Modeling selective narrowband light absorption in coaxial InAs-GaAs0.1Sb0.9 nanowires with partial shell segment coverage

Vertical III-V nanowire (NW) arrays are promising candidates for infrared (IR) photodetection applications. Generally, NWs with large diameters are required for efficient absorption in the IR range. However, increasing the NW diameter results in a loss of spectral selectivity and an enhancement in the photodetector dark current. Here, we propose a nanophotonic engineering approach to achieving spectrally-selective light absorption while minimizing the volume of the absorbing medium. Based on simulations performed using rigorous coupled-wave analysis (RCWA) techniques, we demonstrate dramatic tunability of the short-wavelength infrared (SWIR) light absorption properties of InAs NWs with base segments embedded in a reflective backside Au layer and with partial GaAs0.1Sb0.9 shell segment coverage. Use of a backside reflector results in the generation of a delocalized evanescent field around the NW core segment that can be selectively captured by the partially encapsulating GaAs0.1Sb0.9 shell layer. By adjusting the core and shell dimensions, unity absorption can be selectively achieved in the 2 to 3 μm wavelength range. Due to the transparency of the GaAs0.1Sb0.9 shell segments, wavelength-selective absorption occurs only along the InAs core segments where they are partially encapsulated. The design presented in this work paves the path toward spectrally-selective and polarization-dependent NW array-based photodetectors, in which carrier collection efficiencies can be enhanced by positioning active junctions at the predefined locations of the partial shell segments.


Introduction
Vertical III-V nanowire (NW) arrays are promising materials for optoelectronic applications due to their distinct properties compared to the bulk and thin-film systems. It has been theoretically and experimentally shown that light can strongly be absorbed in arrays of III-V NWs with micron-scale lengths with an overall material saving of ∼93% [1][2][3][4]. In addition, their efficient defect-free strain relaxation allows for a broad range of III-V compounds to be heteroepitaxially grown on lattice-mismatched substrates such as Si [5][6][7][8].
Of particular interest is the use of III-V NW arrays for infrared (IR) photodetection applications, due to their potential to overcome traditional tradeoffs between response speed and external quantum efficiency [9]. For such applications, InAs NW arrays provide an excellent platform due to their small bandgap and high carrier mobility [10,11]. In addition, high detectivity under room-temperature performance can be obtained via NWbased photodetectors due to a reduction in the volume of the absorbing medium and consequently dark current [12,13]. Generally, NWs with large diameters are required for efficient absorption in the IR range [14]. However, increasing the NW diameter results in a loss of spectral range selectivity and an enhancement in dark current due to the corresponding increase in material volume [15]. Therefore, novel methods for achieving spectrallyselective and narrowband light absorption while minimizing the volume of the light absorption medium and array fill factor are highly desired for applications in NW-based IR photodetectors with low-size, weight, power, and cost (SWaP-C) metrics. However, reports on nanophotonic engineering using delaminated NW array membranes and the influence of the backside reflectors on the optical properties of substrate-free NW arrays are limited.
Regardless of the method used for NW growth, starting substrates are needed to guide their vertical orientation and can serve as robust handling carriers for further fabrication processes. However, it has been shown that NWs can be delaminated from their native substrate for fabrication in substrate-free applications [16][17][18]. In addition, the use of delaminated NW arrays as the active medium can significantly reduce the photodetector dark current by eliminating the substrate contribution. In a recent publication, we demonstrated a complete fabrication procedure for substrate-free InAs NW-based photodetectors, including epitaxial growth of InAs NW arrays followed by delamination, transferring, device processing, and Si substrate recycling for NW array regrowth [7]. Successful delamination was realized through metal deposition on the backside of a NW array membrane. Such a backside metallic layer enables three key functions: (i) it serves as a backside contact; (ii) it acts as a mechanical anchor to hold the NWs in their original vertical orientation; and (iii) it functions as a backside reflector to enhance light absorption.
In this study, we investigate the influences of a backside metal reflector layer on the absorption spectra of InAs NW arrays and take advantage of standing wave patterns generated above the metal reflector for wavelength-selective absorption in the short-wavelength infrared (SWIR) range in NW arrays. Coaxially heterostructured NW arrays consisting of InAs core segments that are partially encapsulated by GaAs 0.1 Sb 0.9 shell layers are used for large tunability in the SWIR range, especially by consideration of the standing wave pattern. Embedding the bases of InAs NWs in Au backside contact layers results in periodic evanescent fields between adjacent NWs. However, often a single optical mode dominates the optical response. The position, spatial extent, and coupling between neighboring NWs depend mainly on the NW geometry and wavelength of incident light [19], as well as the period of the array.
