1. Introduction

Because the signal-to-noise ratio (SNR) requirement for a given infrared (IR) imaging application is a key factor in determining the operating temperature of an IR focal plane array (FPA), it has a major impact on the size, weight, power, and lifecycle cost of the cooled imaging system. For an IR detector with high internal quantum efficiency (IQE) operating under low background conditions, the SNR may be limited solely by dark current noise. In an ideal “nBn” unicarrier barrier structure with no sidewall leakage or generation-recombination current (because there is no junction), the dark current is due entirely to the diffusion of thermally-generated carriers in the quasi-neutral absorber region (AR). In this case, both the dark current density J_d ≅ qn_i²(T)/(τN_d) and the IQE ≅ 1−e^−αL increase with AR thickness L assuming L is much thinner than the minority-carrier diffusion length). Here $q$ is the electron charge, n_i is the intrinsic carrier concentration, N_d is the absorber doping, $\tau$ is the minority carrier lifetime, and $\alpha$ is the optical absorption coefficient. In a diffusion limited nBn detector, the SNR is proportional to the product of the incident signal power Φ_sig(W) and the sensor detectivity:

It should be possible, however, to increase the operating temperature of such an nBn detector structure without degrading the SNR if light trapping can be exploited to maintain high IQE even as the AR thickness is reduced. We show in the present work that this can be accomplished using a metallic grating to couple the incident optical power to in-plane propagating surface plasmon-polariton (SPP) modes, so as to create a long optical path length in very thin absorbers. For example, in an nBn structure with a bulk InAs_0.91Sb_0.09 absorber having an absorption coefficient of α ≈4000 cm⁻¹ at λ = 3.3 µm, the optimal absorber thickness is L_max ≈3.15 µm and the single-pass IQE is 72% (for lossless carrier collection). However if plasmonic coupling can be used to achieve the same IQE when the AR is a factor of 10 thinner (L = 0.3 µm), $D*$ is enhanced by more than a factor of three. This would allow an operating temperature of 180K for a conventional device with thick AR to increase by 20K without any loss of SNR, while a conventional device operating temperature of 260K could be increased by 35K without affecting the SNR.

Several previous investigations of quantum well (QWIP) [1–6], quantum dot (QDIP) [7–10], and quantum cascade (QCD) [11,12] IR photodetectors [13], as well as solar cells [14,15], have employed diffraction gratings to enhance the device efficiency. In particular, redirecting the light can boost the IQE of devices that absorb very weakly at normal incidence (QWIPs, QCDs), or have very thin ARs (organic solar cells). An early application to QWIPs achieved nearly 90% IQE by using reflection gratings and cladding layers to divert normally incident light into modes that experienced total internal reflection [16,17]. More recently, transmission gratings were used to couple light into plasmon modes, which enhance the optical responsivities of QDIPs and QCDs by 5- to 10-fold [8,13]. The smaller period length of plasmonic gratings make them more suitable for small pixels than diffraction gratings, though they are also subject to optical losses within the metal films used to support the plasmons.

In this work, two-dimensional (2D) subwavelength metallic gratings were fabricated on top of backside-illuminated nBn MWIR detectors with thin InAsSb absorbers, in order to enhance IQE. The gratings coupled normally-incident photons from the backside into SPP modes that propagated along the plane at the grating-AR interface. As a result, the effective optical thickness becomes equal to the lateral extent of the pixel, so that nearly 100% of the SPP modes can be absorbed even when the AR is thin. In an earlier work, we showed that one-dimensional (1D) gratings substantially increased the IQE of an InAsSb nBn detector [13], although the enhancement occurred only for light polarized perpendicular to the grating lines, due to the SPP mode polarization. Here, 2D square gratings enhance the IQE regardless of polarization, yielding a much stronger effect.

2. Numerical Simulation of the IQE Enhancement

We performed detailed numerical simulations of the interaction of incident light with grating structures and of the optical absorption within the nBn device structures, for comparison with experimental results. The inverted nBn structure, shown schematically in Fig. 1, is designed to allow IR illumination entering through the semi-transparent GaSb substrate to pass through the contact, barrier, and absorber layers, before coupling to the SPP mode residing near the grating-semiconductor interface. The coupling of incident light to the SPP mode is optimized when the coupling strength equals the total power loss due to propagation in the SPP mode (so-called critical coupling) [18]. This loss includes both parasitic absorption in the metal and useful absorption in the narrow-gap semiconductor. Generally, the critical-coupling condition for a given grating design must be determined from detailed simulations.

