Black phosphorus nanodevices at terahertz frequencies: photodetectors and future challenges

The discovery of graphene triggered a rapid rise of unexplored two-dimensional materials and heterostructures having optoelectronic and photonics properties that can be tailored on the nanoscale. Among these materials, black phosphorus (BP) has attracted a remarkable interest thanks to many favorable properties, such as high carrier mobility, in-plane anisotropy, the possibility to alter its transport via electrical gating and direct band-gap, that can be tuned by thickness from 0.3 eV (bulk crystalline) to 1.7 eV (single atomic layer). When integrated in a microscopic field effect transistor (FET), a few-layer BP flake can detect Terahertz (THz) frequency radiation. Remarkably, the in-plane crystalline anisotropy can be exploited to tailor the mechanisms that dominate the photoresponse; a BP-based field effect transistor can be engineered to act as a plasma-wave rectifier, a thermoelectric sensor or a thermal bolometer. Here we present a review on recent research on BP detectors operating from 0.26 THz to 3.4 THz with particular emphasis on the underlying physical mechanisms and the future challenges that are yet to be addressed for making BP the active core of stable and reliable optical and electronic technologies.


INTRODUCTION
The rising interest in Terahertz (THz) radiation (loosely defined as the 0.1−10 THz frequency range, 30 -3000 µm wavelength range) has been triggered in the last decade by a wealth of applications in security, biomedical imaging, gas sensing, non-destructive testing and materials analysis, non-contact imaging of coatings and composites, non-invasive medical diagnosis of tumors and dental diseases [1]. However, the full exploitation of this underdeveloped portion of the electromagnetic spectrum requires the development of sensitive and performing systems exploiting powerful, stable and coherent sources as well as fast, sensitive and portable photodetectors. These key priorities prompted a major surge of interdisciplinary research for the investigation of different technologies in-between optics and microwave electronics and a large variety of material systems offering ad-hoc properties to target the needed performance and functionalities.
In this context, several room-temperature (RT), on-chip integrated, detection technologies, suitable for real-time frame acquisition and based on distinctive physical mechanisms have been recently proposed and implemented [2]. Amongst them, the present most common architectures rely on semiconductor micro-bolometers [3], fast non-linear rectifying electronics such as Shottky diodes [4], high electron mobility transistors (HEMTs) and field effect transistors (FETs) [5,6]. The latter can be realized with standard complementary metal-oxide semiconductor (CMOS) or silicon technology and have already shown potential for the development of performing and cost effective THz detection systems [7].
Two-dimensional (2D) layered materials, such as graphene [8,9], BP [10,11] or transition metal dichalcogenides (TMDs) [12], display an exceptional technological potential for devising flexible photodetectors that can operate over the broad frequency range from the visible to the THz. respect to that occurring in the armchair direction (4246 m/s) [22]. Since κ is proportional to the square of the speed of sound, the material thermal conductivity along the y-axis (κ y ) is larger than its thermal conductivity along the x-axis (κ x ). Therefore, the direction of maximum thermal conductance lies perpendicularly to the direction of maximum electrical conductance.
A suitable method to determine the crystalline quality and in-plane orientation of an exfoliated few-layer BP flake (Figure 1b) is micro-Raman spectroscopy. Indeed, Raman spectra present three characteristic peaks at 362, 440, and 468 cm −1 (Figure 1c) corresponding to the A g 1 , B 2g , and A g 2 phonon modes, whose relative intensities change if the incident light is polarized along the x-axis, the y-axis, or at a 45° angle between the two axis (this direction is typically labeled as Daxis) [23]. (c) Micro-Raman spectra collected by exciting BP flakes along the z-axis with the 532 nm line of an Nd-YAG pumping laser and by varying the polarization between the armchair (x), the zigzag (y), and the 45° orientation angle: peaks are found at 362, 440, and 468 cm −1 , corresponding to the A g 1 , B 2g , and A g 2 vibrational modes, respectively. Reprinted from ref. [11] with permission of John Wiley & Sons, Inc.
Owing to this unique set of physical properties, black phosphorus promises new functionalities over a variety of device architectures, like sources, modulators, passive components and photodetectors. For example, owing to its ultrafast nonlinear optical response, it has been proposed as a saturable absorber in the telecom band (1400 nm -1600 nm) for the realization of passively mode-locked lasers [24].
Recently, Huber et al. [25] revealed the ultrafast (~50 fs) switching dynamics of interface polaritons in SiO 2 /BP/SiO 2 heterostructrures. The spectral purity and coherence of the activated phonon-plasmon-polariton modes can provide a versatile and robust technological platform polariton-based mid-infrared optoelectronic devices and, remarkably, for ultrafast plasmonic applications.
