Design of an on-chip electrically driven, position-adapted, fully integrated erbium-based waveguide amplifier for silicon photonics

Peiqi Zhou; Peiqi Zhou; Bo Wang; Xingjun Wang; Xingjun Wang; Xingjun Wang; Bing Wang; Yandong He; John E. Bowers

doi:10.1364/OSAC.413492

1. Introduction

In the past decade, the field of silicon photonics has made considerable progress toward silicon-based large-scale optoelectronic integration technology. According to Moore's law, the scaling of integrated circuits doubles every two years. Similarly, the scale of optical devices in silicon photonics is expected to increase significantly. This could satisfy the demand for high information transmission rates and large information transmission capacities in optical communication networks in the future [1–2]. However, on-chip optical losses increase with the increasing number of integrated silicon photonic devices, and this critical issue must be solved. The device losses in integrated silicon photonic devices is much larger than that in their discrete counterparts. The total on-chip losses from different photonics components, such as silicon-based modulators (2–3 dB/mm [3–4]), photodetectors (<0.1 dB [5–6]), other passive devices (0.5 dB [7]), along with the propagation losses of most silicon photonics platforms (greater than 30 dB/m [8]) can easily exceed 20 dB. This has a serious effect on the transmission performance of the system. To integrate hundreds of thousands of photonic devices on a chip in the future, on-chip amplification must be adopted for loss compensation. On-chip amplification is one of the most important problems in silicon photonics technology. Hence, the on-chip integrated waveguide amplifier will become increasingly necessary in complex large-scale integrated systems. Although silicon itself cannot be used as an efficient light source device because of its indirect band gap characteristics, there are two main research directions for the realization of silicon-based waveguide amplifier for the 1.5 µm communication band: semiconductor optical amplifier (SOA) and erbium (Er)-doped waveguide amplifier (EDWA).

Although III-V semiconductors are considered as good light source materials because of their direct band gap, the direct epitaxial growth of III-V semiconductor layers on silicon substrates is difficult due to the large lattice mismatch. High-quality III-V semiconductor devices are presently integrated into silicon photonics chips by hybrid or heterogeneous integration technology, such as bonding and film transfer [9,10]. Moreover, the short lifetime of the upper level carrier will cause a large gain compression and recovery effect along with the density distribution of the data stream [11]. Thus, there is a large defect in the optical signal itself when SOAs are used for high-speed amplification and modulation.

Alternatively, EDWAs with a much longer excited-state lifetime offer a potential solution for amplification at high speeds and are widely studied in integrated photonics. They use low-loss waveguides, with cores doped with trivalent Er ions to boost the optical signal. The waveguides can be efficiently pumped with a laser at a wavelength of 980 nm or 1480 nm, and they exhibit gain in the 1550 nm region after the stimulated emission of photons. Unlike other hybrid-integrated light sources, EDWAs can be used in monolithic integration, which acts as an optical path connected with other optical devices on the same Si substrate [12]. Researchers have made progress in fabricating EDWAs based on Er-doped materials, such as Er:Ti:LiNbO₃ and other glass matrix [13–15], with gains as high as 10 dB/cm. Xin et al. [16] demonstrated an optical frequency synthesizer using a fully integrated silicon-based Er-doped bent gain waveguide in 2019. In 2020, Li et al. [17] presented the first silicon photonic data link with monolithic Er³⁺:Al₂O₃ waveguides, integrated with a silicon microdisk modulator, and a germanium photodetector integrated on a single chip. These achievements show that the integration of EDWAs with other optical devices in silicon photonic systems is possible. However, all these schemes still have some problems. EDWAs need external pump light sources such as the 980 nm pump lasers for horizontal waveguide coupling. This weakness complicates the optoelectronics integration scheme and prevents the full integration of amplifiers with the silicon photonic system. Most Er-doped gain materials are insulating media, with poor conductivity. Hence, it is difficult to directly excite the gain material with electric injection. Therefore, integrated electric-pumped EDWAs have not yet been demonstrated. EDWAs also need to be locally fabricated on the silicon photonic chip, which selectively provides optical gain for the areas that require amplification. This will provide better flexibility with the back-end-of-line fabrication of the waveguide amplifiers, thus leading to higher monolithic integration with other silicon photonic devices. However, such a fabrication method has not been realized yet. In addition, there is no relevant report on the combination of EDWAs and mature III-V semiconductor (SOA) technology. Amplifier development in the future should focus on combining the two technologies to fully mine their advantages.

