Very high temperature annealing of Cu₂O obtained by the bifacial oxidation of free-standing Cu foils

Abstract

Cu₂O has been obtained via the thermal oxidation of free-standing Cu foils with a thickness of 127 μm under Ar and O₂ at 1020 °C followed by controlled cooldown at −5 °C at low pressure under an inert flow of Ar. We obtain single crystal grains of Cu₂O with sizes of ∼500 × 500 μm² which have a cubic crystal structure, but these extend only halfway through the bulk down to a layer of Kirkendall voids due to the bifacial oxidation of the Cu. The voids are nearly eliminated by annealing between 1120 °C and 1160 °C under Ar which also leads to grain growth. However, the out diffusion of the voids through the single crystal Cu₂O grains is accompanied by the formation of holes at the surface. We show that the layer of voids can be removed by polishing the Cu₂O down to ∼10 μm in order to preserve the single crystal nature of the grains obtained at 1020 °C while keeping the thermal budget to a minimum and discuss the limitations in exploiting the Cu₂O obtained in this way for the fabrication of devices.

---

1. Introduction

Cu₂O is a p-type metal oxide semiconductor that has a cubic crystal structure and a direct energy band gap of 2.1 eV. It is an archetype for the study of excitons that were observed for the first time in Cu₂O by Gross et al.¹ It has also been suggested to be suitable as a solar cell absorber given that it has a high absorption coefficient of α ∼ 10⁵ in the visible² but so far solar cell device efficiencies have been limited to less than 10%.³ In addition, Cu₂O has been shown to have very good photocatalytic properties for water splitting⁴ but also for CO₂ reduction.⁵

Consequently, Cu₂O is still an active topic of ongoing investigation that attracted even more attention after the observation of giant Rydberg excitons with principal quantum numbers up to n = 25 by Kazimierczuk et al.⁶ which in turn instigated further interest into the possibility of adding long-range interactions to the physics of exciton–polaritons that were recently detected in a SiO₂/Ta₂O₅/Cu₂O/Ta₂O₅/SiO₂ Fabry–Pérot cavity by Orfanakis et al.⁷ Giant Rydberg excitons are attractive as solid-state counterparts of Rydberg atoms that are used in quantum computers, but so far, giant Rydberg excitons with n > 10 and polaritons have only been observed in naturally occurring crystals of Cu₂O. It is necessary then to grow high crystal quality Cu₂O on par with that occurring in nature.

In the past, Cu₂O has been obtained by many different methods such as molecular beam epitaxy (MBE),⁸ atomic layer deposition (ALD)⁹ pulsed laser deposition (PLD)¹⁰ electrodeposition (ELD)¹¹ aerosol assisted chemical vapor deposition (AACVD)¹² successive ionic layer adsorption-reaction (SILAR)¹³ and e-beam evaporation (EB)¹⁴ but the crystal quality and phase purity of the Cu₂O obtained using most of the methods listed above is not comparable to that of naturally occurring single crystals. Only Steinhauer et al.¹⁴ observed Rydberg excitons up to n = 6 in Cu₂O crystals obtained by thermal oxidation of 700 nm Cu deposited by e-beam evaporation (EB) on Si. Rydberg excitons with higher principal quantum numbers up to n = 10 have only been observed in (a) free standing Cu₂O prepared by thermal oxidation of Cu foils and (b) Cu₂O ingots grown by the optical float zone method using Cu₂O feed and seed rods obtained by thermal oxidation of 3–7 mm diameter Cu rods.

Early efforts in obtaining single crystal Cu₂O by thermal oxidation of Cu date back to the 1950's^15–18 but these were not always successful and polycrystalline Cu₂O with small grains were obtained. Interestingly, high crystal quality Cu₂O was successfully and consistently obtained in the 1960's by Toth et al.¹⁹via the high temperature oxidation of Cu foils in air between 1020 °C and 1040 °C followed by annealing at higher temperatures between 1085 °C and 1115 °C for times ranging between 5 and 150 h. The average annealing temperature for 0.76 mm thick Cu was 1085 °C while that used for 0.38 mm Cu was 1115 °C. The Cu₂O was retracted rapidly in less than 10 s at the end of annealing and the CuO that formed on top of the Cu₂O was removed in HNO₃ (aq) or by the use of abrasives. Large grains of 160 mm² were obtained from 0.203 mm and 0.254 mm thick Cu after oxidation at 1035 °C for 60 min and annealing at 1120 °C for 5 h. In contrast the Cu₂O obtained from 0.762 mm thick Cu had to be annealed for 100 h.¹⁹

After the breakthrough of Toth et al.¹⁹ subsequent investigations focused mostly on the growth of single crystal ingots of Cu₂O by the optical, float zone method which allows one to cut wafers with a specific thickness that are flat. More specifically, Cu₂O was obtained in the 1970's by Brower et al.²⁰via the floating zone method using Cu₂O feed rods prepared by thermal oxidation of Cu rods with diameters of 6.3 mm in air at 1050 °C for 96–100 h. A few years later Schmidt et al.²¹ also obtained Cu₂O by the floating zone method that was subsequently annealed in air between 900 °C to 1050 °C. Many years later Chang et al.²² prepared Cu₂O feed and seed rods via the thermal oxidation of high purity Cu rods with diameters between 4 and 7 mm that were oxidized in air for 3 days at 1045 °C. Cu₂O was grown by the optical float zone method and was cut into wafers with a thickness of ∼1 mm and diameters of 7 mm after which they were annealed in air at 1045 °C for 1 to 4 days at one day intervals.²² Similarly, Frazer et al.²³ prepared polycrystalline feed and seed rods of Cu₂O by thermal oxidation of copper metal rods at 1045 °C for 3 days. These were used to grow single crystal Cu₂O ingots by the floating zone method. Finally, Lynch et al.²⁴ prepared Cu₂O seed rods via the thermal oxidation of 5 mm Cu metal rods at 1100 °C for 40 hours in air that were used to grow single crystal Cu₂O by the optical float zone method and observed excitons with principal quantum numbers up to n = 10.

