1. Introduction

The design of nonimaging light concentrators is important for developing efficient solar cells with the examples given by compound parabolic concentrators [1] and Köler integrators [2]. Due to large size of such concentrators compared to the illuminating wavelength (λ), their design is guided by the geometrical optics leading to a fundamental tradeoff between the concentration factor, C, and angle-of-view (AOV), θ, in such structures which can be expressed as: C=1/sin²θ.

Similar concept of concentration of light on small photodetector mesa can be used for decreasing the thermal noise of mid-wave infrared (MWIR) and long-wave infrared (LWIR) focal plane arrays (FPAs) [3,4]. The thermal noise decreases with reduction of the photodetector area. This is especially important for uncooled cameras where the thermal noise is one of the factors limiting the imaging quality. Currently, a limit for the photodetector mesa size in MWIR FPAs is close to ∼2.5λ [5,6]. Smaller mesas are usually not used because of the anticipated problems: reduced area fill-factor with the smaller photodetectors on the chip with the same pitch and diffraction of light at the edges of the mesas. However, in principle, the solution to these problems can be found by a proper design of structures which can collect the light from a broader area and deliver it to a compact photodetector mesa. The designs of such light-collecting structures have been developed in two limiting cases: (a) macroscale (characteristic dimensions ∼10λ-100λ) dielectric structures [7–14] and (b) wavelength-scale Si microcone arrays integrated with Schottky barrier detectors [15,16].

The designs of macroscale dielectric structures are based on principles of geometrical and/or diffractive optics. Similar to nonimaging light concentrators, they allow achieving large concentration factors by the expense of AOVs. As an example, commercial microlens arrays [3] have AOV<2° due to their relatively long focal distances, which is too small for many applications. By using high-index microspheres in contact with the photodetector mesas, AOVs can be increased up to 20° in front-illuminated structures [9]. Up to 100 times broadband MWIR photocurrent gain was reported for individual pixels equipped with spherical microlenses [8], but the microspheres are rather difficult to assemble in large-scale FPAs without defects [9]. More recently, it was proposed to use integrated microlenses [10], metalenses [11,14], dielectric microdisk antenna arrays [12], and axilenses [13], however AOVs of such structures are still rather limited.

Silicon microcone arrays appeared as a novel approach to design and fabrication of light-concentrating structures due to simple, inexpensive, and parallel manufacturing of large-scale arrays by anisotropic wet etching technology. Dielectric microcones permit tight focusing of light [17]. However, the practical designs were developed for very compact, wavelength-scale microcones with the sidewall surface covered with a thin layer of metal, where the concentration effect was achieved due to plasmonic adiabatic compression towards the apex of the tip of microcones [18]. The mechanism of photocurrent enhancement is rather complicated in such structures and may include formation of plasmonic hot spot at the tip of microcones leading to an increase of the internal photoemission efficiency [15]. Both designs of direct microcones covered with Al [15] and inverted microcones covered with Cu [16] nanofilms were realized and showed improved broadband performance of Schottky detectors in near-IR regimes over similar devices with flat barriers. The wavelength-scale dimensions of microcones used in these works, however, were too small to expect any contribution of internal dielectric resonant properties of microcones to their photoelectric response.

In contrast, the subject of this paper is related to operation of Si microcone arrays in a mesoscale regime where the characteristic dimensions of microcones correspond to several wavelengths. In this regime the microcones are large enough to support high-quality-factor (Q) resonant modes. To the best of our knowledge, this regime was not studied in microconical concentrators. However, it has a tremendous potential to solve an old problem of Si photodetectors related to their small quantum efficiency at the photon energies below the fundamental absorption edge of silicon. In previous studies of all-silicon spherical Mie-resonators, it was demonstrated that IR photons confined in high-Q resonant devices stay in the cavity for very long times, thus increasing their probability to be absorbed [19]. It resulted in a photocurrent response enhancement at photon energy values below the absorption edge of silicon where the absorption coefficient is extremely low.

