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Abstract
We report a measurement of the quantum efficiency for a surface plasma wave (SPW)-coupled InAs/In0.15Ga0.85As/GaAs dots-in-a-well (Dwell) quantum dot infrared photodetector (QDIP) having a single-color response at ∼10 µm. A gold film perforated with a square array of complex, non-circular apertures is employed to manipulate the near-fields of the fundamental SPW. The quantum efficiency is quantitatively divided into absorption efficiency strongly enhanced by the SPW, and collection efficiency mostly independent of it. In the absorption efficiency, the evanescent near-fields of the fundamental SPW critically enhances QDIP performance but undergoes the attenuation by the absorption in the Dwell that ultimately limits the quantum efficiency. For the highest quantum efficiency available with plasmonic coupling, an optimal overlap between Dwell and SPW near-fields is required. Based on experiment and simulation, the upper limit of the plasmonic enhancement in quantum efficiency for the present device is addressed.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Adding a thin metal film perforated with a 2-dimensional (2D) array of holes, referred to as a metal photonic crystal (MPC), significantly enhances the photoresponse of infrared (IR) detectors by coupling to surface plasma waves (SPWs) [1], an effect that is closely related to the extraordinary optical transmission [2,3,4]. Propagating SPWs bound to an MPC/detector interface and localized plasma resonances associated with hole geometry impact the evanescent near-fields extending into an absorber region adjacent to it. Particularly, the near-field perpendicular to the MPC/detector interface interacts strongly with carriers in low dimensional structures such as quantum wells (QWs) and quantum dots (QDs) [1,5–14]. At mid- and long-wavelength IR (MWIR and LWIR), this coupling has been confirmed with a dots-in-a-well (Dwell) quantum dot infrared photodetector (QDIP), providing a significant improvement of electron confinement in individual QDs and stress relief at the InAs QD surface, as an established detector [1,6–11,15].
Several research groups have reported the enhancement of QDIP performance by SPW coupling [1,6–14]. However, the published results show significant variation with enhancements ranging from less than 2× to greater than 30× but no investigations to resolve this large measurement range have been reported. In this work, we investigate the interaction of SPW near-fields, both polarized parallel and perpendicular to the QD stack in the Dwell absorber and therefore with the quantum efficiency that is a critical measure of detector performance. The quantum efficiency is analyzed with the absorption efficiency of the intersubband transitions from the ground state of a QD that directly affects plasmonic enhancement and the collection efficiency of the carriers at excited states by thermionic emission over or tunneling through potential barriers that mostly depends on the band structure of the absorber. To our knowledge, quantitative analysis of absorption efficiency separated from its collection efficiency in a QDIP has been not reported since the first QDIP over two decades ago [16].
While Dwells can have more than one intersubband transition for multi-color detection, single-band color detection is important for some applications [17]. This can be achieved with an engineered MPC. Aperture engineering from a simple circle to a more complex cross shape, referred to as Celtic cross (CX), has been introduced to manipulate the SPW near-fields [11]. In this work, the CX MPC shown in Fig. 1 is employed for a single-band wavelength response that exclusively enables the coupling to the fundamental SPW. With CX MPC-integrated QDIPs, quantum efficiency is examined experimentally and compared with that from finite difference time domain (FDTD) simulation and reflection pole method. The comparison with two identical QDIPs, one with and the other without CX MPC, allows the separation of absorption efficiency from quantum efficiency that clarifies its contribution to the evanescent decay of SPWs. We focus on the absorption properties of the Dwell and their correlation to plasmonic enhancement. It strongly depends on the overlap of SPW near-fields vertically and horizontally with Dwell absorber but isn’t a relation simply proportional to the absorption efficiency. This is primarily due to a characteristic of the SPW bound to the MPC/QDIP interface; SPW near-fields enhance Dwell absorption but are also attenuated by it in the evanescent decay from the interface. Under this correlation, we find important parameters from the design and performance of a device that can explain the large variation of plasmonic enhancement in the reported data. Finally, the upper limit on the plasmonic quantum efficiency available with optimal device condition is addressed.
Fig. 1. A top-down SEM image of the 2D array in the CX MPC. Inset: A top-down SEM image of a single CX aperture designed for exclusive excitation of the fundamental SPW. The inset square is 3.1 ×3.1 µm2.
