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Abstract
Cost-effective and high-responsivity photodetectors at a telecommunication wavelength of 1550 nm are highly desired in optical communication systems. Differing from conventional semiconductor-based photodetectors, several planar hot-electron photodetectors (HE PDs) that operate at 1550 nm have been reported. However, these devices were often comprised of many planar layers and exhibited relatively low responsivities. Herein, we propose a design of high-performance planar HE PDs consisting of five layers. Utilizing Fabry-Pérot (FP) resonance, the nearly perfect absorption of the proposed device can be achieved at the targeted wavelength of 1550 nm. Simulation results show that FP resonance orders are crucial for the optical absorption efficiencies, and then electrical responses. Analytical electrical calculations reveal that, benefiting from the strong absorption (>0.6) in the ultrathin Au layer with a thickness of 5 nm and the low Schottky barrier (0.5 eV) of Au-MoS2 contact, predicted responsivity of proposed HE PD at zero-order FP resonance is up to ∼10 mA/W. Our design provides a new approach to realize low-cost and efficient photodetection for optical communication technology.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the burgeoning development of optical communication technology, telecommunication C-band (1530-1565 nm) with center wavelength of 1550 nm has been attracting considerable interests due to the lowest optic losses for the optical fiber long-haul transmission [1]. As an optical-electrical transducer, photodetectors are key components in the optical communication system [2]; however, conventional silicon (Si) photodetectors are not suitable for detecting photons with energy below Si band gap (1.12 eV), corresponding to light wavelength beyond 1100 nm. Thus, motivated by CMOS compatible Si photodetection at working wavelength of 1550 nm, several strategies have been proposed and experimentally demonstrated, such as manipulation of defect states in the silicon lattice [3], two-photon absorption [4], and using a deposited polysilicon active layer [5]. Currently, indium gallium arsenide (InGaAs) photodetectors are often used to capture the energy of near-infrared light signal travelling in the optical fiber [6]. Although the outstanding responsivities and detectivities, the performances of InGaAs photodetectors are strongly dependent with device temperature. In addition, both InGaAs and strategy-enhanced Si photodetectors are fundamentally limited by their intrinsic material properties, including optical absorption coefficient, band gap, carrier mobility, and doping concentration.
Instead of semiconductor-based photodetection, hot-carrier photodetection based on internal photoemission mechanism provides alternative route to convert optical signals into electrical signals [7–14]. In the context of hot-carrier photodetection, the energy of optical signal is deposited in metallic materials, resulting in the generation of energetic carriers (hot electrons and holes) [15]. The generated hot carriers may have sufficient energy to surmount the Schottky barrier of metal-semiconductor contact and can be collected by adjacent semiconductor, leading to a stable photocurrent [16]. One the one hand, although reported high responsivities at telecommunication wavelength of 1550 nm [2], hot-hole photodetectors that utilized the contacts between metals and p-type semiconductors suffered from poor performances in dark current density and detectivity [17]. On the other hand, hot-electron photodetectors (HE PDs) based on the metal-semiconductor (n-type) junctions with working wavelength ranging from ultraviolet to the near infrared bands have been demonstrated [18]. Among these devices, HE PDs with various nanostructures, such as deep-trench/thin metal design [5], architecture of asymmetric metal-semiconductor-metal waveguide [19], structure of locally oxidized of silicon on silicon on insulator substrate [20], and plasmonic metal-insulator-metal configuration [21] can efficiently operate at 1550 nm, but their preparations usually require complicated and costly fabrication techniques. In virtue of suitable light-trapping mechanisms, planar HE PDs are considered to have huge advantages for low-cost and large-scale photodetection, but good trade-off between optical absorption and electrical transport in metal layers must be ensured for enhanced responsivities [22]. In order to improve the performances of planar HE PDs, it is favorable to adopt ultrathin but highly absorptive metal layers for efficient hot-electron photodetection. Therefore, planar HE PDs often harness one or two distributed Bragg reflectors (DBRs) with at least a dozen layers to trap incident optical signal in optically thin metal layers [23–28], which may increase the internal stress between different layers and result in a challenge for fabrication. Overall, planar HE PDs working at 1550 nm with: 1) a few layers, 2) ultrathin metal layer that serves as mainly absorbable material, 3) and outstanding responsivities, are expected to promote optical communication technology.