 

Fig. 1 Schematic of the nBn structure’s epitaxial layers with a 1D or 2D grating on top. The blue regions of the grating are germanium, while the orange regions are gold. (b) Band diagram for the structure with a 360mV operating bias applied to the top side with the grating (not shown), which is to the right side of the diagram.

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To determine the optimal coupling condition for our experiments, we numerically simulated the relevant nBn device structure with various 1D and 2D gratings on top, and using experimental input to fit some of the key material parameters. A finite-element method implemented in COMSOL was used to solve Maxwell’s equations. Both normal and oblique optical incidence were modeled, using periodic and non-periodic boundary conditions to model gratings of infinite and finite (individual pixel) extent, respectively. The light was incident uniformly over the top of the detector and originated in the GaSb layer. We used simulated reflection and absorption spectra for the grating-coupled nBn detectors to determine the grating period (p), height (h), and duty cycle (c) that maximized absorption in the AR. The relevant grating parameters are defined below and illustrated in Fig. 2(a):

 

Fig. 2 Schematics of: (a) 1D, (b) 2D Ge square grating, and (c) 2D Au grating showing the definitions of the period (p), height (h), and width (w). The coordinate system used to describe the incident field (red vector) and the two polarizations are shown in (a).

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Band structure parameters for the various semiconductor layers were taken from Vurgaftman et al. [19], while frequency- and temperature-dependent optical constants n and k were obtained using the interpolation technique described in Ref [20].· Frequency-dependent optical constants for Au were measured by IR spectral ellipsometry, and found to agree well with literature values [21].

The simulations allowed the slope of the grating sidewalls to vary, since various fabrication methods used in the process development produced different sidewall angles. However, the results reported in the figures assume a single slope of 70°, for consistency with the measured devices that were fabricated using the “lift-off” procedure described below. Since the simulation assumes light originating within a semi-infinite GaSb substrate, reflection losses at the first substrate surface were manually added to allow comparison with the experimental external quantum efficiency (EQE). We further assume 100% collection of the photogenerated carriers, with no recombination losses within the AR. The resulting error should be negligible because the absorber thickness of 0.5 μm thick is far less than the diffusion length of ≥10 µm that is estimated from the experimental lifetime of ≈200 ns and mobility > 1000 cm²/V-s for minority holes at 120 K. Transport simulations yield > 99% carrier collection when the diffusion length exceeds 3 µm [22,23]. As a result, we equate the absorption fraction within the AR and the IQE, and use these terms interchangeably.

Simulations were performed for flat mirrors and the three grating topologies shown in Fig. 2(a) 1D Ge lines, (b) 2D Ge squares, and (c) 2D Au squares. As expected, the plasmon resonance wavelength (λ_p) depends primarily on the grating period, with λ_p ≈3.4p at normal incidence for λ_p between 3 and 5 μm. An optimal design can be obtained by choosing a period based on the desired resonance wavelength, adjusting the grating height and duty cycle to maximize the coupling, and then readjusting the period to fine-tune the resonance.

Simulations show approximately 33% optical absorption within a 0.5-μm-thick InAsSb AR in an nBn structure using a simple Au mirror that provides a second pass through the AR. For the same nBn structure using a 1D grating instead, the simulation predicts that 85% of the incident light which is polarized perpendicularly to the grating lines (PPGL) is absorbed within the AR near resonance (λ_p = 3.3 µm for p = 900 nm), for an optimized grating height of 90–120 nm and duty cycle of 50–60%. This includes 19% absorption during the first vertical pass through the AR, leaving 81% of the PPGL light to reach the grating and couple into SPP modes. Of this, about 81% is absorbed in the AR, while most of the remaining 15% of the incident light is dissipated as heat in the Au grating. For unpolarized light, only half of the photons that reach the grating (81% of the incident light) couples into SPP modes (40.5%), while the rest are reflected. During the second pass through the AR, 19% of the reflected light is then absorbed which means that 59% of the unpolarized light is absorbed in the AR (near resonance).