We show that the otherwise delocalized HE 11 mode [19] in the 2 to 3 μm wavelength range can be selectively absorbed in InAs NW core segments by adding partial GaAs 0.1 Sb 0.9 shell layers with dimensions corresponding to the position and spatial extent of the evanescent field of the mode. The GaAs 0.1 Sb 0.9 layers are transparent at this wavelength range and only act to enhance absorption of the otherwise delocalized HE 11 mode. Wavelengthselective absorption is enhanced by a factor of ∼10 at positions along the InAs core segments where they are encapsulated by the shell. The absorption wavelength can be manipulated as a function of core segment length and the partial shell segment geometry. Moreover, narrowband wavelength selectivity can be controlled by tuning the length of the InAs NW core segment. Such site-specific absorption in InAs NWs can be exploited for enhancement of carrier collection efficiency by positioning active p-n junctions at the predefined locations of GaAs 0.1 Sb 0.9 shell layers. The design approaches highlighted in this work enable novel, low-SWaP-C, NW-based IR photodetector membranes with tunable narrowband selectivity along specific NW locations.

Methods
Due to the lack of analytical solutions for light-scattering in nanowire arrays, optical simulations are performed using the rigorous coupled wave analysis (RCWA) technique via the DiffractMOD simulation engine of Synopsys TCAD RSoft ® . Thanks to the lateral periodicity of NW arrays, the RCWA method is suitable for the study of electromagnetic wave interactions within ordered NW arrays with laterally non-homogeneous refractive indices.
In this method, the principle of conservation of energy is satisfied, therefore reflectance, transmittance and subsequently absorption can be calculated based on the incident electromagnetic field, and the light-scattering problem can be written in terms of a superposition of the coupled waves and Fourier transforms of the refractive indices perpendicular to the direction of the incident beam propagation. Reflection and transmission measurement planes are positioned above the maximum and minimum planes of simulation domain, respectively. Therefore, absorption through the structure can be calculated by ( ) is the reflectance from the array and ( ) l T is the transmittance through the membrane. Absorption is calculated over an incident wavelength range of 1 to 3 μm using 11×11 number of plane-wave harmonics. For completeness, note that the contour plots shown in figure 5 and S5 are calculated with the scattering matrix method, [19,20] which is in essence equivalent to RCWA or the Fourier modal method (FMM) [21]. In addition, the accuracy of the RCWA method is examined by finite element method (FEM), using Wave Optics Module in Comsol Multiphysics. Figure S1 shows the accuracy evaluation results performed for a similar structure with both FEM and RCWA methods. Both methods demonstrate good agreement with average point-to-point deviation of 0.16% and total absorption difference of 0.03% over the 1 to 3 μm spectral range. A detailed comparison of FEM and RCWA methods has been previously reported for modeling of optical properties of NW array systems [22].
InAs NW core segments are used as the main absorption medium covered by partial GaAs 0.1 Sb 0.9 shell segments to tune wavelength-selective absorption. The GaAs 0.1 Sb 0.9 shell material is selected due to lattice matching with the InAs core. In addition, the InAs-GaAs 0.1 Sb 0.9 material system provides a type-II broken gap which can be suitable for tunneling diode photodetectors with high responsivity [23,24]. Geometrical parameters of the InAs-GaAs 0.1 Sb 0.9 partial core-shell NW structure are defined as shown in figure 1. The base of the InAs NW core segment is embedded with a depth of 150 nm in a 300 nm-thick Au layer, which acts as the backside reflector. The length of the InAs core and GaAs 0.1 Sb 0.9 shell segments are defined by L C and L S , respectively. The diameter of the InAs core segment is defined by D C and the diameter of the GaAs 0.1 Sb 0.9 shell segment is defined by D S = D C + 2T S , where T S is the shell thickness. Moreover, E C and E S are defined as the exposed core segment length and the length of the extension of the axial shell segment above the core segment, respectively.
Unless otherwise stated, a square unit cell with constant pitch (P) of 1000 nm is used, which previously was demonstrated to be well-suited for SWIR absorption [14]. The real (n) and imaginary (κ) components of the refractive index for InAs and Au were obtained from the RSoft materials library and n-and κ-values for GaAs 0.1 Sb 0.9 were obtained from [25]. Unless otherwise stated, the surrounding medium is set as air with n-value equal to 1. Where noted, different encapsulation media with refractive indices ranging from 1 to 1.54 are also investigated.

