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The ability to tune the photon absorptance spectrum is an attracting way of tailoring the response of devices like photodetectors and solar cells. Here, we measure the reflectance spectra of InP substrates patterned with arrays of vertically standing InP nanowires. Using the reflectance spectra, we calculate and analyze the corresponding absorptance spectra of the nanowires. We show that we can tune absorption resonances for the nanowire arrays into the ultraviolet by decreasing the diameter of the nanowires. When we compare our measurements with electromagnetic modeling, we generally find good agreement. Interestingly, the remaining differences between modeled and measured spectra are attributed to a crystal-phase dependence in the refractive index of InP. Specifically, we find indication of significant differences in the refractive index between the modeled zinc-blende InP nanowires and the measured wurtzite InP nanowires in the ultraviolet. We believe that such crystal-phase dependent differences in the refractive index affect the possibility to excite optical resonances in the large wavelength range of 345 < λ < 390 nm. To support this claim, we investigated how resonances in nanostructures can be shifted in wavelength by geometrical tuning. We find that dispersion in the refractive index can dominate over geometrical tuning and stop the possibility for such shifting. Our results open the door for using crystal-phase engineering to optimize the absorption in InP nanowire-based solar cells and photodetectors.
© 2014 Optical Society of America
1. Introduction
Low-cost semiconductor nanowire structures are an attractive prospect for further miniaturization and mass production of nano-optical devices [1]. Recently, semiconductor nanowires have stimulated great interest for new functionalities in for example photodetectors [2,3], solar cells [4–10], light-emitting diodes [11], and lasers [12–14].
Currently, there is a large interest for optimizing the light-matter interaction in nanowire arrays by varying the geometrical dimensions of the nanowires [5,6,8–10,15–23]. The ability to control the growth and to tune the dimensions of these nanoscale structures represents a significant step toward optimized opto-electronics applications. There, an efficient coupling of light into the semiconductor and a minimization of the reflection over a broad range of wavelengths and angles of incidence is often desired [11,24]. For example, a reduction of the reflection can increase the sensitivity of photodetectors [15–17] as well as increase the efficiency of solar cells [4,17,22]. Understanding the reflection properties can also be used to improve the out-coupling of light from light-emitting diodes [11].
Furthermore, nanowire arrays show absorption resonances whose wavelength position can be tuned by varying the diameter of the nanowires. Specifically, it is the HE11 waveguide mode in individual nanowires that gives rise to the absorption peak observed at the longest wavelength [5,15,16]. Here, we show that the absorption resonances in InP nanowire arrays can be tuned into the ultraviolet (UV) wavelength range by decreasing the nanowire diameter. We chose InP nanowires since InP is a direct band gap material with a band gap energy of Eg = 1.34 eV (corresponding to 925 nm in wavelength). InP is thus suitable for photovoltaic applications due to the good matching of the band gap with the solar spectrum [4] as well as for photodetectors in the visible and the ultraviolet. We note that the absorption in InP nanowire arrays has been measured previously in the visible wavelength range [22].
Here, we extend the analysis of the absorption in InP nanowire arrays to the UV region by extracting absorptance spectra from measured reflectance spectra [18]. Furthermore, we have simulated the absorption in the nanowire arrays using a three-dimensional scattering matrix method [25], and we compare the theoretical results with the experimental data. We find in general very good agreement between modeling and experiments, showing that modeling can be used as an efficient guide also for designing nanowire-based opto-electronic devices aimed for the UV range [26–33]. Interestingly, the remaining differences between modeled and measured spectra indicate significant differences in the dielectric function between the modeled zinc-blende and the measured wurtzite InP nanowires in the ultraviolet. To support this claim, we investigated how resonances in nanostructures can be shifted in wavelength by geometrical tuning. We find that dispersion in the refractive index can dominate over the geometrical tuning and stop the possibility for such shifting.
In the coming sections the paper is organized as follows. Section 2 describes the experimental and theoretical approach to investigate the reflection and the absorption behavior of InP nanowires. In Section 3, we experimentally and theoretically show and discuss the effect of the geometrical dimensions on the reflectance and the absorptance spectrum of InP nanowires. Finally, in section 4, we conclude our findings.
