Rydberg excitons in Cu2O microcrystals grown on a silicon platform

Cuprous oxide (Cu2O) is a semiconductor with large exciton binding energy and significant technological importance in applications such as photovoltaics and solar water splitting. It is also a superior material system for quantum optics that enabled the observation of intriguing phenomena, such as Rydberg excitons as solid-state analogue to highly-excited atomic states. Previous experiments related to excitonic properties focused on natural bulk crystals due to major difficulties in growing high-quality synthetic samples. Here, the growth of Cu2O microcrystals with excellent optical material quality and very low point defect levels is presented. A scalable thermal oxidation process is used that is ideally suited for integration on silicon, demonstrated by on-chip waveguide-coupled Cu2O microcrystals. Moreover, Rydberg excitons in site-controlled Cu2O microstructures are shown, relevant for applications in quantum photonics. This work paves the way for the wide-spread use of Cu2O in optoelectronics and for the development of novel device technologies. Cu2O is of great interest for its excitonic properties, yet challenges in its fabrication means that most experiments focus on naturally occurring samples. Here, scalable thermal oxidation is reported for the growth of Cu2O with low-defect content, allowing the observation of Rydberg excitons.

L ight-matter interactions in the direct-band-gap semiconductor cuprous oxide (Cu 2 O) are widely governed by excitons, quasi-particles arising from electron-hole Coulomb interactions, which can be observed up to room temperature due to their large binding energy. As a result of the unique excitonic properties, intriguing condensed-matter quantum phenomena have been demonstrated, e.g. spectroscopic signatures of quantum-degenerate exciton gases 1,2 as well as giant Rydberg excitons 3 exhibiting signatures of quantum coherences 4 and quantum chaotic behavior 5 . As the exciton ground statethe socalled paraexcitonis decoupled from the radiation field in unstrained Cu 2 O, paraexcitons can reach lifetimes up to microseconds 6 rendering them a prime candidate for excitonic Bose-Einstein condensation 7 . Apart from quantum optics, recent reports have reinforced the significant potential of Cu 2 O as a lowcost, non-toxic material in areas such as photocatalysis 8 , solar water splitting 9 , and solar cell devices 10 showing promising photovoltaic efficiencies and marked excitonic effects 11 . Various methods have been reported for the growth of Cu 2 O thin films and single crystals 12 , in particular molecular beam epitaxy 13,14 , magnetron sputtering 15,16 in combination with thermal annealing 17 , electrodeposition 18 , thermal oxidation 19 , and the floating zone method 20 . However, state-of-the-art quantum optics experiments still focus on natural bulk crystals originating from mines, clearly underlining that significant progress in Cu 2 O growth is required to surpass inherent limitations of natural samples. Recent literature emphasized that for the observation of Rydberg states with principal quantum numbers higher than the current record value of n = 25 samples with lower impurity concentrations are required 21 . In addition, scalable fabrication techniques suitable for obtaining micro-/nanostructures and compatible with standard silicon processing are needed to deploy the full potential of this material in advanced device technologies, for instance integrated quantum photonic circuits.
In this work, we present Cu 2 O growth by a scalable thermal oxidation process, which resulted in microcrystal structures with very low point defect and impurity levels. Our method offers the opportunity for combining high-quality Cu 2 O with silicon-based integrated photonics, which we demonstrate by on-chip coupling of exciton luminescence to a silicon nitride waveguide. In single Cu 2 O microcrystals studied at cryogenic temperatures under continuous-wave excitation we demonstrate luminescence from excited np Rydberg states in lithographically site-controlled structures, exhibiting excellent agreement with a hydrogen-like quantum number dependence. Due to the exceptional optical material quality and the unique excitonic properties, our Cu 2 O microcrystals are highly promising for enabling new integrated photonic device architectures relevant for quantum information processing and quantum sensing.

Results and discussion
Growth and photoluminescence properties. The growth of Cu 2 O microcrystals relied on a scalable single-step thermal oxidation process schematically depicted in Fig. 1a. Copper films (thickness~700 nm) were deposited by electron beam evaporation on silicon substrates covered with a thermal SiO 2 layer. Thermal oxidation in a tube furnace resulted in Cu 2 O films with microcrystalline morphology, which can be seen in the top-view and cross-sectional scanning electron microscopy images. The Cu 2 O microcrystals showed terrace-like structures on the surface (Supplementary Fig. 1) and faceted grains with sizes in the μm range. As-deposited copper and samples after thermal oxidation to Cu 2 O were characterized by X-ray diffraction (XRD) measurements (Fig. 1b) to determine their phase composition. For asdeposited copper, the expected face-centered cubic structure and texturing along the [111] direction was found. The presented single-step thermal oxidation method resulted in phase-pure Cu 2 O with cubic cuprite structure. For samples fabricated with different growth conditions comparable microcrystal morphology as well as similar XRD results were obtained ( Supplementary  Fig. 2).