Result and discussion
In our previous work, we have shown a complete procedure for fabrication of substrate-free InAs NW-based photodetectors,realized through NW array delamination and backside metal deposition [7]. As reported for both thin-film and NW geometries, the effective light path increases through introduction of a backside reflector [15,16,26]. In this work, the effect of the backside reflector on light absorption in InAs NW arrays is investigated via optical modeling. Figures 2(a) and (b) show the simulated absorption spectra of periodic arrays of InAs NWs with different diameters without and with a 300 nm-thick backside Au contact layer, respectively. The InAs NW core diameter (D C ) ranges from 100 nm to 600 nm in 100 nm increments for a constant NW core segment length (L C ) of 2.5 μm. As depicted in figure 2(a), increasing the NW diameter results in absorption at longer Figure 1. Schematic representation of periodic InAs NWs with partial GaAs 0.1 Sb 0.9 shell segments. Also shown is the simulation domain and the definition of related geometrical parameters where the L C and D C are defined as core length and diameter, respectively. The L S and T S are defined as shell length and thickness, respectively. The E C and E S are defined as the exposed core segment length and the length of the extension of the axial shell segment above the core segment, respectively.
wavelength. For instance, selective absorption wavelength is increased from 1050 nm for D C = 200 nm to 1400 nm for D C = 300 nm. By further increasing the diameter, the absorption peak shifts toward longer wavelengths. However, wavelength-selective absorption effects due to radial mode resonance are diminished as the linewidth is expanded to the point that, for D C = 500 nm, only ∼69% of the total incident light over the 1 to 3 mm range is absorbed in the InAs NW array. Since the radial mode resonances depend primarily on D C and are independent of the NW array pitch [27], increasing D C while keeping the pitch constant leads to a rise in the surface filling factor, making the NW array behave more like a planar medium. Therefore, as the fill factor increases, the top surface reflection from NWs also increases, which results in a loss of absorption intensity, as verified by the modeling results in figure 2(a). In addition, increasing D C makes it possible for different modes to be coupled in the NWs and consequently leads to linewidth broadening or degradation of wavelength-selective absorption, as shown in figure 2(a) [28].
By embedding the base segments of InAs NWs to a height of 150 nm in a reflective Au film, the broadband light absorption effect is enhanced. As depicted in figure 2(b) for D C = 500 nm, ∼92% of the incident light over the SWIR range is absorbed in InAs NW arrays. This can be explained by considering the effective light path increase through the NWs due to reflection from the Au backside film that acts as an almost perfect reflector in this wavelength range. The corresponding contour plots for InAs NW array membranes without and with the backside reflector layer are shown in figure S2. The plots show absorption as a function of core diameter over the SWIR range. As shown, by increasing D C for NW structures both without and with backside reflector, Figure 2. Absorption spectra of InAs NW array membranes for diameters ranging from 100 to 600 nm (a) with and (b) without a backside Au reflector. The NW length is constant at 2500 nm for all data sets. absorption with 90% intensity (shown with dashed line) shifts to longer wavelengths and broadens. This trend is more noticeable for D C 350 nm with a backside reflector, demonstrating a tradeoff between longer wavelength absorption and selectivity for InAs NW arrays.
Increasing the diameter of the NWs in periodic arrays can enhance broadband absorption. However, the key advantages of NW-based PDs are the possibilities of achieving room-temperature (i.e. uncooled) and ultra-high detectivity in the IR range due to the small volume of the absorbing materials [29,30]. Minimizing the volume of the NW array is very important, since the PD dark current scales typically with the dimensions of the absorbing medium. Additionally, increasing the NW diameter results in a loss of the radial mode resonance, which is one of the promising benefits of NW arrays for wavelength-selective absorption. Therefore, it is desirable to obtain strong wavelength-selective absorption while keeping the light absorption medium as low in volume as possible in order to break the trade-off between responsivity and dark current for high-detectivity in the SWIR spectral range.
When considering the planar Au layer without NWs present, since Au serves as a near-perfect reflector in the IR range, non-absorbed incident light reflects back and consequently interferes with the incident light, which results in the formation of standing waves. For normally incident x-polarized light, the electric field associated with the incident beam (E i ) can be described as where E 0 is the amplitude of the incident electric field, k is the wavenumber, z is the vertical distance from the center of the Au layer such that z = 150 nm marks the topside surface of the Au reflector, and e x is the unit vector. Likewise, the electric field associated with the reflected beam (E r ) can be described as = E e E e , r r ikz x where E r is the amplitude of the reflected electric field. The peak intensity position of the standing waves can be calculated by considering E i and E .
r The total field in air, E , tot is the superposition of these components, namely: With good approximation of perfect reflection from the Au back contact film, it can be considered that The tangential component of E tot should be close to zero at the interface of the perfect metal, which results in a phase change by π for E ; r therefore, = -E E .
r i As a result, standing waves in the region above of the Au film with arise. In the absence of NWs above the mirror, the peak intensity positions of the standing wave pattern can be calculated as 2 where lis the incident wavelength and m is an integer. Figure 3(a) shows the E-field density profile of the standing wave pattern above the Au film for different wavelengths in the 1 to 3 μm range. As illustrated in figure 3(a), as the incident wavelength increases, the peak E-field density positions expand and the separation between the centers of the standing waves increases, since the separation is given by l/2.
