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Surface phonon polariton characteristics of bulk wurtzite ZnO crystal
Physica B 406 (2011) 115–118
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Physica B journal homepage: www.elsevier.com/locate/physb
Surface phonon polariton characteristics of bulk wurtzite ZnO crystal S.C. Lee n, S.S. Ng, K.G. Saw, Z. Hassan, H. Abu Hassan Nano-Optoelectronics Research and Technology Laboratory, School of Physics, Universiti Sains Malaysia, 11800 Penang, Malaysia
a r t i c l e in f o
abstract
Article history: Received 14 April 2010 Received in revised form 24 September 2010 Accepted 16 October 2010
The surface phonon polariton (SPP) mode of bulk wurtzite (a-) zinc oxide (ZnO) crystal is investigated by means of p-polarized infrared attenuated total reflection (ATR) spectroscopy. From the ATR spectrum, a strong absorption dip corresponds to the SPP mode of bulk a-ZnO is clearly observed at 529 cm 1. The experimental SPP mode showed good agreement with the theoretical SPP mode deduced from the surface polariton dispersion curve generated by the semi-infinite anisotropic crystal model. & 2010 Elsevier B.V. All rights reserved.
Keywords: Anisotropic Attenuated total reflection Surface phonon polariton Zinc oxide
1. Introduction Recently, wurtzite (a-) structure zinc oxide (ZnO) semiconductor has gained substantial interest in the research community. Owing to its direct wide band gap energy ( 3.4 eV at 300 K) and high excitonic binding energy ( 60 meV at 300 K), ZnO and ZnO-related compounds are widely used in the development of the shortwavelength optical devices [1]. Apart from that, ZnO-based devices have a much lower cost as compared to the III-nitrides based devices due to the availability of fairly high-quality ZnO bulk single crystals and simpler crystal-growth technology [2]. At present, much research devoted to ZnO semiconductors has been directed towards the understanding of its optical and electronic properties. However, the research on its surface phonon polariton (SPP) properties is still rare and has not received sufficient attention. In general, SPP is a transverse magnetic (TM) vibration mode resulting from the coupling of a photon with a transverseoptic (TO) phonon in the infrared (IR) region [3]. It is distinguished from the surface exciton polariton (SEP) that the SEP is resulting from the coupling of a photon with an exciton in the band gap frequency region [4]. In addition, the SEP exhibits the effect of spatial dispersion while this effect is absent for the SPP [5]. A comprehensive review dealing with the polariton (photon coupled with elementary excitation such as phonon, exciton, plasmon, magnon, etc.) can be found in Refs. [6,7]. In 1993, Beletskii et al. [8] studied the SPP of ZnO thin film grown on the sapphire (Al2O3) substrate. However, the SPP mode of ZnO cannot be figured out easily and clearly due to the superimposition
n
Corresponding author. Tel.: + 604 6535325; fax: + 604 6579150. E-mail address: [email protected] (S.C. Lee).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.10.036
of the film reststrahlen band with the Al2O3 that exhibits multioptical phonon modes behavior. Moreover, it has been reported that SPP provides application in the development of some sensors, spectroscopic and photonic devices [9–12]. Considering the fundamental physical properties and the potential application of ZnO semiconductors, there is an absolute need for thorough studies on the SPP properties of this material. In this work, the SPP characteristics of bulk a-ZnO crystal are investigated experimentally and theoretically. To detect the SPP, p-polarized IR attenuated total reflection (ATR) experiment in the Otto configuration is employed. Due to the uniaxial optical anisotropic features in a-ZnO, an anisotropy model is used in the theoretical calculation. The required optical parameters used in the theoretical study are obtained by means of polarized IR reflectance measurements. Through this study, a clear picture of the SPP mode of a-ZnO is obtained.
2. Material and methods One side polished commercial undoped bulk a-ZnO wafer grown by the hydrothermal method was used in this study. The size of the sample was about 1.1 1.1 cm2 and the thickness was about 1 mm. The root mean square roughness of the sample as determined from the atomic force microscope is about 4.78 nm. Overall, the ZnO sample exhibited a predominantly clean and smooth surface morphology. Room temperature s- and p-polarized far IR reflectance measurements have been carried out using a Fourier transform IR spectrometer (Spectrum GX FTIR, Perkin Elmer). A wire grid polarizer was used in the polarization measurements. The angle of incidence was set to 301 using a variable angle reflectance
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accessory. For the p-polarized IR ATR measurement, a single reflection diamond ATR accessory (GladiATR, PIKE Technologies) with an internal incident angle of 451 and a refractive index of 2.4 was used [13]. In order to excite the SPP, a small air gap was adjusted between the diamond prism and sample using a spacer (Otto configuration) [14]. All the measurements were taken at frequencies ranging from 300 to 700 cm 1. The spectra were recorded using 256 scans and a spectral resolution of 4 cm 1.