Moreover, thanks to the inherent in-plane anisotropy, BP has been exploited to devise highspeed photodetectors with polarization sensitivity in the visible and near-infrared range [10,26]. Recent works from our group [11,27] have also demonstrated the first implementations of THz detectors realized with antenna-coupled FETs based on BP flakes, where we took advantage of the in-plane material anisotropy, combined with specific coupling designs, to trigger different physical dynamics to mediate light detection.

TERAHERTZ DETECTION MECHANISMS IN BP-BASED FETs
The basic principle of photodetection is the conversion of absorbed photons into an electrical signal. Unlike the case of visible light or near-infrared radiation, the energy carried by a THz photon (hν = 4 meV for ν = 1THz) is not large enough to excite an optical transition across the energy gap of BP, i.e. does not create extra free carriers. For this reason, the generation of an electrical signal induced by the incoming radiation must rely either on electronic or thermal effects.
The integration of a BP flake within a FET can trigger both dynamics when light is impinging on it. Under this configuration, three main effects can indeed take place in the device: the over-damped or resonant plasma-wave, the thermoelectric and the bolometric effects [27].
The activation of the plasma-wave mechanism in a FET detector can be interpreted as deriving from the non-linear dependence of the FET channel current on the gate voltage (V G ) near the pinch-off point. These devices have the advantage that the responsivity can be maximized with V G , while measuring the output at the drain with no source-drain bias applied, thus dramatically reducing the noise caused by a dc current. This physical effect, predicted by Dyakonov and Shur [28], results in a dc voltage generated along the channel of a FET in response to the oscillating electromagnetic field applied, in a strongly anti-symmetric architecture, between the source (S) and gate (G) electrodes.
In order to funnel the free space THz radiation in the deeply sub-wavelength active element, a proper light harvesting scheme is needed. The typical approach is the exploitation of planar dipole antennas whose arms are connected to the S and top-gate electrodes (Figure 2a). This allows the ac field carried by the THz wave to be asymmetrically fed into the transistor channel, simultaneously modulating the density and drift velocity of carriers. This leads to a rectified current proportional to the square amplitude of the field itself, hence to the intensity of the incoming radiation. At RT, the collective density oscillations (plasma-waves), launched from the source side of the FET, are overdamped, i.e. they decay before reaching the drain (D) contact. In this regime, the detection is inherently broadband and can be well described by a distributed resistive self-mixing scheme [29]. According to the theoretical models, the amplitude of the photoresponse (Δu p in the case of a photovoltage) is expected to vary as a function of the applied gate voltage (V G ) and can be retrieved from the dc transfer characteristics of the FET via the relation [30]: where U a is the amplitude of the ac radiation field, R L is the finite impedance of the measurement setup including the readout circuitry, and η is a proportionality factor that takes into account the coupling efficiency of the THz antenna. The asymmetric antenna design generates a field enhancement between the G and S contacts of the FET. With reference to Figure 2a, this can also result in a temperature difference between the source and the drain side of the transistor. Therefore, under THz illumination, a thermal gradient can arise along the channel, leading to the diffusion of carriers from the hot to the cold regions. This phenomenon is the basis for the thermoelectric effect; if a thermal difference (ΔT) is applied along a material with non-zero Seebeck coefficient (S B ), electrically connected by two metallic leads, a voltage difference V T develops between the two contacts and V T = S B ·ΔT. Since BP is typically a ptype degenerate semiconductor at RT, the value of S B is positive and depends on the gate voltage following the Mott relation: Where k B is the Boltzmann constant, e is the (positive) elementary charge, σ(E) is the conductivity as a function of energy and the derivative is evaluated at the Fermi energy E F . At room temperature S B values as large as 335 µV/K have been found in few-layer BP flakes [31]. Therefore, if THz radiation impinges on an asymmetric antenna structure, both the thermoelectric and plasma wave effects can take place. However, it is still possible to select the active mechanism by exploiting the relative orientation of the antenna and the crystal directions. Indeed, the thermoelectric effect is maximized when the thermal gradient along the FET channel is maximum. This is achieved by placing the S-D axis parallel to the armchair direction, where κ is at its minimum and σ is at its maximum value. In this configuration, the lack of energetic balance between the hot-side and cold-side of the channel is mainly compensated by the carrier diffusion, resulting in a large thermoelectric voltage that typically overshadows the plasma-wave effect [11]. By choosing a different orientation, for example at 45° between the x and y directions (D axis), the thermoelectric contribution can be reduced and the plasma-wave mechanism is observed [27].
