Band Gap Engineering of SnO2 by Epitaxial Strain: Experimental and

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Band Gap Engineering of SnO2 by Epitaxial Strain: Experimental and Theoretical Investigations Wei Zhou, Yanyu Liu, Yuzhe Yang, and Ping Wu* Department of Applied Physics, Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Faculty of Science, Tianjin University, Tianjin 300072, People’s Republic of China ABSTRACT: The effect of mis-match strain on the structural, electronic, and optical properties in SnO2 epitaxial thin films has been systematically investigated by the experimental and theoretical methods. Our results indicate that the tensile strain exists in the thin film and decreases with the thickness of epitaxial samples. Besides, the optical band gap significantly reduces with increasing the tensile strain in the bc plane. Our hybrid functional calculations present that the narrowing of band gap of SnO2 under tensile strain is due to the weakening of bonding and antibonding split, which results from the disorder of SnO6 octahedra, and the biaxial strain is found to be more efficient than the uniaxial strain for tuning the band gap of SnO2.

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Experimentally, the epitaxial SnO2 thin film with (100) orientation often grows on the (0001)-Al2O3 substrate, which introduces the biaxial tensile strain in the bc plane of SnO2 thin film. However, to our knowledge, the compressive investigations of the epitaxial strain effect on the physical properties of SnO2 are still lacking in the experimental and theoretical reports. Therefore, we will study the structural, electronic, and optical properties of SnO2 thin film under the epitaxial strain. In addition, the electron transition between the valence band and the conduction band determines the optical properties of materials. Therefore, it is of importance to obtain the accurate band gap. In the previous reports based on the local-density approximation (LDA) or generalized gradient approximation (GGA), the range of the band gap of SnO2 is from 0.65 to 1.8 eV,13−16 which is much smaller than the experimental value. Thus, a more reliable method of hybrid functional was adopted in this work to investigate the underlying mechanism for the optical properties of SnO2 under the epitaxial strain.

INTRODUCTION With high electrical conductivity and optical transparency at the visible region, the transparent conductive oxide (TCO) materials have been widely used in optoelectronic devices and other application fields.1−3 Among the TCO materials, tin dioxide (SnO2) has gained extensive attention of researchers over the past decades owing to its excellent electrical, optical, and electro-chemical properties, which is also attractive for potential applications such as solar cells and flat panel displays.4−7 As a wide band gap semiconductor, SnO2 has a band gap of 3.6 eV at room temperature, whereas, because of the relatively large band gap compared with the visible light (with photon energy 1.7−3.1 eV), the application of SnO2 as ideal photocatalytic and photovoltaic materials is limited. It is well-known that the external pressure and internal strain can alter the electronic structure of semiconductors to improve their properties because the band structure of semiconductors could be modified by the interatomic distances and relative positions of atoms. For example, several recent experimental and theoretical studies have shown that the strain and stress can be used to tune the band gap of TiO2, ZnO, MgO, and CdO.8−12 Especially, the effect of uniaxial compressive pressure applied on the c axis of SnO2 has been theoretically reported by Saniz et al. with GW approximation.13 Their results pointed out that the band gap of SnO2 was enlarged with increasing the pressure. The increasing rate of band gap with pressure is 0.027 eV/GPa under the uniaxial strain. Since the substrate often subjects the film to the mis-match strain in the application of semiconductor thin films, it is possible to adjust the band gap of SnO2 by lattice mis-match between the epitaxial thin film and the underlying substrate. Thus, it is necessary to investigate the mis-match strain effect on the band gap and electronic structure of SnO2 thin film, which is useful for its application. © 2014 American Chemical Society

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EXPERIMENTAL AND COMPUTATIONAL DETAILS Pure epitaxial SnO2 thin films with different thickness were grown on the polished Al2O3 (0001) substrates by reactive magnetron sputtering with a base pressure of 10−7 Torr. And the deposition was carried out in an Ar(10 sccm)/O2(20 sccm) atmosphere at 10−2 Torr. The 99.999% pure Sn target was sputtered at 60 W. During the deposition process, the substrate temperature was maintained at 750 °C. The film thicknesses were about 30, 60, 100, and 130 nm, respectively, which were determined by the surface stylus profiler (AMBIOS Tech Received: January 16, 2014 Revised: March 1, 2014 Published: March 3, 2014 6448

