1. Introduction

There has been significant recent interest in the application of radio-frequency (RF) circuits or free space radiation for (optical frequency) light detection and material characterization applications. The use of free space microwave radiation for bulk material characterization or IR detection is many decades old [1–3], and more recently has been used for the measurement of carrier dynamics in semiconductor materials [4]. The rapid recent development of RF technologies, which have been spurred primarily by the continued growth of the wireless communication field, provide a cost-effective and compact infrastructure for new photonic devices leveraging RF frequency signals, and allowing for chip-scale versions of free-space RF technologies. Unlike the majority of devices which comprise the field of RF photonics (whose focus is largely on the modulation and de-modulation of optical carrier signals at RF frequencies [5–7]), we focus here on the small but growing subfield encompassing devices where RF signals are modulated by optical signals. Such an approach opens the door to entirely new functionality, where RF signals can either be modulated/controlled at very high rates (akin to optical circuits), or alternatively, with great sensitivity to incident optical signals. The most recent examples of such devices are the microwave- or lumped element- kinetic inductance detectors (M-KID and LE-KID, respectively). These detectors consist of resonant RF microstrip or coplanar waveguide resonant LC circuits fabricated from superconducting materials, resulting in extremely high Q (>10⁶) RF resonances [8–10]. The high-Q resonators are coupled to a single busline (also of superconducting material) carrying a signal at the resonant frequency of the LC resonator. Light incident on the resonator structure is absorbed by the superconducting material which generates quasiparticles and alters the surface impedance of the metal film. This results in a dramatic change in the resonator Q which can be read out as a change in amplitude or phase of the RF signal on the busline. The high-Q of the resonator allows for extremely sensitive detection, as well as the multiplexing of numerous detectors along a single busline, as each detector can be designed to have a unique resonant frequency (in addition to its extremely high Q). Thus, simultaneous readout of 1,000’s of detectors can be achieved on a single busline by careful spectral filtering of the transmitted signal [11–13].

The –KID class of detector has applications in astronomy and astrophysics due to the broad spectral range of the detectors (from X-rays to mm- and sub-mm wavelengths) [14, 15] and sensitivities high enough to resolve single photon absorption events [16, 17]. However, these detectors require low temperature operation (dictated by the T_c of the superconducting material) and exhibit long recovery time constants [18, 19] which limits the detector bandwidth to the low kHz range. Recently, a room temperature detector was proposed and demonstrated [20], consisting of a split-ring resonator coupled to a microstrip busline fabricated on a semiconducting material, as shown schematically in Fig. 1(a). The equivalent circuit for such a detector is a transmission line with a capacitively-coupled RLC shunt. Representative experimental RF detector spectra are shown in Fig. 1(b) for changing gap size (equivalent to a change in the capacitance of the RLC circuit). Light incident on the detector generates electron hole pairs in the absorbing material, which changes the local RF conductivity and effectively ‘shorts’ the capacitive gap. This short alters the resistance of the RLC circuit and quenches the circuit resonance [Fig. 1(d)]. The change in the transmitted RF signal across the circuit then corresponds to a measure of the light intensity incident on the detector.

 

Fig. 1 (a) Overhead and cross-sectional schematic of single-element detector with relevant dimensions. (b) RF response (insertion loss, S₂₁) of detectors fabricated on a SI GaAs wafer as a function of split gap size. (c) 3D schematic of photo-excited detector with (d) experimental data showing RF spectra of dark (blue solid) and photo-excited detector (blue dashed), demonstrating the quenching of the RF resonance under photo-excitation.

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Figure 1 shows the structure and response of the resonant RF photodetectors (RRFPs) presented here. The Q of the RRFPs is orders of magnitude less than superconducting –KIDs resulting in a significant decrease in the RRFP sensitivity. Initial responsivity for the devices driven with a 3dBm RF source on resonance showed responsivities of ~1 V/W [20]. However, despite their weak response, the RRFP detectors did demonstrate several appealing qualities, including configurations that allow readout of multiple detector responses on a single busline (multiplexing), room temperature operation, and potential for very fast response times (orders of magnitude faster than the –KID detectors). Moreover, the RRFP architecture can utilize a variety of absorber materials, thus offering significant control over operational wavelength and detector response. Therefore, the RRFP architecture could have a range of applications, including material metrology, direct integration of photonic devices with microwave circuitry, and simultaneous (multiplexed) readout of high speed detector arrays.

