1. Introduction

In recent years, atomically thin two-dimensional (2D) materials such as transition-metal dichal cogenides (TMDCs), graphene and black phosphorus (BP) have received burgeoning amount of interest due to their unique physical properties. Compared with the bulky material, they exhibit novel optical, electric, mechanical and thermal properties due to the mono-few-layer thickness [1–4]. 2D materials emerged as a new platform to achieve novel optical and electrical properties in ultra-compact sizes. Among these 2D materials, the layered BP is currently intensely investigated for its promising applications in electronics [5–8] and optoelectronics [9,10]. Compared with other 2D materials, BP shows some characteristics, such as strong interlayer interaction, higher carrier mobility compared to MoS₂ and tunable band gap compared to the zero bandgap of graphene. Moreover, BP has a direct band gap for all number of layers, ranging from 0.3 eV for bulk to 2 eV for monolayer [11–14]. Therefore, the multi-layer BP may allow for photodetection in a wide spectrum such as the entire visible spectrum, mid-infrared (MIR) and far-infrared (FIR). BP has been recently investigated for potential applications including field effect transistors [15,16], heterojunction p-n diode [17], photovoltaic devices [18], and photodetectors [19].

However, the optical electric devices based on 2D materials also exhibit a limited light absorption due to their inherent atomically thin thickness. In order to enhance the interaction of light-matter for 2D materials as an active layer, several light trapping strategies have been proposed, such as integrated waveguides [20–25], diffraction gratings [26], folded configuration [27], direct coupled resonators [28], and plasmonic nanostructures [29–40]. For example, Wang’s group demonstrated a high responsitivity graphene/silicon-heterostructure waveguide photodetector [25]. The waveguide can enable the absorption of evanescent light, resulting in high absorption. And according to Seungbum Rim’s research, an effective light trapping configuration for thin-film solar cells is introduced [27]. By utilizing a V-shaped light trapping configuration that substantially increases the photocurrent generation efficiency, the device can convert the absorbed photons into photocurrent with a conversion efficiency of 52%. Among these methods, plasmonic nanostructure is quite potential for the light enhancement due to the process convenience and small device footprint. By introducing the plasmonic nanostructure, incident light absorbed by such nanostructures can be efficiently converted into plasmonic oscillations at the resonance wavelength, which leads to a significant enhancement of the local electric field. The localized surface plasmon resonance (LSPR) can be excited in metal nanostructures, which is an effect that produces the strong peak in absorption spectra, as well as strong enhancement of the local electric fields surrounding the nanostructures. When a beam of light hits the metal nanostructures, if the incident photon frequency matches the vibration frequency of the metal nanostructures, the nanostructures will have a strong absorption enhancement effect on the photon energy, and the local surface plasmon resonance will occur. Plasmonic nanostructure can efficiently take advantage of the LSPR properties, which develops a new method to realize absorption enhancement for the ultra-thin 2D materials.

It is known that plasmonic nanostructures can be usually classified into many different shapes, such as the nanoparticles, nanoscale gratings and so on. Previous works have demonstrated the effect of different shapes of plasmonic nanostructures on the interaction of light-matter for 2D materials as an active layer. For example, a plasmon resonance enhanced multicolor photodetector by coupling graphene with gold nanoparticles was presented [41]. By integrating with plasmonic nanostructures, the photocurrent can be greatly enhanced up to 1,500%, with the external quantum efficiency reaching up to 1.5%, which is about one order of magnitude better than previously reported graphene devices. And according to T.J. Echtermeyer’s research, several different plasmonic nanostructures including nanoparticles and gratings were employed [13]. Among these nanostructures, the grating structures show the best performance. Combining graphene with grating structures, the efficiency of graphene-based photodetectors can be increased by 20 times. Therefore, in our study, the plasmonic nanostructure was selected as the grating structure.

