Binary copper oxide semiconductors: From materials towards devices

Abstract

Copper-oxide compound semiconductors provide a unique possibility to tune the optical and electronic properties from insulating to metallic conduction, from bandgap energies of 2.1 eV to the infrared at 1.40 eV, i.e., right into the middle of the efficiency maximum for solar-cell applications. Three distinctly different phases, Cu₂O, Cu₄O₃, and CuO, of this binary semiconductor can be prepared by thin-film deposition techniques, which differ in the oxidation state of copper. Their material properties as far as they are known by experiment or predicted by theory are reviewed. They are supplemented by new experimental results from thin-film growth and characterization, both will be critically discussed and summarized. With respect to devices the focus is on solar-cell performances based on Cu₂O. It is demonstrated by photoelectron spectroscopy (XPS) that the heterojunction system p-Cu₂O/n-AlGaN is much more promising for the application as efficient solar cells than that of p-Cu₂O/n-ZnO heterojunction devices that have been favored up to now.

1 Introduction

In August 1925, document 1.640.335 was filed at the US patent office as a patent granted to L. O. Grondahl for a unidirectional current-carrying device based on a Cu₂O-metal contact 1. It marked the beginning of current semiconductor electronics long before the Ge and Si era started. From 1926 on L. O. Grondahl and P. H. Geiger worked on a copper-Cu₂O-solar cell 2. In spite of the historical importance, Cu₂O as a naturally p-type conducting semiconductor material 3, 4 never gained great interest (neglecting the special focus on the excitonic properties and Bose–Einstein condensation). Currently, there is renewed interest especially on Cu₂O with respect to solar-cell applications. With a bandgap energy of 2.1 eV Cu₂O is not positioned at the energies around 1.4 eV that, according to the Shockley–Queisser limit (SQL), give maximum efficiencies for single junction solar cells 5. The SQL predicts efficiencies of about 20% for Cu₂O but current experimental data are only about 3%, i.e., there is a lot of room for improvement. Up to now there is no report on successful n-type doping of Cu₂O and hence homojunction diodes are out of reach. This is why, so far, the focus has been on heterojunction solar cells devices in combination with ZnO as the n-type transparent conducting window layer.

Typical prototype heterojunction solar cells consist of four components: (i) the absorber layer and (ii) its metal contacts, (iii) the so-called window layer and (iv) its metal contacts. Combining p-type absorber layers and n-type window layers (as in the present case) one inherently faces the problems of lattice mismatch, of band alignment and band offsets (spikes and cliffs in the conduction and valence bands), and of low interface quality due to defects. The p-type absorber layer itself defines the photophysics (absorption coefficient, direct and indirect bandgap, bandgap energy, etc.) and the transport properties (electrical conduction, electron and hole mobilities, minority and majority carrier transport characteristics, etc.). The n-type window layer, e.g., of ZnO or GaN semiconductors with large bandgap energies, are transparent with respect to visible and IR spectral range and possess excellent electronic transport properties as well as ease of metal-contact formation.

The effort of identifying new, prospective p-type absorber layers for heterojunction solar cells has led to intensive research work on the CuInGa(Se)₂ system 6, and by taking issues of sustainability and scarcity of elements into account for the kesterites 7. Cu₂O seems to be an attractive alternative in terms of abundance, sustainability, nontoxicity of the elements, and numerous methods for thin-film deposition that facilitate low-cost production. However, the future and prospect of a copper-oxide-based thin-film solar-cell system has to be demonstrated by a critical look at its established physical properties and at those that need to be further investigated and improved, and by identifying properties that are undetermined so far.

2 The physics of copper oxides

2.1 Cu₂O (cuprite)

Cu₂O (see Fig. 1 for the crystal structure) is one of the stable phases of the three well-established copper-oxide compounds (the others are Cu₄O₃, CuO). It crystallizes in a simple cubic Bravais lattice 8–10. The space group is () or . Its unit cell contains six atoms, the four copper atoms are positioned in a face-centred cubic lattice (turquoise balls), the two oxygen atoms are at tetrahedral sites forming a body-centred cubic sublattice (red balls). As a consequence, oxygen atoms are fourfold coordinated with copper atoms as nearest neighbors, and copper atoms are linearly coordinated with two oxygen atoms as nearest neighbors (see Tables 1 and 2 for resulting crystallographic and physical properties, respectively). Natural crystals of Cu₂O can be found worldwide, most crystals of high quality with low density of structural defects and inclusions stem from Zaire in Africa 11. High-purity crystals used in the early investigations on exciton properties and nowadays on Bose–Einstein condensation 12 were provided by the Smithsonian Institute.

Figure 1. (online color at: www.pss-b.com) Crystal structure of Cu₂O shown by four unit cells. The big turquoise spheres represent copper, the small red spheres represent oxygen. As can be seen, each copper atom is linearly coordinated by two oxygen atoms.

Table 1. Crystallographic properties of Cu₂O 8–10.

lattice constant	4.2696 ± 0.0010 Å
space group	(224)
bond length Cu–O	1.849 Å
separation O–O	3.68 Å
separation Cu–Cu	3.012 Å
cell volume	(77.833 ± 0.055) × 10^−24 cm^3
formula weight	143.14
density	5.749–6.140 g/cm^3
melting point	1235 °C

Table 2. General properties of Cu₂O 8–10.

* After Ref. 38, ** After Ref. 39.
Young's modulus	30.12 GPa
shear modulus	10.35 GPa
c11	116.5–126.1 GPa
c12	105.3–108.6 GPa
c44	12.1–13.6 GPa
thermal expansion coefficient	2.3 × 10^−7 K^−1 (283 K)
Fröhlich coupling constant α	0.21*
ε(0)	7.11
ε(∞)	6.46
electron affinity χ	≈3.1 eV (300 K)
work function Φ	≈4.84 eV (300 K)
deformation potentials**	De = 2.4 eV, Dh = 2.2 eV

Bulk synthetic crystals of Cu₂O can be prepared by several methods such as oxidizing copper sheets, by melt growth, by floating zone growth, and by hydrothermal growth (see Ito et al. 11 for details).

Cu₂O thin films can be grown by almost any kind of deposition technique, e.g., electrodeposition, sol–gel, spray, sputtering 13–18. A wide variety of substrates were used such as sapphire, glass, etc. Deposition on these substrates typically results in textured films with grain sizes varying from 40 to 100 nm. For epitaxial growth of cubic Cu₂O cubic MgO substrates offer the best choice in terms of lattice match. Both possess cubic unit cells with comparable lattice parameters, i.e., a(MgO) = 4.213 Å and a(Cu₂O) = 4.269 Å.

Molecular beam epitaxy 19, 20, chemical vapor deposition 21, 22, and pulsed laser deposition 23, 24 have been used to obtain epitaxial films of high crystalline quality. Two substrate orientations have been chosen: MgO(100) and MgO(110). Epitaxial relationships have been established with Cu₂O (110)//MgO (001) and Cu₂O(001)//MgO(110), but also cube on cube growth of Cu₂O(001) on MgO(001) has been observed 19, 20, 22–24. Substrate preparation and substrate temperature play a crucial role, similar to the results reported for the somewhat related high-T_C cuprate superconductors on MgO substrates. Simply taking into account the small lattice mismatch, one would expect a cube to cube growth with a (001) orientation of Cu₂O. Instead a 45° in-plane rotation (see Fig. 2) with respect to the cubic cell of the substrate has been observed that gives a four (edges of the cubic Cu₂O cell) to three (face diagonals of MgO) relationship. In the MBE work of Kawaguchi et al. 19, similar results were obtained, and it was concluded that the surface-energy anisotropy rather than the lattice mismatch is the prominent factor determining the orientation relationship.

Figure 2. (online color at: www.pss-b.com) (110)-oriented Cu₂O grows with an inplane rotation of 45° with respect to the substrate (MgO) cubic cell as schematically illustrated. Four times the edge of the Cu₂O cubic cell matches three times the diagonal of the face of the MgO cubic cell, yielding a tensile mismatch of 3.94% of the Cu₂O film (after Ref. 24).

Cu₂O films of very good texture 15 but polycrystalline in nature can be obtained by sputter deposition techniques. Substrate orientation plays a minor role, instead sputtering power, plasma conditions, and substrate temperature have the major influence. However, by sputtering single-orientation films of Cu₂O(011) on MgO(011) could be deposited, while by comparison, the deposition on MgO(001) showed three orientations (111), (011), and (002). Since the (011) orientation was 70 times stronger than (002) it was concluded that the natural tendency towards (011) growth still dominates 17.

