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Abstract
A plasmonic-coupled, InAs-based quantum dot photodetector fabricated for mid-wave infrared photonics is reported. The detector is designed to provide a broadband absorption [full width at half maximum (FWHM) ≳ 2 µm] peaked at ∼5.5 µm, corresponding to transitions from the ground state of the quantum dot to the quasi-continuum resonance state above the quantum well. From the coupling of this transition to the surface plasma wave (SPW) excited by an Au film atop the detector, fabricated with a 1.5 µm-period, 2-dimensional array of square holes, a narrowband SPW enhancement peaked at 4.8 µm with an FWHM less than 0.5 µm is achieved. At ∼90 K, a peak responsivity enhanced ∼5× by the plasmonic coupling is observed. Simulation reveals that this enhancement corresponds to collecting ∼6% of the incident light; ∼40% of the total absorption by the SPW excitation at the peak wavelength.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Mid-wave infrared (MWIR) detection has many applications in chemical sensing, thermal imaging, and heat scavenging [1]. HgCdTe alloys, Sb-based III-V strained layer structures, and As-based quantum dot (QD) and quantum well (QW) materials have been investigated for these applications [2–4]. Several attempts to examine plasmonic effects that utilize near- and far-fields carried by surface plasma waves (SPWs) - collective excitation of surface electrons coupled to electromagnetic waves - to improve the detector performance with various materials, also have been reported [5–14].
Recently, quantum dot infrared photodetectors (QDIPs) have been studied for their direct coupling to SPWs particularly in long-wave infrared (LWIR) by integrating plasmonic couplers on them [15–19]. While they have inherently poor quantum efficiency as a result of the low fill factor of the QDs, the photoexcitation in such low dimensional structures is dramatically increased by the electric near-field in the SPW that is normal to a QD stack, and leads to significantly enhanced detector performance. As a plasmonic coupler, an Au film perforated by a 2-dimensional (2D) hole array, referred to as a metal photonic crystal (MPC) in our work, has been widely employed. The enhanced performance is closely related with extraordinary optical transmission (EOT) through the array of subwavelength holes associated with the SPW excitation [20]. A ∼15× - 30× enhancement in responsivity and detectivity by the coupling to an MPC at LWIR has been demonstrated with several QDIPs [16,18,19].
QDIPs typically have two major absorption categories [21]. One is, as mentioned above, a transition from the ground state of a QD to a bound state in its potential barrier for LWIR (∼8–12 µm) which strengthens at high bias, where both tunneling through and thermionic emission over the barrier become available. The other is a transition from the ground state to the quasi-continuum state above the barrier for MWIR (∼3–6 µm) which can dominate at low bias. For convenience, these transitions are denoted as Eb and Eqc respectively. Most previous reports and review articles have focused on the plasmonic coupling to Eb for LWIR [16–19]. While Eqc is not as high compared with Eb in absorption strength, it contributes to photocurrent at low bias where the carrier collection in Eb is less efficient. This implies lower dark current, and as a result improvement of responsivity and detectivity in this transition. Furthermore, it has working temperature higher than Eb by kBT ∼ Eqc > Eb (kB: Boltzmann constant, T: temperature) and is relatively broad as a result of coupling to multiple levels in the quasi-continuum state, unlike Eb which involves a single bound level. It therefore enables high-temperature detection and local wavelength tuning through the variation of the coupler patterning.