We also simulated 2D gratings having the Ge square and Au square configurations illustrated in Figs. 2(b) and 2(c), respectively. If the 2D grating approximates a superposition of two orthogonal thin line gratings, we expect an optimal duty cycle of roughly the square of 50%, i.e., 25%. However, the two perpendicular gratings in the 2D configuration are not actually separable, so mode perturbations associated with the Au region cannot be neglected, and the optimal duty cycle may deviate considerably from 25%.

Figures 3(a) and 3(b) plot the maximum IQE vs. grating height and duty cycle calculated for (a) Ge square and (b) Au square gratings, respectively, with fixed periods of 900 nm. The maximum absorption of 83% for the Ge square topology occurs at a grating height of 180–200 nm and a duty cycle of 35-45%. On the other hand, the maximum IQE of 81% for the Au square topology occurs at a grating height of 120 nm and a duty cycle of only 20%. For the latter design, the optimal grating height is only 90–100 nm when the duty cycle is >30%, whereas it increases rapidly to 200 nm when the duty cycle is 10%. For optimal grating designs that yield the highest IQEs, less than 1% of the power is reflected at the resonance wavelength. This implies nearly perfect coupling between the incident light to the SPP mode.

 

Fig. 3 Maximum IQE vs. duty cycle and grating height for gratings with 900 nm period of (a) the Ge square configuration (b) the Au square configuration.

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It will be seen from the experimental spectra presented below that besides resonantly coupling incident light to the SPP modes, the 1D and 2D gratings also produce diffraction features at shorter wavelengths. As a result, the light is diffracted at large angles with respect to normal for all wavelengths below the diffraction cut-off. The interplay between path length and absorption for the diffracted light can result in an apparent second peak in the IQE spectrum at a wavelength ≈3.0 µm. Our finding that up to about 300 nm the diffraction strength increases substantially with Ge thickness is consistent with the conclusion of ref [20]. that the optimal height for a square diffraction grating is ≈⅓ λ_s where λ_s is the wavelength in the semiconductor. This effect is stronger for the Ge square design because the optimal gratings are taller.

The dependence of the SPP resonance wavelength on angle of incidence is typically understood in terms of momentum conservation including both the polar and azimuthal angle:

 

Fig. 4 Simulation of the IQE vs. wavelength for light polarized perpendicularly to the grating at three different normal and off-normal angles. The simulation employs a Au square 2D grating with 880nm period, 20% duty cycle, and 120 nm height. The spectrum for a flat Au mirror is also shown for comparison. The angles are defined at the air/semiconductor interface. The maximum incidence angle for an f/2 optical system is about 14 degrees.

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If the long-term goal is to integrate plasmonic gratings with FPAs having finite pixel dimensions, we must also consider how many grating periods are needed to attain significant enhancement of the IQE. While Figs. 3 and 4 assumed a single unit cell with periodic boundary conditions, which is equivalent to employing a grating of infinite extent, we also modeled gratings defined on finite mesas. For the 1D full mesa simulations 3 periods of air were added on either side with perfectly matched boundary conditions beyond that. The light was incident uniformly over the top of the grating and originated in the GaSb layer. The simulation for the finite case must span the full mesa volume, and so include many grating periods. In order to lower the computational burden, we simulated only 1D gratings, assuming that the dependence on number of periods should be qualitatively similar for 2D. We see from Fig. 5 which plots the IQEs calculated for 1D gratings of varying sizes, that as few as 10 periods (fitting on a 9-µm-wide mesa) are sufficient to enhance the peak absorption to 87% of that attainable with an infinite grating (black curve). This is well over twice that attainable with a flat Au mirror (magenta curve). Gratings with 20 periods (18-μm-wide mesa) and above yield at least 95% of the benefit of an infinite grating.

 

Fig. 5 Simulated IQE for a 1D grating with 900 nm period,100 nm height, and 50% duty cycle residing on a square mesa, for a series of total grating periods (which also define the mesa dimensions) The black curve represents a mesa of infinite extent (infinite number of periods), while the magenta curve corresponds to replacing the grating with a flat Au mirror.