2. Experiment
The QDIP used in this work was grown on a semi-insulating (SI) GaAs substrate by molecular beam epitaxy. The absorption region of the detector has a total thickness of 930 nm, sandwiched by n+-GaAs layers for ohmic contact: 200 nm-thick at the top, and 2 µm-thick at the bottom. It consists of 15 stacks of the Dwell structure shown in Fig. 2(b). Each device is fabricated with a 300-µm-diameter open aperture for incident light on a 410 × 410 µm2 mesa. Two single-pixel QDIPs, one integrated with a CX MPC and the other for reference with an as-grown QDIP surface, were individually fabricated on isolated dies so that each detector has a single aperture which is the opening for normal incident light on its front side to interact with the QD stack. Figure 2 schematically shows the CX device used in this work with the QDIP structure. The CX MPC was fabricated with a 100 nm-thick Au film with the period of the hole array, p, set to 3.1 µm and processed with standard photolithography and electron-beam evaporation. Photoresponse was measured with Nicolet 6700 Fourier Transform Infrared Spectrometer and Stanford Research Systems fast Fourier transform 770 network analyzer with a 800 K blackbody source. The single-band response in the CX device allows evaluation of the quantum efficiency at the peak wavelength without the use of bandpass filters. This CX aperture was used for consistency with previous report. Because of its relatively large opening area in the inset of Fig. 1, on the other hand, it could induce a broader peak than a p/2-diameter circular aperture which has the narrowest SPW excitation at a given period [11]. Measurement temperature was set to ∼10 K to reduce thermal noise.
Fig. 2. Schematic illustrations of (a) a QDIP integrated with a CX MPC on the top circular aperture and (b) the magnification of a rectangle at its corner that shows the layer structure of the device with the details of a single QD stack in the enlargement. The negative bias in the text means the applied field is in the growth direction from the bottom to the top of the device. In (a), the dimension of the CX hole used in the simulation was indicated on a enlarged unit pattern at the top.
The SI GaAs substrate is transparent across the wavelength range of interest in this work. For accurate measurements, the contribution of any light not directly incident onto the detector aperture that scatters into and diffuses through this non-absorbing substrate must be eliminated. To shield the devices from the scattered light outside of the aperture, the remaining area of the front surface and all four side surfaces of each die were covered by ∼300 nm-thick Au films and IR-shielding paste, as illustrated in Fig. 2(a). This IR blocking lowered the measured responsivity and detectivity approximately by an order of magnitude, confirming the importance of the careful blocking. This scattering contribution through the substrate could be, to some extent, one of the major reasons for the large variation in reported plasmonic enhancements [1,6–13].
3. Results
For an MPC with a 2D square hole array pattern integrated onto a photodetector, there are SPW excitations at wavelengths given by [1,2]:
Figure 3 shows the photoresponse spectra from the QDIPs at biases of -3.4 V and 3.8 V: (a) for the reference device, and (b) for the CX device. As mentioned above, the reference device has two broad peaks near λ1 and λ2, most evidently at the negative bias. Owing to the instrumental noise limit (∼10 pA), the dark current from I-V characteristics in the inset of Fig. 3(b) is instrument-limited for bias between -3.2 V and 3.6 V. Both devices show increased responsivity with bias but a reduced detectivity beyond -3.4 V and 3.8 V as a result of the increasing background noise. The response at these biases which is the highest was chosen for comparison with the simulation for better accuracy.
Fig. 3. Plots of responsivity vs. wavelength of (a) the reference device and (b) the CX device at 3.8 (red) and -3.4 (blue) V. In (a), a peak shift by QCSE is observed. In (b), the dashed lines indicate the peak splitting of the fundamental SPW resulting from the CX shape that leaves a hump at each polarity (∼10.3 µm at 3.8 V and ∼9.8 µm at -3.4 V) by QCSE. Inset: I-V curves of both devices. The color code in (a) is identically applied to (b). All measurements were performed at ∼10 K.
