1. Introduction

High sensitivity mid-infrared photodetection has typically relied on interband transitions in narrow-gap semiconductors. HgCdTe interband detectors are dominant for wavelengths longer than 5 μm; however, their toxicity and difficulty in device fabrication has fueled the search for other designs [1]. One well-known alternative, quantum-well infrared photodetectors (QWIPs) using intersubband transitions (ISBTs) in quantum wells, has been investigated since late 1980s [2]; QWIPs can be realized with less-toxic materials and mature, high-yield III-V semiconductor processes [1–3]. Unfortunately, conventional QWIPs have difficulty competing with interband detectors—QWIPs suffer from low signal due to two fundamental limitations.

First, the absorption coefficients of ISBTs are relatively low, typically ∼ 10³ cm^-1, one order of magnitude lower than interband transitions [4]. Second, ISBTs require light with a vertical electric field, not included in normally incident light [2,3]. To generate vertical electric fields from normal incidence, various oblique incidence configurations have been incorporated. However, optical coupling with incident light remains fundamentally inefficient.

Recently, interest in QWIPs has been revived thanks to breakthroughs in metamaterials research. Metasurface QWIPs, with a QWIP integrated as the dielectric layer in a metal-dielectric-metal (MDM) plasmon cavity, fundamentally resolve both signal limitations and present a competitive alternative to interband detectors [5–8]. The MDM cavity rotates the horizontal electric field of normal incidence to vertical through magnetic coupling [9–11], and light from an area much greater than the cavity’s geometrical dimensions is confined in the small volume of the dielectric (QWIP) layer—greatly enhancing electric field intensity [5–7,12–14]. Due to the electric field rotation and enhancement by the MDM cavity, metasurface QWIPs exhibit outstanding absorption for normal incidence, enabling high signal (e.g., external quantum efficiency up to 78%) [15] and even room temperature operation [6,7]. However, improved absorption realized by metasurface QWIPs challenges the design principles developed for conventional QWIPs.

In conventional QWIPs without any absorption-enhancement mechanisms (low-absorption regime), the number of quantum wells N_w must be large (typically, N_w = 25–100). Interestingly, large N_w does not enhance the signal—the responsivity R or external quantum efficiency (conversion efficiency) QE. R and QE are given as the product of the ISBT absorption efficiency by the quantum wells, $ \eta $_abs, from here simply called absorption efficiency, and photoconductive gain g. However, due to their opposite N_w dependence ($ \eta $_abs ∝ N_w and g ∝ 1/N_w), increasing N_w does not enhance R and QE (Supplement 1) [2, 3]. Instead, large N_w enhances the signal-to-noise ratio—detectivity D*, the fundamental figure of merit for infrared detectors. Increasing N_w decreases detector noise [16,17], improving D* even though the signal is not enhanced.

For QWIPs with absorption-enhancement mechanisms such as metasurface QWIPs (high-absorption regime), the relationship between N_w and detector performance (R, D*, etc.) drastically changes. In a detector with highly enhanced absorption, $ \eta $_abs can reach saturation and ultimately lose dependence on N_w [17]. However, g remains proportional to 1/N_w [3]. Since the N_w dependence in $ \eta $_abs and g no longer cancel, R and QE become proportional to 1/N_w. In contrast, N_w dependence of D* is greatly weakened (Supplement 1). Therefore, in the high-absorption regime, minimizing N_w has been recommended to maximize detector signal [3,5,14]; the ultimate metasurface QWIP should contain only a single quantum well (N_w = 1) [5].

Metasurface QWIPs with N_w = 1 have been actually fabricated [7,8,15,18–20], and have demonstrated both high R and QE. However, the anticipated superiority of N_w = 1 metasurface QWIPs over detectors with larger N_w has not been confirmed experimentally; only numerical studies on the effects of N_w on $ \eta $_abs can been found [21,22]. Furthermore, in experimentally demonstrated metasurface QWIPs, the assumptions of the high-absorption regime have not necessarily been fulfilled; $ \eta $_abs of N_w = 1 detectors is far from saturation ($ \eta $_abs ≈ 1), only reaching $ \eta $_abs ≈ 0.25 at most due to unavoidable free carrier absorption in the metal and contact layers [7,15,21,22]. Therefore, practical metasurface QWIPs are expected to show behavior between the low- and high-absorption regimes, raising the possibility that detectors with larger N_w can show superior performance to N_w = 1 detectors.