2.2 Band structure of Cu₂O

The direct transition from the highest valence band to the lowest conduction band occurs at the Γ-point of the Brillouin zone schematically shown on the right of Fig. 3 with and without spin-orbit coupling (λ). The valence band is predominantly d-like in character built up from the 3d¹⁰ states of Cu (in a pure ionic description Cu⁺, O²⁻), while the lowest conduction band has 4s Cu like character. The Γ_25′ valence band is split by spin-orbit interaction (Δ_so = 0.1338 eV) into and , the lowest conduction-band state derived from Γ₁ is the state.

Figure 3. (online color at: www.pss-b.com) Energy-band diagram of Cu₂O in the vicinity of the Γ-point. On the right the irreducible representations of the bands, the interband transitions as well as the corresponding band splittings are given, where spin-orbit interaction is neglected (λ = 0) and where it is accounted for (λ ≠ 0) (after Refs. 28–35).

Thus the lowest fundamental absorption transitions (neglecting excitonic features) are parity forbidden (, ) 25–37. Direct and allowed optical transitions are and . The four transitions are named according to the wavelengths of their spectral positions yellow, green, blue, and indigo, respectively (see Fig. 3). They are accompanied by pronounced excitonic transitions with very large exciton binding energies ranging from 46 to 150 meV allowing not only to study the ground-state properties but also many details of the Rydberg excited states 25–28, 33–37. The series limits coincide with the onset of the fundamental band-to-band absorption, which for the yellow series is 2.17 eV (4.2 K).

The other interband transition energies at 4.2 K are: ΔE() = 2.304 eV (limit of the green exciton series) 28, ΔE() = 2.624 eV (limit of the blue exciton series) 33, ΔE() = 2.755 eV (limit of the indigo exciton series) 33.

On the left of Fig. 3, the band dispersion is shown schematically. It has been studied by cyclotron resonance experiments 38, 39. The carrier effective masses in Cu₂O (polaron masses), expressed in units of the free electron mass m₀ are given in Table 3. The experimental data are taken from 38, while theoretical predictions originate from Ref. 40, where the masses were calculated along the Γ–X, Γ–M and Γ–R directions. As mentioned above, the valence band is split by spin-orbit interaction into the and states, with the negative spin-orbit coupling energy the state is at the top of the valence band. As a consequence, this state has a light-hole mass that is roughly half of the electron effective mass. Electron and light-hole masses are isotropic within experimental error 39.

Table 3. Electron and hole masses from experiment 38 and from DFT calculations 40.

mass	band	theory				experiment
		Γ–X	Γ–M	Γ–R	average
^+ After polaron correction (see Ref. 38).
m*e		0.92	0.92	0.92	0.92	0.99 (0.93^+)
m*lh		0.36	0.36	0.36	0.36	0.58 (0.56^+)
m*hh		2.83	0.91	0.72	1.49
m*soh		0.21	0.25	0.27	0.24

2.3 Density functional theory (DFT) within the local density approximation (LDA): Band-structure calculations

For a full understanding of the electronic and optical properties of the copper-oxide systems ab initio calculations are mandatory. However, the three known different copper oxides, Cu₂O, Cu₄O₃, and monoclinic CuO, are a challenge for standard ab initio investigations based on DFT. The crucial ingredient in the theoretical description is the exchange-correlation functional. Figures 4 and 5 show the density of states and the band structure, respectively, of the three different Cu–O compounds. The results are derived within the LDA. The corresponding Brillouin zones are sketched in Fig. 6. It is well known that LDA underestimates bandgaps. In agreement with other calculations 41, the monoclinic phase of CuO is actually metallic within LDA. One calculation using LDA + U 42 shows the opening of a bandgap and predicts an indirect semiconductor with a bandgap of 1 eV. However, this calculation needs to be considered with caution, and more advanced methods like hybrid functionals or GW calculations are necessary to assess this prediction. It is worth noting that other published band structures of CuO 41, 42 are not shown for the primitive but for the crystallographic unit cell. For Cu₄O₃, our calculation also yields a metallic ground state in LDA. To our knowledge, there are no published band-structure calculations of this structure. Cu₂O is the copper oxide structure for which most theoretical investigations were performed. Our calculations are in good agreement with other LDA calculations 43–45 and show an underestimation of the bandgap by 1.5 eV. Using LDA + U the bandgap is only increased by a few meV and is still well below the experimental value 45, 46. Hybrid functionals 47, 48, pseudo-self-interaction methods 49, and self-consistent GW calculations 50–52 yield very good agreement of the bandgap with experimental data. For the latter, a standard single-shot GW calculation is not enough to obtain a correct bandgap. The drawback of GW is the high demand for computation time. However, the accuracy e.g., of optical properties is much better than with hybrid functionals 53. For elastic constants and bulk modulus already LDA and GGA give very good results 54, as for such calculations basically differences in total energies rather than details of the band structure are important. The results of the electronic structure emphasize that more advanced methods, ideally GW calculations, are necessary also for the CuO and Cu₄O₃ systems to obtain reliable results for the electronic structure.

Figure 4. Calculated band structures of Cu₂O, Cu₄O₃, and CuO.

Figure 5. Calculated density of states (DOS) of Cu₂O, Cu₄O₃, and CuO.

Figure 6. (online color at: www.pss-b.com) Brillouin zones of cubic Cu₂O, tetragonal Cu₄O₃, and monoclinic CuO.

On SrTiO₃, CuO can be also grown in a tetragonal phase 55. For this tetragonal structure, a large number of theoretical investigations exist that also analyze the magnetic ground state of CuO. Basically, two stable phases with c/a = 0.9 56–58 and c/a = 1.1 56, 58, or c/a = 1.3 57 are found. Depending on the applied method, different antiferromagnetic (AF) ground states are found: hybrid functionals AF-II (c/a = 0.9) and AF-IV (c/a = 1.3), self-interaction correction (sic) AF-II (c/a = 0.9 and c/a = 1.1). From a theoretical point of view, an interesting structure is the cubic phase of CuO, which has not yet been experimentally observed. This phase would form the transition between the two stable insulating tetragonal phases. Because the two tetragonal phases are insulating, one also expects an insulating state for this cubic phase. However, for this structure LDA/GGA + U as well as hybrid functionals yield only a metallic phase 56, 57. Therefore, the cubic phase can be seen as something like a benchmark for different exchange-correlation functionals. One study predicts an insulating state of cubic CuO using an extended Hubbard-based corrective functional 59, while there are no calculations for CuO in any phase based on the GW correction.

2.4 Electrical and transport properties: The role of defects

Already in 1951, in a review article about copper oxide rectifiers 4, W. Brattain described the origin of Cu₂O as a semiconductor by “copper oxide is a defect semiconductor…the main impurity centers, acceptors in this case, are probably vacant copper ion lattice sites”. Nothing has changed concerning the validity of this statement, nowadays it is well established that Cu₂O is a natural p-type semiconductor, whose carrier concentration depends on the amount of cation deficiency (nonstoichiometry) 60.

Theoretical studies 42, 61–66 on the role of intrinsic defects in Cu₂O agree that the simple copper vacancy and the vacancy in the so-called split configuration have the lowest formation energies (in Cu-poor and Cu-rich conditions, see Fig. 7) compared to the other possible intrinsic acceptors, which are oxygen interstitials (in octahedral and tetrahedral coordination, see Fig. 7). The transition level (0/−) of V_Cu is at 0.23 eV (0.28 eV in Raebiger et al. 61) and for V_Cu,split at 0.47 eV. The formation energies of both defects are very similar (1.15 and 1.14 eV) and at least 0.7 eV lower than that of oxygen interstitials 66.

Figure 7. (online color at: www.pss-b.com) Formation energies for intrinsic p-type defects in Cu₂O in (a) Cu-rich–O-poor conditions and (b) Cu-poor–O-rich conditions. The solid dots denote the transition levels (after Ref. 66).

Temperature-dependent Hall effect measurements on oxidized copper sheets and thin films prepared by magnetron sputtering yielded activation energies in the range from 0.19 to 0.4 eV 4, 67–71.