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3. Device Design and Fabrication

The backside-illuminated nBn structure shown in Fig. 1 was grown by molecular beam epitaxy (MBE) on a transparent, lightly n-doped GaSb (n ≈10¹⁶ cm⁻³) substrate. At T = 120 K, the bandgaps of the heavily-doped (n ≈10¹⁷ cm⁻³) bottom-contact superlattice (SL1) and the “not-intentionally-doped” (NID) electron barrier layer superlattice (SL2) were approximately 610 and 960 meV, respectively [25], as compared to 330 meV for the 500-nm-thick InAs_0.91Sb_0.09 absorber. A bulk-like alloy was chosen for the absorber because its nearly isotropic optical properties maximize the absorption of both normally-incident plane waves and grating-coupled transverse SPP modes. On the other hand, a type-II superlattice such as either InAs/GaInSb or InAs/InAsSb would be less effective, since its absorption of out-of-plane-polarized light would be suppressed near the band edge. The absorber thickness of 500 nm was selected to be only 1/5 of the optical attenuation length α = 1/α based on the estimated absorption coefficient of α ≅ 4000 cm ⁻¹ at λ = 3.3 µm. The background doping in the NID absorber was n ≈5x10¹⁵ cm⁻³, as determined from Hall measurements on test structures. The final 30 nm of the absorber was heavily n-doped (≈7x10¹⁷ cm⁻³), followed by 10 nm of InAs (n ≈7x10¹⁷ cm⁻³) to facilitate electrical contacting.

While the use of a wide-bandgap superlattice for the bottom contact reduces optical losses and thermal generation noise, collection of the photo-excited minority holes requires a bias voltage to overcome the hole barrier produced when the conduction bands of the n-type absorber and wider gap n⁺ contact are aligned with the Fermi level at equilibrium. The required voltage is roughly equal to the bandgap difference, about 350 mV. The measured operating bias (defined as the voltage at which the EQE reaches 95% of its maximum value) for the samples reported here, ranged from 340 to 450 mV.

A major challenge was to fabricate gratings with control and uniformity sufficient to realize strong coupling to the SPP modes. While dry etching provides a nearly ideal grating profile, loading effects can substantially vary the etch depth as the duty cycle and period are varied. Furthermore, ion bombardment during the dry etch can cause surface damage that induces excess dark current. While wet etching minimizes the surface damage, it also tends to produce rounded and less uniform profiles that degrade the grating coupling efficiency. We avoid these pitfalls by developing an alternative method that defines the grating in a thin, highly uniform dielectric spacer layer which is over-coated with metal. While several candidate spacer dielectrics were considered, we chose germanium since it processes cleanly, is IR transparent and has a favorable match to the refractive index of the absorber.

To fabricate the gratings, we first used electron-beam (EB) lithography to define the grating pattern in an EB resist deposited on top of the nBn structure. Next, a layer of germanium was deposited to a precise thickness equaling the target height of the grating. The structure was then immersed in photoresist remover and “lifted-off”, leaving behind germanium lines or squares, depending on the grating topology. Finally, Ti/Au was deposited over the periodic germanium features to form the metal grating.

However, the process had to be modified to realize Au-square gratings because it required exposure of the EB resist in a continuous grid rather than discrete squares. The resulting proximity exposure effects degraded the lift-off patterning. So instead, we began with a blanket deposition of Ge, followed by EB lithography and dry etching. The C₄F₈/SF₆ dry etch process was optimized to provide nearly vertical sidewalls. Moreover, since the dry etch selectivity between Ge and InAs is effectively infinite, the grating height was again precisely defined by the Ge deposition thickness.

While a damage layer may be formed by ion bombardment during the dry etch, its depth is minimal since the etch chemistry does not react with InAs.

As seen in Fig. 6, the Ge square and Au square 2D gratings produced by these two processes are highly uniform and reproducible. A further advantage is that they favorably position the bottoms of the grating teeth in close proximity to the absorber, which thereby has a strong overlap with the SPP mode.

