Abstract: We investigate the light absorption enhancement in waveguide Schottky photodetector integrated with ultrathin metal/silicide stripe, which can provide high internal quantum efficiency. By using aab0-quasi-TE hybrid modes for the first time, a high absorptance of 95.6% is achieved in 5 nm thick Au stripe with area of only 0.14 μm2, without using resonance structure. In theory, the responsivity, dark current, and 3dB bandwidth of the corresponding device are 0.146 A/W, 8.03 nA, and 88 GHz, respectively. For most silicides, the quasi-TM mode should be used in this device, and an optimized PtSi device has a responsivity of 0.71 A/W and a dark current of 35.9 μA.
© 2017 Optical Society of America
Schottky photodetectors (PDs) [1,2] based on internal photoemission (IPE)  have been used for many years in area of communication [4,5] and imaging [6,7]. A Schottky barrier, which is the basic structure of a Schottky PD, can be formed in the interface between lightly doped semiconductor and metal/silicide. In IPE process, the hot carriers created by light absorption in metal/silicide have chance to be emitted over the Schottky barrier and collected in the semiconductor as photocurrent. In recent years, the IPE effect is combined with plasmonics, and can be used to harvest solar energy  or create sensitive photodetectors and spectrometers .
Since the detected photo energy can be lower than the semiconductor bandgap energy. Schottky PD provides one of the solutions [2,10] to infrared photodetection in Silicon photonics , which has been known as the key technology of the next-generation communications systems. At present, the reported Schottky PDs have bottlenecks on their low responsivities, which are decided by the internal quantum efficiencies (IQEs) and the optical absorptances.
Several methods are proposed to improve the low IQE. By choosing materials or using image force effect  (from bias voltage controlling), the Schottky barrier height ΦB can be lowered to improve IQE, and that is why p-type silicon (p–Si) is often used, given that Schottky barriers are usually lower thereon than on n-type silicon (n-Si). However, the reduction of ΦB leads to a large dark current, which needs to be reduced by using cryogenic operation temperature. The embedding metal structures into semiconductor provides multi-Schottky barriers, and then the hot carriers generated near the Schottky contact interfaces get more chance to be emitted . Furthermore, the surrounded metallic structures with small sizes below the hot carrier attenuation length can enhance IQE efficiently by utilizing hot carrier reflections, which occurs in the multiple interfaces and provide the un-emitted hot carriers more chances to be emitted [14–16]. The metal/silicide nanoparticles (NPs) embedded in the semiconductors can achieve much higher IQE in theory, but increase the difficulties of getting high light absorptance in the meantime . We argue that this concept is a promising solution with potential to realize high performance Schottky PDs in the future. The adoption of ultrathin metal/silicide (several nanometers thick), as a more practical solution for IQE enhancement, has been researched theoretically and experimentally [6,17,18], and this enhancement can also be attributed to the hot carrier reflections, which occurs in the two borders of the ultrathin film. To get high light absorptances in ultrathin films, resonance optical structures are usually used to increase the light-matter interaction lengths.
For the surface-illuminated type Schottky PD, the resonance optical structures for absorptance enhancement include Fabry-Perot (F-P) cavities , gratings , and optical antennas. The F-P resonance can increase the absorptance in both the thick  and ultrathin [6,17] metals/silicides to 60% ~near 100% at resonance wavelength. The metallic gratings, as one-dimensional periodic metallic structures, can convert the vertical incident light to the horizontal resonance Surface Plasmon Polariton Bloch Waves (SPP-BWs) supported by the metal-semiconductor surfaces, and then light-matter interaction lengths increase strongly. Absorptances of 80%~100% at resonance wavelengths are also achieved in grating structures  and two-dimensional periodic metallic structures . By utilizing localized surface plasmon resonance [22–24], SPP-BW , and standing-wave resonances of short-range SPPs , the optical antennas can concentrate the light at resonance wavelength in the absorption areas, and then improve the absorptances. In most researches mentioned above, the metals are not thin enough to increase the low IQEs (on the order of 1% ). In an exceptional device in , the combination of 2 nm thick PtSi film and F-P cavity provides a high responsivity of 0.25 A/W at 1500 nm, but the device should operate at 40 K. The low ΦB leads to a large dark current density, on the other hand, as bulk devices, the F-P cavity and grating structures have too large contact areas (>100 μm2) which are bad for the dark current suppression.
