SiGe shell of the grown samples was determined. To quantify the Ge content, samples were prepared by focused ion beam (FIB) for cross-sectional TEM studies. Figure 18 The cross-sectional bright field (BF) TEM image of A has the cross section aligned along the

[0001] direction. The hexagonal symmetry of the six {1-100} facets of the SiGe shell surrounding the Si shell and GaP core is evident ( Figure 18B). The Ge content was evaluated by averaging over multiple positions from each of the six facets, each facet being represented in Figure 18 C by different symbols □, ○, ◇, △ and denoted. It was thus analyzed that the Ge content was uniformly distributed in the SiGe shell and was about 60.0 ± 0.5 atomic % in this particular case.

[0177] Figure 19 The incorporation of Ge into the SiGe shell and the growth mode are depicted. Figure 19 A shows along its y-axis the atomic % of Ge incorporated into the SiGe shell determined by EDX spectroscopy (as a function of the atomic % Ge content in the precursor gas mixture in the MOVPE chamber along its x-axis). Figure 19 B - D show respectively the HAADF STEM images of samples grown at 600 °C with a 60 atomic % Ge content input; 67 atomic % incorporated showed F - M growth, the HAADF STEM images of samples grown at 700 °C with an 80 atomic % input; 66 atomic % incorporated showed S - K growth, and the HAADF STEM images of samples grown at 700 °C with a 99 atomic % input; 91 atomic % incorporated showed V - W growth.

[0178] To further reveal the SiGe shell growth mechanism, it is useful for all the heterostructures studied to plot the Ge content incorporated in the resulting shell determined by EDX spectroscopy as a function of the Ge content in the precursor gas flow in the MOVPE chamber. This is shown in Figure 19 A, where a higher concentration of Ge was observed at the lower deposition temperature of 600 °C compared to growth carried out at the higher temperature of 700 °C. For the same input Ge amount (in the gas phase in the precursor gas mixture) during MOVPE growth, the fact that the Ge content of the SiGe shell is higher at the lower temperature can be understood as follows. The two precursor gases, disilane (Si2H6) and germane (GeH4), have different decomposition temperatures, about 640 °C 30 for Si2H6 and about 300 °C for GeH4. This means that at 600 °C, Si2H6 is not completely thermally decomposed, so the relative amount of available Ge that can be incorporated into the shell is higher. The net result is that at 600 °C, the ratio of Ge in the SiGe shell is higher than in the precursor gas mixture. On the other hand, at 700 °C, more Si2H6 has decomposed, so more Si is available for deposition and the relative amount of Ge incorporated into the shell is reduced.

[0179] The cubic Si / SiGe system is characterized by different growth modes with Ge content; therefore, the lattice strain in the SiGe shell increases, and this is also observed for the hexagonal phase. For most samples (less than 80 atomic % for Ge content grown at 600 ° C and less than 60 atomic % for Ge content grown at 700 ° C, Figure 19 A) shows a uniform layer formation, which indicates the Frank-van der Merwe (FM) layer-by-layer growth mode. In addition, all samples with up to 80 atomic % Ge content grown at 600 ° C are defect-free. Figure 19 As can be observed in A and 19C, samples with Ge contents above 60 at% grown at 700°C exhibit thin SiGe layers, combined to form islands. For high Ge contents, strain accumulation after some layers of layer-by-layer growth leads to strain relaxation through transition to island growth. This morphology is characteristic of the well-known Stranski-Krastanov (SK) growth mode. The sample with 80 at% Ge grown at 600°C (which is the point where the transition from FM to SK growth mode occurs) is the exact point where defects start to appear, while all samples below this point are defect-free. Furthermore, for growth at 700°C, when Ge contents above 90 at% are observed, in most cases the SiGe shell is characterized only by island growth and is therefore controlled by the Volmer-Weber (VW) growth mode ( Figure 19 A, 19D). It should be noted that the island ( Figure 19 C, 19D) do not appear to exhibit the typical pyramidal or dome shapes observed in heterostructures with cubic crystal structures. Because the shape of the island structures formed during SK and VW growth depends on the surface energy, one skilled in the art would expect that the same shape would occur for hexagonal crystal structures or for growth on the sidewalls of the nanowires. On the other hand, it was observed that for growth performed at 600°C, layer-by-layer growth continued until a Ge content of 80 atomic % ( Figure 19 A, 19B). This difference in morphology can be explained by a combination of strain and different diffusion lengths of adatoms at different growth temperatures, which has already been explained for the metastable layer of cubic SiGe. In particular, strain increases with the Ge content in the shell, and at high temperatures, the adatom diffusion length is longer. Therefore, the adatoms can diffuse over a longer distance to relieve the strain by forming islands. On the other hand, at lower temperatures, the adatom diffusion length is shorter, and thus the adatom diffusivity is too low to form islands within the time frame available for growth. As a result, a continuous metastable layer with gradually increasing strain is grown. In summary, the strain is increased by Figure 19 It is observed that at a growth temperature of 600 °C, not only is Ge incorporation more efficient, but also the layer-by-layer defect-free growth continues up to higher Ge contents, well above about Si0.35 Ge 0.65 The expected direct bandgap transition stoichiometry of .