Basically, III-V semiconductors are favorable in material reliability and device fabrication compared with II-VI semiconductors, popular for mid- to long-wave infrared (IR) detectors. This work explores an InAs-based QDIP, focusing on the plasmonic effects on Eqc for its feasibility of MWIR applications. A couple of points regarding its significance should be emphasized. One is the fabrication of plasmonic couplers which require sub-µm scale features to cover MWIR. This is achieved with interferometric lithography (IL), highly flexible for the selection of target wavelength and promising for the coupler integration on focal plane arrays (FPAs) in production yield/cost. The other is a quantitative analysis of the SPW contribution to the photoresponse of plasmonic-coupled QDIPs, which is critical to the design of both QDIPs and couplers for their combined performance and to the guidance for future applications of plasmonics to IR sensing and imaging. The optical properties of Au noticeably change with wavelength and must be considered in MWIR coupler design. For the fabrication of MPCs, i-line IL which is a low-cost, large-area, and scalable technology, is employed. Rigorous coupled wave analysis (RCWA) is used to understand the characteristics of the QDIP and the plasmonic enhancement. It allows measurement of the SPW contribution to the QDIP response that is very important for the optimal design of photodetectors as well as plasmonic couplers. The physics of photoexcitation in MWIR using Eqc, different from LWIR relying on Eb, is addressed with its importance in practical applications.
2. MPCs in MWIR
As the wavelength of light focused on this article shifts to MWIR, the optical properties of the Au film vary and affect the plasmonic effects on Eqc. For SPWs excited at the interface between an Au film and a QDIP, as discussed later, their propagation length, Lspw, along the interface and penetration depth, δspw, into the QDIP impact on plasmonic coupling. These indicate the extent of the SPW near-fields and are written as [22]:
Figure 1(a) is a Drüde model plot of ɛm′ and ɛm″ of Au versus λ [23,24]. Figure 1(b) is a plot of Lspw (blue, left y-axis) and δspw (red, right y-axis) versus λ of Eq. (1) with the Au film having the ɛm′ and ɛm″ in Fig. 1(a) on a GaAs substrate. In Fig. 1(b), both are decreased with the shift of λ for example from 10 to 5 µm; Lspw = 270 µm and δspw = 2.7 µm at λ = 5 µm, which are considerably smaller than Lspw = 1.1 mm and δspw = 10.8 µm at λ = 10 µm. Particularly, the reduced δspw that is directly related to the coupling strength is critical to plasmonic enhancement. Although this may restrict absorber design in practical applications, the MWIR detection by QDIPs has its own advantages and the Au characteristics at this range can be compromised for better design, as seen later. In the given structure, |ɛm′|, ɛm″ >> ɛd′ for Au and ɛd″ << 1 for GaAs. The Lspw and δspw from the Au/GaAs in Fig. 1(b) will be applied to the MPC/QDIP of this work for the similarity of the QDIP to GaAs in dielectric properties, as discussed in the Appendix. It is emphasized that Fig. 1 refers to an unpatterned, Au blanket film on a GaAs substrate. Both Lspw and δspw are reduced further when the absorption in the QDIP and the patterning of the aperture array in the Au film are considered [25,26].
Fig. 1. (a) A plot of ɛm′ and ɛm″ of Au versus wavelength calculated from a Drüde model with the plasma and the scattering frequency given in the Appendix. (b) A plot of Lspw (extent of the SPW along the Au/GaAs interface; left y-axis) and δspw (evanescent decay of the SPW into GaAs; right y-axis) versus wavelength from Eq. (1) with the ɛm′ and ɛm″ in (a). In (a) and (b), dashed lines correspond to λ = 5 and 10 µm.
3. Experiment
Figure 2(a) presents the layer structure of the QDIP employed in this work. It was grown by molecular beam epitaxy. A study on the growth conditions has been reported elsewhere [27]. On the left panel, the absorber under the 200 nm-thick n+-GaAs top ohmic contact layer consists of 30 QD layers with Si-doped InAs QDs and In0.15Ga0.85As/GaAs QWs, sandwiched by Al0.1Ga0.9As layers, as illustrated at the top of Fig. 2(b). Its total thickness is 1.8 µm. In Fig. 2(b), the core part of each layer is denoted as a QD/QW region, where a 2 monolayer InAs QD is asymmetrically divided by a 1 nm-thick In0.15Ga0.85As layer. This is different from dot-in-well (Dwell) structures previously employed that consist of InAs QDs buried in an InxGa1-xAs/GaAs QW at each layer while their epitaxial conditions were identically maintained [16,18,27]. The bottom of Fig. 2(b) shows cross-sectional images of the QDIP by transmission electron microscope (TEM), which partially reveal the QD stack. The left image shows a high magnification of a single QD layer where a QD is outlined by contrast difference. The physical shape appears flatter and wider than previously reported Dwells, and as seen later, the current-voltage (I-V) characteristic of this QDIP is noticeably different from that of typical Dwell QDIPs [16,28]. Further structural and electrical analysis of the core regions along their design rules will be reported elsewhere.