Thermal oxidation of copper can lead to different oxide phases 12 ; Cu 2 O growth was reported to proceed via the random nucleation of islands, which exhibit a cube-on-cube epitaxial relationship at the metal-oxide interface (low oxygen partial pressures) 22 or non-epitaxial orientations (above critical oxygen partial pressures depending on the copper surface) 23 . For the range of experimental parameters corresponding to the growth conditions used in this study (800-850°C, p~1 mbar of synthetic air) the initial stages of copper oxidation include epitaxial oxide formation accompanied by rapid two-dimensional growth 24 . The XRD results before and after thermal oxidation (Fig. 1b)  In addition to growth on planar silicon substrates covered with thermal SiO 2 , we show the integration of Cu 2 O microcrystals with pre-patterned silicon nitride waveguides (see Methods section). Site-controlled microstructures were obtained by thermal oxidation of lithographically defined copper rectangles (length 20 μm, width 10 μm) using the same parameters as described above. The optical material quality was assessed by means of roomtemperature photoluminescence spectroscopy of Cu 2 O grown on both planar substrates and on waveguide structures. In the latter case, waveguide-coupled Cu 2 O luminescence was collected from the cleaved silicon nitride side facet (see experimental setup in Supplementary Fig. 3). Distinct free exciton emission was observed ( Fig. 1c) for both types of samples, exhibiting a characteristic lineshape resulting from multiple phonon-assisted recombination processes with spectral overlap 13 . At photon energies attributed to copper vacancies or single/double-charged oxygen vacancies 12 no marked luminescence was observed. Additional data for microcrystalline Cu 2 O films from different batches and grown under different conditions can be found in Supplementary Fig. 4, which shows spectra with very similar characteristics. Hence, the presented single-step thermal oxidation process is a robust method for the realization of microcrystalline Cu 2 O films with very low point defect levels, ideally suited for the on-chip integration with waveguide structures. Compared to previous literature reports on Cu 2 O growth on silicon (e.g. refs. [16][17][18] ), our results demonstrate a unique combination of excellent optical material quality, sitecontrolled growth and suitability for photonic circuit integration, which holds great promise for enabling integrated devices with novel functionalities based on excitons in Cu 2 O. In the following, we will focus on photoluminescence spectroscopy of single Cu 2 O microcrystals at milli-Kelvin temperatures to probe their fundamental excitonic properties.
Point defects and yellow 1s excitons. Local deviations from the ideal cuprite crystalline structure, e.g. vacancy point defects, extrinsic impurities or microscopic strain, have a significant impact on the relaxation of excitons in Cu 2 O and the related photon emission. Low point defect densities are highly important for efficient cooling of the exciton gas in Cu 2 O as trapping at defects is a limiting factor for exciton lifetimes. The latter were found to be significantly shortened for increasing oxygen vacancy concentrations 26 . Furthermore, it has been suggested that relaxation processes involving vacancies can lead to heating due to phonon emission 27 , which is detrimental for achieving cold exciton gas temperatures. Photoluminescence spectroscopy experiments were conducted in a dilution refrigerator (sample stage base temperature around 40 mK) to assess the optical material quality of Cu 2 O microcrystals at milli-Kelvin temperatures. The results were compared to natural bulk Cu 2 O as benchmark (crystal originates from a selected high-quality geological sample used in previous literature 1,2,6 ). Spectra normalized to the yellow 1s orthoexciton emission that were acquired at a laser power of 50 μW (corresponding to a peak intensity of 3 kW cm −2 ) and an excitation wavelength of 532 nm are presented in Fig. 2a, showing considerably reduced emission related to oxygen vacancies for the case of Cu 2 O microcrystals. An emission feature around 1.95 eV was observed for both Cu 2 O microcrystals and the natural bulk sample, which has been reported repeatedly in literature. It was attributed to phononassisted transitions and defect emission in close spectral proximity 14,27,28 with the latter potentially being correlated with local strain in the sample 29 . The ratio of excitonic over defect emission for the measurements shown in Fig. 2a was found to be about five times higher for the Cu 2 O microcrystals compared to the bulk sample. Additional data for different samples and natural bulk crystal positions as well as further discussion can be found in Supplementary Fig. 5. In addition to intrinsic point defects, excitons and their luminescence properties may be influenced by the presence of extrinsic impurities. The latter can lead to the formation of bound excitons, which show multiple emission lines in the energy range around~2.00 eV, below the phonon-assisted orthoexciton transition 30 . In Fig. 2b, we directly compare photoluminescence spectra obtained from synthetic Cu 2 O microcrystals and from the natural bulk crystal under identical experimental conditions (excitation power 50 nW). It is evident that all peak-like features related to excitons bound to extrinsic impurities are absent in Cu 2 O microcrystals, once more validating the excellent purity and material quality of our samples. Moreover, we assess the energy level structure of yellow 1s excitons in Cu 2 O microcrystals by monitoring luminescence from different phonon-assisted transitions (Fig. 2c). The emission features were assigned according to previous literature 31 and the energy splitting of 1s excitons into orthoexcitons and paraexcitons separated by 12 meV in unstrained Cu 2 O was validated. The influence of strain on the luminescence spectra of Cu 2 O microcrystals is discussed in Supplementary Fig. 6.
