Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# Direct-bandgap emission from hexagonal Ge and SiGe alloys

## Abstract

Silicon crystallized in the usual cubic (diamond) lattice structure has dominated the electronics industry for more than half a century. However, cubic silicon (Si), germanium (Ge) and SiGe alloys are all indirect-bandgap semiconductors that cannot emit light efficiently. The goal1 of achieving efficient light emission from group-IV materials in silicon technology has been elusive for decades2,3,4,5,6. Here we demonstrate efficient light emission from direct-bandgap hexagonal Ge and SiGe alloys. We measure a sub-nanosecond, temperature-insensitive radiative recombination lifetime and observe an emission yield similar to that of direct-bandgap group-III–V semiconductors. Moreover, we demonstrate that, by controlling the composition of the hexagonal SiGe alloy, the emission wavelength can be continuously tuned over a broad range, while preserving the direct bandgap. Our experimental findings are in excellent quantitative agreement with ab initio theory. Hexagonal SiGe embodies an ideal material system in which to combine electronic and optoelectronic functionalities on a single chip, opening the way towards integrated device concepts and information-processing technologies.

This is a preview of subscription content, access via your institution

## Relevant articles

Open Access articles citing this article.

• ### Ultrawide-bandgap semiconductor of carbon-based materials for meta-photonics-heterostructure, lasers, and holographic displays

AAPPS Bulletin Open Access 27 January 2023

• ### Prospects and applications of on-chip lasers

eLight Open Access 04 January 2023

• ### Highly efficient nonlinear optical emission from a subwavelength crystalline silicon cuboid mediated by supercavity mode

Nature Communications Open Access 18 May 2022

## Access options

Rent or buy this article

Get just this article for as long as you need it

\$39.95

Prices may be subject to local taxes which are calculated during checkout

## Data availability

All data underlying this study are available from the 4TU ResearchData repository at https://doi.org/10.4121/uuid:68e75799-0378-4130-9764-b80cb1f2319b.

## References

1. Iyer, S. S. & Xie, Y. H. Light emission from silicon. Science 260, 40–46 (1993).

2. Miller, D. A. B. Silicon integrated circuits shine. Nature 384, 307–308 (1996).

3. Ball, P. Let there be light. Nature 409, 974–976 (2001).

4. Canham, L. Gaining light from silicon. Nature 408, 411–412 (2000).

5. Green, M. A., Zhao, J., Wang, A., Reece, P. J. & Gal, M. Efficient silicon light-emitting diodes. Nature 412, 805–808 (2001).

6. Vivien, L. Silicon chips lighten up. Nature 528, 483–484 (2015).

7. Atabaki, A. H. et al. Integrating photonics with silicon nanoelectronics for the next generation of systems on a chip. Nature 556, 349–354 (2018).

8. Wang, J. et al. Multidimensional quantum entanglement with large-scale integrated optics. Science 360, 285–291 (2018).

9. Cheben, P., Halir, R., Schmid, J. H., Atwater, H. A. & Smith, D. R. Subwavelength integrated photonics. Nature 560, 565–572 (2018).

10. Soref, R., Buca, D., Yu, S.-Q. & Group, I. V. Photonics: driving integrated optoelectronics. Opt. Photonics News 27, 32–39 (2016).

11. Raffy, C., Furthmüller, J., Bechstedt, F. Properties of hexagonal polytypes of group-IV elements from first-principles calculations. Phys. Rev. B 66, 075201 (2002).

12. De, A. & Pryor, C. E. Electronic structure and optical properties of Si, Ge and diamond in the lonsdaleite phase. J. Phys. Condens. Matter 26, 045801 (2014).

13. Cartoixà, X. et al. Optical emission in hexagonal SiGe nanowires. Nano Lett. 17, 4753–4758 (2017).

14. Rödl, C. et al. Accurate electronic and optical properties of hexagonal germanium for optoelectronic applications. Phys. Rev. Mater. 3, 034602 (2019).

