Letter pubs.acs.org/NanoLett
Crystal Phase-Dependent Nanophotonic Resonances in InAs Nanowire Arrays Nicklas Anttu,*,†,‡ Sebastian Lehmann,†,‡ Kristian Storm,‡ Kimberly A. Dick,‡,§ Lars Samuelson,‡ Phillip M. Wu,*,‡ and Mats-Erik Pistol‡ ‡
Division of Solid State Physics and The Nanometer Structure Consortium (nmC@LU), Lund University, Box 118, S-22100 Lund, Sweden § Centre for Analysis and Synthesis Box 124, S-22100 Lund, Sweden, Lund University, Box 124, S-22100 Lund, Sweden S Supporting Information *
ABSTRACT: Nanostructures have many material, electronic, and optical properties that are not found in bulk systems and that are relevant for technological applications. For example, nanowires realized from III−V semiconductors can be grown into a wurtzite crystal structure. This crystal structure does not naturally exist in bulk where these materials form the zinc-blende counterpart. Being able to concomitantly grow these nanowires in the zinc-blende and/or wurtzite crystal structure provides an important degree of control for the design and optimization of optoelectronic applications based on these semiconductor nanostructures. However, the refractive indices of this new crystallographic phase have so far not been elucidated. This shortcoming makes it impossible to predict and utilize the full potential of these new nanostructured materials for optoelectronics applications: a careful design and optimization of optical resonances by tuning the nanostructure geometry is needed to achieve optimal performance. Here, we report and analyze striking differences in the optical response of nanophotonic resonances in wurtzite and zinc-blende InAs nanowire arrays. Specifically, through reflectance measurements we find that the resonance can be tuned down to λ ≈ 380 nm in wurtzite nanowires by decreasing the nanowire diameter. In stark contrast, a similar tuning to below λ ≈ 500 nm is not possible in the zinc-blende nanowires. Furthermore, we find that the wurtzite nanowires can absorb twice as strongly as the zinc-blende nanowires. We attribute these strikingly large differences in resonant behavior to large differences between the refractive indices of the two crystallographic phases realized in these nanostructures. We anticipate our findings to be relevant for other III−V materials as well as for all material systems that manifest polytypism. Taken together, our results demonstrate crystal phase engineering as a potentially new design dimension for optoelectronics applications. KEYWORDS: InAs nanowire array, nanophotonic resonance, zinc-blende, wurtzite
crystal phase in nanostructures made out of III−V semiconductor materials.13−21 This phase is not thermodynamically stable in the bulk-form of these materials under ambient conditions where only the zinc-blende structure exists.22−25 Because III−V semiconductor materials are highly relevant for optoelectronics applications, it is important to understand the optical response of this new phase and in particular to elucidate the refractive index of these nanostructured materials. However, while the zinc-blende phase of III−V nanostructures has been widely studied through, for example, ellipsometry,24 so far there
The classical linear optical response of a bulk material is described by its wavelength-dependent refractive index n(λ).1 However, the optical response in nanostructures also strongly depends on the nanostructure geometry and dimensions.1−11 This yields an additional, and attractive, level of control whereby the wavelength of optical resonances can be tuned by tailoring the size and shape of the nanostructures.2,5 Such strong light−matter interaction can be used, for example, for increasing the absorption and emission rates in nanostructured solar cells and light emitting diodes, respectively.3,12 An additional very interesting mechanism for controlling the optical properties of nanostructured materials is through engineering of crystallographic phases that are not accessible in the bulk. For example, it is possible to realize the wurtzite © XXXX American Chemical Society
Received: June 19, 2014 Revised: August 8, 2014