The photoresponse of the QDIP depends on both the magnitude and the polarity of the applied bias as a result of asymmetric quantum-confined Stark effect (QCSE) from the pyramidal shaped QDs [15]. QCSE leads to a slight peak shift at opposite bias polarities in the reference device. For the CX device, on the other hand, a strong peak at 10.3 µm for -3.4 V and at 9.8 µm for 3.8 V is observed (λ0,1) with an extremely weak peak at 7.1 µm (λ1,1) in both bias polarities for the suppression of higher order SPWs by the CX shape. The details of the aperture engineering for CX MPC was reported elsewhere [11]. The resulting photoresponse in Fig. 3(b) therefore can be regarded as single-wavelength detection, dominated by the fundamental SPW at λ0,1. The splitting at λ0,1 is due to the complex hole shape that includes both a narrow and a wide gap indicated in the inset of Fig. 1. The QCSE thus explains the highest photoresponse at different gaps [narrow (wide) gap in the inset of Fig. 1 at negative (positive) bias] [11,20,21].
The peak responsivity at -3.4 V (3.8 V) is increased from 41 mA/W (61 mA/W) for the reference device to 873 mA/W (1727mA/W) in the CX device. The detectivity shows a comparable enhancement from 4.7 × 108 (8.3 × 108) to 1.4 × 1010 (2.5 × 1010) cmHz1/2/W at -3.4 V (3.8 V). These enhancements, ∼21× at -3.4 V and ∼28× at 3.8 V for responsivity and identically ∼30× for detectivity, are qualitatively similar to those in previous report [1]. The measurement results are summarized in Table 1. In Fig. 3, the λ1 of the reference device is very close to the λ1,0 of the CX device at negative bias. Such a coincidence desirable for the comparison with simulation seen later, was aimed from the choice of the hole period of the CX MPC. Hereafter, this work concentrates on the photoresponse of these devices at negative bias.
Table 1. Summary of QDIP performance near 10 K.
4. Discussion
4.1 Plasmonic quantum efficiency
For a generation-recombination, noise-limited photoconductive detector, the quantum efficiency, η, is [22,23]:
where Rp(λ) is the responsivity at the wavelength λ; h, c, and e are, Planck's constant, speed of light, and electron charge; G is the photoconductive gain. The Rp in Eq. (2) can be replaced by that of the CX device, Rcx, peaked at ∼λ0,1 for plasmonic quantum efficiency, ηcx ∼ ηcx(λ0,1). Similarly, it can be replaced by the responsivity of the reference device, Rref, for its quantum efficiency, ηref. The G in Eq. (2) is expressed as $G = i_n^2/4e{I_d}\Delta f$, where in and Id are noise current over the bandwidth Δf and the dark current in the inset of Fig. 3(b), respectively, which are independent of the plasmonic excitation. In the experiment, the noise power spectral density was measured from ${{{i_n}} \mathord{\left/ {\vphantom {{{i_n}} {\sqrt {\Delta f} }}} \right. } {\sqrt {\Delta f} }}$ for G. Then by applying the data in Table 1 to Eq. (2), ηref is ∼0.03% and ηcx ∼0.9%. Thus, the plasmonic enhancement of quantum efficiency in the experiment, β = ηcx/ηref, is ∼30×, retaining a similar tendency to the detectivity but higher than the enhancement of responsivity by the difference of G in Table 1. This is probably due to minor change in the I-V characteristics expected from slight spatial variation of epitaxial layer parameters across the wafer.Basically, the quantum efficiencies of the QDIP are impacted by: 1) the small absorbing volume of self-assembled QDs and 2) relaxation of excited carriers before they are collected to the photocurrent. Then, the ηref with a plane wave normally incident on the reference device, can be expressed as [24]:
where ηref,a(λ) is absorption efficiency and ηref.c(λ) is the efficiency for the collection of an excited-state electron in Dwell to a free electron that contributes to the photocurrent. In the reference device, ηref,a can be written as: where r ∼0.33 is regarded as the reflectance of the GaAs at the front surface of the QDIP, f = α × (z1 – z2), with α = α(λ) as the wavelength-specific absorption coefficient, and z1 (= -0.2 µm) and z2 (= -1.13 µm) are the locations of the top contact layer/absorber and the absorber/bottom contact layer interfaces along the z-axis from Fig. 2(b), respectively. The absorption by the top n+-GaAs contact layer, is insignificant at our LWIR, and is not considered. Equation (4) is derived under the assumption that none of the light transmitted through the active region contributes to the photocurrent, i.e. the reflection and scattering of the transmitted light at the back surface of the substrate is neglected. The ηref,a in Eq. (4) then corresponds to the absorbed fraction of the light incident on the QD stack of which the intensity decreases exponentially along the -z axis.An SPW near-field excited at and propagating along the MPC/QDIP interface has a characteristic evanescent decay into the QDIP