15. Shen, Y. et al. Silicon photonics for extreme scale systems. J. Lightwave Technol. 37, 245–259 (2019).

16. Thomson, D. et al. Roadmap on silicon photonics. J. Opt. 18, 073003 (2016).

17. Muñoz, P. et al. Silicon nitride photonic integration platforms for visible, near-infrared and mid-infrared applications. Sensors 17, 2088 (2017).

18. Wang, R. et al. III–V-on-silicon photonic integrated circuits for spectroscopic sensing in the 2–4 µm wavelength range. Sensors 17, 1788 (2017).

19. Poulton, C. V. et al. Coherent solid-state LIDAR with silicon photonic optical phased arrays. Opt. Lett. 42, 4091–4094 (2017).

20. Soref, R. Enabling 2 μm communications. Nat. Photon. 9, 358–359 (2015).

21. Vincent, L. et al. Novel heterostructured Ge nanowires based on polytype transformation. Nano Lett. 14, 4828–4836 (2014).

22. Qiu, Y. et al. Epitaxial diamond-hexagonal silicon nano-ribbon growth on (001) silicon. Sci. Rep. 5, 12692 (2015).

23. Pandolfi, S. et al. Nature of hexagonal silicon forming via high-pressure synthesis: nanostructured hexagonal 4H polytype. Nano Lett. 18, 5989–5995 (2018).

24. He, Z., Maurice, J. L., Li, Q. & Pribat, D. Direct evidence of 2H hexagonal Si in Si nanowires. Nanoscale 11, 4846–4853 (2019).

25. Dushaq, G., Nayfeh, A. & Rasras, M. Hexagonal germanium formation at room temperature using controlled penetration depth nano-indentation. Sci. Rep. 9, 1593 (2019).

26. Hauge, H. I. T. et al. Hexagonal silicon realized. Nano Lett. 15, 5855–5860 (2015).

27. Hauge, H. I. T., Conesa-Boj, S., Verheijen, M. A., Kölling, S. & Bakkers, E. P. A. M. Single-crystalline hexagonal silicon-germanium. Nano Lett. 17, 85–90 (2017).

28. Würfel, P. The chemical potential of radiation. J. Phys. C 15, 3967–3985 (1982).

29. Lasher, G. & Stern, F. Spontaneous and stimulated recombination radiation in semiconductors. Phys. Rev. 133, A553 (1964).

30. Moss, T. S. The interpretation of the properties of indium antimonide. Proc. Phys. Soc. B 67, 775–782 (1954).

31. Wirths, S. et al. Lasing in direct-bandgap GeSn alloy grown on Si. Nat. Photon. 9, 88–92 (2015).

32. Prasankumar, R. P., Choi, S., Trugman, S. A., Picraux, S. T. & Taylor, A. J. Ultrafast electron and hole dynamics in germanium nanowires. Nano Lett. 8, 1619–1624 (2008).

33. Yablonovitch, E., Allara, D. L., Chang, C. C., Gmitter, T. & Bright, T. B. Unusually low surface-recombination velocity on silicon and germanium surfaces. Phys. Rev. Lett. 57, 249–252 (1986).

34. Lush, G. B. B-coefficient in n-type GaAs. Sol. Energy Mater. Sol. Cells 93, 1225–1229 (2009).

35. Semyonov, O., Subashiev, A., Chen, Z. & Luryi, S. Radiation efficiency of heavily doped bulk n-InP semiconductor. J. Appl. Phys. 108, 013101 (2010).

36. Trupke, T. et al. Temperature dependence of the radiative recombination coefficient of intrinsic crystalline silicon. J. Appl. Phys. 94, 4930 (2003).

37. Miller, D. A. B. Attojoule optoelectronics for low-energy information processing and communications. J. Lightwave Technol. 35, 346–396 (2017).