[0180] The growth kinetics were studied in more detail, and in particular the growth rate as a function of time and temperature. The linear dependence of the SiGe thickness on the growth time indicates that the growth rate is approximately constant ( Figure 20 A). This suggests that the growth rate limiting step is determined by surface dynamics rather than by, for example, bulk diffusion. However, the growth rate depends on the Ge content. For growth performed at 600°C, the shell thickness at 22 min of growth is roughly independent of the Ge content. For longer growth times, the growth rates begin to differ; in particular, the growth rate of samples with Ge contents in the range of 11-13 atomic % is significantly lower than the growth rate of samples with Ge contents in the ranges of 27-33 atomic % and 43-49 atomic % (for which the rates are almost identical). This is indicated by the smaller slope of the 11-13 atomic % Ge sample, and therefore a thinner shell. For growth at 700°C, the thickness of the 27-33 atomic % Ge range is doubled relative to the same atomic % Ge range at 600°C.

[0181] In addition, growth rate studies were performed using a series of samples grown for the entire range of SiGe stoichiometries and for two different temperatures: 600 and 700°C. Figure 20 In Figure 2, the growth rate is shown as a function of Ge content for two deposition temperatures of the SiGe shell. With respect to Ge content, two distinct regimes can be observed. First, a regime with low Ge content is characterized by a significant increase in growth rate with increasing Ge content. In this regime, strain does not affect the growth kinetics, but rather the increase in growth rate can be attributed to increased hydrogen desorption from the growth surface due to Ge. In effect, Ge serves to lower the activation energy for hydrogen desorption, thereby freeing up more surface sites for Si and Ge growth species. This results in an increase in growth rate with increasing Ge content. A second regime is found in the high Ge content region, characterized by a decrease in growth rate as a function of Ge content. Two different reasons have been proposed to explain this behavior: high strain and / or reduced reactive hydride adsorption. In the first case, strain begins to dominate, and the resulting reduction in growth rate is attributed to strain accumulation due to the very high Ge content. Note that as the lattice constant increases, so does the diffusion energy barrier, making diffusion more difficult. Consequently, lower diffusion means lower growth rate. A second reason for the decrease in growth rate at high Ge content is reduced reactive hydride adsorption. This is explained by a lower precursor adsorption coefficient, leading to a lower growth rate. Figure 20The competition between these different effects is clearly seen in B and is consistent with previous studies. Although the correlation of the growth rate with the Ge content of the shell shows the same trend for the two temperature studies (600 and 700°C), the quantitative behavior is different. In the case of growth at high temperature (700°C), the peak growth rate is found to be higher and a smaller Ge content is reached compared to the growth at low temperature (600°C). This behavior can be understood by similar mechanisms as discussed above in terms of adsorption and desorption. In fact, for higher temperatures, in addition to the decomposition of the precursor, both adsorption atom diffusion and hydrogen desorption increase, which explains the significantly higher peak growth rate of the shell grown at 700°C. In addition, the 700°C curve cuts off relatively quickly due to the start of SK growth. In fact, Figure 20 B further reinforces the statement that for growth at 600 °C, layer-by-layer defect-free growth continues until above the Si where a direct bandgap transition is expected. 0.35 Ge 0.65 Higher Ge content.

[0182] One aspect of the method according to the present invention relates to the growth of single-crystalline defect-free SiGe having or on a hexagonal diamond crystal structure. According to the present invention, the growth temperature leads to a significant difference in the morphology of the resulting SiGe layer: SiGe layers grown at lower temperatures exhibit uniform layer-by-layer FM growth, while at higher temperatures and for the same Ge content, island-based SK growth dominates. The maximum stoichiometry achieved for defect-free smooth layer film growth is 77 atomic % Ge, which is significantly higher than the predicted direct bandgap transition at 65 atomic % Ge. In addition, it was observed that at a growth temperature of 600°C, layer growth continues significantly further up to this high value. This therefore enables the use of hexagonal SiGe in optoelectronic applications.

[0183] Examples of GaP / Si / SiGe core / multi-shell nanowires according to the present invention were formed in a low-pressure (50 mbar) Aixtron Close Coupled Showerhead (CCS) MOVPE reactor. In this case, however, the Si shell thickness was kept to a minimum of 10-12 nm. This likely served as a sacrificial buffer layer to trap any P or Ga species from the GaP core and prevent them from diffusing into the SiGe shell.

[0184] Directly after the Si shell growth and in the same growth process, the SiGe shell is grown. This is done by cutting off the Si2H6 precursor gas and gradually reducing the temperature of the MOVPE growth chamber to 600 or 700°C. Once the target temperature is reached and stabilized, Si2H6 and GeH4 are introduced into the chamber and their flow rates are adjusted to meet the desired stoichiometry. The Si2H6 molar flow rate is increased from 2.87×10 -7 To the high end of 1.00×10-4 Adjustment is performed, and GeH4 is adjusted from the low end of 3.66×10 -6 to the high-end 3.33×10 -4 Adjustments were made to obtain the desired ratio. Hydrogen (H2) was used as the carrier gas for the precursors, and the total flow rate to the reactor was 8.2 L / min. At the end of the SiGe shell growth, the precursor flow was terminated, the heating element was turned off, and the chamber was allowed to cool to room temperature.

[0185] For transmission electron microscopy (TEM) studies, two different sample preparation methods were used. In standard axial analysis, the nanowires were mechanically transferred to a holey carbon TEM grid. For cross-sectional TEM studies, a FIB was used to prepare the nanowires. In both cases, a JEM ARM200F aberration-corrected TEM operating at 200 kV was used for HRTEM and STEM analysis. For chemical analysis, a JEM ARM200F aberration-corrected TEM equipped with a 100 mm 2 EDX measurements were performed on the same microscope equipped with an EDX silicon drift detector.

[0186] TEM lamellae. TEM lamellae were prepared using a FEI Nova Nanolab 600i dual-beam system. To this end, the nanowires were initially transferred from the growth substrate to a Si wafer using a nanomanipulator and then aligned parallel to one another. Electron- and ion-beam-induced metal deposition was used to coat these nanowires to protect them during the procedure. The lamellae were cut by milling with 30 kV Ga ions, and subsequent thinning steps using 30, 16, and 5 kV ion milling were used to minimize Ga-induced damage in the areas imaged by TEM.