In this study, we compare metasurface QWIPs with N_w = 1 and N_w = 3 for various cavity designs and experimentally clarify the N_w dependence of fundamental properties such as R and D* for the first time. Contrary to the predictions of the high-absorption regime model, we find that N_w = 3 detectors are consistently superior to their N_w = 1 counterparts. N_w = 1 detectors indeed show higher R, as predicted by the high-absorption regime model. However, rather following predictions of the low-absorption model, greatly reduced noise—even sufficient to overcome the reduced R—leads to higher D* and thus superior detector performance for N_w = 3 metasurface QWIPs, regardless of cavity design. Thus, metasurface QWIPs actually operate in an intermediate regime, combining features of both the low- and high-absorption regimes.

Furthermore, D* for a metasurface QWIP with an N_w = 3 QWIP layer and a wired etched square MDM cavity design reaches an extremely high value (background limited D*_BG = 6.4×10¹⁰ cm Hz^1/2/W at 7.0 μm), beyond the theoretical limits of interband detectors (D*_BG = 5.3×10¹⁰ cm Hz^1/2/W at the same wavelength) [4,17]. Such extraordinary D*_BG has been anticipated for ISBT detectors with sufficiently narrow linewidths [17]. Here, we experimentally realize narrow spectral response via the double resonances of the electron waves in the QWIP layer and electromagnetic waves in the plasmon cavities unique to metasurface QWIPs [7,15]. Increasing N_w further reduces dark current, which is combined with the previously demonstrated narrow angular response and dark current reduction of our wired etched square cavities [7,19] to dramatically reduce detector noise, maintain sufficient signal, and thus greatly improve detectivity. Our results provide a clear roadmap for developing metasurface QWIPs with optimized QWIP layers and plasmon cavities that realize outstanding detectivities, particularly attractive for ultrasensitive chemical sensing, never achievable with conventional interband detectors.

2. Methods

Before discussing specific metasurface QWIPs, we first describe the general design, fabrication and characterization processes used in this study.

2.1 QWIP layer design and crystal growth

QWIP layers with N_w = 1 and N_w = 3 were fabricated via molecular beam epitaxy—GaAs quantum wells (Si doping density: 3×10¹⁸ /cm³) and undoped Al_0.3Ga_0.7As barriers are sandwiched between highly doped GaAs ohmic contact layers [23]. For N_w = 3 QWIP layers (total thickness T = 288 nm), two additional periods were added to our previous N_w = 1 QWIP layer design (T = 200 nm) (Figs. 1(a), 1(b)) [7,15,19,20].

 

Fig. 1. Layer-by-layer structure (left) and conduction band profiles (right) of a) N_w = 1 and b) N_w = 3 QWIP layers. The dashed line indicates the position of the Fermi level in the QWIP. c) Unpolarized responsivity R spectra of Brewster-angle detectors made with N_w = 1 (red) and N_w = 3 (blue) QWIP layers.

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2.2 Fabrication of Brewster-angle detectors

To evaluate the fundamental responsivity profiles of QWIP layers, Brewster-angle incidence detectors were fabricated [7]. These detectors have no absorption enhancement and thus operate in the low-absorption regime, serving as counterparts to the metasurface QWIPs with enhanced absorption.

2.3 Fabrication of metasurface QWIPs

For metasurface QWIP fabrication, QWIP layers were transferred from their original GaAs substrate to a 650-nm-thick Au substrate via Au-Au diffusion bonding followed by removal of the original GaAs substrate [7]; 100-nm-thick Au top layers were then patterned on the exposed QWIP layer surface to form MDM cavities. Four different MDM cavity designs were fabricated, corresponding to designs for metasurface QWIPs from our previous reports—wired etched squares [7], unetched squares [15], etched stripes, and unetched stripes [19]. Etched designs have the QWIP layer removed outside the MDM cavity, reducing the electrical area of the detector. Dark current due to applied voltage and dark current noise both decrease with reducing electrical area, as shown in previous studies of metasurface QWIPs with identical N_w, leading to improved D* [5,7,19,24]. By comparing etched and unetched detectors, we can further evaluate the interplay between noise reduction from adding N_w and from reducing electrical area by etching (Supplement 1). Cavity dimensions such as length L and period P for each design were numerically determined to give resonance at 6.7 μm, and metasurface detectors with several different cavity lengths L around the target value were fabricated on the same chip for systematic evaluation of detectors with different peak wavelengths. Each metasurface QWIP is a 100×100 μm² square containing numerous periodically arranged cavities.