The temperature dependence of the hole mobility (Arrhenius plot) is shown in Fig. 8. The dominant contributions to the mobility are phonon scattering at high temperatures and ionized impurity scattering at low temperatures (below 200 K) (67 and refs. therein). The measurements need to be extended to low temperature, which is not trivial since for high mobility and hence low carrier concentration (around 10¹⁶ cm⁻³ at RT) a carrier freeze out occurs at temperatures below 200 K, while for high carrier concentrations one finds significantly lower mobilities.

Figure 8. (online color at: www.pss-b.com) Temperature-dependent Hall mobilities of Cu₂O films grown at a growth temperature of 600 K (blue circle) and of 1070 K (red square). Open symbols represent monocrystalline Cu₂O from various references (see Ref. 67). Lines represent theoretical limits by LO phonon scattering, scattering by ionized impurities for the two samples (after Ref. 67).

Are the Cu₂O electrical properties really controlled by intrinsic defects or are they controlled by extrinsic impurities? It is believed that Cu₂O is a p-type semiconductor by nature, copper vacancies are believed to act as shallow acceptors. Positron annihilation spectroscopy is very useful to study the vacancies in semiconductors, but has up to now not yet applied to Cu₂O.

2.5 Donors and acceptors in Cu₂O

Effective mass theory (EMT) can be used to estimate the donor and acceptor binding energies E_B in Cu₂O. The binding energies of the EMT donors and acceptors can be estimated using Eq. (1):

• ((1))

With ε(0) = 7.1 (see Table 2) and m*_e = 0.99 m₀ and m*_lh = 0.58 m₀ 38 one obtains binding energies of 266 and 156 meV for the EMT donor and acceptor, respectively. Although this is only a rough estimate that neglects central cell effects, the values indicate that it will be more difficult to obtain n-type than p-type material. With E_D = 266 meV only a small fraction of the donors will be ionized at room temperature and concentrations well above 10¹⁸ cm⁻³ are needed to overcome the p-type conduction due to the cation vacancies. This also raises the questions as to the solubility limits of possible donors. The discussion on type conversion of Cu₂O is controversial and still ongoing 72, 73.

Among the possible extrinsic acceptors, a clear undebated picture has evolved with respect to nitrogen doping (silicon doping has been investigated, but it will not be considered here, since Si is not a simple substitutional impurity but gives rise to silicate formation inside Cu₂O 74, 75). With nitrogen doping (provided, e.g., by a N₂ flow in the plasma of the RF magnetron sputter system) it was possible to change the hole density by two orders of magnitude from 10¹⁵ to 10¹⁷ cm⁻³. It is postulated that nitrogen is incorporated on the oxygen site and forms a shallow acceptor (binding energy around 160 meV) 76–78. Other group V elements (P, As, Sb) have not been investigated.

The role of hydrogen in Cu₂O has been treated theoretically using screened hybrid DFT 79. The formation energies as a function of Fermi energy for various hydrogen-related defects are shown in Fig. 9. Scanlon and Watson 79 first examined the stability of interstitial hydrogen on tetrahedral and octahedral sites, bond centred and in two antibonding configurations. Unexpectedly, the tetrahedral interstitial site was found to have the lowest formation energy, in contrast to many nitrides and oxides where a position next to the anions (bond centred or antibonding) is preferred. The authors also examined the interaction of hydrogen with the cation and anion vacancies. As one can see from Fig. 9, hydrogen on oxygen sites is predicted to be in the +1 charge state over almost the entire range of Fermi energies 79. It turns from a donor state into an acceptor state for Fermi energies very close to the conduction band, i.e., it would act as an amphoteric dopant. The interaction of hydrogen with the Cu vacancy (H–V_Cu in Fig. 9) gives rise to a complex H–V_Cu, which according to the theoretical results (i) has the lowest formation energy of 0.17 eV of all hydrogen-related defects and (ii) is an amphoteric defect that changes from donor to acceptor when the Fermi energy is located in the middle of the bandgap. Thus, hydrogen should passivate the intrinsic Cu vacancy acceptors and thus pin the Fermi level to midgap 79. Corresponding experiments are not available up to now.

Figure 9. (online color at: www.pss-b.com) Calculated formation energies for intrinsic p-type (blue), n-type (red), and hydrogen impurity (green) defects in Cu₂O in (a) Cu-rich–O-poor conditions and (b) Cu-poor–O-rich conditions. The solid dots denote the transition levels (after Ref. 79).

2.6 Cu₄O₃ (Paramelaconite)

Paramelaconite was discovered in 1870 as a mineral in the Copper Queen mine located at Bisbee (Arizona, US). A first crystallographic determination of its structure was done by Frondel 83, and another by O'Keeffe and Bovin 80. In both studies, a body-centered tetragonal cell with similar lattice parameters was found. It should be noted, however, that the number of Bragg reflections and, more importantly, its intensity distribution is quite different. Though the newer data have entered the literature, so far, the investigations by Frondel 83 have neither been confirmed nor rebutted. Thus, there remain some doubts whether the same mineral paramelaconite was investigated. To date, it has only been synthesized as thin films, never as a bulk material. The crystallographic data 80–83 are collected in Table 4.

Table 4. Crystallographic properties of Cu₄O₃80.

space group	I4I/amd (no 141)
lattice constants	a = 5.837 Å
	a  = 5.83 Å 83
	a  = 5.817 Å 82
	c = 9.832 Å
	c  = 9.88 Å 83
	c  = 9.893 Å 82
cell volume	338 Å^3
cell content	4 [Cu4O3]
formula weight	302.18
density	5.93 g cm^−3
distances
the Cu^+–oxygen rod
Cu(1)–O(1)	(2×)	1.867 (6) Å
O(1)–O(1)		3.735 (11) Å
the Cu^2+–oxygen rod
Cu(2)–O(2)	(2×)	1.916 (1) Å
Cu(2)–O(1)	(2×)	1.966 (6) Å
O(1)–O(2)	(2×)	2.559 (9) Å
O(1)–O(2)	(2×)	2.920 (1) Å
the O(1)–Cu tetrahedron
O(1)–Cu(1)	(2×)	1.867 (6) Å
O(1)–Cu(2)	(2×)	1.966 (6) Å
Cu(1)–Cu(2)	(2×)	2.919 (1) Å
Cu(1)–Cu (2)	(2×)	3.229 (1) Å
the O(2)–Cu tetrahedron
O(2)–Cu(2)	(4×)	1.916 (1) Å
Cu(2)–Cu(2)		2.919 (1) Å
Cu(2)–Cu(2)		3.229 (1) Å

The paramelaconite structure (tetragonal symmetry) is closely related to that of SrCu₂O₂ 84, which has the same symmetry and similar cell dimensions. The Cu⁺–O rods are identical in the two compounds, whereas Sr replaces the O(2) of paramelaconite (see Fig. 10). Apart from oxidation studies, mainly sputter deposition was employed 85–91. Annealing in air indicates that Cu₄O₃ is stable up to 250 °C 89. The optical and electrical properties of this material are still “terra incognita”.

Figure 10. (online color at: www.pss-b.com) Crystal structure of Cu₄O₃. The crystal is built up by stacks of two-fold coordinated copper atoms (similar to Cu₂O) and four-fold coordinated copper atoms (similar to CuO).

2.7 CuO (Tenorite)

Cupric oxide occurs in the form of a mineral called tenorite. The crystallographic data are collected in Table 5. One notes that there are four CuO molecules in the unit cell and two CuO units in the primitive cell (Fig. 11). The symmetry is monoclinic 92.

Table 5. Crystallographic properties of CuO 92.

space group	C2/c (No. 15)
unit cell	a = 4.6837 Å
	b = 3.4226 Å
	c = 5.1288 Å
	β = 99.54°
	α, γ = 90°
cell volume	81.08 Å^3
cell content	4 [CuO]
formula weight	79.57
density	6.515 g cm^−3
distances
Cu–O	1.96 Å
O–O	2.62 Å
Cu–Cu	2.90 Å
melting point	1201 °C

Figure 11. (online color at: www.pss-b.com) Crystal structure of CuO shown by four unit cells. Copper is planar four-fold coordinated by oxygen atoms, whereas the oxygen is coordinated by four copper atoms in a slightly distorted tetrahedron.