that is given approximately by ${e^{ - \Delta z}}$ with $\Delta \sim{-} \frac{{2\pi n_d^2}}{{\lambda \sqrt {|{{\mathop{\rm Re}\nolimits} ({{\varepsilon_{Au}}} )} |} }}\left[ {1 - i\frac{{{\mathop{\rm Im}\nolimits} ({{\varepsilon_{Au}}} )+ n_d^2}}{{2{\mathop{\rm Re}\nolimits} ({{\varepsilon_{Au}}} )}} + i\frac{{\lambda \alpha }}{{2\pi {n_d}}}} \right]$ from Eq. (1). The derivation is in the Appendix. In the square bracket, the last term reflects the additional decay or attenuation in the presence of QD absorption with finite α although the first two terms are retained even for α = 0 and describe a characteristic of the SPW bound to the interface. This is a rough approximation valid for a blanket metal film and a semi-infinite absorber but explicitly reveals each contribution to SPW decay in the CX device. The role of α in the evanescent decay will be clearer in the comparison with a simulation later. As a result of selection rules that strongly favor the absorption in a QD for light polarized in the z-axis, the near-field component directed into the QDIP dominates absorption. For these reasons, Eq. (4) is not directly applicable to ηcx.
The relaxation of photoexcited carriers before they can join the photocurrent lowers the collection efficiency. In the Dwell, this is more probable for the bound-to-bound intersubband absorption at λ1 than the bound-to-continuum absorption at λ2 because the λ1 transition requires tunneling or thermionic emission across the QD-QW barrier to contribute to the photocurrent. The collection efficiency is therefore more critical to ηref at λ0,1 ∼λ1. ηref,c is a characteristic of the device layer structure and does not, to the first order, depend on the plasmonic coupling and so should be invariant between the reference and the CX device.
4.2 Absorption in plasmonic near-fields
By approximating the ηref of Eq. (3) to that of Eq. (2), ηref,c can be separated from ηref, if α is known. In the ηref,a of Eq. (4), however, α is not simply obtained from materials properties because of low dimensional QDs embedded in a multiple-layers. In this work, α is taken as a homogeneous material-fitting parameter determined with an electromagnetic simulation of the CX device. For the comparison with experiment, the wavelength dependence of α was assumed to be identical to the wavelength variation of the photoresponse shown in Fig. 3(a) and for convenience its value at λ0,1 is used below to represent the absorption. The details of the simulation based on FDTD are summarized in the Appendix [25–27].
As mentioned earlier, the electromagnetic fields of an SPW excited in the CX device are very different from those of light normally incident on the reference device by their characteristic bound to the MPC/QDIP interface. In this work, the spatial overlap of the absorber with the SPW near-fields, proportional to the plasmonic coupling to the λ1 transition, is used for the evaluation of effective absorption efficiency of the CX device, ηcx,a ∼ηcx/ηref,c, from Eqs. (2) and (3), in the simulation. To keep consistency, this approach was applied to the ηref,a of the reference device. The variation of the overlap with α reveals how SPW near-fields are affected by the absorption properties of Dwell. For the highest photoresponse by plasmonic coupling, ηcx,a should be maximized. However, the overlap of the SPW fields with the absorber is not simply related to α and as a result to ηcx,a, which is eventually limited by α in the achievable enhancement. This key issue is discussed below with FDTD simulation that determines α of the given QDIP.
The spatial overlap, expressed as Icx,z(α, z) and Icx,x(α, z) in the simulation, is shown in Figs. 4(a) and 4(b); the details are in the Appendix. Here, Icx,z and Icx,x are the near-field intensities of the fundamental SPW at λ1,0 along the z- and x-axes shown in Fig. 2(b) respectively, averaged over a unit cell in the xy plane for each z. The hole shape employed in the simulation is shown at the top of Fig. 2(a). In the simulation, both devices were assumed to have identical Dwell and I-V characteristics so they have the same intersubband transition oscillator strength for λ0,1 ∼λ1. Then, the absorption at z is proportional to α(ρIcx,z+ Icx,x) for the CX device and to αIref,x for the reference device. The weighting factor for Icx,z, ρ ∼ 8 [28], is a result of the polarization dependence of the QD intersubband transitions as explained in the Appendix. Its significance will be discussed later. Iref,x is the x-component electric field intensity of the normally incident plane wave in the absorber of the reference device, averaged in the same way as Icx,x. The polarization of the incident field was assumed along the x-axis. Then, there is no electric field along z in the reference device for plane wave at normal incidence and the corresponding Iref,z = 0.