2.4 Optical characterization

Numerical simulation was performed using rigorous coupled wave analysis and finite element method depending on the structures and required accuracy. GaAs quantum wells were treated as a uniaxial material with ISBT absorption in the vertical direction and free-carrier absorption in the lateral directions. Wavelength-dependent dielectric constants for Au and semiconductors were taken from literature [25,26]. Free-carrier absorption in the semiconductor layers due to doping was expressed by adding a Drude term. Further details can be found in our previous reports [7,15,19,20].

Experimental total absorption A_TOT for all metasurface QWIPs was evaluated from reflection spectra r_TOT for s-polarization at a narrow angular distribution around an incidence angle θ = 26° using Fourier-transform infrared (FTIR) spectroscopy and taking A_TOT = 1 – r_TOT [7,15,20]. Based on the measured A_TOT spectra, pairs of metasurface QWIPs with N_w = 1 and N_w = 3 having nearly equivalent total absorption spectra (both center wavelength and height) for each cavity design were selected and compared so that the differences in detection performance can be simply attributed to the different N_w.

Responsivity spectra were collected using FTIR at 78 K; the current signal of the detector was amplified and fed to the FTIR external port. Quantified R and QE values were based on a calibrated HgCdTe detector. Note that QE and R are intrinsically related by the relation:

2.5 Electrical characterization

Before discussing the electrical characterization of our metasurface QWIPs, we formally define several terms [15,19]. Dark current I_D is the current present in a biased detector without incident radiation due to thermally excited electrons which shows the inherent transport properties of the detector. Background current I_BG is the current inevitably generated during normal operation of a biased detector due to exposure to incident radiation from a room-temperature background ambient (298 K). The background photocurrent I_P,BG is the contribution of photoexcited electrons to the background current: I_P,BG= I_BG – I_D. The background photodetector noise i_n,BG is generation-recombination noise in the QWIP due to thermally excited electrons and photoexcited electrons in response to the background ambient [3], written as:

Two types of D* can be defined. The background-limited detectivity D*_BG, when the photodetector is exposed to environmental illumination and noise primarily comes from photoexcited carriers, is calculated as:

I_D was measured with the detector covered by a cold shield with a blackbody coating cooled to a sufficiently low temperature (≤ 78 K). For I_BG measurements, the cold shield is removed, exposing the detector to background radiation from a 298 K ambient with a 162° field of view (FOV). A 162° FOV is sufficiently large because the radiation power density incident on the detector from the background ambient is 98% of the power density of the usually discussed 180° FOV [4,17]. I_D and I_BG were measured with a source meter. The dark current noise spectral density i_n,D/Δf^1/2 was measured at 1.125 kHz using a fast Fourier transform analyzer [7,15,19]. Photoconductive gain g is then determined from Eq. (2) with I_P,BG = 0. Measured g further allows us to determine experimental $ \eta $_abs from QE, using the relationship $ \eta $_abs=QE/g (Supplement 1).

Some asymmetry in bias-voltage dependence is present in currents, noise spectral density, and g (Fig. S5) due to dopant inhomogeneity. In the main text we focus on the positive bias regime which showed higher R_peak values and gave the most stable results for i_n,D, as in our previous papers [7,15,19,20]. We would like to note that due to the wafer transfer process, the QWIP layer in the metasurface QWIPs and that in the Brewster-angle detectors are flipped from each other [7]. For consistent comparison throughout this work, we define the sign of the upper electrode of the Brewster-angle detectors as opposite to that of the metasurface QWIPs.

3. Results

3.1 Relative performance of N_w = 1 and N_w = 3 Brewster-angle detectors

We first discuss the performance of the Brewster-angle detectors. When comparing the properties of each QWIP layer, we consider the 3-to-1 ratio (Table 1), which describes the ratio of a particular property (R_peak, $ \eta $_abs, g, D*, etc.) in N_w = 3 detectors relative to N_w = 1 detectors. For the Brewster-angle detectors, all values used for determining 3-to-1 ratios can be found in Table S1. We note that g showed a remarkable consistency for all Brewster-angle detectors and metasurface QWIPs with the same N_w over our investigated bias range (Fig. S5a). Therefore in this paper, we assume g is inherent to the QWIP layer and we use an average g, from here called g_avg, when discussing all N_w = 1 or N_w= 3 detectors.