Fig. 2. (a) Left: A schematic device structure of the QDIP used in this work. The absorber consisted of 30 QD layers sandwiched by a 50 nm-thick Al0.1Ga0.9As layer and an n+-GaAs ohmic contact layer on a semi-insulating GaAs substrate with a total thickness of 1.8 µm. Right: A schematic layered structure used in RCWA simulation that corresponds to that on the left with the composition averaged over the whole absorber. (b) Top left: Details of the structure in a single QD layer. Bottom: Cross section TEM images for the QD stack in 3 different magnifications [from low (right) to high (left) magnification]. The left image reveals the outline of a single QD structure. (c) An SEM image of the MPC used in this work at bird eye's view. Inset: A magnification of the detailed structure of a square aperture with the dimension of a single period of the MPC.
The dimensions of a mesa device and a square opening on it for MPC were set to 440 × 440 µm2 and 380 × 380 µm2 respectively, as depicted in the left panel of Fig. 2(a). An Au MPC was fabricated on the QDIP using i-line IL and electron-beam evaporation [29]. A 2D square array of square holes having a period, p, of 1.5 µm was fabricated with ∼90 nm-thick Au stripes, roughly 3× the skin depth of Au at MWIR [30]. As confirmed later, this p was set to work at the Eqc of the given QDIP. The fabrication was achieved by a first IL exposure for a one-dimensional (1D) stripe photoresist pattern and Au deposition on the opening area followed by a lift-off process, and repeating with a second IL/Au deposition/liftoff sequence perpendicular to the first 1D pattern. A thin Cr film (∼5 nm) was deposited between the QDIP and the Au film in each deposition to promote Au adhesion. Figure 2(c) shows a scanning electron microscope (SEM) image of the MPC on the QDIP. Owing to the double deposition, as seen in the inset of this figure, the resulting aperture shape is a well-defined square with open dimensions of ∼1.1 × 1.1 µm2 separated by ∼400 nm-wide Au stripes. This geometry exactly matches the hole shape available in our simulator which assumes square or rectangular-type holes and is therefore expected to provide precise comparison with experiment. For convenience, the QDIP integrated with this Au film is referred to as MPC device. A reference QDIP from the same growth was processed without the MPC for the evaluation of plasmonic effects on the MPC device.
The photoresponse was measured using a Nicolet 6700 Fourier transform IR spectrometer and a Stanford Research Systems fast Fourier transform 770 network analyzer with an 800 K black body. All measurements were performed at ∼90 K. Bias polarity follows the rule used in previous work (positive bias corresponds to the top MPC as the anode) [16].
4. Results
Figure 3(a) shows the spectral response from the reference device (blue) and the MPC device (red) under a bias, Vb, of −1.8 V. The reference device of this figure has a broad response labeled Eqc with a peak at λqc ∼5.5 µm and a full width at half maximum (FWHM) of ∼2 µm. In the MPC device, this peak is nearly maintained at the right side of the strongest peak. The inset corresponds to the spectral response at Vb = −3.6 V, where the Eb of the given QDIP is clearly identified at 8.7 µm from both devices. Because of the presence of the MPC that was not designed to couple to this transition and even lowers light transmission as discussed below, Eb reveals an intensity reduction in the MPC device which corresponds to ∼85% of the reference device at its peak. In the inset of Fig. 3(a), the reference device has the FWHM of Eb ∼1.2 µm, narrower than that of Eqc, implying the transition to a single bound state compared with Eqc where multiple levels above the QW barrier are involved.