38. Staudinger, P., Mauthe, S., Moselund, K. E. & Schmid, H. Concurrent zinc-blende and wurtzite film formation by selection of confined growth planes. Nano Lett. 18, 7856–7862 (2018).

39. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

40. Perdew, J. P. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008).

41. Tran, F. & Blaha, P. Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential. Phys. Rev. Lett. 102, 226401 (2009).

42. Borlido, P. et al. Large-scale benchmark of exchange–correlation functionals for the determination of electronic band gaps of solids. J. Chem. Theory Comput. 15, 5069–5079 (2019).

43. Schleife, A., Rödl, C., Furthmüller, J. & Bechstedt, F. Electronic and optical properties of MgZnO and CdZnO from ab initio calculations. New J. Phys. 13, 085012 (2011).

44. Kriegner, D., Wintersberger, E. & Stangl, J. xrayutilities: A versatile tool for reciprocal space conversion of scattering data recorded with linear and area detectors. J. Appl. Cryst. 46, 1162–1170 (2013).

45. Kölling, S. et al. Atom-by-atom analysis of semiconductor nanowires with parts per million sensitivity. Nano Lett. 17, 599–605 (2017).

46. Kölling, S. et al. Impurity and defect monitoring in hexagonal Si and SiGe nanocrystals. ECS Trans. 75, 751–760 (2016).

47. Jacobsson, D. et al. Phase transformation in radially merged wurtzite GaAs nanowires. Cryst. Growth Des. 15, 4795–4803 (2015).

48. Alexander, M. N. & Holcomb, D. F. Semiconductor-to-metal transition in n-type group IV semiconductors. Rev. Mod. Phys. 40, 815 (1968).

49. Chen, H. L. et al. Determination of n-type doping level in single GaAs nanowires by cathodoluminescence. Nano Lett. 17, 6667–6675 (2017).

50. Katahara, J. K. & Hillhouse, H. W. Quasi-Fermi level splitting and sub-bandgap absorptivity from semiconductor photoluminescence. J. Appl. Phys. 116, 173504 (2014).

51. Einstein, A. Zur Quantentheorie der Strahlung. Phys. Z. 18, 361–391 (1917).

52. Ortolani, M. et al. Long intersubband relaxation times in n-type germanium quantum wells. Appl. Phys. Lett. 99, 201101 (2011).

53. Virgilio, M. et al. Modeling picosecond electron dynamics of pump-probe intersubband spectroscopy in n-type Ge/SiGe quantum wells. Phys. Rev. B 86, 205317 (2012).

54. Virgilio, M. et al. Combined effect of electron and lattice temperatures on the long intersubband relaxation times of Ge/SixGe1-x quantum wells. Phys. Rev. B 89, 045311 (2014).

55. Klingshirn, C. F. Semiconductor Optics (Springer, 2012).

56. Green, M. A. Intrinsic concentration, effective densities of states, and effective mass in silicon. J. Appl. Phys. 67, 2944–2954 (1990).

57. Varshni, Y. P. Temperature dependence of the energy gap in semiconductors. Physica 34, 149–154 (1967).

58. Viña, L., Logothetidis, S. & Cardona, M. Temperature dependence of the dielectric function of germanium. Phys. Rev. B 30, 1979–1991 (1984).

59. Polimeni, A. et al. Effect of temperature on the optical properties of (InGa)(AsN)/ GaAs single quantum wells. Appl. Phys. Lett. 77, 2870 (2000).

60. Reshchikov, M. A. Temperature dependence of defect-related photoluminescence in III-V and II-VI semiconductors. J. Appl. Phys. 115, 012010 (2014).

61. Leroux, M. et al. Temperature quenching of photoluminescence intensities in undoped and doped GaN. J. Appl. Phys. 86, 3721 (1999).

62. Bacher, G. et al. Influence of barrier height on carrier dynamics in strained InxGa1−xAs/GaAs quantum wells. Phys. Rev. B43, 9312–9315 (1991).