2. Materials and methods
We fabricated arrays of vertically standing InP nanowires on InP (111)B substrates with a fixed period (P) of 500 nm but varying average nanowire diameter (D) and length (L) from array to array. The nanowires were fabricated by Au-particle-catalyzed metal-organic vapor phase epitaxy (MOVPE) following the vapor-liquid-solid growth mechanism [34]. The nanowire diameter was controlled by varying the size of the Au particles defined by electron beam lithography. The nanowire length was in turn controlled by varying the growth time. Figure 1(a) shows a scanning electron microscopy (SEM) image of an array of nanowires with a diameter of approximately 50 nm and a length of about 2200 nm. All nanowire dimensions quoted in this work were determined by measuring approximately 100 nanowires for each sample with the NanoDim software [35]. We further note that the investigated nanowires were controllably grown in the wurtzite crystal structure by using H2S [36].
Fig. 1 (a) 15° tilted SEM top view image of a periodic InP nanowire array fabricated by metal-organic vapor phase epitaxy. (b) Schematics of a vertical nanowire array with period (P) and nanowires of diameter (D) and length (L) together with indicated interaction of the light with a nanowire array. Here, light is incident from the top, and part of the incident light is absorbed in the nanowires. Note that in the analysis in this work, we assume that the reflection occurring at the top air-superstrate/nanowire interface is negligible since the nanowires cover only a small fraction of the substrate surface. Instead, we assume that only the reflection from the bottom nanowire/substrate interface contributes to the total reflectance (R) [18]. Thus, the reflected light makes a double pass through the nanowire array where it is partially absorbed by the nanowires.
For the optical experiments, we used a Filmetrics thin-film analyzer to measure the reflectance of the nanowire arrays [16]. The measurements were performed in the wavelength range of 200 nm to 1100 nm. The light was normally incident toward the sample and focused through an objective with a numerical aperture (NA) of 0.28. The reflected light was collected with the same objective. In order to get access to the absorptance spectrum of the nanowire array, we used an approximation [18, 37] to extract the absorptance from measured reflectance spectra. In this approximation, we assume that light is reflected at the interface between the nanowire array and the substrate and that the light is partially absorbed during the dual-pass through the nanowire array [see Fig. 1(b) for a schematic]. This absorption decreases the reflectance of the nanowire array sample (R) from the value of Rsub (the reflectance of the corresponding planar substrate). In general, the absorptance of the nanowires is given by
where T is the transmittance into the substrate. Under the above dual-pass approximation, we havewhere we use measured values for a planar substrate for Rsub. Thus, by measuring R and Rsub, we can obtain values for both T and A. We notice that in this approximation, surface roughness or anti-reflection properties of the nanowires, which could enhance the coupling of light into the substrate and therefore decrease Rsub from that of a planar substrate, would be observed as an increase in A [18]. However, we could not observe any surface roughness in SEM images, and the nanowires cover less than 3% of the substrate surface. Therefore, we do not expect a noticeable decrease of Rsub from that of a planar substrate. Thus, we expect that the A calculated through Eq. (2) gives a good approximation for the absorption in the nanowires.To theoretically analyze the optical response of the nanowire array, we solved Maxwell’s equations using a scattering matrix method (SMM) [25]. The Maxwell’s equations describe the propagation and scattering of light. Therefore, in this way, we take fully into account the diffraction of light by the nanowires, by using for the nanowires and the substrate the wave-length dependent refractive index of InP. The three geometrical parameters used in the model are the period of the nanowire array (P) as well as the diameter (D) and the length (L) of each nanowire in the array. Here, we consider light normally incident toward the nanowire array from the top side. For the refractive index of the InP, we use tabulated values [38]. Note that since the refractive index for the fabricated wurtzite InP nanowires is not known, we use the well-known values for zinc-blende InP in the modeling for both the nanowires and the substrate. Furthermore, photoluminescence experiments show that there are no observable strain effects on the band edge energies for nanowires of similar diameters as our nanowires [39]. Also, the considered diameters are sufficiently large so that there are no noticeable electronic confinement effects. Therefore, we believe that the bulk refractive index of InP describes the optical response of the nanowire material well.
With this modeling method, we can calculate both R and T of the nanowire array. Thus, we can calculate the modeled absorptance through Eq. (1), that is, by A = 1 – R – T (which we denote as the modeled absorptance). Furthermore, to check the validity of the dual-pass approximation used for extracting A in the experiments, we can calculate from the modeled R and Rsub a corresponding extracted absorptance from the modeling through Eqs. (1) and (2).