In this work, we present a design of planar HE PDs that employ a five-layer light-trapping structure to absorb incident signal with wavelength of 1550 nm. Our design constructures an optical microcavity to excite Fabry-Pérot (FP) resonance, leading to strong absorption (>0.6) in an ultrathin gold (Au) layer and fine hot-electron collection simultaneously. Moreover, benefitting from the usage of low barrier 0.5 eV Schottky contact between molybdenum disulfide (MoS2) and Au, the analytically predicted responsivity is about 10 mA/W at 1550 nm that is prominently greater than that of Tamm plasmon-based HE PDs with a lot of layers [23] and is closed to that of hot-hole photodetectors [2]. Detailed optical evaluations were performed to unveil the physics behind FP resonances. It is found that the order of FP resonance is a key factor for the device performance as the electrical field enhancement in the Au layers reduces with the increase of resonance orders, thus degrades the responsivities. Our study may provide a promising approach to achieve cost-effective, high-performance, and integrated photodetection for optical communication systems.
2. Results and discussions
Figure 1(a) illustrates the schematic and structure parameters of the proposed device which consists of a DBR, an ultrathin Au (top Au) layer serving as mainly absorbable material, an optically thick Au (bot-Au) layer with thickness of 150 nm, and a MoS2 interlayer sandwiched by two Au layers. The device is supported by a silica substrate. DBR with central wavelength of 1550 nm is composed of periodically alternative SiO2 and TiO2 layers. The thicknesses of SiO2 and TiO2 layers are fixed throughout this study and are obtained by dividing a quarter of central wavelength by the refractive indexes of SiO2 and TiO2 at 1550 nm, respectively. The thicknesses of top Au and MoS2 layers are denoted as d1 and d2, respectively. As shown in Fig. 1(b), photoelectric conversion of HE PDs relies on three consecutive micro processes, namely, hot-electron generation, transport, and collection. When the optical signals illuminate on the device, energies are deposited in both Au films due to the excitation of optical resonance. As a result, electrons around Fermi level (EF) are excited to higher levels by intra-band transition. The generated hot electrons with energy of E exceeding EF diffuse to two Au-MoS2 interfaces, accompanying with transport loss caused by electron-electron and electron-phonon scatterings. Upon arriving at the interfaces, the over-barrier hot electrons are injected into MoS2 and are collected by electrodes of outside circuit while below-barrier hot electrons are blocked by Schottky barrier. The collected hot electrons contribute to a detectable electrical signal. With the derived optical constants [29–31], optical responses were evaluated by solving Maxwell’s equations in a finite-element platform [32], as shown in Fig. 1(c). When the DBR pair number is 1, d1 = 5 nm, and d2 = 101 nm, optical absorption (Atotal) spectrum of the proposed device exhibits a prominent peak with strength of about 0.99 at 1550 nm. The appearance of absorption peak can be ascribed to the excitation of FP resonance [27]. We also investigated the wavelength-dependent absorption in the top Au (Atop), MoS2 (AMoS2 ), and bot-Au (Abot) layers. It is shown that Atop at 1550 nm is beyond 0.6, that contributes to main part of Atotal. The AMoS2 at 1550 nm is weak (∼0.1) because of the small imaginary part (∼0.0083) of refractive index. As shown in Fig. 1(d), when the numbers of DBR pairs increases from 0 to 6, peak position of Atotal spectra remains unchanged, but the peak strength increases first and then decreases. For efficient operation of HE PDs, the strong absorption in two Au layers (AAu = Atop + Abot) is prerequisite. Therefore, we investigated the relationships between AAu and DBR pair numbers, as shown in Fig. 1(e). We found that compared to AAu of bare planar Au-MoS2-Au structure at 1550 nm, DBR with pair number of 1 assist light-trapping in two Au layers. It is considered that as the DBR pair number is zero, the optical absorption is decreased because the confined electric filed within the MoS2 interlayer can leak into air through the ultrathin top Au layer with thickness of 5 nm that is less than the skin depth of electric field. Moreover, DBRs with pair number beyond 1 prevent incident light from permeating into device, leading to a decreased absorption in Au layers. Thus, we considered that DBR pair number can tailor the DBR optical properties, and then device optical responses (i.e., Atotal and AAu). The DBR reflection spectra as a function of DBR pair numbers are shown in Fig. 1(f). Generally, enhanced absorption in two Au layers associated with the excitation of FP resonance requires a suitable reflection efficiency of DBR. Therefore, based on the optimal evaluation, DBR pair numbers of 1 was chosen for an optically superior and ultrathin top Au layer.