In this work, using exact numerical solution of Maxwell equations we show that similar resonant enhancement of photocurrent response can take place in mesoscale regime in dielectric microcones. A realistic calculation of either the absorption efficiency or the photocurrent response of the devices is beyond the goal of this paper and it would require a precise knowledge of the specific device structures with all parameters. However, we calculate photon fluxes traversing the photodetectors with the characteristic dimensions 4 µm at the base of such microcones and show that they display strongly pronounced spectral peaks of the photon fluxes. They take place due to resonant trapping of photons inside the microcones that can be used for increasing the quantum efficiency of photodetectors due to increased absorption. Thus, this effect allows developing multispectral imaging through such microcones. The power enhancement factors (PEFs) of the proposed microcones are defined in the case of plane wave illumination as a ratio of the photon flux detected in the presence of microcons to the flux determined by the same detector without microcones. In addition to resonant trapping of photons, such microcones also have non-resonant light concentrating properties due to effect of taper on light transmission. Actually, such non-resonant light concentrating properties can be realized in mesoscale structures with arbitrary shapes [20].

We need to clarify at this point that two types of microcones can normally be observed: rectangular or octagonal base, depending on the experimental conditions [21,22]. The angle of the sidewalls depends on the orientation of the wafer, etchant, shape and orientation of the photoresist mask. If the photoresist is patterned as an array of squares, aligned with [110] direction on a (100) wafer, the (111) system of planes is preserved along the microcones’ sidewalls making an angle of 54.7° with the wafer. To simplify analysis, we somewhat simplified the geometry and considered such microcones with a circular cross-section. The larger/smaller base was assumed with the 14/4 µm diameters. Three designs are proposed: (i) inverted microcones heterogeneously integrated with front-illumianted FPAs, (ii) inverted microcones monolithically integrated with metal-Si Schottky barrier photodetectors, and (iii) regular (not inverted) microcones monolithically integrated with near-surface photodetectors. The advantage of the first design is that proposed Si microcone array can be integrated with the most efficient MWIR FPA fabricated in different material systems such as II-VI or III-V semiconductor superlattices, quantum dots, and quantum well photodetectors. We show, however, that PEF<10 and AOV<10° in this case. The advantage of the second design is that fabrication of Si microcones can be simply added as a second-step processing of the same wafer containing pre-fabricated metal-Si Schottky barrier detectors. Due to strong reflectivity of the smaller base of microcone covered with metal, the resonant trapping of photons is greatly enhanced in such structures leading to PEFs>20. Most interestingly, some of the PEF spectral peaks do not shift with angle of incidence leading to overlap of TE and TM polarized peaks with AOV>30°. This property is highly attractive for developing multispectral imaging with ∼100 nm bands and large AOVs. Finally, we consider the third design with regular (not inverted) microcones. We included this case in our analysis to compare theoretically the performance of regular and inverted microcones. We show that the optical properties of such microcones are close to single-pass contact microlenses. They don’t display resonant properties, but similar to high-index microspheres [9] they are capable of focusing incident light beams on tiny photodetector regions with very large AOVs.

In Section 2 we consider the geometries and the underlying theoretical models for three (i)-(iii) cases, respectively. Finally, in Section 3 we present conclusions.

2. Numerical design of microcones

Silicon etching has been studied due to its applications in the fabrication of microelectromechanical systems (MEMS) [23]. A solution called tetramethyl ammonium hydroxide (TMAH) or KOH are frequently exploited for the anisotropic etching process of Si (100) substrates with the (111) system of planes exposed [24–26]. The higher density of atoms on the surface of (111) planes is believed to be responsible for the strong reduction of the etch rate once such planes are exposed. As shown in Fig. 1(a), the often used microstructure (for passive fiber alignment etc.) is the ordinary V-groove obtained if the surface of the Si wafer is pre-patterned with the photoresist stripes and etching of the V-grooves takes place between them. Vector algebra shows that the angles between the (111) and (100) systems of planes are 54.7°, as shown in Fig. 1(a).

 

Fig. 1. (a) Geometrical sketch illustrating a profile of V-grooves with (111) oriented sidewalls, which can be fabricated by anisotropic wet etching of Si (100) wafers. The angle formed by the sidewalls with the surface of the wafer is 54.7°. (b) Top-view SEM image of a square array of microcones with octagonal cross-section obtained by etching through a lattice of photoresist squares. Oblique-angle SEM image of Si microcones with (c) approximately square cross-section and 54.7° angle as well as (d) octagonal cross-section and 45° angle.

