Intrinsic photomixing detector based on amorphous silicon for envelope mixing of optical signals

In this work, a promising device for direct optical envelope mixing, the Intrinsic Photomixing Detector (IPD) based on hydrogenated amorphous silicon, is reported. The IPD directly generates a photocurrent proportional to the nonlinear mixing of two optical modulation envelope functions. Experiments illustrate efficient mixing in the visible range at low light levels down to ϕ 1 = 4.36 mW/cm 2 (444 nm) and ϕ 2 = 1.03 mW/cm 2 (636 nm). Modulation frequencies exceeding the MHz range are demonstrated. Electro-optical simulations identify defect-induced electrical field screening within the absorber to cause the nonlinear mixing process, opening-up the opportunity to tailor devices toward application-specific requirements. The IPD functionality paves the way toward very simple but high-performance photodetectors for 3D imaging and ranging for direct optical convolutional sensors or for efficient optical logic gates. Using amorphous silicon provides a photodetector material base, which can easily be integrated on top of silicon electronics, enabling fill factors of up to 100%


INTRODUCTION
Within the last few decades, hydrogenated amorphous silicon (a-Si:H) attracted wide research interest in fields of optoelectronic applications, e.g., solar cells, 1 thin-film transistors, 2 photodetection, 3 or multispectral sensing, 4 due to its high absorption coefficient in the visible range, 5 versatile bandgap tuning, 6,7 low-temperature manufacturing, 8 and doping 9 capabilities.Besides classical application examples, a-Si:H has recently gained interest in the field of optical communication systems as this class of material enables wavelength conversion at high data rates due to nonlinear optical processes. 10n a-Si-H waveguides, optical (N)AND logic gate operation in the time domain at GHz frequencies has already been demonstrated utilizing four-wave mixing Bragg scattering, a third-order nonlinear process. 11Mixing processes, such as heterodyning, are also applicable in the RF 12,13 and RADAR technology. 14Furthermore, frequency mixing techniques are well-established, e.g., to generate THz radiation. 15However, this principle requires expensive, high intense laser sources and a nonlinear medium 10,16,17 or device 18 to mix the frequencies of the stimulating radiation.High-speed nonlinear graphene-based devices have been reported for mixing the envelope of two optical signals 19 or an electrical signal and an optical modulated signal 20,21 achieving modulation bandwidth in the GHz range.Besides lacking scalability and reproducibility, the 2Dmaterial-based approach actually suffers from low efficiencies so that typically irradiances exceeding 100 mW/cm 2 are required. 20pubs.aip.org/aip/appFurthermore, established envelope frequency mixing devices, such as the photonic mixer device used for 3D imaging, utilize a smart but rather complex device architecture and signal processing to realize sum/differential frequency generation of an optical signal and an additional electrical signal. 22Although this technology is highly approved, it has drawbacks due to the complexity so that geometrical fill factors stagnate at ∼22% due to extensive electrical circuitry. 23n contrast to these techniques, we propose a very simple and scalable low-cost approach to mix the envelope intensity of two amplitude modulated light sources by utilizing a well-designed field optimized a-Si:H p-i-n photodiode, the Intrinsic Photomixing Detector (IPD) [cf.Fig. 1(a)].For that, electro-optical simulation models have been developed to study and optimize the device structure and physics.The simulation results are presented in the section titled Electro-optical simulation.The proposed detector enables envelope intensity mixing at irradiances below 5 mW/cm 2 and modulation frequencies exceeding MHz.Besides 3D imaging and optical ranging capabilities, we identify potential key applications of this device in fields of optical communication systems and optical (analog) computing.Optical AND logic gate functionality derived from a frequency analysis is demonstrated in the supplementary material.The mature thin-film process technology further allows for lowtemperature sensor integration on top of silicon electronics with pixel fill factors of 100%.24,25 ELECTRO-OPTICAL SIMULATION Photogating A comprehensive electro-optical simulation model of modulated dual-light-beam current measurements on the IPD based on a-Si:H has been developed using the software AFORS-HET.26 Further details on the simulation model are given in Ref. 27 and in the section titled Methods.This model enables establishing a consecutive understanding of charge carrier generation and transport processes within the sensor structure at different illumination scenarios.Steady-state simulation results of the internal electric field profile E(x) across the intrinsic layer (i-layer) for varying wavelengths and in the dark state are given in Fig. 1(b).The local electrical field particularly determines the overall charge collection efficiency since an absolute low (or even positive) internal E-field prevents charges to be transported toward the respective electrical contact.In the dark state, the electrical field profile coincides with Crandall's non-uniform field theory.28 Depending on the illumination scenario, a photo-induced internal charge transport barrier is generated due to deep trap-induced screening of the built-in field in a-Si:H photodiodes.27,29,30 That barrier is located at a position x = x E=0 where the E-field vanishes or becomes positive.Electrons that are generated within the i-layer region surrounded by the p-doped layer and x E=0 are not able to drift toward the n-type a-Si:H.In result, these electrons will not contribute to a photocurrent.To derive a physical understanding of the envelope mixing in the a-Si:H IPD, we propose and define a charge carrier collection zone with the length xcz starting at the position x E=0 and ending at the i-n interface (here: x = xi = 1520 nm) at the rear end of the detector.If the illumination scenario does not result in a E-field collapse (E < 0 for 0 ≤ x ≤ xi), the collection zone xcz and the i-layer thickness xi become equal.Dichromatic or multispectral illumination can result in a huge collection zone expansion and hence to a significant increase in the photocurrent compared to monochromatic illumination, as shown in Fig. 1(b) and Refs.31-33. Fr simulations, dichromatic illumination with wavelengths in the visible range of λ 1 = 444 nm (ϕ 1 = 14.8 mW/cm 2 ) and λ 2 = 636 nm (ϕ 2 = 42.4 mW/cm 2 ) have been used to demonstrate the field enhancement principle for this specific detector and absorber composition.The specific E-field characteristics result in a nonlinear photoresponse for that illumination scenario.In this case, the collection zone length and the intrinsic absorber thickness become equal xcz = xi = 1526 nm [cf.pink line, Fig. 1(b)], whereas a quenching and vanishing electric field at x E=0 occurs for monochromatic 444 nm illumination, only.In the latter case, a field reversal at the position x E=0 takes place reducing the collection Here, xcz represents the collection zone length that equals the i-layer thickness for the dark state, 636 nm, and dichromatic illumination.444 nm illumination leads to a field reversal at x E=0 and thereby a reduced collection length x czblue .This design enables an exploitable nonlinear photoresponse.