Table 1. Relation between N_w and $ \eta $_abs, g, R_peak, i_n,D, i_n,BG, D*_D, and D*_BG in the low- and high-absorption regimes, and for actual Brewster-angle and metasurface QWIPs with wired etched square cavities

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g_avg = 1.2 for the N_w = 3 Brewster-angle detector (at a peak bias V_peak of 0.53 V) and g_avg = 2.6 for N_w = 1 (V_peak = 0.39 V) gives a 3-to-1 ratio of 0.46. The fundamental responsivity spectra of the N_w = 1 and N_w = 3 Brewster-angle detectors are shown in Fig. 1(c). R_peak values of 4.7 mA/W (peak QE, QE_peak= 0.086%; V_peak = 0.39 V) for N_w = 1 and 7.0 mA/W (QE_peak = 0.12%, V_peak = 0.53 V) for N_w = 3 give an 3-to-1 ratio of 1.5. In contrast, $ \eta $_abs = 0.10% for the N_w = 3 detector and $ \eta$_abs = 0.033% for N_w = 1 give a 3-to-1 ratio of 3.0.

The 3-to-1 ratios for the Brewster-angle detectors show good consistency with predictions for the low-absorption regime, as will be covered in the Discussion section. Although the peak wavelengths λ_peak for R_peak are different for N_w = 1 (6.7 μm) and N_w = 3 (7.0 μm) Brewster-angle detectors, we do not consider the small difference in λ_peak an essential problem in this paper. We have regularly observed such shifts; a similar discrepancy in λ_peak was consistently observed for the same QWIP layer (N_w = 1) in our previous studies [15,19,20] only because of our wafer transfer process. Note that in this paper, we will discuss detector performance with respect to bias voltage rather than to average applied electric field. Electric field distribution in QWIPs with small N_w is not homogeneous [28–31], therefore average applied electric field is not a good metric here.

3.2 Relative performance of N_w = 1 and N_w = 3 wired etched square cavity detectors

For discussing metasurface QWIP performance in the main text, we focus on detectors with wired etched square cavities—our highest-performance cavity design—with N_w = 1 and N_w = 3. Regardless of cavity design, however, the behavior of N_w = 1 and N_w = 3 metasurface QWIPs is remarkably consistent (Supplement 1). The wired etched square cavities consist of a periodic array of Au square patches with length L and period P, connected by thin wires (width W = 100 nm) in an “S-shape” design with folding length S which provides electrical connection between square cavities while preserving their original resonance (Fig. 2(a), (b)) [7]. The QWIP layer outside the patches and wires is removed by dry etching. A pair of N_w = 1 and N_w = 3 detectors with (L, P, S) = (1.19, 2.0, 0.34) and (1.22, 2.5, 0.39) in μm, respectively (Figs. 2(c), (d)), have nearly identical A_TOT spectra from both experiments and numerical simulation (Fig. 2(e)) [7,15].

 

Fig. 2. a, b) Schematics and c, d) scanning electron micrographs of N_w = 1 (a, c) and N_w = 3 (b, d) wired etched square detectors. e, f) Experimental (solid) and calculated (dashed) total absorption A_TOT for s-polarized light at θ = 26° incidence, and absorption efficiency $\eta_{\mathrm{abs}}$ for θ = 0° for N_w = 1 (red) and N_w = 3 (blue) wired etched square detectors.

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The most striking difference between N_w = 1 and N_w = 3 metasurface QWIPs appears in the bias voltage-dependence of R_peak (Fig. 3(a)). R_peak values for the N_w = 1 detectors have a clear peak with increasing bias, consistent with previous studies for N_w = 1 QWIP layers [30]; N_w = 3 detectors have a more plateau-like profile similar to conventional multi-well QWIPs [2]. Figure 3(a), (b) also show another noteworthy result—upon increasing N_w from 1 to 3, maximum R_peak, indicated by black arrows in Fig. 3(a), is reduced (R_peak = 2.8 A/W, QE_peak = 51% for N_w = 1; R_peak = 2.1 A/W, QE_peak = 36% for N_w = 3) despite the presence of additional absorbing quantum wells. In fact, for all cavity designs R_peak of N_w = 3 metasurface QWIPs is reduced compared to their N_w = 1 counterparts (Fig. S5b).

