Antenna-enhanced high-resistance photovoltaic infrared detectors based on quantum ratchet architecture

Manipulation of intersubband transitions by engineered quantum-well (QW) structures is a key technology for mid-infrared region applications. Quantum cascade lasers have become dominant mid-infrared light sources.¹ In quantum-well infrared photodetectors (QWIPs), the necessity of an incident electric field vertical to the QWs has long been a problem.^2,3 However, recent progress in nanophotonics, particularly plasmonic antennas, has essentially solved the coupling issue with normally incident radiation.^4–9 

The majority of QWIPs have belonged to the photoconductive type. Nevertheless, the dark current due to bias voltage induces significant generation–recombination noise and limits the device operation to cryogenic temperatures. For imaging devices or uncooled detectors, photovoltaic (PV) QWIPs are advantageous because they do not require biasing and thus exhibit no dark current. PV-QWIPs based on asymmetric QW structures have been demonstrated since the early days of QWIP research.^10–12 The most promising scheme in this regard would be quantum cascade detectors (QCDs).^13–16 Performance enhancement of QCDs by incorporating micro/nanophotonics has also been attempted.^17–22 

In QCDs, the electrons are transported by tunneling and longitudinal optical (LO) phonon scattering through stairs of subbands. The difficulty in QCD design lies in the trade-off between responsivity and resistance.^15,16 For suppressing dominant Johnson noise, it is necessary to raise the resistance (R₀) area (A) product. Since the birth of QCDs, there have been various trials for improving R₀A, by methods such as thickening the barriers,^15,23 changing materials,^15,24,25 diagonal transition,²⁶ and using coupled QWs.²¹ However, these efforts have remained within the framework of binary energy profiles.

In this Letter, we present a high-resistance PV-QWIP architecture, which we call a quantum ratchet detector (QRD), where the R₀A is raised by suppressing the overlap of wavefunctions using a step QW²⁷ to trap electrons at a distant location. With the aid of responsivity enhancement by optical antennas,^28–30 a single-period detector demonstrated a maximum background-limited specific detectivity of 6.8 × 10¹⁰ cmHz^1/2/W at 6.4 μm, 77 K as well as a background-limited-infrared-photodetector (BLIP) temperature of 98 K. This performance is achieved through a high resistance of 6.0 × 10⁴ Ωcm², 29 times greater than conventional QCDs with a similar design.

Dark state and background state are key concepts in infrared detectors. In the dark state, the detector is covered with a cold shield and no radiation is incident. In the background state, the detector is exposed to radiation from a 300 K environment. The parameters corresponding to these two states are indicated by subscripts DK and BG, respectively.

Figure 1 quantitatively displays the significance of the spatial and energetic distances between S₁ and S_j on R₀A for a model PV-QWIP (see supplementary material S2). The colors indicate the G_1j between the ground state S₁ at the origin and a state S_j with an identical wavefunction shape virtually placed at (Δz, ΔE). As S_j moves away spatially (rightward) or energetically (upward), the conductance of the path exponentially decays. The horizontal singular peak at ΔE = ℏω_LO = 36 meV indicates the LO phonon scattering of GaAs.

For the energy ΔE of each state, the design freedom is limited, since this is determined by the target wavelength and energy step close to ℏω_LO. However, we have sufficient freedom in the spatial location of the wavefunctions Δz, which should be maximized so long as faster forward transition than backward is achieved. Quantitatively, G_1j decreases by one order of magnitude for a spatial distance of Δz₀ = 2.1 nm and an energetic distance of ΔE₀ = 14.5 meV. Considering the slope Δz₀/ΔE₀, a spatial distance sufficiently exceeding Δz ∼5.2 nm for a typical energy step of ΔE ∼ ℏω_LO is necessary for a significant reduction in the conductance. A structure keeping the wavefunction as far away as possible, preferably about 10 nm, would be necessary.

A band diagram of the proposed QRD made from GaAs/Al_xGa_1-xAs is shown in Fig. 2(a). The thickness of each layer (in nm) of the device region is as follows: 9.05/5.09/5.65/11.31(0.32)/5.65(0.25)/5.65/1.70/3.96/1.98/3.96/2.54/3.96/3.11/3.96, where AlGaAs barriers with x = 0.40 are shown in bold, the doped layer (Si, 1 × 10¹⁸ cm⁻³) is underlined, and () denotes the x value of Al_xGa_1-xAs for some well regions.