63. Lourenço, S. A. et al. Effect of temperature on the optical properties of GaAsSbN/GaAs single quantum wells grown by molecular-beam epitaxy. J. Appl. Phys. 93, 4475–4479 (2003).

64. Schenk, H. P. D., Leroux, M. & De Mierry, P. Luminescence and absorption in InGaN epitaxial layers and the van Roosbroeck-Shockley relation. J. Appl. Phys. 88, 1525–1534 (2000).

65. Lambkin, J. D. et al. Temperature dependence of the photoluminescence intensity of ordered and disordered In0.48Ga0.52P. Appl. Phys. Lett. 65, 73–75 (1994).

66. Feldmann, J. et al. Dependence of radiative exciton lifetimes in quantum. Phys. Rev. Lett. 59, 2337–2340 (1987).

67. ’tHooft, G. W., van der Poel, W. A. J. A., Molenkamp, L. W. & Foxon, C. T. Giant oscillator strength of free excitons in GaAs. Phys. Rev. B 35, 8281–8284 (1987).

68. Bellessa, J. et al. Quantum-size effects on radiative lifetimes and relaxation of excitons in semiconductor nanostructures. Phys. Rev. B 58, 9933–9940 (1998).

69. Jiang, N. et al. Long minority carrier lifetime in Au-catalyzed GaAs/AlxGa1-xAs core-shell nanowires. Appl. Phys. Lett. 101, 023111 (2012).

70. Virgilio, M. et al. Radiative and non-radiative recombination in tensile strained Ge microstrips: photoluminescence experiments and modeling. J. Appl. Phys. 118, 233110 (2015).

71. Schubert, E. F. Light-Emitting Diodes (Cambridge Univ. Press, 2006).

72. Benz, G. & Conradt, R. Auger recombination in GaAs and GaSb. Phys. Rev. B 16, 843–855 (1977).

73. Galler, B. et al. Experimental determination of the dominant type of Auger recombination in InGaN quantum wells. Appl. Phys. Express 6, 112101 (2013).

74. Haug, A., Kerkhoff, D. & Lochmann, W. Calculation of Auger coefficients for III-V semiconductors with emphasis on GaSb. Phys. Status Solidi 89, 357–365 (1978).

75. ’t Hooft, G. W., Leys, M. R. & Talen-v.d. Mheen, H. J. Temperature dependence of the radiative recombination coefficient in GaAs-(Al, Ga)As quantum wells. Superlatt. Microstruct. 1, 307–310 (1985).

76. Mayer, B. et al. Monolithically integrated high-β nanowire lasers on silicon. Nano Lett. 16, 152–156 (2016).

77. Drexhage, K. H., Kuhn, H. & Schäfer, F. P. Variation of the fluorescence decay time of a molecule in front of a mirror. Phys. Chem. Chem. Phys. 72, 329 (1968).

78. Drexhage, K. H. Influence of a dielectric interface on fluorescence decay time. J. Lumin. 1–2, 693–701 (1970).

79. Yoo, Y. S., Roh, T. M., Na, J. H., Son, S. J. & Cho, Y. H. Simple analysis method for determining internal quantum efficiency and relative recombination ratios in light emitting diodes. Appl. Phys. Lett. 102, 211107 (2013).

80. Schmidt, T., Lischka, K. & Zulehner, W. Excitation-power dependence of the near-band-edge photoluminescence of semiconductors. Phys. Rev. B 45, 8989–8994 (1992).

81. D’Agostino, D. et al. Monolithically integrated widely tunable coupled cavity laser source for gas sensing applications around 2.0μm wavelength. In Advanced Photonics OSA Technical Digest Paper JT5A.1 (Optical Society of America, 2015).

82. Latkowski, S. et al. Monolithically integrated widely tunable laser source operating at 2 μm. Optica 3, 1412–1417 (2016).

83. Assali, S. et al. Growth and optical properties of direct band gap Ge/Ge0.87Sn0.13 core/shell nanowire arrays. Nano Lett. 17, 1538–1544 (2017).