Fig. 3. (a) Spectral response from the MPC device (red) and the reference device (blue) at Vb = −1.8 V. Inset: their spectral response at Vb = −3.6 V. The absorption transitions, Eqc for MWIR and Eb for LWIR, are identified on the response curve from the reference device. A black and a light blue dashed line indicate λp and λqc respectively. (b) Spectral response curves of the MPC (left) and the reference (right) device obtained with a band pass filter (3.7 - 4.9 µm) along the variation of Vb that correspond the range of wavelength indicated by a screened area in (a). (c) I-V curves of both devices. All the measurements were performed at ∼90 K.
This work focuses on the SPW coupling to the Eqc for MWIR that prevails in the photoresponse for|Vb| ≲ 2 V, where Eb is insignificant. The photoresponse enhancement by this coupling generates a strong peak identified with a black dashed line at λp = 4.84 µm in the spectrum from the MPC device of Fig. 3(a). Its apparent FWHM from the baseline is 0.54 µm. This results from the interaction of the absorber with the near-field carried by the fundamental SPW of which the peak wavelength can be simply predicted from $\; p\sqrt {{\varepsilon _d}^{\prime}} $∼ 4.8 µm ≅ λp under the conditions of|ɛm′|, ɛm″ >> ɛd′∼ 10.2 and ɛd″ << 1 at this wavelength as an approximation [16,31]. These parameters will be explained in the Appendix. Then, the second-order SPW coupling is expected to occur at ∼ $p\sqrt {{\varepsilon _d}^{\prime}/2} \; \sim $ 3.4 µm. As seen in Fig. 3(a), this peak is not clearly observable since the reference device has very poor response at this short wavelength. Another reason could be the size of the square opening that is relatively large (> p/2) and a dipole induced across it becomes weak at this wavelength [20,22,31]. It means the coupling of the QDIP to higher order SPWs is hardly available for this device and the peak at the λp in Fig. 3(a) is therefore the unique observable by the coupling to the SPW excitation.
For an accurate measurement of plasmonic enhancement of the responsivity by such a narrowband SPW over the broadband Eqc, a 3.7–4.9 µm band pass filter (IWBP 3650∼4950, Hangzhou Multi IR Technology, China) which exclusively passes the photoresponse near λp was used. Figure 3(b) shows the responsivity curves obtained with the filter that correspond to those in the range of wavelength indicated by the shaded area in Fig. 3(a). The transmittance of the filter (∼0.93) was considered in the calculation. In Fig. 3(b), the peak wavelength of the MPC device is identically reproduced at 4.8 µm while that of the reference device appears at 4.9 µm because of the truncation by the filter. The peak responsivities at Vb = −1.8 V from this figure are 1.16 A/W and 0.26 A/W for the MPC and the reference device, respectively. Figure 4(a) is a plot of responsivity versus bias from these devices. In this figure, responsivity increases with Vb, as expected from typical QDIP performance, and is considerably higher in the MPC device than the reference device. It confirms the plasmonic effects by the coupling to the fundamental SPW. Figure 4(b) shows a plot of plasmonic enhancement, a responsivity ratio of the MPC to the reference device in Fig. 4(a), versus bias. The enhancement in the figure is within 4.5–5.5 over the whole range of the bias except for Vb ∼0. This result depends on the band width of the filter used in Fig. 3(b). Figure 3(c) shows the I-V characteristics measured at ∼90 K. As expected, the dark current of the MPC device is almost indistinguishable from that of the reference device.
Fig. 4. (a) A plot of responsivity versus bias. (b) A plot of plasmonic enhancement [responsivity ratio of the MPC to the reference device in (a)] versus bias. The solid lines in each plot are for eye guiding.