It should be emphasized at this point that all previous efforts into the growth of Cu₂O crystals via the optical float zone method were carried out using Cu₂O feed and seed rods prepared by the thermal oxidation of Cu rods in air up to temperatures of 1100 °C. The Cu rods had diameters up to 7 mm, so the Cu₂O ingots also had small diameters. The Cu₂O wafers were annealed between 1000 °C and 1050 °C and the time taken to obtain high crystal quality Cu₂O was of the order of many tens of hours i.e. days. It should also be noted that Cu₂O has not been grown by the Czochralski method due to the lack of suitable crucibles.

Besides all of the ongoing efforts into the growth of Cu₂O via the optical float zone method the thermal oxidation of Cu foils is also an active topic of ongoing investigation. For instance, Mani et al.²⁵ investigated the thermal oxidation of Cu (99.9%) foils with a thickness of ∼0.12 mm at 1050 °C in air at atmospheric pressure for 1 h. The Cu₂O was annealed at 1130 °C for 15 h in air by increasing the temperature at a rate of 0.1 °C min⁻¹. After annealing the Cu₂O was cooled at 0.1 °C min⁻¹ between plateaus of 1100, 1080, and 1050 °C, which were maintained for ∼20 h each. For temperatures below 1050 °C, the pressure was adjusted to maintain the Cu₂O phase. Finally, at 700 °C the sample was quenched using a flow of cold Ar.²⁴ More recently Xiao et al.²⁶ showed that during oxidation of Cu the Cu₂O grains undergo rapid diffusion and move preferentially in the vertical growth direction to release the strain through the generation of Frank partial dislocations which grow by absorbing V_Cu and penetrate through the bulk. The Frank partial dislocations tend to slip along the lattice plane with the densest atoms, and the crystal rotates on the sliding surface, triggering grains to orient in a specific direction. Xiao et al.²⁶ showed that (111)-oriented Cu₂O with small grains are obtained by surface energy-dominated growth while the (110) oriented Cu₂O is obtained by strain-energy-driven grain growth.

Very recently we showed that high crystal quality and phase purity Cu₂O may be obtained in a controlled way via the thermal oxidation of Cu at 1020 °C under Ar and O₂ after annealing the Cu under H₂ which is very effective in reducing the bulk content of CuO in the Cu₂O.²⁷ After oxidation the Cu₂O was annealed for 60 min at 1040 °C resulting into ∼500 × 500 μm² single crystal grains. The entire process lasted ∼6 hours. The Cu₂O crystals obtained in this way consisted of (110) and (220) high index grains like those of Xiao et al.²⁶ but the Cu₂O crystal was retracted from the heated zone at 800 °C under a flow of Ar. The surface of the Cu₂O was covered by a semi-transparent layer of 10 nm CuO that acts as a natural passivation layer preventing the oxidation of the underlying Cu₂O upon exposure to air.²⁷ However, the single crystal grains of Cu₂O obtained in this way do not extend throughout the bulk due to the formation of a Kirkendall void layer (KVL) at the middle of the foil that was first identified but not directly observed by Toth et al. in the 1960's.¹⁹ Recently Xiao et al.²⁶ observed this irregular KVL in Cu₂O by scanning electron microscopy (SEM). However, the Cu₂O of Xiao et al.²⁶ was derived by thermal oxidation of a 200 μm thick Cu foil at 1040 °C up to 3 h in air after which it was held at 1050 °C for 2 h under Ar but the Cu was in direct contact and constrained with corundum slides (Al₂O₃). The KVL must be removed as this will limit the lifetime of Rydberg excitons with large radii. Moreover, these voids are detrimental for devices e.g. p–n junction solar cells since there are allot of crystallographic imperfections in their vicinity with deep states residing in the energy gap of Cu₂O that will inevitably lead to the recombination of the photogenerated electron–hole pairs and which in turn will reduce the efficiency of solar cells.

Here we aim to obtain free standing Cu₂O with large single crystal, high purity grains via the oxidation of Cu foils in a time and cost-effective manner that can be used for the subsequent observation of Rydberg excitons. We show that annealing the Cu₂O above 1100 °C leads to grain growth and the elimination of the KVL but also to the formation of holes on the surface of the Cu₂O due to the out diffusion of the vacancies and voids. We argue that it is better to remove the KVL by polishing in order to preserve the single crystal nature of the Cu₂O grains residing above the KVL and keep the thermal budget to a minimum which in turn will make it feasible to isolate a single crystal grain for the purpose of optical spectroscopy. We also discuss the limitations in exploiting the Cu₂O obtained in this way for the fabrication of devices.