Fig. 4. Semi-log plots of (a) Icx,z and (b) Icx,x for the fundamental SPW at λ0,1 vs. z with the variation of α from 0 to 0.12 µm−1. In each figure, z = 0 corresponds to the MPC/QDIP interface, and the light green and the yellow stripes indicate the absorber and the CX MPC, respectively. The dashed line in each figure means the middle of the absorber (zm = -0.665 µm). Inset in (a): Magnification of a dotted box in (a) for the details near the MPC/QDIP interface. Inset in (b): Plot of Rcx (reflectance), Tcx (transmittance), and Acx (absorption) vs. wavelength in the CX device structure obtained from the simulation for α(λ0,1) = 1.2 × 10−3 µm−1. Note that Acx shows the splitting at 10.1 µm and 10.6 µm (red and blue arrow heads) for the fundamental SPW mainly excited across the wide and the narrow gap in the inset of Fig. 1 respectively that matches the peak shift under QCSE in Fig. 3(b). 2D field plots of (c) electric field intensities, |Ecx,z|2 and (d) |Ecx,x|2 of the fundamental SPW at λ0,1 defined in Appendix on the xy plane of the unit pattern at zm [dashed lines in (a) and (b)] when α = 1.2 × 10−3 µm−1. The arrow at the scale bar indicates the |Ecx,x|2 ( = 0.21) of the reference device at the same α which is constant across the xy plane. The bold dashed line in each panel corresponds to the CX aperture illustrated in Fig. 2(a) that was used in the simulation. The polarization of the incident light was parallel to the x-axis.
In Figs. 4(a) and 4(b), Icx,z and Icx,x roughly exhibit an exponential, evanescent decrease along the -z-axis from the MPC/QDIP interface. The inset of Fig. 4(a) reveals the detailed variation of Icx,z near the interface. This agrees well with a simple planar model from theoretical predictions [29]. The ratios of Icx,z provide insight into the decay:
In Eq. (4), ηref,a increases with α. In Fig. 4(a), on the other hand, Icx,z(z) is reduced as α increases, demonstrating a more complex relationship between α and ηcx,a. This can be confirmed with βsim, defined as [30]:
Figure 5(a) is a plot of Icx,z, Icx,x, and Iref,x integrated over z1 to z2 vs. α at λ1,0. As the α increases to 0.12 µm−1, Icx,z and Icx,x decrease noticeably beyond α ∼0.01while Iref,x is slightly reduced but almost constant at the given range. In this figure, Iref,x is a little higher than Icx,x but considerably lower than Icx,z. This clearly supports the significance of the near-field component perpendicular to the absorber and the ρ in Eq. (5) associated with it which directly depends on epitaxy condition. The βsim of Eq. (5) at λ1,0 is shown in Fig. 5(b). Both Rcx and Rref vanish for α = 0 and βsim is only physically valid for nonzero α but approaches a finite value (∼22) as α → 0 in the simulation. In Fig. 5(b), βsim decreases to 13.7 whereas the ηref,a of Eq. (4) is increased to 0.07 when α varies from zero to 0.12 µm−1. As seen in Figs. 4(a) and 4(b), this is mainly due to the attenuation of the SPW near-fields with α. At higher α, the SPW becomes more tightly bound to the MPC/QDIP interface and its evanescent fields are attenuated further at the absorber with Ω < 1. For sufficiently large α, it results in a significantly decreased overlap with the absorber, implying dropped βsim (or ηcx,a) and ultimately overwhelming the increased ηref,a of Eq. (4). This is one of the most important results of the present work. Figure 5(b) therefore predicts a critical relation between ηref and the plasmonic enhancement associated with it.