 

Fig. 3. a) Bias-voltage dependence of peak responsivity R_peak for N_w = 1 (red) and N_w = 3 (blue) wired etched square detectors. Arrows indicate peak bias voltage V_peak giving R_peak. b) Experimental (solid) and calculated (dashed) unpolarized R spectra for the N_w = 1 detector at V_peak = 0.5 V and N_w = 3 detector at V_peak = 0.7 V.

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When we consider the 3-to-1 ratios for metasurface QWIPs, the reduced R_peak for the N_w = 3 metasurface QWIP leads to a 3-to-1 ratio of 0.75. g_avg at V_peak for N_w = 3 (1.1) and N_w = 1 (2.5) detectors gives a 3-to-1 ratio of 0.44 (Tables 1 and 2). $ \eta $_abs, determined from R_peak and g_avg, increases from 0.20 to 0.33 as N_w increases from 1 to 3 (Fig. 2(f), Table 2), giving a 3-to-1 ratio of 1.7 for $ \eta $_abs. Metasurface QWIPs with different cavity designs show similar 3-to-1 ratios (Table S3). In contrast to the Brewster-angle detectors, the reduced 3-to-1 ratio for R is suggestive of high-absorption regime behavior; the actual, more complex behavior of metasurface QWIPs will be fully described in the Discussion section.

Table 2. Properties of N_w = 1 and N_w = 3 metasurface QWIPs with wired etched square cavities at V_peak^a

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Note that comparisons of A_TOT and $ \eta $_abs in Fig. 2(e), (f) and for the different cavity designs (Figs. S1–S3) indicate A_TOT remains mostly comprised of non-ISBT free-carrier absorption from metal and contact layers, not $ \eta $_abs from the ISBTs—consistent with results from previous numerical simulations [7,15,21].

Although R_peak in the N_w = 3 detector is reduced, this does not lead to lower D*. Surprisingly, the wired etched square N_w = 3 detector has higher detector performance, namely superior D* than the N_w = 1 detector, despite reduced R_peak. The drastically reduced noise—i_n,D and i_n,BG (Table 2)—in the N_w = 3 detector fully compensates for reduced R_peak. Past 0.3 V and across the entirety of the bias voltage range (Figs. 4(a), (b)), I_D, I_BG and i_n,D (thus also i_n,BG) for the N_w = 3 detector are greatly reduced compared to the N_w = 1 detector, over two times lower at V_peak (Table 2). The background noise equivalent power i_n,BG/R_peak for the N_w = 3 detector is improved as well, only 0.16 pA Hz^-1/2 compared to 0.24 pA Hz^-1/2 for the N_w = 1 detector. Similar reductions in I_D, I_BG and i_n,D are in fact observed for N_w = 3 metasurface QWIPs regardless of cavity design (Table S2, Fig. S4); a detailed explanation for this behavior is found in the Supplement 1.

 

Fig. 4. a) Bias-voltage dependence of dark current I_D (solid) and background current I_BG (dashed) of metasurface QWIPs with wired etched square cavities with N_w = 1 (red) and N_w = 3 (blue). Corresponding current densities shown on right axis in a) (electrical areas are 1.135×10⁻⁴ cm²). b) Dark current noise i_n,D and c) average photoconductive gain g_avg for both detectors. Error bars in c) represent standard deviation based on measured g values for all detectors in this manuscript. d) Background-limited detectivity D*_BG for N_w = 1 and N_w = 3 metasurface QWIPs with wired etched square cavities. Error bars are based on the standard deviation of the g_avg values used in the calculation of D*_BG. The dashed line corresponds to D*_BG,ideal for an ideal photoconductor, 5.3×10¹⁰ cm Hz^1/2/W at 7.0 μm, 300 K, and a 180° FOV.