ARTICLE
pubs.aip.org/aip/applength to x czblue = 1213 nm.The collection zone concept is essential to further explain and exploit intrinsic envelope mixing of two modulated light sources in the a-Si:H IPD.

Envelope mixing
In this section, electro-optical device simulations are presented and discussed to systematically investigate the origin of intrinsic envelope mixing at irradiance levels below mW/cm 2 considering the previously introduced collection zone (xcz) concept.
In simulation, two monochromatic light sources with the wavelengths λ 1 = 444 nm (ϕ 1peak = 14.8 mW/cm 2 ) and λ 2 = 636 nm (ϕ 2peak = 42.4 mW/cm 2 ) have been modulated with a rectangular stimuli and frequencies of f 1 = 11 kHz and f 2 = 9 kHz, respectively.Light modulations have been modeled as a consecutive sequence of quasistatic DC simulations.In this scenario, the modulation frequencies f 1 and f 2 have been chosen to be far below the cut-off frequency of fc ≈ 2.24 MHz of the detector to ensure the reliability of the simulation method and remain the quasi-static limit in both the simulations and the measurements, thus ensuring comparability.Further details on the cut-off frequency determination are given in the section titled Methods.Considering the predefined collection zone xcz allows for quantifying the maximum number of electrons ncz(t) that can potentially contribute to the photocurrent by integrating the amount of photogenerated electrons along the respective collection zone at a specific time t.The number of collectable electrons has been calculated taking into account the generation rate G(x, t) of photo-induced charge carriers, In a-Si:H p-i-n photodiodes, the major photocurrent contribution can be associated with ncz by neglecting hole contributions since electron mobilities exceed that of holes by orders of magnitude. 34igure 2 , for example, at f = 2, 4, 6 kHz, etc.Since the amount of collectable photogenerated electrons ncz(t) mainly determines the device current density j(t), 34 this value has to have a direct impact on the sensor signal at exactly the same time positions due to the collection zone collapse, as verified in Fig. 2(c).Along the lines of previously shown ncz distortions, the current features in the time domain consecutively exhibit additional mixing frequency components in the frequency domain j(f ) that are exactly located at Further electro-optical simulations have been conducted to study the influence of defect density distributions within the intrinsic layer on the envelope mixing.The simulation results of the current amplitude at fmix = 2 kHz are given in Table I and reveal that the envelope intensity mixing completely vanishes once the amount of deep dangling bond states is reduced significantly by ten orders of magnitude.While mixing frequency components are preserved by reducing the amount of extended tail states ten orders of magnitude and keeping the dangling bond state densities constant, sum and differential frequencies vanish once dangling bonds are reduced ten orders of magnitude in the defect model.Initial defect density values are consistent with the literature and match fundamental device characterization (cf. the supplementary material for j-V characteristics and responsivity).This result indicates that deep dangling bond states are essential to enable envelope intensity mixing in this specific device structure, material, and illumination scenario.Since the utilized fabrication technique of amorphous silicon IPDs allows to tailor material properties, including defect distributions precisely and reliably, the mixing process can be tuned toward specific applications.Furthermore, the simulations confirm the proposed hypothesis of defect-induced E-field screening to be the origin of envelope mixing in a-Si:H IPD.The simulation results