Because R_esp is inversely proportional to N_w, N_w = 1 gives the highest R_esp.^7,9,22 In addition, for a single-period structure, the influence of the energy profile at individual parts can be straightforwardly observed and compared. Therefore, we employ N_w = 1. Both sides of the device region in Fig. 2 are Ohmically connected to electrodes through highly doped contact layers. The structure was designed aiming at a responsivity peak at λ = 6.3 μm.

For rapid transport of electrons from the active well W₁ to a distant location, we employed a step QW made of a shallow floor and a deep well as the second well, W₂ (Ref. 27) [represented by a red frame in Fig. 2(a)]. This structure is made possible by the use of a GaAs/AlGaAs material system, which permits an arbitrary conduction band offset by composition x. S₇ and S₈ are formed by tunnel coupling between the second states of W₁ and W₂, and the fundamental state S₆ of W₂ is located at ∼ℏω_LO below those levels. Electrons excited from S₁ to S₇ or S₈ by infrared absorption relax to S₆ at a rate of Γ_for = 8.7 × 10¹¹ s⁻¹ by LO phonon scattering (see supplementary material S3). This process is faster than the backward transition (Γ_back = 3.9 × 10¹¹ s⁻¹) downward (to S₁) or leftward (to the left contact). Thus, the electrons preferentially flow in the right direction with a probability of p_e = Γ_for/(Γ_back + Γ_for) = 0.69.

The structure from W₃ was designed so that each subband descends by ∼ℏω_LO based on an earlier work.²³ The barriers here are slightly thicker than in the original study but are unified to the same thickness for easy interpretation of the results.

In this study, a conventional QCD with similar design parameters shown below is also discussed for a straightforward comparison [Fig. 2(b)]: 9.05/5.37/5.65/1.13/3.96/1.41/3.39/1.70/3.96/1.98/3.96/2.54/3.96/3.11/3.96.

The conduction band forms a binary profile made of only two levels. The extraction region from W₄ is identical to that from W₃ in Fig. 2(a). Electrons excited from S₁ to S₇ or S₈ relax to S₆, which is ∼ℏω_LO below S₇/S₈, at a rate of Γ_for = 1.22 × 10¹² s⁻¹, faster than the backward rate of Γ_back = 4.7 × 10¹¹ s⁻¹; p_e = 0.72 is expected.

The locations of the gravity centers of the squared wavefunctions with respect to the ground state of the structures in Fig. 2 are plotted in Fig. 1. Note that the G_1j values for j = 8 and 7 are overestimated by 1–2 orders of magnitude in Fig. 1, since the actual wavefunctions for S₈ and S₇ have a very different form than the assumed shape. In the reference QCD, the G_1j values for j = 6 and 5 exhibit a substantial contribution to $∑ j G 1 j$⁠. Therefore, these states short-circuit the electron flow to the ground state S₁ and limit R₀A to a low level. A more quantitative discussion is provided in supplementary material S2.

In contrast, in the proposed QRD, the location of S₆ is more distant by 9 nm than the reference QCD by the employment of the step QW, which suppresses the conductance by several orders of magnitude. Once the electrons are moved to such a far location, the backward transition from S₆ to the ground state S₁ then becomes negligible; S₆ functions as a ratchet to restrict the flow of electrons to one direction. Having no short-circuit path, QRDs can achieve drastically enhanced R₀A.

We fabricated both structures in Fig. 2 and compared their properties. The QWIP layer grown by molecular beam epitaxy on a GaAs substrate was transferred to a Au substrate by wafer bonding and removal of the original substrate. The transferred QWIP layer includes the device region and contact layers consisting of a 20-nm-thick n-GaAs layer (Si, 2 × 10¹⁸ cm⁻³) and a 28-nm-thick heavily doped layer (Si, 5 × 10¹⁸ cm⁻³, and seven periodic δ-doped layers of 3 × 10¹² cm⁻²) for nonalloyed Ohmic contact with the electrodes.³³ The actual QW structures suffered from fabrication errors, which are taken into consideration in the band diagrams in Fig. 2.