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Figure 4(c) clearly shows the remarkable reduction in g (g_avg). Following Eq. (2), g is proportional to i_n,D²/I_D. The over two times reduction in i_n,D and I_D at V_peak naturally leads to an over two times reduction of g (g_avg) at V_peak as well (Table 2). D*_BG [calculated using Eq. (3)] in the N_w = 3 detector is nearly 1.5 times higher, 6.4×10¹⁰ cm Hz^1/2/W, than D*_BG for the N_w = 1 detector (4.3×10¹⁰ cm Hz^1/2/W) at V_peak despite the diminished R_peak (Fig. 4(d)). D*_BG in the N_w = 3 wired etched square detector at 7.0 μm is remarkably high, even past the maximum theoretically achievable D*_BG for an interband photoconductor at the same wavelength (5.3×10¹⁰ cm Hz^1/2/W) over a bias range of 0.5–0.75 V (Fig. 4(d)). This extremely high D*_BG, one of the most significant findings in this work, arises from a combination of properties unique to metasurface QWIPs and the distinctive features of the wired etched cavity design. Full details are discussed in the next section.

4. Discussion

4.1 Comparison of 3-to-1 ratios for Brewster-angle and metasurface QWIPs with low- and high-absorption regime models

Our results represent the first systematic experimental investigation of the effects of N_w on QWIPs without and with absorption enhancement, and confirm characteristic behaviors for both Brewster-angle detectors and metasurface QWIPs. Table 1 shows a comparison of detector behavior with predicted low- and high-absorption regimes. We first note that the 3-to-1 ratios for g_avg for Brewster-angle QWIPs (0.46) and metasurface QWIPs (0.44) are nearly identical—higher than the expected g_avg (0.33), but within a reasonable range. For the Brewster-angle detectors, the 3-to-1 ratio for $ \eta $_abs (3.0) matches the ratio for the low-absorption regime (3.0). Due to the higher ratio for g_avg, the resultant 3-to-1 ratio for R (1.5) is also somewhat higher than anticipated (1.0), leading to enhanced R with increased N_w, instead of R being independent of N_w as in the low-absorption regime model. The 3-to-1 ratios for i_n,D (0.60) and i_n,BG (0.64) clearly demonstrate reduced noise due to additional N_w leading to improved D*. The high 3-to-1 ratios for D*_D (2.5) and D*_BG (2.3) are in good agreement with predictions for the low-absorption regime (3.0 and 1.7, respectively). Thus, overall, behavior of Brewster-angle detectors fits reasonably in the low-absorption regime.

In contrast, metasurface QWIPs demonstrate complex, intermediate behavior—R behaves similar to the high-absorption regime, but D* follows low-absorption regime behavior, ultimately leading to superior performance of N_w = 3 metasurface QWIPs versus their N_w = 1 counterparts. The most unique result for metasurface QWIPs is the 3-to-1 ratio for R—upon increasing N_w from 1 to 3, the 3-to-1 ratio for R for metasurface QWIPs of all cavity designs decreases to around 0.75, in contrast to 1.5-fold increase for Brewster-angle QWIPs. The diminished R with increasing N_w represents the first experimental confirmation of behavior agreeing with the previously proposed high-absorption regime model [3,17]. However, the observed reduction in R is not as dramatic as expected (0.33). This moderate reduction in R can be understood by $ \eta $_abs. The 3-to-1 ratio of 1.7 for $ \eta $_abs sits in an intermediate regime between low- and high-absorption regimes (3-to-1 ratio: 3.0 and 1.0, respectively); roughly half of the 3-to-1 ratio for $ \eta $_abs of 3.0 for the Brewster-angle detectors. Enhancing $ \eta $_abs by adding additional wells is not as effective for metasurface QWIPs compared to conventional QWIP layers. $ \eta $_abs for practical metasurface QWIPs is not yet fully saturated and thus actually displays some N_w dependence; $ \eta $_abs can still increase—additional wells could absorb electromagnetic energy that would otherwise be absorbed by free carriers in the metal and contact layers [7,21,22]. While R demonstrates high-absorption regime behavior, noise in metasurface QWIPs still decreases with increasing N_w, as indicated by the 3-to-1 ratios for i_n,D, and i_n,BG (0.43 and 0.50, respectively). For both i_n,D and i_n,BG, the 3-to-1 ratios are smaller than the 3-to-1 ratio for R, indicating reduction in noise is greater than the reduction in R. Thus, 3-to-1 ratios for D*_D (1.7) and D*_BG (1.5) for metasurface QWIPs show increasing D* with increasing N_w.