84. Kumar, A. et al. On the interplay between relaxation, defect formation, and atomic Sn distribution in Ge(1−x)Sn(x) unraveled with atom probe tomography. J. Appl. Phys. 118, 025302 (2015).

Download references

## Acknowledgements

We thank D. Buca, A. Polimeni, J. de Boeck and C. Palmstrøm for discussions. We thank R. van Veldhoven for the technical support of the MOVPE reactor and providing the MQW samples. We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at PETRA III and we thank F. Bertram for assistance in using beamline P08. This project received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement number 735008 (SiLAS), the Dutch Organization for Scientific Research (NWO) and from a Marie Skłodowska-Curie Action fellowship (GA number 751823). We acknowledge Solliance, a solar energy R&D initiative of ECN, TNO, Holst, TU/e, imec, Forschungszentrum Jülich, and the Dutch province of Noord-Brabant for funding the TEM facility. We thank the Leibniz Supercomputing Centre for providing computational resources on SuperMUC (project number pr62ja).

## Author information

Authors

### Contributions

E.M.T.F, C.M. and Y.R. carried out the growth of wurtzite nanowire cores. E.M.T.F. carried out the growth of hex-SiGe shells and analysed the data. A.D. and D.B. carried out the photoluminescence spectroscopy. A.D. analysed the optical data. M.A.J.v.T., A.D. and V.T.v.L. performed time-resolved spectroscopy on single nanowires; K.K. performed optical finite difference time domain simulations. J.R.S., C.R., J.F. and S.B. performed the DFT calculations. D.Z. and J.S. performed the XRD measurements. S.K. performed the APT characterization. M.A.V. performed the TEM analysis. J.R.S., J.F., S.B., J.E.M.H. and E.P.A.M.B. supervised the project. F.B. contributed to the interpretation of data and E.M.T.F., A.D., D.Z., S.B., J.J.F., J.E.M.H. and E.P.A.M.B. contributed to the writing of the manuscript. All authors discussed the results and commented on the manuscript

### Corresponding author

Correspondence to Erik P. A. M. Bakkers.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Schematic illustration of the nanowire growth process.

a, The core nanowire growth starts with a GaAs (111)B substrate patterned with Au catalyst seeds, which is introduced in the MOVPE reactor and annealed at a temperature higher than the eutectic temperature forming an alloy between the catalyst seed and the substrate. b, Next, the GaAs gas precursors (TMGa and AsH3) are introduced, and Au-catalysed GaAs core nanowires are grown. To proceed with the SiGe shell growth, Au seeds are chemically etched away from the GaAs cores and the surface of the cores is repaired (c), and the sample is reintroduced to the MOVPE reactor (d). A hex-Si1 − xGex shell is epitaxially grown around the GaAs cores from precursors (Si2H6 and GeH4). (The molecules are drawn with the freely available MolView Software (http://www.molview.org/)). The 30° tilted scanning electron microscopy images in the bottom panels of ad are representative of the results of the growth steps in the top panels, with insets in b and c displaying a magnified image of the nanowire. e, A 30° tilted-overview representative scanning electron microscopy image of hex-Ge/GaAs Core shells corresponding to what is shown in Fig. 2, confirming the uniformity of the growth across the sample.

### Extended Data Fig. 2 Crystal quality of the wurtzite GaAs nanowire cores.

a, Bright-field TEM images recorded in the [11$$\bar{2}$$0] zone axis of five representative GaAs core nanowires of a pure wurtzite crystal (stacking faults indicated with red lines), with a stacking-fault density of 0–6 stacking faults per micrometre. b, A zoomed-in bright-field TEM image of the top part of one of the nanowires in a (blue circle), indicating the purity of the crystal structure. c, HAADF-STEM image of the red box in b, displaying the ABAB stacking of the GaAs atomic columns, which is the hallmark of the hexagonal crystal structure. The red shading highlights a stacking fault forming one cubic layer in the hexagonal structure.