Not much is known about the electronic structure of CuO. The research focus up to now was on optical properties in the visible-IR and on Raman scattering (see below). Investigations of the interband absorption and hence of the bandgap energy as well as on the nature of transition, i.e., direct or indirect, are very scarce and the results do not provide an unambiguous assignment 93–96. Koffyberg and Benko 93 conclude that an indirect allowed bandgap is present at 1.35 eV at RT in agreement with Marabelli et al. 94 who, however, do not draw any conclusion concerning the type of transition. By temperature-dependent studies they could demonstrate that at 10 K the absorption edge has shifted to about 1.57 eV 94. A recent theoretical study 42 predicts CuO to be an indirect semiconductor with an energy gap at 1 eV.

According to Wu et al. 42, the conduction band minimum occurs at the point D(1/2,0,1/2). Note that this calculation refers to the Brillouin zone of the simple monoclinic structure, which is not the correct one. The characters of the top valence band and the lowest conduction bands are mainly determined from 3d orbitals of Cu.

Since the conduction-band minimum is not at Γ, the conduction-band (electron) effective mass is not isotropic (for the Brillouin zone and assignment of the relevant directions see Fig. 6). Hence, the longitudinal (l, along the direction DΓ) and transversal (t, plane perpendicular to DΓ direction) masses have to be distinguished. Wu et al. 42 calculated m_l = 0.78 m_o and m_t = 3.52 m_o, respectively. For the average hole effective mass they obtained m* = 1.87 m_o.

CuO is also believed to be intrinsically p-type with copper vacancies as acceptors being responsible for the hole conduction.

In summary, for both compounds, Cu₄O₃ and CuO, crystallographic data on the lattice structure, on the positions of Cu and O atoms as well as on bond lengths are available, but almost no information exists on band structure and bandgap energies, on effective masses, etc. In what follows, we attempt to provide some of the lacking information by reporting some first results of our investigation of the synthesis, of the structural characterization, and of the electrical and optical properties Cu–O compounds. We also critically assess the possibilities of device realization with a special emphasis on solar cell concepts.

3 Experimental investigation of Cu–O compounds

3.1 Synthesis and characterization methods

The samples were prepared by RF-magnetron sputtering using a 3-inch Cu target in a mixture of Ar and O₂ (reactive gas). The substrate temperature was below 100 °C (unheated substrate). With a power of 75 W typical growth rates obtained are 1.4 µm in 10 min. Substrates used were glass, sapphire, and GaN on sapphire. In a second set-up, an ion source (RIM type) was used for sputtering, here the substrates could be heated up to temperatures of 700 °C. The films were analyzed by X-ray diffraction (Siemens D 5000) in the Θ−2Θ geometry. In order to ascertain the crystallographic structure (pole figures) 4-circle measurements were performed on a URD6/TZ6 (Freiberger Präzisionsmechanik). Electrical characterization was carried out by Hall effect measurements. For the optical absorption measurements, a UV–VIS Lambda 900 spectrometer was used, while for the determination of the complex dielectric function spectrometric ellipsometry was employed. Raman scattering experiments were performed on a Renishaw in Via microscope system. Low-temperature and temperature-dependent luminescence experiments were carried out using a HeCd-laser for excitation (325 nm).

3.2 Structural properties

Varying the oxygen flow in the sputter process allows one to synthesize copper oxides of different stoichiometry, in particular, the three crystalline phases Cu₂O, Cu₄O₃, CuO. For very small oxygen flows, metallic copper is deposited. With increasing flow (see below), stable conditions for the preparation of Cu₂O are achieved. It turns out that for the unheated substrates the XRD reflections of the (200) and (111) lattice planes of Cu₂O (see Fig. 12) are not at the position corresponding to the cubic lattice constant (dotted lines in Fig. 12). Annealing in N₂ flow at temperatures of 735 and 950 °C for times of 10 min and 2 h results in a shift of the position of the diffraction peak towards the established value (the remaining small deviation might originate from the stress in the films caused by the difference in thermal expansion coefficients of film and substrate).

Figure 12. (online color at: www.pss-b.com) Diffraction patterns of Cu₂O samples annealed at different temperatures and annealing durations. Black line: as-grown; red line: 735 °C for 10 min; green line: 735 °C for 2 h; blue line: 930 °C for 10 min; magenta line: 930 °C for 2 h.

However, as the deposition was carried out at RT the large deviation of the (200) reflection observed in the as-grown films cannot originate from stress due to different thermal expansion of substrate and film. Azanza Ricardo et al. 97 ruled out that grain interactions are the origin. They postulated a two-phase model with the main phase consisting of strongly textured grains and a second phase, which is polycrystalline and untextured, to account for the compressive strain. However, such an explanation is very unlikely in our case because of the huge shifts of the reflection positions. The shifts can only be attributed to a nonstochiometric occupancy of the unit cell due to oxygen deficiency or oxygen excess.

SEM images reveal an average grain size of 40 nm for as-grown films that changes significantly upon annealing at 735 and 930 °C, which leads to grain sizes of around 300 and 400 nm, respectively (see Fig. 13). This has also a major influence on the optical and electrical data, as will be outlined below.

Figure 13. SEM images of Cu₂O annealed at different temperatures for 10 min: (a) as-grown, (b) 400 °C, (c) 735 °C, and (d) 930 °C. There is no significant change at 400 °C, grains start growing at 735 °C and attain a size of ca. 400 nm at 930 °C.

The systematic change in lattice parameters can be observed when the substrate temperature is increased in the growth process. Figure 14 shows corresponding results starting from an unheated substrate (substrate temperature caused by the plasma around 100 °C) to a heated substrate at 700 °C. In XRD both the (111) and (200) reflections were observed, and were used to calculate the lattice parameter (see Fig. 14). The lattice parameter starts at 0.444 nm for an unheated substrate and continuously decrease to the lattice constant of bulk Cu₂O with increasing growth temperature. This is similar to the behavior of the as-grown and subsequently annealed films.

Figure 14. (online color at: www.pss-b.com) Lattice constant determined from the positions of the Cu₂O (111) orientation (black squares) and Cu₂O (200) orientation (red circles) in comparison with the bulk value (dashed line) as a function of the substrate temperature.

Depositing films at 400 °C and tuning the oxygen flow allows one to evaluate the growth window of Cu₂O. As can be seen from the XRD investigations, Cu₂O can be grown over a rather wide range of oxygen flows. However, there is only a limited range (3–5 sccm, hatched area in Fig. 15) where it is free from secondary phases (at least from what can be deduced from XRD). Metallic copper inclusions are found at low oxygen flows (<3 sccm), and the appearance of CuO can be noted (see Fig. 15) at high flows (>6 sccm). The films always show a mixture of (200) and (111) orientations, which is likely to originate in missing substrate orientation when glass substrates are used. This changes immediately when the substrate offers an epitaxial relation and close lattice matching, facilitating single-crystalline growth, as is the case with MgO substrates. In Fig. 16, the results for a deposition at 400 °C on a MgO (100) substrate are shown. Before deposition, the substrate was annealed at 600 °C in vacuum for 2 h. The X-ray diffractogram shows the (110) and (220) reflections of Cu₂O together with the (200) reflection of the MgO substrate, no reflections of different lattice planes are found. This confirms the above-mentioned results that the relationship Cu₂O(110)||MgO(110) achieved by 45° rotation is favored.

Figure 15. (online color at: www.pss-b.com) Evolution of the observed reflection positions as a function of oxygen flow in the growth for the series of sputtered copper-oxide samples. The dashed lines represent bulk values from the literature.

Figure 16. (online color at: www.pss-b.com) XRD diffraction pattern of a Cu₂O layer sputter deposited on MgO (upper diffractogram) in comparison with a spectrum of the substrate (lower diffractogram).

The Cu₂O composition as measured by the diffraction angle of the (200) lattice plane is stable (unheated substrate) for oxygen flows between 3 and 3.7 sccm (see Fig. 17). For higher flows (3.8 to 4.6 sccm), we obtain a significant shift to higher angles before a narrow (4.7 to 5.2 sccm) plateau is reached close to the lattice constant of paramelaconite ((220) orientation). At higher flows (5.5 to 8 sccm) only CuO with () orientation is synthesized.