While the surface-illuminated Schottky PDs has unique application in imaging and other areas , the waveguide Schottky PDs can be used in the integrated Si photonic circuits. The active areas of less than 1 μm2 have been reported in integrated Schottky PDs based on SOI nanowire waveguides [26,27]. It should be noted that the compact Schottky areas are important for lowering the dark currents and the power consumptions. In theory, the waveguide Schottky PD can absorb all the optical power of the propagating bound modes. However, the performance improvements of waveguide Schottky PDs still face challenges. Responsivities of most the reported waveguide Schottky PDs are below 0.1 A/W [4,5,26,28,29]. A recent record-high responsivity of up to 0.12 A/W at 1550 nm was measured . Following the mode nomenclature of , the ssb0 mode (known as the long-range SPP) with low optical confinement can achieve near 100% end-fire coupling efficiency [31,32], however, its low mode power attenuation (MPA)  leads to a long absorption length (about 500 μm) [31,32], and then the Schottky contact area of about 56~500 μm2 is too large. sab0 mode with high optical confinement in metal can provide high MPA to reduce the absorption length, however, its high optical confinement leads to low end-fire coupling efficiency (~20%) , which limits its absorptance (and thus responsivity). In short, the existing devices suffer from the trade-off among the absorptance, dark current, and operation speed. When using ultrathin metals/silicides to improve IQEs, the high absorptance seems to be more difficult to realize. Since the MPAs of the propagating mode in waveguides with ultrathin silicides are too low, micro-ring resonators (MRRs) [33,34] with high Q-factor are used (to ensure long photon lifetime), but the effective bandwidth of devices is limited in the meantime, as a result, the bandwidth-efficiency product in  is limited to ∼10.5 GHz. Besides, given that the resonance wavelengths are very sensitive to the specific material characteristics and device geometries in fabrication, the drift of the narrow response spectrums of the high-Q MRRs remains a problem for specific wavelength operation. Zhu et.al . have proposed and optimized a horizontal metal-insulator-silicon-insulator-metal nanoplasmonic slot waveguide with ultrathin silicides (to get high IQE), and an optimized TaSi2 detector was estimated to have responsivity of 0.07 A/W, speed of 60 GHz, and dark current of 66 nA at room temperature.
In this work, by realizing enhanced light absorption in tiny volume , we propose the waveguide Schottky PD with high performances in terms of responsivity, dark current, and 3dB bandwidth simultaneously. In the proposed plasmonic waveguides, the ultrathin metals /silicides (to ensure high IQEs) are integrated to the Si nanowire waveguides, which are widely used in the integrated Si photonic circuits . In Section 2, the plasmonic waveguide structure is presented and the IQEs are calculated. In this waveguide, the silicides are classified to metal-like and non-metal-like type. In Section 3, the mode characteristics of plasmonic waveguide with metals/metal-like silicides are analyzed. We present the mode hybridization between aab0 mode and quasi-TE mode for the first time, to best of our knowledge. By utilizing the aab0-quasi-TE hybrid modes (plasmonic-photonic hybrid modes), our structure can provide a high absorptance of 95.6% in 5 nm thick Au stripe with area of only 0.14 μm2, without using any resonance structure. The high absorptance and large IQE of 12.2% result in large responsivity of 0.146 A/W. Besides, the small contact area brings low dark current of 8.03 nA at room temperature and a large 3dB bandwidth of 88 GHz, which also benefits from no resonance structure adoption. In Section 4, the non-metal-like silicides are studied. Quasi-TM mode should be used in this case. The optimized responsivity of 2-nm PtSi device is estimated to be 0.71 A/W (benefits from low Schottky barrier height), but the large device area leads to a high dark current of 35.9 μA. All these structures can be fabricated by mature technologies with acceptable fabrication tolerance. The conclusion is made at last. While the Schottky PDs with two-dimensional materials induced have been reported with good performances , our study can promote the performance improvements of the pure integrated Schottky PDs, moreover, we hope our mode analysis can inspire the researches of the two-dimensional materials induced devices.