### Extended Data Fig. 3 Ge content calibration curve.

A calibration curve for the incorporated atomic fraction of Ge in the as-grown SiGe shells discussed in Fig. 2e, f and Fig. 5. Owing to growth kinetics, the input percentage of gas precursors in the MOVPE reactor does not always match the actual incorporated atomic percentage in the grown Si1 − xGex shell structures. To map the compositional output onto the input Ge fraction, the real content of four Si1 − xGex shells was measured by EDX-STEM and plotted as solid black circles. The compositions of additional samples were determined based on their input Ge fraction by interpolating the EDX-STEM data points and are indicated by blue triangles. The error bars for the black data points represent the standard deviation in the composition across three different analysed nanowires per sample. The accuracy of EDX in STEM is confirmed by determining the composition of a single sample, corresponding to MOVPE input Si0.10Ge0.90, with both EDX-STEM and APT. The APT data is shown in Extended Data Fig. 6 and was performed on three different nanowires. Both techniques yielded almost the same Ge composition—0.74 and 0.75 respectively—which is within the standard deviation across the whole sample. The reproducibility of this calibration method is also confirmed by photoluminescence, where almost identical spectra are observed for two different samples grown with the same input.

### Extended Data Fig. 4 Full series of symmetric (0008) reflections of hex-Si1 − xGex.

a, An RSM of as-grown wurtzite GaAs nanowires on a cub-GaAs substrate, containing the wurtzite-GaAs (0008) reflection and the cub-GaAs (444) reflection. b, An RSM for a sample similar to that in a but with a thick Ge shell, including the cub-GaAs (444) substrate reflection and the hex-Ge (0008) reflection. c–f, Additional RSMs are shown for samples with Si1 − xGex shells, for x = 0.92 (c), for x = 0.86 (d), for x = 0.74 (e) and for x = 0.61 (f). The intensities (Int) of the reflections are colour-coded on a logarithmic scale, in units of counts per second (cps). A clearly increasing shift of Qout-of-plane can be observed for increasing Si content, corresponding to a decreasing lattice constant. For the RSMs in d and e a reflection from a parasitic, epitaxial cub-SiGe layer is also found. g, Tabulated hexagonal lattice parameters of all measured hex-Si1 − xGex samples with corresponding error values extracted from XRD measurements. The errors given take into account the accuracy of defining the peak position with a two-dimensional fit as described, as well as the scattering of the individual lattice parameter values extracted from the evaluation of multiple peaks. EDX-STEM was used to determine the composition of some samples and the rest were interpolated on the basis of the curve in Extended Data Fig. 3.

### Extended Data Fig. 5 Crystal-truncation-rod scan and polar scan.

For a representative sample with Si0.20Ge0.80 shells and a GaAs core, a scan along the asymmetric [$$\bar{1}$$01L] nanowire crystal truncation rod is shown, covering a total of three wurtzite reflections, [$$\bar{1}$$015], [$$\bar{1}$$016] and [$$\bar{1}$$017]. L refers to a crystallographic coordinate according to the HKiL Miller-Bravais (i = −(H + L)) index notation. In addition, also the cubic [224] substrate reflection and the parasitic cub-SiGe epilayer is visible (as a double-peak feature around the [224] reflection). In between the wurtzite reflections no additional reflections are visible, which indicates that only the pure wurtzite 2H phase is present in the nanowire system. The inset shows an XRD polar scan around the [$$\bar{1}$$016] reflection, confirming the six-fold symmetry of the wurtzite lattice. Each reflection, seen in the polar scan, is separated by a sample rotation of exactly 60° from the next reflection (φ rotation axis, χ tilt axis). The absence of additional Bragg reflections in between indicates a pure wurtzite phase and high crystal quality.