5. Discussion
In order for the near-fields of the fundamental SPW to achieve the highest plasmonic coupling in photoresponse, a QDIP should be designed so that its absorber is spatially within δspw(λp) from the MPC/QDIP interface [25]. In Fig. 2(a), the depth of the bottom of the absorber from the interface is ∼2 µm including the top contact layer. This is less than δspw(λp) ∼ 2.5 µm from Fig. 1(b) and therefore the whole absorber can be assumed to interact with the near-fields carried by the SPW, and the device structure in Fig. 2 satisfies the design restriction on δspw. Also, Lspw(λp) ∼250 µm in Fig. 1(b) is less than the device dimension and may not be a critical issue for plasmonic enhancement at the given device but should be considered in the application of FPAs where typical pixel size is ∼ 20 µm at MWIR, significantly smaller than Lspw(λp).
RCWA simulation was carried out to predict the highest absorption by a given device structure, which is important to QDIP design and understanding of the absorption mechanism by the MPC correlated to EOT. The detail of the simulation is summarized in the Appendix. Following the derivation of our previous report, we focus on the absorption coefficient of the QD stack, α, and determine it with the RCWA and the experimental data [25]. We analyze the plasmonic enhancement in the QDIP and quantify its actual absorption by the coupling to the MPC with this α that is nearly independent of plasmonic coupling. This procedure allows an estimate of the absorption in the QD stack by the SPW excitation.
In the simulation, as a rough approximation, the photoresponse of the reference device in Fig. 3(a) is assumed to be linearly proportional to α(λ). Under this condition, the absorption by the QD stack in the reference device, AR, was calculated with the layer structure shown at the right panel of Fig. 2(a) (except for the MPC at the top) by RCWA. For the best AR matching the photoresponse from the experiment, least square fit was employed with α as a fitting parameter. It determined αF(λqc) = 0.0157 µm−1 [32]. This spectral absorption coefficient, denoted by αF(λ) below to mean the value from the fitting, is slightly greater than the highest possible value at the peak wavelength of Eb ∼0.01 µm−1, estimated from a different Dwell QDIP [25]. With αF, the reflection and transmission of the reference device structure, RR and TR, were calculated through 1 = RR + TR + AR. The AR obtained from the simulation is presented in Fig. 5 (blue line). As discussed below, it is practically a replica of the photoresponse of the reference device shown at Fig. 3(a) in lineshape because of the assumption on the αF in the least square fit although they are not exactly the same. The layer structure of the reference device used in RCWA has no MPC and the AR associated with it therefore includes the absorption only by the QD stack without plasmonic effects in the simulation. In Fig. 5, AR(λqc) = 0.022 ( = 2.2%).
Fig. 5. Spectral AS, AM, and AS -AM of the MPC device structure and AR of the reference device structure from experiment and RCWA. It should be noted that AS and AR are from RCWA, and AM is from the experiment while AR is from the simulation but practically a replica of the experimental photoresponse of the reference device in Fig. 3(a) through αF in lineshape. The arrow on left side identifies the second-order SPW expected from RCWA. Inset: Spectral RS, TS, and AS of the MPC device from RCWA under the assumption of RS + TS + AS = 1 with the αF from the curve fitting. In both figures, AS is indicated with black lines. The dashed line in each figure means λspw obtained in the text.