To solve the aforementioned issues, in this paper, we have proposed a novel on-chip, electrically driven, position-adapted, fully integrated erbium-doped waveguide amplifier. This device integrates a III-V semiconductor vertical-cavity-emitting pump laser on a silicon-based hybrid Er waveguide amplifier, which solves the issues of integrated electrically driven EDWAs, and realizes the full integration of amplifiers for silicon photonic systems without external pump light sources. This scheme achieves local on-chip amplification. After the wafer-level fabrication of other devices, the back-end-of-line deposition of the gain structure is performed at the chip level. These amplifier structures can be selectively fabricated on the waveguide areas that require amplification, which provides more flexibility for monolithic integration with other silicon photonic devices. The proposed structure can overcome or avoid the inherent difficulties of both EDWA and SOA and combine these two types of materials together in a silicon photonic chip. The development of bonding technology can integrate the low-cost semiconductor integrated pump source, such as vertical cavity surface emitting laser, and the Er-based gain materials on the same silicon substrate. The semiconductor materials can provide a high efficiency pump for Er-based materials through the design of a suitable vertical cavity. The Er-based materials are fabricated as a hybrid waveguide structure with CMOS compatible technology, and the gain materials are also optimized to provide high-gain amplification with high-speed modulation. By combining these technologies, the advantages of EDWA devices and III-V semiconductor light sources can be harnessed. The proposed technique offers straightforward, monolithic fabrication of the EDWA that yields high-gain amplification with an electric pump. And the proposed device thus realizes full on-chip integration of waveguide amplifiers for silicon photonic systems without external pump light sources.

The organization of the rest of the manuscript includes the design, modeling and discussion of the proposed amplifier. Correspondingly, the design section demonstrates the design idea of the device in detail, including the resonant cavity, pump active layer and specific waveguide structure. The modeling section establishes an accurate theoretical model to give a more realistic prediction of device performance. And the discussion section systematically analyzes the amplification, frequency response characteristics and the device manufacturability. Such research may open up a new development direction for the state of silicon-based integrated optical amplifiers.

2. Design

2.1 General structure

An Er-based waveguide amplifier can enhance optical signals on a robust, low-cost microchip. Similar to silicon-based fibers, many waveguide platforms, such as SOI and silicon-nitride, used in integrated optics have low losses in the 1.5 µm window, which provides the impetus for using EDWAs in photonic circuits. Figure 1 shows a co-integrated silicon photonics chip with Er-based waveguide amplifiers. For an integrated silicon photonics chip, the signal generated by an external laser enters the processing modules through the waveguide optical path, and it is collected by the detection module for subsequent integration with CMOS devices. The optical amplification can be carried out for different transmission paths with the fabrication of local amplifiers, including loss compensation in the waveguides while signal processing and transmission between modules. Traditionally, as shown in Fig. 1(a), an external 980 nm or 1480 nm pump light is launched into the chip by a taper fiber. MUX is used to multiplex pump and signal light transmission, and a symmetric Y-junction is applied for pump transmission. The external pump scheme increases the complexity of the integrated system, which limits the large-scale integration of silicon photonic devices. Instead, we propose a more simplified scheme with pump-integrated Er-based waveguide amplifiers for silicon photonics systems, as shown in Fig. 1(b). The Er-based waveguide amplifiers are integrated with integrated III-V semiconductor pump lasers above, which enables local electrically driven amplification. These hybrid waveguides are used to deal with the transmission losses in any path that needs amplification, which is position-adapted with better flexibility. This scheme realizes the full integration of amplifiers for the silicon photonic system without external pump light sources.