2. Methods

Cu foils with a thickness of 127 ± 4 μm and technical grade purity of 99.99% were cut and trimmed into rectangular pieces having different length to width ratios as shown in Fig. 1(a). All of the Cu foils had a width of 10 mm and were trimmed in such a way so that the grain direction due to rolling ran parallel to the long side. The length of the Cu foils was 20, 30 and 40 mm. Both sides of the Cu foil were polished to remove the ridges due to rolling after which they were flattened out between clean glass slides and their corners bent to form supports as shown in Fig. 1(b). Subsequently, the Cu was cleaned in isopropanol under ultrasonic vibration for 10 min in order to remove particles that got embedded into the Cu, dried with N₂ and annealed under a flow of Ar and H₂ in a 1′′ hot wall, chemical vapor deposition (CVD) reactor capable of reaching 1200 °C, that was fed by a manifold consisting of four mass flow controllers connected to Ar, NH₃, O₂ and H₂. The reactor was initially purged with Ar and H₂ at room temperature for 10 min in order to remove traces of air after which the temperature was ramped up to 1000 °C at 30 °C min⁻¹. Upon reaching 1000 °C the same flow of Ar and H₂ was maintained for 180 min to reduce all oxides and promote grain growth. Cool-down was carried out under the same flow of Ar and H₂ all the way down to room temperature. A constant flow of 100 ml min⁻¹ Ar and 100 ml min⁻¹ H₂ at 10 mbar was maintained throughout the entire process. The Cu foils were removed at room temperature after purging with Ar and stored under vacuum in a desiccator with silica gel. The Cu foils with an overall length of 30 or 40 mm exhibited concave bending as shown in Fig. 1(c).

Fig. 1 Schematic diagram of (a) Cu foil with l = 20, 30 and 40 mm; w = 10 mm and t = 127 μm laid flat on a quartz boat (b) Cu with l′ ∼ 16 mm; w′ ∼ 6 mm and t = 127 μm standing on bent point corners (c) Cu with l′ ∼ 36 mm; w′ ∼ 6 mm and t = 127 μm showing the bending s = 3 mm that occurs after annealing under Ar and H₂ at 1000 °C.

The Cu was converted into Cu₂O in a different 1′′ hot wall reactor capable of reaching 1100 °C which was initially purged at room temperature for 10 min using a flow of 100 ml min⁻¹ Ar and 100 ml min⁻¹ H₂ to remove air after which the temperature was ramped up to 900 °C at 30 °C min⁻¹ by maintaining the same flow of Ar and H₂ at 1 atm. At 900 °C the ramp rate was reduced to 10 °C min⁻¹ until 1020 °C in order to prevent a temperature overshoot. Cu has a melting point of 1085 °C. At 1020 °C the same flow of Ar and H₂ was maintained for a further 30 min at 1 atm after which the flow of H₂ was interrupted and a flow of 100 ml min⁻¹ Ar was maintained for 15 min in order to purge the H₂ and admit O₂. Subsequently the Cu foil was oxidized for 30 min under a flow of 100 ml min⁻¹ Ar and 10 ml min⁻¹ O₂. After oxidation the Cu₂O was cooled down in a controlled fashion at −5 °C min⁻¹ under a flow of 100 Ar at 10⁻² mbar all the way down to room temperature. A schematic illustration of the thermal oxidation of Cu at 1020 °C under Ar and O₂ is illustrated schematically in Fig. 2.

Fig. 2 Schematic representation of the process used for the growth of Cu₂O by thermal oxidation of Cu under Ar: O₂ (a) temperature ramp (b) short reduction and anneal of Cu under Ar: H₂ (c) purging of hydrogen (d) and (e) thermal oxidation and (f) controlled cool down.

Finally, the Cu₂O crystals obtained in this way were annealed in a different 1′′ hot wall reactor capable of reaching 1500 °C, that was fed by a manifold also connected to Ar, O₂ and H₂. In this case the reactor was initially purged with 100 ml min⁻¹ Ar at room temperature for 10 min in order to remove traces of air after which the temperature was ramped up to 1140 °C at 30 °C min⁻¹ and 1 atm. Upon reaching 1140 °C the same flow of Ar was maintained for 1, 2, 3 and 4 hours at 1 atm. Cool-down was carried out under the same flow of Ar at −5 °C min⁻¹ all the way down to room temperature. In addition, Cu₂O crystals were annealed at 1120, 1140 and 1160 °C for 60 min employing the same flows, ramp rate and cool down conditions.

The Cu₂O was inspected by optical transmission microscopy before and after annealing; the surface and section of the Cu₂O was also inspected by scanning electron microscopy (SEM) in order to identify the extent of the KVL while the crystal structure and phase purity was measured by X-ray diffraction (XRD) using a Rigaku Miniflex in the Bragg–Brentano θ–2θ geometry with a Cu K-a source and wavelength of 1.54Å at scan rate of 1° min⁻¹.

Finally, the KVL in the Cu₂O with no annealing was removed by polishing from the back side; this was achieved by using sapphire as a holder for the brittle Cu₂O crystal that was covered by solid transparent wax. The wax on top of the Cu₂O was heated in a VT 6060P Thermo Scientific drying oven at 100 °C and 100 mbar in order to remove bubbles that formed during the melting of wax which upon cooling fixed the crystal in position. The Cu₂O was polished from the back side down to 10 μm using an Allied Opti Prep Precision Polishing System with ∼0.5 μm diamond lapping surface. The structural properties of the Cu₂O obtained in this way were also investigated on section by SEM.