A similar effect is also expected when InAs NW arrays are introduced to the system even though the above equivalence | | | | = E E r 0 is no longer valid due to incident beam absorption in InAs NW arrays. In order to comprehensively understand the light interaction behavior in InAs NW arrays, E-field density profiles are modeled for different incident wavelengths. Figures 3(b) and (c) show the E-field density profiles for different wavelengths from 1 to 3 μm in InAs NW array membranes without and with a backside reflector, respectively, at constant D C = 300 nm and L C = 2500 nm. Figures 3(d) and (e) show the light absorption profiles corresponding to figures 3(b) and (c), respectively. In both cases, regardless of the inclusion of a backside Au contact layer, the incident light is absorbed in the InAs NW array membranes in the SWIR range, but optimal absorption occurs at a wavelength of ∼1.4 μm due to radial mode resonance (i.e., diameter-dependent selective absorption through the HE 11 guided mode in the NW) [19] at this wavelength. As shown in figures 3(d) and (e), most of the incident light is absorbed near the top of the NWs up to a distance of 1 μm from the top surface.
For membranes without backside reflectors and for incident wavelengths > 1.4 μm, the absorption intensity decreases as the incident wavelength increases and light absorption occurs mainly along the edges of the NWs, as shown in figure 3(d).The same behavior of the HE 11 mode showing strong field intensity along the NW sidewalls has been previously shown for NWs with diameters 700 nm [15]. On the other hand, the effect of the backside reflector is observable for all wavelengths in the SWIR range, as shown in figure 3(c). When the incident light and non-absorbed reflected light interfere, periodic evanescent fields are generated around the NWs and extend between adjacent NWs. This phenomena can be confirmed by observing the corresponding absorption profiles in figure 3(e), where light absorption occurs periodically along the NW length compared to the absorption profile of NW arrays without backside reflectors in figure 3(d). This effect is more obvious for longer wavelengths in the 2 to 3 μm range. The periodic evanescent modes are not coupled into NWs due to their small diameters and can be referred to as the delocalized mode [27,31,32]. Similar to standing waves formed over the Au reflector layer in figure 3(a), by increasing the wavelength of incident light, the centers of the evanescent modes shift upward along the InAs NWs and their axial extent increases, resulting in a reduction of optical coupling for a given NW as illustrated in figure 3(e).
The center of the decoupled modes for InAs NW arrays with backside Au contact approximately coincide with the center of the standing waves above the Au film (i.e., without InAs NW). This can be explained by the effective refractive index of the fundamental HE 11 mode (n eff HE , 11 ). The HE 11 guided mode is the dominant IR absorbing mode in small-diameter NWs [14,15,33,34]. In the absence of NWs, the mode is a plane wave with phase propagation defined by where n eff HE , 11 increases with NW diameter, D C . Thus, increasing D C results in a shorter spatial oscillation period for the mode at a given (free-space) wavelength. The figure S3(a) shows n eff HE , 11 as a function of D C for InAs NW arrays with P = 1000 nm. For small values of D C , the change in n eff HE , 11 from n is minimal and only becomes influential for D C > 200 nm. For example, for D C = 300 nm in the 2 to 3 μm range, n eff HE , 11 varies between 1.12 and 1.08. This causes a compression of the evanescent modes by 12% to 8% in the z-direction compared to the standing waves in the absence of NWs where = n 1. The effect of NW pitch on n eff HE , 11 at constant D C = 300 nm is shown in figure S3(b) of the SI document, where pitch is varied between 400 nm and 1000 nm.