In this work, we demonstrate the ability to control the response of our RRFPs, using two distinct approaches: one rooted in the choice of optical/semiconductor materials and the other using the RF resonant geometry of the device. First, we show that by varying the absorber material, we can dramatically change the detector responsivity, as would be expected for a photoconductive device. Second, we demonstrate that significant improvements in responsivity can be achieved by modifying the RF circuit geometry. In particular, by engineering the overlap regions of strong RF field enhancement and optical excitation, we can boost detector response by at least a factor of four. We spatially and spectrally characterize the RRFP detectors (at both RF and optical frequencies), for a range of detector sizes and detector materials. The detectors are modeled using commercially available electromagnetic simulation software and the simulations show good agreement to the experimental results. The results we present not only offer detector elements with significantly improved detector response, but offer insight into the de-sign of circuit elements with even greater improvement in detector performance and a range of potential applications.

2. Detector fabrication and experimental set-up

The basic detector geometry is shown in Fig. 1(a). All of the fabricated detectors have 1mm square SRR structures with chamfered corners to decrease scattering loss. The SRR structures are evanescently coupled to the busline with a coupling gap of 30µm. The microstrip lines (busline and SRR) are 50µm wide, 0.5µm thick Au with a 10nm Ti adhesion layer. These are patterned using standard UV photolithography, metallization and lift-off processes. The detector ground plane is 0.5µm thick Au with a 10nm Ti adhesion layer. The RF spectra of the fabricated structures are characterized using an Agilent 5230A Performance Network Analyzer (PNA) with GSG probes that are calibrated using a Short-Load-Open-Thru technique to move the measurement reference planes to the probe tips. Representative plots of insertion loss (S₂₁) for varying SRR capacitive gap widths (G1) in unilluminated RRFP detector structures are shown in Fig. 1(b). Note that the characteristic impedance of the microstrip lines in the RF circuits is ~100Ω which introduces an impedance mismatch between the probes and our RF circuit. In addition, the thin Au used for the RF circuitry (compared to the RF wavelengths) will also result in some additional RF signal loss. Both of the above will result in less than ideal RF characteristics, but do not have a significant impact on the underlying physics investigated in this work.

Five absorber materials were investigated: semi-insulating (SI) GaAs, high-resistivity (HR) Si, epitaxial GaAs, epitaxial InAs, and epitaxially grown In_xGa_1-xAs/GaAs quantum wells (QWs) in a GaAs matrix. We used wafers obtained from commercial vendors for the semi-insulating (SI) GaAs and high-resistivity (HR) Si detectors and fabricated the RF circuit directly on the wafer, as shown in Fig. 2(c). The three epitaxially grown absorber layers were each grown on SI GaAs wafers in a SVT molecular beam epitaxy (MBE) system. The epi-GaAs sample simply consists of 500nm of undoped GaAs grown on the SI GaAs wafer. The QW sample consists of 13 periods of In_0.15Ga_0.85As/GaAs QWs (10nm/20nm) grown on a 300nm GaAs buffer layer. The InGaAs QW sample is designed to have a ground state transition at a wavelength of 950nm at room temperature (confirmed by photoluminescence measurements).

 

Fig. 2 (a) Spectral response and (b) spatial response experimental set-ups. Inserted plot in (b) shows the beam profile for the exciting laser in the spatial response set-up. Cross-sectional schematic of detector using (c) wafer absorbing material and (d) epitaxial absorber.

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Because of the unintentional doping of InAs substrates (which will quench the RF signal on the microstrip transmission line), we grow our InAs absorber sample on a SI GaAs wafer, which will have a large lattice mismatch to our InAs epi-layer. The InAs sample consists, from the substrate up, a 200nm GaAs buffer, followed by a 100nm GaSb layer, and then 500nm of InAs (undoped). This follows the approach of [21], which demonstrated that the GaSb layer can be used to minimize lattice mismatch induced defect propagation into the epi-InAs. For the detectors using epitaxial material, a mesa of epi-material was patterned to sit in the SRR capacitive gap, and all other epi-material was etched. Thus the RF circuit was effectively fabricated on the SI GaAs wafer and the epi-material sits only in the capacitive gap of the SRR, as shown in Fig. 2(d). This approach is necessary for epi-layer materials which are either strong photoconductors or have unintentional doping, in order to prevent losses along the microstrip lines, away from the resonator capacitive gap.