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Figure 1. Crystal phase-dependent optical response of wurtzite and zinc-blende nanowire arrays with nanowires of similar dimensions. SEM images of (a) zinc-blende InAs nanowire arrays with nanowires of diameter D = 73 ± 4 nm and length L = 1940 ± 270 nm; (b) wurtzite InAs nanowire arrays with D = 73 ± 2 nm and L = 2160 ± 60 nm; and corresponding high-resolution TEM images demonstrating the characteristic bilayer stacking sequences for (c) zinc-blende and (d) wurtzite. The period for both square arrays is p = 500 nm, so the area coverage of nanowires in both arrays is π[(D/2)/p]2 = 1.7%. (e) Schematic illustration of how light interacts with the nanowire arrays. In dilute arrays, as we have here, the reflectance spectrum is complementary to the round-trip absorption in the nanowires of the light reflected at the interface between the nanowire array and the substrate. (f) Measured reflectance spectra for both arrays (bottom), from which the absorptance in the nanowires (top) was extracted (see Methods and ref 33). For short wavelengths (96% for all the arrays studied (Figure 1c−d and Supporting Information Figures S2 and S3), demonstrating our control over the crystal phase. To study the crystal phase-dependent optical response of the wurtzite and zinc-blende InAs nanowires, we measured the reflectance, R, of each nanowire array for wavelengths in the range of 400 < λ < 850 nm (see Methods for details). We chose InAs for this model study because its small zinc-blende phase band gap (0.34 eV)23 enables sensitive detection of light absorption by the nanowires in the visible wavelength range. Furthermore, we designed our arrays to have less than 5% area coverage so that incident light would be absorbed by the individual nanowires during the round-trip that the light makes upon reflection from the interface between the nanowire array and the substrate (Figure 1e).31−33 This enables us to extract the absorptance A of the nanowires from the measured reflectance spectrum and isolate it from the absorption that occurs in the thick, opaque substrate (see Methods and ref 33). Comparison of the optical response of zinc-blende and wurtzite arrays (Figure 1f) with nearly identical dimensions reveal striking differences (see Figure 1a−d for SEM and TEM images of these nanowires of approximately 73 nm in diameter and 2000 nm in length). The wurtzite nanowire array shows a clear dip in the reflectance at λ = 469 nm and a complementary peak of A = 0.94 in the absorptance, typical for resonant
have been no experiments to study and understand the classical linear optical response of the recently emerging wurtzite III−V materials. Here we use crystal phase-engineered InAs nanowire arrays as a model system to compare the optical response between the wurtzite and zinc-blende phase of III−V materials in a broad wavelength range. To this end we fabricated zinc-blende and wurtzite arrays with nanowires of similar dimensions and demonstrate, using reflectance measurements, a strongly crystal phase-dependent optical response where the possibility to excite optical resonances depends on the crystal phase. Our results open a new avenue for tailoring the interaction of light with matter and thus demonstrate that nanostructures hold much more promise for photonics than predicted before. To compare the optical response of zinc-blende and wurtzite nanostructures, we grew arrays of zinc-blende and wurtzite InAs nanowires on zinc-blende InAs substrates (see Methods and refs 16 and 17 for details of the growth). Because the wavelength at which an optical resonance forms in nanowires depends mainly on their diameter (Supporting Information Figure S1),26−30 we controlled and set the diameter, D, of the nanowires in each of the arrays to a constant value and varied this diameter in the different arrays in the range of 30−115 nm (Supporting Information Table S1). To verify the dimensions and the crystal phase of the fabricated nanowires, we used scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The results of our microscopy analysis reveal that we succeeded to B
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Figure 2. Diameter dependence of absorption peaks in wurtzite and zinc-blende InAs nanowire arrays. Absorptance spectra of (a) zinc-blende and (b) wurtzite InAs nanowire arrays with varying nanowire diameters. All arrays have a period of p = 500 nm, and the diameters are shown in the legend. The inset shows short wavelength spectra for four arrays with D = 31 ± 2, 40 ± 2, 46 ± 2, and 57 ± 2 nm measured with an ultraviolet setup (see Methods). Both wurtzite and zinc-blende arrays show an absorption resonance in the form of a peak of A for the largest diameters, and the wavelength position of the resonance blue-shifts with deceasing diameter. However, strikingly, the resonance stops at approximately 500 nm for the zinc-blende arrays, whereas it continues to shift down to 380 nm for the wurtzite arrays. Thus, we find a strong crystal-phase dependence for the excitation of the nanophotonic resonance in the nanowires. Please note that the length of the nanowires is constant within each array and varies from 1 to 5 μm among the arrays (see Supporting Information Table S1), whereas the resonance wavelength is determined predominantly by the nanowire diameter (see Supporting Information Figure S7).