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If the photoresist is patterned as a 2D periodic array of squares, the anisotropic wet etching results in an array of microcones exemplified in Fig. 1(b). Depending on the experimental conditions [21–26], it is possible to realize Si microcones with approximately square cross-section and angle of sidewalls close to 54.7° or microcones with the octagonal cross-section and angle of sidewalls close to 45°, as illustrated in Figs. 1 (c) and 1(d), respectively. In this work, we are more interested in microcones with square cross-section and 54.7° of the sidewalls. We refer a reader to Refs. [21–26] for details of fabrication of such microcones.

2.1 Inverted microcones heterogeneously integrated with front-illuminated FPAs

We begin with the design illustrated in Fig. 2(a) which shows that the Si microconical array can be fabricated with the pitch and size of the tips of the microcones matching the period and size of the photodetector mesa in a front-illuminated FPA, respectively. The heterogeneous integration of the microcone array with the photodetector array requires their optical alignment which in principle can be achieved using a liquid layer (adhesive or a photoresist) with an ability to solidify, which would enable slight adjustments of the mutual position of these arrays aimed at maximizing the signal detected by the pixels. Due to the fact that only a micron-scale accuracy is required, such heterogeneous integration can be a feasible task. The back surface of the Si slab (top surface in Fig. 1(a)) can have an antireflection coating.

 

Fig. 2. (a) Inverted Si microcones heterogeneously integrated with the front-illuminated FPA exemplified by strained-layer type II superlattice and (b) corresponding theoretical model; (c) inverted Si microcones monolithically integrated with the metal-Si Schottky photodetectors and (d) corresponding theoretical model; (e) regular Si microcones monolithically integrated with the near-surface detectors and (f) corresponding theoretical model.

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The distance between the tips of the microcones and mesas can be minimized by applying a gentle pressure. The idea is to minimize the gap filled with adhesive, epoxy, or photoresist below ∼λ/2 which would allow reducing the reflection loss at this interface, especially if the index of FPA is close to the index of Si. This condition would be well preserved for example in the case of integration with rapidly maturing III–V InAs/In^xGa^1−xSb strained-layer type II superlattice (T2SL) detectors and quantum well and dot III-V detectors [6].

To simplify our theoretical model, the Si substrate of the microconical array shown in Fig. 2(a) was completely removed and the small base of the microcone was considered to be in a close contact (without a gap) with the photodetector mesa, as schematically shown in Fig. 2(b). In a more detailed way this is illustrated in Fig. 3(a). We assumed that the index of the photodetector substrate is equal to that for Si. If the photodetectors are fabricated using III-V semiconductors, the index mismatch between these materials and Si microcones would produce a slight reflection at their interface, but qualitatively the results would be close to the predictions of our model. We assumed a circular cross-section of microcones with the large base D_l = 14 µm, small base D_s = 4 µm, and height h=7.07 µm.

 

Fig. 3. (a) EM field distribution calculated at normal incidence for inverted Si microcone with the circular cross-section and with the large base D_l = 14 µm, small base D_s = 4 µm, and height h=7.07 µm. (b) The PEF spectra calculated using a square monitor with the 4 µm side placed 100 nm below the surface of Si substrate (shown as a “Detector” in (a)). It is seen that at θ=5° the resonant PEF peaks have positions identical to the normal incidence case (indicated by the vertical dashed lines for dominant peaks) for both polarizations of incident light, and they remain the same for TE polarized waves at θ=10°.

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The numerical modeling was performed using 3-D finite difference time domain (FDTD) calculations by Lumerical software for incident plane waves with λ=4 µm. The photon flux was calculated using a “Transmission” (T) monitor which provides the flux measurement without perturbing it. Square T-monitor with the wavelength-scale sides (4 µm) was placed 100 nm below the surface of FPA to estimate the potential photo-response of the front-illuminated photodetector.