3.2. Theoretical model for the surface polariton dispersion curve and p-polarized IR ATR spectra The surface polariton (SP) dispersion relation can be obtained by solving the electromagnetic equation directly using the boundary conditions at the interface between two different media or transfer matrix approach when dealing with multilayer structures [17–19]. For vacuum/semi-infinite crystal system, the implicit SP dispersion relation is given by
a0 a1 þ ¼ 0, e?1 e?2
3. Theory 3.1. Theoretical model for polarized IR reflectance spectra In general, the optical parameters of a material can be determined via numerical fitting using a suitable dielectric function model. For a-crystal with crystal axis along the growth direction and perpendicular to the propagation direction, the dielectric function model is given by [15] ! o2LOj o2 iogLOj ej ðoÞ ¼ e1,j 2 , ð1Þ oTOj o2 iogTOj where eN is the high-frequency dielectric constant, oLO and oTO are, respectively, the longitudinal-optic (LO) and TO phonon frequencies. gLO and gTO are, respectively, the LO and TO phonon damping constants. The subscript j stands for parallel (99) and perpendicular (?) vibration modes with respect to the optical c-axis. The geometry of the sample’s orientation and the coordinate system used are described in Fig. 1. The equations for the wave propagation for s- and p-polarization in a uniaxial medium are, respectively, given by [16] s-polarized ðE ? c-axisÞ : q2zi ¼ e?i ðo=cÞ2 q2x ,
ð2Þ
p-polarized ðE J c-axisÞ : q2zi ¼ e?i ðo=cÞ2 ðe?i =e99i Þq2x ,
ð3Þ
Here, E is the electric field vector. o and c are, respectively, the angular frequency and the velocity of light in the vacuum (3 108 ms 1). The subscript i denotes the layer media, i.e., i¼1 for the medium of incidence and i¼ 2 for the measured sample. qx is determined by e1 and the angle of incidence y given by pffiffiffiffiffi ð4Þ qx ¼ e1 ðo=cÞsiny For vacuum or air medium, e1 is isotropic, i.e., e1 ¼ e991 ¼ e?1 ¼1. The s- and p-polarized IR reflectivity, i.e., Rs and Rp for two layers media can be evaluated, respectively using [16] 2
Rs ¼ 9ðqz1 qz2 Þ=ðqz1 þqz2 Þ9 ,
ð5Þ 2
Rp ¼ 9ðe?2 qz1 e?1 qz2 Þ=ðe?2 qz1 þ e?1 qz2 Þ9
ð6Þ
Fig. 1. Geometry of the sample’s orientation and coordinate system used. The incident angle is measured from the c-axis. e1 is the dielectric constant of the medium of incidence (vacuum). e? and e99 are the dielectric functions of bulk a-ZnO in the perpendicular and parallel vibration modes with c-axis, respectively.
ð7Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where a0 ¼ k2x ðo=cÞ2 and a1 ¼ ðe?2 =e992 Þk2x e?2 ðo=cÞ2 . a0 and a1 are, respectively, the field decay constants in the vacuum and a-ZnO. kx is the wave vector of the SP along the x-direction. An explicit form for Eq. (7) is given by [17] sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e992 ðoÞe992 ðoÞe?2 ðoÞ , ð8Þ kx ðoÞ ¼ kvac ðoÞ 1e992 ðoÞe?2 ðoÞ where kvac(o)¼ o/c, namely the light wave in the vacuum. In the p-polarized IR ATR measurement, the SPP in the sample can be excited by kp, in which its wave vector is in the x-direction and is given by [14] kp ðoÞ ¼ kvac ðoÞnp siny
ð9Þ
Note that y must exceed the critical angle of the prism so that the incidence radiation can be totally reflected and an evanescent wave with wave vector kp can be generated behind the base plane of the prism. In this work, the theoretical ATR spectrum of bulk a-ZnO crystal is computed based on the standard transfer matrix formulation, where a three layers structure, i.e., diamond prism/air-gap/ZnO was employed. More details about the standard transfer matrix formulation of IR (ATR) reflectance spectrum can be found in Ref. [16].
4. Results and discussion 4.1. Polarized IR reflectance measurements Fig. 2 shows the polarized IR reflectance spectra in the range 300–700 cm 1 for bulk a-ZnO. Lines for the LO99(?) and TO99(?) phonon frequencies of a-ZnO are also shown in Fig. 2. A reflection band located between the TO and LO frequencies can be clearly observed in both polarized IR reflectance spectra. Apart from that, a significant dip can be observed at 580 cm 1 in the p-polarized IR reflectance spectrum (Fig. 2(b)). This resonance feature is related to the phonon anisotropy in a-ZnO. In general, for air/semi-infinite crystal system and in the absence of phonon damping, this dip occurs when Rp E0 and is located in between LO99 and LO? frequencies. However, if damping is present, the position of this dip will be slightly shifted. In addition, it will encounter a broadening effect, i.e., mainly caused by LO99 damping for undoped sample. Thus, for a sample with large damping, this dip is difficult to be observed in the p-polarized IR reflectance spectrum, especially for highly doped sample (due to the effects of LO-plasma coupling). Since the reflectivity for s-polarization measurement is only depends on e? (as shown in Eq. (5)), one set of phonon parameters is sufficient to fit the s-polarized IR reflectance spectrum. However, for p-polarization measurement, the reflectivity depends on both e? and e99 (as shown in Eq. (6)). Therefore, two sets of phonon parameters are required to fit the p-polarized IR reflectance spectrum.
S.C. Lee et al. / Physica B 406 (2011) 115–118
117
Fig. 2. Room temperature (a) s- and (b) p-polarized IR reflectance spectra of bulk a-ZnO measured at an incident angle of 301. The solid and the dotted lines indicate the theoretical and experimental IR reflectance spectra, respectively.