Fig. 1. Co-integrated silicon photonics chip with Er-based waveguide amplifiers. (a) Traditional on-chip amplification scheme for silicon photonics system with external pump light source. (b) Proposed on-chip electric-pumped amplification scheme for silicon photonics system without external pump light source. (c) Basic structure of the local Er-based waveguide amplifier.

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Figure 1(c) shows the basic structure of the local Er-based waveguide amplifier. In this structure, an Er-based gain layer is deposited on the transmission waveguide to provide high-speed and large-capacity optical signal amplification. Then, the III-V semiconductor light emitting structure, which provides high electrical-optical conversion efficiency, is hybrid-integrated on the gain layer as the electrically driven light source to pump the Er-based gain materials. In addition, inverted-tapers are designed to couple and decouple the signal evanescently from a silicon photonic waveguide to a larger-cross-section Er-based waveguide, as illustrated in Fig. 1(c). This completes the design of the indirect electrically pumped Er-based waveguide amplifier for on-chip amplification.

Figure 2 shows the detailed structure of the on-chip electrically pumped Er-based waveguide amplifier. As Fig. 2(a) shows, the amplifier structure is based on an Er-based hybrid waveguide optically pumped by the heterogeneous integrated electroluminescent III-V semiconductor vertical-cavity-emitting laser. The III-V semiconductor pump source provides high electrical-optical conversion efficiency, while the Er-based waveguide amplifier provides high-speed and large-capacity signal amplification. Er-based materials, such as Er³⁺-doped oxide material or Er silicate compound, are selected as gain layers due to their long luminescence lifetime and better CMOS technology compatibility. These gain materials do not exhibit transient channel crosstalk and offer increased integration potential [18,19]. The strained GaAs multiple quantum well (MQW) structure is used in the design of the 980 nm pump active region. The III-V gain layers can be heterogeneously integrated (bonded) [10] on Si, which displays good performance. Quantum dot structures can also act as a candidate for future expansion [20,21]. Further, the defect density of GaAs grown on silicon is lower than that of InP, and the silicon-based GaAs pump source is more reliable than InP [11,22,23]. Compared with the traditional heterojunction active layer structure, the energy of carriers in the limited quantum structure has discontinuous discrete values, and this leads to a stepped density of state. The changes in the valence band brought about by the strain also decrease the threshold current density. The active layer of strained GaAs MQW structure has the following advantages: low threshold current, high quantum efficiency, large output power, wide modulation bandwidth, and low temperature dependence [24]. To increase the emission intensity of the III-V pump source and to improve the absorption efficiency of Er³⁺ to pump light, the active layers are all placed in a vertical cavity. The distributed Bragg reflector (DBR) structure is adopted as the resonator, which is designed at pump wavelength for strong pump resonance. In this case, the pump light is reflected multiple times in the resonator to enhance the absorption of Er³⁺, while it also maintains a wide gain spectrum for the signal light. After evanescent coupling, the Er-based gain material located in the resonant cavity has a waveguide effect on the signal light in the horizontal direction, so that the optical gain is generated when the signal light passes through the Er-based waveguide horizontally. The interaction between the cavity and waveguide is studied through the design and optimization of the optical field distribution in the cavity and waveguide. The cavity has a strong absorption enhancement effect on the Er-based material and leads to small waveguide loss.

Fig. 2. Structure of the silicon-based Er silicate waveguide amplifier with heterogeneous integrated electroluminescence III-V semiconductor vertical-cavity-emitting pump laser. (a) 3-D design of the amplifier structure. (b) Cross section of the amplifier structure.