### Extended Data Fig. 6 APT characterization of hex-Ge and Si0.25Ge0.75.

a, c, Ge (red) and Si (cyan) is shown to form a shell around the hexagonal Ga (green) and the As (blue) core. a, A three-dimensional volume reconstruction of part of a hex-GaAs/Ge core/shell nanowire with thicknesses of 35 nm/80 nm. For clarity, only a slab of 50 nm thickness of the entire 1.4-µm-long analysis is shown. c, A three-dimensional volume reconstruction of part of a hex-GaAs/Si0.25Ge0.75 core/shell nanowire with thicknesses of 35 nm/46 nm. For clarity, only a slab of 40 nm thickness of the entire 1.1-µm-long analysis is shown. b, d, A plot of the atomic species concentration in the Ge (Si0.25Ge0.75) shell in the rectangles in a (white) and c (yellow) as a function of the radial distance across the core/shell structure. Every data point in the plot represents a 2-nm slice taken along the entire length of the nanowire analyses excluding the cubic top part of the nanowire. Constant incorporation of As at a level of approximately 400 parts per million (b) (200 parts per million (d)) is observed in the entire shell while the Ga concentration quickly drops to a value close to the noise level of ~10 parts per million. e, A radial profile of the SiGe core/shell structure from the APT measurement integrated over a 1.0-µm length of the structure showing a Ge content of around 0.75 as shown in d. On the dotted rectangular volume of e, we carry out a nearest-neighbour analysis for Si atoms as previously used to evaluate random alloys of GeSn83,84. The nearest-neighbour analysis evaluates the distances between each pair of Si atoms and its first (to fourth) neighbours (NN1 to NN4). f, In b and d and f, the atomic concentration of the individual elements is plotted in the volume of the shaded regions indicated in a, c and e. A plot comparing the nearest-neighbour analysis on the measurement data to a randomized dataset. This gives us no indication of Si clustering and has been established as a reliable way to evaluate random alloys46.

### Extended Data Fig. 7 LSW fit of photoluminescence-spectra on hex-Ge.

LSW fits were performed both on low-temperature (4 K), excitation-density-dependent photoluminescence spectra of hex-Ge as plotted in Fig. 3a, as well as on a temperature series of photoluminescence spectra of hex-Ge at an excitation density of 1.8 kW cm−2 as plotted in Fig. 3b. Additional fitting results are given here, with a full description of the model given in the Methods section ‘The LSW model’. a, d, The bandgap and the quasi-Fermi-level splitting as a function of excitation density and temperature, respectively. b, e, The electron temperature as function of excitation density and temperature, respectively. c, f, The Urbach-tail coefficient γ also as a function of excitation density and temperature, respectively. g, An LSW fit, plotted as a dashed green line, which was performed on a low-excitation-density (ExDens) (45 W cm−2) photoluminescence spectrum, plotted as a red line, at a temperature of 80 K. Two vertical dotted lines indicate the bandgap (BG) on the left in black and the quasi-Fermi-level splitting Δμ to the right in blue. At this lattice temperature all dopants are ionized and the Δμ equals the electron-Fermi level, so these numbers are used to determine the electron quasi-Fermi level.

### Extended Data Fig. 8 Arrhenius plots of hex-Si0.20Ge0.80 with varying quality and their growth parameters.

a, The plots show the same data as presented in the left panel of Fig. 4c, but here presented in an Arrhenius representation. For the lowest-quality sample III, two non-radiative processes are found with activation energies of 16 meV and 91 meV. For sample II only a single activation energy is found, of 34 meV, whereas sample I does not show any decay in intensity over the full measured temperature range. The photoluminescence intensities at 4 K are proportional to the absorption cross-sections, which scale approximately with the volume fractions of the samples that fit within the 5-µm-diameter laser spot. The volume ratios are 1:0.32:0.033 for samples I:II:III, respectively, where only 5/8 of the volume of sample I was counted (see Extended Data Fig. 8b). The measured photoluminescence intensities extrapolated to 4 K are proportional to 1:0.3:0.04 for the same samples, closely agreeing with the probed volumes. b, Tabulated growth parameters of the three different hex-SiGe samples studied, with increasing quality and the dimensions of the nanowires presented in Fig. 4b, c. The total diameter is the core diameter plus twice the shell thickness.