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Figure 1. (a) XRD results of epitaxial thin films with different thickness (the inset is the ϕ-scan of the (110) reflection (ψ = 45°)), (b) the rutile structure of SnO2 and a schematic illustration of the sample structure, and (c) the lattice constant a (black squares) and the estimated biaxial stress (red circles) as a function of film thickness.

Figure 2. (a) Raman spectra of epitaxial SnO2 thin films of 30, 60, and 130 nm (the arrow indicates the peak shift). The inset is the biaxial stress of the SnO2 films as a function of the shift in the A1g peak position from the bulk value. (b) The circles are the experimental data and the solid lines are the fitting curves with Gaussian function.

strain of SnO2, the relaxation of crystal with the lattice constants b and c fixed was performed until the stress along a axis was free. The specified in-plane strain was defined as ε = (c − c0)/c0, where c is a new lattice parameter.

Model XP-1). The crystalline structure and the epitaxial relationships of the deposited films were examined by the Xray diffraction (XRD) (Rigaku D/Max-RA) using Cu Kα radiation. The residual stress in the thin films was characterized with the Raman spectroscopy by using a confocal microscope, and the 532 nm line forms a frequency-doubled Nd:YAG laser. The optical properties were measured with the UV−vis−IR JASCO-670 spectrophotometer. In this article, all calculations were performed with the Vienna ab initio Simulation Package (VASP) based on the density functional theory (DFT).17 The Projector-augmented wave (PAW) was used for the electron−ion interactions.18 The generalized gradient approximation (GGA) with PBE functional19 and the HSE06 hybrid-functional20 with a mixing parameter of a = 0.32 were employed to evaluate the exchangecorrelation energy. The number of k points and the cutoff energy were increased until the calculated total energy converged within an error of 1 × 10−5 eV/atom. Therefore, the cutoff energy of 500 eV with 9 × 9 × 13 k points was set. The energy convergence tolerance was set to below 5 × 10−6 eV/atom. The lattice vectors and atomic coordinates were relaxed until the Hellmann−Feynman force on each atom is reduced to less than 0.01 eV/Å. To simulate the epitaxial biaxial

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RESULTS AND DISCUSSION

Figure 1a depicts the θ−2θ X-ray diffraction patterns for all samples. It shows only (200) and (400) peaks of rutile SnO2, which indicates the exclusive a-axis orientation. The top-inset shows the ϕ-scan of the (110) reflection (ψ = 45°) with the thickness of 30, 60, and 130 nm. The tilt angle (ψ) presents the angle between the reflection plane and substrate surface plane. All measured samples show a 6-fold symmetry, which implies the epitaxial growth of SnO2 thin films in this work.21 Because of the larger lattice constant of Al2O3 than that of SnO2, the tensile strain in the bc plane and the compressive strain along the a-axis direction can be expected in the epitaxial SnO2 thin film. With increasing the film thickness, the tensile stress in the bc plane will be released, which makes the a-axis recover to the normal length. This is consistent with our experimental observation that the value of lattice constant a monotonically increases with the thickness of epitaxial thin films (Figure 1b). 6449

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It also indicates that the thicker thin film will have the smaller epitaxial stress. The magnitude of residual stress in the epitaxial thin film can be estimated from the elastic stiffness (Cij) and the out-of-plane lattice strain. For the case of SnO2 with (100) orientation, both the out-of-plane stress and lattice strain along the b axis direction can be assumed to be zero because the mis-match lattice strain along the b axis between SnO2 and Al2O3 substrate is very small (less than 1%). Then, the stress in the film (σfilm) can be simply expressed as σfilm = (σb + σc)/2 = (C12 + C13 − C11 − C33 × C11/C13) × εa