In QDIPs, Eqc is physically not equivalent to Eb in several respects. First of all, it includes multiple excited levels and a selection rule resulting from the parity of the levels should be considered in the transitions between them. In a symmetric QW model, any transition between bound states of the same parity is forbidden in the interaction with light. However, the energy levels in the quasi-continuum state are loosely bound to the QD/QW region with their eigenfunctions partially delocalized over the potential profile of which the symmetry is perturbed by applied bias. Then, the selection rule may be disturbed and more levels above it would be available for Eqc regardless of parity. This can be a partial answer to the FWHM of Eqc broader than that of Eb. Also, the anisotropy of the photoresponse due to QD shape and the degree of quantum confinement in Eqc should be different from those in Eb. The QD profile in the magnification of Fig. 2(b) is not similar to that in the Dwell of previous experiments [16,19]. While more rigorous approach to the calculation of eigenfunctions and the consideration of QD shape is beyond the scope of this work, the plasmonic enhancement associated with Eqc must be understood on the basis of these physical differences.
In QDIPs, all electrons excited by intersubband absorption such as Eb or Eqc are not collected into ohmic metals. This is because some of them must tunnel through or thermionically pass over the QW potential barriers to join photocurrent. Generally, their collection efficiency is lower than 1. However, Eqc is expected to be better than Eb in this case since the electrons excited from the deep QD ground state to the quasi-continuum state have in principle no additional potential barriers that suppress their escape from the QD/QW region of Fig. 2(b). Moreover, each level in the quasi-continuum state has resonant transmission, assisting minimal IR emission by the electrons in this state that could be captured back to the lower bound states of the QW [33]. Collection efficiency, although it is mostly unaffected by plasmonic effects, must be clarified for the exact calculation of actual absorption enhanced by the coupling to SPWs. In our previous work, it was estimated as ∼0.5 for the maximum value of a plasmonic-coupled QDIP utilizing Eb [25]. For these reasons, the collection efficiency of 1 is assumed for Eqc in the discussion below. This doesn't contradict the AR from the RCWA shown in Fig. 5 that represents the simulated absorption by the QD stack of the reference device implicitly at the same condition. This will be applied to the simulation of the MPC device.
On the equal basis, the absorption by the QD stack in the MPC device under plasmonic coupling at the identical Vb, AM, can be conjectured from Fig. 3(a) since both devices in this figure have been already in the same unit and the AR in Fig. 5 is very close to the photoresponse of the reference device shown at Fig. 3(a) in lineshape. Then, AM can be obtained from a conversion of the photoresponse from the MPC device in Fig. 3(a), with a scaling factor determined with the reference device [34]. This is presented in Fig. 5 (red line). In this figure, both curves in Fig. 3(a) are thus reproduced as AM and AR with preserving individual lineshape and their intensity ratio. Then, AM = 0.056 ( = 5.6%) at λp = 4.84 µm. This implies approximately 6% of the incident light is absorbed by the QD stack with the coupling to the fundamental SPW at λp for the given Vb [34]. It should be emphasized again that AM is not a result from the simulation but a rescaled, experimental curve, and interpreted as the absorption by the QD stack under the plasmonic coupling. Because RCWA itself can't provide this particular absorption separately without accurate material parameters and transition strength, this work presumably regards the phenomenological curve in Fig. 5 as AM for the comparison presented below.
With the same layer structure given at the right panel of Fig. 2(a) and the αF from the least square fit, the reflection, RS(λ), transmission, TS(λ), and absorption, AS(λ) associated with the SPW excitation, including both metal and semiconductor contributions in the MPC device as a result of the coupling to the incident radiation field, can be simulated with RCWA. The absorption by the excitation of SPWs in the MPC device, AS, is shown in Fig. 5 and its inset (black lines). The RS and TS from the RCWA simulation, satisfying 1 = RS + TS + AS, are presented in the inset of this figure. Owing to the EOT through the MPC, TS is up to 0.507 at 4.78 µm near λp while it decreases rapidly with increasing wavelength. This provides a partial answer to the intensity reduction of Eb at the MPC device in the inset of Fig. 3(a). On the other hand, AS has the maximum value of 0.142 at λS = 4.78 µm, which is very close to λp, only 0.06 µm to the red. This small shift is probably due to the material parameters employed in the simulation that could be slightly different from the actual values. Since this peak shift in the absorption is insignificant, their arithmetic average, λspw = 4.81 µm can be regarded as the peak wavelength of the fundamental SPW. The simplification of the device structure on the right panel of Fig. 2(a) and the material parameters described in the Appendix were supported by this coincidence only with ±0.03 µm (or ±0.6%) fluctuation. A vertical dashed line in Fig. 5 corresponds to λspw.