TABLE I. Simulated current amplitudes on the mixing frequency f mix
for different defect distributions within the intrinsic absorber layer.More detailed information on the simulation analysis is given in the supplementary material.further serve as a base for envelope mixing experiments, which are presented in the section titled Experimental results.

EXPERIMENTAL RESULTS
In this section, experimental results on envelope intensity mixing in the IPD are presented.First, measurements are conducted in the kHz range to verify the simulation result within the quasistatic limit metrologically and provide a further understanding of the envelope mixing.Results in the MHz range show a proof-ofprinciple with settings fulfilling requirements of potential applications, e.g.optical ranging or 3D imaging, in terms of modulation frequency and irradiances of each wavelength.A schematic of the utilized setup is given in Fig. 3(c).Experimental and electro-optical simulation parameters exactly match (λ 1 = 444 nm and λ 2 = 636 nm; modulation frequencies f 1 = 11 kHz and f 2 = 9 kHz).The irradiance levels in this experiment are ϕ 1 = 14.8 mW/cm 2 and ϕ 2 = 42.4 mW/cm 2 , respectively.The bias voltage of the detector has been fixed to 0 V to exclude external voltage induced influences on the build-in field.Details on the measurement procedures are given in the section titled Methods.Further details on the fabrication of the device are given in the supplementary material.Figure 3(a) shows the detector response in the time domain and the corresponding FFT signal in the frequency domain.In the time domain [cf.Fig. 3(a)], the sum of the photocurrent densities for monochromatic illumination (blue and red lines showing the modulation stimuli) significantly differs from and drops below the detector response for dichromatic illumination.This measurement result agrees with the previously derived theory presented in the section titled Electro-optical simulation.The sensor output is quenched for monochromatic λ 1 = 444 nm illumination resulting in additional signal components in the frequency domain [cf.Fig. 3(b)].The features are located at the frequency positions f = n × f 1 + m × f 2 with n, m ∈ Z/{0}, which is in agreement with the simulation results.The delay times of the sensor visible in the photocurrent transient signals in the time domain at the positive edges of the red illumination can be attributed to filling of trap states in amorphous silicon 35 and are thus a result of the detector itself.Such time delays are not visible in reference measurements utilizing crystalline photodetectors.Since these latencies in the response time only appear at the modulation frequency, they just influence multiples of f mod in the frequency domain without interacting at the intrinsic envelope mixed signals.
The signal-to-noise ratio (SNR) of the differential frequency, here located at f 1 − f 2 = 2 kHz, is ∼40 dB, indicating I. the highefficiency and sensitivity of the intrinsic photomixing detector and II.that irradiance levels can further be reduced in future experiments.As expected, conventional crystalline photodetectors (e.g., Hamamatsu S1337-66BK) did not show internal frequency mixing at these irradiance levels.Significantly higher irradiances would be required to enable envelope intensity mixing 17,[36][37][38] due to the inversion symmetrical crystallographic material composition.