3. Results and discussion

We will begin by considering the preparation and properties of Cu which is important in obtaining high crystal quality and purity Cu₂O. A typical SEM image of a 127 μm thick Cu (99.99%) foil, as received, is shown in Fig. 3(a). The surface is not flat, and ridges run along the rolling direction that were removed by polishing as shown in Fig. 3(b). The Cu consists of small grains with sizes of 5 to 10 μm as shown in Fig. 3(c) and exhibited clear and well resolved peaks in the XRD corresponding to the (111), (200) and (311) crystallographic planes of the face centered cubic (fcc) crystal structure of Cu as shown in Fig. 4(a). We did not detect any peaks corresponding to CuO or Cu₂O. However, traces of oxides exist on the surface and inside the bulk Cu which must be eliminated in order to obtain high crystal quality and phase purity Cu₂O. Previous investigations have shown that a large flow of H₂ is very effective in reducing CuO and Cu₂O into metallic Cu. CuO is reduced to Cu₂O by H₂ at approximately 60 °C while complete reduction from Cu₂O to metallic Cu occurs at 480 °C.²⁸ Consequently, the Cu was annealed under Ar and H₂ at 1000 °C and 10 mbar for 3 hours to reduce all oxides and remove oxygen but also to promote grain growth. A typical SEM image of the 120 μm Cu foil after annealing is shown in Fig. 3(d) and (e). The Cu consists of grains as large as 200 μm and the surface is flattened to an extent due to the sublimation of Cu that occurs under the flow of Ar and H₂ at 10 mbar and 1000 °C which is lower than the melting point of Cu i.e. 1085 °C. The Cu exhibited clear peaks in the XRD after annealing as shown in Fig. 4(a) corresponding to the (111), (200) and (311) crystallographic planes of the fcc crystal structure of Cu. We find that annealing promotes the intensity of the peak corresponding to Cu grains with the (200) crystallographic orientation. The improvement in the crystal quality of the Cu is due to the fact that H₂ dissociates catalytically into H on the surface of Cu and penetrates into the Cu lattice promoting grain growth and eventually the formation of a single crystal. It has been shown that polycrystalline Cu, Ni, and Co foils can’t be converted into single crystals during annealing at high temperatures under Ar without H₂.²⁹ The Cu foils with lengths of 30 and 40 mm exhibited bending along their length as shown in Fig. 2(c). This is attributed to a reduction in the dislocation density and vacancies which in turn results in a crystal lattice with lower internal strain and an increase in ductility. This is not desirable as the Cu may come into contact and react with the underlying quartz during oxidation. Furthermore, the Cu₂O will also be bent, strained and difficult to process further. As such the length of the free-standing Cu foils must be limited to less than 30 mm in order to obtain relatively flat Cu₂O.

Fig. 3 SEM image of (a) Cu as-received showing the direction of rolling (b) Cu after polishing (c) Cu after fine polishing revealing grains with sizes up to 10 μm (d) and (e) Cu after annealing under Ar: H₂ at 1000 °C for 3 h showing the formation of grains with sizes >200 μm (f) Cu₂O after thermal oxidation at 1020 °C consisting of grains with sizes >200 μm (g) and (h) higher magnification images of Cu₂O showing that the surface is considerably flatter than that of Cu (i) section of Cu₂O showing the Kirkendall void layer at the middle extending over 50 μm at places.

Fig. 4 XRD of (a) Cu as received and Cu after annealing under Ar: H₂ at 1000 °C for 3 h; inset shows the fcc crystal structure of Cu. (b) Cu₂O after annealing at 1120 °C, 1140 °C and 1160 °C for 3 h. (c) Cu₂O after annealing at 1140 °C, for 2, 3 and 4 h. (d) Crystal structure of Cu₂O.

Recently we showed that in order to obtain high crystal quality and phase purity Cu₂O it is necessary to prevent the thermal oxidation of the Cu during the temperature ramp just prior to the thermal oxidation by using Ar and H₂ as illustrated schematically in Fig. 2(a)–(c).²⁷ The thermal oxidation of the Cu at 1020 °C occurs at the top and bottom surfaces as shown in Fig. 2(d) and is completed in 30 min as shown schematically in Fig. 2(e). However, the growth of high crystal quality and phase purity Cu₂O is also dependent on the conditions used for cool-down. In the past we removed the Cu₂O crystal rapidly from the heated zone under a flow of Ar after the temperature reached 800 °C similar to Toth et al.¹⁹ who obtained Cu₂O from Cu that was subsequently annealed between 1085 °C and 1130 °C for times ranging between 5 and 150 h; the Cu₂O was retracted rapidly in less than 10 s at the end of annealing and the CuO that formed on top of the Cu₂O was removed in HNO₃ (aq) or by the use of abrasives. Others like, Mani et al.²⁵ obtained Cu₂O by thermal oxidation of Cu in air at 1050 °C for 60 min and 1 atm and quenched using a flow of cold Ar at 700 °C.²⁵