Table 1 Optical parameters of bulk a-ZnO obtained from the model fit of polarized IR reflectance spectra.
? 99 a
eN
oTO (cm 1)
oLO (cm 1)
gTO (cm 1)
gLO (cm 1)
3.70a 3.78a
411 384
589.8 571.8
10.5 10.0
12.0 15.8
Taken from Ref. [20].
In this work, the phonon parameters are adjusted until the theoretical spectra give the best fit to the experimental spectra for both the s- and p-polarization measurements. The results of fitting are shown in Fig. 2. From Fig. 2, it is found that the theoretical spectra are in reasonable agreement with the experimental spectra. The best-fit parameters are listed in Table 1. Note that, the values of eN?(99) are taken from Ref. [20]. These parameters are used to simulate the theoretical ATR spectrum and SP dispersion curve, which will be discussed in the next section.
Fig. 3. Room temperature p-polarized IR ATR spectra of bulk a-ZnO crystal. The solid and the dotted lines indicate the experimental and the calculated ATR spectra, respectively.
4.2. p-polarized IR ATR measurement Fig. 3 shows the p-polarized IR ATR spectra (experimental and calculated) of bulk a-ZnO. The thickness of the air gap used in the ATR simulation is 2.7 mm. Qualitatively, the experimental and calculated frequencies of all the features are in good agreements. However, the intensity of the reflectivity between the two spectra showed less agreement. Similar mismatch has been reported by Hamilton et al. [19]. The mismatch of the intensity is probably due to the experimental variations in the vacuum gap and the incident angle. From Fig. 3, a strong absorption dip is clearly observed at 529 cm 1. In general, this strong absorption dip is resulted from the resonance at a frequency where the wave vectors of the incident radiation and the SP are matched, namely, o (photon)¼ck (photon)¼ o (phonon). In other words, it corresponds to the SPP mode, i.e., the intersection between the SP dispersion curve and the kp line (will be shown later). Apart from that, a weak and broad dip can be observed at 580 cm 1. However, this dip is not attributed to SPP mode because the SPP mode should be located between the TO? and LO99 frequencies of ZnO [21]. Furthermore, there is no intersection of the kp line and the SP dispersion curve around this
frequency region (see Fig. 4). Therefore, this dip is not caused by the SPP. The presence of this dip is due to the anisotropic feature in a-ZnO. Similar descriptions regarding to this dip are given previously in the interpretation of the p-polarized IR reflectance spectrum. In order to verify the strong absorption dip in the ATR spectrum is due to SPP, the SP dispersion curve is simulated based on Eqs. (1) and (8), as shown in Fig. 4. The phonon damping constants in Eq. (1) have been ignored to ensure the calculation of the SP dispersion curve is made in the lossless limit, i.e., gLO?(99) ¼ gTO?(99) ¼0. Also shown in Fig. 4 are the light wave in the vacuum (kvac) and the light waves in the diamond prism (kp). The details of the SP dispersion curve are discussed below. The SP dispersion curve is divided into two parts, i.e., the regions for solutions of kx okvac and kx 4kvac. The condition of the existence for solutions of kx is summarized in Table 2. From Table 2, it is found that the solutions of kx 4kvac occur when both a0 and a1 are real quantities, as indicated by branches A and B in Fig. 4. While the solutions of kx okvac occur when either or both a0 and a1 are imaginary quantities. However, attention is focused on the region of kx 4kvac since this region is inaccessible by the common IR reflectance and transmission techniques.
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obtained from the intersections of the kp line and the SP dispersion curve (535 cm 1). The discrepancy is about 1.1%, calculated based on Dospp ¼ ðosppðtheoryÞ osppðexperimentÞ Þ=osppðtheoryÞ 100%. This small discrepancy has probably come from the perturbing effect of the prism, which depends on the air gap between the prism base and the sample [19]. Besides, the discrepancy is probably due to the quality of sample, which is not considered in the theoretical calculation.
5. Conclusion
Fig. 4. Theoretical SP dispersion curve of bulk a-ZnO simulated using the parameters obtained from the model fit of polarized IR reflectance spectra. The medium dash line is the light wave in the vacuum (kvac), the dash dot–dot line indicates the light wave in the ATR prism (kp) when y ¼ 451. The intersection of the kp line and branch A corresponds to the SPP mode.
Table 2 Condition of the existence for solutions of kx.
Acknowledgements
o (cm 1)
e?
e99
a0
a1
kx (cm 1)
o o oTO 99 oTO 99 o o o oTO? oTO? o o o547 547 o o o oLO99 oLO99 o o o oLO? oLO? o o o 626 626 o o o 636 636 o o o 644 o 4644
e? 41 e? 41 e? 40 e? 40 e? 40 0o e? o 1 0o e? o 1 0o e? o 1 e? 41
e99 41 e99 o0 e99 o0 e99 o0 0o e99 o1 0o e99 o1 e99 41 e99 41 e99 41
Imaginary Imaginary Real Imaginary Imaginary Imaginary Real Imaginary Imaginary
Imaginary Imaginary Real Real Imaginary Imaginary Real Imaginary Imaginary
kx o kvac kx o kvac kx 4kvac –a kx o kvac kx o kvac kx 4kvac –a kx o kvac
a
In-depth experimental and theoretical studies on the SPP mode of bulk a-ZnO have been reported. Through p-polarized IR ATR measurement, a strong absorption dip corresponds to the SPP mode of ZnO is found at 529 cm 1. This result is in good agreement with the calculated spectrum generated using the standard transfer matrix formulation based on three layers structure, i.e., diamond prism/air-gap/ZnO. Moreover, the origin of the observed feature is confirmed by the theoretical SP dispersion curve simulated by means of anisotropy model. The discrepancy between the experimental and theoretical SPP mode of ZnO is about 1.1%.