3. Results and discussion
Experimentally, we have studied the effect of varying the geometrical parameters of the InP nanowire arrays on their optical response. In the first experiment we use a nominally fixed length of the nanowires (L ≈1.9-2.4 µm) and vary their diameter (D) from 50(1) nm to 84(2) nm for the fixed period of 500 nm [see Fig. 2(a) for the absorptance spectra and Fig. 2(b) for the reflectance spectra]. Here, the number in the parenthesis denotes the standard deviation in the measured dimensions. We find a distinct peak in the absorptance [Fig. 2(a)]. We attribute this peak to resonant absorption through the HE11 waveguide mode. This mode shows up at the longest wavelength among the waveguide modes of a nanowire [17], and we denote therefore this peak as the long-wavelength absorption peak and indicate it by the curved arrow in Fig. 2(a). We observe that this peak shifts towards shorter wavelengths (higher photon energies) when the diameter of the nanowires decreases. For D ≈50 nm, the absorption peak is in the UV range (λ ≤ 400 nm), i.e. suitable for UV-sensitive detectors.
Fig. 2 (a) Extracted absorptance and (b) measured reflectance spectra of InP nanowire arrays for a fixed length (L ≈ 1.9-2.4 µm) and different diameters of the nanowires. (c) Wavelength position of the long-wavelength absorption peak of InP nanowire arrays as a function of diameter and length.
We have studied in total 80 different InP nanowire arrays with lengths in the range of 1.1-1.3 µm, 1.9-2.4 µm, and 2.9-3.7 µm and diameters ranging from 32(2) nm to 84(2) nm. Notably, we find that we can tune the wavelength position of the long-wavelength absorption peak from 460 nm to 340 nm by decreasing the nanowire diameter from 80 nm to 40 nm [Fig. 2(c)]. Due to this strong tunability, we focus on this peak in the following. We note that decreasing the diameter of the nanowires results in a weaker absorption at the wavelength of this peak (approximately 70% for D ≈50 nm and 95% for D ≈84 nm) [Fig. 2(a)]. This decrease could for example originate from the decreasing amount of absorbing InP material in the nanowires with decreasing diameter.
In contrast to the strong diameter dependence, no clear dependence of the wavelength position of the long-wavelength absorption peak on the length of the nanowires could be observed [Fig. 2(c)]. In Fig. 3, we show the absorptance and reflectance spectra for different values of L in more detail. The length of the nanowires was varied from 1.1-1.3 µm to 2.9-3.7 µm for a fixed diameter of D ≈80 nm. For increasing L, we find that the peaks in the absorptance broaden and become less pronounced. At the same time, the absorptance increases at all wavelengths. We see also from these spectra that the position of the absorption peak does not depend noticeably on the length of the nanowires. Furthermore, the average value of reflectance for λ < 500 nm is 7.6% for L ≈1.1-1.3 µm. This value drops to less than 1% for the length of 2.9-3.7 µm due to increased absorption in the nanowires, which decreases the amount of light that can contribute to the measured reflectance after the reflection at the nanowire/substrate interface [see Fig. 1(b)].
Fig. 3 (a) Extracted absorptance as determined from measured reflectance spectra of InP nanowire arrays shown in (b) for a fixed diameter (D ≈80 nm) and different lengths (L).
In Figs. 4(a) and 4(b), we compare the modeled and the extracted absorptance spectra for varying diameters. The lengths of the nanowires are in the range of 1.1 to 1.3 µm and the diameters vary from 82(2) nm to 32(2) nm. First, regarding modeled spectra, we find good agreement between the modeled absorptance and the absorptance extracted under the dual-pass assumption in the modeling [Fig. 4(a)]. This good agreement highlights the validity of the dual-pass approximation, that is, Eqs. (1) and (2), used for extracting the absorptance in the experiments [Fig. 4(b)]. Next, the modeling results confirm the experimental observations that the absorption resonances in these InP nanowire arrays are blue-shifted into the UV region when decreasing the diameter of the nanowires. We note that the best agreement between modeling and experiments is achieved for larger diameter nanowires, with poorer agreement for smaller diameter nanowires. Specifically, the long-wavelength absorption peak becomes weak and stops blue-shifting with decreasing diameter in the modeling, showing a limiting wavelength of 390 nm [Fig. 4(c)]. In the experiments, this long-wavelength peak continues to shift to a wavelength of 345 nm for the smallest diameters where the peak value decreases for diameters less than 40 nm [Fig. 2(c) and Fig. 4(c)]. We believe that this difference arises from the fact that we measured on wurtzite InP nanowires and modeled for zinc-blende InP nanowires.