In this paper, we employ a BP photodetector based on a nanoscale plasmonic grating structure to enhance the optical absorption. Optical characteristics of the grating structure are thoroughly analyzed by absorption spectrum, optical field intensity and power flow. Through the comparative study on the results, the BP photodetector based on plasmonic nanostructure that can realize super absorption was obtained. In addition, the absorption coefficient and responsitivity of the 20-layer BP photodetector were calculated systematically. The electrical characteristics of this BP photodetector are also demonstrated to evaluate the performance of the photodetector by taking dark current into consideration. Our photodetector demonstrates a super absorption structure, which effectively exploits the local plasmonic enhancement effect to achieve a significant enhancement factor and enhance both the light absorption and responsitivity. It paves a new way for efficiently enhancing the photodetection performance of BP. In addition, high sensitivity of the photodetector is crucial for sensing applications such as biomedical detection when the signal to be identified is weak. The high responsitivity together with absorption enhancement of BP with plasmonic nanostructure make it a good alternative to the traditional photodetectors.

2. Device structure

To analyze LSPR effect in metal nanostructure, we compare the absorption enhancement of the BP photodetector with the grating structures based on three different plasmonic materials and the photodetector without grating as a control device. Figure 1(a) shows the three-dimensional schematic diagram of BP photodetector. As illustrated in the inset of Fig. 1(a), a schematic diagram of the BP crystal structure is demonstrated. The atoms are arranged in a BP lattice to produce two directions: the zigzag and the armchair, leading to its unusual in-plane anisotropic electrical and optical properties. Firstly, the back-gate BP photodetector is placed on the buried oxide layer with a thickness of 200 nm. Then the nanoscale grating nanostructure is deposited on the BP. The nanoscale plasmonic grating is introduced to enhance the optical absorption by utilizing the LSPR effect. The surface electrons provided by the metal nanostructure play an important role in the resonance coupling with the incident photons. The BP has a thickness of 11.5 nm, which is approximately equivalent to the thickness of BP atoms with 20 monolayers. Source and drain electrodes are placed on the buried oxide layer. And a voltage is applied to the silicon substrate as a back gate, which electrically modulates the device.

 

Fig. 1 (a) Schematic diagram of 20-layer BP-based photodetector. (b) The exclusive absorption in the BP layer of the nanoscale grating structures for three different grating materials and no grating. And the exclusive absorption in the graphene layer of the Al grating structures (green line).

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In our work, the optical characteristics of the 20-layer BP photodetector are thoroughly analyzed by optical field intensity and absorption spectrum with a calculation method based on three-dimensional Maxwell's equation. As illustrated in Fig. 1(b), the exclusive absorption in the BP layer with the nanoscale grating structure of three different grating materials and without nanoscale grating is compared. Besides, the exclusive absorption in the graphene layer with the Al grating structure is also demonstrated in this figure. The field polarization has been chosen to be along the major axis of the grating. There are two absorption peaks in the absorption spectrum, corresponding to two resonance modes. The resonant mode corresponding to the first absorption peak is transverse mode, whose dipole oscillation is along the zigzag direction of BP. And the resonant mode corresponding to the second absorption peak is longitudinal mode, whose dipole oscillation is along the armchair direction of BP [42]. As shown by the black, red, blue and pink solid lines in Fig. 1(b), the peak absorption of BP is enhanced to 71%, 69% and 76% at 714 nm, respectively. Compared to the absorption in the BP layer, the peak value of graphene absorption curve that appears at 444 nm can reach 56%, which is almost the same as the absorption of BP. However, the absorption peak of BP is enhanced 74.7% at 714 nm compared to the absorption peak of graphene. Many references have studied the optical absorption of different two-dimensional materials utilizing different nanostructures. According to Liu Yuan’s research, plasmon resonance enhanced multi-color photodetector by graphene is demonstrated [41]. Graphene with Au nanoparticles on glass shows a plasmonic resonance peak around 515 nm with a peak absorption of 21%. And a BP photodetector with silicon photonics and nanoplasmonics was studied in Chen Che’s research [43]. The wavelength range studied in this paper is near infrared. The total optical absorption of the nanogap−BP hybrid structure is near 24% at 1.52 μm. According to Corey Janisch’s research, the enhanced absorption and photoluminescence generation from MoS2 monolayers coupled with a planar nanocavity was demonstrated [44]. The exclusive absorption of monolayer MoS₂ is increasing to nearly 70% at a wavelength of 450 nm. And according to Li Han’s research, a scheme that supports plasmon on a continuous monolayer BP by using a diffraction grating was represented [45].The wavelength range studied in this paper is far infrared. The exclusive absorption of monolayer BP is nearly 50% at a wavelength of 9.5 μm. In addition, based on Jiang Tao Liu’s research, enhanced absorption of monolayer MoS₂ with resonant back reflector was demonstrated [46]. The absorption of monolayer MoS₂ with silver films is about 22%. In comparison, the BP photodetector in our paper has a higher absorption. A reasonably strong inter-band transition in Al is localized in a narrow energy range around 1.5 eV (800 nm). Below and above this energy, the inter-band transition is weak. Thus, Al is expected to support long-lived LSPRs with high optical cross-sections [47]. According to the Drude model, the plasma frequencies of Ag (1.370 × 10¹⁶ rad/s) and Au (1.372 × 10¹⁶ rad/s) are lower than that of Al (2.243 × 10¹⁶ rad/s), which illustrates that Al can be well excited at short wavelengths compared to Au and Ag, such as visible band [48]. Al is not only an abundant and cheap material compared to the noble metals, but also may have some novel properties. Furthermore, Al will be active from 200 nm to just below 800 nm, because the real part of its dielectric function is negative from 200 nm to 800 nm [49]. Moreover, the light source in the simulation is planar wave and the wavelength range covers the visible band, which is roughly consistent with the wavelength range where Al is active. Therefore, although the Ag and Au systems have been intensely investigated for many years because of the favorable dielectric properties in the research of LSPR, the material of nanoscale grating in our research is selected as Al. And according to ref 50, the complex refractive indexes (n_xx = 3.16 + 0.0623i, n_yy = 2.83, n_zz = 3.54 + 0.135i) are used to simulate 11.5 nm thick BP. In the simulation of optical characteristics, the absorption of source and drain electrodes can be ignored.