 

Fig. 6 (a) Ge squares as deposited (left) and after Au deposition (right). (b) Ge as deposited for Au square gratings

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Each test die contained 24 grating patterns defined within 150 µm x 150 µm regions. The grating patterns were composed of either 1D lines or 2D Ge or Au-squares. Another 16 such regions were left blank to define reference devices covered with flat mirrors. After the patterns were transferred to the Ge spacer layer (all of the Ge was removed from the mirror samples), 160 µm × 160 µm mesas centered on the Ge pattern were wet etched. Then 140 µm × 140 µm regions centered on each mesa were patterned in photoresist, followed by the deposition and lift-off of 200-250 nm of Au deposited over a 5-nm-thick Ti adhesion layer that formed the metal gratings or mirrors. The Au thickness was selected to assure overfill of the spaces between the Ge patterns to form a 1D or 2D metallic grating with a continuous backplane as illustrated in Fig. 6. The metal gratings were in direct contact with the underlying semiconductor providing topside Ohmic contacts to the detectors. Both the mirrors and gratings had metal fill-factors of 77% with respect to the total mesa area.

Forty detector mesas with varying grating periods were fabricated on each test die, while the grating height, corresponding to the thickness of the Ge spacer layer, remained fixed. The devices reported below employed duty cycles of 50% for the 1D gratings and 25% for the 2D Ge-square and Au-square gratings. The simulations predicted that for the optimal grating height those duty cycles should yield IQE values within 5% of the theoretical maxima.

4. Experimental Characterization and Results

Figure 7(a) plots dark current densities vs. bias voltage for detectors with Ge-square gratings, Au-square gratings, and flat mirrors at 150 K. At the operating bias of 375 mV, the dark currents for devices with Ge-square gratings are ≈20 nA/cm², which is comparable to that for a diffusion-limited, 4-µm-thick nBn detector operating ≈10 K colder [26]. This is the improvement expected based on the difference in AR thickness, combined with the dependence of n_i²~T³e^Eg/kT dependence for diffusion-limited dark current. The dark current for detectors with Au square is also shown in Fig. 7(a). In this case, the dark current is ≈30 times higher than for those with Ge square gratings. The low, diffusion limited dark current for the Ge squares appears to result from passivation of the semiconductor surface that occurs during processing. The increased current in the Au square gratings is probably due to a lack of this passivating step and to surface damage incurred during an additional dry etch step. The details of the passivation and difference in dark current will be the subject of further investigation.

 

Fig. 7 (a) Dark current densities at 150K for the nBn detectors patterned with Ge and Au square gratings and mirrors. The current densities are J = 20 and 700 nA/cm², respectively at the operating voltage of 375 mV. The dark currents for reference mirror samples (no grating) are also shown. (b) Temperature dependence of the current density at the bias voltage for four devices, including mirror and grating devices.

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Figure 7(b) shows the temperature dependence of the dark current. For a diffusion limited diode the activation energy (ε_a) should be equal to the zero temperature band width (ε_g(0)), ≈333 meV for InAs_0.91Sb_0.09. Generation-recombination (GR) current should result in a much smaller activation energy ≈165meV. The value of 338meV seen here is consistent with diffusion and indicates that GR current is negligible as expected for an nBn structure.

Optical measurements were performed with illumination entering through polished, but uncoated, 500-μm-thick semi-transparent n-GaSb substrates. The detector spectral response was obtained by correlating the detector photocurrent with the wavelength of flood illumination from a broadband IR source coupled through a Fourier transform infrared spectrometer (FTIR). The spectra were normalized with respect to the FTIR spectrum of the IR source using the on-board DTGS detector, and corrected for the DTGS detector frequency response and the Dewar window transmission. The normalized spectra were then rescaled to absolute optical responsivity by measuring the photocurrent resulting from illumination by a calibrated 1000 K blackbody source which passed through a narrow-band filter centered at 3.3 µm and was then focused by an aberration-corrected f/4 lens system to a spot small enough to underfill the 140 µm-wide grating. This illumination provided a 7° maximum angle of incidence on the substrate, which following refraction, corresponds to 2° off normal incidence on the grating surface within the semiconductor. Grating-edge proximity effects may be ruled out because no significant changes were observed as the spot size was varied from 65 to 130 µm. The beam was polarized for some experiments by placing a wire-grid polarizer between the lens and the sample Dewar. The relative polarizer orientation was determined by rotating the polarizer to positions of minimum and maximum signal from devices with 1D gratings.