Fig. 5. (a) A plot of the Icx,z, Icx,x, and Iref,x integrated over z1 - z2 vs. α at λ1,0. (b) A plot of βsim in Eq. (5) of this work and the plasmonic enhancement reported in [11] vs. α at λ0,1 (See Appendix for the details.). (c) A plot of SPW propagation length [L's for a bulk absorber (brown) and an SI GaAs substrate (black), Lq for the CX device] vs. α at λ0,1 with Au dielectric constant of -4853 + i2201 from the condition of [18]. For bulk absorbing substrate, the real part of its dielectric constant of 3.3 was assumed. For the QDIP, the layer structure shown in Fig. 2(b) was used with composition average. A dashed vertical line in each figure indicates the optimal α = 1.2 × 10−3 µm−1 obtained from the simulation. Other lines are for eye guiding.
In Fig. 5(b), the βsim for α = 1.2 × 10−3 µm−1 coincides with βex = 21.3 [28]. Figures 4(c) and 4(d) present the 2D plots of the near-field intensities at λ0,1 in the xy plane at zm for this α. These figures clearly reveal the spatial variation of both z- and x-component of the near-field along the CX aperture. The z-directed SPW field intensity in Fig. 4(c) is strong across the narrow gap while its x-directed component from Fig. 4(d) is relatively weaker and shows less hole-dependent. This demonstrates the reliability of the simulation and supports the significance of dipole excitation across the narrow gap at the given wavelength.
As seen in Fig. 4(b), the SPW attenuation along the interface is also affected by α. Although the condition of Ξ ∼ 0.4 > e−1 is satisfied in the penetration of the near-field for the range of α in Fig. 4(a), this was obtained under the assumption of an infinite array of holes. Experimentally, the actual number of periods in the CX MPC is less than 100 along the 300-µm lateral size of the MPC, and any interruption in SPW propagation can lower the Icx,z and Icx,x of Fig. 4 and as a result ηcx. For a blanket Au film with no pattern, the SPW propagation length, L, is given as [29]
The SPW propagation on a hole array-patterned metal film decays at the length scale much shorter than that on the blanket metal film assumed in Eq. (6) [32], due to the coupling to the radiative field, and actual Lq could be reduced further. If the metal film for an MPC has lateral dimension significantly less than the actual Lq, this can be also another reason for the dispersion in reported plasmonic enhancements [1,6–11]. From the lateral size of the MPC ( = 300 µm) comparable to the effective Lq of the fundamental SPW, it can be concluded that the SPW propagates along the interface without serious interruption by the device boundaries and therefore the Icx,z and Icx,x from the simulation shouldn't be affected much. These support the experimental results with good agreement in the evaluation of βsim at the given α. Eventually, α, a characteristic of the Dwell, is the most important parameter that determines the relative attenuation of SPW near-fields along as well as perpendicular to the MPC/QDIP interface, and primarily impacts ηcx,a.
4.3 Upper limit of plasmonic quantum efficiency
As seen in the inset of Fig. 4(b), the transmittance and reflectance of the given device are evidently nonzero. Also, plasmonic coupling doesn't guarantee complete absorption of incident light in a QDIP. Then, the upper limit of ηcx would be ideally up to the total absorption, Acx ( = 1 - Tcx - Rcx, where Tcx and Rcx are the transmittance and reflectance of the CX device respectively), meaning perfect energy transition and ηref,c = 1 without any types of loss at target wavelength [33]. Then, ηcx would be saturated to Acx, and β can be greater for lower ηref since Acx is limited by MPC design and QDIP dielectric properties.