On a 160-μm-square QWIP layer, square Au patch antennas (side length: L) were periodically arranged (period: P) by electron beam drawing and liftoff in a 100-μm-square detector area. The fabricated antenna-enhanced QRD is shown in Fig. 3(a). On the Au patch side, the current laterally flows through the contact layer and reaches the surrounding electrode.³⁴ The QW structure in Fig. 2 rotated to the left by 90° is sandwiched between the Au patch and Au substrate. The electrode potential of the extractor side with respect to the W₁ side is defined as the bias voltage V_b. The Au patches were optimized to maximize the responsivity: (L, P) = (0.87, 2.00) for QRD and (0.88, 1.90) for reference QCD in micrometers.

Electric field distribution of the QRD at the responsivity peak obtained by finite element analysis is displayed in Fig. 3(b). At the active QW (white dotted line), vertical electric field intensity is magnified 178 times at maximum.

The fabricated devices were installed in a cryostat with ZnSe windows, and their responsivity spectra were measured with a Fourier transform infrared spectrometer by feeding the amplified current signal to the external port. When required, lock-in measurement with a step-scan mode was used. The spectral responsivity was quantified based on a calibrated HgCdTe detector.

The current–voltage relationship was measured with a source meter. The i_nsd was measured with a fast Fourier transform analyzer connected to a current amplifier in two environments: dark state and background state. The cryostat is equipped with a rotatable cold shield at 29 K with a blackbody coating. For the dark state, the detector was covered with the cold shield, while for the background state it was exposed to a 300 K environment with a field of view of 162°. See supplementary material S4 for details on fabrication, calculation, and characterization.

Figure 4(a) shows the current–voltage relationship for dark and background states. At zero bias, a photovoltaic signal higher than the dark current by several orders of magnitude is observed by background illumination. The dark current of the QRD is much lower than that of the QCD.

Figure 4(b) shows the responsivity spectra at 77 K. The value of R_esp,p at zero bias for QRD was 0.207 A/W (EQE = 0.040, λ = 6.40 μm), which was 36% of R_esp,p = 0.570 A/W for the reference QCD (0.106, 6.67 μm). However, by increasing the value of V_b, R_esp increased, and eventually both detectors exhibited similar maximum R_esp,p values (QRD: R_esp,p = 0.949 A/W, EQE = 0.183; QCD: 0.931 A/W, 0.174). As shown in Fig. 4(c), two or three peaks emerge in R_esp,p as V_b increases.

Compared with QCDs, in QRDs, more precise band alignment seems to be required for electron transport at zero bias. In addition, despite the design efforts aiming at an identical peak wavelength, the observed responsivity peak positions of the fabricated QRD and QCD showed a discrepancy. We attribute the incompleteness to inappropriate material parameters, particularly the conduction band offset, in the QW design. We also observed a change in the properties due to wafer bonding. Further refinement of the QW design and fabrication process is necessary.

Because η_abs is determined by the doping to the active QW, it should be identical in both detectors. Therefore, the maximum EQE of ∼0.18 for the peak bias would represent η_abs. In this situation, the electrons are forcibly extracted to the right side; thus, p_e ∼ 1 could be assumed (see supplementary material S5).

We can evaluate p_e at zero bias from the ratio of R_esp,p at zero bias to that at peak bias from Eq. (2), since η_abs is almost the same at peak bias and zero bias, and p_e at peak bias is almost 1. At zero bias, p_e = 0.61 is estimated for the reference QCD, fairly consistent with the predicted value. In contrast, p_e = 0.22 for the QRD. With future optimization, improvement by a factor of ∼3 is expected.

Figure 4(b) also presents the maximum R_esp based on calculation, which is 40% higher than the observed maximum R_esp. This could be due to excess absorption loss in the fabricated detectors or an overestimation of the imaginary part of the dielectric constant of W₁ used in the calculation. However, this discrepancy would be within a reasonable range.