[0187] In another embodiment according to the present invention, high-quality, defect-free hexagonal diamond Si and Ge can be grown on a hexagonal nanowire substrate. These hexagonal phases of Group IV semiconductors exhibit improved electronic and optical properties for optoelectronic applications. Although hexagonal diamond Si is a well-characterized indirect semiconductor, experimental data and reliable calculations for hexagonal diamond Ge are scarce, and there is no agreement on its band gap properties. Using the aforementioned ab initio density functional theory, the exact structure, electronic, and optical properties of hexagonal Ge can be determined. Given the well-known sensitivity of Ge electronic structure calculations to underlying approximations, the performance of several exchange-correlation functionals, including meta-GGA and hybrid functionals, can be tested. For cubic Ge, atomic geometry and band structure consistent with available experimental data were verified. The same approach was applied to predict the electronic and optical properties of hexagonal diamond Ge. According to another aspect of the present invention, an optoelectronic device is constructed from hexagonal diamond Ge as a direct semiconductor, which has only a weakly dipole-active minimum optical transition, a small band gap, a large crystal field splitting, and a highly anisotropic effective mass. The unexpectedly small direct band gap and the lowest oscillator strength of the optical transition are explained by the band symmetry and backfolding of the diamond structure.

[0188] Integrating materials characterized by efficient interaction with light into silicon technology holds high technological value. However, copper interconnects between transistors on a chip pose a greater challenge than reducing transistor size. One viable solution to this critical bottleneck is optical interconnects. Diamond-structured silicon, an indirect bandgap material, cannot be used for this purpose. Several attempts to obtain optical emission from silicon for telecommunications applications have met with limited success.

[0189] Despite their chemical similarities, Si and Ge are very different in their optical properties. Ge, one of the most important and commonly used semiconductors, crystallizes in a cubic diamond structure (space group 1000) under ambient conditions, just like Si. ), whose indirect band gap is about 0.7 eV. Diamond-structured Ge is characterized by poor light emission efficiency due to the indirect nature of its fundamental band gap. However, its direct band gap energy is close to the indirect band gap energy, and significant engineering work is underway to convert Ge into an efficient gain material for monolithic integration on Si chips. In order to increase the interest in Ge for possible active optoelectronic applications such as light-emitting diodes or lasers, it is necessary to break the k-selection rule that prohibits optical dipole transitions at the minimum band gap of Ge. To this end, ingenious approaches have been proposed, for example, based on strain generation, nanostructuring or amorphization.

[0190] In addition to the thermodynamically stable diamond structure, other metastable allotropes of Ge have been explored for optical applications. Ge in the hexagonal diamond structure (space group P63 / mmc), sometimes also referred to as wurtzite Ge, has attracted increasing attention as a promising material for optoelectronics. In the hexagonal diamond phase, the Ge atoms are characterized by the same tetrahedral nearest neighbor coordination as in the cubic diamond structure, but instead of ABC stacking of adjacent Ge bilayers along a three-fold symmetry axis, the hexagonal diamond phase is characterized by AB stacking. Therefore, cubic Ge in the diamond structure is also called 3C-Ge, and hexagonal Ge in the hexagonal diamond structure is also called 2H-Ge (see Figure 21 Hexagonal diamond Ge was first obtained using ultraviolet laser ablation at low pressure. More recently, it has been grown as core-shell nanowires on top of a wurtzite-GaP nanowire template, similar to what has been achieved for hexagonal diamond Si. Other approaches to hexagonal Ge nanowires have also been proposed. In addition, by exploiting strain-induced phase transitions, Ge nanowires characterized by homojunctions of different polytypes can be synthesized.

[0191] In the hexagonal Brillouin zone (BZ) of the hexagonal diamond structure, the L point of the diamond structure BZ, located on the cubic

[111] axis, maps to the G point. Therefore, the lowest conduction band minimum (CBM) at the L point of cubic Ge folds onto the G point, providing a 2H-Ge direct bandgap semiconductor. Comparing hexagonal Si and Ge, it seems that breaking the k-selection rule is easier in Ge because the original and backfolded conduction bands are very close in energy. The exact ordering of the lowest conduction band at G is extremely important because the material's electron radiative lifetime strongly depends on the symmetry of these states.

[0192] Together with optical emission or absorption measurements of photon energies comparable to the band gap size, accurate electronic structure calculations can provide detailed answers about conduction band ordering and optical transition strengths. Although Ge is an elemental material, experience gained from calculations of diamond-structured Ge has proven that Ge is a difficult system for accurate band structure studies. On the other hand, it is crucial to consider spin-orbit coupling (SOC) and to treat the shallow Ge 3d shell as valence electrons. On the other hand, the approximation used to describe the exchange and correlation (XC) contributions to electron-electron interactions significantly affects the k-space position of the lowest conduction band minimum and the size of the direct and indirect band gaps.

[0193] Applying density functional theory (DFT), the Kohn-Sham (KS) band structure obtained within the local density approximation (LDA) or any form of the generalized gradient approximation (GGA) is insufficient, as the system is incorrectly predicted to be metallic. Furthermore, the band gap is extremely sensitive to the value of the lattice constant. Therefore, an accurate description of the atomic geometry is essential. Beyond semilocal XC functionals, more sophisticated methods are required to reliably obtain quasiparticle states.