4.2 Comparison of D* for ideal interband and ISBT detectors

Greatly reduced noise in our wired etched square cavity N_w = 3 metasurface QWIP leads to the exceptionally high D*_BG observed. From here, we discuss the combination of mechanisms reducing noise in our detector. The 300 K background detectivity of an ideal interband photoconductor D*_BG,ideal is a standard performance benchmark for infrared photodetectors—the maximum D*_BG theoretically achievable when the detector with a 180° FOV is exposed to radiation from a 300 K ambient [4].

D*_BG,ideal for a detector with R_peak at λ_peak is calculated from the definitions of R_peak [Eq. (1)], A, and i_n,BG, following Eq. (3), treating I_D as negligible (I_BG ≈ I_P,BG), and applying the definition of I_P,BG from the Supplement 1:

The solid line in Fig. 5(a) describes the absorption profile of an ideal interband photoconductor that perfectly absorbs all light below its cutoff wavelength λ_c, and none above λ_c [$ \eta $_abs,ideal (λ) = 1 for λ < λ_c; $ \eta $_abs,ideal (λ) = 0 for λ > λ_c]. Applying Eq. (4), D*_BG,ideal was calculated for an ideal interband photoconductor (solid line, Fig. 5(b)) [1,17].

 

Fig. 5. a) Comparison of absorption efficiency $\eta_{\mathrm{abs}}$ profiles for ideal interband detector with a cutoff wavelength λ_c = 7 μm and an ideal ISBT detector with a Gaussian profile centered at λ_peak = 7 μm and a FWHM of 9%. Inset shows Gaussian fit to the experimental $\eta_{\mathrm{abs}}$ of the N_w = 3 metasurface QWIP with wired etched square cavities with an FWHM of 9%. b) Relationship of D*_BG with cutoff wavelength for an ideal interband photoconductive detector (solid line) and with center wavelength for an ideal ISBT photoconductive detector with a 9% Gaussian profile. Stars correspond to maximum D*_BG for N_w = 3 and N_w = 1 metasurface QWIPs from this manuscript (red and blue) and previously reported D*_BG for photoconductive mid-infrared metasurface QWIPs at 78 K: Ref. [7] (green) and Ref. [6] (yellow).

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Our N_w = 3 metasurface QWIP is best described by a Gaussian fit with a 9% linewidth (Δλ/λ_peak—here Δλ is the full width at half maximum—inset in Fig. 5(a)) rather than a Lorentzian function [3,5,17]. An ideal ISBT detector with the same linewidth and perfect absorption at a distinct λ_peak [$ \eta $_abs,ideal (λ_peak) = 1] is shown by the dashed line in Fig. 5(a). Applying Eq. (4), D*_BG,ideal was also calculated for ISBT detectors with various λ_peak values (dashed line, Fig. 5(b)). D*_BG,ideal values much larger than for interband detectors can be realized, particularly at longer wavelengths, because ISBT detectors have no sensitivity outside of their narrow spectral response, thus suppressing background current generation and noise.

For metasurface QWIPs, the MDM cavity resonance provides additional linewidth reduction. Compared to the N_w = 3 Brewster-angle detector (Δλ = 1.09 μm, 16% FWHM) with an identical QWIP layer, the linewidth of our N_w = 3 metasurface QWIP (Δλ = 0.62 μm, 9% FWHM) is reduced by nearly half; similar reductions are seen for metasurface QWIPs regardless of cavity design. The double resonances of the QWIP layer for the electron waves and MDM cavity for the electromagnetic waves, unique to metasurface QWIPs, are essential for reducing noise beyond the limits of conventional ISBT detectors.

The star symbols in Fig. 5(b) are maximum reported D*_BG of our N_w = 1 and N_w = 3 metasurface QWIPs at 78 K and previously reported D*_BG values at 78 K for photoconductive metasurface QWIPs in the mid-infrared [6,7]. Only our N_w = 3 detector demonstrates D*_BG beyond the ideal interband photoconductor limit at 78 K. For photovoltaic metasurface QWIPs, D*_BG reaching the ideal interband detector limit has been reported, but not yet surpassed this limit [32]. Very high D*_BG has also been reported for photoconductive THz metasurface QWIPs. However, the very narrow FOV (54°–60°) for the D*_BG measurements makes comparison with ideal detectors difficult [27,33].