(1)

where the εa = (a − a0)/a is the out-of-plane lattice strain (a is the measured lattice constant and a0 is the unstrained lattice constant). Taking into account the elastic stiffness components from the previous experiment (C11 = 262 GPa, C33 = 450 GPa, C12 = 177 GPa, and C13 = 156 GPa),22 eq 1 reduces to σfilm = −342εa GPa. Figure 1b shows the biaxial stress as a function of the film thickness. It indicates that a compressive stress forms in the thin film. The biaxial stress is relieved with increasing the film thickness, which is expected considering that the lattice strain will be relaxed when the thin film grows thicker. Besides the XRD analysis, the Raman spectrum is a useful method to determine the residual stress state of thin films, which has been successfully performed to investigate the epitaxial ZnO thin films by Harriman et al.23 The Raman results of epitaxial thin films with thickness of 30, 60, and 130 nm are shown in Figure 2a. In addition to the multiple peaks of Al2O3 vibration modes, the typical A1g vibration mode of SnO2 is also observed. It can be found that the peak of A1g shifts to the high wavenumber with decreasing the film thickness. To obtain the accurate position of the A1g peak, the Gaussian function was used to fit the Raman spectra as shown in Figure 2b. The determined peak positions are 651, 642, and 636 cm−1 for thin films with thickness of 30, 60, and 130 nm, respectively. Compared with the value in the bulk SnO2 of 634 cm−1,24 the blue shifts in the thinner films imply that the compressive stress due to the epitaxial strain actually exists in the thin films. The inset in Figure 2a shows the biaxial stress of the films as a function of the A1g peak shift from the bulk value. The linear fit was used to estimate the relationship between the biaxial stress and the wavenumber shift (Δω), which can be written as σ (GPa) = 0.184Δω (cm−1). Although the calculated slope is a little larger than the value of 0.102 GPa/cm−1 reported by Peercy et al. from bulk SnO2 under hydrostatic pressure,24 our results still indicate that the Raman spectroscopy is an effective method to quantify the residual biaxial stress resulting from the epitaxial lattice strain in SnO2 thin films. To further explore the effect of lattice strain on the optical properties of SnO2, the optical absorption spectrum of samples with different thickness were examined. For the direct band gap transition, such as SnO2, the absorption coefficient α can be expressed as α(hv)2 ∝ (hv − Eg)1/2/hv.25 Then the optical band gap can be estimated from the plot of α(hv)2 vs photon energy hv. Figure 3 shows that the red-shift of absorption edge takes place when the thin film grows thinner. The above structure analysis has pointed out that the tensile strain in the bc plane will decrease with increasing the thickness of the thin film. That is to say, the tensile strain in the bc plane of SnO2 can make the photon absorption move to the low energy region. Meanwhile, the calculated optical band gap shows that with increasing the

Figure 3. Plot of (αhv)2 vs phonon energy of SnO2 thin film, and the inset is the experimental optical band gap.