Figure 5(a) shows the temperature dependence of i_nsd for both the dark and background states. Lower noise for the QRD is confirmed. The inset shows the Arrhenius plot displaying the temperature dependence of R₀A for dark current. At 77 K, QRD and QCD exhibit R₀A = 6.0 × 10⁴ and 2.1 × 10³ Ωcm², respectively. Resistance improvement by 29 times was achieved using the ratchet architecture. Both detectors present linear behavior throughout the temperature range studied and demonstrate fair agreement with the calculated values. The experimental activation energies derived from the slopes are 158 and 131 meV for QRD and QCD, respectively. In the band diagrams in Fig. 2, these activation energies with respect to Fermi energy are located between S₇ and S₆ for QRD and between S₆ and S₅ for QCD. This means that even S₅ influences the R₀A in the reference QCD. In contrast, S₆ of the QRD exerts a minor influence on R₀A, directly showing the advantage of the ratchet architecture.

Moreover, the observed i_nsd,DK's are well described as ∼(4k_BT/R₀)^1/2 and thus surely limited by the Johnson noise. On the other hand, i_nsd,BG's are constant below ∼100 K for both detectors; i.e., both detectors are in the BLIP region. T_BLIP, defined as the temperature giving identical dark- and background-origin noise components (2 × i_nsd,DK² = i_nsd,BG²), is 98 and 94 K for QRD and QCD, respectively. All of these noise properties indicate the excellent performance of QRD.

Figure 5(b) shows the $D BG *$ spectra at 77 K. At zero bias, $D BG *$ values are 3.5 × 10¹⁰ and 5.5 × 10¹⁰ cmHz^1/2/W for QRD and QCD, respectively. As Eq. (4b) predicts, the QRD could not surpass the QCD with a higher R_esp. Nevertheless, a high R₀A makes possible a higher $D BG *$ in a wider V_b range. Therefore, the maximum $D BG *$ at a finite V_b again showed the higher performance of QRD: 6.8 × 10¹⁰ and 6.4 × 10¹⁰ cmHz^1/2/W for QRD (V_b = +0.18 V) and QCD (V_b = +0.04 V), respectively. If the R_esp of the QRD was raised by a factor of ∼3 by improving the band alignment, zero bias $D BG *$ equivalent to that of the QCD and a much higher $D BG *$ at an optimum V_b could be achieved. In addition, T_BLIP as high as 110 K would be expected (see supplementary material S1 and S5).

Figure 5(b) also displays the theoretical limit of $D BG *$ by black curves. The solid line corresponds to interband detectors; our detectors nearly meet this criterion. However, for narrow-band detectors like QWIPs, this limit does not apply.^15,35 The theoretical limit for a detector with a similar bandwidth (Gaussian profile with a full width at half maximum of 6%) is also plotted by the dotted line, showing that there is still room for improvement.

Finally, we comment on the temperature dependence of the responsivity. Many QCDs have demonstrated room-temperature responsivity, including the same material system as ours.¹⁸ Nevertheless, both detectors in this study exhibited a quick responsivity drop at around T = 140 K, and we could not observe a significant signal at room temperature (see supplementary material S2 and S5). Because η_abs has no remarkable temperature dependence, the problem clearly lies elsewhere. Moreover, because this feature is common for both detectors, the problem is not due to the ratchet configuration. Our preliminary electron transport calculation suggests that the electron supply through our thick first barriers are bottlenecks at high temperatures. However, we would like to leave this for future work.

In summary, we proposed a PV-QWIP architecture with a drastically improved resistance by a step QW ratchetting the flow of electrons. Combined with optical antennas, a single-period detector demonstrated a maximum $D BG *$ of 6.8 × 10¹⁰ cmHz^1/2/W at 6.4 μm, 77 K, and T_BLIP of 98 K for normal incidence. While severe requirement for band alignment was also revealed, these achievements would be sufficient for proving the significance of QRDs. Improvement of zero bias p_e by refining the design and fabrication is expected.

A step QW is a versatile structure with a large amount of design freedom, and it has demonstrated interesting opto-electronic functions. If a step QW were used as the active well, λ_p could be tuned by V_b,³⁶ although the spectral change in our QRD was not so substantial (see supplementary material S5). In particular, optical nonlinearity in step QWs has been extensively studied.³⁷ While a GaAs/AlGaAs material system is suitable for a wide mid-infrared range, this range can be further extended by antenna enhancement of nonlinearity, such as second harmonics. The QRD proposed here could serve as a starting point for fabricating diversified functional devices.