[0194] In fact, the 3C-Ge band structure has also been calculated, approximating the XC self-energy within Hedin's GW approximation, and it is expected that this state-of-the-art excited state method is also applicable to hexagonal diamond Ge. However, the computational cost of Green's function calculations is very high, and it may be infeasible to apply them to more complex systems (such as alloys, doped or defective crystals, surfaces or interfaces). It is worth noting that the empirical pseudopotential method (EPM) commonly used for 3C-Ge can also help to reduce the computational cost. However, empirical methods that reproduce the experimental data of 3C-Ge very accurately will require additional assumptions to be reliably applied to 2H-Ge.

[0195] This paper provides a detailed analysis of the electronic and optical properties of 2H-Ge, with particular attention paid to the selection of accurate and computationally efficient XC functionals for ground-state and excited-state calculations. The functionals are first tested against experimental data on 3CGe. They are then used to provide a detailed analysis of the electronic and optical properties of 2H-Ge. In light of potential optoelectronic applications, particular attention is paid to conduction band ordering, direct and indirect band gaps, band splitting, effective mass, optical transition strength, and radiative lifetime.

[0196] All calculations were performed with the Vienna Abinitio Simulation Package (VASP) using the projected augmented wave (PAW) method and a plane wave cutoff of 500 eV. Shallow Ge 3d electrons were explicitly included as valence electrons. BZ integration was performed using 12 × 12 × 12 (3C-Ge) or 12 × 12 × 6 (2H-Ge) Γ-centered k-points (unless otherwise stated), ensuring convergence to a total energy of 1 meV / atom. Atomic geometry and elastic properties were calculated using (semi-)local XC functionals using LDA and the GGA parameterization methods PBE, PBEsol (an improved version of the PBE functional optimized for solids), and AM05.

[0197] The ground-state atomic structure, the isothermal bulk modulus B0 and its pressure derivative B′0 were determined by a series of fixed-volume relaxations and subsequent fitting of the resulting energy versus volume curves to the Vinet equation of state (EOS). The internal unit cell parameters were relaxed until the Hellmann-Feynman force dropped below Including SOC was found to have essentially no effect on the lattice parameters and only a small effect on the elastic constants. This observation is consistent with general conclusions for other simple solids and zinc-blende semiconductors.

[0198] It is well known that the KS band structure calculated in LDA or GGA significantly underestimates all band gaps and interband transition energies. On the other hand, quasiparticle calculations in the state-of-the-art GW approximation are challenging and computer-intensive for Ge, as SOC must be included to account for 3d electrons and calculate full dynamical screening.

[0199] Moreover, self-consistent calculations of the GW quasiparticle band structure are needed to overcome the problem of negative fundamental band gaps in the LDA / GGA starting electronic structures of both 3C-Ge and 2H-Ge (see Sections III and IV). One reason for the negative band gap is an overestimation of the pd repulsion. This is a direct result of the underestimated binding energy of the Ge 3d electrons within the LDA or GGA, which pushes the p-like valence band maximum (VBM) to higher energies. An improved description of the localized d states can be achieved by utilizing the Hubbard parameter U of the 3d electrons within the DFT+U method, at the expense of introducing an adjustable parameter. The DFT+U method was tested using a small but reasonable value of U = 1.3 eV with the Dudarev method, which reproduces the lattice constant of 3C-Ge and is consistent with the approximately U screened by the dielectric constant of bulk Ge. 原子 =15eV is roughly consistent with the atomic Coulomb integral diagram.

[0200] In the short-range Fock exchange fraction a = 0.25 and the inverse of the screening length The HSE06 hybrid functional is used to calculate reliable band structures for cubic and hexagonal Ge in the absence of a finite element. The HSE06 functional has been shown to yield reasonable indirect and direct band gaps for Ge and a variety of other sp semiconductors. The most important contribution to the band gap opening within the GW method is due to the screening exchange component of the electron self-energy. Coulomb holes, a secondary contributor to the GW self-energy, primarily influence the absolute position of the single-particle energy. In the HSE06 functional, the Fock exchange fraction a simulates the nonlocal nature of the self-energy and the screening of electron-electron interactions through an average dielectric constant of 1 / α.

[0201] As a computationally inexpensive alternative to hybrid functionals, we also consider Tran and Blaha's meta-GGA functional, MBJLDA, which is based on a modified Becke-Johnson (MBJ) exchange functional. The MBJLDA functional yields reasonable band gaps not only for 3C-Ge but also for other semiconductors. The significantly reduced computational cost allows the application of the MBJLDA functional to more complex systems. In particular, strained, disordered, or defective systems with larger supercells become computable, as in the case of potential optoelectronic applications of 2H-Ge. Furthermore, both hybrid and meta-GGA functionals allow for easy inclusion of SOC.

[0202] Considering optoelectronic applications (e.g., laser emission), the global optical emission properties of 2H-Ge near the fundamental absorption edge can be characterized by the optical transition matrix elements of the near-edge transitions and the radiative lifetime of the material. Here, the optical transition matrix elements are calculated in the longitudinal gauge. They are the matrix elements of the momentum operator p between the conduction band c and the valence band v at a given k point.<ck|p|vk> given.

[0203] The optical matrix elements at point G can be related to the characteristic quantities from k·p perturbation theory by introducing the average value of the squared momentum matrix elements on the spin-orbit degenerate states i, j = 1, 2 in the conduction and valence bands at the center of the region.

[0204]

[0205] Then, the Kane energy is

[0206]

[0207] and the (dimensionless) optical oscillator strength

[0208]

[0209] where ⊥ / || represents light polarized perpendicularly to or parallel to the c-axis of the hexagonal diamond structure. For 3C-Ge, these two directions are equivalent due to the isotropy of the material.