Figure 17. Position of the reflection with the highest XRD intensity vs. oxygen flow for the series of sputtered copper-oxide samples. The horizontal lines show the literature values of different copper-oxide XRD reflections. By an increase of the oxygen flow the reflection shifts from a position around the Cu₂O (200) direction to the Cu₄O₃ (220) direction, which indicates a phase change. At an oxygen flow of 5.5 sccm the Cu₄O₃ (220) reflection vanishes and the CuO () reflection appears at 35.5° (dashed lines are a guide to the eye).

3.3 Structure identification and verification of the symmetry (pole figures)

For three representative samples, one for each copper-oxide phase Cu₂O, Cu₄O₃, and CuO, respectively, pole figures were measured by 4-circle X-ray diffraction to obtain further evidence that the assignment of the reflections observed in the 2-circle Θ−2Θ scans are correct. For a pole figure, the measurement set-up is as follows: the Θ angle (sample holder) and the 2Θ angle (detector) are set to the values where the diffraction peak will be observed in a Θ−2Θ scan. The two additional circles in the measurement are χ and φ. χ is the tilt angle of the sample. At the beginning of the measurement, it is zero like in a Θ−2Θ scan. φ is the rotation angle of the sample, where the rotation axis is perpendicular to the sample surface. In the measurement χ, was varied from zero to 80 degrees in two-degree steps and for each χ-angle, the sample was rotated around φ from zero to 360 degrees in four degree steps. Figure 18 shows the pole figures of the Cu₂O (200), the Cu₄O₃ (220), and the CuO () reflection. The first two just have a spot in the middle of the pole figure because (200) is the preferred orientation in Cu₂O films, as is the (220) orientation for the Cu₄O₃ films. In the pole figure of the Cu₂O (111) reflection (not shown), one only observes a ring at a tilt angle of 54°. This fits nicely to the value for the angle between the (111) and (200) planes which is 54.7°. The pole figure shows a ring due to a fiber texture of the samples.

Figure 18. (online color at: www.pss-b.com) Pole figures of the Cu₂O (200) orientation at 2θ = 42.3°, the Cu₄O₃ (220) orientation at 2θ = 43.8°, and the CuO () orientation at 2θ = 35.5°.

In the pole figure of the CuO () reflection, a spot in the center and a ring are observed. The spot belongs to the () reflection as the preferred orientation and the ring is the reflection of the () lattice plane.

Thus, the 4-circle measurements demonstrate and confirm the existence of three individual phases that by properly adjusting the oxygen flux can be prepared with high phase purity.

3.4 Electrical properties

The growth windows of the three copper-oxide compounds are shown in shaded areas in Fig. 19 where the behavior of the specific electric resistance as a function of the oxygen flow is presented. The films change from highly resistive to low resistivity by two orders of magnitude for each compound. This striking behavior is also reflected in the hole carrier densities versus oxygen flow as obtained from Hall effect measurements (Fig. 20). For Cu₂O the carrier densities start around 10¹⁵ cm⁻³ and increase up to 10¹⁹ cm⁻³, for Cu₄O₃ a similar trend is observed. For CuO the lowest carrier densities are around 10¹⁷ cm⁻³, which increase up to 10²⁰ cm⁻³.

Figure 19. Specific resistance from van der Pauw measurements as a function of the oxygen flow for the series of sputtered copper-oxide samples. Within the different copper-oxide phases the specific resistance decreases with increasing oxygen flow, whereas an increasing resistance indicates a phase change (lines are a guide to the eye).

Figure 20. Carrier concentrations of the series of sputtered copper-oxide samples determined from Hall measurements. The carrier concentration increases with increasing oxygen flow and reaches saturation before dropping sharply at each phase change (dashed lines are a guide to the eye).

This strongly suggests that tuning the stoichiometry around the correct stoichiometric composition of the three compounds (oxygen poor to oxygen rich) allows the electrical conductivity and hole density to be increased, most likely due to the creation of copper vacancies.

3.5 Optical properties

As-grown films and those annealed at 930 °C were investigated by spectrometric ellipsometry. Figures 21 and 22 show the results for the real and imaginary parts ε₁ and ε₂ of the dielectric function. With Eqs. (2) and (3) the refractive index and the extinction coefficient were calculated, which allows one to also derive the absorption coefficient and the reflectivity using Eqs. (4) and (5):

• ((2))

• ((3))

• ((4))

• ((5))

Figure 21. (online color at: www.pss-b.com) Real part of the dielectric function ε₁ of Cu₂O of an as-grown film (black line) and a film annealed at 930 °C (red line) obtained by spectroscopic ellipsometry measurements.

Figure 22. (online color at: www.pss-b.com) Imaginary part of the dielectric function ε₂ of Cu₂O of an as-grown film (black line) and a film annealed at 930 °C (red line) obtained by spectroscopic ellipsometry measurements. The characteristics of the as-grown and annealed Cu₂O are quite similar, but the as-grown film does not show the excitonic features in the range of 2–3 eV.

A fit to the imaginary part of the dielectric function is shown in Fig. 23. The line positions obtained by fitting with Gaussians are marked with numbers 1 to 7, starting from 2.59 eV (1), 2.71 eV (2), 2.89 eV (3), 3.31 eV(4), 4.27 eV (5), 4.75 eV (6), and 5.24 eV (7). The data are in good agreement with recent work published by Haidu et al. 98 and by Ito et al. 99. Ito et al. 99 attributed the first two lines to the blue and indigo exciton transitions with mean quantum number n = 1. Both transitions are dipole allowed (see also Park et al. 101). In Haidu's work 98, a Cu₂O single crystal was used, the highly textured Cu₂O films obtained by annealing at 930 °C thus have comparable optical properties.

Figure 23. (online color at: www.pss-b.com) Gaussian fit to the imaginary part of the dielectric function ε₂ to determine the transition energies. The positions are marked by arrows.

In the calculated absorption spectrum (Fig. 24), these transitions can also be identified. The obtained absorption coefficient rises only very slowly, reaching a value of 1 × 10⁵ cm⁻¹ at an energy of approximately 2.6 eV.

Figure 24. (online color at: www.pss-b.com) Absorption coefficient of an as-grown Cu₂O film (black line) and a film annealed at 930 °C (red line). The annealed film shows well-defined excitonic peaks in the range 2.0–3.0 eV, which correlate with the transitions shown in Fig. 3.

Malerba et al. 100 made a detailed analysis of the absorption coefficient in the range from 1.95 eV to 2.7 eV. They included the various contributions (direct forbidden, indirect) into their analysis, which is shown in Fig. 25. Above the yellow exciton series (>2.15 eV) the absorption coefficient is in the mid-10³ cm⁻¹ range and then starts to increase by one and a half orders of magnitude 100. Extrapolating the energy gap from the slope of the transmission spectrum mostly results in a bandgap energy much higher than the experimentally established value. Various explanations have been given for these observations. The most obvious and convincing reason is that the low absorbing part from 1.9 to 2.4 eV is just not resolved in the measurements.

Figure 25. (online color at: www.pss-b.com) Absorption coefficient data obtained on bulk and thin-film Cu₂O samples compared with different literature data (for details see Ref. 100). The solid line is the fit obtained with the expressions discussed in Ref. 100. The different contributions due to direct and indirect transitions are also shown (after Ref. 100).

In Fig. 26, we compare the optical properties of Cu₄O₃ and CuO as measured by spectrometric ellipsometry. The transition energies in ε₂(ω) are marked with arrows and the corresponding values are given in Table 6.

Figure 26. (online color at: www.pss-b.com) Imaginary part of the dielectric function ε₂ for Cu₄O₃ (black) and CuO (red). The numbered arrows show the positions of possible interband transitions or of excitons.

Table 6. Transition energies ε₂(ω), in eV, of Cu₄O₃ and CuO in comparison with Cu₂O.

labelling	Cu4O3	CuO	Cu2O
E1	1.80	1.66	2.59
E2	2.34	2.07	2.71
E3	3.08	2.68	2.89
E4	3.53	3.46	3.31
E5	3.9	6.0	4.27
E6	5.29		4.75
E7	5.68		5.24

One notes a significant shift of the first transition in Cu₄O₃ compared to Cu₂O, but the ε₂(ω)-spectrum has a similar rich structure. Due to the lack of reliable band-structure calculations, these transitions cannot be unambiguously identified, but may serve as a starting point for the description of the band structure of both compounds, Cu₄O₃ and CuO. To this end, it cannot be decided whether the nature of intraband valence to conduction band transition is direct or indirect, but the absorption coefficient as a function of photon energy of all three compounds differs considerably. This is shown in Fig. 27, where also the energy is marked when the absorption coefficient reaches a value of 1 × 10⁵ cm⁻¹. Going from Cu₂O via Cu₄O₃ to CuO the photon energy shifts from 2.7 eV via 2.4 eV to 2.1 eV. These still preliminary data indicate that Cu₄O₃ could be a better absorber material than Cu₂O (and better than CuO, in particular, since CuO exhibits significantly lower hole mobilities).