3. Results and discussion

Because the LSPR effect and light absorption are sensitive to the shape and size of the nanostructure, we set the different parameters (i.e., the height of grating, h and the width of grating, w) of the nanoscale grating to search the optimized parameters and reach super absorption. As a result, we firstly take the height of the grating into consideration. As illustrated in Fig. 2(a), the absorption of BP for eight different heights is plotted. It is obviously that there are two absorption peaks. And the first absorption peak has barely varied with the change of height when the wavelength is less than 600 nm. An absorption peak will appear in the wavelength range of 425-500 nm, where the maximum absorption can almost reach 56% at 470 nm. However, the absorption of BP shows a strong dependence of the resonance wavelength on the height of grating in the wavelength range of 650-800 nm. For example, as shown by the black and yellow solid lines in Fig. 2(a), the absorption peak of BP is enhanced to 48% at 750 nm. Therefore, the absorption can be enhanced by adjusting the height at the wavelength range of 650-800 nm. Furthermore, as the height decreases, there will be a red shift at the wavelength corresponding to the second absorption peak. To demonstrate the effect of height on the absorption, we plotted the absorption spectra as the function of the height of grating under the illumination of p-polarized [see Fig. 2(b)] and s-polarized states [see Fig. 2(c)], respectively. For the p-polarized incidence as shown in Fig. 2(b), the absorption peak value can reach 87.5% at 735 nm when the height is 5 nm. However, for the s-polarization case in Fig. 2(c), the situation is significantly different, in which the relatively higher absorption merely covers much narrower wavelength range. Moreover, there is a very weak absorption when the wavelength range is from 600 to 800 nm and when the height is higher than 20 nm. Figure 2(d) shows the Poynting vector distribution of the nanoscale grating structure in the Y-Z plane at a wavelength of 700 nm for p-polarized and s-polarized incidences, respectively. From Fig. 2(d), it is clearly that the amplitude of the Poynting vector is very strong around the grating and decreases significantly through the nanoscale grating and BP layer for both p-polarized and s-polarized incidences, which illustrates the LSPR effect. It can be seen that the Poynting vector is mainly concentrated surrounding the nanostructures, indicating the strong enhancement of the local electric fields. However, the Poynting vector distribution for s-polarization case is a little different from the distribution for p-polarized incidence. As it can be seen from the middle part of the Fig. 2(d) for s-polarization, the two vortices formed around the grating will significantly prevent energy from flowing to BP layer, which will result in a smaller absorption cross section compared to the p-polarization case. This is similar to the Young’s interference. At the position where the light intensity is zero, the light disappears at some interference fringes, for example, the centers of the vortices [51].

