Complementary split-ring resonator antenna coupled quantum dot infrared photodetector

The inter-sublevel transitions in semiconductor quantum dots (QDs)¹ can be exploited to realize photodetectors for the mid-infrared (mid-IR) spectral range.^2–4 Several advantages have been envisaged for the quantum dot infrared photodetector (QDIP) with respect to the quantum well infrared photodetector (QWIP),⁵ such as:⁶ possibility of normal-incidence excitation; reduced thermal generation and relaxation rates of electrons; low dark current. Several comprehensive reviews^4,7–10 have been written in order to discuss the issues and potentialities of detectors based on QDs. Among several limitations, the low absorption strength, for light polarized along in-plane directions, associated to transitions from the ground QD shell to the outermost shells or to the continuum, strongly limits the QDIP responsivity at normal incidence. Many efforts have been focused on the implementation on QDIPs of optically resonant structures, such as photonic^11,12 or plasmonic crystals,^13–17 aimed at increasing the coupling efficiency with normally incident light. Several systems are mentioned in Ref. 7. Another approach typically used for the enhancement of the detector performance is based on nanoantennae capable of concentrating the field in low-sized volumes.¹⁸ In Ref. 19 performance improvements of a QWIP, based on an array of patch antenna micro-cavities, were presented. In Ref. 20, the resonant coupling between a complementary split-ring-resonator (CSRR) metamaterial and the active region of a quantum cascade detector (QCD) was shown. A similar CSRR antenna concept, as we show in this letter, can be used for enhancing the responsivity of a QDIP.

For our study, as a proof of principle, we used a simple single-layer QDIP asymmetric structure analogous to the one presented in Refs. 21–23. The latter is based on a single layer of self-assembled InAs/GaAs QDs (2.4ML grown at 0.088ML/s), coupled via a GaAs(5 nm)/Al_0.33Ga_0.67As(3.5 nm)/GaAs(2 nm) structure to an In_0.21Ga_0.79As QW. By means of scanning electron microscopy (SEM), a QD density n_QD = 2.1 × 10¹⁰cm⁻² was estimated.

The electronic structure of the lens shaped QDs was computed by means of Nextnano++,²⁴ using the experimentally determined QD geometry and the inter-band spectrum obtained from the low-temperature photoluminescence (not shown).²³ The conduction band (CB) profile of the structure is shown in Fig. 1, and was computed using the method described in Refs. 22 and 23. In the inset of Fig. 1, it is possible to observe how the structure was engineered in order to position the Fermi level (red dashed line) above the s shell of the QDs. The electrons sitting on the QD s shell can be excited by means of mid-IR optical radiation towards the continuum above the GaAs band edge, generating a photocurrent. This type of detector works for zero (photovoltaic operation)²⁵ and negative values of the applied voltage V_bias.

The layer was processed in square mesas of side lengths between 20 μm and 750 μm. The 300 nm thick n⁺ − GaAs top contact was thinned, by means of wet chemical etching, down to 50 nm. A layer of Ge/Au/Ni/Au was deposited on the bottom contact by electron beam deposition and alloyed by rapid thermal annealing. On the top contact, a layer of Ti(10 nm)/Au(100 nm) was deposited, on which the nanoantenna array was defined, using a fabrication technique based on an electron beam lithography step followed by Ar⁺ ion-beam etching for the metal patterning.

The nano-antenna design is based on the split-ring resonator (SRR) geometry.²⁶ In particular, the electric SRR,^27,28 consisting of two inductive loops (L) interrupted by a central capacitive gap (C) (Fig. 2(a)), is used in its complementary (CSRR) design.^29,30 Such a system can be effectively treated as an LC circuit, showing a resonant behaviour at $λ L C ∼ L C$^31–33 (LC mode). The unit cell of the CSRR 2D square array and a SEM micrograph of a resonator obtained after the metal etching procedure are shown in Fig. 2(a).

