Intense Quantum Confinement Effects in Cu - American

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Intense Quantum Confinement Effects in Cu2O Thin Films Panagiotis Poulopoulos,† Sotirios Baskoutas,*,† Spiridon D. Pappas,‡ Christos S. Garoufalis,†,§ Sotirios A. Droulias,† Atieh Zamani,|| and Vassilios Kapaklis|| Materials Science Department and ‡School of Engineering, Engineering Science Department, University of Patras, 26504 Patras, Greece § Department of Environment Technology & Ecology, Technological Institute of Ionian Islands, 2 Kalvou Sq, 29100, Zakynthos, Greece Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden

)

†

ABSTRACT: Thin Cu2O films in the thickness range 0.75
230 nm have been prepared on high-quality corning glass, quartz, and Si(100) substrates by radio frequency magnetron sputtering of Cu targets and subsequent oxidation in a furnace under air. Ultraviolet
visible light absorption spectroscopy experiments reveal a blue shift of the energy between the top valence and the first excited conduction subbands. The shift increases smoothly as the film thickness decreases. The maximum value observed for the thinnest film is very large, reaching a value of 1.2 eV. Such a shift was not easy to be observed in the past due to the very small Bohr radius of Cu2O. The experimental results, which indicate the presence of intense quantum confinement effects, are well-described by theoretical calculations based on the potential morphing method in the Hartree
Fock approximation.

1. INTRODUCTION Metal oxides in thin film or nanoparticle form have been attracting intense scientific interest during the last decades due to their unique properties for sensors, electronics, optoelectronics, photovoltaics, and photocatalysis.1
4 Especially, the two oxides of Cu, which are cuprous oxide (Cu2O) and cupric oxide (CuO), are considered among the most important semiconductors with band gap Eg in the range of 1
2.2 eV.5
7 The controllable tuning of the band gap Eg is a key parameter for the application of the nanosized semiconductors in optoelectronics; see, for example, refs 4 and 8. The band gap depends strongly on the particle size or thin film thickness, and often, it increases as the size/thickness decreases; that is, a blue shift of the band gap occurs due to quantum confinement effects.9 Cu2O presents some peculiarities that do not facilitate the observation of quantum confinement effects. Although it is a direct gap semiconductor with a band gap of 2.1 eV, the transition probability from the top of the valence band to the bottom of the conduction band is very small; more precisely, such dipole transitions are forbidden; that is, Cu2O has a direct forbidden band gap.10
12 Consequently, the optical absorption at the band gap is negligible and does not allow for a quantitative analysis for the determination of the gap position. Moreover, the Bohr radius of excitons at band gap is very small, only about 0.7 nm.12 In order for quantum confinement effects to be significant, particles or films of comparable thickness to this size have to be fabricated, a task that is not easy. The absorbance for this material starts to be significant only at higher energies, where one encounters dipole allowed transitions between the top of the valence band and the second lower conduction sub-band. r 2011 American Chemical Society

In this work, we demonstrate intense quantum confinement effects for the dipole allowed transitions in Cu2O thin films. The gap EB for the dipole allowed transitions is about 2.6 eV for the thicker films and blue shifts in a smooth way reaching a maximum value of ∼3.8 eV for the thinnest film of 0.75 nm. Such a strong blue shift due to quantum confinement effects has not been demonstrated previously for any copper oxide. The results are compared to theoretical calculations based on the potential morphing method13 (PMM) in the Hartree
Fock approximation.8,14
16 Actually, the PMM solves the Schr€odinger equation for any arbitrary interaction potential and is based on the adiabatic theorem of quantum mechanics,17 which states that if the Hamiltonian of the system varies slowly with time, then the nth eigenstate of the initial Hamiltonian will be carried into the nth eigenstate of the final Hamiltonian. A good agreement between theory and experiment is observed. This combined experimental and theoretical work provides a better insight on the quantum confinement effects in nanoscaled systems.

2. EXPERIMENTAL DETAILS Thin Cu films with thickness up to 140 nm were deposited on various substrates such as corning glass, quartz, and Si(100) by radio frequency (r.f.) magnetron sputtering. The deposition temperature was about 50 °C. The base pressure of the vacuum chamber was 1  10
7 mbar. The Ar pressure during deposition had been kept constant with the help of a fine valve. Several films Received: April 5, 2011 Revised: June 19, 2011 Published: June 22, 2011 14839

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Figure 1. Kiessig fringes appear in the XRR spectrum of a 33 nm thick Cu film (data points). The continuous line is a simulation after the GenX code.