film thickness the change of optical band gap reduces gradually. This implies the release of mis-match strain in the thin film dose not follow the linear relationship with the film thickness, which is consistent with the trend of lattice constant variation. When the thin film grows thick enough, the effect of mis-match epitaxial strain can be ignored. Additionally, it is also found that the obtained optical band gap for the thin film of 130 nm is a little larger than the standard band gap of SnO2 (3.597 eV). This may come from the influences of defects, such as oxygen vacancy and structural defect, which is in accord with the previous reports.26 The analysis of electronic structure is important for further understanding the origin of epitaxial strain effect on the optical properties in the SnO2 system. Therefore, the DFT calculations were performed in this work. As far as we known, the standard DFT calculation method has the shortcoming of underestimating the band gap for the oxides, which is against for calculating the accurate optical properties. To avoid this inaccuracy, the hybrid functional method was used, which can give good results of the band structure calculations for the oxide compounds. From calculations, the equilibrium lattice constants of SnO2 from HSE06 (PBE) are a = 4.724 Å and c = 3.175 Å (a = 4.725 Å and c = 3.20 Å). The calculated values are much closer to the experimental results of a = 4.738 Å and c = 3.183 Å, which indicates our calculations can give reliable information for the crystal structure. Besides the structural calculations, the band structure of SnO2 in the equilibrium state was also calculated with both PBE and HSE06 methods, shown in Figure 4. To align the band structures, the method proposed by Moses et al. is adopted in this work.27 The position of the VBM in the bulk with respect to the averaged electrostatic potential is determined first and then the averaged electrostatic potential in a bulk-like region with respect to the vacuum level. The slab model containing 6 unit cells and oriented along the c direction was used for surface calculations. The band gap from PBE is only about 0.9 eV, while the HSE06 corrects the band gap to 3.5 eV, which yields a good agreement with the previous theoretical results and experimental value (3.597 eV).28 Since the optical transition is determined by the band structure, the more reliable optical properties from HSE06 can be expected for SnO2. It also can be observed that the expansion of band gap by HSE06 calculations comes from both the upshift of conduction band and the down6450

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Figure 4. Calculated (a) band structure and (b) density of states of SnO2 in the equilibrium structure (zero energy is set at the Fermi level of PBE result).

Figure 5. Calculated (a) structure parameters and (b) band gap of SnO2 under strain.

Figure 6. Calculated (a) total density of states and (b) projected density of states of SnO2 under the epitaxial strain (zero energy is set at the Fermi level of unstrained system).

valence band maximum of SnO2 mainly consists of O-2p and Sn-4d states, while the conduction band minimum (CBM) forms by the hybridization between O-2p and Sn-5s states. We turn now to the effects of biaxial strain in the bc plane of SnO2. For the epitaxial experiment of SnO2 growing on the (0001) Al2O3 substrate, the lattice mis-matches along the b and

shift of valence band. The lowering of the valence band is induced by the reduced self-interaction in HSE06 calculations for the O-2p states, which mainly compose the valence band maximum (VBM). The similar case was also reported by Janotti et al. for the rutile TiO2 system.29 In addition, the calculated total and projected density of states (Figure 4b) show that the 6451