Besides the antenna-based devices, reference devices were processed, for which the top contact was left uncovered. Metallic pads of Ti(10 nm)/Pt(50 nm)/Au(200 nm) were finally deposited on the top contacts: they define the ohmic contacts and facilitate the wire bonding procedure. A schematic representation of the devices is shown in Fig. 2(b). For the processed devices, the distance separating the QD plane from the CSRR/GaAs interface is z_QD ≃ 90 nm. The proximity between the QD plane and the CSRRs is exploited for the near-field coupling between the antenna modes and the QDIP active region. The performance of an antenna coupled device is compared with the one of a reference device without resonators (mesa surface S_mesa = 750 μm × 750 μm). As it can be observed in Fig. 2(c), the dark current has the same behavior, as a function of the applied bias, on both devices. Due to the presence of the AlGaAs stopping layer, between the QW and the QDs, and the thick GaAs spacer, between the QD layer and the bottom contact, low values of dark current were observed on both devices: at V_bias= −30 mV, current densities of 2.12 × 10⁻¹⁰A/cm² and 7.1 × 10⁻¹¹A/cm² were measured on the reference and the antenna coupled devices, respectively. These values are lower than the ones reported for tunnel QDIPs^34,35 and QD QCDs.³⁶ 

While the spectral response of the detectors was characterized by means of FTIR spectroscopy, using a normal incidence configuration for the device excitation, as shown in Fig. 2(b), the absolute responsivity was measured exciting the device by means of a quantum cascade laser (QCL) emitting at λ = 6.8 μm, light polarized along the direction ⊥ to the central capacitive gap of the CSRR. Using a procedure similar to the one described in Ref. 25, knowing the value of the responsivity at λ = 6.8 μm, the photocurrent spectra could be calibrated.

The results are shown in Fig. 2(d), both for the reference and the antenna coupled devices, at T = 10 K and V_bias = 0 V. The presence of the resonators strongly affects the spectral response of the photodetector and, as shown in Fig. 2(d), a significant polarization anisotropy is observed. The QD photoresponse is peaked at λ_QD = 6.6 μm (see black dotted and dash-dotted curves in Fig. 2(d)). The spectral signature of the CSRRs is observed at λ_LC = 7.4 μm for the LC mode (polarization ⊥ to the capacitive gap). Several further resonances are observable, for both polarization directions, between 3.5 μm and 5.5 μm, which are associated to the excitation of Bragg-like modes, at wavelengths $λ i j = ( ε G a A s ε A u ) / ( ε G a A s + ε A u ) × d / i 2 + j 2$ (with i, j integers), related to the unit cell side length d.^37–39 These modes have the same nature as the ones observed in metallic periodic structures already adopted for QDIPs.^13–17 The splitting of the (±1, 0) and (0, ±1) resonances is attributed to slight unintentional deviations, associated to the experimental configuration, from a perfectly normal incidence condition, which introduce in-plane wavevector components.³⁷ Other effects on the resonance positions are associated to the shape of the sub-wavelength holes.^40,41

The values of the responsivity R and the quantum efficiency ξ = hc/(qλ) × R (where q is the electron charge), measured on the two devices at λ_LC = 7.4 μm and λ₀₁ = 4.9 μm, are listed in Table I. The quantum efficiency ξ of the two detectors is expressed as

where N_QD is the electron sheet density in the QD layer; the quantities G^ref and G^CSRR are coefficients quantifying the optical coupling between the incident radiation and the QDIP active region; σ_ip and σ_z are the values of the cross-sections associated to the photogeneration process,²² for light polarized along the in-plane (ip) and growth (z) directions. For this type of QDIP, we estimated experimentally a ratio σ_z/σ_ip ≃ 4.5. The CSRRs, for normally incident light (ip polarized), generate field components along both the ip and z directions, producing a more efficient coupling with the QDs. The experimentally estimated enhancement factors η_CSRR(λ) = R_CSRR(λ)/R_ref(λ) for incident light polarized along the directions $∥$ and ⊥ to the central capacitive gap are shown in Figs. 3(a) and 3(b), respectively. At λ_LC = 7.4 μm, a responsivity enhancement η_LC = 1.7 is estimated. A significantly higher value η₀₁ = 9.8 is estimated at λ₀₁ = 4.9 μm. In order to study the spectral properties of η_CSRR, the 2D CSRR array was simulated by means of CST Microwave Studio^®42 using the actual dimensions shown in Fig. 2(a). The simulated transmission spectra are shown in Figs. 3(a) and 3(b) (green dashed lines) for the two polarization directions of the incident field. A good agreement is found between the positions of the maxima in transmission and the ones for η_CSRR(λ). The field enhancement (FE) distributions computed for the (0, 1) and the LC modes are shown in Figs. 3(a) and 3(b), respectively. The CSRR optical coupling coefficient, corresponding to the field component E_l, is given by