No solution.
From Fig. 4, it can be seen that the kp line intersects the kx line at two points, i.e., 535 and 634 cm 1. However, only the former intersecting point that lies on branch A is assigned to the SPP mode of a-ZnO because its frequency is located in between TO? and LO99 frequencies of ZnO (as mentioned previously). This SPP mode is known as real SPP mode. It occurs when both e? and e99 are negative (condition for the localization of surface charges) and both a0 and a1 are real quantities [22]. Note that, the real values of a0 and a1 indicate that the propagation of the SPP is decayed away from the interface of vacuum/ZnO into the bulk. While, the latter intersecting point that lies on branch B is not due to the SPP mode since both e?and e99 are positive. The presence of branch B is due to the anisotropic properties in a-ZnO. It was absent in the SP dispersion curve for cubic structure crystal [23]. The results suggest that when explicit form of the SP dispersion relation (Eq. (8)) is employed to determine the real SPP modes, the following conditions must be fulfilled, i.e., (i) e? and e99 are negative, (ii) a0 and a1 must be the real quantities. The frequency of the strong absorption dip in the experimental ATR spectrum (529 cm 1) is close to the theoretical SPP mode
The authors would like to thank the Malaysian Government, Ministry of Higher Education Malaysia (MOHE), and Universiti Sains Malaysia for the Fundamental Research Grant Scheme (FRGS) (Grant no. 203/PFIZIK/6711127) and Research Universiti (RU) Grant (Grant no. 1001/PFIZIK/811135). References [1] C. Klingshirn, Phys. Status Solidi B 244 (2007) 3027. [2] U. Ozgur, Y.I. Alivov, C. Liu, A. Teke, M.A. Reshchikov, S. Dogan, V. Avrutin, S.J. Cho, H. Markoc, J. Appl. Phys. 98 (2005) 041301. [3] S.L. Cunningham, A.A. Maradudin, R.F. Wallis, Phys. Rev. B 10 (1974) 3342. [4] R.N. Philp, D.R. Tilley, Phys. Rev. B 44 (1991) 8170. [5] J. Lagois, Solid State Commun. 39 (1981) 563. [6] E.L. Albuquerque, M.G. Cottam, Phys. Rep. 376 (2003) 225. [7] E.L. Albuquerque, M.G. Cottam, in: Polaritons in Periodic and Quasiperiodic Structures, first ed., Elsevier, Amsterdam, 2004. [8] N.N. Beletskii, A.N. Brukva, T.N. Nikolaeva, V.P. Cherkashin, Phys. Status Solidi B 184 (1994) 403. [9] I. Balin, N. Dahan, V. Kleiner, E. Hasman, Appl. Phys. Lett. 94 (2009) 111112. [10] J.J. Greffet, R. Carminati, K. Joulain, J.P. Mulet, S. Mainguy, Y. Chen, Nature 416 (2002) 61. [11] P.B. Catrysse, S.H. Fan, Phys. Rev. B 75 (2007) 075422. [12] A.J. Huber, N. Ocelic, R. Hillenbrand, J. Microsc. 229 (2008) 389. [13] PIKE Technologies Inc., ATR-theory and applications, PIKE Technologies, Madison, Application Note, 2005. [14] H.J. Falge, A. Otto, Phys. Status Solidi B 56 (1973) 523. [15] F. Gervais, B. Piriou, J. Phys. C: Solid State Phys. 7 (1974) 2374. [16] T. Dumelow, T.J. Barker, S.R.P. Smith, D.R. Tilley, Surf. Sci. Rep. 17 (1993) 151. [17] M.G. Cottam, D.R. Tilley, in: Introduction to Surface and Superlattice Excitations, second ed., Cambridge University Press, Cambridge, 1989. [18] E.L. Albuquerque, M.G. Cottam, Solid State Commun. 81 (1992) 383. [19] A.A. Hamilton, T. Dumelow, T.J. Parker, S.R.P. Smith, J. Phys., Condens. Mater. 8 (1996) 8027. [20] N. Ashkenov, B.N. Mbenkum, C. Bundesmann, V. Riede, M. Lorenz, D. Spemann, E.M. Kaidashev, A. Kasic, M. Schubert, M. Grundmann, G. Wagner, H. Neumann, V. Darakchieva, H. Arwin, B. Monemar, J. Appl. Phys. 93 (2003) 126. [21] S.S. Ng, Z. Hassan, H.Abu Hassan, Appl. Phys. Lett. 90 (2007) 081902. [22] T. Dumelow, D.R. Tilley, J. Opt. Soc. Am. A 10 (1993) 633. [23] S.S. Ng, Z. Hassan, H.Abu Hassan, Surf. Rev. Lett. 16 (2009) 355.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Surface phonon polariton characteristics of bulk wurtzite ZnO crystal S.C. Lee n, S.S. Ng, K.G. Saw, Z. Hassan, H. Abu Hassan Nano-Optoelectronics Research and Technology Laboratory, School of Physics, Universiti Sains Malaysia, 11800 Penang, Malaysia
a r t i c l e in f o
abstract
Article history: Received 14 April 2010 Received in revised form 24 September 2010 Accepted 16 October 2010
The surface phonon polariton (SPP) mode of bulk wurtzite (a-) zinc oxide (ZnO) crystal is investigated by means of p-polarized infrared attenuated total reflection (ATR) spectroscopy. From the ATR spectrum, a strong absorption dip corresponds to the SPP mode of bulk a-ZnO is clearly observed at 529 cm 1. The experimental SPP mode showed good agreement with the theoretical SPP mode deduced from the surface polariton dispersion curve generated by the semi-infinite anisotropic crystal model. & 2010 Elsevier B.V. All rights reserved.