Figure 27. (online color at: www.pss-b.com) Absorption spectra of Cu₂O (black), Cu₄O₃ (red), and CuO (blue). The horizontal and vertical dotted lines indicate the energies where the absorption coefficient reaches 1 × 10⁵ cm⁻¹ in the spectra.

3.6 Photoluminescence properties

All copper oxides have in common that they are weakly or even nonluminescent systems. In particular, CuO is “dark” black and luminescence data on this material have rarely been collected and reported. It has been recently claimed that CuO nanostructures exhibit several luminescence bands/signals ranging from as high as 4 eV down to 1 eV (102, 103, and references therein). However, the copper oxide nanostructure samples investigated were not at all phase pure CuO and definitely contained Cu₂O, and additionally substrate luminescence effects were not clearly eliminated in studies reporting on luminescence of CuO 104. Thus, today, the conclusion that luminescence from CuO is nonexistent is still valid.

On the other hand, Cu₂O unambiguously shows several luminescence signals, however, these are weak in intensity. The latter is due to the fact that optical transitions require parity change, which is not given between the energetic highest valence band and lowest conduction band of the direct semiconductor Cu₂O. The corresponding spin forbiddance of the transition resulting in the weak luminescence is partly broken by three possible effects: (a) defects within the crystal, (b) the decay of ortho-excitons, or (c) phonon-assisted transitions. The majority of the luminescence studies reported were performed on thermally oxidized copper, and the observed broad luminescence bands of Cu₂O have been assigned to doubly charged oxygen vacancies (V) at 1.72 eV (720 nm), singly charged oxygen vacancies (V) at 1.53 eV (810 nm), and copper vacancies (V_Cu) at 1.35 eV (920 nm). This assignment is very consistently used in literature 105–109, 11, but the exact peak positions and especially the relative intensities strongly depend on the used growth process as well as sample processing. The two high-energy bands were only observed at low measuring temperatures in the past, whereas the copper-vacancy band at low energies dominates the spectra at room temperature. In high-quality material, e.g., floating-zone grown single crystals, one can observe the additional recombination of the 1s ortho-exciton via an electric quadrupole transition at temperatures of 4.2 K at an energy of 2.03 eV (610 nm), and respective phonon side bands via electric dipole transitions 109. Furthermore, at the same temperature phonon-assisted recombination of para-excitons can occur in such samples.

Polycrystalline, magnetron-sputtered Cu₂O thin films usually do not exhibit excitonic recombination lines in the as-prepared condition, but clearly show all three defect luminescence bands, as depicted in Fig. 28. Furthermore, a more or less weak luminescence band is observable at about 1.63 eV (760 nm), which might be assigned to the existence of some fractions of a metastable Cu_xO_y defect phase (sometimes assigned to Cu₃O₂ for which we found no evidence) within such sputtered thin films. It has been reported that such an energetic position of the luminescence might be used as an identification of this metastable phase 110. The temperature-dependent PL of sputtered thin films, which is also shown in Fig. 28a, reveals that all bands are visible up to room temperature, which is in contrast to the above-mentioned thermally oxidized samples published some time ago. This difference is likely due to the today more sensitive PL/CL systems, because the intensity of the high-energy bands drops with increasing temperature in the same situation, as described above: the luminescence at 1.35 eV (920 nm) dominates the room-temperature spectrum. For temperatures above 100 K, one can extract out of those data the bandgap dependence of Cu₂O as a function of temperature using the semiempirical Varshni relation with α being about −3.5 × 10⁻⁴ eV/K. Finally, annealing can significantly improve the quality of such polycrystalline Cu₂O thin films. After a treatment at 600 °C in an argon atmosphere, the low-energy defect bands disappear, and the phonon-assisted recombination of ortho-excitons becomes clearly visible at 2.019 eV (614 nm), as shown in Fig. 29.

Figure 28. (online color at: www.pss-b.com) (a) Photoluminescence spectra of magnetron sputtered Cu₂O thin films as a function of temperature. A HeCd laser (325 nm) was used for excitation. (b) Temperature dependence of the PL intensity of the different bands.

Figure 29. (online color at: www.pss-b.com) Cathodoluminescence spectrum measured at ∼10 K of a polycrystalline Cu₂O thin film, which was prepared by magnetron sputtering followed by annealing in argon atmosphere at 600 °C. The spectrum shows phonon-assisted ortho-excitons.

3.7 Raman investigations

Figure 30 depicts the Raman spectra of the three copper-oxide phases identified in the series of RF-magnetron sputtered samples. The spectra were recorded in the backscattering geometry at room temperature. A polarized 633-nm excitation laser was focused onto the sample surface using a 50× objective. The same objective was used to collect the scattered light, which was then dispersed by a spectrometer with a focal length of 250 mm and recorded by a CCD detector. The system's spectral resolution is about 1.5 cm⁻¹.

Figure 30. (online color at: www.pss-b.com) Raman spectra of the three different copper-oxide compounds CuO, Cu₄O₃, and Cu₂O, respectively.

Raman spectra of CuO have been reported by several authors. The first studies were motivated by the close structural relation to superconducting compounds such as YBa₂Cu₃O_x or La₂CuO₄ 111–114, which contain CuO planes. For a better understanding of the properties of such superconductors, Chrzanowski and Irwin 115 carried out the first temperature-dependent Raman-scattering experiments of cupric oxide in 1989 and successfully identified the three allowed Raman modes. Since then, the vibrational modes of CuO have been extensively studied using infrared and Raman spectroscopic methods. Goldstein et al. 116 studied polarization and angle-dependent Raman spectra of CuO. Infrared spectra can be found in the works of Kliche et al., Hagemann et al., Guha et al., and Kuz'menko et al. 117–120. Reimann and Syassen 121 carried out pressure-dependent experiments, whereas Irwin and Wei 122 analyzed the frequency shifts of vibrational modes in CuO due to different oxygen isotopes. The influence of temperature was investigated by Chrzanowski and Irwin, Hagemann et al., and Irwin and Wei 115, 118, 122. The results of neutron-scattering experiments are discussed by Yang et al. 123 and Reichard et al. 124

CuO crystallizes in a monoclinic structure belonging to the (C2/c) space group, (cf. Table 5). It has two CuO units, i.e., four atoms, in its primitive unit cell, leading to nine optical and three acoustic phonon branches 115, 116. The symmetries of the zone-center modes are given by the following irreducible representations 115:

• 

Only the three modes of A_g and B_g symmetry are Raman active. The acoustic modes have A_u and B_u symmetry (A_u + 2B_u). The remaining six modes (3A_u + 3B_u) are infrared active. In a (x,y,z)-coordinate system where the y-axis is parallel to the twofold rotational axis 125, the Raman tensors for the monoclinic structure are given by 126:

• 

The CuO spectrum in Fig. 30 reveals two signals at about 290 and 340 cm⁻¹, which have A_g and B_g symmetry, respectively. The second mode, which is also of B_g symmetry, can be distinguished in the Raman spectrum as a rather feeble signal at about 620 cm⁻¹. In most spectra shown in the literature, this signal is stronger than in the CuO spectrum depicted in Fig. 30. A likely reason for the weakness of the latter signal is the strong polarization dependence of this particular mode 118. In the literature, there is an agreement about the assignment of the Raman modes, however, the reported mode positions vary considerably.

As mentioned above, Cu₂O crystallizes in a cubic structure of space group 127, 128. Its primitive cell contains two Cu₂O units, i.e., six atoms, yielding 15 optical phonon modes in addition to the three acoustic phonon modes. Huang 129 performed the first group theoretical analysis of the vibrational modes already in 1963. According to Kroumova et al. 130, the symmetries of the vibrational modes at k = 0 are given by:

• 

Modes with E_u and T symmetry are twofold and threefold degenerate, respectively. The three acoustic phonons possess T_1u symmetry. All three modes with T_1u symmetry are infrared active. Vibrations belonging to the threefold degenerate T_2g symmetry are the only Raman-active modes in this material. The A_2u and E_u modes are silent modes. Following the notation of Loudon, the Raman tensors for the Raman-active vibrations in the space group are 126:

• 

The axes of the (x,y,z)-coordinate system are parallel to the edges of the cube whose body diagonals correspond to the threefold rotational axes of the crystal 125.