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The cross section of the device is shown in Fig. 2(b). The structure (from bottom to top) comprises a silicon substrate, a bottom SiO₂/Si₃N₄ DBR reflector, a waveguide layer, an Er-based gain layer, a bonding dielectric layer, a III-V MQW pump active layer, a bonding layer, a top AlGaAs/GaAs DBR reflector, and electrodes. The waveguide provides low-loss optical transmission and can be made of a SOI waveguide or a silicon nitride waveguide structure. The width and height of the waveguide are optimized to ensure the single guided mode with low propagation loss of the light field. The Er-based gain layer is deposited on the waveguide layer, which is fabricated into a horizontal hybrid waveguide structure. This structure couples most of the optical field in the waveguide to the gain layer and allows effective amplification. Moreover, a SiO₂ spacer is added between the waveguide and the gain layer to reduce the guiding effect in the high refractive index material. This can effectively adjust the optical field distribution in the waveguide cross section. Finally, the III-V active layer is bonded on the gain layer by the bonding process. During signal transmission along the waveguide, the gain material absorbs the electroluminescent pump light from the III-V active layer and provides a large optical gain to the signal light.

2.2 Vertical pump resonant cavity

The gain layer and the III-V pump active layer are both placed in a vertical pump resonant cavity, which has two DBR reflectors with a central wavelength of 980 nm. The reflectivity of these DBR structures is the key to decide pump efficiency, which directly affects the differential quantum efficiency, threshold current density, and output pump power. The refractive index differences between the two DBR materials should be relatively large to achieve high reflection with fewer periods. For the top DBR structure, Al_xGa_1-xAs/GaAs materials with aluminum composition were selected for periodic growth to meet the needs of lattice matching. This kind of semiconductor reflector can be epitaxially grown on InP substrate with low fabrication cost. The refractive index of Al_xGa_1-xAs material decreases with the increasing proportion of aluminum [25]. However, the Al_xGa_1-xAs material with high aluminum content is easily oxidized. Therefore, Al_0.9Ga_0.1As is usually used as the low refractive index (3.0) material of DBR, while GaAs is used as the high refractive index (3.5) material. For the bottom DBR structure, SiO₂ (low refractive index 1.44) /Si₃N₄ (high refractive index 2.0) periodic alternate layers are selected as dielectric reflectors. These SiO₂/Si₃N₄ dielectric films have good material compatibility with Si substrate and have almost no absorption in the pump wavelength band. The optical thickness of these media can be reduced to a quarter of a wavelength. Hence, the 81.7-nm-thick Al_0.9Ga_0.1As/ 70.0-nm-thick GaAs and 170.1-nm-thick SiO₂/ 122.5-nm-thick Si₃N₄ are chosen for a single periodic alternate layer in the bottom and top DBR structures, respectively. By applying the principle of multilayer interference, DBR reflectors with high reflectivity can be designed. Generally, the transfer matrix method is used to calculate the reflectivity spectrum and the bandwidth of DBR reflectors.

Figure 3 shows the reflectivity spectra of DBR with different periodic pairs (N = 4–28). It can be seen from the reflectivity curves in Fig. 2 that the reflectivity variations are similar for both Al_0.9Ga_0.1As/GaAs top DBR and SiO₂/Si₃N₄ bottom DBR structures. There is no depression at the central wavelength, 980 nm. The curve increasingly flattens near the center wavelength with the increase in the number of periodic pairs. The reflectivity increases with the increase in the number of pairs and approaches 100%, as shown in the inset of Fig. 3. For SiO₂/Si₃N₄, the reflectivity increases with N faster than that for Al_0.9Ga_0.1As/GaAs. The reflectivity bandwidth is also wider. This is because SiO₂/Si₃N₄ has larger refractive index difference and higher DBR thickness. In the fabrication of such a pump device, the higher the reflectivity of DBR, the better the performance. However, the total number of DBR pairs must be carefully designed. The increases in reflectivity is at the expense of bandwidth. With a higher number of periodic pairs, the series resistance in the device becomes larger, and the absorption of light will increase. The difficulty of the process also increases the growth costs. Therefore, it is necessary to optimize the design to obtain higher reflectivity with less growth pairs. Thus, the optimized growth pairs of Al_0.9Ga_0.1As/GaAs are set as 24 (the reflectivity is calculated as 99.8%) for the top DBR reflectors, with a reflectivity bandwidth of ∼120 nm. The optimized growth pairs of SiO₂/Si₃N₄ are set as 14 (the reflectivity is calculated as 99.9%) for the bottom DBR reflectors, with a reflectivity bandwidth of ∼200 nm.