Exciton relaxation was further studied by assessing its excitation power dependence. For this purpose, the incident laser power was varied and the luminescence spectra were integrated in an energy range covering bound excitons, phonon-assisted transitions and the direct quadrupole line (Fig. 2d). The integrated intensity of the Cu 2 O microcrystal is in excellent agreement with a linear relationship (slope 0.995 ± 0.008) for excitation powers spanning more than two orders of magnitude, showing slight sub-linear behavior at elevated excitation levels. On the other hand, deviations from a linear power dependence were significantly more pronounced for the natural bulk crystal. Sub-linear power dependence of excitonic emissions in Cu 2 O has been previously observed in experiments using natural bulk samples 30,32,33 and synthetic crystals grown by the floating zone method 34 using various types of laser excitation. It has been attributed to an efficient non-radiative two-body recombination process, which can be explained by Auger decay 35 , by the formation of short-lived biexcitons 36 or by exciton interconversion via spin exchange 37 . The estimated recombination rates reported in literature vary considerably as the process is expected to be sensitive to Cu 2 O crystal symmetry and the resulting band structure; hence it has been anticipated that Auger recombination is associated with broken band symmetries in the vicinity of impurities 7 , which would explain the less pronounced two-body decay in low-defect-density Cu 2 O microcrystals.
Rydberg excitons of the yellow np series. After initial experiments in the middle of the last century, Rydberg excitons in Cu 2 O have recently attracted considerable attention due to the experimental demonstration of principal quantum numbers up to n = 25 in absorption measurements using natural bulk crystals 3 . For synthetic Cu 2 O films in the thickness range of few micrometers and below, Rydberg excitons up to n = 4 have been found 38,39 . Previous studies on natural bulk Cu 2 O crystals indicated that under above-band excitation Rydberg excitons are generated via collision processes of 1s excitons 28,40 . The question arises if Rydberg states can also be observed in the Cu 2 O microcrystals presented here, which was assessed by means of photoluminescence experiments. Results obtained for varying incident laser powers are presented in Fig. 3a (spectra normalized to their respective maxima). Emission peaks corresponding to Rydberg excitons up to n = 6 were identified at intermediate excitation, which can also be seen in the exemplary spectrum shown in Fig. 3b. The 2p peak showed a markedly asymmetric lineshape consistent with previous literature on bulk Cu 2 O crystals 28,40,41 , whereas the relative emission intensities from np states differed in our case. The minor peak between the 2p and 3p energy level is attributed to 1s excitons of the green series 28 . Rydberg exciton emission showed broadening for increasing excitation power, which can be explained by a combination of phonon scattering and density-dependent effects 40 ; the red shift indicates a bandgap decrease due to laser-induced sample heating. Most importantly, the power-dependent measurements verify the robustness of Rydberg excitons in Cu 2 O microcrystals as their emission was detected in a wide range of excitation conditions. To reduce the line broadening, measurements were performed at considerably lower excitation powers. The spectral overlap of states with higher quantum numbers could be reduced and the observation of Rydberg excitons with n = 7 was possible, which is further detailed in Supplementary Fig. 7 and the related discussion. Additional photoluminescence spectroscopy data from different samples is shown in Supplementary Fig. 8, validating that Rydberg excitons can be consistently observed in Cu 2 O microcrystals.