According to the group-theoretical analysis above, the Raman spectrum of a perfect Cu₂O crystal should exhibit only one Raman signal belonging to the three-fold degenerate T_2g mode. The Raman spectrum of a sputtered Cu₂O film shown in Fig. 30 exhibits pronounced differences, as it reveals a multitude of Raman signals. However, it is similar to the experimental spectra of bulk Cu₂O crystals reported in the literature 131–135. It is worth noting that the reported Raman spectra vary significantly in the mode intensities and the number of observed modes. The reasons for this are manifold, most importantly, via the instability of the Cu₂O that leads to a variety of intrinsic defects and a tendency towards nonstoichiometry 131. Additional effects due to different excitation conditions (i.e., in resonance and off resonance with the excitonic transitions of Cu₂O) 136, due to a dependence on the scattering geometry and polarization conditions 134, and due to the surface treatment of the samples 137 also play a role, but are less significant. Nonstoichiometry due to the formation of point defects such as vacancies, interstitials, or antisite defects has two major effects. On the one hand, the translational symmetry is broken and the corresponding selection rules no longer strictly hold, e.g., the point defects reduce the local symmetry such that the distinction between Raman-allowed and Raman-forbidden lattice vibrations diminishes. On the other hand, depending on the specific point defect and its compatibility with the lattice, local vibrational modes may be introduced, which may also be Raman active. The Raman spectra of Cu₂O are typical examples of such effects as the dominant Raman signals observed are actually due to IR-active modes or defect modes rather than due to the nominally Raman-active mode. Basically, one observes all lattice modes at about 90 cm⁻¹ (T_2u), 110 cm⁻¹ (E_u), between 140–160 cm⁻¹ (T_1u TO, LO), at about 350 cm⁻¹ (A_2u), and between 630–660 cm⁻¹ (T_1u TO, LO), and in the vicinity of 515 cm⁻¹ the only Raman-active T_2g mode. Additional features at 220 cm⁻¹ (2 E_u) and in the range between 400 and 490 cm⁻¹ are assigned to multiphonon Raman scattering. In many Raman spectra an additional signal at 200 cm⁻¹ is observed that is due to local vibrations of Cu on O sites 131. This feature is not observed in the spectrum of Cu₂O in Fig. 30.

No Raman spectra of Cu₄O₃ have been reported in the literature yet. Its crystal structure is tetragonal, belonging to the (I4₁/amd) space group with 14 atoms in its primitive unit cell 80. Thus, there are a total of 42 zone-center vibrational modes. According to Kroumova et al. 130, their symmetries are:

• 

The three acoustic phonon modes are of A_2u and E_u symmetry. Infrared-active vibrations in a perfect structure have A_2u and E_u symmetry and Raman-active modes are of A_1g, B_1g, and E_g symmetry. The remaining vibrations are silent modes. Raman tensors are given by Loudon 126 for a (x,y,z)-coordinate system where the z-axis is parallel to the fourfold axis 125:

• 

In the spectra of Cu₄O₃ in Fig. 30, at least five Raman signals can be distinguished. These are located at about 175, 280, 320, 530, and 610 cm⁻¹. Thus, the spectrum of Cu₄O₃ is distinctly different from those of CuO and Cu₂O. Despite the fact that the number of Raman signals observed is close to the number of single-phonon Raman signals expected for a perfect Cu₄O₃ crystal, no assignment of the peaks can be made at this stage. In particular, in the light of the analysis of the Cu₂O spectra in the literature, it may be anticipated that some of these strong signals are also due to local modes, nominally forbidden modes, or multiphonon Raman scattering.

Figure 31 shows the evolution of the observed frequencies of the strongest Raman signals in the series of sputtered samples as a function of oxygen flow used in the fabrication process. It can be clearly seen that it is possible to distinguish between the three different copper-oxide phases by Raman spectroscopy.

Figure 31. Appearance of the Raman lines as a function of the oxygen flow in the series of sputtered copper-oxide samples and correlation with the occurrence of the three copper-oxide phases, Cu₂O, Cu₄O₃, and CuO.

In summary, the Raman spectra of CuO and Cu₂O have been investigated fairly well, but further experiments on Cu₄O₃ are required to obtain a similar level of understanding. Raman spectroscopy is sensitive to the stoichiometry of the copper oxides. Thus, Raman spectroscopy in conjunction with other spectroscopic techniques such as photoluminescence spectroscopy will yield valuable information about point defects in these materials that have a major impact on the optoelectronic properties.

4 Metal contacts on copper oxide

From the work function 138 of Cu₂O (∼5 eV), it can be deduced that contacts such as beryllium, carbon, cobalt, nickel, selenium, rhodium, tellurium, rhenium, iridium, platinum, and gold can potentially form ohmic contacts (see Fig. 32). Gold is employed in the vast majority of publications. Despite the fact that silver with its relatively low work function is not amongst these candidates, silver paste was used besides nickel and graphite to obtain ohmic contacts by Georgieva et al. 139. Also, Assimos and Trivich 140 achieved ohmic contacts using colloidal graphite paint.

Figure 32. Work function of different metals after Ref. 138.

From Auger electron spectroscopy and electrical measurements yielding the barrier height, Olsen et al. 141 concluded that most metals reduce cuprous oxide to form a copper enriched region (see also Ref. 142), or that a large surface density of states is introduced. Olsen et al. 141 also claimed that, with the exception of non-reacting gold, where the interface can be considered to have a “normal” structure, all metal/cuprous oxide interfaces appear to have copper-enriched regions, or even pure copper layers as Herion et al. 143 state, originating from straight reduction and/or subsequent interdiffusion phenomena 144.

Also worth mentioning is the work of Olsen et al. 145 who deduced that Tl would not reduce cuprous oxide and subsequently investigated Yb, Mg, Mn, Al, Au, and Tl contacts. They found that all contacts, except Au and Tl, showed metal–oxygen bonds. Although no indication for a reduction of Cu₂O by Tl was found, there was still a copper-enriched region, which they concluded originates from preferential oxygen sputtering from the cuprous oxide matrix during the evaporation process of Tl.

In view of photovoltaic applications, the necessity of further research towards the reduction of the contact resistance is given. This may be achieved by a degenerate layer between the Cu₂O absorber and metal contact.

5 Heterostructures, band offsets and solar cells: Devices

5.1 Thin-film transistors

Transparent semiconducting (TSO) and conducting (TCO) oxides 146 are integral components of flat-panel displays and solar cells (see below). High field-effect mobilities and the possibility to use low-temperature deposition and processing are the key issues for current metal oxide semiconductor based thin-film transistors (TFT). A comparison between transparent n-type TFTs from oxides and the amorphous and polysilicon technology is presented in Table 1 of Ref. 147. With respect to p-type oxides, TFTs based on Cu₂O 148–153 and SnO_x 154–157 have been fabricated and the transistor parameters have been determined (see Table 2 in Ref. 147). The electrical performance of a Cu₂O TFT by Zou et al. 149 (the mobility of 4.3 cm²/V s and the ON/OFF ratio of 3 × 10⁶) allowed the authors to conclude 147 that it “re-opens the study of this semiconductor after more than 80 years”.

5.2 Solar cells

In the mid-1970s, Cu₂O gained renewed interest since it was considered as a low-cost material for solar cells. This renaissance took only about 10 years and the interest on Cu₂O decreased. The developments made during that period are collected in the review of Rai 144 from 1988.