Here we employed a slow cool down rate to suppress the formation of CuO in Cu₂O as illustrated schematically in Fig. 2(f). More specifically after the completion of thermal oxidation the temperature was reduced from 1020 °C down to 820 °C in a controlled fashion at −5 °C min⁻¹ under a flow of 100 ml min⁻¹ Ar at 10⁻² mbar in order to suppress a transition through the CuO/Cu₂O phase-boundary at low and intermediate temperatures which would lead to the precipitation of CuO inside the bulk of the Cu₂O. This is consistent with Chang et al.²² who prepared an ingot of Cu₂O by the optical float zone method that was cut into wafers with a thickness of ∼1 mm and diameters up to 7 mm after which the Cu₂O wafers were annealed in air at 1045 °C for 1 to 4 days at one day intervals. The Cu₂O was removed from the furnace and cooled in air; it reached room temperature in 10 min, but this quenching led to the formation of CuO.²² It was shown that the density of the Cu vacancies was reduced by slow cooling at −5 °C min⁻¹ which also led to a suppression of the formation of CuO on top of the Cu₂O.²¹ Similarly, Frazer et al.²³ prepared Cu₂O ingots by the floating zone method. Crystal slices of Cu₂O were annealed in a box furnace at 1045 °C for one to five days and cooled to room temperature at a rate of 5 °C min⁻¹. The formation of CuO was suppressed by annealing and slow cooling, which resulted in an increase of phase purity by a factor of 540 ± 70. Consequently, the elimination of O₂ by maintaining a flow of Ar at 10⁻² mbar during cool down at −5 °C min⁻¹ prevents the precipitation of CuO inside the bulk of Cu₂O.

A typical image of the Cu₂O obtained here is shown in Fig. 5(a). The red-ruby Cu₂O observed in transmission is very similar to a naturally occurring red ruby crystal of Cu₂O which is shown in Fig. 5(b) but a semi-transparent layer of CuO is expected to form on top of the red-ruby Cu₂O. This may be understood as follows: the basic starting point for oxidation of copper to cuprous oxide is 4Cu(s) + 2O₂ (g) → 2Cu₂O(s) after which the Cu₂O will be inevitably react with O₂ at the surface according to 2Cu₂O (s) + O₂ (g) → 4CuO(s) leading to the formation of CuO. The surface layer of CuO is semi-transparent for otherwise we would not be able to see through the Cu₂O crystals of this work under an optical transmission microscope. As such we suggest that the CuO has a thickness of the order of a few tens of nm's similar to what we found previously by TEM/HRTEM.²⁷

Fig. 5 Typical images of Cu₂O obtained by optical transmission microscopy (a) as grown at 1020 °C (b) natural crystal (c), (d), (e), (f) Cu₂O after annealing at 1140 °C for 1, 2, 3 and h. respectively.

A typical SEM image of the Cu₂O crystal is shown in Fig. 3(f)–(h). We find that the Cu₂O consists of grains that have sizes up to ∼500 × 500 μm². Interestingly the surface of the Cu₂O is flatter than the Cu after annealing. The Cu₂O exhibited strong peaks in the XRD corresponding to the (111), (110) and (220) crystallographic planes of the cubic crystal structure of Cu₂O. According to Xiao et al.²⁶ strain-driven growth leads to the formation of the (110) and (220) oriented crystallographic planes of Cu₂O but (111) oriented Cu₂O with small grains are obtained by surface energy-dominated growth. It is important to note however that Xiao et al.²⁶ applied strain by constraining the Cu between corundum (Al₂O₃) slides in contrast to the free standing Cu₂O obtained in this work. Despite the fact that we obtain large, single crystal grains of Cu₂O they do not extend all the way through the bulk. The bifacial thermal oxidation of Cu at 1020 °C occurs on the front and back side of the Cu and leads to the formation of a KVL halfway below the surface. A typical SEM image of the KVL is shown on section in Fig. 3(i). We suggest that vacancies and voids are generated at the interface between Cu and Cu₂O due to the large difference in the lattice constants of Cu₂O i.e. a = 4.2696 Å and that of Cu, a = 3.615 Å. The voids grow larger as the two oxidation fronts move into the bulk of Cu. This KVL was originally identified by Toth et al.¹⁹ in an indirect way i.e. by measuring the resistance along a section but was observed directly by SEM only recently by Xiao et al.²⁶ Consequently, the crystal from top to bottom consists of (i) a compact, semi-transparent thin layer of CuO (ii) single crystal grains of Cu₂O (iii) a layer of Kirkendall voids (iv) single crystal grains of Cu₂O and finally (v) a CuO layer on the back as depicted schematically in Fig. 3(f). Obviously the KVL and the semi-transparent surface layer of CuO must be eliminated.

We have tried to remove the KVL by annealing the Cu₂O at 1120 °C, 1140 °C and 1160 °C for 60 min; SEM images on plan and section are shown in Fig. 6(A) to (C) respectively. We also annealed the Cu₂O at 1140 °C under Ar for 2, 3 and 4 hours; plan view images are shown in Fig. 7(A) to (C) respectively. One may observe the formation of well defined, steps and holes in Fig. 6(A) after annealing the Cu₂O at 1120 °C for 60 min; the formation of the holes at the surface is attributed to the out-diffusion of copper vacancies and Kirkendall voids during recrystallization so that the energy of the crystal is minimized. The circular holes after annealing at 1120 °C are empty and have a diameter of ∼1 μm. We find that the areal density of the holes exhibits a strong increase after annealing at 1140 °C as shown in Fig. 6(B). The holes appear as black dots in optical transmission. Interestingly we observe that most of the holes are filled up with individual lamellas that are oriented in various directions and protrude above the surface as shown in Fig. 6(B) and the Kirkendall voids do not form an extended layer as shown in Fig. 3(i). The Kirkendall voids are nearly eliminated after annealing at 1160 °C as shown in Fig. 6(C) but the diameter of the holes has increased up to ∼10 μm. We estimate that the diffusion coefficient is of the order of 10⁻¹⁰ at 1160 °C which is quite high, taking a vacancy migration activation energy of ∼1.0 eV and D₀ ∼ 10⁻⁶ m² s⁻¹. In short, the KVL can be reduced significantly by annealing above 1200 °C but this inevitably leads to the formation of holes in the vicinity of the surface.