[0210] The radiative lifetime τ at temperature T, which is a global measure of the light emission properties of a material, is given by the thermally averaged recombination rate:

[0211]

[0212] Among them A cvk represents the radiative recombination rate of the vertical optical transition between the conducting state |ck> and the valence state |vk>, with a single particle energy of ε ck and ε vk , and the weight of k point is w kThe radiative recombination rate is

[0213]

[0214] where n eff is the refractive index of the effective medium consisting of the Ge sample and its environment (set to 1 in the following). The squares of the momentum matrix elements are averaged over all directions corresponding to the emission of unpolarized light. Equation (5) is given in the independent (quasi)particle approximation, i.e., electronic effects are neglected, which can however be easily taken into account. In Equation (4), it is assumed that the thermalization of electrons and holes after their injection is more efficient than radiative (or non-radiative) recombination. While the convergence of the radiative lifetime to the number of bands is very fast, we need 72×72×72 (3C-Ge) or 72×72×36 (2HGe) k points to sample the BZ with sufficiently high accuracy.

[0215] Regarding the diamond structure of germanium, the lattice constants, elastic properties, and cohesive energy of 3C-Ge have been calculated using various XC correlation functionals (see Table S4). Comparison with experimental values ​​reveals the expected trend: LDA tends to over-bind, while the inclusion of gradient corrections (particularly within PBE) leads to an underestimation of the chemical bond strengths. The functionals PBEsol and AM05 provide the best agreement with experiment. However, they still slightly overestimate the experimental lattice constants. Additional improvement can be achieved through DFT+U calculations (see Table S4), at the expense of the adjustable parameter U. Furthermore, the isothermal bulk modulus B0, its pressure derivative B′0, and the cohesive energy agree with experiment.

[0216] Subsequently, the band structure of 3C-Ge including SOC was calculated using PBEsol, HSE06, and MBJLDA functionals with PBEsol lattice constants (see Figure 22 and Table S5).

[0217]

[0218] a X-ray diffraction at T = 298.15 K

[65]

[0219] b At T = 298.15K

[66] , the elastic modulus C 11 and C 12 Ultrasonic measurement, using the relationship B0 = (C 11 +2C 12 ) / 3Get

[0220] c From reference

[67]

[0221] d X-ray diffraction at T = 10

[68]

[0222] e From fitting EOS to room temperature experimental data for various pressures

[69]

[0223] f From fitting the Vinet EOS to room temperature experimental data for various pressures

[70]

[0224] Table S4. Lattice constant a0, isothermal bulk modulus B0, its pressure derivative B0, and cohesive energy E of 3C-Ge coh Experimental (Exp.) values ​​are given for comparison.

[0225] The states at the high-symmetry points of the BZ are labeled according to two-group notation. The small difference between the PBEsol and experimental lattice constants corresponds to an isotropic tensile strain of <0.4%. The volume deformation potential of the direct band gap (the most volume-sensitive interband transition) amounts to -9.0 eV (MBJLDA), which means that the direct band gap difference due to lattice constant differences is less than 0.1 eV. For comparability, all calculations of the electronic and optical properties presented below are based on the PBEsol lattice constants.

[0226] Unlike experimental findings, GGA functionals such as PBEsol give negative KS band gaps for 3C-Ge (see Table S5), which is why they are not suitable for describing the electronic structure of this material. The band ordering, band energy, and spin-orbit splitting Dso obtained using the more complex HSE06 functional are in good agreement with the experimental results. Comparing the HSE06 and MBJLDA band structures close to the fundamental band gap, we find similar indirect and direct band gap. In addition, the spin-orbit splitting of the p-state is roughly the same. Moving further away from the band gap, the difference between the HSE06 and MBJLDA band energies increases. However, this is not a critical issue here, as we are mostly interested in the optoelectronic properties controlled by the electronic structure near the band gap. In particular, and The ordering of the conduction band minima is appropriate, and their energy distances are only slightly underestimated compared to experiment (independent of temperature). Note that GW corrections on the HSE06 or MBJLDA band structures are known to overestimate the band gap.

[0227] In Table S5, the electron and hole effective masses for the relevant band extrema are compiled. In addition to the band masses at the G point, the masses of the conduction band minima at the L point, parallel and perpendicular to the LG line, are given. These masses are derived from the corresponding HSE06 and MBJLDA band structures. The HSE06 masses are in good agreement with the experimental values. The MBJLDA functional slightly overestimates the experimental band masses, which is consistent with previous observations and the generally lower bandwidths in MBJLDA calculations compared to HSE06 calculations (see Figure 22 ).

[0228] Given the findings regarding 3C-Ge, we rely on the PBEsol functional for the structural properties of 2H-Ge. The electronic and optical properties of hexagonal diamond Ge will be investigated using the HSE06 and MBJLDA functionals. This strategy is justified by the fact that both allotropes of Ge are characterized by similar chemical bonding properties—i.e., they are both tetrahedral insulators. Therefore, the performance of these functionals should be largely transferable.

[0229]

[0230] a Schottky barrier electrical reflectivity at 10K

[72]

[0231] b Magnetic absorption at 1.5 K and 293 K

[73]

[0232] c Fine structure of the optical absorption edge at 291K

[74]

[0233] Table S5. Band energies and spin-orbit-induced band splittings Δ of 3C-Ge at high-symmetry points in the BZ calculated using PBEsol, HSE06, and MBJLDA functionals with PBEsol lattice constants. so Experimental low temperature and room temperature values ​​are provided for comparison. All values ​​are in eV.