Fig. 4 (a) Absorptance spectra in nanowire arrays obtained by modeling. Here, red shows modeled absorptance spectra and black depicts absorptance spectra obtained from modeled reflectance spectra under the dual-pass approximation where light is reflected at the nanowire/substrate interface and partially absorbed in the nanowires (see Fig. 1(b)). (b) Measured absorptance spectra as a function of nanowire diameter. The spectra in (a) and (b) have been shifted vertically for clarity. The spectrum for the largest diameter (D/L = 82/1100 nm) is not shifted and each following spectrum is shifted down by an absolute value of 15%. (c) Wavelength position of the main peak (the long-wavelength absorption peak) as a function of nanowire diameter.
Notice that the wavelength-position of a diameter-dependent resonance in nanowires is expected intuitively to shift linearly with diameter according to λpeak = bD where b is a constant. Thus, we would not expect from this relation a stop in the blue-shifting of the resonance with decreasing diameter, but such a stop is observed here [Fig. 4(c)]. However, it is actually the optical path length that is kept constant after the rescaling of the geometrical dimension, and the optical path length depends also on the wavelength-dependent refractive index. Thus, the resonance-peak wavelength should scale according to λpeak = cRe[n(λpeak)]D where c is a constant. From the modeled λpeak and D [Fig. 4(a)] together with n(λ) for the zinc-blende InP nanowires [Fig. 5(a)] it is possible to get values for c. We extract c = 1.41 for D > 60 nm, which yields λpeak in a region where the stop of the blue-shifting of the peak has not yet happened. Now that we have a value for c, we can calculate λpeak(D) for zinc-blende InP [Fig. 5(b)]. Here, we find that the peak wavelength blue-shifts with decreasing wavelength for large diameters. However, we notice that the blue-shifting of the peak stops [solid line in Fig. 5(b)] when n(λ) changes character from increasing to decreasing with decreasing wavelength at λ ≈400 nm [Fig. 5(a)]. Instead, the dispersion in Re[n(λ)] is so strong here, that we predict several absorption peaks for a given diameter in the range of 65 nm < D < 80 nm in the wavelength region of λ < 400 nm [dashed line in Fig. 5(b)]. However, such absorption resonances are expected to be strongly damped due to the high absorption coefficient, or, equivalently, the large Im(nInP), in this wavelength region. Thus, we find that the dispersion in the refractive index can become so strong that it dominates the possibility to wavelength-shift optical resonances in nanostructures by geometrical tuning.
Fig. 5 (a) Tabulated refractive index of zinc-blende InP [38]. (b) Peak wavelength λpeak = cRe[n(λpeak)]D for zinc-blende InP, calculated with c = 1.41 as determined from modeling.
We note that similar crystal-phase-dependent differences have been previously reported for InAs nanowires [37] where the absorption peak in zinc-blende InAs nanowires stopped blue-shifting with decreasing diameter at longer wavelengths compared to similarly sized wurtzite InAs nanowires. There, the stop of the shifting of the peak was predicted correctly for zinc-blende InAs by modeling (note that for zinc-blende InAs the refractive index is known, and the modeling could be performed in contrast to the case of wurtzite InAs).
To summarize, in the current work, the resonant peak stops shifting at a wavelength of 390 nm for zinc-blende InP in the modeling. In contrast, the peak stops shifting at a wavelength of 345 nm for wurtzite InP in the measurements. This discrepancy in the resonant behavior is a strong indication that the refractive indices of zinc-blende InP and wurtzite InP are considerably different in the UV region, similar to the case of InAs.
4. Conclusion
We have shown theoretically and experimentally that absorption resonances in InP nanowire arrays can be tuned into the UV region. Specifically, this tuning is achieved by decreasing the diameter of the nanowires. In contrast to this observation, a change in the length of the nanowires does not change the wavelength position of the absorption resonances, but broadens them.
Interestingly, the absorptance resonance, which shows up at the longest wavelength, shifts with decreasing diameter down to λ ≈345 nm in the measurements whereas it stops at λ ≈390 nm in the electromagnetic modeling. We believe that this large discrepancy in resonant behavior arises from the fact that we (1) measured on wurtzite InP nanowires whereas we (2) performed modeling for zinc-blende InP nanowires due to the lack of knowledge of the refractive index of wurtzite InP. Therefore, we find clear indication that the refractive index of zinc-blende InP differs considerably from that of wurtzite InP. This discovery is of high importance for the nanoscience community since the crystal-phase of nanowires can be well-controlled during epitaxial fabrication. Our results show that the crystal-phase enters as an additional important parameter for optimizing the optical response of InP nanowires.
Acknowledgments
This work was performed within the Nanometer Structure Consortium at Lund University (nmC@LU), and was supported by the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), the EU project NWs4Light in the framework of the FP7 Program, the Knut and Alice Wallenberg Foundation, and by nmC@LU.
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