On the other hand, in order to activate selectively the bolometric effect, a symmetric antenna structure is needed. In fact, this mechanism arises as a consequence of the uniform heating of the FET channel when the antenna funnels the impinging THz beam. This can be achieved in a totally symmetric device architecture, like the one shown in Figure 2b, where the plasma-wave and thermoelectric effects would be inhibited. The amplitude of the bolometric photovoltage (V b ) is directly related to the temperature dependence of the conductivity via the relation [27]:

SUB-TERAHERTZ DETECTION
The activation of these three detection effects in BP-based FETs has been recently engineered and demonstrated in the sub-THz frequency range (265 GHz -640 GHz) [11,27,32]. The fabrication of BP-FETs begins with the mechanical transfer of thin flakes (~ 8 -15 nm) on an insulating substrate under an inert atmosphere. In Refs. [11,27] single flakes were individually contacted with S and D electrodes consisting of a proper adhesion layer/metal sequence (Cr/Au [11] or Ni/Au [27]). The shape of the electrodes was defined by aligned electron beam lithography (EBL). A SiO 2 layer was then deposited on the sample via Ar sputtering, so that the exposed face of the BP-flake is fully encapsulated within it. This step prevents degradation due to the chemical reaction of BP with oxygen, which is known to modify the electrical device performances over time and deteriorate the flake itself [33]. The top-gate electrode was aligned with the center of the channel via EBL and defined via thermal evaporation of an 80 nm layer of Cr/Au. The dominant detection dynamics mainly depends on two device parameters: (i) the symmetric (or asymmetric) antenna design and (ii) the relative orientation between the source-drain axis and the crystalline in-plane direction.
Three different combinations of antenna design and crystal orientation with respect to the channel direction were tested. Sample A (Figure 3a) was equipped with an asymmetric planar bowtie antenna (total dipole length 500 µm) with the S-D axis oriented along the armchair direction of the BP flake. The total channel length was 2.7 µm and the gate width was 580 nm. The estimated room temperature field effect mobility (µ FE ) for this device was µ FE = 470 cm 2 V −1 s −1 . Sample B (Figure 3c) was equipped with an asymmetric 1 mm long bow-tie antenna with the S-D axis oriented at 45° with respect to the armchair direction. The total channel length was 1.8 µm and the gate width was 1.0 µm. For this device a mobility µ FE = 330 cm 2 V −1 s −1 was obtained. Sample C (Figure 3e) was equipped with a symmetric 500 µm long bow-tie antenna with the S-D axis oriented along the zigzag direction. The total channel length was 900 nm and the gate width was 450 nm. For this device a mobility µ FE = 380 cm 2 V −1 s −1 was found.
Experiments were carried out at room temperature with a ~ 300 GHz, linearly polarized, radiation produced by a tunable electronic source. The THz beam, modulated by a mechanical chopper, was focused on the detector by a set of off-axis parabolic mirrors, reaching a spot diameter of 4 mm in the focal point. The photoresponse was measured in photovoltage mode [27]: the S contact was kept grounded and a dc voltage (LIA) was measured at the D electrode with a lock-in amplifier. The amplitude of LIA was proportional to the incoming THz intensity and the detector responsivity (R ν ) was varied by changing the gate bias. R ν , defined as the ratio between the output signal and the input optical power, is evaluated using the following expression [11]: Where the factor π/√2 is a normalization coefficient that takes into account the rms value of the fundamental sine wave Fourier component of the square wave produced by the chopper, G n is the gain of the preamplifier, P tot is the average electromagnetic power, S t is the beam spot area and S λ is the diffraction limited area (S λ = λ 2 /4). Figure 3b shows R ν as a function of V G for Sample A. The comparison with the dependence of the Seebeck coefficient with respect to V G [11], proportional to the predicted photothermoelectric response V T , shows a good qualitative agreement, demonstrating the activation of the thermoelectric effect.
On the other hand, as depicted in Fig. 3d, the R ν vs. V G plot for sample B, obtained by shining a 294 GHz radiation, exactly follows the dependence of the photoresponse Δu p predicted by the Dyakonov-Shur theory (Fig. 3d). This difference between samples A and B is caused by the different relative orientation between the S-D axis and the crystalline in-plane direction in the two cases.