Figure 8(a) shows the experimental (solid) and simulated (dotted) EQEs at T = 120 K for a 1D grating with period 900 nm, height 100 nm (near the optimal value), and duty cycle 50%. Results are shown for both perpendicular (red) and parallel (blue) polarizations of the incident light, along with data for a flat mirror device on the same wafer (black). The spectrum for polarization perpendicular to the grating lines shows strong enhancement of the EQE near the plasmon peak at λ ≈3.3 μm, while the corresponding spectrum for parallel polarization shows a much weaker peak near 3 μm. Since the parallel polarization cannot couple to SPP modes, this shorter-wavelength resonance can be attributed to diffraction as discussed above. At resonance, the EQE for both polarizations is strongly enhanced over that of the mirror sample, whose response does not depend on polarization. The simulated results are qualitatively similar to the measurements, although they predict somewhat stronger resonances for reasons that will be discussed below.

 

Fig. 8 Experimental (solid) and simulated (dotted) external quantum efficiencies at T = 120 K for a 1D grating with period 900 nm and 50% duty cycle. Red curves represent light polarized perpendicular to the grating (TM), while blue represents parallel polarization (TE). The black curve shows data for a flat mirror sample residing on the same chip. The grating heights are (a) 100 nm and (b) 220 nm, which is less optimal.

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Figure 8(b) plots the EQE vs. wavelength for a device with a 1D grating height of 220 nm rather than 100 nm. With this non-optimal height, the plasmonic resonance for perpendicular polarization (near λ ≈3.8 μm in this case) is much less prominent. Instead, both polarizations display maxima near λ ≈3.1 μm. These are due to competition between the onset of diffraction with decreasing wavelength and the reduction of absorption as the diffraction angle decreases.

Figure 9 shows corresponding experimental EQEs for 2D Ge-square gratings with 25% duty cycle, 195 nm height, and three different grating periods: 900 nm (green), 975 nm (blue), and 1050 nm (cyan), along with results for a mirror sample (black). As expected for a 2D grating and normally-incident light, all of the results are nominally independent of polarization. The spectrum for each grating device displays a diffraction feature and a plasmon resonance peak, which both shift to longer wavelength as the grating period increases. In contrast, the spectrum for the mirror sample shows no prominent features. As in the 1D grating case, the simulations are qualitatively consistent with the data.

 

Fig. 9 Experimental EQEs for both polarizations at T = 120 K for 2D Ge-square gratings with height 220 nm, duty cycle 25%, and three different periods, along with data for a mirror sample.. All of the results are nominally independent of polarization.

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We also varied the height of the 2D Ge-square grating. Values of the measured EQE and the associated IQE are given in Table 1 along with the simulation results. While the direction of the change is consistent with the simulations, the measured IQE values are all somewhat lower than predicted. Due to the difficulty of determining weak peak positions on a sloping background the peaks were estimated from the enhancement, i.e. EQE(grating)/EQE(mirror).

Table 1. Comparison of experimental and simulated quantum efficiencies at 120 K for 2D Ge and Au square gratings with 900 nm period.

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The experimental EQE spectra for 2D Ge square gratings with 900 nm period and five different heights are shown in Fig. 10(a). Figure 10(b) plots the enhancement spectra, i.e., the ratio of EQE at a given wavelength to that measured for a flat mirror sample. While the SPP resonance wavelength is nearly independent of Ge thickness, the maximum enhancement at the peak is much stronger near the optimal height of ≈195 nm. Note also that a diffraction feature near λ ≈3.0 μm appears in the spectra for the thickest gratings. Figure 10(c) plots the measured peak enhancement as a function of grating height for 3 different periods. Whereas our simulations predict that the optimal grating height should scale with resonance wavelength, the maximum enhancement is at h ≈195 nm for devices with all 3 grating periods. The enhancement also increases with grating period. The longer in-plane propagation length enabled by coupling to the SPP modes becomes increasingly beneficial when absorption in the bulk material weakens at wavelengths approaching the cutoff. Because the strong enhancement persists near the band edge, (e.g., 1050nm pitch in Fig. 9), a plasmonically-enhanced detector with somewhat shorter cut-off wavelength (and hence lower dark current at a given operating temperature) will exhibit nearly the same QE as a conventional detector having a longer cut-off.

 

Fig. 10 (a) EQEs at 120 K for 2D Ge-square grating devices with 900 nm period and a series of grating heights (inset) Ratio of the EQE of grating device to the EQE of a flat mirror. (b) Experimental QE enhancement defined as EQE_grating/EQE_mirror.for 0.9um grating (c) Experimental QE enhancement vs. grating height for 2D Ge-square gratings with 3 different periods.