2. IQE evaluation and device structure
The responsivity Resp of a Schottky PD can be presented by:18,37–40] have been proposed to describe the IPE process, and evaluate the IQEs. In the mode proposed  by Elabd and Kosonocky, the hot carriers are assumed to reflect between the internal metal surfaces, during when hot carriers get chance to be emitted over the single Schottky barrier, and the inelastic scattering mechanisms are taken into account via a hot carrier attenuation length (L). Scales et al.  extended this thin-film reflection model, deriving the escape probability through a double Schottky barrier. The thin-film reflection model can be fit to the experiment results with varied L , and have be used in many thin-film waveguide Schottky PD studies [28,32,33]. It should be noted that this model is rigorously valid only for temperature of 0 K, but can also result very approximate for estimating the IQEs at room temperature. In this paper, this model is used for IQE calculation of thin film Schottky PD with single barrier at room temperature. In Table 1, L and ΦB of the common metals/silicides used in our calculations are listed. Only p-Si is considered.
The film thickness is denoted by t. As Fig. 1 shows, the IQE is very sensitive to L and ΦB. When ΦB is not low enough, the decrease of t has little promotion on the IQE improvement, e.g., the IQE of p-Si/Al Schottky PD increase from 1.1% to 1.8% when t decreases from 50 nm to 5 nm. As for device using Au, the IQEs are 6%, 12.2%, and 16.8% for t = 25 nm, 5 nm, and 3 nm, respectively. In p-Si/PtSi PD with t = 2 nm, theoretical IQE can be as high as 60%, but the dark current density is also high due to the low ΦB.
In this work, the plasmonic waveguide proposed by us is constructed by Si nanowire waveguide with ultrathin metal/silicide stripe covered, as Fig. 2 shows. The waveguide cross-sections are slightly different between metals and silicides because of different fabrication methods  (see Fig. 2(b)-2(c)). The width and height of Si core are fixed to 600 nm and 220 nm in the latter calculations. The metal/silicide stripe consists of a linear tapered part and a rectangle part, whose lengths are respectively denoted by ls and lt. wm and hm (<10 nm) denote the width and height of the metal/silicide stripe, respectively.
The plasmonic waveguide sections with tapered stripe and straight stripe covered are named as tapered section and straight section for short. The tapered section can convert the injected photonic mode to the modes in the plasmonic waveguide with negligible reflection loss. In this work, we provide a systematic mode analysis for this kind of plasmonic waveguide. This analysis can throw light on how to achieve high absorptance within tiny volume. The absorptance A can be given by30], with fields confined in the metal/silicide areas can be found. To the contrary, they are cut-off when using non-metal-like silicides, which are more like lossy dielectrics. Most of the silicides are non-metal-like. PtSi is a widely-used example. These two conditions are respectively discussed in Section 3 and Section 4. The wavelength is fixed to 1550 nm in these studies.
3. Metals/metal-like silicides
3.1 Mode analysis
Here we study the mode characteristics of the two-core plasmonic waveguide with FEM mode-solving tool (from COMSOL). Al and Au are used in the effective index calculations. The real parts of effective indices and α (i.e., MPAs) are presented in Fig. 3.
All the bound modes, which have refractive indices with real part larger than nsio2 (1.44, λ = 1550 nm), have been shown in Fig. 3. The properties of sabm modes and aabm modes are generally consistent with the reported work . Their high optical confinements bring large MPAs. As hm increases, both the real and imaginary parts of their effective indices decrease, and the high order modes are gradually cut-off. The quasi-TE mode and quasi-TM mode are similar to their counterparts in pure Si waveguide in terms of effective index real parts and optical field distributions, which make these quasi-photonic modes to have low MPAs. In Fig. 4, sab0, aab0, quasi-TE, and quasi-TM modes are shown in log(|E| + 1) for clarity.