Fig. 3. Reflectivity spectra of DBR with different periodic pairs (N = 4, 8, 12, 16, 20, 24, 28). (a) Reflection spectrum for Al_0.9Ga_0.1As/GaAs top DBR reflector. (b) Reflection spectrum for SiO₂/Si₃N₄ bottom DBR reflector. The insets show the relationship between DBR growth pairs and reflectivity at 980 nm central wavelength.

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2.3 III-V active layer

The III-V active layer based on MQW structure is used as the electroluminescence pump layer. This structure can increase the carrier energy and enhance the electroluminescence effect. It mainly includes n-type region, MQW region, p-type region, and the corresponding electrodes. For the 980 nm high power pump, the InGaAs/GaAsP strain-compensated quantum well material is selected as the active region. The difference of lattice constants between these two materials introduces strain in the epitaxial growth of quantum wells. This will change the structure of the valence band, further reducing the asymmetry between the conduction band and the valence band. This strain compensation structure has a larger band gap, which improves the emitting efficiency of quantum wells and increases the gain. For the design of the device structure, the components of the quantum well material play a decisive role in the pumping wavelength. The band gap of In_1-xGa_xAs well material and GaAs_1-xP_x barrier material is as follows [26].

(1)$$InGaAs:{ }E{g_1}(x) = 1.424 - 1.548x + 0.478{x^2}, $$

(2)$$GaAs{P}:{ }E{g_2}(x) = 1.424 + 1.12x + 0.21{x^2}. $$

When the design wavelength of the device is 980 nm, the band gap of the quantum well In_xGa_1-xAs material should be 1.242/0.98 = 1.267 eV. It can be seen from Fig. 4(a) that with the increase in the indium composition, the band gap decreases, and the corresponding lasing wavelength shifts to the longer wavelength direction. Here, the composition of indium is chosen as 0.12, considering the band gap.

Fig. 4. Design of the MQW structure. (a) Emitting wavelength versus indium composition. (b) Threshold power density versus number of quantum wells.

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The input threshold current density of the MQW emission is closely related to the quantum well structure. For a conventional MQW laser, there are three design parameters: the thickness of the well (t_w), the total thickness of the active material (d = t_w×N), and the total thickness of the multilayer material (T = t_w×N+(N-1)×t _{buffer layer}). The threshold current density is given by the following equation [27].

(3)$${J_{th}} = e[B({n_{th}},{t_w})n_{th}^2 + A({n_{th}},{t_w})n_{th}^3]d. $$

Figure 4(b) shows the relationship between the number of quantum wells and the threshold power density. Although the MQW structure can reduce the threshold current of pump emission, the extent of the reduction is affected by the number of quantum wells. Initially, the threshold current density decreases rapidly with the increase in the number of quantum wells, and then begins to increase. The threshold current density of the device is relatively high when the number of quantum wells is small. This is mainly because the quantum well gain grows slowly with the increase in the injected carrier concentration. Then, the gain increases rapidly with the increase in the number of quantum wells, resulting in a drop in the threshold current density. The number of quantum wells is also a limiting factor. When the number of equivalent quantum wells exceeds 12, the limiting effect of MQW on the optical field is gradually weakened. Hence, the threshold current density begins to increase due to the partial leakage of optical field. Considering the cost of material growth and the difficulty in the implementation of the technology, the number of quantum wells is set as 12. The threshold current density in this structure is calculated to be approximately 2 kA/cm².