In previous section, α = 1.2 × 10−3 µm−1 provided the best fit to the observed βex. In Fig. 5(b), however, βsim doesn't have noticeable variation with α roughly up to 0.01 µm−1. In the consideration of the experimental uncertainty inevitably involved in measurement, the range of α for the good agreement of βsim with βex can be extended to this value as a rough approximation. Under this assumption, the ηref,a in Eq. (4) becomes 6.2 × 10−3. Then, the ηref,c of Eq. (3) = ηref /ηref,a ∼0.05 [34]. If this ηref,c applies to the CX device, the effective absorption efficiency, ηcx,a, defined earlier could be as high as:
Here, this ηcx,a corresponds to the highest actual absorption efficiency in the CX device expected from the plasmonic coupling to the QD stack. It should be noted that the ηcx,a in Eq. (7) is compatible with Acx ∼0.2 at λ0,1 in the inset of Fig. 4(b). The absorbing volume of a QD array, significantly smaller than for a QW or a bulk absorber, is a major reason for the poor ηref,a in the QDIP [17]. Then, the low α obtained in this work agrees with this QD characteristic and high plasmonic coupling resulting in Eq. (7) therefore impacts the QD absorption dramatically. This is crucial in any measure of detector sensitivity such as signal-to-noise ratio where plasmonic enhancement has more significance in QDIP than other LWIR detectors. While QDIP suffers from poor quantum efficiency by low α, it has the advantage of a low dark current level, very favorable for improving device performance since SPW near-fields don't impact the dark current [15]. On the contrary, the ηref,c associated with α needs some explanation. While further study to narrow down the range of ηref,c [α as well in Fig. 5(b)] is required, the separation of a collection efficiency insensitive to plasmonic effects from the quantum efficiency is an important issue in understanding it on low dimensional absorbers such as QDs and QWs. As described earlier, collection efficiency is very critical to ηref at λ0,1 ∼λ1 but is primarily related to the design of the QD stack, not of the MPC. Basically, higher ηref,c is important for better ηref. Improvement of ηref,c is mostly related to the layer structure enclosing the QDs through the alloy composition and thickness of the well and barrier layers, and their epi-quality. Recently, a QDIP with higher ηref (i.e., ∼0.023 for 6 QD stacks) was reported [28]. Although its ηref,a and ηref,c were not explicitly resolved, these results show a possibility of better quantum efficiency in QDIPs. In this work, ηref,c and α are assumed to be material properties independent of the MPC but this should be also examined. Nonetheless, it is evident that the IR absorption of the CX device doesn't exceed the Acx at the target wavelength.In Figs. 5(a) and 5(c), the overlap and propagation of the near-fields are attenuated with increasing α. Although Ξ > e−1 for all α in Fig. 4(a), the effective ηcx,a and as a result β varies with several design parameters. One of them is the thickness of an absorber. While it also affects ηref, a thick absorber lowers Ξ and ultimately ηcx. The detectivity enhancement of ∼15× in previous article, only a half of that in Table 1 [10,35], could be partly attributed to its 1.9 µm-thick absorber which is almost twice that of this work, resulting in Ξ ∼0.1 < e−1 from Fig. 4(a). This emphasizes the importance of the total structure including the QD stack design optimizing the plasmonic enhancement. The location of an absorber also affects ηcx. Figures 4(a) and 4(b) suggest that an absorber closer to the MPC/QDIP interface can couple to the fundamental SPW more effectively. If the thickness of the top contact layer is reduced from 0.2 µm to 0.1 µm, for example, the Icx,z and Icx,x at z = -0.1 µm (the top contact layer/absorber interface) show more than 19% and 17% enhancement respectively for all α. The thickness and location of the absorber is therefore very important to plasmonic enhancement. These design rules should be considered for better ηcx,a.
The QDIP-SPW coupling is primarily dependent on α and absorber design associated with it, and these are likely the major reasons for the large range of reported plasmonic enhancements [1,6–11]. The ρ in Eq. (5) that is directly determined by the epitaxy condition through the geometric shape and size of QDs is another strong factor to ηcx; higher ρ is a necessary condition for better ηcx. As discussed in our previous work, the dimension and shape of a hole in MPC design so-called aperture engineering affects SPW excitation, and its decay into a detector can contribute to the dispersion in the reported data [11]. The magnitude and line broadening of Acx at SPW resonance are also influenced by aperture engineering.
The near-field intensity by Ξ > e−1 and the lateral size for the CX MPC comparable to Lq suggest that the plasmonic coupling of this work is close to the condition for optimal βsim (= βex ≈ 21) in the given QDIP and MPC. The ηcx,a in Eq. (7) that approaches Acx at λ0,1 supports this conclusion. Many imaging applications such as focal plane arrays (FPAs) employ backside illumination with top bump bonding to silicon readout circuitry, opposite to the front side illumination used in this work. In FPAs, better ηcx and therefore β (∼2-3×) under invariant α is available along with higher Icx,z and Icx,x, associated with increased Acx (or the upper limit of plasmonic enhancement) by the conservation of Tcx and the elimination of the double-pass through the absorber on reflection from the top contact metallization [9,36]. However, the suppression of the SPW resonance by the presence of pixel boundaries and the crosstalk between neighbor pixels must be considered [37]. It should be noted that the MPC dimension and Lq of this work are much greater than the typical dimension of a pixel size (∼30 µm), implying reduction of ηcx in actual FPAs. The crosstalk is an issue to ηcx as well as imaging resolution but can be minimized by physical separation of the pixels with reflective barriers perpendicular to the QD stack which enhances the absorption by multipath effects.