### Extended Data Fig. 9 Relative photoluminescence intensity between compositions.

Here the relative photoluminescence intensities are given for the samples presented in Fig. 5. We note that only measurements on ensembles of as-grown standing wires are included where an equal number of wires is probed, and so the Si0.35Ge0.65 sample is not included. For this comparison all the samples were excited with an excitation density of 5 kW cm−2 at a temperature of 4 K using the same MCT detector and the same KBr beamsplitter. The samples are found to be very similar in intensity despite the change in setup efficiency, a variation in total excited volume due to thickness differences and potentially strain-induced nonradiative recombination centres for high Si-content samples. Because of these additional factors, no conclusive experimental argument can be made on whether the material becomes more efficient for higher Si contents. Additionally, we acknowledge that, despite efforts, we have not been able to measure photoluminescence spectra from wires with x < 0.65, which suggests that the direct–indirect-bandgap transition lies near this point.

### Extended Data Fig. 10 External radiative efficiency.

a, Integrated photoluminescence intensities of hex-SiGe in comparison with high-quality InGaAs/InP multiple quantum well (QW) samples as measured in a micro-photoluminescence setup using 1,030-nm wavelength, 125-pJ pulses. The photoluminescence intensities of both the MQWs and the hex-SiGe wires were corrected using their respective absorption and emission efficiencies as given in the Methods section ‘External radiative efficiency of hex-SiGe’. b, A cross-sectional schematic demonstrating the layer structure of the InGaAs/InP multiple QW sample, showing a total absorption thickness of 625 nm. The bandgap wavelengths (WL) of the layers that are not lattice-matched to InP are indicated. c, A schematic illustration of the geometry of our horizontally oriented hex-SiGe nanowire, showing the emission into a NA = 0.48 cassegrain objective with a NA = 0.22 obscurity. The polarization of the emitted light is indicated as V and H for vertical and horizontal, respectively.

### Extended Data Fig. 11 Comparison between different generations of hex-Ge samples.

a, Photoluminescence spectra from the first hex-Ge shells, which were grown using wurtzite-GaP cores, thus creating many defects caused by the large lattice mismatch between the core and the shell. b, The first hex-Ge shells grown on lattice-matching GaAs cores where the hex-Ge is grown at a temperature of 600 °C. c, Spectra of hex-Ge shells grown at a temperature of 650 °C, further improving the optical quality.

## Rights and permissions

Reprints and Permissions

## About this article

### Cite this article

Fadaly, E.M.T., Dijkstra, A., Suckert, J.R. et al. Direct-bandgap emission from hexagonal Ge and SiGe alloys. Nature 580, 205–209 (2020). https://doi.org/10.1038/s41586-020-2150-y

Download citation

• Received:

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41586-020-2150-y

## This article is cited by

• ### Prospects and applications of on-chip lasers

• Zhican Zhou
• Xiangpeng Ou
• John E. Bowers

eLight (2023)

• ### Ultrawide-bandgap semiconductor of carbon-based materials for meta-photonics-heterostructure, lasers, and holographic displays

• Arwa Saud Abbas

AAPPS Bulletin (2023)

• ### Progress in group-IV semiconductor nanowires based photonic devices

• Sudarshan Singh
• Samaresh Das
• Samit K. Ray

Applied Physics A (2023)

• ### Highly efficient nonlinear optical emission from a subwavelength crystalline silicon cuboid mediated by supercavity mode

• Mingcheng Panmai
• Jin Xiang
• Sheng Lan

Nature Communications (2022)

• ### Highlighting photonics: looking into the next decade

• Zhigang Chen
• Mordechai Segev

eLight (2021)

## Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

## Search

### Quick links

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing