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Abstract
Surface nano-gratings of different periods are fabricated on a Ga-doped ZnO (GaZnO) thin film with a high electron concentration for the study of their surface plasmon (SP) resonance behaviors in the near-infrared range. The dispersion curve of the surface plasmon polariton (SPP) based on the ellipsometry measurement of the GaZnO dielectric constant helps in designing the grating period for effective SPP excitation. Spectral depressions of grating reflection under certain incident polarization conditions, corresponding to SP resonance features, are observed in the wavelength range between 1400 and 2200 nm. From the numerical simulation of light scattering from a GaZnO grating structure based on the measured dielectric constant and the fitted Drude model, we can identify either SPP or localized SP modes among the observed SP resonance features. Essentially, it is difficult to excite below 1600 nm SPP at an air/GaZnO interface due to its lossy nature. The potential application of SP resonance on GaZnO is evaluated.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Because of the favored characteristics of relatively lower loss, transparent conducting oxides (TCOs), such as indium-tin-oxide, highly Al-doped ZnO, and Ga-doped ZnO (GaZnO), and metallic nitrides, such as titanium nitride, zirconium nitride, and hafnium nitride have been considered for plasmonic applications, besides various noble metals, in the near-infrared range for optical-communication device fabrication [1–3]. In a TCO material, if electron concentration can reach 1021 cm−3, the real part of its dielectric constant can become negative beyond ∼1300 nm in wavelength. Hence, at the interface between this TCO material and a dielectric medium, including air, surface plasmon (SP) resonance can be induced in the near-infrared range. TCO materials have been used for forming metasurfaces, such as GaZnO nano-disk array [4], GaZnO nano-hole array [5], and GaZnO/ZnO nano-disk array [6], for demonstrating their SP resonance behaviors in the infrared range. Also, the properties of epsilon-near-zero of GaZnO and Al-doped ZnO around 1500 nm in wavelength have been used for producing significant changes of permittivity upon light irradiation [7–10]. Such a fast response can be used for all-optical switching and modulation. In the near-infrared range, the plasmonic absorption of TCOs can also be used for generating hot carriers to increase the photocurrent of a photovoltaic device [11,12]. Therefore, a TCO material is useful for solar cell application in both visible and near-infrared ranges. It can help in extending the sunlight harvest spectral range beyond 1100 nm in a Si solar cell.
SP resonance can be classified into two categories, including surface plasmon polariton (SPP) with propagating characteristics and localized surface plasmon (LSP) with the feature of local oscillation. For waveguide-type optoelectronics application, SPP excitation and its propagation characteristics, including propagation length and lateral energy confinement range, are important issues. For the applications of enhanced absorption, such as in a photodetector and a photovoltaic device, the spectral position and strength of an LSP mode are of great concern. In particular, for the application of enhanced sunlight harvest, an LSP mode of a shorter wavelength in the near-infrared range is preferred for absorbing stronger sunlight. In this situation, the use of a TCO can have the transparent conducting function in the visible range and the sunlight-harvest enhancement function in the near-infrared range. Therefore, the understandings of the excitation conditions of SPP and LSP and their resonance behaviors on a TCO surface are important to evaluate the usefulness of such a material for plasmonic applications. Among different nanostructures for studying SP resonance, a nano-grating is commonly used because it can support either SPP or LSP. In a grating structure with connected plasmonic material, SPP can be excited if the grating period is carefully chosen for producing an effective momentum compensation scheme. Meanwhile, various LSP modes can be induced on individual grating ridges. The generations of various LSP modes rely on the grating ridge geometry and excitation condition. Wavelength-dependent dielectric constant is the key parameter for determining the SP resonance behavior of a material. The dielectric constant of a TCO material varies depending on its growth condition. For modeling the metal-like dielectric constant of a TCO material, the Drude model has been considered for obtaining the fitting parameters [13,14]. Other models, such as Drude-Lorentz [4,15] and Drude-Gauss models [16], were also considered for including the semi-dielectric behavior of a TCO material.
GaZnO has been widely grown with various techniques, including pulsed laser deposition and metalorganic chemical vapor deposition [17,18]. Recently, this research team has successfully grown GaZnO thin films and nanowires with molecular beam epitaxy (MBE) to achieve an electron concentration higher than 1021 cm−3, mobility larger than 30 cm2/V-s, and hence resistivity close to 10−4 Ω-cm [19–21]. The GaZnO nanowires were formed based on the vapor-liquid-solid growth mode by using Ag nanoparticles as growth catalyst [22,23]. Although the dielectric constant and SP resonance properties of GaZnO in the near-infrared range have been discussed, the SP resonance behaviors of a GaZnO nano-grating have not been fully studied yet. In this paper, we design and fabricate two grating structures of different periods on a GaZnO thin film of a high electron concentration grown with MBE and measure their SP resonance behaviors under different excitation polarization conditions. The dielectric constant of GaZnO, obtained through ellipsometry measurement, is used to plot the SPP dispersion curve for designing grating period and to build a Drude model for numerical simulations on light scattering from the GaZnO nano-gratings. Based on these results, we can distinguish SPP from LSP resonances in the observed SP resonance features. In section 2 of this paper, the GaZnO growth conditions, the ellipsometry measurement data, the fitting results based on the Drude model, and the grating design considerations are presented. The fabrication conditions of the GaZnO gratings and their reflection behaviors are shown in section 3. The numerical simulations for comparing their results with the experimental data are demonstrated in section 4. The potential applications of the SPP and LSP resonances on GaZnO are evaluated in section 5. Finally, the conclusions are drawn in section 6.
2. GaZnO growth, ellipsometry measurement, and grating design
A GaZnO thin film of 300 nm in thickness is grown on a double-polished c-plane sapphire substrate with radio-frequency (RF) assisted MBE. The growth conditions include 250 oC in substrate temperature, 332 oC in Zn effusion cell temperature, 730 oC in Ga effusion cell temperature, 1 sccm in O flow rate, 300 W in RF power, and 120 min in growth duration. Based on Hall measurement, we obtain 1.09 × 1021 cm−3 in electron concentration, 35.9 cm2/V-s in electron mobility, and 1.59 × 10−4 Ω-cm in resistivity. With the left and right ordinates, Fig. 1(a) shows the wavelength-dependent refractive index, n, and extinction coefficient, k, respectively, of the GaZnO thin film based on ellipsometry measurement. From the equation of
Fig. 1. (a): Wavelength-dependent refractive index, n, (blue curve with the left ordinate) and extinction coefficient, k, (black curve with the right ordinate) of the GaZnO thin film based on ellipsometry measurement. (b): Real part, ɛ’, (blue continuous curve with the left ordinate) and imaginary part, ɛ”, (black continuous curve with the right ordinate) of the dielectric constant of the grown GaZnO thin film. Here, the red and green dashed curves are plotted for fitting the measured results of ɛ’ and ɛ” based on the Drude model.
we can obtain the real and imaginary parts (ɛ’ and ɛ”, respectively) of the dielectric constant of GaZnO, as shown in the blue (with the left ordinate) and black (with the right ordinate) continuous curves, respectively, of Fig. 1(b). Here, one can see that beyond 1130 nm in wavelength, ɛ’ becomes smaller than unity. Also, beyond 1320 nm, ɛ’ becomes negative that is the necessary condition for inducing SP resonance at the interface between GaZnO and a dielectric medium (including air).
The red and green dashed curves are plotted in Fig. 1(b) for fitting the measured results of ɛ’ and ɛ” based on the Drude model as
Based on the measurement results of ɛ’ and ɛ” in Fig. 1(b), we can plot the SPP dispersion curve excited at a smooth air/GaZnO interface to show the blue continuous curve in Fig. 2. Here, the slant dotted lines correspond to the light lines in air with different incident angles, as labeled. It is noted that the SPP dispersion curve can be plotted only up to ∼0.93 eV, beyond which ɛ’ is positive and hence no SP resonance can occur. Below ∼0.775 eV, no dielectric constant data are available. In Fig. 2, we also plot the dashed blue curve to show the SPP dispersion curve for extending the lower energy limit based on the fitted Drude model. Although the two dispersion curves are not exactly the same, their key features, such as the energy of the turning point, are similar. To study the SPP behavior at the air/GaZnO interface, surface grating structures are formed for compensating the momentum mismatch between an SPP mode and a plane wave. Meanwhile, on the ridge structure of a grating, LSP resonance can be induced for understanding its property. The SPP behavior is determined by its position on the dispersion curve. When an SPP lies beyond or is close to the turning point of the dispersion curve at ∼0.787 eV or ∼1576 nm (labeled by point T in Fig. 2), the lossy nature makes its excitation and observation difficult. On the other hand, a smaller grating period leads to a smaller grating ridge width and hence a shorter-wavelength LSP resonance. Also, a larger ridge height can result in a stronger LSP resonance. However, the fabrication cost of a small-period grating can be quite high. Meanwhile, in implementing a grating of a small period, it is usually difficult to achieve a large ridge height. Considering all aforementioned factors, we design two grating structures with periods at Λ1 = 750 nm and Λ2 = 1100 nm for comparing their differences in SPP and LSP behaviors. With the grating structures of 750 and 1100 nm in period, the SPP dispersion curve is left-shifted by 2π/Λ1 = 8.37 × 106 and 2π/Λ2 = 5.67 × 106 m−1 to become the green and red dashed curves (including the continuous and dashed curves based on the measurement data and the fitted Drude model, respectively), respectively, in Fig. 2. Here, the portion of the shifted SPP dispersion curve with Λ1 = 750 nm below the turning point intersects the light line of −60-degree incidence at point A. At this intersection, which corresponds to ∼0.765 eV in energy or ∼1620 nm in wavelength, SPP can possibly be excited. However, because point A is close to the turning point, the excitation of this SPP mode can be difficult. The portion of the shifted SPP dispersion curve with Λ2 = 1100 nm below the turning point intersects the light line of −45-degree incidence at point B. At this intersection, which corresponds to ∼0.61 eV in energy or ∼2033nm in wavelength, SPP can more possibly be excited because this point is further away from the turning point.
Fig. 2. Continuous (dashed) blue curve on the right: Dispersion curve of SPP at the smooth air/GaZnO interface based on the measurement data (the fitted Drude model). “T” indicates the turning point of the dispersion curve. Continuous and dashed green curves on the left (Continuous and dashed red curves in the middle): Dispersion curves of SPP on an air/GaZnO interface grating structure with Λ1 = 750 nm (Λ2 = 1100 nm) based on the measurement data and the fitted Drude model, respectively. The slant dotted lines show the light lines in air with different incident angles, as labeled. The horizontal dashed lines and the intersection points labeled by “A” and “B” indicate the possible conditions for exciting SPP.
3. Experimental implementations
The two grating structures are fabricated based on Lloyd’s interferometry lithography for patterning a photoresist [24] and inductively coupled plasma reactive ion etching (ICPRIE) for forming grating ridges. Figure 3 schematically illustrates the grating structure with the defined coordinate system and dimension parameters, including ridge width w, ridge height h, and GaZnO thickness d (d = 300 nm). The x-z and y-z incidence planes with incident angles θ and φ, respectively, are considered for reflection measurement. When light is incident in the x-z (y-z) plane, there are two possible polarizations, one is along the y- (x-) axis and the other lies in the x-z (y-z) plane. Figures 4(a) and 4(b) show the scanning electron microscopy (SEM) images of different magnifications for the grating structure of Λ1 = 750 nm. Figure 4(c) shows an atomic force microscopy (AFM) image (3 µm x 3 µm in dimension) of this grating. Figure 4(d) demonstrates a line-scan profile showing the grating ridge structure. Here, one can confirm that the grating period, Λ, is ∼750 nm. We can also estimate the ridge height, h, to give ∼140 nm and the ridge width, w, to be in the range of 220-250 nm. In Figs. 4(c) and 4(d), one can see a small groove near the center of a grating ridge. This small groove is caused by the thinner photoresist near the ridge center such that GaZnO is slightly etched here during the ICPRIE process. Figures 5(a)–5(d) show the results similar to Figs. 4(a)–4(d), respectively, for the grating structure of Λ2 = 1100 nm. Here, we can estimate the ridge height, h, to give ∼100 nm and the ridge width, w, to be in the range of 500-530 nm. As shown in Figs. 4(d) and 5(d), the geometry of grating ridge varies slightly from one to another. The non-uniform grating structure is caused by the non-uniformities of the laser beam used for forming interferometry, the thickness of the applied photoresist for patterning a grating, and the dry etching process for fabricating grating ridges. Such a non-uniformity in ridge geometry does not affect the excitation of SPP because the grating period is fixed. However, it can affect the LSP resonance wavelength. The LSP resonance feature becomes broadened and weakened.
Fig. 3. Schematic illustration of the GaZnO nano-grating structure and the definitions of structure parameters and coordinate system. The incident angle with respect to the z-axis is defined as θ (φ) in the x-z (y-z) incidence plane.
Fig. 4. (a) and (b): Plane-view SEM images of the GaZnO grating of Λ1 = 750 nm with two different magnifications. (c): AFM image (3 µm x 3 µm in size) of the GaZnO grating of Λ1 = 750 nm. (d): Line-scan profile of the AFM image in part (c).
Fig. 5. (a)-(d): Results similar to Figs. 4(a)–4(d), respectively, for the GaZnO grating of Λ2 = 1100 nm.
For monitoring the absorption of SP resonance, we collect the light of specular reflection from the top side of a grating structure. For comparison, in Figs. 6(a) and 6(b), we show the reflectance spectra of a GaZnO (denoted as GZO in the figures) thin-film sample (d = 300 nm) at various incident angles under the conditions of transverse-electric (TE) and transverse-magnetic (TM) polarizations, respectively. Under the TE-polarized condition, there is a reflectance depression between 1000 and 1200 nm at each incident angle. This feature is caused by the fact that the refractive index of GaZnO is around unity in this wavelength range such that most incident power can penetrate into the GaZnO layer and is more effectively absorbed by or transmitted through this layer. Under the TM-polarized condition, the reflectance spectra are essentially similar to those under the TE-polarized condition. However, the general reflectance level decreases with increasing incident angle. The reflection behavior at 60 degrees in incident angle is quite different from those of other incident angles. In the visible range, the reflectance is almost zero. The different behavior of reflectance at 60 degrees in incident angle is caused by the Brewster effect, with which the incident TM-polarized light can be totally transmitted. When the refractive index of GaZnO is 1.7, the Brewster angle is 59.5 degrees. Under either TE- or TM-polarized condition, the reflectance spectrum shows no clear depression in the spectral range beyond 1320 nm, in which SP resonance is expected to occur.
The reflection spectra of the GaZnO grating structure with period Λ1 = 750 nm under the TE- (TM-) polarized condition when light is incident in the x-z (y-z) plane are shown in Fig. 6(c) [6(d)]. Under either of these two incidence conditions, the incident polarization is along the grating ridge direction and hence no SP resonance can be excited. Therefore, the reflectance spectrum at each incident angle, θ (φ), in Fig. 6(c) [6(d)] is similar to the corresponding curve of the GaZnO thin-film sample in Fig. 6(a) [6(b)]. However, as shown in Fig. 7(a), when light is incident in the x-z-plane, under the TM- or x-z-polarized condition, under which a component (the x-component) of the incident polarization lies across the grating ridges, the reflectance spectra are quite different from the corresponding curves of thin-film GaZnO shown in Fig. 6(b). In particular, depressions can be observed beyond 1400 nm in all the cases of different incident angles. As indicated by the vertical thick arrows in Fig. 7(a), the wavelength of depression minimum increases with increasing incident angle from ∼1500 nm at θ = 5 degrees to ∼1620 nm at θ = 60 degrees. The reflection spectra of the GaZnO grating structure of Λ1 = 750 nm under the TE- or x-polarized condition when light is incident in the y-z plane are shown in Fig. 7(b). In this situation, as indicated by the vertical arrow, a reflection depression can be observed at each incident angle, φ, around 1500 nm, which is the same as the depression minimum wavelength at θ = 5 degrees in Fig. 7(a). The reflection depressions beyond 1400 nm in Figs. 7(a) and 7(b) correspond to the SP resonances in the GaZnO grating structure. However, it is unclear whether they correspond to SPP or LSP modes. In particular, in the case of Fig. 7(a), a wavevector component along the x-axis is provided by the incident light. Whether the reflection depressions correspond to possibly excited SPP modes needs to be carefully examined through simulation study.
Fig. 6. (a) and (b): Reflectance spectra of a GaZnO (GZO) thin-film structure (d = 300 nm) at various incident angles under the conditions of TE and TM polarizations, respectively. (c) [(d)]: Reflectance spectra of the GaZnO grating of Λ1 = 750 nm at different incident angles, θ (φ), under the TE- (TM-) polarized condition when light is incident in the x-z (y-z) plane.
Fig. 7. (a) [(b)]: Reflectance spectra of the GaZnO grating of Λ1 = 750 nm at different incident angles, θ (φ), under the TM- (TE-) polarized condition when light is incident in the x-z (y-z) plane. (c) and (d): Results similar to parts (a) and (b), respectively, for the GaZnO grating of Λ2 = 1100 nm. The vertical dashed lines indicate the wavelength of systematic perturbation caused by the change of grating set in the measurement system.
Figures 7(c) and 7(d) show the results similar to those in Figs. 7(a) and 7(b), respectively, for the grating structure of Λ2 = 1100 nm. In this case, the measurement spectrum is extended to the range of 300-2200 nm. Beyond 1900nm in wavelength, the signal becomes noisier because the light source intensity diminishes. The vertical dashed line in either Fig. 7(c) or 7(d) indicates the wavelength of systematic depressions at ∼1930nm. This perturbation is caused by the change of grating set in the measurement system. In spite of the perturbing depressions at ∼1930nm, reflection depressions corresponding to SP resonances can still be clearly identified in either Fig. 7(c) or 7(d). In Fig. 7(c), the wavelength of reflection depression minimum increases from ∼1610 nm at θ = 5 degrees to ∼2140 nm at θ = 60 degrees. In Fig. 7(d), the wavelength of reflection depression minimum is slightly shifted from ∼1610 nm at θ = 5 degrees to ∼1630 nm at θ = 45 degrees. At θ = 60 degrees, the depression is unclear. The identification of either SPP or LSP resonance for those depression features requires further studies with simulation.
4. Simulation method and results
To identify the possible SPP and LSP resonance behaviors observed in Figs. 7(a)–7(d), numerical simulation studies on the reflection behaviors from the grating structures are undertaken. For numerical computations, in the grating structure with Λ1 = 750 nm (Λ2 = 1100 nm), h = 140 nm and w = 220 nm (h = 100 nm and w = 500 nm) are chosen. The reflection behavior from a 300-nm GaZnO thin film is also evaluated for comparison. Three-dimensional simulations are conducted with the commercial software COMSOL, which is based on the finite-element scheme. In simulation, the computation domain is chosen to be a rectangular parallelepiped consisting of a lower half-space of sapphire, a middle layer of GaZnO (including the grating ridges) and an upper half-space of air (excluding the grating ridges). To simulate the grating structure, the size of the computation domain along the x-axis is set to be a grating period with the Bloch periodic boundary condition imposed at its two ends. The size of the computation domain along the y-axis (the grating ridge extension dimension) is chosen to be 300 nm also with the Bloch periodic boundary condition imposed at its two ends. The computation domain along the z-axis covers 650 nm in sapphire, the whole GaZnO layer including the ridge height, and 660 nm in air. For simulating the infinite extensions in the + z- and -z-direction, two perfectly matched layers (each of 200 nm in thickness) are placed at the top and bottom of the computation domain. To investigate the scattering behaviors of the GaZnO thin-film and grating structures, we launch a plane wave from the upper half-space of air in the x-z (y-z) plane at an incident angle θ (φ) with respect to the z-axis, as shown in Fig. 3. By using COMSOL, the incident plane-wave field is generated by an appropriate surface current in the air region and the total electromagnetic field is numerically calculated. Then, we can compute the reflected power in air, the power absorbed in the GaZnO region, and the transmitted power into the sapphire layer. The refractive index of the sapphire substrate is set at 1.75. The Drude model with the fitting parameters described above is used for the dielectric constant of the GaZnO layer.
Figures 8(a) and 8(b) show the simulation results of reflectance spectra under the conditions of TE- and TM-polarized incidences, respectively, from the air side of the GaZnO thin-film sample. The results are similar to the corresponding measurement data shown in Figs. 6(a) and 6(b). In particular, the reflectance depressions in the range of 1000-1200 nm are consistent between simulation and measurement results. It is noted that in the reflectance measurement, we collect the reflected light in a small cone along the specular direction. However, in simulation, we evaluate the upward-propagating power for the reflectance result, i.e., we actually integrate the scattered power in all directions in air. Therefore, although the simulation results can show the important features for comparing with the measurement data, the two sets of result cannot be exactly the same. Figure 8(c) shows the simulation results of reflectance spectra from the grating structure of Λ1 = 750 nm at different incident angles, θ, under the TM-polarized condition when light is incident in the x-z plane, corresponding to the experimental case shown in Fig. 7(a). Although the corresponding curves at the same incident angle are not exactly the same between Figs. 7(a) and 8(c), both show depressions at the wavelengths within the range of 1400-1700nm. In experiment, the wavelength of the depression minimum shifts monotonically from ∼1500 nm to ∼1620 nm when the incident angle increases from 5 to 60 degrees. In simulation, as the incident angle increases from 5 to 60 degrees, the wavelength of the depression minimum also shifts from ∼1500 nm to ∼1620 nm, as indicated by the vertical arrows. The depressions in the simulation results are deeper, when compared with the experimental data. This is so because the ridge geometry of the grating structure is not uniform such that the overall SP resonance becomes dispersive and hence weaker in experiment. However, in simulation, the ridge geometry is assumed to be uniform. Also, in simulation we assume a semi-ellipse ridge morphology, which can be different from the real grating structure. Figure 8(d) shows the simulation results of reflectance spectra from the GaZnO grating structure of Λ1 = 750 nm at different incident angles, φ, under the TE-polarized condition when light is incidence in the y-z plane, corresponding to the experimental case shown in Fig. 7(b). Here, one can see the depressions with the minimum wavelengths all around 1500 nm, as indicated by the vertical arrows. The results in Fig. 8(d) are similar to those in Fig. 7(b), again indicating the consistency between simulation and experiment.
Fig. 8. (a) and (b): Simulation results of reflectance spectra at different incident angles under the conditions of TE- and TM-polarized incidences, respectively, from the air side of the GaZnO thin-film structure, corresponding to the experimental results shown in Figs. 6(a) and 6(b), respectively. (c) [(d)]: Simulated reflectance spectra of the GaZnO grating of Λ1 = 750 nm at different incident angles, θ (φ), under the TM- (TE-) polarized incidence condition when light is incident in the x-z (y-z) plane, corresponding to the experimental results shown in Fig. 7(a) [7(b)].
Figures 9(a1)–9(a12) show the evolution of charge distribution on the surface of the GaZnO grating of Λ1 = 750 nm at the wavelength of 1500 nm under the TM-polarized excitation when light is incident in the x-z plane at the incident angle of θ = 5 degrees, corresponding to the case of the red curve in Fig. 8(c). This wavelength corresponds to the reflectance minimum indicated by the vertical red arrow in Fig. 8(c), i.e., the SP resonance peak under the aforementioned excitation condition. Parts (a1) through (a12) of Fig. 9 show the instantaneous charge distributions at the times t = jT/12 (j = 0-11), respectively, where T is the period of electromagnetic oscillation. The blue and red colors represent the opposite charges. The charge distributions shown in Figs. 9(a1)–9(a12) illustrate no clear propagation behavior and hence indicate that the SP resonance is essentially a quadrupole LSP feature with one grating ridge as a resonance unit. It is noted that the slight different phases in charge oscillation between the three successive ridges are caused by the phase retardation of oblique incidence. Similar to Figs. 9(a1)–9(a12), Figs. 9(b1)–9(b12) show the evolution of charge distribution on the surface of the same GaZnO grating at the wavelength of 1620 nm under the TM-polarized excitation when light is incident in the x-z plane at the incident angle of θ = 60 degrees, corresponding to the case of the violet curve in Fig. 8(c). Figures 9(b1)–9(b12) demonstrate the mixture of a rightward-propagating (along the + x direction) pattern and a local oscillation feature. The rightward-propagating pattern is caused by the incident and reflected waves. The local oscillation corresponds to an LSP resonance mode. If there is an SPP mode at point A shown in Fig. 2, we should see a leftward-propagating (along the -x direction) pattern in the charge oscillation of Figs. 9(b1)–9(b12). However, we cannot see such a pattern in Figs. 9(b1)–9(b12), indicating that it is difficult to excite such an SPP mode. Because the wavelength of 1620 nm is close to the turning point of the SPP dispersion curve (see Fig. 2), the lossy characteristics make the excitation of an SPP mode in this spectral range difficult. Therefore, the reflectance depression features within the wavelength range of 1400-1700nm in Figs. 7(a) and 8(c) are mainly caused by LSP resonances on grating ridges. When the incident angle increases, the projected ridge size becomes larger such that the LSP resonance wavelength becomes longer, as shown in Figs. 7(a) and 8(c). Such LSP resonance features can be excited as long as there is an incident polarization component along the x-axis, i.e., the direction across the grating ridges. When light is incident in the y-z plane, under the TE- or x-polarized excitation, LSP resonance can also be excited. In this situation, whatever the incident angle is, the projected grating ridge geometry is always the same as that of normal incidence (θ = φ = 0). Therefore, the LSP resonance wavelength is fixed and is almost the same as that in the case of θ = 5 degrees with light incidence in the x-z plane, i.e., ∼1500 nm in Fig. 7(a) and 8(c). Figures 10(a) and 10(b) show the distributions of electric field magnitude in the grating structure of Λ1 = 750 nm, corresponding to the cases in Figs. 9(a1)–9(a12) and 9(b1)–9(b12), respectively. By comparing Fig. 10(a) with 10(b), one can see that light can penetrate deeper into the GaZnO and sapphire layers at the shorter LSP resonance wavelength when the incident angle is smaller. Under the LSP resonance conditions, strong local resonance field distributions can be observed in the grating ridges.
Fig. 9. (a1)-(a12): Charge distributions on the surface of the GaZnO grating with Λ1 = 750 nm at the wavelength of 1500 nm under the TM-polarized excitation when light is incident in the x-z plane at the incident angle of θ = 5 degrees. Parts (a1) through (a12) show the instantaneous charge distributions at the times t = jT/12 (j = 0-11), respectively, where T is the period of electromagnetic oscillation. The blue and red colors represent the opposite charges. (b1)-(b12): Results of charge distributions on the surface of the GaZnO grating with Λ1 = 750 nm similar to parts (a1)-(a12) except that the resonance wavelength is 1620 nm and the incident angle is θ = 60 degrees.
Fig. 10. (a) and (b): Distributions of electric field magnitude in the grating structure of Λ1 = 750 nm, corresponding to the cases in Figs. 9(a1)–9(a12) and 9(b1)–9(b12) at the wavelengths of 1500 and 1620 nm, respectively. (c) and (d): Distributions of electric field magnitude in the grating structure of Λ2 = 1100 nm, corresponding to the cases in Figs. 12(a1)–12(a12) and 12(b1)–12(b12) at the wavelengths of 1610 and 2030nm, respectively.
Figures 11(a) and 11(b) show the results similar to Figs. 8(c) and 8(d), respectively, for the grating structure of Λ2 = 1100 nm. The simulation results in Figs. 11(a) and 11(b) are obtained by assuming d = 300 nm, h = 100 nm and w = 500 nm. They are to be compared with the experimental data in Figs. 7(c) and 7(d), respectively. As shown in Fig. 11(a), by increasing grating period, under the TM-polarized excitation with the x-z plane incidence, two reflection depressions can be observed in each incidence-angle case when the incident angle, θ, is larger than 15 degrees. The longer-wavelength depression significantly red shifts with increasing incident angle. The broad single depression in the case of 5 or 15 degrees in incident angle implies that it can be a merged feature consisting of two SP resonance modes. The simulation results in Fig. 11(a) are very similar to the experimental results in Fig. 7(c) although the shorter-wavelength feature at θ = 30, 45, or 60 degrees is unclear in the experimental result. In simulation, the depression minimum red shifts from ∼1610 nm at θ = 5 degrees to ∼2150 nm at θ = 60 degrees. This variation behavior is quite consistent with that of the experimental results (from ∼1610 to 2140 nm). The shorter- and longer-wavelength features in an incidence-angle case of two depressions correspond to an LSP and an SPP mode, respectively [25]. The feature in an incidence-angle case of single depression corresponds to the mixture behavior of an LSP and an SPP mode. As shown in Fig. 11(b), under the TE-polarized excitation with the y-z plane incidence, only one reflection depression with the minimum around 1610 nm can be observed in each incidence-angle case. These simulation results are again consistent with the experimental data shown in Fig. 7(d). Under this excitation condition, at any incident angle, there is always a polarization component crossing grating ridges for exciting the same SP resonance mode. In this situation, only LSP resonance can be excited because the incident wave does not provide a wavevector component along the x-axis.
Fig. 11. (a) and (b): Simulated results similar to those in Figs. 8(c) and 8(d), respectively, for the GaZnO grating of Λ2 = 1100 nm.
Figures 12(a1)-12(a12) show the time evolution of charge distribution, similar to those in Figs. 9(a1)–9(a12), respectively, for the grating of Λ2 = 1100 nm at 1610 nm under the TM-polarized excitation with θ = 5 degrees in the x-z incidence plane. These charge distributions show a complicated evolution pattern, including a local oscillation feature and other components. Such a behavior can be caused by the mixture of an LSP and an SPP mode. Figures 12(b1)-12(b12) show the time evolution of charge distribution, similar to those in Figs. 12(a1)–12(a12), respectively, at 2030nm under the TM-polarized excitation with θ = 45 degrees in the x-z incidence plane. Here, one can clearly observe a leftward-propagating (along the -x direction) charge-distribution pattern. Such a leftward-propagating behavior confirms that this SP resonance feature corresponds to an SPP mode, which is designated as point B in Fig. 2. Figures 10(c) and 10(d) show the distributions of electric field magnitude in the grating structure of Λ2 = 1100 nm, corresponding to the cases in Figs. 12(a1)–12(a12) and 12(b1)–12(b12), respectively. Compared to the similar results in Figs. 10(a) and 10(b), which correspond to LSP resonances, one can see that with SPP resonance, light does not much penetrate into grating ridges. Instead, the SPP energy is mainly distributed on the GaZnO surface. Light penetrates more into grating ridges in Fig. 10(c) because this resonance feature includes an LSP component.
Fig. 12. (a1)-(a12): Charge distributions on the surface of the GaZnO grating, similar to Figs. 9(a1)–9(a12), respectively, for the grating of Λ2 = 1100 nm at the wavelength of 1610 nm under the TM-polarized excitation when light is incident in the x-z plane at the incident angle of θ = 5 degrees. (b1)-(b12): Results of charge distributions on the surface of the GaZnO grating with Λ2 = 1100 nm, similar to parts (a1)-(a12) except that the resonance wavelength is 2030nm and the incident angle is θ = 45 degrees.
5. Discussions
Based on the measured dielectric constant of GaZnO and the fitted Drude model, in Fig. 13(a), we compare the real (with the left ordinate) and imaginary (with the right ordinate) parts of dielectric constants, i.e., ɛ’ and ɛ’’, respectively, of GaZnO with those of Au and Ag in the wavelength range of 1350-2200 nm. In this wavelength range, ɛ’ becomes negative in GaZnO. The dielectric constants of Au and Ag were obtained from experimental measurements [26]. In the concerned spectral range, the magnitude of either real or imaginary part of dielectric constant in GaZnO is significantly smaller than the corresponding value of Au or Ag. In particular, the smaller ɛ” of GaZnO indicates its significantly lower absorption, when compared with Au or Ag. From the data in Fig. 13(a), we can evaluate the propagation lengths and transverse penetration depths of SPPs excited at the air/GaZnO, air/Au, and air/Ag interfaces to give Figs. 13(b) and 13(c), respectively [27]. In Fig. 13(b), one can see that the SPP propagation length at the air/GaZnO interface is much smaller than those at the air/Au and air/Ag interfaces. In the concerned spectral range, the SPP propagation length in the GaZnO case is always shorter than 1 micron. In Fig. 13(c), the penetration depths on the air and material (GaZnO, Au, or Ag) sides are presented with the left and right ordinates, respectively. Although the penetration depth in GaZnO is significantly larger than those in Au and Ag, the penetration depth in air of the SPP excited at the air/GaZnO interface is much smaller than the corresponding value of the SPP excited at either air/Au or air/Ag interface. Therefore, the SPP at the air/GaZnO interface has a better energy confinement in the lateral dimension. However, its propagation length is much shorter, when compared with Au or Ag. Such a conclusion can be extended to the case of SPP at the interface between a dielectric and one of the three materials under comparison. Hence, depending on a particular application, GaZnO might not be a good choice in plasmonic waveguide application in the near-infrared range [28]. In this application aspect, the other issue deserving discussion is the spectral range of SPP excitation. As shown in the dispersion curves of Fig. 2, the experimental data in Figs. 7(a) and 7(c), and the simulation results in Figs. 8(c) and 11(a), it is difficult to excite an SPP mode when the operation point is close to the turning point of the dispersion curve. In other words, SPP can be well excited only when the operation wavelength is far above 1576 nm. Such an SPP mode might find applications in certain areas. However, the SPP excitation spectral range is inconsistent with the optical communication window of <1600 nm. The turning point of the dispersion curve can be shifted to a higher energy if the electron concentration of GaZnO can be further increased. However, the currently achieved concentration of ∼1 × 1021 cm−3 may have reached the limit in such a material. This issue may also limit the SPP application of GaZnO.
Fig. 13. (a): Real (with the left ordinate) and imaginary (with the right ordinate) parts of dielectric constants, i.e., ɛ’ and ɛ’’, respectively, of GaZnO, Au, and Ag. (b): SPP propagation lengths at the air/GaZnO, air/Au, and air/Ag interfaces. (c): Lateral penetration depths of SPP at the air/GaZnO, air/Au, and air/Ag interfaces on the air (with the left ordinate) and material (with the right ordinate) sides.
Regarding the enhanced-absorption application of GaZnO, SP can increase the material absorption around its resonance wavelength. Figures 14(a) and 14(b) show the absorption spectra of the GaZnO grating structure of Λ1 = 750 nm based on experiment and simulation, respectively, when the incident angle is 30 degrees. To obtain the experimental results, we use an integration sphere to collect all the scattered lights on the incident and transmitted sides of the sample for obtaining the reflected and transmitted power percentages, respectively. The absorbed power percentage or absorbance can be evaluated by subtracting the reflected and transmitted power percentages from unity. The four curves in either Fig. 14(a) or 14(b) correspond to the four different excitation conditions, including the TE and TM polarizations in the cases of the x-z and y-z incidence planes. Under the condition of TM (TE) polarization in the case of the x-z (y-z) incidence plane, SP resonance can be excited. In Fig. 14(a), by comparing either the two TM-polarized or the two TE-polarized curves, one can see that GaZnO absorption in the case with SP resonance extends to cover a longer-wavelength range, in which SP resonance occurs, and becomes stronger. Note that it is unreasonable to compare the absorption results of a grating structure with those of the GaZnO thin-film structure because the GaZnO volumes per unit planar area are different between the two structures. The corresponding simulation results shown in Fig. 14(b) are consistent with the experimental data although the simulated SP resonances are stronger due to the assumed uniform grating ridge geometry. Under the TM-polarized incidence condition, in either experimental or simulation result, absorption peaks within the range of 1250-1300 nm can be observed no matter whether SP resonance is excited. These absorption peaks are related to the reflection depressions in the same wavelength range shown in all cases, including the grating structures of two different periods and the thin-film structure, as demonstrated in Figs. 6(b), 6(d), 7(a), 7(c), 8(b), 8(c), and 11(a). This feature has nothing to do with SP resonance and can be caused by the change of the real part of GaZnO dielectric constant into the range of 0-1 in this wavelength range. This absorption feature represents another advantage of using GaZnO for enhancing absorption in the near-infrared range even though it has nothing to do with SP resonance. In particular, for a Si solar cell using a TCO as transparent conductor in the visible range, the enhanced sunlight absorption in the near-infrared range represents an extra benefit.
Fig. 14. (a): Experimental results of GaZnO absorption in the grating structure of Λ1 = 750 nm under the labelled four excitation conditions with the incident angle at 30 degrees. (b): Simulation results corresponding to the experimental data in part (a).
6. Conclusions
In summary, we have grown a GaZnO thin film of a high electron concentration with MBE and fabricated surface nano-gratings of two different grating periods. Depressions in the reflection spectra within the wavelength range between 1400 and 2200 nm were observed. Based on the ellipsometry measurement for obtaining the dielectric constant of GaZnO, we could plot the dispersion curve of the SPP at the air/GaZnO interface to design an appropriate grating period for exciting SPP. Also, based on the Drude model with its parameters obtained from the fitting to the measured dielectric constant, we performed numerical simulations on light scattering from such GaZnO grating structures for differentiating SPP from LSP features. These results brought us with the conclusion that below 1600 nm, it is difficult to excite SPP at an air/GaZnO interface due to its lossy nature. Although SPP can be excited beyond 1600 nm, its propagation length is much shorter than that at an air/Au or air/Ag interface although its lateral energy confinement is stronger. However, SP resonance on a GaZnO surface can significantly induce enhanced absorption in the near-infrared range for light harvest application.
Funding
Ministry of Science and Technology, Taiwan (MOST) (MOST 105-2221-E-002-159-MY3, MOST 106-2221-E-002-163-MY3, MOST 107-2221-E-002-152, MOST 107-2923-M-002-005-MY3); Air Force Office of Scientific Research (AFOSR) (AOARD-17IOA087).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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