In order to observe the diameter effect, the E-field density profile is shown in figure S4 for InAs NW arrays with D C = 100 nm and 200 nm with L C = 2500 nm for direct comparison with the previous result of D C = 300 nm. For all the three diameters, the evanescent field is more noticeable at wavelengths longer than the diameter-dependent radial mode resonance and follows the same trend as described above. The main difference is in the position and axial extent of the evanescent field along the NWs. It is apparent that for NWs with smaller diameters, the position of the evanescent field between the NWs is more comparable with a standing wave above the bare Au film (i.e., figure 3(a)). This is in good agreement with the calculated n eff HE , 11 shown in figure S3, demonstrating that n eff HE , 11 becomes more comparable to the free space value for smaller NW diameters. Similarly, decreasing the NW array pitch results in an increase in the density of the light absorbing medium and, consequently, an increase in n eff HE , 11 and a corresponding compression of the decoupled modes in NW-adjacent fields at any given wavelength.
As described above, the position, spatial extent, and separation of the evanescent modes depend mainly on the NW core segment diameter and wavelength of incident light. Based on this principle, we demonstrate a new approach for tuning the IR absorption spectra of coaxially heterostructured periodic NW arrays. We show that the otherwise decoupled mode in the 2 to 3 μm wavelength range can be selectively absorbed in InAs NW core segments by adding partial GaAs 0.1 Sb 0.9 shell segments with dimensions and positions matched to the behavior of evanescent fields.
Simulation are performed for InAs-GaAs 0.1 Sb 0.9 core-shell NW arrays with base segments embedded in Au contact layer to a depth of 150 nm. First, NW geometries with full shell layer coverage of the InAs core segment are considered. With reference to the schematic representation in figure 1, the geometric parameters are defined as follows: L C = 2500 nm, L S = 2300 + T S nm, D C = 300 nm, where T S = 25-150 nm. In this model, comparable axial and radial growth rate of the shell segment is assumed, such that E S = T S . In this way, for practical purposes of preventing short-circuit pathways between the shell segment and the Au contact, a spacer region of E C = 50 nm is included in the modeled geometry. Figure 4(a) shows the absorption spectrum over the SWIR range for InAs-GaAs 0.1 Sb 0.9 core-shell NW array membranes with different shell thickness values ranging from 25-150 nm. The addition of a shell segment with 25 nm thickness extends the 90% absorption spectral range from 1.4 μm (peak absorption wavelength for InAs core segment alone with 300 nm diameter) to longer wavelengths (i.e., ∼1.85 μm). Similar trends are observed by increasing the shell thickness, meaning that longer wavelengths can be absorbed. Considering that the shell material is completely transparent for wavelengths 1.9 μm, all of the incident light is absorbed by the InAs core segment. Therefore, the shell segment extends the absorption range to longer wavelengths without increasing the volume of the light absorbing medium. Some distinguishable peaks can be observed at wavelengths > 2500 nm for thicker shell segments, specifically at shell thickness values of 100, 125, and 150 nm. This may be addressed by considering the influence of the evanescent field as discussed earlier, whereby the shell segment can trap the delocalized mode outside of the core such that it can be absorbed by the InAs segment.
In order to further explore this concept, simulations are performed for structures with partial shell coverage. The geometric parameters are defined as follows: L C = 2500 nm, L S = 700 nm, D C = 300 nm, T S = 25-150 nm, and E C = 1350 nm. Here, the GaAs 0.1 Sb 0.9 shell segment length and position are intentionally chosen to match the size and position of the evanescent field at 2.6 μm based on figure 3(c). Figure 4(b) shows the absorption spectra of partial core-shell structures with the above dimensions. As shown, for all shell thicknesses 50 nm, only a single absorption peak is observed in the 2 to 3 μm wavelength range. For T S = 150 nm, close to unity absorption at a peak wavelength of 2.62 μm is obtained, which is attributed to a suitable fit between the evanescent field position and shell geometry. This point can be demonstrated further by shifting the shell position along the length of the InAs core segment. For this set of simulations, partial core-shell structures with L C = 2500 nm, L S = 700 nm, D C = 300 nm, T S = 150 nm, and E C = 1350 nm are chosen (solid dark blue line in panel (b) of figure 4). Relative to its initial position in figure 4(b), the shell segment is shifted in 100 nm increments upward and downward along the central InAs core, corresponding to values of E C between 1150 nm and 1550 nm. As shown in figure 4(c), by shifting the GaAs 0.1 Sb 0.9 shell downwards and upwards, the peak at 2.62 μm is shifted to shorter and longer wavelengths, respectively. However, the peak absorption intensity is decreased noticeably, which indicates that for optimal narrowband wavelength-selective absorption, a specific shell geometry including thickness and position must be assigned.