Keywords: Anisotropic Attenuated total reflection Surface phonon polariton Zinc oxide
1. Introduction Recently, wurtzite (a-) structure zinc oxide (ZnO) semiconductor has gained substantial interest in the research community. Owing to its direct wide band gap energy ( 3.4 eV at 300 K) and high excitonic binding energy ( 60 meV at 300 K), ZnO and ZnO-related compounds are widely used in the development of the shortwavelength optical devices [1]. Apart from that, ZnO-based devices have a much lower cost as compared to the III-nitrides based devices due to the availability of fairly high-quality ZnO bulk single crystals and simpler crystal-growth technology [2]. At present, much research devoted to ZnO semiconductors has been directed towards the understanding of its optical and electronic properties. However, the research on its surface phonon polariton (SPP) properties is still rare and has not received sufficient attention. In general, SPP is a transverse magnetic (TM) vibration mode resulting from the coupling of a photon with a transverseoptic (TO) phonon in the infrared (IR) region [3]. It is distinguished from the surface exciton polariton (SEP) that the SEP is resulting from the coupling of a photon with an exciton in the band gap frequency region [4]. In addition, the SEP exhibits the effect of spatial dispersion while this effect is absent for the SPP [5]. A comprehensive review dealing with the polariton (photon coupled with elementary excitation such as phonon, exciton, plasmon, magnon, etc.) can be found in Refs. [6,7]. In 1993, Beletskii et al. [8] studied the SPP of ZnO thin film grown on the sapphire (Al2O3) substrate. However, the SPP mode of ZnO cannot be figured out easily and clearly due to the superimposition
n
Corresponding author. Tel.: + 604 6535325; fax: + 604 6579150. E-mail address: [email protected] (S.C. Lee).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.10.036
of the film reststrahlen band with the Al2O3 that exhibits multioptical phonon modes behavior. Moreover, it has been reported that SPP provides application in the development of some sensors, spectroscopic and photonic devices [9–12]. Considering the fundamental physical properties and the potential application of ZnO semiconductors, there is an absolute need for thorough studies on the SPP properties of this material. In this work, the SPP characteristics of bulk a-ZnO crystal are investigated experimentally and theoretically. To detect the SPP, p-polarized IR attenuated total reflection (ATR) experiment in the Otto configuration is employed. Due to the uniaxial optical anisotropic features in a-ZnO, an anisotropy model is used in the theoretical calculation. The required optical parameters used in the theoretical study are obtained by means of polarized IR reflectance measurements. Through this study, a clear picture of the SPP mode of a-ZnO is obtained.
2. Material and methods One side polished commercial undoped bulk a-ZnO wafer grown by the hydrothermal method was used in this study. The size of the sample was about 1.1 1.1 cm2 and the thickness was about 1 mm. The root mean square roughness of the sample as determined from the atomic force microscope is about 4.78 nm. Overall, the ZnO sample exhibited a predominantly clean and smooth surface morphology. Room temperature s- and p-polarized far IR reflectance measurements have been carried out using a Fourier transform IR spectrometer (Spectrum GX FTIR, Perkin Elmer). A wire grid polarizer was used in the polarization measurements. The angle of incidence was set to 301 using a variable angle reflectance
116
S.C. Lee et al. / Physica B 406 (2011) 115–118
accessory. For the p-polarized IR ATR measurement, a single reflection diamond ATR accessory (GladiATR, PIKE Technologies) with an internal incident angle of 451 and a refractive index of 2.4 was used [13]. In order to excite the SPP, a small air gap was adjusted between the diamond prism and sample using a spacer (Otto configuration) [14]. All the measurements were taken at frequencies ranging from 300 to 700 cm 1. The spectra were recorded using 256 scans and a spectral resolution of 4 cm 1.