Fig. 1. (a) Schematic and structure parameters of HE PDs. (b) Energy band diagram and electrical configurations. EC and EV are the conduction and valence band edges in MoS2, respectively. The Schottky barrier of Au-MoS2 contact is denoted as Φb. (c) The absorption spectra of the proposed five-layer planar HE PD. The dependences of (d) total absorption, (e) absorption in two Au layers, and (f) reflection of bare DBR on the number of DBR pairs.
Besides the dependence of Atotal on DBR pair numbers, the impacts of changing d1 and d2 on Atotal were also investigated, as depicted in Figs. 2(a) and 2(b), respectively. Figure 2(a) shows that: (1) as d1 increases from 5 to 65 nm, resonance wavelength blue shifts; (2) with an appropriate d1 (5-15 nm), most of the light can be absorbed by two Au films; (3) further increasing d1, most of the light is directly reflected by the DBR and top Au film. It is clear from Fig. 2(b) that there are four total absorption bands ranging from 1300 nm to 1800 nm when d2 increases from 60 nm to 660 nm, showing the high tunability in the near infrared band. Meanwhile, device also exhibits high flexibility because one can use four MoS2 interlayer thicknesses (d2 = 101, 288, 474, and 660 nm) to achieve FP resonance at the targeted wavelength of 1550 nm. To get more insight into FP resonance in this planar structure, phase accumulation (P) within the microcavity consisted of top-Au + DBR, MoS2 interlayer, and bot-Au + substrate was examined by using the optical transfer-matrix method [11,28]. P can be expressed as P = (P1 + P2)/2π, where P1 (P2) is the phase shift due to the reflection for the wave incident on top-Au + DBR (bot-Au + substrate) from MoS2 medium. P was normalized by 2π. Figures 2(c) and 2(d) depict the contour maps of P as a function of d1 and d2, respectively. One can see in Fig. 2(c) that there is a contour line corresponding to P = 0. The profile of absorption band presented in Fig. 2(a) coincides with this contour line. Similarly, the profiles of four absorption bands shown in Fig. 2(b) are coincident with four contour lines depicted in Fig. 2(d) corresponding to P = 0, 1, 2, and 3. We concluded that FP resonances occur when the phase accumulations within the microcavity satisfy the condition of P1 + P2 = 2πm, in which m is the FP resonance order and m = 0, 1, 2, 3… [27]. Therefore, one can tailor FP resonance orders at 1550 nm by adjusting MoS2 thickness. It is necessary to study the dependences of device responses, including optical absorption and electrical output, on the resonance order m.
Fig. 2. Contour maps of absorption spectra as a function of (a) top Au layer thickness (d1) and (b) MoS2 layer thickness (d2). (c) and (d) Phase accumulation (P) corresponding to (a) and (b).