The (optical) spectral response of detectors was measured using a white light source filtered through a monochromator and chopped before being focused on the sample, as shown in Fig. 2(a). The detectors are driven at resonance with an Agilent (HP) 8341B RF sweep generator sourcing 3 dBm. The transmitted RF signal was measured with a Pasternak PE 8013 10MHz-18.5GHz zero-biased Schottky RF detector which feeds into the lock-in amplifier, synchronized to the optical chopper. The detector response is measured as a function of the monochromator wavelength and the resulting optical spectrum is normalized to the incident optical power spectrum as measured in the same set-up with a Thorlabs PM30 power meter. Figure 3 shows the normalized room temperature spectral response of the epi-GaAs and HR-Si detector samples, showing the expected absorption edge at each material’s band edge.

 

Fig. 3 Normalized spectral response of the epi-GaAs (black) and HR-Si (red) detector samples.

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The responsivity and spatial response of the detectors was measured using the set-up shown in Fig. 2(b). Here laser light is collimated and focused on the sample via a ½” diameter, 1” focal length BK7 lens, where the long focal length is required in order to avoid the microwave probes. The inset to Fig. 2(b) shows the beam spot size for the 785nm laser used in this experiment, which has a full width half maximum (FWHM) of approximately 10µm. The laser is modulated at 50Hz with a 50% duty cycle for the responsivity measurements. The RRFPs are driven at resonance and the transmitted RF signal is collected and fed into the lock-in amplifier. The DC lock-in output is collected for a range of laser powers. Neutral density filters are used to access low incident powers for the laser while allowing the laser to operate at higher current densities and thus stable output powers. Incident laser power is measured using a broadband power meter and responsivities are characterized using the incident, not absorbed, laser power. The absorbed laser power will be ~30% less than the incident laser power due to reflection from the semiconductor surface. For spatial measurements, the laser is mounted on a 1D motorized translational stage to allow positioning of the laser spot across the surface of the sample. Linear scans of the sample response were collected, travelling through the capacitive gap either perpendicular or parallel to the microstrip busline.

Driven modal simulations of the devices were carried out using the finite element based software HFSS®. The substrate is modeled as a constant permittivity dielectric and all metallic components were modeled as finite conductivity boundaries. Radiation boundary conditions were assigned to all exterior boundaries of the simulation domain, except the ground plane. The remaining computational area was characterized as a vacuum domain. Wave ports were placed on the external boundary of each end of the microstrip line. The two-dimensional Eigen value problem was solved to find the waveguide modes so the modal complex propagation constants and characteristic impedances can be computed. The generated mode patterns were used as excitation for the device and also for computation of the S-parameters. In addition to the determination of the RRFP’s RF spectra, we used our simulations to extract the electric fields of our devices on resonance, which we plot in figures below at the top surface of the device substrate.

3. Results and discussion

The presented RRFP architecture can be integrated with a range of absorber materials. Choice of absorber material not only allows for control of operational wavelengths of the detectors but also responsivity. Though in this work we investigate absorbing substrates with or without epilayer absorbers, the RRFP architecture also allows for transparent substrates, with absorbing materials placed in the capacitive gap. In all cases the detector response is directly related to the conductivity of the absorber material under illumination, and in this regard is very similar to a traditional photoconductive detector. However, our detector measures changes in the transfer function of a microwave RLC circuit driven on resonance due to a change in RLC resistance vs. simply a change in the quasi-DC voltage across a traditional photoconducting element. The conductivity of the semiconductor can be written as:

In an ideal detector, both the mobility and the EHP lifetime are independent of carrier concentration, resulting in a linear response. However, at high carrier concentrations, both mobility and EHP lifetime decrease, due to increased effects of additional scattering mechanisms (Auger recombination, electron-electron scattering, etc.) [22, 23]. Additional nonlinearity at high pumping powers may result from the shift of the quenched RLC resonance compared to the ‘dark’ circuit. The trade-off between linearity and responsivity can be clearly seen in Fig. 4, which shows the change in the transmitted signal through our RF detector circuit as a function of incident optical power for 5 different absorber materials. Narrow bandgap InAs shows the most linear response, but also the weakest responsivity. Both effects can be attributed to the rapid EHP recombination in InAs at room temperature [24], which more than negates the somewhat higher mobility of epitaxial InAs compared to our other absorber materials. The short lifetime of the epi-InAs results in low carrier concentrations and consequently a weak, though linear, response. Note that the InAs absorber RRFP is pumped with a 980nm laser, which has a photon energy three times the InAs bandgap, and thus is a less than efficient optical pump. Thus the results for the InAs absorber RRFP shown in Fig. 4 underestimates the InAs responsivity if pumped with a longer wavelength optical source. The InGaAs/GaAs QW sample was pumped below the GaAs bandedge but above the QW ground state transition (with a 904nm laser diode). This sample shows a significantly stronger response when compared to the InAs, which can be attributed to both the more efficient pumping and the improvement in carrier lifetime of the epitaxial QWs [25, 26]. However, the QW response is still more than an order of magnitude weaker than the bulk GaAs response, as expected due to the limited volumetric fill factor of the QWs. Finally, the HR Si sample shows the highest sensitivity, with responsivities as high as 1,000 V/W at low optical powers. The HR Si clearly shows significant nonlinearity in response resulting from the larger carrier concentrations achievable with the long carrier lifetimes (on the order of 100’s of µs) [27] for photoexcited EHPs in Si. The combination of the detector nonlinearity and the limitations in response time associated with the resonant RF circuit indicates that the detectors presented here are unlikely to find application in RF photonic applications requiring highly linear detection [28–30] of optical signals modulated at microwave frequencies [5–7]. However, for applications requiring either multiplexed detection schemes or direct RF readouts of optical signals (or material properties) at low-GHz frequencies, our detector architecture may have benefits.

 

Fig. 4 Transmitted (readout) signal as a function of incident optical power for RRFPs with capacitive gaps G1 = 20µm using different absorber materials: epitaxial InAs (green), InGaAs/GaAs QWs (blue), and epitaxial GaAs (grey), as well as wafers of SI GaAs (black) and HR Si (red).

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Figures 3 and 4 demonstrate that the choice of optical absorber material in the detector design cannot only determine operational wavelength of the detector, but also its responsivity and the linearity of that response. In addition, though it is not the focus of this work, the choice of absorber material also strongly affects the time response of the detector via the EHP lifetime and charge carrier mobilities [31, 32]. The absorber material, however, is not the only parameter available to engineer the responsivity of RRFP devices. Detector responsivity also depends significantly on the geometry of the RF circuit and the location of EHP generation. The latter can be clearly seen in Fig. 5, where the response to a fixed laser intensity is plotted as a function of the incident laser position on the SI-GaAs detector with the 80µm gap size.

 

Fig. 5 (a) Simulated electric field distribution, on resonance, for the bottom arms of the SRR on a RRFP resonant circuit with 80µm capacitive gap. (b) Detector response as a function of the position of the incident laser along the bottom arms of the RF resonant detector simulated in (a).

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The data in Fig. 5 shows a strong variation in detector response with the position of the incident laser. In this respect, the RRFP differs significantly from a traditional photoconductive device. In a standard photoconductor, a largely uniform DC field between the detector contacts will result in a uniform spatial response across the detector surface. In Fig. 5, however, it is observed that the RF detector response varies significantly with spatial location along the surface of a single detector. When comparing the linear scans of detector response to the simulated RF field intensity for the resonant circuit, it becomes clear that the detector response is maximized at the locations where the RF field is enhanced. We also observe local maxima in our detector response at locations where bends in our SRR result in fringing fields extending out from under the microstrip lines, such as at the $x=\pm 500\mu m$ positions on the bottom arms of the SRR. Intuitively, this can be understood by thinking of the excited EHPs as generating a localized loss in the RF circuit. The stronger the overlap of this localized loss with the RF field, the stronger the detector response. Thus, the strongest detector response is observed at locations where the RF field is strongest. While for a given detector geometry a wide range of responsivities can be achieved dependent on the position of the incident light, the above results also suggest that the detector responsivity to be engineered using design of the RF resonator. Figure 6 shows the detector response as a function of position along the bottom arms of the SRR, parallel to the microstrip busline [Fig. 6(c)], and across the SRR, perpendicular to the busline and through the center of the capacitive gap [Fig. 6(b)] for four detector structures fabricated on SI GaAs wafers, identical except for the capacitive gap size.