Furthermore, site-controlled Cu 2 O microstructures (Fig. 3c) were achieved by lithographic patterning of the copper film before oxidation. We demonstrate luminescence from excited Rydberg states in a circular Cu 2 O microstructure with 5μm diameter (Fig. 3d). The intensity ratio of np states was different compared to Cu 2 O microcrystals, which could be explained by variations in microscopic strain 41 . The Rydberg exciton energies were evaluated as a function of n −2 for results obtained from sitecontrolled microstructures, from not site-controlled microcrystals and from a natural bulk crystal (Fig. 3e). Excellent agreement with a linear relation was found and exciton binding energies of 98 meV and 97 meV were deduced for the synthetic samples and the natural bulk crystal, respectively. The extracted exciton binding energies concur with previous findings using bulk crystals, obtained from both photoluminescence (97 meV 40 ; 98.5 meV 41 ) and absorption measurements (98 meV 42 ). Hence our results demonstrate the realization of site-controlled, micrometer-sized Cu 2 O structures as host platform for Rydberg excitons, which goes beyond the state of the art of Cu 2 O growth on silicon and opens up opportunities for unprecedented photonic device architectures. For instance, our technology will enable applications in nonlinear quantum optics relying on interactions between Rydberg states 43 , as clear signatures of the Rydberg blockade effect have been recently reported for principal quantum numbers around n = 6 21 . To observe Rydberg states with higher principal quantum number n, it will be promising to explore Cu 2 O microcrystals with larger size as well as different excitation schemes that mitigate luminescence broadening 40 and the potential influence of free carriers induced by above-band excitation 21 .
In summary, we have presented the growth of Cu 2 O microcrystals showing excellent optical material quality with very low point defect and impurity levels, combined with the integration on a silicon platform including the on-chip coupling to silicon nitride waveguide structures. The fabrication method for obtaining high-quality Cu 2 O films via a scalable thermal oxidation process has guiding significance for diverse areas where this low-cost, non-toxic material is employed, such as photovoltaics and photocatalysis. Furthermore, the demonstration of Rydberg excitons in Cu 2 O microcrystals and their integration on silicon have far-reaching implications for future applications in photonic quantum information processing. For instance, Rydberg states in Cu 2 O have been proposed for the realization of novel solid-state single-photon sources 44 and giant optical nonlinearities 45 . Hence our work lays the foundation for a platform technology enabling solid-state Rydberg excitations on-chip, which is envisioned to result in integrated devices capable of generating and manipulating light at the single-photon level.

Methods
Growth of Cu 2 O microcrystals on silicon substrates. The deposition of copper films (thickness~700 nm) was performed by electron beam evaporation onto pieces of silicon wafers with 150 nm thermal SiO 2 . A thin intermediate titanium layer (thickness~5 nm) was employed to improve the film adhesion on the substrate surface. Samples with structured Cu 2 O were realized by patterning the copper film using an electron beam lithography lift-off process. Thermal oxidation was carried out in a tube furnace connected to a vacuum pump. Before growth experiments the system was evacuated and purged multiple times using high-purity synthetic air (Air Liquide Alphagaz 2). Cu 2 O samples were grown by thermal oxidation at a pressure around 1 mbar and setpoint temperatures of 800°C or 850°C . The temperature was kept constant for 1 h or 5 h after reaching the setpoint value, followed by natural sample cool-down.
Sample characterization. The morphologies of Cu 2 O films and microstructures were characterized by scanning electron microscopy imaging of the sample surfaces and of cross-sections obtained by mechanical cleaving. X-ray diffraction measurements were performed by specular scans using a PANalytical Empyrean system. Radiation from a sealed copper tube was used in combination with a secondary graphite monochromator in Bragg-Brentano geometry. Phase analysis was carried out relying on powder patterns from the database PDF2, International Center for Diffraction Data, using 004-0836 for Cu and 005-0667 for Cu 2 O.
Photoluminescence spectroscopy. All photoluminescence spectroscopy experiments were performed using a Horiba iHR550 spectrometer and a continuous-wave, diode-pumped solid-state laser emitting at 532 nm. Room-temperature spectra were acquired using an objective (NA = 0.82) for excitation and collection. Spectroscopy at milli-Kelvin temperatures was performed relying on a cryogen-free dilution refrigerator (Bluefors) with a base temperature around 10 mK. Optical side-access windows with anti-reflective coatings were used for laser excitation of the samples mounted on a dedicated stage controlled by piezoelectric actuators, which had a base temperature around 40 mK. The laser was focused by a lens (NA = 0.50) inside the cryostat to a spot diameter around 1.2 μm (full width at half maximum); the power was measured at the outermost cryostat window.
Waveguide integration of Cu 2 O microstructures. Commercial silicon wafers covered with 3.3 μm wet thermal oxide and 335 nm of stoichiometric silicon nitride deposited by low-pressure chemical vapor deposition were used as substrates. Waveguides with a width of 1 μm were fabricated using electron beam lithography and reactive ion etching using CHF 3 /CF 4 /O 2 gas chemistry. Integrated Cu 2 O microstructures were realized by an electron beam lithography lift-off process and thermal oxidation at 850°C for 1 h. Photoluminescence spectroscopy of the waveguide-integrated device was performed using an Acton SpectraPro spectrometer with 750 mm focal length, excitation normal to the sample surface (continuous-wave 532 nm laser) through an objective (NA = 0.28) and collection from the cleaved waveguide facet using another objective (NA = 0.65).

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.