As shown in Fig. 3(a), we plotted spectra of AAu with different MoS2 thicknesses of d2 = 101, 288, 474, and 660 nm in which four peaks at 1550 nm correspond to four resonance orders of m = 1, 2, 3, and 4, respectively. We found in Fig. 3(a) that the peak strength of AAu reduces with the increase of d2. In contrast, the absorption efficiency of AMoS2 at 1550 nm increases with the increase of d2, as shown in Fig. 3(b). It is well known that optical absorption is a local quantity that can be calculated by integrating the product of frequency, local electric field strength and the imaginary part of the dielectric permittivity over the full volume of the absorbable material [33]. Therefore, for a fixed dielectric permittivity at 1550 nm, the dependences of AAu and AMoS2 at 1550 nm on m are determined by the relationships between electric field strength and m. We defined the electric filed enhancement factor (|Ee/E0|2) at 1550 nm as the ratio of simulated electric field strength (|Ee|2) to the incident electric field strength (|E0|2). It is shown in Fig. 3(c) that enhancement factor curves exhibit some wave nodal points within MoS2 interlayer. It was found that the number of nodal points increases with m and can be written as 2m+1. Additionally, |Ee/E0|2 in top Au layer reduces with the increase of m. We then integrated |Ee/E0|2 at 1550 nm with different m over corresponding absorbable materials, i.e., two Au and MoS2 layers. These two integral quantities, namely, FAu and FMoS2, describe the overall effects of electric field enhancement associated with FP resonance on the optical absorption in two Au and MoS2 layers, respectively. One can see in Fig. 3(d) that FAu reduces with the increase of m but FMoS2 increases with the increase of m. Consequently, with the increase of m, AAu decreases but AMoS2 increases, as shown in Figs. 3(a) and 3(b).
Fig. 3. Optical absorption in (a) both Au layers and (b) MoS2 layer as a function of wavelength with different d2. (c) The spatial distribution of electric field enhancement factors for different resonance orders at 1550 nm. (d) Integral of enhancement factors over two Au layers and MoS2 layer for different m.
After detailed optical investigations of the device at resonance wavelength of 1550 nm, our attentions were paid to the electronic processes that are qualitatively characterized through analytically probability-based calculations in which the power of incident light was set to 1 [11,34–36]. It is shown in Fig. 4(a) that the energy distributions of the flux of generated hot electrons (Ngen) at m = 1, 2, 3, and 4 significantly deviate from Fermi-Dirac distribution. One can see that E-dependent Ngen decreases with the increase of m due to the reduction of AAu. The non-equilibrium hot electrons diffuse to the two Au-MoS2 interfaces, experiencing thermalization loss that can be quantitatively described by a quantity of transport probability (Ptran). Ptran can be written as
Fig. 4. The energy distributions of the flux of (a) generated hot electrons (Ngen) and (b) hot-electrons that reaching two Au-MoS2 interfaces (Ntran) at 1550 nm for different resonance orders of m = 1, 2, 3, and 4. (c) The proportion (αabove) of above-barrier hot electrons for Ngen and Ntran. (d) The flux of collected hot electrons (Ncol) as a function of energy (E).
After quantitative analysis of three hot-electron processes in two Au-MoS2 junctions, we obtained the wavelength-dependent responsivities in top (Rtop) and bottom (Rbot) Au layers with d2 = 101, 288, 474, and 660 nm, as shown in Figs. 5(a), 5(b), 5(c), and 5(d), respectively. Device responsivity spectra (Rtotal = Rtop + Rbot) were also plotted. It is found that for all four MoS2 thicknesses, although hot electrons generated in both Au layers can be collected by two Au-MoS2 junctions, Rtop mainly contributes to Rtotal because most of incident light energy is deposited in the top Au layer. It is also found that Rtotal at zero-order resonance (i.e., d2 = 101 nm) is 9.9 mA/W. It is noted that this value of responsivity is significantly larger than that of previously reported HE PDs [e.g., 0.25 mA/W in Ref. 20, 0.1 mA/W in Ref. 21, and 0.8 mA/W in Ref. 23], and is closed to that of hot-hole photodetector [e.g., 12.5 mA/W in Ref. 2, 13 mA/W in Ref. 37, and 12 mA/W in Ref. 38]. Meanwhile, peak strength of Rtotal spectra decreases with the increase of d2, i.e., the increase of m. This decrease of responsivity with m can be ascribed to the increase of absorption in MoS2, as shown in Fig. 3(b). Moreover, the full widths at half-maximums (FWHMs) are 123.5, 64.8, 45.2, and 35.3 nm for d2 = 101, 288, 474, and 660 nm, respectively. Therefore, for some other applications that emphasize on narrowband outputs, such as hot-electron sensors and nanodiodes [13,14], the tradeoff between peak responsivity and FWHM must be taken into account.
Fig. 5. Responsivity spectra: Rtotal, Rtop, and Rbot with d2 = (a) 101, (b) 288, (c) 474, and (d) 660 nm.