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c axis directions are less than 1% and 13.8%, respectively.21 Therefore, the strain imposed on the c axis of SnO2 crystal was set to vary from −4% to 14% in our calculations. The strain along the b axis was not taken into account in this work due to its very small value in experiment. Thus, the relaxation of crystal with the given lattice constants b and c was performed until the stress along the a axis was free. Figure 5a plots the structural parameters versus the strain along the c axis direction. It is observed that the lattice constant a shrinks with the strain, while the crystal volume increases gradually. This implies the a axis of rutile SnO2 displays a relatively weak ability to keep the crystal volume when the bc plane is distorted. We also note that the change in the equatorial Sn−O bond length is weaker in magnitude than the change in lattice constant a. It indicates stretching the Sn−O bonds is more difficult than to reduce the rectangular distortion of the base of the SnO6 octahedra, which is similar with the case for SnO2 under uniaxial pressure by Saniz et al.13 The variety of band gap for SnO2 under the biaxial strain is shown in Figure 5b. The value of calculated band gap reduces from 3.74 to 2.41 eV with the c axis strain increasing from −4% to 14%. The change rate of band gap with stress was also calculated, and the stress is estimated using the compliance tensor model of eq 1. The obtained value of change rate is 0.046 eV/GPa, which is much larger than the value of 0.027 eV/GPa reported by Saniz et al. for imposing only the uniaxial strain along c axis in SnO2.13 It implies that the biaxial epitaxial stain gives a higher efficiency for tuning the band gap of SnO2 crystal. The change of the band gap can be observed more clearly from the calculated density of states, as shown in Figure 6. It can be seen that the conduction band shifts down to the valence band when the strain is imposed on the crystal. As far as we know, the valence and conduction bands of SnO2 exhibit the bonding and antibonding characters, respectively. Hence, the mis-match strain tends to decrease the bonding and antibonding split. For example, the estimated energy gap of bonding and antibonding for Sn-p and O-p states decreases about 0.9 eV from the unstrained structure to 12% strained structure. However, the structure of the SnO6 octahedra in the rutile SnO2 is mainly determined by the O-2p state. Figure 6b depicts the projected density of states of O-2px and O-2pz states. We notice that the peak intensity of O-2px and O-2pz near the valence band maximum displays different variation trends. It implies the disorder of SnO6 octahedra takes place, which is consistent with our analysis for the crystal structure. This change also can be clearly observed from the calculated density distribution of VBM charge, which is mainly constituted by O-2p states, as shown in Figure 7. For the unstrained structure, the VBM charge distribution of equatorial O atoms in the SnO6 octahedra parallel to the apical axis of the octahedral, while that of apical O atoms is oriented perpendicular to the apical axis. With increasing the tensile strain, the VBM charge distribution shows more delocalization character, and the bond angle (middle Sn−apical O−equatorial O) is changed inducing by the disorder of SnO6 octahedra. That is to say, the changes of both bond length and bond angle in the strained SnO2 crystal result in the band gap narrowing. Besides the electronic structure, the absorption coefficient of SnO2 under different strain was also calculated, as presented in Figure 8. Obviously, the red shift of the absorption edge occurs with increasing the strain imposed along the c axis direction. When the strain is strong enough, the absorption edge will enter into the visible light region and the photon absorption in