The mode hybridization [43,44] has been found between TM mode and high order TE modes in vertically asymmetric waveguide. In this two-core waveguide, there are also mode hybridization between aab0 mode (TM-polarized plasmonic mode) and quasi-TE mode (quasi-photonic mode), as the red circles in Fig. 3 shows. Both these two hybridized modes have comparable vertical and horizontal components, and they are similar to each other. Just like aab0 mode, these modes also have strong fields in the metal area, so they also have large MPA (see Fig. 3). At the same time, they are similar to quasi-TE mode, so the injected TE mode can be converted into these modes effectively with proper conversion structures. The unique properties of these plasmonic-photonic hybrid modes are very helpful to absorb light in metals within tiny volumes. The hybrid mode with larger real part of effective index is marked as mode A and the other one is mode B (see Fig. 5). One can clearly see that, the Ey components of both mode A&B are asymmetric with respect to both x and y axes (just like aab0 mode). Besides, the |Ex| and |Ey| components are comparable for both mode A&B.
The injected TE mode can be converted to the quasi-TE mode when wm is away from the mode hybridization area. Otherwise, its power can be injected to the hybrid modes with high MPA. The injected TM mode can only be converted to quasi-TM mode with low MPA. Therefore, TE mode is used as source in this case.
3.2 Mode conversion and light absorption
The optical simulation method is mainly based on 3D FDTD . The eigenmode expansion (EME) method  is also used for mode conversion analysis. The electromagnetic fields at the end of tapered section (in xy plane), which are denoted by and , are derived from 3D FDTD. and are the electromagnetic fields of the normalized mth eigenmode of the straight section (i.e. , m = 1, 2, 3 …, m is ranked according to the real parts of mode effective indices). Then the mode coupling coefficient am is given by
The mode power transmission Am( = |am|2/Psource) is the ratio between the mode power of mth eigenmode at the tapered section end and the source power. Then the total absorptance A can be calculated by the addition of the tapered section absorptance (Ataper) and the straight section absorptance:Fig. 6(a) shows, the modified segmented taper has lengths of lt1 and lt2 for two segments, and wt denotes the end width of the first one. The TE mode is converted to quasi-TE mode in the first segment, as the blue arrow indicates, and then the quasi-TE mode is converted to the hybrid modes in the second segment, as shown by the green arrows. The power transmissions (A2 and A3) to mode A&B depends on the specific taper geometries, and may be about zero. In this way, the diffraction loss and reflection loss can be kept very low, and TE mode can be converted to the aab0-quasi-TE hybrid modes effectively. The absorptance derived from Eq. (2) is named AFDTD(z), which is compared to AEME(z) in Fig. 6(b).
The results from two methods fit well, with maximum error of about 2%. The detailed parameters can be found in Table 2, which also contains the results of Al devices. The optimized wm depends on material properties and hm. The higher optical confinement one hybrid mode has in the metal area, the larger MPA it gets, in the meantime, the more difficult TE mode can be converted to it.
As for the 5 nm thick Au stripe device, the optimized wm is 70 nm, and then the responsivity is estimated to be 0.146 A/W with IQE of 12.2% and absorptance of 95.6%. The Schottky contact area is 0.1435 μm2 (ls = 1.5 μm). If we set ls to 3.5 μm, the absorptances are 73.0% and 88.6% for wm of 60 nm and 80 nm, respectively. Hence, the fabrication tolerance can be accepted if we increase the length of the straight section, and it can be further increased by changing the straight section to a slow-varying taper which covers the mode hybridization area.
3.3 Dark current and bandwidth
The dark current is given by 
The operation speed is limited by the time of the hot carriers transiting between the contacts and the RC delay. The transit time limited bandwidth is given by 11] or electron beam lithography, the distance between the contacts can be only several hundred nanometers. Therefore, we assume W to be 0.5 μm, which is realizable. Then ftransit is 88 GHz. The RC limited bandwidth fRC is given by
4. Non-metal-like silicides
4.1 Mode analysis
PtSi, with low Schottky barrier energy (Si:P-doped) and long hot hole attenuation length, is a typically non-metal-like silicide in our structure. The effective indices of bound modes are calculated with different hm and wm, as Fig. 7 shows. wsi and hsi are fixed to 600 nm and 220 nm, respectively.