were prepared at pressures between (1
2)  10
3 mbar. The r.f. power had been kept constant at about 20 W with the help of a feedback power supply and a matching circuit. Thickness evaluation and structural characterization were performed with the help of a standard powder diffractometer (SEIFFERT) with Co- and Ni-filtered CuKa1 radiation (λ = 0.154059 nm). Figure 1 plots a X-ray reflectivity (XRR) pattern for a thin Cu film on Si(100). The appearance of many Kiessig fringes18 in the XRR pattern indicates high homogeneity in the film thickness and very small surface roughness. The position of the fringes allows for an accurate determination of the film thickness. A rigorous analysis of the pattern can be done via the GenX code.19 The roughness profile in the simulations of the experimental data is introduced as a sinusoidal modulation of the layer thickness. The final calculated roughness values correspond to the root-mean-square (rms) value of this sinusoidal modulation. The GenX fitted pattern is also included in Figure 1 (continuous line). From the fitting one determines a Cu film thickness dCu = 33 nm with rms roughness Rrms = 0.56 nm. The model that is used in the simulation procedure also includes a top layer of native Cu2O formed from the spontaneous oxidation of the surface of the Cu film, when it is exposed to the ambient air, with thickness dCu2O = 1.4 nm and rms roughness Rrms = 0.12 nm. With the help of this thickness evaluation, a quartz balance system (Inficon XTM/2) was calibrated and used for measuring the thickness of the films with accuracy of (0.1 nm. The films were then placed in a furnace at a temperature of about 230 °C. At this temperature, the films react with oxygen and pure Cu2O forms. Usually oxidation time of less than 1 h is enough even for the thickest films to be transformed to Cu2O; see, for example, refs 20 and 21. Indeed, in Figure 2, we show X-ray diffraction (XRD) pattern from a 140 nm film grown on Si(100) of Cu before and after oxidation. The diffraction positions of the film before oxidation coincide with the ones of pure metallic polycrystalline Cu powder (see vertical lines22) and after oxidation with polycrystalline Cu2O.23 The XRD results were identical irrespective of the material used as substrate. To have an alternative verification for the formation of Cu2O by the oxidation process, we have performed Rutherford backscattering spectrometry (RBS) on a Cu film, which was oxidized for 30 min at 230 °C. RBS measurement was accomplished with 2 MeV He+ ion beam incident impinging on the sample and backscattered into a detector with the geometry at 170° relative to the incident beam direction. The result of such an analysis is

Figure 2. In the down part is presented the XRD pattern of a 140 nm Cu thin film grown on Si(100) by r.f. magnetron sputtering. On the top is shown the XRD pattern of the same film after annealing in a furnace at 230 °C under air for 50 min. Pure Cu2O was formed, and no trace of Cu or CuO is found, as the comparison with the XRD angles of powder reference samples reveals.22
24

Figure 3. RBS spectrum of a Cu2O film (data points). The continuous line is the result of a fitting after the SIMNRA software.

displayed in the Figure 3 below and gives information about the average composition ratio between Cu and O elements. Using the calculated concentration for Cu, the oxygen content of the film was confirmed by integrating the oxygen spectra between the interface and the surface edge and also by fitting the spectrum in this range using the Rutherford Backscattering Spectroscopy analysis package (SIMNRA) software.25 The Si substrate thickness was treated as a free parameter. The substrate composition was assumed to be stoichiometric of Si. The O/Cu ratio is found to be ∼0.5625 (56.25%). This is within the experimental accuracy another indication of Cu2O formation. (The accuracy of the RBS composition is roughly ∼5% for the Cu data and for the oxygen data ∼10%.) Finally, the ultraviolet (UV)
visible spectra were recorded at room temperature in the transmission geometry with the help of 14840

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a Perkin-Elmer Λ-35 UV
visible spectrometer at the wavelength range 200
1100 nm.

3. THEORY In the effective mass approximation, the Hamiltonian for the electron hole system can be written as8,14
16 H ¼


p2 2 p2 2 e2 1 e h
þ V ðr Þ þ V ðr Þ
∇ ∇ e h e h 0 0 2me  2mh  ε reh

ð1Þ where me* (mh*) is the effective electron (hole) band mass, ε is the effective dielectric constant, reh is the electron
hole distance is the finite depth well confinein three dimensions, and Ve(h) 0 ment potential of electron (hole). As in our previous work,15 we will also use here a reliable expression for the dielectric constant ε developed by Hanken26 and used by several authors27,28 and which has the following form 2 !  3 R0 R0 exp
þ exp
7
6 6 Fe Fh 7 1 1 1 1 6 7 7 61
¼