It is worthwhile to have a look at his conclusions and suggestions for future work 144. The poor performances were linked to a few but essential issues:

(i) Control of the conductivity of the p-type layer by doping – an issue that has been solved by nitrogen doping. (ii) Schottky barrier solar cells have copper-rich or oxygen-deficient surfaces that limit the performance and will always suffer from this problem (Schottky-type solar cells with Cu₂O are today no longer of relevance). (iii) Heterojunction solar cells should be investigated by which the chemical reactions at the interface between the two materials can be controlled and the reduction of Cu₂O to Cu can be avoided. Indeed, in the last 8–10 years the investigations on cuprous oxide as a solar-cell material have put the focus on heterostructure systems and almost exclusively used ZnO as the n-type transparent window layer. The status of research on the Cu₂O/ZnO single cells is summarized in Table 7. Still, the main three deposition techniques are electrochemical deposition 158, thermal oxidation 143, 160, 163, and sputtering/pulsed laser deposition (plasma deposition) 159, 161. The cell structures were p-Cu₂O/n-ZnO, in some cases with an intermediate undoped ZnO layer. The n-type ZnO was either undoped or highly doped with the donor elements Al or Ga. The efficiencies range between 0.4 and 3.8% 143, 158–164.

Table 7. Solar-cell performances of various Cu₂O-heterojunction diodes.

deposition methods	cell type	cell parameter				illumination	reference
		VOC (V)	ISC (mA/cm^2)	FF	η (%)
electrochemical	Cu2O/ZnO	0.59	3.8	0.58	1.28	AM 1.5	158
rf-sputtering	Cu2O/i-ZnO/ZnO	0.26	2.8	0.55	0.4	AM 1.5	159
thermal oxidation	Cu2O/CH3CN photo-electrochemical cell	0.78–0.82	3–4	0.5–0.6	–	AM 1.5	160
pulsed laser deposition	Cu2O/ZnO:Al	0.4	7.1	0.44	1.2	AM 2	161
vacuum arc plasma evaporation	Cu2O/ZnO:Ga	0.41	6.94	0.53	1.52	AM 2	162
thermal oxidation/RF sputtering	Cu2O/ZnO	0.33	2	0.25	–	–	143
thermal oxidation/ion beam sputtering (ZnO)	ITO/ZnO/Cu2O	0.59	6.78	0.5	2.01	AM 1.5	163
thermal oxidation/pulsed laser deposition (ZnO)	Cu2O/ZnO/ZnO:Al	0.69	10.1	0.55	3.83	AM 1.5	164

Maximum values for the open-circuit voltage V_OC are around 0.87 V, short-circuit currents I_SC around 10 mA/cm² and fill factors FF at 0.6. The limitations in the performance were in part attributed to interface defects, crystal orientation, and grain sizes, series resistance due to the high resistivity of the absorber layer, and in recent reports to the minority-carrier transport length 165, 166.

The band discontinuities and the actual band offsets between ZnO and Cu₂O have not been taken into account for an explanation of the low efficiencies. By photoelectron spectroscopy (XPS) the band offset was determined to be 2.17 eV in the valence band and 0.97 eV in the conduction band (167 and refs. therein). With these large offsets especially in the conduction band small efficiencies of the cells are inherently to be expected. The influence of the large discontinuity in the conduction band on the performance in terms of the above-mentioned parameters is discussed in detail in the work of Minemoto et al. 168 (see Fig. 3 in Ref. 168). Only by reducing the offsets can the minority carrier transport be improved, thus the quest for a material with good alignment of the conduction band is on.

An alternative window material is GaN, and from the XPS investigations the conduction-band offset was determined to be 0.24 eV, a considerably smaller offset (see Fig. 33). Moreover, aligning the conduction bands to completely avoid a CBO in order to prevent the corresponding conversion efficiency losses in a heterojunction solar cell, can be made possible by alloying GaN with Al. An Al content of around x = 0.2 will be sufficient to align the conduction bands of Cu₂O and Al_xGa_1–xN 169, 170. For Cu₂O on ZnO, the conduction-band offset is 0.97 eV. To align the conduction band by alloying with Mg is much more difficult since the Mg_xZn_1–xO alloy system shows a phase separation at around x = 0.45 with structural phase transition from wurtzite to rock salt structure 171, 172. As outlined in Ref. 167 even for the highest achievable Mg content and staying within the wurtzite crystal structure an offset in the conduction band between Mg_xZn_1-xO and Cu₂O of 0.2 eV remains.

Figure 33. (online color at: www.pss-b.com) Band alignment and valence-band and conduction-band offsets of ZnO, GaN, and Cu₂O.

Nothing is known about the band offsets within the copper-oxide compounds, i.e., Cu₂O with respect to Cu₄O₃ or CuO and for CuO/GaN or CuO/ZnO. This information would allow model configurations such as Cu₂O/CuO in a tandem cell arrangement.

5.2.1 The cell structure

For the lab cell structure, we used a superstrate configuration with an n-type GaN layer on sapphire (both sides polished) as the window layer. Cu₂O and Cu₃O₄ were deposited by RF-sputtering (unheated substrates) on the GaN template. Contact areas were defined by photolithography and ion-beam etching. Ohmic contacts Ti/Au on GaN and Au on the copper oxides were fabricated by evaporation of the metals and subsequent annealing for contact formation.

Current–voltage characteristics with AM1.5G and without illumination have been measured and are compared for two cell structures Cu₂O/GaN and Cu₄O₃/GaN (see Figs. 34 and 35). The characteristic cell data were (in brackets for Cu₄O₃): I_sc = 2.1 (0.15) mA/cm², U_oc, = 0.85 (0.87) V, FF = 0.78 (0.67), η = 0.14 (0.009)%. The two-absorber layers with an intended thickness of approximately 600 nm differ in carrier concentration (higher for Cu₄O₃) and hole mobility (lower for Cu₄O₃). Nevertheless, it is the first experimental result of the application of paramelaconite in a solar-cell device. The cell parameters for GaN/Cu₂O may be looked at as promising especially if one takes into account that the deposition of Cu₂O was made at room temperature, resulting in small grains (diameter 25–35 nm), which have a significant influence on the electronic transport.

Figure 34. (online color at: www.pss-b.com) Current–voltage (I–V) measurements without (blue) and with (red) AM1.5G illumination of a GaN/Cu₂O heterojunction solar cell.

Figure 35. (online color at: www.pss-b.com) Current–voltage (I–V) measurements without (blue) and with (red) AM1.5G illumination of a GaN/Cu₄O₃ heterojunction solar cell.

6 Outlook

In this report, we summarized and outlined the potential and possibilities of the copper-oxide compound semiconductors towards applications. Basic needs are a better understanding of the band structure of Cu₄O₃ and CuO that call for a cooperative effort of experiment and theory. There is a clear demand for the spectroscopy of the valence-band structure by UPS and angle-resolved photoelectron spectroscopy. But also the knowledge about the conduction-band states is essential for a better theoretical modelling of the band structure. This can be obtained by electron energy loss spectroscopy (EELS) in combination with ellipsometry. Epitaxial growth on MgO by MBE and CVD will make it possible to separate grain-related from bulk-related transport properties. With superior material quality, the study of excitonic features, already evident in these preliminary studies on Cu₄O₃ and CuO, will be possible and certainly may drive the system into the interest of Bose–Einstein condensation studies.

The knowledge about the band offsets between the three different copper compounds and the band alignment of the bands in heterostructures with ZnO and GaN will have an influence on the realization of low-dimensional devices as well as on possible arrangements in tandem solar cells. Ferromagnetism has been reported for Cu₂O:Co and Cu₂O:Mn and should be further explored. The most appealing feature of the metal-oxide compounds is that only two elements in different valences and bonding arrangements contribute a whole plethora of fascinating physical properties. Furthermore, alloying the copper oxides with sulfur offers a new degree of freedom towards multifunctional oxide-based semiconductors that clearly fulfill the most important criteria of the future: availability, sustainability, nontoxicity (elements of hope), and ease of synthesis.

Biographical Information

Bruno K. Meyer received his Ph.D. in 1983 at the University of Paderborn for his work on magnetic resonance investigations on hydrogen centers in alkali halides. He continued to work with optically detected EPR and ENDOR intrinsic defects in III–V semiconductors, especially in GaAs and GaP, which was summarized in the habilitation in 1987. In 1990, he went as a Professor to the Technical University Munich. Since 1996 he has been a Professor at the Justus-Liebig-University Gießen and Managing Director of the 1st Physics Institute. After working for more than 10 years on bandstructure and defect properties of GaN, his interest shifted towards the wide-bandgap oxides with applications in electro- and thermochromics (VO₂, TiV-oxides) and electronics (ZnO, ZnOS). The review article expresses his current research focus on semiconducting binary oxides.