The partial core-shell geometry shown in the insets of figures 4(b) and (c) requires selective GaAs 0.1 Sb 0.9 shell formation along the InAs NW core segment. Although selective radial epitaxy has been demonstrated for NWs grown using the vapor-liquid-solid mechanism, the approach is mainly feasible when the core segment crystal structure can be well-controlled during particle-assisted synthesis. For example, Namazi et al have demonstrated selective growth of GaSb shell segments on InAs NW core regions with zinc blende crystal structure, while GaSb growth was suppressed along wurtzite phase InAs core regions [35]. For NW growth via seed-free methods that are less conducive to crystal phase engineering, partial shell formation at site-specific locations along the core segment can be more reasonably achieved through multiple selective chemical etching steps, as schematically depicted in figure S5(a). Thus, to simplify the device processing scheme, coaxial NW structures with shell layers that encapsulate only the tips of the core segments are desired ( Figure S5(b)), while still enabling wavelength-selective light absorption. Figure S6 shows the evanescent field along InAs NWs with D C = 300 nm and lengths varied between L C = 1250 nm and 5000 nm. Comparing the results shown in figure S6 reveals that the axial extent and position of the evanescent field along the InAs NWs is periodic and not affected by the length of the core segment. Hence, the length and diameter of the InAs core segment can be rationally designed such that the desired evanescent field of specific wavelength is positioned near the NW tip and such that the deposition of a GaAs 0.1 Sb 0.9 segment only in the corresponding tip location enables selective narrowband light absorption.
In order to demonstrate this point, simulations are performed to study the effect of the InAs core length (L C ), while keeping the position of the shell segment at a fixed height above the Au mirror. The same geometry as in the previous simulation is used but with different core segment lengths decreasing from 2500 nm to 2000 nm in 100 nm increments. For L C = 2500 nm, the top-most 300 nm region of the tip of the core segment is not covered by the GaAs 0.1 Sb 0.9 shell; whereas, for L C = 2000 nm, the top of the InAs core segment is covered by a GaAs 0.1 Sb 0.9 shell such that E S = 200 nm. As represented in figure 4(d), the length of the exposed core segment tip does not affect the intended absorption wavelength and all cases reveal > 95% absorption at ∼2.6 μm. The main influence is on the linewidth of the absorption line, insofar as increasing the core segment length results in linewidth broadening, which effectively represents a reduction in spectral selectivity. This can be explained by considering that as the length of the core segment decreases, the core-shell overlap also decreases. Thus, the evanescent field at any given wavelength can only be coupled through a shell segment that captures a portion of the otherwise decoupled mode. We show that otherwise decoupled modes in the 2 to 3 μm wavelength range can be selectively absorbed in InAs NW core segments by adding partial GaAs 0.1 Sb 0.9 shell layers with thickness and position corresponding to the desired evanescent field. The GaAs 0.1 Sb 0.9 layers are transparent in this wavelength range and only act to enhance absorption of the evanescent field. Wavelength-selective absorption is localized to positions along the InAs core segments where they are partially encapsulated. The absorption wavelength can be manipulated as a function of the partial shell segment position, length, and diameter. Moreover, narrowband wavelength selectivity can be controlled by tuning the length of the InAs NW core segment.
A series of additional simulations are performed based on the NW tip-encapsulated partial shell structure. Figure 5 shows contour plots of light absorption in arrays of NWs with InAs core segments of constant diameter, D C = 300 nm, with GaAs 0.1 Sb 0.9 shell segments at their tips with L S = 700 nm and E S = T S . Absorption is plotted over the SWIR range while the InAs core segment length, L C , is varied from 700 to 4000 nm for different shell segment thicknesses of 100, 150, and 200 nm. For wavelengths less than 2 μm, most incident light is absorbed by the core and shell, and wavelength-selective absorption is not realized. For instance, for structures with T S = 150 nm and L C = 2050 nm, the total absorption over the 1 to 2 μm range is ∼84%.
By tuning L C and T S , selective absorption peaks can be freely shifted in the 2 to 3 μm spectral range such that near-unity absorption is realized for particular core-shell geometries. By increasing L C , the absorption peaks are shifted toward longer wavelengths for all values of T S , as indicated by the black arrows in figure 5, which shows good agreement with the trend in the position of the delocalized mode. This can be explained by the evanescent field pattern defined by n eff HE , 11 for the bare InAs core segment. As depicted in figure 3(c), increasing the incident light wavelength shifts the position of the evanescent field upward along each InAs NW. Additionally, figure S6(a) demonstrates that for the range of NW lengths considered here, L C does not affect the presence or position of the delocalized mode. Thus, at longer wavelengths, the anti-nodes of the standing wave of the otherwise decoupled mode, which are shifted upward along the InAs core segment, can coincide with the position of the partial GaAs 0.1 Sb 0.9 shell segment at the NW tip as L C increases. For all values of T S in the incident wavelength range beyond 2 μm, the periodic nature of the near-unity absorption peaks along the L C axis (i.e., red fringes in figure 5) supports the notion that the position of the evanescent field at any given wavelength scales with l/2.