We examined the angular performances of the proposed HE PDs, with which both the transverse electric (TE) and transverse magnetic (TM) incidences must be considered. Figures 6(a) and 6(b) show that the strong optical absorption in two Au layers can be sustained over a broad range of incident angle (θ) with a blue shift in the resonance with the increase in θ. Additionally, the behaviors of angular responsivity were investigated, as shown in Figs. 6(c) and 6(d). It is shown that the resonance wavelength still lies in the communication C-band for θ less than 30°. Meanwhile, the strong peak responsivity maintains when θ is about 40°. This moderate angle sensitivity of device responses is expected to boost the performance stability of devices. We considered that this angular performance originates from usage of high refractive index MoS2 (real part of MoS2 refractive index is 4.16 at 1550 nm) because the angular sensitivity of resonance wavelength for planar FP cavity decreases with the square of refractive index of dielectric interlayer [39].
Fig. 6. Absorption in two Au layers (AAu) as a function of incident angle (θ) under (a) TE and (b) TM illumination. (c) and (d) Responsivity (Rtotal) corresponding to (a) and (b).
Finally, for comparison purposes, we have investigated the role of interlayer material which thickness is denotes by dx in the optical and electrical responses of five-layer planar HE PDs, as shown in Fig. 7(a). Besides MoS2, three interlayer materials are chosen: Ge, Si, and CdSe. The Schottky barriers of the Au-Ge, -Si, and -CdSe contacts are 0.59, 0.73, and 0.8 eV [40], respectively. At 1550 nm, the real (imaginary) parts of refractive indexes of Ge, Si, and CdSe are 4.28 (0.01), 3.4764 (0), and 2.40 (0), respectively. To achieve FP resonance at 1550 nm, dx must be precisely determined, as depicted in Fig. 7(b). It is found that dx is in proportion to m but is inversely proportional to real part of refractive index of interlayer material. It is shown in Fig. 7(c) that AAu at 1550 nm for Si and CdSe as interlayer material reveal independence on m. It is because that the imaginary part of refractive index is zero, leading to a zero absorption in Si and CdSe interlayers. However, AAu at 1550 nm for Ge as interlayer material is inversely proportional to m, as similarly shown in Fig. 3(a). Using established photoelectric models, Rtotal at 1550 nm corresponding to different interlayer materials are obtained, as shown in Fig. 7(d). Although AAu for MoS2 as interlayer at four resonance orders exhibit relatively weak absorption compared to that for Si and CdSe as interlayers, Rtotal for MoS2 interlayer is remarkably greater than that for three other materials due to a much lower barrier being formed in the Au-MoS2 contact. According Fowler’s law, the wavelength-dependent Rtotal(λ) can be written as
Fig. 7. The schematic of the five-layer planar HE PDs with different interlayer materials (MoS2, Ge, Si, and CdSe). For the targeted wavelength of 1550 nm, different interlayer materials associated with different (b) thicknesses, (c) absorption in two Au layers, and (d) responsivities at m = 1, 2, 3, and 4. The color representations for interlayer materials in (a) are also applied to (b)-(d).
3. Conclusions
In summary, a design of five-layer planar HE PD working in the telecommunication C-band was proposed. Unlike previously reported planar HE PDs with many layers, our proposed device harnessed five layers to excite FP resonance within a planar structure, leading to strong absorption (>0.6) at 1550 nm in an ultrathin Au layer that can relieve the hot-electron thermalization loss and enhance electrical output. Employing transfer matrix method, resonance order was introduced to reveal the underlying physics of FP resonance. Comprehensive studies about the correlations between optical and electrical responses with different FP resonance orders were carried out. Through harnessing low Schottky Au-MoS2 barrier, the responsivity of proposed device at zero-order resonance is about 10 mA/W, which far exceeds that of previously reported planar HE PDs and is closed to that of hot-hole photodetectors. Our work is expected to facilitate the efficient, low-cost, and large-area photodetection for optical communication technology.
Funding
National Natural Science Foundation of China (11904248); Natural Science Foundation of Guangxi Province (2020GXNSFBA159008).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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