Fig. 6 SEM images of Cu₂O annealed at 1120 °C, 1140 °C and 1160 °C for 1 h under a flow of Ar shown in panels A, B and C respectively; also shown for completeness corresponding images of Cu₂O obtained by optical transmission microscopy showing the red-ruby Cu₂O. (a) Empty pinholes and steps appear on the surface after annealing at 1120 °C for 1 h. (b) The density of the pinholes is larger after annealing at 1140 °C for 1 h; some of the pinholes are filled with crystals having a lamella crystal structure and some are empty; also shown the KVL on section showing voids that have a size of ∼5 μm (c) Similar pinholes are observed after annealing at 1160 °C for 1 h; the KVL has been nearly eliminated as shown on section.

Fig. 7 SEM images of Cu₂O annealed at 1140 °C for 2, 3 and 4 h under a flow of Ar at 1 atm shown in panels A, B and C respectively; different magnifications are shown top to bottom as indicated by the arrows in each case. One may observe the occurrence of partially and completely filled pinholes as well as steps on the surface in all three cases.

In addition to varying the temperature of annealing we also varied the time of annealing. Typical SEM images of the Cu₂O annealed at 1140 °C for 2, 3 and 4 h. are shown in Fig. 7(A) to (C) respectively. One may again observe the formation of holes on the surface of the Cu₂O crystal, some of which are hollow, and others filled with individual lamellas that are oriented in various directions and protrude above the surface as shown in Fig. 7(A). The recrystallization of these lamellas occurs with increasing time and ordered facets develop as shown in Fig. 7(B) and (C) after annealing at 1140 °C for 3 and 4 h respectively. In addition, one may observe the filling of the empty holes. In all cases recrystallization has led to the formation of steps on the surface. Before elaborating further, it is interesting to point out that these spherical protrusions extend downwards into the bulk Cu₂O up to 30 μm as shown by the SEM section images of the Cu₂O after annealing at 1040 °C up to 4 h in Fig. 8(A) and (B). All of the Cu₂O crystals annealed between 1120 and 1160 °C for 1 h exhibited clear peaks in the XRD as shown in Fig. 4(b); one may observe only peaks corresponding to the (110), (220) and (111) crystallographic orientations of Cu₂O annealed at 1120 °C for 1 h and the emergence of peaks corresponding to the (111), (200) and (220) crystallographic orientations of Cu upon annealing at 1140 °C and 1160 °C for 1 h. The high temperature annealing was carried out under inert Ar to prevent the reaction of the Cu₂O with O₂ which would lead to the formation of CuO. The use of Ar translates into a lack of oxygen, so the Cu₂O is losing oxygen and Cu is precipitating into the voids above its melting point i.e. 1085 °C that's why we observe semi-spherical protrusions on the surface and peaks corresponding to Cu in the XRD. Similar trends are observed after annealing the Cu₂O at 1140 °C for 2, 3 and 4 h. Moreover, we find that the Cu₂O is compressively strained, and the strain is ∼0.94% before annealing but is reduced to ∼0.46% after annealing. The strain in the Cu₂O during thermal oxidation of Cu occurs due to the difference in the lattice constants as well as thermal expansion coefficients of Cu and Cu₂O.

Fig. 8 SEM images of Cu₂O on section after annealing at 1140 °C for 4 h. (A) A reduction in the extent of the KVL layer and isolated spherical voids are observed (B) section showing filled up holes below and above the surface (C) a section of the polished Cu₂O obtained at 1120 °C with no post growth annealing.

From the above it is evident that the KVL must be removed by polishing not by annealing in order to preserve the single crystal nature of the Cu₂O grains. This may be achieved by polishing the Cu₂O crystal from the back side. However, the Cu₂O crystal is brittle and not easy to cleave in straight lines due to the fact that it consists of interlocked polygon grains. In addition, the Cu₂O crystal is not perfectly flat. In general, the Cu₂O crystals obtained via the thermal oxidation of free-standing Cu with a length to width ratio >2 exhibited bowing and were bent along the lateral direction. The Cu₂O crystals obtained from Cu with l/w = 1 were bent along all sides.

In order to obtain a relatively flat piece of crystal from the Cu₂O we had to remove the corner supports and then apply pressure between two glass slides. The Cu₂O broke into irregular pieces similar to the natural red-ruby Cu₂O crystal fragments that were used by Kazimierczuk et al.⁶ for the observation of giant Rydberg excitons as well as Orfanakis et al.⁷ who integrated them into a SiO₂/Ta₂O₅/Cu₂O/Ta₂O₅/SiO₂ Fabry–Pérot cavity. The natural Cu₂O crystals in both of these cases had dimensions of ∼3 mm × 3 mm.^6,7 The Cu₂O pieces that we obtained have similar dimensions of ∼5 mm × 5 mm. A section of the Cu₂O after polishing is depicted in Fig. 8(C) showing that the KVL has been removed successfully without annealing.

Finally, the semi-transparent layer of CuO at the surface also has to be removed by polishing. CuO is a p-type metal-oxide semiconductor that has an indirect energy gap of 1.4 eV and will absorb photons bouncing back and forth between the mirrors of a cavity. The CuO will absorb photons and also act as a sink for the photogenerated electron and holes which will recombine in a non-radiative fashion in the near vicinity of the surface especially via deep states in the energy gaps of the CuO and Cu₂O that are related to crystallographic imperfections that form due to the difference in their lattice constants. Nevertheless, it is important to keep in mind that this layer of CuO acts as an excellent passivation layer for the underlying red ruby Cu₂O so it can be stored for extended periods of time under ambient conditions.