where $FE l = | E l | / | E i n |$ and E_in is the incident field. In Fig. 3(d), the FE_ip and FE_z distributions of the LC mode are shown. The significantly higher value of η_CSRR observed at λ₀₁ is explained by the larger effective surface associated to the (0, 1) mode, with respect to the localized LC mode (see Figs. 3(a) and 3(b)), therefore involving a higher number of QDs in the photogeneration process. For the reference sample, $G i p r e f ≃ 0.7$ is the coupling coefficient for normal incidence excitation, having considered the effects of the reflection at the vacuum/GaAs interface. Using the computed FE distributions in Eqs. (1) and (2), $η L C c o m p = 3.9$ and $η 01 c o m p = 19.3$ were calculated for the modes at λ_LC and λ₀₁, respectively. The measured enhancement factors were found to be ∼2 times smaller as the computed ones. This discrepancy can be explained taking into account, for the reference sample, the effects of stray reflections within the substrate, especially at the bottom surface; this contribution is significantly lower for the antenna coupled device, due to the low transmission of the 2D CSRR interface. Moreover, the wet etching technique adopted for the top contact thickness reduction can easily produce inhomogeneity on the top surface of the mesas: regions with a top contact thickness larger than the expected value can be present within the device mesa. The LC mode, as it can be observed from the FE distributions shown in Fig. 3(b), is localized within the “plates” of the central capacitive gap and an effective surface S_LC can be defined, within which the electric field $E a b s ( x , y , z Q D ) ≡ | E x | 2 + | E y | 2 + | E z | 2 ≤ E a b s m a x / e$⁠; the ratio between the areas of the unit cell S_unit = d² and S_LC is ≃ 11.3. A normalized responsivity enhancement can be calculated for the LC mode as: $η L C n o r m = 11.3 × η L C ≃ 19$⁠. As shown in Fig. 3(c), despite their proximity to the CSRR antennae, the QDs are coupled to the “tail” of the LC FE distribution (⁠ $FE a b s m a x = 4.5$ at z = 90 nm). At z = 0 (⁠ $FE a b s m a x = 44$⁠), a responsivity enhancement factor ∼ 12 times higher is expected.

In order to estimate the specific detectivity D*, we measured the background current I_BG generated by the devices without a cryo-shield (NA = 1) and in absence of an incident optical signal: values of 1.9 nA and 2.9 nA were measured for the antenna-coupled and reference devices, respectively. From the study of the temperature dependence of I_dark and I_BG, T_BLIP ≃ 55 K was estimated for both devices. Analogously to what was shown in Ref. 25, taking into account the thermal noise and the dark and BG contributions to the shot noise,^43,44 we estimated $D * = R S m e s a / 2 q ( I d a r k + I B G ) + 4 k B T / R Q D I P$ (where $R Q D I P$ is the QDIP differential resistance). For λ = λ_LC, at V_bias= −30 mV and $T = 10 K , D C S R R * = 1.5 × 10 8 J o n e s$⁠, was estimated for the CSRR coupled device and $D r e f * = 0.7 × 10 8 J o n e s$⁠, for the reference device. The enhancement of the specific detectivity (∼2.1) confirms the performance improvements observed for the responsivity.

The relatively low values of R and D^* are inherently related to the detector structure based on a single layer of QDs, which has a significantly lower efficiency with respect to multi-layer QDIPs, for which responsivity values more than five orders of magnitude higher are reached.^45–47 A significant increase of the quantum efficiency can be achieved by including an extraction layer, enhancing the escape of the photoexcited electrons from the QDs. In Ref. 25, for a similar structure based on InGaAs capped QDs, a quantum efficiency about sixty times higher was reported, for photovoltaic operation.

In conclusion, we have demonstrated the responsivity enhancement on a single-layer QDIP, driven by the coupling of the detector active region with the localized LC mode of CSRR antennae. Within the LC active surface, a normalized responsivity enhancement of ∼19 was estimated. The great potentiality of such approach can be exploited for the realization of a next generation of devices with higher values of responsivity and detectivity. Etching techniques can be used to pattern the top mesa surface allowing both to remove inactive QDs and to position the detector active region within the “capacitor plates” of the resonators, below the top surface level. This would lead to a significant increase of the responsivity and the reduction of the dark current.¹⁹ An improved SRR near-field antenna coupling approach could be suitable also for the implementation on multiple-layer QDIPs. Within the mid-IR spectral range considered in this letter, only a limited number of QD layers could be included within the LC mode volume. For far-infrared and terahertz QDIPs, due to the larger size of the resonators, a more efficient coupling could be attained for structures based on a larger number of QD layers.

This work was financed by the Swiss National Science Foundation (SNF). We acknowledge the support from the technical staff of the FIRST-lab and the Binnig and Rohrer Nanotechnology Center (BRNC).