Figure 3. Refractive index of wurtzite and zinc-blende InAs and consequent optical resonances in nanowires. (a) Real part and (b) imaginary part of the refractive indices for wurtzite InAs and zinc-blende InAs. Note that the representative refractive index of wurtzite InAs (blue squares) is extracted through full three-dimensional electromagnetic modeling from measured spectra, whereas the refractive index of zinc-blende InAs is taken from wellknown, tabulated values.24 The dashed lines are inserted to guide the eye. (c) Modeled electric field |E|2 in the x−z cross-section for x-polarized normally incident light with |Einc|2 = 1 and λ = 469 nm, performed with Comsol Multiphysics. Here, six wurtzite nanowires of D = 73 nm and L = 2160 nm are shown, placed in a periodic array of 500 nm in period. For the nanowire material, the extracted refractive index n(λ = 469 nm) = 4.50 + i0.93 was used (see panels a and b ), whereas for the substrate the tabulated24 refractive index of zinc-blende InAs is used. (d) Same as that in panel c, but for zinc-blende nanowires of L = 1940 nm. Because of a nanophotonic resonance in the wurtzite nanowires, light is coupled more efficiently into the wurtzite nanowires, as evident from the much higher |E|2 values at the tip of the nanowires in panel c as compared to that in panel d. This funneling leads to a stronger absorption in the wurtzite nanowires than in the zinc-blende counterparts, as evident from the much faster decay of |E|2 along the nanowire axis in panel c as compared to that in panel d.
behavior.26−30 In strong contrast, the zinc-blende nanowire array has a flat, nonresonant response in both R and A for λ < 500 nm, with A = 0.72 at λ = 469 nm. Furthermore, the
effective absorption coefficient for the wurtzite nanowire array at λ = 469 nm, as extracted from the measured reflectance spectrum (see Methods), is αeff = 1.1 × 10−6 m−1, whereas that C
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of the zinc-blende nanowire array is αeff = 0.49 × 10−6 m−1. Thus, at λ = 469 nm, the wurtzite InAs nanowires absorb more than twice as strongly per volume semiconductor material as the zinc-blende InAs nanowires. To further elucidate the differences in the optical response between the two crystal phases, we studied the diameter dependence of the absorptance spectra (Figure 2a,b). We found that both wurtzite and zinc-blende arrays show an absorptance peak for the largest nanowire diameters that shifts to shorter wavelengths with decreasing diameter (Figure 2a,b) as typically expected for diameter-dependent nanophotonic resonances.26−30 For the wurtzite arrays this shift occurs throughout our measurement range to λ < 400 nm (Figure 2b). However, in strong contrast the absorptance peak of the zinc-blende arrays does not shift to wavelengths below λ = 500 nm (Figure 2a). Additional measurements of the wurtzite nanowire arrays in the ultraviolet regime (see Methods) revealed that the absorptance peak for the wurtzite arrays also stops shifting toward shorter wavelengths for decreasing diameters (inset in Figure 2b). However, this “stop” occurs at a considerably shorter wavelength (λ ≈ 380 nm) than what is observed for the zinc-blende arrays. Thus, the possibility to excite nanophotonic resonances in the nanowires depends strongly on the crystal phase in an unexpectedly large wavelength range covering 120 nm in wavelength (0.8 eV in photon energy). To gain a deeper understanding of the origin of the different optical response of the wurtzite and zinc-blende nanowire arrays, we extracted a representative isotropic refractive index n(λ) in the wavelength range 400−550 nm for the wurtzite InAs nanowires. These values were extracted from the measured spectra with detailed three-dimensional electromagnetic modeling (see Methods) and compared to the wellknown tabulated24 values for zinc-blende InAs (Figure 3a,b). Most strikingly, Re(n) of wurtzite InAs increases with decreasing λ for λ < 500 nm, whereas Re(n) of zinc-blende InAs shows a contrary behavior in the same wavelength range (Figure 3a). This is an important finding because the common expectation is that optical resonances shift to shorter wavelengths with decreasing diameter.26−30 However, this simple assumption is strictly true only if the refractive indices of the constituent materials are wavelength-independent. Notably, for the zinc-blende nanowires the “stop” of the peakshift at λ = 500 nm occurs when Re(n) changes character from increasing to decreasing with decreasing wavelength (see Supporting Information section 2 for technical details of why this type of a change could stop the shifting). Regarding the absorption of light, we note that Im(n) for zinc-blende InAs is larger than that extracted for wurtzite InAs in the entire wavelength range we probed (Figure 3a,b). Because the absorption coefficient of a bulk material is proportional to Im(n), one might expect that zinc-blende InAs nanowires should absorb stronger than wurtzite InAs nanowires for equal dimensions in our experiments. However, the resulting absorption is additionally proportional to the electric field strength inside the nanowires.5 Because the electric field strength can be high at an optical resonance in nanostructures,5 these resonances can strongly increase the absorptance. In other words, for λ < 500 nm, light does not couple as efficiently into small-diameter zinc-blende InAs nanowires as it does when coupling resonantly into small-diameter wurtzite InAs nanowires. To further substantiate this interpretation, we simulated the electric field distribution (Figure 3d,e) for the