3.2. Theoretical model for the surface polariton dispersion curve and p-polarized IR ATR spectra The surface polariton (SP) dispersion relation can be obtained by solving the electromagnetic equation directly using the boundary conditions at the interface between two different media or transfer matrix approach when dealing with multilayer structures [17–19]. For vacuum/semi-infinite crystal system, the implicit SP dispersion relation is given by
a0 a1 þ ¼ 0, e?1 e?2
3. Theory 3.1. Theoretical model for polarized IR reflectance spectra In general, the optical parameters of a material can be determined via numerical fitting using a suitable dielectric function model. For a-crystal with crystal axis along the growth direction and perpendicular to the propagation direction, the dielectric function model is given by [15] ! o2LOj o2 iogLOj ej ðoÞ ¼ e1,j 2 , ð1Þ oTOj o2 iogTOj where eN is the high-frequency dielectric constant, oLO and oTO are, respectively, the longitudinal-optic (LO) and TO phonon frequencies. gLO and gTO are, respectively, the LO and TO phonon damping constants. The subscript j stands for parallel (99) and perpendicular (?) vibration modes with respect to the optical c-axis. The geometry of the sample’s orientation and the coordinate system used are described in Fig. 1. The equations for the wave propagation for s- and p-polarization in a uniaxial medium are, respectively, given by [16] s-polarized ðE ? c-axisÞ : q2zi ¼ e?i ðo=cÞ2 q2x ,
ð2Þ
p-polarized ðE J c-axisÞ : q2zi ¼ e?i ðo=cÞ2 ðe?i =e99i Þq2x ,
ð3Þ
Here, E is the electric field vector. o and c are, respectively, the angular frequency and the velocity of light in the vacuum (3 108 ms 1). The subscript i denotes the layer media, i.e., i¼1 for the medium of incidence and i¼ 2 for the measured sample. qx is determined by e1 and the angle of incidence y given by pffiffiffiffiffi ð4Þ qx ¼ e1 ðo=cÞsiny For vacuum or air medium, e1 is isotropic, i.e., e1 ¼ e991 ¼ e?1 ¼1. The s- and p-polarized IR reflectivity, i.e., Rs and Rp for two layers media can be evaluated, respectively using [16] 2
Rs ¼ 9ðqz1 qz2 Þ=ðqz1 þqz2 Þ9 ,
ð5Þ 2
Rp ¼ 9ðe?2 qz1 e?1 qz2 Þ=ðe?2 qz1 þ e?1 qz2 Þ9
ð6Þ
Fig. 1. Geometry of the sample’s orientation and coordinate system used. The incident angle is measured from the c-axis. e1 is the dielectric constant of the medium of incidence (vacuum). e? and e99 are the dielectric functions of bulk a-ZnO in the perpendicular and parallel vibration modes with c-axis, respectively.
ð7Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where a0 ¼ k2x ðo=cÞ2 and a1 ¼ ðe?2 =e992 Þk2x e?2 ðo=cÞ2 . a0 and a1 are, respectively, the field decay constants in the vacuum and a-ZnO. kx is the wave vector of the SP along the x-direction. An explicit form for Eq. (7) is given by [17] sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e992 ðoÞe992 ðoÞe?2 ðoÞ , ð8Þ kx ðoÞ ¼ kvac ðoÞ 1e992 ðoÞe?2 ðoÞ where kvac(o)¼ o/c, namely the light wave in the vacuum. In the p-polarized IR ATR measurement, the SPP in the sample can be excited by kp, in which its wave vector is in the x-direction and is given by [14] kp ðoÞ ¼ kvac ðoÞnp siny
ð9Þ
Note that y must exceed the critical angle of the prism so that the incidence radiation can be totally reflected and an evanescent wave with wave vector kp can be generated behind the base plane of the prism. In this work, the theoretical ATR spectrum of bulk a-ZnO crystal is computed based on the standard transfer matrix formulation, where a three layers structure, i.e., diamond prism/air-gap/ZnO was employed. More details about the standard transfer matrix formulation of IR (ATR) reflectance spectrum can be found in Ref. [16].
4. Results and discussion 4.1. Polarized IR reflectance measurements Fig. 2 shows the polarized IR reflectance spectra in the range 300–700 cm 1 for bulk a-ZnO. Lines for the LO99(?) and TO99(?) phonon frequencies of a-ZnO are also shown in Fig. 2. A reflection band located between the TO and LO frequencies can be clearly observed in both polarized IR reflectance spectra. Apart from that, a significant dip can be observed at 580 cm 1 in the p-polarized IR reflectance spectrum (Fig. 2(b)). This resonance feature is related to the phonon anisotropy in a-ZnO. In general, for air/semi-infinite crystal system and in the absence of phonon damping, this dip occurs when Rp E0 and is located in between LO99 and LO? frequencies. However, if damping is present, the position of this dip will be slightly shifted. In addition, it will encounter a broadening effect, i.e., mainly caused by LO99 damping for undoped sample. Thus, for a sample with large damping, this dip is difficult to be observed in the p-polarized IR reflectance spectrum, especially for highly doped sample (due to the effects of LO-plasma coupling). Since the reflectivity for s-polarization measurement is only depends on e? (as shown in Eq. (5)), one set of phonon parameters is sufficient to fit the s-polarized IR reflectance spectrum. However, for p-polarization measurement, the reflectivity depends on both e? and e99 (as shown in Eq. (6)). Therefore, two sets of phonon parameters are required to fit the p-polarized IR reflectance spectrum.
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Fig. 2. Room temperature (a) s- and (b) p-polarized IR reflectance spectra of bulk a-ZnO measured at an incident angle of 301. The solid and the dotted lines indicate the theoretical and experimental IR reflectance spectra, respectively.