The AS from the RCWA hardly dependent of Vb, is assumed to contain the absorption fully associated with the SPW excitation and some of it must be detected in AM. This means the AS in Fig. 5 shouldn't be less than the AM in the same figure. Then, the contribution of the fundamental SPW to the absorption by the QD stack of the given QDIP at λspw, γ, can be represented by:
In Fig. 5, AS(λspw) = 0.142, implying ∼14% of the incident radiation field was consumed for the excitation of the fundamental SPW at its peak wavelength. The simulation reveals that this value is mostly maintained at the range of hole dimension for ∼0.4–1.2 µm. With AM(λspw) = 0.056 from Fig. 5, γ ∼0.4 by Eq. (2). This means ∼40% of the AS at λspw is transferred into the absorber for photoresponse, and the remaining ∼60% is ascribed to the losses through various mechanisms including the metal film around λspw [35]. One of the fundamental issues in this field which has not been properly analyzed yet is the highest plasmonic enhancement that is achievable with a given combination of a photodetector and a coupler. This is because certain energy losses in the SPW excitation is inevitable but their clear separation from AS is unavailable. As discussed earlier, AM cannot exceed the AS subtracted by such losses [The AS - AM in Fig. 5 which corresponds to them is not negative for the whole range of λ.] [25]. Then, the γ of Eq. (2), as an alternative approach, could be a reference in measuring or predicting the highest plasmonic enhancement.
The γ ∼40% of Eq. (2) implies a room for its further increase by optimizing MPC and QDIP design although it requires more rigorous treatment of the loss mechanisms for better accuracy. Indeed, AM primarily depends on the absorber and MPC employed in a device, and can be improved along the design rules suggested in our previous work [25]. The AS in Fig. 5 should be regarded as the upper limit for the SPW excitation expected from experiment since the simulation doesn't consider the variation of the coupler qualities such as crystallinity and interfacial properties, critically affected in film preparation. The SPW near-fields undergo faster attenuation both along and perpendicular to the MPC/QDIP interface due to the presence of an absorber, and the Lspw predicted in Eq. (1) that is also critical to plasmonic enhancement shows additional reduction by the fabrication of a hole pattern into a blanket film [25,26]. For these reasons, some marginal variation in AS with these correlations must be counted in the comparison with experiment. Nonetheless, the γ from Fig. 5 provides a quantitative assessment of the plasmonic enhancement in detector performance.
Finally, the fundamental SPW resonance maintains a relatively narrow FWHM compared with the Eqc which has an intrinsic broadening associated with the multiple levels in the quasi-continuum state. In Fig. 3(a), the FWHM of the peak by the fundamental SPW after background subtraction is slightly less than 0.5 µm. This corresponds to ∼a fourth of that observed from the Eqc peak in the reference device of Fig. 3(a). The simulation suggests further reduction of FWHM is available by controlling the square hole size to ∼p/2 while maintaining similar peak intensity. Together with the plasmonic enhancement observed in Fig. 4(b), this allows narrowband sensing and imaging over the broad Eqc of QDIP at MWIR with a specific wavelength detection selected by λspw. The fine tuning of λspw is simply available by the variation of MPC pattern period. Basically, the line broadening of the SPW excitations in experiment is affected by hole size fluctuation of an MPC. Wafer-scale IL employed in this work can not only minimize this issue but also provide high tuning precision of the pattern period down to sub-µm scale. By means of non-contact lithographies at i-line used for this work (IL for a periodic pattern and proximity photolithography for the localization of the pattern on a device aperture or individual pixels), a cost-efficient fabrication of such an MPC that can be customized for any target wavelength from near- to long-wave IR is directly applicable on existing FPAs without damaging active materials at their front side. These suggest strong potential of IL-processed, plasmonic-coupled QDIPs to MWIR chemical and imaging sensors.