Considering that the Cu₂O crystals are very brittle especially after removing the KVL by polishing down to a few tens of μm, it is difficult to use them as substrates for the subsequent deposition of other n-type oxides e.g. ZnO and processing to make p–n junction solar cell devices. One way of overcoming these difficulties is to bond them onto a rigid substrate after removing the voids which would allow subsequent processing to be carried out, but the Cu₂O would have to be doped during growth with a suitable p-type impurity in order to increase its conductivity and reduce resistance as the Cu₂O crystals in our case did not contain any intentional p-type impurities. Nevertheless, we must point out that the free standing Cu₂O crystals obtained using the method described here is not cost effective or justified for the fabrication of competitive solar cell devices. Lower cost methods such as reactive sputtering of Cu₂O are more suitable as described by Shibasaki et al.³ who fabricated an all-oxide solar cell with an efficiency of ∼10%.

4. Conclusions

Cu₂O has been obtained via the thermal oxidation of Cu under Ar and O₂ at 1020 °C followed by controlled cooldown at −5 °C at 10⁻² mbar under an inert flow of Ar. We obtain single crystal grains of Cu₂O with sizes of ∼500 × 500 μm² which have a cubic crystal structure and extend down to a layer of Kirkendall voids that form in the middle due to the bifacial oxidation of the Cu in ∼6 hours without annealing the Cu₂O. Annealing between 1120 °C and 1160 °C leads to a significant reduction of the Kirkendall voids and grain growth up to 3 × 3 mm² but also the formation of 10–20 μm deep holes due to the extensive out diffusion of the Kirkendall voids that are gradually filled with Cu upon increasing the annealing temperature due to a transition through the Cu₂O/Cu phase boundary. The growth of the free standing Cu₂O carried out in this way uses a high thermal budget but one may isolate individual Cu₂O grains after removing the KVL by polishing for the purpose of optical spectroscopy without the need for extensive, long annealing, thereby minimizing as much as possible the thermal budget. The Cu₂O crystals obtained in this way are not cost effective for the fabrication of competitive, all-oxide, solar cell devices for which lower cost methods such as reactive sputtering are more suitable.

Author contributions

Matthew Zervos, G. Georgiadis, were responsible for the growth and annealing of the Cu₂O, x-ray diffraction, optical transmission microscopy and writing up; Ioannis Paschos, Matin Ashurov and Pavlos Savvidis were responsible for scanning electron microscopy, atomic force microscopy, polishing and writing up.

Conflicts of interest

There are no conflicts of interest to declare.

Data availability

All data supporting this article has been included in the mani manuscript.

Acknowledgements

The authors acknowledge funding from the Innovation Program for Quantum Science and Technology (2023ZD0300300) and the Innovation Resource Allocation of Westlake University-Zhejiang Provincial Natural Science Foundation of China under Grant No. XHD24A2401