7 εðR0 Þ ε∞ ε∞ ε0 6 2 5 4

Figure 4. Normalized optical (light) absorption spectra for four thin Cu2O films fabricated on quartz substrate. The spectra have been vertically shifted for clarity. The thickness of the films is marked on each absorption spectrum.

oscillator with the well-known eigenfunctions29 Φnlm ðr, θ, ϕÞ ¼ r l e
ðmω=2pÞr 1 F 1 ð
n, l þ 3=2, λr 2 ÞYlm ðθ, ϕÞ 2

ð2Þ where R0 is the mean distance between the electron and the hole27,28 and approximately takes the values27 0.69932R or R15, where R is the radius of the cluster and represents the half of the confining parameter that is the diameter of the cluster. ε0 and ε∞ are the static and optical dielectric constants, respectively, and Fe,h are given as follows !1=2 p ð3Þ Fe, h ¼ 2me, h ωLO where ωLO is the frequency of LO phonons. Similarly, studying the case of thin films, we substitute approximately in the above formula 2 the mean distance between the electron and the hole R0 with d/2, where d is the thin film thickness and represents the confining parameter. As regards the height of the finite depth well confining potentials Ve(h) 0 for electrons and holes, we have shown in our previous study14 that it is independent of the nanostructured semiconductor material and depends exclusively on the matrix energy band gap Eg(M) by a simple linear relation of the form V0 = 0.08 3 Eg(M). Assuming also that the confining potential has the same value for both electron and hole, we set for our thin film system 8 d > : 0:08 3 Eg ðMÞ jzj g 2 where z represents the direction perpendicular to the film. The Hartree
Fock equations are solved in an iterative manner until self-consistency is achieved. In each iteration, the PMM8,13
16 is employed as a subroutine for the calculation of the corresponding energies and wave functions and, thus, the Hartree
Fock potential for the next iteration. The reference system for PMM is set to be the three-dimensional harmonic

ð5Þ

where 1F1(
n, l + 3/2, λr ) is the hypergeometric function. It should be noted here that adopting the harmonic oscillator as a reference system does not affect our results because the PMM needs only a known reference system to start the morphing process and finally to give the eigenfunctions and eigenvalues for the unknown system, independently from the choice of the initial reference system.13 When the procedure reaches a self-consistent solution, then the exciton energy is calculated by the sum of the corresponding electron and hole energies 2

30

~h ~e þ E EðXÞ ¼ E and the effective band gap is given by

ð6Þ 8,14
16

EB ¼ Eg þ EðXÞ

ð7Þ

where Eg is the bulk band gap energy.

4. RESULTS AND DISCUSSION In Figure 4, the normalized light absorption spectra of four Cu2O films of thickness between 0.75 and 5.4 nm are shown. By normalization, (i) we divide the transparency T of the films with the TS of the substrate, (ii) we use the formula absorbance =
log (T/TS), and (iii) we scale the edge-jump for the absorption edge of all samples to unity. The substrate is quartz in order to be optically transparent for the whole interval of measurements up to about 6.5 eV. Corning glass becomes opaque after 4 eV; however, up to 4 eV, no difference is observed for the light absorption of Cu2O grown on corning glass or quartz. The signalto-noise ratio is very high even for the 0.75 nm thin sample. No absorption edge was found at 2.1 eV, in agreement with previous studies on bulk samples and films thicker than the ones of Figure 4.12 Strong absorption is observed at higher energies and corresponds, as aforementioned, to dipole-allowed transitions from the top of valence band to the first excited sub-band of 14841

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we have performed calculations for all of the states (n, l, m): (011), (01
1), and (010). The results that we are taking are depicted in Figure 5. The dashed line (excit1) corresponds to the (011) and (01
1) initial states of the harmonic oscillator, which have the same energy, and the gray line (excit0) corresponds to (010) initial state of the harmonic oscillator. The effective band gap is calculated according to the relation 7, and both the theoretical and the experimental results are depicted in Figure 5. The theoretical line includes values for the effective band gap for film thickness down to 0.5 nm. Comparison between the theoretical curve and the experimental data shows good agreement, indicating that the observed blue shift can be attributed to the effect of quantum confinement. Figure 5. Band gap energy of thin Cu2O films by experiment (data points) and theory (line). Excit0 corresponds to the initial electron excited wave function of the harmonic oscillator with (nlm) = (0, 1, 0) and excit1 to the initial electron excited wave functions of the harmonic oscillator with (nlm) = (0, 1, 1) and (nlm) = (0, 1,
1).