We defined the power enhancement factor (PEF) as a ratio of the photon flux delivered to the T-monitor through the microcone to the flux measured by the same size T-monitor without the microcone. Our definition of PEFs leads to progressively larger PEF values for smaller monitors. We, however, decided to use the monitors with wavelength-scale sizes (4 µm) mainly to represent the minimal physical dimensions of the photodetector mesas which can be fabricated by the existing well-established technologies. Use of the subwavelength monitors leads to much larger PEFs, but we did not include such cases in our analysis in this Section because of the challenging fabrication, alignment, and potential problems with coupling light in small mesas. It should also be noted that the bright spots inside the microcone in Fig. 3(a) represent the maxima of constructive interference which do not necessarily represent the maxima of the photon fluxes measured by the T-monitor.

The PEF spectra calculated for different angles (θ) and polarizations (TE and TM) of incident light are represented in Fig. 3(b). The spectra are vertically shifted for different θ‘s and polarizations (the scale bar representing 5-times enhancement is indicated). The key feature of the inverted microcones illustrated in Fig. 3(a) is related to the fact that such structures trap light due to multiple reflections by their sidewalls. This resonant effect is important because it allows developing multispectral imaging. In addition, resonant enhancement of EM field along the smaller base of the microcone can be used to increase the absorption of light by the detectors. The PEF peaks have ∼100 nm spectral width. The magnitude of PEF peaks in Fig. 3(b) do not exceed 10 for 4 µm detector, but further optimization as a function of dimensions of microcones is required to determine the limits of resonant PEF’s enhancement. The positions of the resonant peaks are determined by the geometry of microcones. Increase of the height of the microcones (keeping the same 54.7° angle of the sidewalls) causes a spectral shift of the PEF peaks and it can also lead to further increase of their Q-factors.

An interesting property of inverted microcones is related to the angular dependence of the enhancement factors (Fig. 3(b)) which shows relatively weak spectral shift of the peak positions with angle of incidence (θ). It is seen that at θ=5° the resonant peaks have positions identical to that at normal incidence and their positions remain the same at TE polarization up to θ=15°. This property distinguishes the microconical arrays from the standard multilayer structures where Bragg reflection displays strong polarization-dependent shift of the stop band with the angle of incidence. The fact that in microcones the resonant peaks have a tendency to overlap in a much wider range of angles and for both polarizations of incident light is related to 3-D nature of trapping light inside the individual microcones.

2.2 Inverted Si microcones monolithically integrated with PtSi Schottky barrier diodes

The design considered in Section 2.1 allows integrating Si microconical arrays with MWIR FPAs fabricated in various material systems, but alignment with the photodetectors would require developing a nonstandard procedure. On the other hand, use of Si-based photodetectors opens a principle possibility to achieve monolithic integration of Si microcones with the photodetectors on the same wafer using the same lithographic process. The geometry of such structures is schematically illustrated in Fig. 2(c), and advantage of monolithic integration of microcones with the detectors is apparent from this image. However, fabrication of efficient MWIR (or LWIR) photodetectors in Si represents a different problem related to small quantum efficiency (QE) of Si detectors.

Silicon, being an indirect bandgap semiconductor can be used as an extrinsic photodetector in MWIR and LWIR ranges. An important milestone was a proposal of metal silicide/Si Schottky barrier detectors which made possible to implement sophisticated readout circuits for both photon detection and electronic readout on a silicon chip [27]. In the MWIR range, most commonly PtSi detector is used. The radiation is transmitted through the p-type silicon and is absorbed in the metal PtSi, producing hot holes which are then emitted over the potential barrier into the silicon [28,29]. It should be noted that QE is usually limited at ∼0.1 level whereas (as an example) generic NASA Earth and planetary spectral imaging applications as well as many other applications require QE>0.5.

Several approaches have been used to increase QE by increasing absorption such as plasmonic resonators, waveguide integrated devices and photonic resonant cavities. In SWIR range, a promising approach is based on using NiSi Schottky-barrier detectors on n-type Si which have approximately 600 meV barrier height required for detection in this spectral range while maintaining a reasonably low dark current density at room temperatures [29,30]. It was shown that QE of NiSi Schottky-barrier photodetectors can be significantly improved as the silicide film thickness is reduced close to its percolation threshold. It was also shown that back illuminated photodetectors with anti-reflection coating and quarter-wave resonant reflector provide higher QE compared to front-illuminated structures with backside reflector [29,30]. Similar approaches can be used in MWIR and LWIR ranges for developing more efficient detectors based on PtSi or AuSi Schottky barrier detectors.