References

1. E. F. Gross, Optical Spectrum of Excitons in the Crystal Lattice, Nuovo Cimento, 1956, 3, 672–701.
2. C. Malerba, F. Biccari, C. L. A. Ricardo, M. D’Incau and P. Scardi, A. Mittiga, Absorption Coefficient of Bulk and Thin Film Cu₂O, Sol. Energy Mater. Sol. Cells, 2011, 95, 2848–2854.
3. S. Shibasaki, Y. Honishi, N. Nakagawa, M. Yamazaki, Y. Mizuno, Y. Nishida, K. Sugimoto and K. Yamamoto, Highly Transparent Cu₂O Absorbing Layer for Thin Film Solar Cells, Appl. Phys. Lett., 2021, 119, 242102.
4. Y. H. Zhang, M. M. Liu, J. L. Chen, S. M. Fang and P. P. Zhou, Recent Advances in Cu₂O-Based Composites for Photocatalysis: A Review, Dalton Trans., 2021, 50, 4091–4111.
5. G. Liu, F. Zheng, J. Li, G. Zeng, Y. Ye, D. M. Larson, J. Yano, E. J. Crumlin, J. W. Ager, L. Wang and F. M. Toma, Investigation and Mitigation of Degradation Mechanisms in Cu₂O Photoelectrodes for CO₂ Reduction to Ethylene, Nat. Energy, 2021, 6, 1124–1132.
6. T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz and M. Bayer, Giant Rydberg excitons in the Copper Oxide Cu₂O, Nature, 2014, 514, 343–347.
7. K. Orfanakis, S. K. Rajendran, V. Walther, T. Volz, T. Pohl and H. Ohadi, Rydberg Exciton–Polaritons in a Cu₂O Microcavity, Nat. Mater., 2022, 21, 767–772.
8. K. Kawaguchi, R. Kita, M. Nishiyama and T. Morishita, Molecular Beam Epitaxy Growth of CuO and Cu₂O Films with Controlling the Oxygen Content by the Flux Ratio of Cu/O, J. Cryst. Grow., 1994, 143, 221–226.
9. T. Iivonen, M. J. Heikkilä, G. Popov, H. E. Nieminen, M. Kaipio, M. Kemell, M. Mattinen, K. Meinander, K. Mizohata, J. Räisänen, M. Ritala and M. Leskelä, Atomic Layer Deposition of Photoconductive Cu₂O Thin Films, ACS Omega, 2019, 4, 11205–11214.
10. S. F. U. Farid, D. Cherns, J. A. Smith, N. A. Fox and D. J. Fermín, Pulsed Laser Deposition of Single-Phase n- and p-type Cu₂O Thin Films with Low Resistivity, Mater. Design, 2020, 193, 108848.
11. A. S. Rahman, M. A. Islam and K. M. Shorowordi, Electrodeposition and Characterization of Copper Oxide Thin Films for Solar Cell Applications, Procedia Eng., 2015, 105, 679–685.
12. H. Liu, V. H. Nguyen, H. Roussel, I. Gélard, L. Rapenne, J. L. Deschanvres, C. Jiménez and D. Muñoz-Rojas, The Role of Humidity in Tuning the Texture and Electrical Properties of Cu₂O Thin Films Deposited via Aerosol-Assisted CVD, Adv. Mater. Interfaces, 2018, 6, 1801364.
13. S. Chatterjee and A. J. Pal, Introducing Cu₂O Thin Films as a Hole-Transport Layer in Efficient Planar Perovskite Solar Cell Structures, J. Phys. Chem. C, 2016, 120, 1428–1437.
14. S. Steinhauer, M. A. M. Versteegh, S. Gyger, A. W. Elshaari, B. Kunert, A. Misiewicz and V. Zwiller, Rydberg Excitons in Cu₂O Microcrystals Grown on a Silicon Platform, Nature Communication, Materials, 2020, 1–11.
15. G. Blankenbur and K. Kassel, Fehlordnung und Elektrisches Verhalten der Ionenund Valenzkristalle, Ann. Phys., 1952, 10, 201–216.
16. J. H. Apfel and L. N. Hadley, Exciton Absorption in Cuprous Oxide, Phys. Rev., 1955, 100, 1689–1691.
17. K. Stecker, Über die Halbleitereigenschaften des Kupferoxyduls. XII Die Leitfähigkeit des Kupferoxyduls innerhalb des Existenzgebietes bei hohen Temperaturen im Bereich kleiner Drucke, Ann. Phys., 1959, 458, 55–69.
18. R. Frerichs and R. Handy, Electroluminescence in Cuprous Oxide, Phys. Rev., 1959, 113, 1191–1198.
19. R. S. Toth, R. Kilkson and D. Trivich, Preparation of Large Area Single-Crystal Cuprous Oxide, J. Appl. Phys., 1960, 31, 1117–1121.
20. W. S. BrowerJr and H. S. Parker, Growth of Single Crystal Cuprous Oxide, J. Cryst. Grow., 1971, 8, 227–229.
21. R. D. Schmidt-Whitley, M. Martinez-Clemente and A. Revcolevschi, Growth and Microstructural Control of Single Crystal Cuprous Oxide Cu₂O, J. Cryst. Grow., 1974, 23, 113–120.
22. K. B. Chang, L. Frazer, J. J. Schwartz, J. B. Ketterson and K. R. Poeppelmeier, Removal of Copper Vacancies in Cuprous Oxide Single Crystals Grown by the Floating Zone Method, Cryst. Growth Des., 2013, 13, 4914–4922.
23. L. Frazer, K. B. Chang, K. R. Poeppelmeier and J. B. Ketterson, Cupric Oxide Inclusions in Cuprous Oxide Crystals Grown by the Floating Zone Method, Sci. Technol. Adv. Mater., 2015, 16, 034901.
24. S. A. Lynch, C. Hodges, S. Mandal, W. Langbein, R. P. Singh, L. A. P. Gallagher, J. D. Pritchett, D. Pizzey, J. P. Rogers, C. S. Adams and M. P. A. Jones, Rydberg Excitons in Synthetic Cuprous Oxide (Cu₂O), Phys. Rev. Mater., 2021, 5, 084602.
25. S. Mani, J. I. Jang, J. B. Ketterson and H. Y. Park, High-Quality Cu₂O crystals with Various Morphologies Grown by Thermal Oxidation, J. Cryst. Grow., 2009, 311, 3549–3552.
26. M. Xiao, P. Gui, K. Dong, L. Xiong, J. Liang, F. Yao, W. Li, Y. Liu, J. Li, W. Ke, C. Tao and G. Fang, Quasi-Single Crystalline Cuprous Oxide Wafers via Stress-Assisted Thermal Oxidation for Optoelectronic Devices, Adv. Funct. Mater., 2022, 32, 2110505.
27. M. Zervos, I. Paschos, P. Savvidis, N. Florini, K. Koutsokostas, P. Komninou and N. Lathiotakis, Cryst. Eng. Commun., 2025, 27, 1977–1985.
28. K. Y. Maimaiti, M. Nolan and S. D. Elliott, Reduction Mechanisms of the CuO(111) Surface Through Surface Oxygen Vacancy Formation and Hydrogen Adsorption, Phys. Chem. Chem. Phys., 2014, 16, 3036–3046.
29. S. Jin, M. Huang, Y. Kwon, L. Zhang, B. W. Li, S. Oh, J. Dong, D. Luo, M. Biswal, B. V. Cunning, P. Bakharev, I. Moon, W. J. Yoo, D. C. Camacho-Mojica, Y. J. Kim, S. H. Lee, B. Wang, W. K. Seong, M. Saxena, F. Ding, H. J. Shin and R. Ruoff, Colossal Grain Growth Yields Single-Crystal Metal Foils by Contact-Free Annealing, Science, 2018, 362, 1021–1025.

---