the conduction band. It is obvious, even by eye inspection, that the absorption edge shows a blue shift, which is very strong for the thinnest sample. This effect may be understood if one considers that the film thickness is smaller than the exciton Bohr diameter for the onset of quantum confinement effects. To have a precise determination of the energy position of the absorption edge (relative error bars of (0.02 eV), one can take the edge position to be determined by the maximum of the first derivative or, equivalently, by the zeroing of the second derivative of the optical absorption with respect to the energy,8 and it corresponds to EB. For the estimation of the relative error bars ((0.02 eV), a set of six samples with thickness between 10 and 70 nm was also measured. For these samples that can be considered as bulklike, the EB values determined with our method were found to be identical with an accuracy better than (0.02 eV. The EB as a function of the film thickness d is shown in Figure 5. One may observe a systematic increase in the EB as the thickness decreases, demonstrating the more and more important role of the quantum confinement effects on the films. The blue shift for the thinnest sample is about 1.2 eV and is the largest quantum confinement effect reported, to our knowledge, for copper oxide semiconductors. Now to investigate the above system theoretically with PMM, we assume that the substrate is the corning glass with Eg(M) = 4.1 eV, and we use the following material parameters: me* = 0.99 m0, mh* = 0.58 m0,31 where m0 is the electron mass, ε0 = 7.54 and ε∞ = 6.46,32 and pωLO = 63.69 meV.33 As it is well-known by existing band structure calculations34
36 and detailed group theoretical analysis,11 the direct transition at Γ is forbidden. Moreover, the density of states near the CBM is almost vanishing, as shown by Ching et al.34 and verified by our own benchmark DFT calculations with the hybrid nonlocal exchange-correlation functional of Becke and Lee, Yang, and Parr (B3LYP). It is noteworthy that our calculations revealed that the B3LYP functional succeeds in predicting the correct gap value of 2.17 eV. As a result, the absorption threshold is related to the second lower conduction sub-band. For these reasons, the Hartree
Fock equation that corresponds to the electron is solved for the first excited state (i.e., starting the PMM procedure from the first excited state of the harmonic oscillator), while the hole equation is solved for the ground state. Concerning the 3-fold degenerate first excited state of the harmonic oscillator,

5. CONCLUSIONS In this work, we show the presence of intense quantum confinement effects in Cu2O films down to a thickness of 0.75 nm. This is demonstrated by the blue shift of the gap EB for the dipole-allowed transitions between the top of the valence band and the second lower conduction sub-band. The EB can be tuned by changing the film thickness, and an enormous blue shift of 1.2 eV is measured from the optical absorption spectra for the thinnest film. The experiment is well described by PMM in Hartree
Fock approximation for all film thickness even down to the thinnest sample. ’ AUTHOR INFORMATION Corresponding Author

*Tel/Fax: +30-2610-96-9349. E-mail: [email protected].

’ ACKNOWLEDGMENT Grant Karatheodori2009, Nr. C.905, and Grant Karatheodori2010-2013, Nr. D.207, of the Research Committee of the University of Patras are acknowledged. ’ REFERENCES (1) Wadia, C.; Alivisatos, A. P.; Kammen, D. M. Environ. Sci. Technol. 2009, 43, 2072. (2) Fernando, C. A. N.; de Silva, P. H. C.; Wethasinha, S. K.; Dharmadasa, I. M.; Delsol, T.; Simmonds, M. C. Renewable Energy 2002, 26, 521. (3) Shifu, C.; Sujuan, Z.; Wei, L.; Wei, Z. J. Hazard. Mater. 2008, 155, 320. (4) Chen, L.; Shet, S.; Tang, H.; Ahn, K.; Wang, H.; Yan, Y.; Turner, J.; Al-Jassim, M. J. Appl. Phys. 2010, 108, 043502. (5) Brattain, W. H. Rev. Mod. Phys. 1951, 23, 203. (6) Yang, Z.; Chiang, C.-K.; Chang, H.-T. Nanotechnology 2008, 19, 025604. (7) Ji, J.-Y.; Shih, P. -H.; Yang, C. C.; Chan, T. S.; Ma, Y.-R.; Wu, S. Y. Nanotechnology 2010, 21, 045603. (8) Baskoutas, S.; Poulopoulos, P.; Karoutsos, V.; Angelakeris, M.; Flevaris, N. K. Chem. Phys. Lett. 2006, 417, 461. (9) Nanda, K. K.; Kruis, F. E.; Fissan, H. NanoLett. 2001, 1, 605. (10) Elliot, R. J. Phys. Rev. 1957, 108, 1384. (11) Elliot, R. J. Phys. Rev. 1961, 124, 340. (12) Biccari, F. Defects and Doping in Cu2O. PhD Thesis; Sapienza
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