When a symmetric THz antenna is employed (sample C) the bolometric effect is expected to occur. The responsivity curve of sample C is shown in Fig. 3f. An immediate difference with respect to the results obtained for samples A and B is the sign change in R ν for V G = -1.1 V. Interestingly, the same sign change is also found in the bolometric coefficient [27]. The direct comparison between the R ν vs. V G and the σ -1 ·∂σ/∂T vs. V G curves shown in Fig. 3f, demonstrates that sample C behaves like a THz bolometer.
Amongst the three reported devices, a maximum responsivity value R ν = 7.8 V/W has been obtained for sample C, corresponding to a noise equivalent power (NEP, defined as the ratio between R ν and the noise spectral density) of 7 nW/√Hz [27]. These pivotal experiments have underlined the potentiality of BP-FETs to be engineered in view of activating specific physical mechanisms, pushing a further research on the topic. Therefore, more recently, the realization of detectors operating in the 0.3-0.65 THz range with a combination of hexagonal boron nitride (hBN) and BP flakes has been reported [32]. Owing to the flatness of hBN and to its compatibility with the honeycomb lattice, the encapsulation of BP in hBN/BP/hBN van der Waals heterostructure leads to extremely inert and air stable devices [32,34]. Furthermore, with this approach, record mobility values have been reached (up to ≈1350 cm 2 V −1 s −1 at room temperature [18] and ≈ 6000 cm 2 V −1 s −1 for T < 30 K [35]).
THz detectors realized with hBN/BP/hBN stacks have also a higher thermal stability with respect to oxide-encapsulated devices. The reported stability, allowed performing low temperature experiments which revealed and a signal-to-noise ratio (SNR) of 2x10 4 at 4 K [32]. Importantly, the selective activation of the three detection mechanisms was demonstrated in a single BP-FET, equipped with an asymmetric antenna and oriented along the D axis. For T < 50 K the detection was dominated by the bolometric effect, whereas at RT there was a simultaneous coexistence of the thermoelectric and plasma-wave effects, whose relative amplitudes were modified by changing the frequency of the incoming radiation [32].

DETECTION AT 3.4 THz
Many interesting applications in the THz frequency range require the use of compact, coherent, broadly tunable, monolithic micro-sources, having high spectral purity. Quantum cascade lasers (QCLs) are certainly the most appropriate in this respect: they operate in the 1.2-5.4 THz frequency range, with peak output powers that can reach watt-level, continuous-wave operation and ultra-narrow linewidth, which make them versatile for applications in high-resolution spectroscopy, gas sensing, and heterodyne detection [36]. To exploit the potential of QCLs, suitable detectors operating at frequencies > 1THz are needed.
FETs can provide efficient THz rectification far beyond their transit-time limited cut-off frequency: Si MOSFETs operating up to 4.3 THz [37] and nanowire-based FET operating up to 2.8 THz have been indeed demonstrated in the last years [38]. In those devices, the transition between a sub-THz to a few-THz detection does not affect the active element (i.e. the rectifier), but only the coupling architecture: the antenna dimensions shrink to match shorter wavelengths.
Following this approach, the operation range of a BP-FET can be shifted to higher frequencies by reducing the antenna dimensions, while maintaining the same impedance (~ 70 Ω for a bow-tie). To match the wavelength generated by a 3.4 THz QCL, a BP-FET equipped with a 32µm long split-bow-tie antenna was fabricated (Fig. 4a). The channel length was set to 900 nm, while the width of the G electrode was 450 nm. The S-D axis was oriented at 45° with respect to the armchair crystalline direction, hence the plasma-wave rectification effect is expected to dominate the detection.
The light beam emitted by the QCL was focused on the detector using a pair of 5 cm focal length Picarin lenses, obtaining a Gaussian shape with ~ 200 µm diameter (Fig. 4b). The device was tested in a photovoltage-mode configuration: the S electrode was grounded, V G was set with a dc voltage generator and the response was measured at the D electrode with a lock-in amplifier. A voltage preamplifier with gain G n = 40 dB was used in the experiments. Figure 4c shows the dependence of R ν , evaluated by using equation 4, as a function of the applied V G : a maximum peak of 4.5 V/W was obtained for V G = 0.65 V.
The predicted plasma-wave response for this sample, calculated from the static dc conductivity as Δu p /(ηU a 2 ) (see eq.1), is depicted in Fig. 4d. A maximum is expected for V G = 0.6 V, whereas for V G < 0.3 V the response is predicted to drop rapidly. The qualitative agreement between the two graphs of Fig. 4c and 4d, confirms that in a sample with a 45°-oriented asymmetric antenna, the response is dominated by the overdamped plasma-wave contribution even at 3.4 THz. This broadband behavior is in agreement with the inherently broadband nature of the overdamped plasma-wave mechanism. Figure 4e shows the NEP of the device, calculated assuming the noise spectral density to be dominated by the Johnson-Nyquist noise: N th = (4R ch ·k B T) ½ , where R ch is the channel resistance and k B is the Boltzmann constant. A minimum NEP of 5 nW/Hz ½ was found for V G = 0.65 V; this value is lower than the NEP obtained at RT for detectors operating at sub-THz frequencies, proving the efficient scalability of the BP-FET device concept over a broad frequency range.