[0234]

[0235] a Piezoelectric reflectivity at 30K

[75]

[0236] b Cyclotron resonance at 4 K in the presence of magnetic fields B oriented in multiple directions

[76]

[0237] c Cyclotron resonance at 1.4 K

[77]

[0238] d Magnetic phonon resonance at 120 K

[78]

[0239] Table S6. Effective electron and hole masses of 3C-Ge in units of free electron mass m. VBM splitting at Γ is heavy-hole-six Light Cavity and spin-orbit splitting holes The heavy hole and light hole masses are averaged in the Γ-X and Γ-L directions. and perpendicular to The conduction band minimum mass at L in both directions.

[0240] Regarding atomic geometry and bonding of hexagonal diamond germanium, the positions of the four atoms in the unit cell of the hexagonal diamond structure are defined by the hexagonal lattice constants a and c and the dimensionless internal unit cell parameter u. In Table S7, the results of calculations of the structural properties of 2H-Ge using various XC functionals are compiled. As already discussed for 3C-Ge, consistent overestimations and underestimations of the bond lengths are observed depending on the choice of functional. The cohesive energy E coh These trends are also reflected in the values ​​of and bulk modulus B0.

[0241] On average, the bond length of 2H-Ge is about the same as the bond length of 3C-Ge. This can be understood by a detailed analysis of the atomic geometry. The Ge-Ge bond parallel to the c-axis (bond length d || =uc and those bonds not parallel to the c-axis (bond length ) forms a distorted tetrahedron. Only when u=1 / 4+1 / 3(c / a) -2 When , all bonds in the distorted tetrahedron have the same length. And u 理想 = 3 / 8 of the ideal hexagonal diamond structure, the bond angles also become the same, and the coordination tetrahedrons are regular.

[0242] From Table S7, it can be deduced that c / a>(c / a) 理想 And u<u 理想 . Maintain relationship d ⊥ <d<d || , resulting in a tetrahedron slightly elongated along the c-axis. For example, we find that for the PBEsol functional, and Average bond length of 2H-Ge Only slightly smaller than the 3C-Ge bond length These findings are consistent with Lawaetz's empirical rule for III-V semiconductor compounds, which states that c / a > (c / a) 理想The calculated value of u almost follows the relationship u = 1 / 4 + 1 / 3 (c / a) -2 , which suggests that the deformation of the bonding tetrahedra in 2H-Ge can be interpreted as a good sharing of the deviations of the bond angles from the ideal values.

[0243] In summary, a relatively strong hexagonal crystal deformation in 2H-Ge was observed, characterized by a large (c / a > (c / a) 理想 and uu 理想 , despite the presence of covalent bonds. The calculated lattice parameters of 2H-Ge are in good agreement with the available experimental data. However, there are few experimental structural parameters in the literature and, in some cases, they were obtained from samples produced by nanostructuring and possibly straining.

[0244]

[0245] a Possible strain of the sample from microindentation

[79]

[0246] b Room temperature X-ray diffraction of unstrained crystalline nanowires

[80]

[0247] Table S7. Structural and elastic properties of 2H-Ge. Structural parameters a, c, and u, as well as the isothermal bulk modulus B0, its pressure derivative B'0, and the cohesive energy E coh Available experimental data are given for comparison.

[0248]

[0249] Table S8. Band energies of 2H-Ge calculated using different XC functionals. As the energy zero point. The crystal field and spin-orbit splitting parameter Δ of VBM have been calculated from the band energy cf 、 and Band energies from the empirical pseudopotential model (EPM) are given for comparison. All energies are in eV.

[0250] The band structure of 2H-Ge including SOC was calculated using HSE06 and MBJLDA functionals for the atomic structure of PBEsol (see Figure 23). For 3C-Ge, local (LDA) and semi-local (PBE, PBEsol, AM05) XC functionals give negative band gaps. The high symmetry states near the band gap are labeled according to the two-group notation. Their energies are also given in Table S8. The state notation is essentially the same as for the wurtzite structure. Due to the additional antisymmetry in the hexagonal diamond crystal structure, some high symmetry states also have well-defined parities, which are indicated by superscripts. The parities of the high symmetry states at the time-reversal invariant momentum (TRIM) points are calculated (see Figure 23 and Table S8), the points are characterized by the relationship k TRIM =-k TRIM +G. At the TRIM points, the displacement of the reciprocal lattice vector G reverses the application of time-flip symmetry. In the hexagonal diamond structure, these TRIM points are the Γ, 3L, and 3M points of the hexagonal BZ. The parity we obtained is partially inconsistent with those given by the prior art. However, the optical oscillator strengths we obtained for near-bandgap transitions (see below) confirm this finding. In addition, the parity is consistent with known prior art results for carbon in the hexagonal diamond structure.

[0251] 2H-Ge is found to be a direct bandgap semiconductor with a bandgap of 0.286 eV (HSE06) or 0.298 eV (MBJLDA). Note that the exact bandgap value is highly sensitive to lattice strain due to the large deformation potential of the gap-forming states. The results are in good agreement with the 0.31 eV (empirical pseudopotential method) or 0.32 eV (HSE06 calculation), which is slightly higher than the GW bandgap of 0.23 eV obtained by existing techniques. For 3CGe, the HSE06 and MBJLDA energies of the near-gap states match very well. Deviations occur for states further out of the bandgap region (see Figure 23 ).

[0252] The conduction band minimum of 3C-Ge is four State. In the direction of

[111] The state is backfolded to state and becomes the conduction band minimum of 2H-Ge. The other L points of 3C-Ge are mapped to points between M and L on the U line of the hexagonal BZ. In the ideal hexagonal diamond structure, the back-folded L point is located at In the relaxed structure, they move slightly along the U line. The minimum of the first conduction band on the U line of 2H-Ge is observed at , which is energetically similar to that of 3C-Ge. The state is almost degenerate.