In our modeling, we studied electromagnetic field enhancement in structures containing an additional platinum (Pt) layer at the bottom base of the Si microcone, as illustrated in Fig. 4(a). The dimensions of the microcone, D_l = 14 µm, D_s = 4 µm, and h=7.07 µm, were selected to be equal to that in Fig. 3(a), to enable comparison between the cases with and without metallic layer. In practical metal/Si Schottky barrier detectors, such metallic layer is a standard part of the design of back illuminated devices. As an example, Cr/Au (5/200 nm) mirror can be deposited on top of the SiO₂ layer separating this mirror from the extremely thin PtSi, AuSi or NiSi silicide layer [29,30]. To simplify our theoretical model, we removed a spacer layer (such as SiO₂) and assumed that Pt mirror with 1 µm thickness is deposited directly at the bottom base of microcone with the 4 µm size.

 

Fig. 4. (a) EM field distribution calculated at normal incidence on the microcone with the same dimensions as in Fig. 3(a), but with a 1 µm thick Pt mirror at the bottom base. Slight absorption effects in the depleted layer of Schottky barrier were modeled by introducing 1% absorption at the 1 µm propagation length in the lowest 1 µm thick section of microcone. (b) Direct comparison of the PEF spectra calculated with (red) and without (blue) Pt mirror using a 4 µm monitor placed 0.1 µm above the bottom base. The blue curve is very close to the θ=0° case in Fig. 3(b) (the positions of monitors is only slightly different in these cases). It is seen that the PEF resonances are dramatically enhanced by the presence of the Pt mirror.

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As shown in Fig. 4(a), a combined effect of a strong reflections by the bottom base of the microcone and its sidewall surfaces consists in formation of extremely strong EM field enhancement approximately one micron above the metallic surface. The exact position of such “hot spot” depends on the geometrical parameters of the microcone. In real device structure where the metallic mirror can be separated from the PtSi silicide layer by the additional SiO₂ layer, its thickness can be adjusted to provide the maximal field enhancement in the PtSi silicide layer to maximize the light absorption and QE of such detectors. It should be noted, however, that like in the case of Fig. 3(a), the maxima of constructive interference do not necessarily represent the maxima of the photon fluxes measured by the T-monitor.

As shown in Fig. 4(b), the photonic fluxes in a submicron proximity to this mirror were studied by comparison of the PEF spectra calculated with (red) and without (blue) this metallic layer. The same monitor with the 4 µm size was placed 0.1 µm above the bottom base in both cases. We also included in our modeling slight absorption effects taking place in the depleted layer of real device structures. It was achieved by introducing 1% absorption at the 1 µm propagation length in the lowest 1 µm thick section of the microcone. It was found, however, that the presence of such weak absorption did not markedly change our results.

The direct comparison of the PEF spectra calculated with and without mirror in Fig. 4(b) reveals a dramatic resonant enhancement of the photonic fluxes near the metallic mirror. The positions of the PEF peaks and the total number of the peaks over the same spectral interval from 3 to 5 µm are found to be different compared to the same size microcones without the metallic mirror. It is seen that some PEF peaks increase by several times in the presence of the mirror reaching the values up to 20. These values do not represent the limits of this design approach. Further increase of PEF values can be achieved by varying the dimensions of the microcone and reducing the detector size.

This effect of resonant enhancement of photon fluxes has a potential to solve an old problem of Si photodetectors related to their small quantum efficiency at the photon energies below the fundamental absorption edge of silicon. Similar to the previous studies of all-silicon spherical Mie-resonators [19], these PEF peaks appear due to the fact that IR photons confined in microcones stay in the cavity for very long times, thus increasing their probability to be absorbed. It can result in a photocurrent response enhancement in the MWIR range (below the absorption edge of silicon) where the absorption coefficient is extremely low. It should be noted that due to the presence of metallic mirror the PEF enhancement peaks can be significantly enhanced in microcones monolithically integrated with PtSi Schottky barrier photodetectors compared to the similar effects in heterogeneously integrated structures. These properties can be used for developing multispectral imaging.