Most of today's optoelectronic systems and applications operate in real-time and require device operation frequencies exceeding kHz.To show the applicability of the nonlinear mixing process at higher modulation frequencies, further measurements at modulation frequencies exceeding MHz but below the device cut-off frequency have been conducted.In this experiment, the light sources limit achievable modulation bandwidth rather than the mixing device itself.The incident light guided on the detector has been modulated using sine waveforms with frequencies of f 1 = 1.024MHz and f 2 = 1.008 94 MHz.The irradiance levels of ϕ 1 = 4.36 mW/cm 2 and ϕ 2 = 1.03 mW/cm 2 are orders of magnitude below those required to achieve envelope mixing in high-speed graphene-based photodetectors, where irradiances of at least 300 mW/cm 2 have been reported to be mandatory 20 for mixing at frequencies beyond 60 GHz for that optimized device concept.Figure 3(d) shows the modulation amplitudes visualized in a FFT using a conventional digital oscilloscope.The inset shows the mixing frequency peak located at fmix =f1 − f 2 ≈ 15 kHz with a SNR of ∼17 dB that is generated by the IPD itself.This result confirms that the envelope intensity mixing process in a-Si:H photodetectors is not just applicable for modulation frequencies in the kHz range but also holds true at higher f near the cut-off frequency of the device that can further be optimized.Table II summarizes the figures of merit achieved by the a-Si:H intrinsic photomixing detector presented in this work.
In the supplementary material, we further propose and demonstrate one potential application for such intrinsic photomixing devices out of amorphous silicon: optical logic AND gates.As applications advance, we believe that such logic gates might play a significant role in future high performance integrated optical communication systems, optical computing, and artificial intelligence (AI).Compared to traditional integrated electronic logic gates that typically require multiple transistors, the IPD pendant just requires one single a-Si:H device that can be fabricated at temperatures <200 ○ C and enables fill-factors close to 100%. 24,25Other application examples comprise ToF 3D imaging to enable real-time 3D machine vision and machine learning, 39 innovative virtual reality and infotainment applications, 40 or robot-assisted surgery. 41In the application as a time-of-flight 3D-imager, one wavelength would be emitted on a scene with the second wavelength acting as an internal reference signal.Measuring the phase delay on the mixing frequency allows to detect a phase delay on the detected scene-illumination signal due to the mixing process.Compared to other indirect ToFsystems, the IPD would act as a mixing device to dramatically reduce the evaluation effort of distinguishing the phase delay of the reflected scene illumination due to the lower measurement frequency.The proposed technique can enable a significant increase in pixel density at a low degree of complexity in the post-processing and potentially higher sensitivities enabled by photogating. 32Additionally, one would result in a technology process suitable for backend CMOS integration.Thereby, it may reduce the complexity and integration effort of the sensor drastically compared to systems such as the established PMD technique.The required irradiance for envelope mixing on the longer wavelength in this proof-of-principle is just a factor of ∼9 above that of a commercially available PMD flexx2 system ARTICLE pubs.aip.org/aip/app(116 μW/cm 42 vs 1.03 mW/cm 2 ), whereas significant performance enhancements of the IPD-technique are to be expected.

CONCLUSION
In this paper, intrinsic envelope intensity mixing in amorphous silicon p-i-n photodiodes, called intrinsic photomixing detectors, in the visible range has been reported.Electro-optical simulations verify that defect-induced field screening enables that mixing process.It could further be verified that deep dangling bond defect states enable mixing in this device structure and material rather than localized tail-states.Experimentally, envelope mixing has been demonstrated utilizing 444 and 636 nm illumination with irradiances below 4.5 mW/cm 2 at modulation frequencies exceeding MHz.The presented mixing is applicable in wide spreading fields, e.g., optical logic gates, time-of-flight 3D imaging, or signal generation and processing.The thin-film IPD can be fabricated at temperatures below 200 ○ C and can easily be integrated on top of silicon electronics with high fill factors.