investigated wurtzite and zinc-blende arrays of D = 73 nm and L ≈ 2000 at λ = 469 nm where the wurtzite array shows the resonance in the measurements (Figure 1f). The results of our simulations show a larger electric field strength at the tip of the wurtzite nanowires and a much faster decay of the light intensity along the nanowire axis compared to the zinc-blende array. We assign these differences to the excitation of the nanophotonic resonance in the wurtzite nanowires. This explains why the wurtzite array absorbs here much stronger than the zinc-blende array even though the Im(n) is larger for zinc-blende InAs. In other words, because of the excitation of the nanophotonic resonance in the wurtzite nanowires, light is funneled into the wurtzite nanowires much more efficiently than into the zinc-blende nanowires. Consequently, the light is absorbed stronger in the wurtzite nanowires, explaining the factor of two difference in the experimentally determined αeff values above. Thus, the different resonant optical behavior in wurtzite and zinc-blende nanowire arrays (Figure 2a,b) originates from differences in the bulk refractive index of the nanowire material (Figure 3a,b), which has not been measured previously for wurtzite InAs. However, theoretical values for the refractive index of wurtzite InAs have been calculated from the predicted electronic band structure of wurtzite InAs.34 We simulated the optical response for wurtzite InAs nanowire arrays using these values, and indeed, we find a “stop” of the shift of the absorptance peak at λ = 430 nm with decreasing diameter of the nanowires, while similar modeling for the zinc-blende nanowire arrays shows the “stop” at λ = 495 nm (Supporting Information Figure S4). Because of this qualitative agreement between our simulated and measured values (λ = 495 nm vs λ = 500 nm for zinc-blende and λ = 430 nm vs λ = 380 nm for wurtzite), we attribute the different resonant optical response of wurtzite vs zinc-blende InAs to the different electronic band structure of wurtzite vs zinc-blende InAs. This behavior is of general nature since we expect changes in the band structure whenever varying the crystal phase for III−V semiconductors35,36 leading consequently to differences in the refractive index and resonant optical behavior as clearly demonstrated here for InAs (Figures 2a,b and 3a,b). In summary, we anticipate that the crystal phase-dependent nanophotonic resonances that we report here for InAs nanowire arrays are general for III−V nanostructured materials, as well as for other material systems that manifest polytypism. Therefore, our study paves the way for a new way of strongly controlling light−matter interaction. Such control could find immediate applications, for example, in photovoltaic and photodetection applications where the utilization of resonances is one of the most promising directions for enhancing the absorption of light.37 Methods. Nanowire Growth. InAs nanowires were grown at 460 °C by metal−organic vapor phase epitaxy (MOVPE) in an AIXTRON 200/4 reactor following the particle-assisted growth mode starting from electron beam lithographically predefined square patterns of Au particles with a 500 nm period on [1̅1̅1̅]-oriented InAs substrates. Trimethylindium with molar fraction χTMIn = 5.15 × 10−6 and arsine with χAsH3 = 1.54−15.4 × 10−5 for wurtzite and 1.54−3.08 × 10−3 for zinc-blende nanowires, respectively, were applied at a total reactor flow of 13 slm and a reactor pressure of 100 mbar. The length of the nanowires was constant within each array and varied in the D