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Figure 11 compares the measured EQE of nBn devices with Au-square gratings with those of Ge-square designs. The Au square gratings had a height of 105nm which is very near optimal for this design. The Au-square designs have slightly higher peak EQE, although the range is narrower because the diffraction features imposed by the Ge square designs are absent from the spectra for the shallower Au-square gratings. Simulations predict that Ge square gratings should have slightly higher performance for optimal designs. However, for the measured designs they are predicted to be similar as the Ge square designs are not at the optimal duty cycle. The performance of both designs is lower than predicted by the simulations. Figure 12 compares the simulated and experimental EQE spectra for a 2D Ge-square grating sample with 900 nm period, 195 nm height, and 25% duty cycle, when illuminated by unpolarized light. While there is good qualitative agreement between the experimental and simulated spectra, the maximum experimental enhancement is only about half of that predicted by the simulation.

 

Fig. 11 Experimental EQE at 120 K for detectors with optimized 2D Au-square (solid) and Ge-squares (dashed) gratings for three different periods.

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Fig. 12 Measured (blue) and simulated (red) EQE vs. wavelength at T = 120 K for a 2D Ge-square grating with 900 nm period, 190 nm grating height, and 25% duty cycle. Dashed lines are simulations with sawtooth roughness of 30nm and 10nm, respectively.

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5. Analysis and Discussion

An explanation for the significant difference in the simulated and experimental EQE is not immediately apparent. One explanation is that the loss in the metallic grating is underestimated by the simulation. However, the optical constants measured for our deposited Au films do not support this interpretation. This continues to hold when the projected ≈1−2% loss due to absorption in the lossy 5-nm-thick Ti layer (deposited to assure adhesion to the semiconductor) is included [27]. Similarly, the deposited Ge was found to be non-absorbing at these wavelengths.

Another possible reason for the difference between the simulated and measured QE is surface roughness at the Au-Ge interface. From SEM images, we estimate the rms roughness of our samples to be much less than 10 nm. We have simulated the effect of this roughness by changing the boundary condition on the current at the Au-Ge interface. The results shown in Fig. 12 are for a sawtooth roughness model. The plasmon peak is affected more strongly than the diffraction feature, consistent with the data. However, the effect is small for realistic values of the roughness. Furthermore, the model shows that roughness causes a shift in the plasmon peak toward longer wavelengths, which is not reflected in the measured data.

Alternatively, the coupling between the incident light and the SPP may be imperfect. This is consistent with the results of [18] that found measurable reflection from similar 1D gratings illuminated by polarized incident light. Even if the coupling is non-ideal the reason remains unclear. Simulations of structures with rounded (rather than sharp) edges, which more realistically replicate the experimental structures, found minimal effect on the coupling efficiencies. While diffraction gratings tend to be relatively insensitive to surface roughness and other non-uniformities, there is some evidence that plasmonic structures are more susceptible to disorder [28]. Further study is needed to determine whether grating non-uniformity affects the detector performance.

Another potential source of discrepancy between the theoretical and experimental coupling coefficients is the implicit assumption in the simulations of a coherent light source. At critical coupling, η_c is greatest for a coherent source because destructive interference then minimizes the light reflected at the grating surface rather than coupled into SPP modes. The blackbody source (with narrow-band filter) that was used in the present experiments has a high degree of temporal coherence although an FPA sensing a broadband input signal will encounter lower coherence.

6. Conclusions

We have simulated and experimentally demonstrated MWIR nBn detectors with 2D plasmonic gratings that resonantly enhance the quantum efficiency of a thin InAsSb absorber. Simulations of the coupling to SPP modes reliably provides optimal design parameters, despite predicting stronger QE enhancement than is observed experimentally. The simulations further project significant enhancement of the QE for gratings with as few as 10 periods, i.e., small enough to fit on an FPA with 10-12 µm pitch. As expected, the QEs for 2D gratings are independent of light polarization at normal incidence. On resonance, the QE enhancements range from 1.6 to 2 for unpolarized light incident on a detector with active absorbing layers only 0.5 µm thick, and yields a peak IQE of up to ≈57% at 3.3 μm. Further work is needed to understand why the measured QEs are lower than those predicted by the simulations.