4.3 Further noise reduction mechanisms in metasurface QWIPs

Compared to ideal ISBT detectors, our metasurface QWIPs do not have perfect absorption at their peak wavelength—additional factors beyond simply narrow spectral response further reduce noise while maintaining sufficient signal. Practically, I_D cannot be neglected in real metasurface QWIPs, and contributes significantly to I_BG and i_n,BG [See Eq. (2)]. Increasing N_w greatly reduces I_D regardless of cavity design, yet only slightly reduces I_P,BG (Figs. 4 and S4, Tables 2 and S2), preserving detector signal while greatly reducing noise; noise reduction approaches for conventional QWIPs can still be applied to metasurface QWIPs.

The exceptionally high D*_BG in N_w = 3 detectors with wired etched square cavities results from two further noise reduction mechanisms unique to the cavities. As seen in earlier studies of N_w= 1 detectors, wired etched square cavities promote narrowed angular response [7,19]. The square cavities connected with wires limit absorption from large angles, suppressing background current generation (I_BG and thus i_n,BG) from unwanted directions [7], while the polarization-independent square cavities maintain high sensitivity for near-normal incidence. Additionally, the etched cavity design reduces the electrical area of the QWIP, which reduces I_D while minimally affecting R, $ \eta $_abs, and I_P,BG thanks to the localized absorption in the cavity (Table 2) [5,14,19]. Thus, etching reduces noise, improving D*_BG [15,19]. The unprecedented combination of noise-reduction features—narrowed spectral response, extra N_w, reduced angular response, and reduced electrical area—combining techniques developed for conventional (increased N_w) and metasurface QWIPs (wired etched cavity designs), leads to the exceptionally high detectivities in this manuscript.

4.4 Future improvements—optimization of N_w in metasurface QWIPs

Even further improvement of detectivity would be possible if an optimum N_w can be determined. Recently, numerical investigations on the effects of N_w on $ \eta $_abs in metasurface QWIPs predicted that N_w = 3 is the ideal value for etched detectors [21,22]. However, this study was limited to specific structures with thick QWIP layers using higher order cavity modes. MDM cavities efficiently function for a dielectric layer sufficiently thinner than λ_peak/(2n) where n is the effective refractive index of the dielectric layer, beyond which non-plasmonic guided modes appear [34–36]. In addition, confinement in a smaller volume with a thinner QWIP layer generates a higher electric field from incident light, thus, high absorption enhancement [13,37]. The thickness of the QWIP layer therefore has an electromagnetic upper limit which restricts the maximum N_w. The optimum N_w depends on a delicate balance among reduced R due to increased N_w, absorption enhancement by the cavities, and further reduced noise. With fully optimized N_w and cavity designs, detectors with D*_BG well beyond interband photoconductors at fully engineered wavelengths could be realized, and would be particularly attractive for ultrasensitive chemical detection such as gas sensing [20,38–40].

5. Conclusions

To summarize, we have experimentally investigated the influence of the number of quantum wells on Brewster-angle and metasurface QWIP performance by comparing detectors with N_w = 1 and N_w = 3 QWIP layers. N_w = 3 metasurface QWIPs are found to be superior—although R is reduced compared to N_w = 1 detectors, detector noise is reduced even more dramatically, leading to improved D*_BG regardless of MDM cavity design.

While Brewster-angle detectors with no metasurface show reasonable agreement with the previously described low-absorption regime for conventional QWIPs, metasurface QWIPs behave in a more complex manner. Although metasurface QWIPs have greatly enhanced absorption, they display behavior combining features of both high-absorption (low 3-to-1 ratio for R) and low-absorption regimes (high 3-to-1 ratio for D*_BG).

A N_w = 3 wired etched square cavity metasurface QWIP resonant at 7.0 μm has an R_peak reduced to only 75% of its N_w = 1 counterpart, but noise is over two times as low due to the additional wells, leading to a 1.5 times higher background-limited D*_BG of 6.4×10¹⁰ cm Hz^1/2/W at peak bias voltage (D*_BG = 4.3×10¹⁰ cm Hz^1/2/W for N_w = 1). This very high D*_BG—made possible because of the narrow spectral response, low dark current, and narrow angular response of the detector—breaks the theoretical limit of D*_BG for an ideal interband photoconductor with the same cutoff wavelength. Finding an optimum N_w for metasurface QWIPs remains a subject of ongoing investigations. Nevertheless, our results demonstrate how reduced noise and narrow linewidths can be realized for metasurface QWIPs, providing a roadmap for detectors that push D* beyond the limits of interband photoconductors, particularly at longer wavelengths.