METHODS
A-Si:H thin-films have been deposited by plasma-enhanced chemical vapor deposition (PECVD) at temperatures below 200 ○ C in a hot-wall MVS multi-chamber deposition system on pre-cleaned glass substrates.Transparent and conductive indium tin oxide (ITO) anode and cathode electrodes have been sputtered in a radio frequency hot-wall sputtering reactor at 13.56 MHz below 50 ○ C. The devices have been structured using standard UV-lithography to 1.6 × 1.8 mm 2 , mounted in dual-inline chip carriers, and contacted via wedge bonding using a semi-automatic TPT HB16 wire bonder.Further fabrication details are given in the supplementary material and in Ref. 43.Thin-film growth rates of a-Si:H and ITO have been determined by cross-sectional back-scatter scanning electron microscopy (SEM) imaging using a FEI Quanta 250 environmental scanning electron microscope.Overall thicknesses of a-Si:H IPD have thoroughly been validated by using a Bruker Dektak XT profilometer.
Electro-optical simulations have been conducted using the simulation software AFORS-HET 26 taking into account an appropriate device model.This model has been used to subsequently develop, fabricate, and characterize the field optimized a-Si:H intrinsic photomixing detector.Low-frequency transient simulations have been performed by a set of consecutive steady-state simulations in the time domain.An overall time of 100 ms has been discretized with a resolution of 990 001 time stamps.Rectangular modulation signals serve as input parameters for the illumination sources.Time and frequency envelope intensity mixing measurements utilize 444 nm Toptica iBEAM-SMART-PT-445CZ_20067 and 636 nm Toptica iBEAM-SMART-636-S-KL-11049 light sources.The lasers have been modulated using conventional function generators (Tektronix AFG2021 and Rhode&Schwarz HMF2550).Transient and FFT signal acquisition has been realized with a Tektronix TDS 2024C digital oscilloscope prior to an I-V conversion utilizing a Femto DHPCA100 amplifier module at a gain of 10 6 .The experimental setup comprises a dichroic cube, a lens, and an optic diffuser to ensure a homogeneous illumination irradiance on the sensor.The bias voltage of the device has been fixed to 0 V to eliminate any influence on the internal electric field and thereby the defect-induced field screening.
The cut-off frequency of the device has experimentally been determined by measuring the series capacitance (122 pF) and resistance (582 Ω) using a Hewlett Packard LCR-meter.

SUPPLEMENTARY MATERIAL
The supplementary material provides in depth information on the fabrication process and basic characterization of the used a-Si:H IPD as well as electro-optical simulations including basic characterization and defect analysis of the envelope mixing process.Further, it gives LTSpice simulations of a logic Gate as one application example.

FIG. 1 .
FIG. 1.(a) Schematic of the Intrinsic Photomixing Detector (IPD) consisting of an E-field optimized a-Si:H p-i-n detector.(b) Simulated internal field profile across the i-layer of the IPD for the non-illuminated state (dark), red wavelength (red), blue wavelength (blue), and dichromatic (pink) illumination.Solid lines represent a negative E-field; dashed lines represent a positive E-field.Here, xcz represents the collection zone length that equals the i-layer thickness for the dark state, 636 nm, and dichromatic illumination.444 nm illumination leads to a field reversal at x E=0 and thereby a reduced collection length x czblue .This design enables an exploitable nonlinear photoresponse.

FIG. 2 .
FIG. 2. Simulated number of collectable electrons ncz (a) in the time and (b) in the frequency domain with and without consideration of the collection zone xcz concept.Here, the blue and red lines indicate the on/off pulse sequence for the 444 nm (f 1 = 11 kHz) and 636 nm (f 2 = 9 kHz) illumination, respectively.Simulated overall detector current (c) in the time and (d) in the frequency domain.Time domain analysis reveals a significantly reduced number of collectable electrons and thereby massive current quenching at specific time positions due to reduced collection zones.Collection zone quenching results in additional mixing frequency components in the frequency domain, as shown in (d).

FIG. 3 .
FIG. 3. Current density of the a-Si:H intrinsic photomixing detector (a) in the time and (b) the frequency domain.The blue and the red lines indicate the on/off pulse sequence for the 444 and 636 nm illumination.As predicted in the simulation section, the frequency domain FFT signal exhibits significant features at the frequency positions f = n × f 1 + m × f 2 with n, m ∈ Z/{0}.Schematic of the measurement setup (c) and current density of the detector in the MHz regime (d).The FFT reveals the expected signal components located at the modulation frequencies f 1 (444 nm) and f 2 (636 nm).The inset shows the mixing frequency at f mix ≈ 15 kHz generated by using a detector.

TABLE II .
Figures of merit of the intrinsic photomixing detector operated at 0 V bias voltage.