 

Fig. 2 (a) The exclusive absorption in the black phosphorus layer of the nanoscale grating structure at eight different heights (i.e., height = 5, 10, 15, 20, 25, 30, 35 and 40 nm) for p-polarized incidence. The exclusive absorption of the black phosphorus layer as the function of the height of the grating for (b) p-polarized and (c) s-polarized incidences, respectively. (d) The Poynting vector distribution of the nanoscale grating (w = 140 nm, h = 5 nm) structure in the Y-Z plane at a wavelength of 700 nm for p-polarized and s-polarized incidence, respectively.

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To illustrate absorption enhancement, the electric field distribution in the X-Y plane at a wavelength of 800 nm for p-polarized incidence is plotted in Fig. 3(a) and 3(b) respectively, which show the electric field distribution in grating/BP interface and the air/grating interface in X-Y plane. From Fig. 3(a) and 3(b), we can see that the electric field intensity is mostly localized at the edges of the grating, which illustrates that the electric dipole behavior expected in the nanostructures exhibits localized plasmon resonances [52]. Moreover, the electric field intensity in the interface of BP and grating is higher than that in the interface of grating and air. This demonstrates that the electric field is mainly concentrated on the BP layer, which is for the benefit of the absorption enhancement of BP.

 

Fig. 3 The electric field distribution in the X-Y plane at a wavelength of 800 nm for p-polarized incidence around (a) the BP/grating interface and (b) the grating/air interface.

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To verify the effect of height on the LSPR effect more intuitively, we plotted the electric field distribution in the Y-Z plane at a wavelength of 800 nm for p-polarized incidence at four different heights of the grating. It is known that the coupling of LSPR between nanostructures will result in near field enhancement in the gap. As shown in Fig. 4, it can be seen that the electric field is mainly concentrated on the gap between the two nanoscale gratings, which is consistent with the theory of near-field coupling between surface plasmon-polariton modes of neighboring nanostructures [53]. And the attenuation of the electric field intensity along the Z-axis is more severe as the height increases. One might think of this variation as the generation of attenuated photons that exists only in the near-field region [54]. Such a field enhancement can improve the light absorption of the BP photodetector, which thereby increases the absorption coefficient and responsitivity. Moreover, the electric field intensity can reach the maximum when the height of grating is 5 nm, further showing the feasibility for obtaining a stronger absorption at lower height.

 

Fig. 4 The electric field distribution in the Y-Z plane at a wavelength of 800 nm for p-polarized incidence at different heights. (a) h = 5 nm. (b) h = 15 nm. (c) h = 25 nm. (d) h = 35 nm.

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To verify the impact of the width of the grating on the optical absorption, the absorption of BP for eight different widths and absorption spectra of p-polarized and s-polarized incident light are plotted in Fig. 5. The same as Fig. 2(a), the absorption-wavelength curve also has two absorption peaks. For the first absorption peak, the maximum absorption increases slightly as the width of grating increases. As for the second absorption peak, the maximum absorption is improved with the increasing width. But the absorption almost no longer increases when the width is higher than 150 nm. As shown by the yellow solid line in Fig. 5(a), the peak absorption of BP can reach 89.8% at 714 nm, which is increased by 38.8% compared to the absorption of black solid line at 675 nm. Furthermore, as the width decreases, there will be a red shift at the wavelength corresponding to the second absorption peak. To verify the impact of width on the optical absorption more clearly, the absorption spectra as the function of the width of grating under illumination of p-polarized and s-polarized incidences are plotted in Fig. 5(b) and 5(c), respectively. From Fig. 5(b), we can see that the absorption spectra shows the dependence of the resonance wavelength on the width in the wavelength range of 425-500 nm and 650-775 nm. For the s-polarization case in Fig. 5(c), there is a super absorption at the narrower wavelength range, which is different from the p-polarization case. The absorption peak above 80% could merely cover the wavelength range of 420-470 nm and 730-800 nm. Figure 5(d) also shows the Poynting vector distribution of the nanoscale grating structure at a wavelength of 700 nm for p-polarized and s-polarized incidences, respectively. As we can see, the Poynting vector distribution for s-polarization case is different from the distribution for p-polarized incidence. For s-polarization, the two vortices formed around the grating will significantly prevent energy flowing to the BP layer, which will result in a smaller absorption cross section. Compared with Fig. 2(d), the amplitude of the Poynting vector of Fig. 5(d) is higher due to the bigger width. Therefore, the maximum absorption peak is obtained when the width of grating is 160 nm.