Table 1 Optical parameters of bulk a-ZnO obtained from the model fit of polarized IR reflectance spectra.
? 99 a
eN
oTO (cm 1)
oLO (cm 1)
gTO (cm 1)
gLO (cm 1)
3.70a 3.78a
411 384
589.8 571.8
10.5 10.0
12.0 15.8
Taken from Ref. [20].
In this work, the phonon parameters are adjusted until the theoretical spectra give the best fit to the experimental spectra for both the s- and p-polarization measurements. The results of fitting are shown in Fig. 2. From Fig. 2, it is found that the theoretical spectra are in reasonable agreement with the experimental spectra. The best-fit parameters are listed in Table 1. Note that, the values of eN?(99) are taken from Ref. [20]. These parameters are used to simulate the theoretical ATR spectrum and SP dispersion curve, which will be discussed in the next section.
Fig. 3. Room temperature p-polarized IR ATR spectra of bulk a-ZnO crystal. The solid and the dotted lines indicate the experimental and the calculated ATR spectra, respectively.
4.2. p-polarized IR ATR measurement Fig. 3 shows the p-polarized IR ATR spectra (experimental and calculated) of bulk a-ZnO. The thickness of the air gap used in the ATR simulation is 2.7 mm. Qualitatively, the experimental and calculated frequencies of all the features are in good agreements. However, the intensity of the reflectivity between the two spectra showed less agreement. Similar mismatch has been reported by Hamilton et al. [19]. The mismatch of the intensity is probably due to the experimental variations in the vacuum gap and the incident angle. From Fig. 3, a strong absorption dip is clearly observed at 529 cm 1. In general, this strong absorption dip is resulted from the resonance at a frequency where the wave vectors of the incident radiation and the SP are matched, namely, o (photon)¼ck (photon)¼ o (phonon). In other words, it corresponds to the SPP mode, i.e., the intersection between the SP dispersion curve and the kp line (will be shown later). Apart from that, a weak and broad dip can be observed at 580 cm 1. However, this dip is not attributed to SPP mode because the SPP mode should be located between the TO? and LO99 frequencies of ZnO [21]. Furthermore, there is no intersection of the kp line and the SP dispersion curve around this
frequency region (see Fig. 4). Therefore, this dip is not caused by the SPP. The presence of this dip is due to the anisotropic feature in a-ZnO. Similar descriptions regarding to this dip are given previously in the interpretation of the p-polarized IR reflectance spectrum. In order to verify the strong absorption dip in the ATR spectrum is due to SPP, the SP dispersion curve is simulated based on Eqs. (1) and (8), as shown in Fig. 4. The phonon damping constants in Eq. (1) have been ignored to ensure the calculation of the SP dispersion curve is made in the lossless limit, i.e., gLO?(99) ¼ gTO?(99) ¼0. Also shown in Fig. 4 are the light wave in the vacuum (kvac) and the light waves in the diamond prism (kp). The details of the SP dispersion curve are discussed below. The SP dispersion curve is divided into two parts, i.e., the regions for solutions of kx okvac and kx 4kvac. The condition of the existence for solutions of kx is summarized in Table 2. From Table 2, it is found that the solutions of kx 4kvac occur when both a0 and a1 are real quantities, as indicated by branches A and B in Fig. 4. While the solutions of kx okvac occur when either or both a0 and a1 are imaginary quantities. However, attention is focused on the region of kx 4kvac since this region is inaccessible by the common IR reflectance and transmission techniques.
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obtained from the intersections of the kp line and the SP dispersion curve (535 cm 1). The discrepancy is about 1.1%, calculated based on Dospp ¼ ðosppðtheoryÞ osppðexperimentÞ Þ=osppðtheoryÞ 100%. This small discrepancy has probably come from the perturbing effect of the prism, which depends on the air gap between the prism base and the sample [19]. Besides, the discrepancy is probably due to the quality of sample, which is not considered in the theoretical calculation.
5. Conclusion
Fig. 4. Theoretical SP dispersion curve of bulk a-ZnO simulated using the parameters obtained from the model fit of polarized IR reflectance spectra. The medium dash line is the light wave in the vacuum (kvac), the dash dot–dot line indicates the light wave in the ATR prism (kp) when y ¼ 451. The intersection of the kp line and branch A corresponds to the SPP mode.
Table 2 Condition of the existence for solutions of kx.
Acknowledgements
o (cm 1)
e?
e99
a0
a1
kx (cm 1)
o o oTO 99 oTO 99 o o o oTO? oTO? o o o547 547 o o o oLO99 oLO99 o o o oLO? oLO? o o o 626 626 o o o 636 636 o o o 644 o 4644
e? 41 e? 41 e? 40 e? 40 e? 40 0o e? o 1 0o e? o 1 0o e? o 1 e? 41
e99 41 e99 o0 e99 o0 e99 o0 0o e99 o1 0o e99 o1 e99 41 e99 41 e99 41
Imaginary Imaginary Real Imaginary Imaginary Imaginary Real Imaginary Imaginary
Imaginary Imaginary Real Real Imaginary Imaginary Real Imaginary Imaginary
kx o kvac kx o kvac kx 4kvac –a kx o kvac kx o kvac kx 4kvac –a kx o kvac
a
In-depth experimental and theoretical studies on the SPP mode of bulk a-ZnO have been reported. Through p-polarized IR ATR measurement, a strong absorption dip corresponds to the SPP mode of ZnO is found at 529 cm 1. This result is in good agreement with the calculated spectrum generated using the standard transfer matrix formulation based on three layers structure, i.e., diamond prism/air-gap/ZnO. Moreover, the origin of the observed feature is confirmed by the theoretical SP dispersion curve simulated by means of anisotropy model. The discrepancy between the experimental and theoretical SPP mode of ZnO is about 1.1%.