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range of 1−6 μm for the different arrays (Supporting Information Table S1). SEM and TEM Characterization. SEM characterization was carried out in a ZEISS Leo Gemini 1560 setup. The nanowire dimensions and their standard deviations were determined by analyzing approximately 70 nanowires for each array from SEM images by the NanoDim software [http://www.nanodim.net/]. For structural TEM characterization, the nanowires were selectively removed from individual arrays and placed on copper grids covered with a lacey carbon layer and investigated in a JEOL-3000F setup. The nanowires showed a hexagonal cross-section. Each reported diameter corresponds to that of a circular cross-section of equal area as that of the measured hexagonal cross-section. Optical Reflectance Measurements. Reflectance spectra were measured with an optical probe (Filmetrics F40) attached to a Zeiss optical microscope, with the light normally incident onto the sample through a 5× objective of numerical aperture of NA = 0.13. The reflected light was collected from a spot of an area of 100 μm × 100 μm (well within each nanowire array of 150 μm × 150 μm in area) through the same objective. Note that the NA = 0.13 corresponds to light incident and collected close to normal angle. The background and the baseline calibrations were performed with a Si reference substrate. Note that the inset in Figure 2b shows short-wavelength spectra measured with an ultraviolet setup with NA = 0.28. Extraction of Absorptance of Nanowires from Measured Reflectance. The reflectance of the sample under the dual-pass assumption (Figure 1e) is given by R ≈ Rsub exp(−2αeffL). Here, Rsub is the reflectance at the substrate interface and αeff is an effective absorption coefficient of the nanowire array.33 Furthermore, for a dilute nanowire array the nanowires do not modify strongly the reflection at the substrate interface from that of a planar, bare substrate.33 Thus, Rsub(λ) ≈ (|nInAs(λ) − 1|2)/(|nInAs(λ) + 1|2) for which we can use tabulated values24 of the nInAs(λ) for the zinc-blende InAs substrate. Hence, from the measured reflectance spectrum R, we can extract the effective absorption coefficient αeff of the nanowire array. Furthermore, since T ≈ (1 − Rsub) exp(−αeffL), we can extract also the absorptance spectrum A = 1 − R − T of the nanowires by just measuring the reflectance spectrum R.33 Notice that this approximation works very well when the nanowires cover 2% of the substrate surface (Supporting Information Figure S5). Furthermore, most of the reflected intensity is expected to end up in the specularly reflected diffracted order, which is collected by our optics (Supporting Information Figure S5). Extraction of a Representative Refractive Index for Wurtzite InAs. For each fabricated wurtzite array that showed an absorptance peak in the experiments with NA = 0.13, first, a wavelength-independent representative isotropic Re(n) for the nanowire material was varied in three-dimensional electromagnetic modeling (see below) until measured and modeled λpeak coincided, yielding the value of Re[n(λpeak)] (blue squares in Figure 3b, one per array). In this step, we used Im(n) = 0.1 and L = 1000 nm, but these specific choices do not affect strongly the extracted Re[n(λpeak)] (Supporting Information Figures S6 and S7). Next, by using the extracted Re[n(λpeak)], Im[n(λpeak)] was determined by identifying, for each array, the Im(n) that gave the best agreement between measured and modeled R(λpeak). Here, the Maxwell equations were solved with a scattering matrix method.38 Each modeled nanowire array consisted of nanowires with length L and a circular crosssection of diameter D on top of an optically infinitely thick
zinc-blende InAs substrate. The nanowires were placed in a square array with period p = 500 nm in both directions.39 Tabulated values of the refractive index n were used for the zinc-blende InAs substrate.24 For the air between and on top of the nanowires, the value of n = 1 was used. Because of the small half angle of the incidence cone in the measurements (7.5° for the NA = 0.13), the incident light of a given wavelength was modeled as a plane wave incident from the top (air) side at normal angle to the array/substrate, and only the specular reflectance was taken into account when modeling the collection of light in the experiments. Notice that this extraction works well for the zinc-blende InAs nanowires for which we can compare the extracted values with the well-known tabulated values of the refractive index of zinc-blende InAs (Supporting Information Figure S8).
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ASSOCIATED CONTENT
S Supporting Information *
Geometrical dimension of all studied nanowire arrays, additional SEM and TEM images, and additional details on wavelength position of resonant peaks. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*(N.A.) E-mail:
[email protected]. *(P.M.W.) E-mail:
[email protected]. Author Contributions †
(N.A. and S.L.) These authors contributed equally to this work. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), the Nanometer Structure Consortium at Lund University (nmC@LU), and the Knut and Alice Wallenberg Foundation. S.L. gratefully acknowledges the support by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD).
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REFERENCES
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