As Fig. 7 shows, only quasi-TE mode and quasi-TM mode are the bound modes in this case. The real parts of the effective indices of both quasi-TE and quasi-TM modes are not sensitive to the silicide geometries. Their filed distributions are similar to those when metal/metal-like silicides are used, as Fig. 4(c)-4(d) shows. Both these modes have inherent low MPA for their low optical confinement in the silicide area. Since the quasi-TM mode has lager MPA, the source should be changed to TM mode in this case.
4.2 Parameter optimization
High MPA of quasi-TM mode needs large wm and hm. But a small contact area is also important for a low dark current, and high IQE needs low hm. In this section, we calculate the dark current of the devices with varied parameters. Since the quasi-TM mode has similar fields with TM mode, the taper section can be left out, i.e., lt is set to 0, and then Ataper is 0 in Eq. (4). A2 is assumed to be 100% (over 95% in fact). The dark current is calculated by Eq. (5). The contact area S is given by wm × ls. When the responsivity is 0.3 A/W, the calculated dark current Idark at room temperature is presented in Fig. 8.
As Fig. 8 shows, a relatively thick and narrow PtSi stripe is a good choice to reduce the dark current. When hm, wm, and ls are respectively 5 nm, 50 nm, and 7.33 μm, the dark current is 3.4 μA, and the responsivity is 0.3 A/W. When hm is 2 nm, the PtSi device can achieve a high responsivity of 0.71 A/W with absorptance of 95% (wm = 50 nm, ls = 77.7 μm), and then dark current is as high as 35.9 μA and NPDR is 50.6 μW. While the PtSi device can achieve a high responsivity in theory, the relatively low absorption ability of the PtSi-Si waveguide leads to a large contact area, and the dark current density is large due to the low ΦB, so the dark current is quite large.
In summary, we have reviewed the performance bottlenecks of the Schottky photodetectors, and then focused on light absorption improvement in ultrathin metal/silicide stripes, which can provide high internal quantum efficiency. For the Si nanowire waveguide with ultrathin metal/silicide stripes, the mode characteristics are systematically studied with diverse materials. The silicides are classified to metal-like and non-metal-like in this plasmonic waveguide. The mode hybridization between aab0 mode and quasi-TE mode are firstly presented (to best of our knowledge) when using metal/metal-like silicide. The aab0-quasi-TE hybrid modes can be coupled from TE photonic mode efficiently, and then absorb light efficiently. In 5 nm Au stripe, a high absorptance of 95.6% (responsivity: 0.146 A/W) is achieved within area of only 0.14 μm2. This small contact area helps for getting a low dark current of 8.03 nA at room temperature and a high 3dB bandwidth of 88 GHz. As for non-metal-like silicide, e.g., PtSi, the quasi-TM mode should be used. Using 2 nm PtSi stripe, the optimized responsivity can be up to 0.71 A/W in theory. However, the low absorption ability of quasi-TM mode leads to a long absorption length of 77.7 μm and a large contact area of 3.9 μm2. Both the low Schottky barrier height and large contact area result in a high dark current of 35.9 μA at room temperature. A relatively narrower and thicker silicide strip is better for dark current suppression in this case. Both these structure can be fabricated by mature technologies. Further improvement of device responsivity can be made by utilizing double Schottky barrier structure, which can further increase the internal quantum efficiency. We argue that this study can promote the research of waveguide Schottky photodetectors, which has potential to detect light in near infrared bands in integrated Si photonic circuits.
National Hi-Tech Research and Development Program of China (2008AA1Z207); Natural Science Foundation of Hubei Province, China (2010CDB01606); Fundamental Research Funds for the Central Universities (HUST: 2016YXMS027); Huawei Innovation Research Program (YJCB2010032NW, YB2012120133, YB2014010026, YB2016040002); Scientific Research Foundation for the Retuned Overseas Chinese Scholars.
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