No solution.
From Fig. 4, it can be seen that the kp line intersects the kx line at two points, i.e., 535 and 634 cm 1. However, only the former intersecting point that lies on branch A is assigned to the SPP mode of a-ZnO because its frequency is located in between TO? and LO99 frequencies of ZnO (as mentioned previously). This SPP mode is known as real SPP mode. It occurs when both e? and e99 are negative (condition for the localization of surface charges) and both a0 and a1 are real quantities [22]. Note that, the real values of a0 and a1 indicate that the propagation of the SPP is decayed away from the interface of vacuum/ZnO into the bulk. While, the latter intersecting point that lies on branch B is not due to the SPP mode since both e?and e99 are positive. The presence of branch B is due to the anisotropic properties in a-ZnO. It was absent in the SP dispersion curve for cubic structure crystal [23]. The results suggest that when explicit form of the SP dispersion relation (Eq. (8)) is employed to determine the real SPP modes, the following conditions must be fulfilled, i.e., (i) e? and e99 are negative, (ii) a0 and a1 must be the real quantities. The frequency of the strong absorption dip in the experimental ATR spectrum (529 cm 1) is close to the theoretical SPP mode
The authors would like to thank the Malaysian Government, Ministry of Higher Education Malaysia (MOHE), and Universiti Sains Malaysia for the Fundamental Research Grant Scheme (FRGS) (Grant no. 203/PFIZIK/6711127) and Research Universiti (RU) Grant (Grant no. 1001/PFIZIK/811135). References [1] C. Klingshirn, Phys. Status Solidi B 244 (2007) 3027. [2] U. Ozgur, Y.I. Alivov, C. Liu, A. Teke, M.A. Reshchikov, S. Dogan, V. Avrutin, S.J. Cho, H. Markoc, J. Appl. Phys. 98 (2005) 041301. [3] S.L. Cunningham, A.A. Maradudin, R.F. Wallis, Phys. Rev. B 10 (1974) 3342. [4] R.N. Philp, D.R. Tilley, Phys. Rev. B 44 (1991) 8170. [5] J. Lagois, Solid State Commun. 39 (1981) 563. [6] E.L. Albuquerque, M.G. Cottam, Phys. Rep. 376 (2003) 225. [7] E.L. Albuquerque, M.G. Cottam, in: Polaritons in Periodic and Quasiperiodic Structures, first ed., Elsevier, Amsterdam, 2004. [8] N.N. Beletskii, A.N. Brukva, T.N. Nikolaeva, V.P. Cherkashin, Phys. Status Solidi B 184 (1994) 403. [9] I. Balin, N. Dahan, V. Kleiner, E. Hasman, Appl. Phys. Lett. 94 (2009) 111112. [10] J.J. Greffet, R. Carminati, K. Joulain, J.P. Mulet, S. Mainguy, Y. Chen, Nature 416 (2002) 61. [11] P.B. Catrysse, S.H. Fan, Phys. Rev. B 75 (2007) 075422. [12] A.J. Huber, N. Ocelic, R. Hillenbrand, J. Microsc. 229 (2008) 389. [13] PIKE Technologies Inc., ATR-theory and applications, PIKE Technologies, Madison, Application Note, 2005. [14] H.J. Falge, A. Otto, Phys. Status Solidi B 56 (1973) 523. [15] F. Gervais, B. Piriou, J. Phys. C: Solid State Phys. 7 (1974) 2374. [16] T. Dumelow, T.J. Barker, S.R.P. Smith, D.R. Tilley, Surf. Sci. Rep. 17 (1993) 151. [17] M.G. Cottam, D.R. Tilley, in: Introduction to Surface and Superlattice Excitations, second ed., Cambridge University Press, Cambridge, 1989. [18] E.L. Albuquerque, M.G. Cottam, Solid State Commun. 81 (1992) 383. [19] A.A. Hamilton, T. Dumelow, T.J. Parker, S.R.P. Smith, J. Phys., Condens. Mater. 8 (1996) 8027. [20] N. Ashkenov, B.N. Mbenkum, C. Bundesmann, V. Riede, M. Lorenz, D. Spemann, E.M. Kaidashev, A. Kasic, M. Schubert, M. Grundmann, G. Wagner, H. Neumann, V. Darakchieva, H. Arwin, B. Monemar, J. Appl. Phys. 93 (2003) 126. [21] S.S. Ng, Z. Hassan, H.Abu Hassan, Appl. Phys. Lett. 90 (2007) 081902. [22] T. Dumelow, D.R. Tilley, J. Opt. Soc. Am. A 10 (1993) 633. [23] S.S. Ng, Z. Hassan, H.Abu Hassan, Surf. Rev. Lett. 16 (2009) 355.