As shown in figure 5, thicker shell layers are needed to trap longer wavelength light, which is consistent with the observed trends in figure 4(b). Therefore, the effect of the shell thickness must be considered for wavelengthselective absorption using partial core-shell NW geometries. With shell segment thickness of 200 nm, as shown in figure 5(c), highly selective absorption can be realized when targeting the long-wavelength range (i.e., narrow red fringes) where InAs is otherwise weakly absorbing. This can be described by considering that the anomalous mode coupling effect of the shell promotes absorption, but the weak absorption of the underlying InAs core segment gives a sharp drop in peak absorption intensity, resulting in a narrow linewidth. At shorter wavelengths, absorption of the InAs core segment is increased as shown in figure 5(b) causing a broadening of the absorption peak in comparison to the case where a thicker partial GaAs 0.1 Sb 0.9 shell is employed.
The influence of the InAs core diameter is shown in figure S7, where D C is varied from 50 nm to 400 nm in 50 nm increments for L C values ranging between 700 nm and 4000 nm, and at a constant T C value of 150 nm. For D C 150 nm, absorption in 2 to 3 μm range is less than 5%. However, for D C = 200 nm, selective absorption is observed staring at a wavelength of approximately 2.25 μm and extended to 3 μm for D C = 400 nm. As D C increases, the selective absorption peak wavelength shifts toward longer wavelengths and broadens along both the L C and wavelength axes, indicating that the tunable range of selective light absorption is enhanced at larger NW core diameters. It is worth noting again that the extent of the evanescent field along the InAs core segment at any constant value of D C is a function of the incident wavelength. For shorter incident wavelengths, the extent of the decoupled mode is correspondingly narrowed.
In all of the above cases, a constant L S value of 700 nm is used for the purposes of direct comparison. However, the shell length plays an important role and L S = 700 nm is not optimally matched for incident wavelengths < 2 μm due to the GaAs 0.1 Sb 0.9 shell segment absorptance, which results in a secondary absorption peak at shorter wavelengths. The effect of L S is investigated for the same geometries in order to decrease the secondary peak absorption intensity as shown in figure S8 (a). Decreasing L S results in a corresponding decrease in the secondary peak intensity until it is quenched at L S = 550 nm. However, the primary peak at ∼2500 nm is also decreased in absorption intensity. The primary peak can be recovered through small adjustments in core segment length such that unity absorption is achieved at L C = 1950 nm, without considerable re-appearance of the secondary peak, as shown in figure S8 (b). Figure 6 shows the simulated absorption spectra of various NW array geometries and summarizes the key features discussed above. Structure A defines an InAs-GaAs 0.1 Sb 0.9 core-shell NW with L C = 1950 nm, D C = 300 nm, L S = 550 nm, E C = 1400 nm and E S = T S = 150 nm, such that the partial shell segment is situated at the tip of the NW. The absorption spectra of four different NW geometries are compared with that of structure A in order to highlight the attributes of the optimized structure for narrowband wavelength-selective light absorption. Structure B defines an InAs-GaAs 0.1 Sb 0.9 core-shell NW with L C = 2500 nm, D C = 300 nm, L S = 550 nm, E C = 1400 nm and T S = 150 nm, such that the shell segment does not encapsulate the NW tip. Structure C defines an InAs-InAs core-shell NW with L C = 1950 nm, D C = 300 nm, L S = 550 nm, E C = 1400 nm and E S = T S = 150 nm. This structure is identical to Structure A, except for the distinction that the core and shell segments are both composed of InAs. Structure D defines an InAs NW with L C = 1950 nm and D C Figure 5. Contour plots of absorption intensity over the 1000 to 3000 nm wavelength range for core-shell InAs-GaAs 0.1 Sb 0.9 structures with partial shell segments at the NW tip, where the NW core segment length is varied between L C = 700 and 4000 nm for different shell thickness values of (a) T S = 100 nm, (b) T S = 150 nm, and (c) T S = 200 nm. In all cases, L S = 700 nm and E S = T S . = 300 nm. Structure E defines an InAs NW with L C = 1950 nm and D C = 600 nm. To summarize and show the effect of the NW shell segment, absorption and E-field density profiles are shown at the primary absorption peak wavelength of 2.48 μm for Structure A in figure 6. As noted above, the shell is transparent at this wavelength, corresponding to the dark absorption profile beyond the NW core segment. Observing the E-field profile reveals that at a wavelength of 2.48 μm, the field is localized at the position of the GaAs 0.1 Sb 0.9 shell segment. Therefore, the shell segment can act as a light guide to localize and concentrate the incident light, such that it can be absorbed in the core segment; whereas, without a shell layer, the core segment itself is only absorbing around 20% of the incident light at a wavelength of 2.48 μm as shown in the absorption spectra in figure 6.