The property particularly important for developing such applications is related to very unusual behavior of these resonant PEF peaks as a function of angle of incidence illustrated in Fig. 5. It is seen that these peaks have a tendency to occupy the same spectral position in a very broad range of angles of incidence and, what is particularly interesting, the position of these peaks calculated at TE and TM polarization of incident light also coincides in a very broad range of θ’s.

 

Fig. 5. The PEF spectra calculated for broad range of angles of incidence in two polarizations (TE and TM) of incident plane waves for a Si microcone containing a metallic mirror at its bottom base. The photon fluxes were calculated by a square 4 µm monitor placed 0.1 µm above the bottom base. It is seen that in the entire range of variation of angles of incidence 0<θ<30° the peak at λ=3.73 µm has the same position as at normal incidence (indicated by the red vertical dashed line) for both polarizations of incident light. This peak along with several other peaks has a magnitude exceeding 10 for all angles in both polarizations of incident light.

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Using the PEF peak at λ=3.73 µm as an example (shown by the red vertical dashed line), it can be seen that it has a magnitude exceeding 10 in the whole range of angles 0<θ<30° with the same spectral position in both polarizations of incident light. Like in the case of microcones without metallic layers considered in Section 2.1, this property takes place due to 3-D nature of trapping light inside the individual microcones that distinguishes this case from the well-known example of planar multilayer structures. Our modeling results in Fig. 5 show, however, that this property is much more pronounced in the structures with stronger optical confinement introduced by the metallic mirror in the microcones. Such mirror can be easily fabricated at the bottom base of microcones monolithically integrated with PtSi Schottky barrier photodetectors.

2.3 Regular Si microcones monolithically integrated with the near-surface detectors

One more case of integration of microcones with photodetectors is represented by regular (not inverted) Si microcones which are fabricated on the top of near-surface Si detectors, as schematically illustrated in Fig. 2(e). The fabrication of such structures is likely to be a nonstandard process. The discussion of the possible fabrication methods for such structures goes beyond the scope of the present numerical modeling work. We made an assumption that the location of photodetector mesas corresponds to the near-surface region of the FPA slab. As shown in Fig. 2(f), we assumed that this depth (d) is below 1 µm and that the photodetectors are centered with the vertical axis of the microcone. In this Section, we also assumed that the square photodetectors have different dimensions such as 1, 1.5, 2, and 4 µm.

From the point of view of light propagation phenomena, such structures are very different from the inverted microcones since the light tends to be not trapped inside the microcones. The incident plane waves are generally subjected to a single-pass propagation scenario. In this regard, the optical properties of such structures are closer to conventional focusing rather than to building strong optical resonances. These properties can lead to formation of “photonic nanojets” similar to the focusing of light by dielectric microspheres [17].

This is illustrated in Figs. 6(a)–(d), where it is shown how the position of the focal point representing “photonic nanojet” is controlled by the height of the microcone for reducing size of the smaller base D_s under condition that the size of the larger base is fixed, D_l = 11 µm. Taking into account that the angle of the sidewalls of the microcone is fixed, reduction of D_s corresponds to the increase of the microcone height.

 

Fig. 6. (a-d) Photonic nanojets produced by the regular (not inverted) microcones with the bottom base 11 µm and different sizes of the top base: 4.9, 4.7, 4.4, and 4.1 µm, respectively. Taking into account the fixed angle of the sidewalls of microcones, reduction of the size of the top base corresponds to the increase of the height of the microcones. The depth of the photonic nanojet is controlled by the geometry of the microcone.

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Fig. 7. Photonic nanojets for microcones with D_l = 15 µm calculated for plane waves incident (a) at normal incidence and (b) at 40°. (c) Power enhancement factors calculated for 1.0 and 1.5 µm detectors as a function of angle of incidence for microcones with the same D_l = 15 µm and a range of parameters D_s indicated in the legend.

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It is seen that the structures can be designed to provide focusing at different depths below the microcones and the depth can be controlled with the high precision by the geometry of the microcones. In the limit of geometrical optics, the position of the focal spot scales with the size of the microcones. For higher microcones, the focusing can be achieved inside the microcones, but such cases are not included in Fig. 6.