6. Summary and conclusions
A plasmonic-coupled, InAs-based QDIP for mid-wave infrared photonics has been demonstrated. A broadband absorption, Eqc, having a peak at 5.5 µm associated with the transition from the QD ground state to the quasi-continuum state above the QW potential barrier has been coupled to the fundamental SPW excited through an Au MPC fabricated with a 1.5 µm-period, 2D square symmetry array of square apertures by i-line IL. In the spectral response, a narrowband SPW enhancement by this coupling has been observed at 4.81 µm with an FWHM ∼0.5 µm over the ∼2 µm-wide broadband Eqc. MWIR response, different from the LWIR in the given QDIP, based on the transition characteristics involved in IR absorption, has been addressed. With ∼6% absorption of the incident radiation field, corresponding to ∼40% of the total absorption by the fundamental SPW excitation from the simulation, ∼5× plasmonic enhancement for mid-IR responsivity has been achieved in the given QDIP and MPC at ∼90 K.
Appendix
In Fig. 2(a), the right panel is the structure used in RCWA, simplified from the actual device structure shown on the left. In this figure, the absorber is represented with the dielectric response and alloy composition averaged over the whole QD stack. The heavily doped top and bottom ohmic contact layers which have a free-electron bulk plasma contribution to the dielectric constant, ɛc, from ɛc = ɛGaAs(1 - ωp2/ω2), were included in the simulation [36]. Here, ωp is the plasma frequency defined by $\omega _p^2 = 4\pi {n_e}{e^2}/{\varepsilon _{GaAs}}m_e^\ast $ with ne, e, ɛGaAs, and $m_e^\ast \; $ the free carrier density, the electron charge, the high frequency dielectric constant of undoped GaAs, and the effective mass of the electron in GaAs, respectively. For this QDIP, ne = 2×1018 cm−3 and $m_e^\ast $ = 0.074me where me is the free electron mass, considering its doping dependence in GaAs [37]. The absorption associated with the free carriers (the imaginary part of ɛc) is negligible for the wavelength range focused on in this work, and was not included at the simulation [38]. The absorber was modeled as an AlxInyGa1-x-yAs quaternary alloy with x = 0.083 and y = 0.013 averaged over the absorber, and as a result the real part of refractive index corresponding to $\; \sqrt {{\varepsilon _d}^{\prime}} $, was assumed to be slightly lower than that of undoped GaAs (∼0.98$\sqrt {{\varepsilon _{GaAs}}} $) for finite x, negligible y, and low doping [39]. Finally, a low-temperature correction was considered in ɛGaAs to reflect its actual value at ∼90 K [40]. Then, ɛd′ ∼10.2 around λp.
The inset of Fig. 2(c) shows the dimensions of an MPC unit cell used for the simulation that retains a square shape. Its thickness was set to 90 nm. While each corner of the square annulus was double in thickness for the experimental patterning, this subtlety was not considered in the RCWA because of insignificant effects of the metal thickness at this range on the absorption near the peak wavelength. The polarization of the radiation field normally incident on the MPC was set to be parallel to one of the principal axes of the hole pattern in the MPC. The plasma and the scattering frequency of Au used in the simulation were 1.4 × 1016 and 8.3 × 1013 Hz, respectively [23]. The RCWA simulation was applied to both reference and MPC devices.
Funding
National Science Foundation (EEC-0812056).
Acknowledgments
Funding for this work was provided primarily by the Air Force Office of Scientific Research and by the Engineering Research Centers Program (ERC) of the National Science Foundation under NSF Cooperative Agreement No. EEC-0812056.
Disclosures
The authors declare no conflicts of interest.
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