 

Fig. 5 (a) The exclusive absorption in the black phosphorus layer of the nanoscale grating structure at eight different widths (i.e., width = 90, 100, 110, 120, 130, 140, 150 and 160 nm) for p-polarized incidence. The exclusive absorption of the black phosphorus layer as the function of the width of the grating for (b) p-polarized and (c) s-polarized incidences, respectively. (d) The Poynting vector distribution of the nanoscale grating (w = 160 nm, h = 5 nm) structure at a wavelength of 700 nm for p-polarized and s-polarized incidences, respectively.

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To calculate the absorption coefficient of the 20-layer BP, the energy bandgap of the 20-layer BP was firstly calculated as 0.095 eV. Therefore, we calculated the absorption coefficient α by utilizing the value of energy bandgap. As shown in Fig. 6, we demonstrated the relation between the absorption coefficient α and wavelength λ for the 20-layer BP. The definition of the absorption coefficient α can be expressed as$\alpha \left(ћ\omega \right) = \frac{{\alpha }_b}{2\pi }\left(\frac{2m_r}{{ћ}^2}\right){\left(ћ\omega -E_g\right)}^{1/2}$, where E_g refers to the energy band gap of semiconductor materials, ћ refers to the Planck constant, and m_r refers to the reduced mass of semiconducting materials. From the absorption coefficient–wavelength curves, it can be noticed that absorption coefficient curve rises first and then drops as the wavelength increases. When the wavelength is 6.5 μm, the absorption coefficient can reach a peak value of 3241 cm⁻¹. And taking the cut-off wavelength into consideration, for the 20-layer BP, the cut-off wavelength is about 13 μm. Compared to the absorption coefficient of fewer layers of black phosphorus, for example, the cut-off wavelength of 5-layer BP is about 2.49 μm, the cut-off wavelength of 20-layer BP red shifts, which can be further extended to far infrared (FIR) region because of the smaller bandgap.

 

Fig. 6 Calculated absorption coefficient and responsitivity for the 20-layer BP photodetector.

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Based on the absorption coefficient, we also calculated the responsiveness of the photodetector. As illustrated in Fig. 6, we demonstrate the dependence of responsitivity on the wavelength for the 20-layer BP photodetectors. It is assumed that the optical power reflection at the surface is zero in an ideal case. In addition to the “intrinsic” photoresponse in conventional detectors, photocurrent is also contributed by the photogating effect in BP phototransistors. The photogenerated free electron and hole pairs are separated by the applied voltage, drifting in opposite directions towards the electrodes. If the holes mobility is much lower than the electron mobility, the photogenerated electrons will cross the channel much faster than the photogenerated holes. Many electrons can contribute to the photocurrent before recombination, leading to the photoconductive gain. If the electrons and holes are trapped in localized states, they act as a local gate. When the photo-generated chargers cross the channel, the oppositely charged carriers remain trapped. That is to say, when the holes are trapped in the localized states, the lifetime of electrons is therefore prolonged. As a result, the longer lifetime of these carriers will lead to a larger photoconductive gain. This is the so-called photogating effect [55–58]. Therefore, the optical gain we used in this simulation is taken from reference [59], which is as high as 10,000 when incident light with low power is applied. From Fig. 6, we can see that responsitivity increases slowly with the increasing of the wavelength and then decreases gradually after reaching the peak. When the wavelength is 9.8 μm, the responsitivity reaches high as 60.94 A/W. For the whole telecommunication windows, the responsitivities of the BP phototransistors are two orders higher than those of Ge or GeSn photodetectors [60]. Further, to demonstrate the effect of grating structure on the absorption, we calculated the responsitivity of BP photodetectors with and without nanoscale grating in the wavelength range of 0-1 μm in the inset of Fig. 6. Taking the actual light absorption of the BP photodetector into account, we set the exclusive absorption of the BP photodetectors with and without grating as 0.898 (from Fig. 4(a)) and 0.214 (from Fig. 1(b)), respectively. As it can be seen from the inset of Fig. 6, the responsitivity of the photodetector with Al grating is almost 4.2 times larger than that of the photodetector without grating. This result shows that the responsitivity of the photodetectors with nanoscale Al grating structure is sure to be greatly improved at visible range.