Figure 7. Calculated charge density distribution of VBM for SnO2 under different strains, unit in e/Å3. The SnO6 octahedra consist of the middle Sn atom and its surrounding O atoms (the axis of the SnO6 octahedra and the charge density orientation of O atom are shown in red lines).

Figure 8. Calculated absorption coefficient of SnO2 with different epitaxial strain (the arrow indicates the increase of the strain).

this region will be enhanced. It is also noticed that the change of optical band gap is about 0.7 eV in our experiment. This value is in the same order of magnitude of the theoretical results and smaller than the calculated band gap difference with strain between 0% and 14% (about 1.0 eV). It implies that the mis-match epitaxial strain in the thin films has been partially released due to the finite thickness of our samples. The defects, such as structural defect and vacancy, can also give influences on the optical properties of samples, which will be investigated in our future work. In spite of this, our investigation still indicates that the strain engineering, especially the epitaxial strain, is an effective approach to modulate the optical band gap of the SnO2 system. 6452

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(10) Yin, W. J.; Chen, S. Y.; Yang, J. H.; Gong, H. G.; Yan, Y. F.; Wei, S. H. Effective Band Gap Narrowing of Anatase TiO2 by Strain along a Soft Crystal Direction. Appl. Phys. Lett. 2010, 96, 221901. (11) Yadav, S. K.; Sadowski, T.; Ramprasad, R. Density Functional Theory Study of ZnX (X = O, S, Se, Te) under Uniaxial Strain. Phys. Rev. B 2010, 81, 144120. (12) Yan, Q. M.; Rinke, P.; Winkelnkemper, M.; Qteish, A.; Bimberg, D.; Scheffler, M.; Van de Walle, C. G. Strain Effects and Band Parameters in MgO, ZnO, and CdO. Appl. Phys. Lett. 2012, 101, 152105. (13) Saniz, R.; Dixit, H.; Lamoen, D.; Partoens, B. Quasiparticle Energies and Uniaxial Pressure Effects on The Properties of SnO2. Appl. Phys. Lett. 2010, 97, 261901. (14) Duan, Y. Electronic Properties and Stabilities of Bulk and LowIndex Surfaces of SnO in Comparison with SnO2: A First-Principles Density Functional Approach with an Empirical Correction of van der Waals Interactions. Phys. Rev. B 2008, 77, 045332. (15) Singh, A. K.; Janotti, A.; Scheffler, M.; Van de Walle, C. G. Sources of Electrical Conductivity in SnO2. Phys. Rev. Lett. 2008, 101, 055502. (16) Li, Z. Q.; Yin, Y. L.; Liu, X. D.; Li, L. Y.; Liu, H.; Song, Q. G. Electronic Structure and Optical Properties of Sb-Doped SnO2. J. Appl. Phys. 2009, 106, 083701. (17) Kresse, G.; Hafner, J. Efficiency of Ab-Initio Total Energy Calcultions for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (18) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758− 1775. (19) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (20) Heyd, J.; Scuseria, G. E.; Emzerhof, M. Erratum: Hybrid Functionals Based on A Screened Coulomb Potential. J. Chem. Phys. 2006, 124, 219906. (21) Dominguez, J. E.; Fu, L.; Pan, X. Q. Epitaxial Nanocrystalline Tin Dioxide Thin Films Grown on (0001) Sapphire by Femtosecond Pulsed Laser. Appl. Phys. Lett. 2001, 79, 614−616. (22) Chang, E.; Graham, E. K. The Elastic Constants of Cassiterite SnO2 and Their Pressure and Temperature Dependence. J. Geophys. Res. 1975, 80, 2595−2599. (23) Harriman, T. A.; Bi, Z.; Jia, G. X.; Lucca, D. A. Frequency Shifts of the E2 High Raman Mode Due to Residual Stress in Epitaxial ZnO Thin Films. Appl. Phys. Lett. 2013, 103, 121904. (24) Peercy, P. S.; Morosin, B. Pressure and Temperature Dependences of the Raman-Active Phonons in SnO2. Phys. Rev. B 1973, 7, 2779−2286. (25) Mills, G.; Li, Z. G.; Meisel, D. Photochemistry and Spectroscopy of Colloidal Arsenic Sesquisulfide. J. Phys. Chem. 1988, 92, 822−828. (26) Zhu, Z.; Ma, J.; Luan, C. N. Structure and Photoluminescence Properties of Epitaxial SnO2 Films Grown on α-Al2O3 (012) by MOCVD. J. Lumin. 2011, 131, 88−91. (27) Moses, P. J.; Miao, M.; Yan, Q.; Van de Walle, C. G. Hybrid Functional Investigations of Band Gaps and Band Alignments for AlN, GaN, InN, and InGaN. J. Chem. Phys. 2011, 134, 084703. (28) Varley, J. B.; Janotti, A.; Van de Walle, C. G. Group-V Impurities in SnO2 from First-Principles Calculations. Phys. Rev. B 2010, 81, 245216. (29) Janotii, A.; Varley, J. B.; Rinke, P.; Umezawa, N.; Kresse, G.; Van de Walle, C. G. Hybrid Functional Studies of the Oxygen Vacancy in TiO2. Phys. Rev. B 2010, 81, 085212.

CONCLUSIONS In conclusion, the tuning structure and band gap of SnO2 epitaxial thin film were investigated experimentally and theoretically in this work. The residual biaxial stress induced by the epitaxial strain was observed and estimated from both XRD and Raman spectroscopy results. The tensile strain induced by the mis-match between SnO2 thin film and Al2O3 substrate was found to decrease with the film thickness. Meanwhile, the optical band gap of samples is significantly reduced by about 0.7 eV with decreasing the film thickness, implying the band gap can be tuned by mis-match strain. Our hybrid functional calculations give agreement with the experimental results and indicate that the narrowing of band gap of SnO2 under tensile epitaxial strain comes from the weakening of bonding and antibonding split, which is induced by the disorder of SnO6 octahedra. The biaxial epitaxial strain is shown to be more efficient than the uniaxial strain for tuning the band gap of SnO2.

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AUTHOR INFORMATION

Corresponding Author

*(P.Y.) E-mail: [email protected]. Phone: +86 (0)22 27408599. Fax: +86 (0)22 27406852. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (51074112 and 11247224). The supercomputing resources were supported by High Performance Computing Center of Tianjin University, China.

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REFERENCES

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