[0253] and Cube Compared with the state, the The state shifts by 0.4 eV, which cannot be understood by simple folding arguments. However, it is consistent with the behavior of Si from diamond to hexagonal diamond structure, while it is clearly different from the small band gap opening in diatomic semiconductors when the structure changes from zinc blende to wurtzite. The state is consistent with the second conduction band in the hexagonal diamond structure state.

[0254] Due to the antisymmetry in the hexagonal diamond structure, the valence band in 2H-Ge does not show the spin-orbit splitting caused by k dispersion along the Γ-M line as occurs in wurtzite semiconductors. According to the kp theory, we can write the energy splitting at Γ as

[0255]

[0256] These equations enable the extraction of the crystal field splitting Δ cf and the spin-orbit splitting parameters parallel and perpendicular to the c-axis and Band ordering at the top of the valence band we discovered for 2H-Ge As in wurtzite semiconductors (except that the band ordering is Γ 7v+ >Γ 9v >Γ 7v- This ordering is consistent with that observed in α-AlN and ZnO (except for AlN and ZnO). Note that the subscript 7v+ denotes bands of identical symmetry; the symbols ± are used only to distinguish upper and lower states. Do not confuse them with even-parity superscripts.

[0257] The crystal field splitting has been extracted from the calculation without SOC, and the spin-orbit splitting parameters have been calculated from the band splitting calculated with SOC using Equation (6). The obtained values ​​are compiled in Table S8. In particular, the directionally averaged spin-orbit splitting The spin-orbit splitting of the VBM in 3C-Ge compares well (see Table S5). The crystal field splitting in 2H-Ge is much larger than that of III-V compounds that crystallize in zinc blende or wurtzite structures under ambient conditions. However, the large crystal field splitting of 2H-Ge is consistent with a significant deformation of the bonding tetrahedron, as indicated by the increase in c / a relative to its ideal value (see Table S7). The large Δ cf make The levels are shifted towards higher energies, thus explaining the observed small direct band gap. It should be emphasized that the quasi-cubic approximation used in the prior art It is not valid for 2H-Ge and causes the splitting parameters to be inconsistent with the numerical values.

[0258] The effective masses of the band energies at Γ are summarized in Table S9. The small electron mass of the conduction band with almost vanishing anisotropy has the characteristics of 3C-Ge in Table S6. On the other hand, in the conduction band minimum The mass tensor at is highly anisotropic, with large masses along the hexagonal c-axis and small masses in planes perpendicular to it. These values ​​are consistent with those in 3C-Ge. Longitudinal and transverse mass at minimum and Qualitatively consistent. The strong directional dependence of the conduction band dispersion is consistent with the identity of the band symmetry. The hole mass also exhibits a strong asymmetry, especially for and bring.

[0259]

[0260] Table S9. Effective electron and hole masses of 2H-Ge in units of free electron mass m. The masses are given for various directions in the BZ. The VBM splitting at G into heavy holes Light Cavity and split holes

[0261] The oscillator strengths for the optical transitions between the three highest valence bands and the two lowest conduction bands of 2H-Ge are given in Table S10. Transitions that are dipole-forbidden due to group theory arguments are indicated by horizontal lines. These symmetry considerations confirm the determined band ordering at the Γ point. exist Figure 24 In

[15] , the corresponding optical matrix elements are plotted along high symmetry lines close to G. It is clear that a transition that is dipole-forbidden at G can be dipole-allowed in its immediate vicinity. As a direct consequence, a transition that is dipole-forbidden at G at zero temperature can become optically active at higher temperatures when electrons and holes fill the band also around G. Furthermore, deviations from a perfect hexagonal diamond structure due to defects, nanostructuring, or surfaces / interfaces can break the k-selection rule, allowing previously dipole-forbidden transitions to become dipole-allowed.

[0262]

[0263] Table S10. Optical transitions between the valence and conduction bands of 2H-Ge, specified as transition energies, optical transition matrix elements, Kane energies, and oscillator strengths. Transitions that are dipole-forbidden due to symmetry are indicated by horizontal lines. Values ​​have been calculated for light polarized perpendicular to and parallel to the c-axis using the HSE06 and MBJLDA functionals.

[0264] Hexagonal diamond Ge is a direct semiconductor with a very weak lowest optical transition, which shows a significant change in luminescence and absorption compared to cubic Ge. This effect can be expected to be stronger than that of Si and SiGe alloys. In order to clearly illustrate the global light emission properties, Figure 25 The radiative lifetime t as a function of temperature is shown in . The lifetime is calculated according to Equation (4) using the transition energies and optical matrix elements obtained using the HSE06 and MBJLDA functionals, which produce comparable results. However, full k-point convergence can only be obtained using the computationally cheaper MBJLDA functional. When we compare the radiative lifetimes of 3C-Ge and 2HGe, we find significant differences. As expected, the radiative lifetime of cubic Ge is largely independent of temperature due to its larger fundamental band gap. Excluding optical transitions away from Γ in the lifetime evaluation does not have any significant effect. On the other hand, the radiative lifetime of hexagonal diamond Ge, which is very high at low temperatures, shortens rapidly above 400K due to the extremely weak oscillator strength of the lowest Γ-Γ transition, when the optically active second conduction band begins to be laid out. In addition, optical transitions away from G contribute significantly to the lifetime. This is easily understood by recalling that the optical matrix elements that vanish at G due to symmetry can be non-zero in the immediate vicinity of the BZ center (see Figure 24 ).