The simulated dark current-gate voltage characteristics of the 20-layer BP photodetector are shown in Fig. 7. There is an approximate linear region that the dark current I_d drops from 265.4 μA at −10 V to 44.9 μA at −1 V when the drain bias V_d is 1 V. The carrier concentration in the BP channel is estimated by the equation n = (V_g-V_th) C_ox, where V_th is the threshold voltage of the transistor, C_ox refers to the gate capacitance per unit area. When the gate voltage is set as −10, −5, 0 and 5 V, the corresponding carrier concentration is 1.553 × 10⁵, 6.904 × 10⁴, 1.726 × 10⁴ and 1.036 × 10⁵ cm⁻³, respectively. It can be noticed from the calculation results that the carrier concentration decreases first and then increases as the gate voltage increases. When a large negative gate bias is applied, there will be a band bending at the BP/drain interface, leading to a barrier for holes moving from the channel to the drain contact. As the negative gate bias increases, band bending at the BP/drain interface decreases, and the carrier concentration is considerably reduced. The behavior of gate dependence indicates that the sensitivity of BP transistors can be tuned easily through regulating the gate voltage.

 

Fig. 7 Transfer curve of the 20-layer BP photodetector.

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The field effect mobility of the BP photodetector can also be calculated according to the equation μ = (L/WC_oxV_d) · (ΔI_d/ΔV_g), where L and W refer to the channel length and width, respectively. The obtained value of mobility is about 2839 cm²V⁻¹s⁻¹, which is higher than reported black phosphorus phototransistors [59]. When the light intensity is not strong enough, the mobility remains unchanged and dark current condition can be used to roughly calculate the mobility approximately. If the light intensity is strong, the carrier concentration will be very high. As a result, the photogenerated carriers will suffer from severe scattering and the mobility will be reduced. The low dark current and high mobility mean the high sensitivity of our BP transistors. What’s more, according to the Hornbeck-Haynes model fitting results [61], a carrier lifetime τ₀ of 58.99 ns can be calculated by the equation τ₀ = (τ₀/τ_tr)τ_tr, where τ_tr = L²/(μV_d) is the carrier transit time between the source and drain electrodes and (τ₀/τ_tr) can be extracted from the fitting results. As a result, the 3dB bandwidth f_3dB = 1/ (2πτ₀) is calculated to be 2.699 MHz, which is larger than that of the reported BP phototransistor (0.156MHz) [61], indicating that this device is more suitable for broadband detection and has the potential for high speed operation.

4. Conclusion

In conclusion, the 20-layer BP photodetector with a nanoscale plasmonic grating structure is proposed. By properly designing the geometric parameters of the nanoscale grating structure, the optical absorption of the BP photodetector can be enhanced significantly. We present a systematic investigation on the effect of interaction of light-matter for BP layer as an active layer by absorption spectra, electric intensity distribution and power flow distribution. In addition, the BP photodetector with a nanoscale grating structure has demonstrated a responsitivity of 60.94 A/W at 9.8 μm, whose cut-off wavelength can be further extended to the middle infrared range. Further, a low dark current of 44.9 μA was achieved at a small operating source−drain bias of 1 V. The high absorption efficiency and high responsitivity, together with low dark current of our BP photodetector, make it a potential alternative to the photodetectors based on other two-dimensional materials and predict a promising future for the high-performance BP photodetectors.