The lateral dimensions of the photonic nanojets are significantly smaller than λ, and they can reach ∼λ/(2n) sizes. This allows efficient coupling of such extremely sharply focused photonic nanojets into compact photodetector mesas. We use the same definition of PEF as a ratio of the power measured by such detector with and without such regular microcone. Similar to the cases of inverted microcones in Sections 2.1 and 2.2, the reduction of the lateral size of the detector leads to higher enhancement factors due to the fact that the power measured without microcone is proportional to the detector size.

The PEF values calculated as a function of the angle of incidence of plane waves are presented in Fig. 7. As shown in Fig. 7(a), at normal incidence the photonic nanojet is so compact that its power can be fully accommodated within the smallest 1 µm detector. Increase of the angle of incidence causes the shift of the focal spot from the central position. However, Fig. 7(b) shows that the shift of the focal spot is rather small even for plane waves incident at 40°, so that a significant portion of the power is still detected by the 1.5 µm detector. More detailed power dependences on the angle of incidence for microcones with different geometrical parameters are presented in Fig. 7(c) for 1.0 and 1.5 µm detectors.

Figure 7 shows that there is a tradeoff between the enhancement factors and AOVs of the proposed structures, so that for smaller detectors larger enhancement factors can be realized by the expense of their AOVs. It should be noted that for detectors larger than 2 µm the PEF can be still higher than 10 at normal incidence and AOV can be larger than 30°. This combination of parameters can be attractive for applications; however, practical realization of monolithic integration of regular microcones with the photodetectors requires further technological development.

3. Conclusions

Mid-wave and long-wave infrared (MWIR and LWIR) cameras required in many applications should be smaller, lighter, require less power, and less cost compared to solutions offered by cryogenically cooled MWIR cameras. Uncooled LWIR can be used for similar missions, but the sensitivity of these microbolometer-based cameras is insufficient. Recently, High Operating Temperature (HOT) MWIR technology based on Type II Strained Layer Superlattice (T2SL) emerged allowing to reduce the thermal noise of the focal plane arrays (FPAs). However, they must be cooled to roughly T=130 K.

In this work, we developed a photonics approach to a problem of reduction of thermal noise based on using Si microconical light-concentrating structures. The idea is to reduce the area and, consequently, the thermal noise of photodetectors while keeping efficient collection of photons in the photodetector mesas with the reduced size. Such microconical arrays can be mass produced by anisotropic wet etching of Si for integration with MWIR and LWIR FPAs.

Using numerical modeling, we developed and compared three different designs of such integration of microconical arrays with FPAs.

The first design (Figs. 2(a) and 2(b)) represents a heterogeneous integration of inverted microcones with the front-illuminated FPAs. The main advantage of this approach is related to high quantum efficiency of T2SL or other material systems used in MWIR photodetectors which can be integrated with the Si microconical arrays. Some potential problems of such heterogeneous integration include optical alignment of microcones with photodetectors; however this integration seems to be feasible considering the required micron-scale accuracy of the alignment. Our modeling predicts resonant peaks of power enhancement on photodetectors in such structures which can be used for developing multispectral imaging with AOVs up to 10°.

The second design (Figs. 2(c) and 2(d)) is represented by monolithic integration of Si microcones with back illuminated PtSi or AuSi Schottky barrier photodiode arrays. The advantages of monolithic integration are based on the perfect alignment of microcones with the photodetectors achievable by using a standard lithography that should lead to minimization of the coupling losses in such structures. However, the problem of this technology is related to small QE of MWIR and LWIR Si photodetectors. Interestingly, our modeling results predict a strong resonant trapping of photons in such structures which can significantly increase the absorption of light and QE of the Si detectors. This effect seems to be quite promising for device applications since we demonstrated in this work that the spectral peak positions of these resonances have a fixed position in a broad range of angles for both polarizations (TE and TM) of incident light. It is shown that the resonant properties of the microcones are suitable for developing multispectral imaging with ∼100 nm bands.

Finally, the regular Si microcones in Figs. 2(e) and 2(f) can be used for sharp focusing of light on extremely compact photodetector mesas in a way which is similar to formation of photonic nanojets by high-index dielectric microspheres. This can be also realized with very large PEFs and AOVs values, but our designs are more hypothetical in this case depending on the manufacturability of the proposed structures.