[0265] The large band gap difference between 3C-Ge and 2H-Ge and its consequences for the temperature-dependent band topology explain the large difference of several orders of magnitude in τ for low temperatures. (Note that similar curves have been published in the prior art for the thermalization of electrons and holes in Ge nanocrystals.) For example, manipulation of the atomic structure of 2H-Ge by creating strain or alloying can lead to and The inversion of the conductive state may significantly improve the light emission properties of hexagonal diamond Ge, thereby providing a broad space for designing its optoelectronic performance.

[0266] The hexagonal diamond (2H) phase of Ge, which can be grown using hexagonal III-V nanowire templates, is considered a good candidate for on-Si optical interconnects and Si-phase-capable quantum light sources due to its predicted direct bandgap. Because experimental data and reliable calculations for 2H-Ge are scarce and often inconsistent, in this work we first establish computational methods for efficient predictive ab initio calculations. We benchmark the performance of several XC functionals from DFT, including meta-GGA and hybrid functionals, to calculate the structural and electronic properties of the experimentally and theoretically well-known diamond-structured (3C)Ge. In a second step, these functionals are used to predict the structural, electronic, and optical properties of hexagonal diamond Ge.

[0267] The atomic structure of 2H-Ge was calculated using the PBEsol functional, which has been shown to yield excellent lattice parameters for the well-studied cubic phase of Ge. The electronic structures of cubic and hexagonal Ge in diamond were calculated using the HSE06 hybrid functional and the MBJLDA meta-GGA, and the results from both methods were found to be consistent and in good agreement with the available experimental data. The conduction band minimum comes from the back folding of the L point of diamond structure Ge to the Γ point of hexagonal BZ, and also comes from the lowest conduction band at Γ of cubic Ge. The conduction band states are pushed to higher energies. The energy order of the three highest valence bands is Although the spin-orbit splittings are similar in the hexagonal and cubic phases, a large crystal field splitting is observed in 2H-Ge. The crystal field splitting is small, only about 0.3 eV. The reason for the band gap. The second conduction band minimum The calculated electron and hole effective masses for cubic Ge are approximately 0.3 eV higher in energy. The values ​​found in the literature are in good agreement, thus providing reliable predictions of the electron and hole effective masses in 2H-Ge.

[0268] The dipole-allowed and dipole-forbidden optical transitions between the highest valence band and the lowest conduction band near the G point and their polarization dependence are consistent with the band symmetry identity. Hexagonal Ge diamond appears to be a semiconductor with a direct fundamental band gap in the infrared, which only exhibits a non-zero but small optical oscillator strength for ordinary light polarization. In contrast, the optical transition to the second lowest conduction band is dipole-allowed and has a large oscillator strength. It is noted that the distance between the first and second conduction bands and the size of the band gap appear to be sensitive to structural parameters. Therefore, a careful study of the luminescence properties (including their temporal dependence) and the absorption edge, also taking into account the effects of strain, is recommended to further elucidate the optical and optoelectronic properties of the promising new material hexagonal Ge diamond.

Claims

1. A light-emitting element comprising a light-emitting portion, wherein the light-emitting portion comprises hexagonal Si 1-x Ge x Compound material, the hexagonal Si 1-x Ge x The compound material has a direct band gap for emitting light, wherein the hexagonal Si 1-x Ge x The compound material is constructed to emit a radiation emission coefficient B at 300K rad Meet 0.7×10 -10 cm 3 / s < B rad < 11×10 -10 cm 3 / s of light.

2. The light-emitting element according to claim 1, wherein the hexagonal Si 1-x Ge x The compound material is constructed to emit radiation at 300 K with a B coefficient B rad Meet 0.7×10 -10 cm 3 / s < B rad < 8.3×10 -10 cm 3 / s of light.

3. The light-emitting element according to claim 1 or 2, wherein the hexagonal Si 1-x Ge x The compound material is configured to emit light between 1.8 µm and 3.5 µm, where 1.8 µm corresponds to x=0.65 and 3.5 µm corresponds to x=1.

0.

4. The light-emitting element according to claim 1 or 2, wherein the hexagonal Si 1-x Ge x The compound material includes hexagonal Si structured to emit light from 1.5 µm to 7.0 µm. 1-x Ge x Strained quantum well structures of different compositions of compound materials.

5. The light-emitting element according to claim 1 or 2, wherein the hexagonal Si 1-x Ge x The compound materials exhibit direct bandgap emission with sub-nanosecond recombination lifetime.

6. The light-emitting element according to claim 1 or 2, wherein the hexagonal Si 1-x Ge x The compound material exhibits a linear dependence of the photoluminescence intensity on the excitation power.

7. The light-emitting element according to claim 1, wherein the hexagonal Si 1-x Ge x The x of compound materials is limited to 0.2 <x<1.0。 8. The light-emitting element according to claim 1, wherein the hexagonal Si 1-x Ge x The x of compound materials is limited to 0.6 <x<1.0。 9. The light-emitting element according to claim 1, wherein the hexagonal Si 1-x Ge x The x of compound materials is limited to 0.2 <x<0.99。 10. The light-emitting element according to claim 1, wherein the hexagonal Si 1-x Ge x The x of compound materials is limited to 0.2 <x<0.9。 11. The light-emitting element according to claim 1, wherein the hexagonal Si 1-x Ge x The x of compound materials is limited to 0.6 <x<0.9。 12. The light-emitting element according to claim 1, wherein the hexagonal Si 1-x Ge x The x of compound materials is limited to 0.6 <x<0.99。 13. The light emitting element according to claim 1, comprising an integral structure, wherein the integral structure comprises a hexagonal Si 1-x Ge x The compound material serves as the cubic Si substrate of the light emitting portion.

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