Comparing the absorption spectra of Structures A and B, the same behavior is observed except for a small red shift in the primary peak wavelength and a ∼20% higher absorption intensity in secondary peak in the case of Structure B. This shows the benefit of Structure A over B, which is not only more practical in terms of synthesis but also partially quenches the secondary peak. The geometry influence is also investigated via Structure C, as shown in figure 6. Wavelength-selective absorption is observed at ∼2.36 μm with 96% absorption. However, the selectivity is reduced compared to Structure A as the bandwidth is increased. This indicates that even though the geometry plays a bigger role in the selective absorption effect, both the material composition and geometry of the NW core and shell segments must be carefully optimized for the highest selectivity. The absorption spectrum shows negligible absorption beyond 2 μm in the case of the InAs NW with 300 nm core diameter (i.e., Structure D). However, for the InAs NW with 600 nm diameter (i.e., Structure E), 90% of the incident light is absorbed over 2 to 3 μm range. Increasing the InAs NW diameter results in higher absorption in the SWIR region, but the larger diameter is expected to also result in an increase in the undesired PD dark current. Importantly, wavelength-selective absorption cannot be realized in the case of larger diameter NWs. The nanophotonic engineering approach introduced in this work can be used to selectively absorb incident SWIR radiation in InAs NW core segments with smaller diameters. Moreover, using this method, the active region of the PD device can be placed in the designed absorption region near the NW tip, which can dramatically increase detectivity.
For all NW array cases discussed thus far, the refractive index of the background medium is selected as = n 1, meaning that no encapsulation medium is assumed. However, from a practical point of view, NW arrays are usually encapsulated in a spacer medium for surface planarization and contacting purposes during the device fabrication process. The encapsulation medium of higher refractive index than air shifts the standing wave pattern located above the Au layer, resulting in a loss of the desired wavelength-selective absorption (unless another anti-node of the standing wave pattern happens to shift to coincide with the location of the shell segment). Figure 7 shows the influence of the background refractive index. Here, absorption spectra are simulated for the case of Structure A when fully embedded in benzocyclobutene (BCB), a common encapsulation medium [11,36] with = n 1.54 [37]. This structure is henceforth referred to as Structure F. The absorption spectrum (red curve) in the 2 to 3 μm range is no longer comparable with that of Structure A (black curve). However, considering that increasing the refractive index modifies the wavelength in the material by l/n, the standing wave pattern becomes compressed along the length of the NW. Figure S9 shows the E-field density profile for an InAs core segment with D C = 300 nm and L C = 2500 nm encapsulated in BCB. Hence, the center of decoupled modes are shifted down along the InAs core axis, which means the length of the core segment can be simply adjusted to capture the desired evanescent field. As shown in figure 7, when L C is shortened from 1950 nm to 1420 nm in the case of Structure G, the same absorption peak at 2.48 μm is recovered (blue curve). The effect of the refractive index on the absorption spectrum is simulated for different refractive indices ranging from n = 1 to n = 1.54, as shown in figure S10.
Lastly, absorption spectrum dependence on the incidence polar angle (θ) is investigated for Structure A under two different azimuthal angles (f) of 0°and 45°for both p and s polarizations, independently. Figure S11 shows absorption spectra for different polar angles ranging from 0°to 75°in 7.5°increments. A strong polarization dependence is observed. For p-polarization and f = 0°, the primary peak absorption intensity is decreased by increasing θ such that at θ = 37.5°the primary peak is completely quenched and by further increasing θ the primary peak is recovered at θ = 75°, while s-polarization maintains a primary peak absorption at > 90%. The observed behavior is promising for polarization detection with several applications including remote sensing, telecommunications, environmental monitoring and more [38]. The s/p ratio is calculated for all angles of θ, which reveals the important point that for the partial core-shell Structure A, both spectral-and polarization-dependent detection can be achieved. Specifically at θ = 37.5°, polarization-dependent optical filtration is realized using Structure A NW arrays with an s/p ratio of ∼5, as shown in figure 8. It is worth mentioning that Structure A has not been specifically designed for polarization-dependent detection and these polarization simulations are performed to demonstrate the concept that partial core-shell structures hold promise for such polarization filtration applications.