Finally, the phenomenological approach to determine α used in this work heavily relies on ρ in Eq. (5). This is decisive in the comparison of experiment with simulation but could depend on the Dwell parameters. Systematic characterization of ρ as well as accurate measurement of α is necessary for further optimization of MPC/Dwell QDIP.
5. Summary and conclusions
The plasmonic quantum efficiency of an InAs-based Dwell QDIP has been investigated with a gold film CX MPC engineered for a single-wavelength response at ∼10 µm. The experimental comparison of two identical QDIPs, one with and the other without CX MPC, allows a quantitative analysis of the quantum efficiency separated into absorption efficiency significantly affected by plasmonic effects and collection efficiency hardly dependent of it. Two major factors associated with the absorption efficiency that can contribute to the wide variation of reported plasmonic enhancements have been examined: spatial overlap of SPW near-fields and their propagation along the MPC/QDIP interface with the absorber. The comparison of the experiment with the results from FDTD simulation and reflection pole method clearly reveals the SPW near-fields critically impact plasmonic quantum efficiency but their attenuation by the presence of the Dwell can limit it along the absorption efficiency of the detector. Based on this correlation, major factors for large variation of plasmonic enhancement and important design rules for both MPC and QDIP have been proposed to achieve optimal plasmonic quantum efficiency within the upper limit.
Appendix
Evaluation of Δ and L
The parameter Δ representing evanescent decay of the z-directed SPW field into a dielectric in the text corresponds to ikz with the wavevector of the SPW in the –z-axis to the QDIP, kz, by [29], and can be approximated as:
Derivation of Icx,z and Icx,x
IR absorption by intersubband QD transitions is polarization-dependent. The quantum efficiency of QDIP is roughly proportional to $\rho {|{{E_z}} |^2} + {|{{E_x}} |^2}$, where Ez and Ex are the z- and x-components of the total electric field in the absorber by incident light on the coordinate shown in Fig. 2(b) (i.e., electric fields perpendicular and parallel to the QD stack respectively) and ρ ∼8 is a multiplier representing the interaction of a QD that dominates with Ez in polarization dependence [1,29]. The SPW near-fields provide an electric field perpendicular to a QD that impacts the intersubband transitions. Then, this formula can be used for CX device with Ecx,z and Ecx,x, the near-fields of the fundamental SPW which are perpendicular and parallel to the MPC/QDIP interface respectively. From the large value of ρ, the overlap of the Ecx,z with the absorber is important to the plasmonic enhancement and as a result to the understanding of ηcx associated with ηref in Eq. (3). In this work, an FDTD simulation was employed to examine the overlap for the aperture shape shown in Fig. 2(a) that mimics the inset of Fig. 1 [11].
In the simulation, both CX and reference devices were assumed to have identical Dwell and I-V characteristics, and a single optical transit of the active region was considered. For the CX device, the quantum efficiency is then proportional to the responsivity associated with the SPW coupling, Rcx, at a given wavelength which can be written as:
In Eq. (12), Drüde model was used for ɛAu [18]. Because the simulation does not include enough granularity to model individual QDs in the absorber, the real part of the refractive index spatially averaged over the absorber in alloy composition and layer thickness (≈ 3.3) was assumed for that of ɛd which doesn't vary much over the range of wavelengths of interest. Then, a key parameter is its imaginary part of the complex ɛd which is not precisely known but directly related to the photoresponse of the QDIP. To retain its spectral characteristics, the photoresponse of the reference device in Fig. 3(a) was employed by assuming this parameter is proportional to this curve. Then, as explained in [30], the absorption coefficient, α, in Eq. (3) becomes available as a fitting parameter for Icx,z and Icx,x in the FDTD that is related to the response curve in Fig. 3(a). It also means the QCSE observed in Fig. 3 were reflected to the simulation through it. In this work, α was varied from 0 to 0.12 µm−1 at λ0,1 with a step of 0.012 µm−1 which is finer than that of previous work for better accuracy.
In the FDTD, Eq. (12) can be rewritten as:
In [11], the plasmonic enhancement, Γ, was defined as:
Funding
Air Force Office of Scientific Research; 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.
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