PERSPECTIVE AND CHALLENGES
The recent progress in the development of photodetectors [10,11], fast electronic and photonic devices [19,24,25], electrode materials in lithium and sodium ion batteries [39], supercapacitors [40] and quantum dots [41], is going to speed up the practical future implementation of BP atomic layers in optoelectronics and nano-optics. Notably, the material shows a great potential for applications where excellent switching speed is required.
Of particular interest for photonics is the exploration of plasmon polaritons -hybrid light matter modes involving the collective oscillation of mobile charges. In graphene, plasmon polaritons have been exploited to confine and manipulate infrared radiation to length scales of tens of nanometres. The imaging of long-range propagating phonon-plasmon-polaritons and their ultrafast optical switching has been also demonstrated in black phosphorous via near-field optical microscopy experiments ( Figure 5). In particular, femtosecond pulses can initiate the plasmonic response in this semiconductor through direct excitation of electrons across the bandgap. The reported switching speed of activated phonon-plasmon-polariton modes in SiO 2 /BP/SiO 2 heterostructures [25] opens an intriguing perspective for the development of ultrafast plasmonic circuits, modulators and switches for a variety of mid-infrared and near infrared nanophotonic applications. The evolution of BP-based technologies is however currently hindered by the limited availability of large area flakes and by the fast material reactivity with oxygen, which leads to its quick deterioration in air. The future implementation of electronic and photonic technologies based on this material system should therefore face three major challenges: (i) the development of controllable and versatile growth techniques; (ii) the improvement of material chemical and electrical properties; (iii) the refinement of the fabrication procedures for long-time stable structures.
On the growth side, the recent progress on BP production by mineralizer-assisted gas-phase transformation method provides an efficient alternative to standard high-pressure synthesis or chemical vapor transport for the growth of large-size, high-quality crystals, also allowing the possibility to add dopants during the growth process [42]. However, high-throughput and scalable synthesis methods are still missing, thus hampering the use of BP for large-scale applications.
Furthermore, the optimization of carrier density via chemical doping during growth is of fundamental importance to improve the performances of BP-based devices; for example, selenium doping has been demonstrated to be beneficial for increasing the responsivity of photodetectors operating in the visible range by more than one order of magnitude [42]. Recently, thin flakes of BP doped with tellurium showed a higher mobility (up to 1850 cm 2 V −1 s −1 at RT) with respect to undoped crystals and, more remarkably, higher stability under ambient exposure [43]. This result provides an interesting solution to the long-standing obstacle of poor environmental stability, circumventing the otherwise mandatory encapsulation of BP via dielectric deposition or mechanical stacking of van der Waals heterostructures, whose fabrication is costly and often demanding.

CONCLUSIONS
Black phosphorus earned an extraordinary potential among the family of 2D semiconductor materials when recent results unveiled its high carrier mobility, high optical and UV absorption, and other attractive properties, which are of particular interest for optoelectronic and photonic applications. The development of photodetectors from the ultra-violet to the near-infrared frequency regions has attracted increasing attention owing to the opportunity of band structure engineering via thickness control and to the peculiar absorption properties stemming from the in-plane crystalline anisotropy of BP.
In this brief review, we have provided a summary of recent achievements in the development of BP-based photo-detectors operating in one of the most technologically appealing region of the electromagnetic spectrum: the far infrared. We discussed detection performances in the 0.3-3.4 THz frequency range, unveiling room-temperature responsivity higher than 4V/W and noise equivalent power lower than 10 nW/Hz ½ , making this technology highly competitive for practical process and quality control apprlications. We also discussed the influence of the strong inplane anisotropy of the material for tailoring the detection dynamics, offering an interesting route for engineering device properties "from scratch". Together with the demonstrated plasmonic response of BP heterostrctures, the present review provides a starting point for future studies and design of BP-based THz photonic, plasmonic and nano-electronic systems.

AKNOWLEDGEMENTS
This work was supported by the European Research Council through ERC grant 681379 (SPRINT), and by the European Union through the program Graphene Core1 -Graphene-based disruptive technologies" Proposal 696656.