 

Fig. 6 (a) Schematic of RF resonant circuit. Detector response as a function of position (b) perpendicular to busline, through capacitive gap and (c) parallel to busline through capacitive gap, for RF resonators with capacitive gaps of 20 µm (green), 40 µm (blue), 80 µm (red), and 120 µm (black). Detector response is collected along the dashed lines in the schematic, dotted lines are guides to the eye. Simulations of RF electric field magnitude on resonance at semiconductor surface for RRFPs with (d) 20 µm, (e) 40 µm, (f) 80 µm, and (g) 120µm capacitive gaps.

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The simulations in Figs. 6(d)-6(g) show the on-resonance RF electric field at the semiconductor surface of the four detector geometries experimentally investigated in Figs. 6(b) and 6(c). As can be seen in these simulations, the enhancement of the electric field in the SRR gap increases significantly with decreasing gap size, as the mode is effectively ‘squeezed’ into a smaller volume between the SRR arms. This increases the enhancement of local (RF) electric field strength and should result in a stronger responsivity for the detector structures with smaller gap sizes. This effect is observed in Figs. 6(b) and 6(c), where we see two distinct effects with decreasing gap size. First, the linear scan of the detector response shifts from a double peak structure, with strong response at the ends of the SRR arms, to a single peak response, with strong response centered in the SRR gap. Second, we also observe a significant increase in the detector responsivity with decreasing gap size, with a $~\times 4$ increase in the transmitted signal for equal incident laser power. Both of these effects are supported by the RF electric field profiles simulated in Figs. 6(d)-6(g).

The responsivity of the RRFP devices, fabricated on a GaAs wafer, as a function of SRR gap size is shown in Fig. 7. Here, for each RRFP device, we position the incident light (785nm laser) at the spatial position on the SRR which produces the largest signal. For the larger gap structures, this is located at the edge of one of the arms. For the smaller gap structures, this is located in the middle of the gap. A clear increase in response is seen as the SRR gap size decreases. As gap sizes decrease below 20µm, however, the gains in responsivity increase only slightly. This is a result of increased reflection of the incident light from the SRR arms, as the laser spot FWHM is ~10µm [Fig. 2(d)]. Therefore, decreasing gap sizes increases shadowing of the semiconductor absorber material from the incident light. Overall, these results show that significant improvement in responsivity can achieved in RRFP devices by engineering RF hot- spots. As can be seen in Fig. 1(b), the change in SRR gap size does not significantly change the RF properties of the SRR (slight change in resonant frequency, little change in resonator Q) but has a drastic effect on the device responsivity. This suggests that resonator designs with engineered RF hot-spots giving even greater field enhancement could be used to further improve the response of the presented detector devices.

 

Fig. 7 Peak responsivity for RF detector structures as a function of SRR gap size (all other SRR geometries are unchanged). Responsivity is measured, for each resonator, at the spatial location where the response is largest. Thus the large gap size structures have the incident light positioned near the edge of the SRR gap, while the smaller gap sizes are measured with the laser spot centered in the gap.

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4. Conclusions

The RRFP device architecture offers a number of potential advantages over traditional photoconductive devices. These include the potential for multiplexing detectors on a single busline, direct integration with RF circuitry, and utility for material metrology. In this work, we demonstrate that significant improvement in device responsivity can be achieved by choice of the photo-absorbing material, which also controls the absorbing wavelength range similar to traditional photoconductive devices. In addition, however, we demonstrate a marked spatial dependence of the device responsivity and show that our detector response is maximum for light incident on regions of the detector with the strongest RF field. This is elucidated by measuring the spatial dependence of the response for SRRs with varying capacitive gap sizes, so that by engineering RF ‘hotspots’, we can significantly enhance detector response. These results demonstrate a substantial improvement in detector response and also offer insight into potential avenues for further improvements by engineering of RF field hotspots in resonant circuit architectures.