In addition, a 1.5 µm high reflective coating is deposited to reduce the leakage of signal light from the lower waveguide to the pump layer. The GaAs buffer layer is used to reduce the diffusion of impurities from the substrate surface to the growth layer and to improve the lattice matching between the substrate and the epitaxial growth layer. The thickness of this buffer layer should be minimized to ensure the growth quality of epitaxial wafers. Above all, the III-V MQW pump structure is demonstrated in Fig. 5.

Fig. 5. Structure of the III-V MQW pump.

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2.4 Hybrid waveguide and loss analyses

A hybrid waveguide structure with a high-gain layer is used for signal light propagation and amplification. In this structure, an on-chip SOI waveguide provides low-loss optical transmission, while the Er-based gain layer located on it produces high amplification. They are fabricated into a horizontal hybrid waveguide structure. The width and height of this straight waveguide are optimized to 450 nm and 220 nm, respectively, to enhance the confinement effect of the loading area on the light field.

The low-loss optical waveguides can be designed by a mathematically rigorous discussion of planar waveguide mode solutions, including guided mode design and loss analyses. To ensure single-mode transmission in the waveguide, the core geometry of the waveguide is carefully designed. According to the effective index method, the waveguide is equivalent to the superposition of two planar waveguides in both x and y directions. The characteristic equation of the guided mode is as follows.

(4)$$\left\{ {\begin{array}{c} {{{k}_0}\sqrt {n_1^2 - N_1^2} h = n\pi + \arctan \sqrt {\frac{{N_1^2 - n_2^2}}{{n_1^2 - N_1^2}}} + \arctan \sqrt {\frac{{N_1^2 - n_3^2}}{{n_1^2 - N_1^2}}} }\\ {{{k}_0}\sqrt {N_1^2 - {N^2}} w = m\pi + 2\arctan \frac{{N_1^2}}{{n_2^2}}\sqrt {\frac{{{N^2} - n_2^2}}{{N_1^2 - {N^2}}}} } \end{array}} \right., $$

where N is the effective refractive index of the guided modes, m, n = 0, l, 2, … corresponding to the order of modules in the x and y directions. w and h correspond to the width and height of the waveguide, respectively. For example, a process-standard 220-nm-thick Si waveguide (or 100-nm-thick Si₃N₄ waveguide) is clad with oxide layers of n₂=1.44 and bottom layers of effective n₃=1.45 (top oxide layer of DBR). The MATLAB simulations of the effective refractive index corresponding to different widths of the silicon optical waveguide are shown in Fig. 6.

Fig. 6. (a) Schematic of waveguide structure parameters. Simulated effective refractive index (λ₀=1550 nm) of guided modes along (b) silicon (220 nm core thickness) and (c) silicon nitride (100 nm core thickness) waveguides for varying waveguide core widths.

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It can be seen from Fig. 6(b) that for a 220-nm-thick Si waveguide, more guided modes propagate in the core as the waveguide width is increased. According to the minimum cut-off width of the non-fundamental mode, the width of the waveguide should be set within 520 nm to avoid high-order mode transmission. It can be seen from Fig. 6(c) that for 100-nm-thick Si₃N₄ waveguide, the width of the waveguide should be set within 3 µm.

The propagation losses should also be considered in the design of Si/Si₃N₄-core strip waveguides. The scattering loss of an optical waveguide mainly includes bulk scattering loss and surface scattering loss. Under the current SOI fabrication process, the bulk scattering of the waveguide can be ignored. The scattering loss that is usually considered is the surface scattering loss, which mainly depends on the surface roughness of the waveguide [28]. The surface scattering loss is calculated as follows.

(5)$${\alpha _{{side}wall}} = {\varphi ^2}\left( {\frac{h}{2}} \right)({n_1^2 - n_2^2} )\frac{{k_0^2}}{{4\pi {n_2}}}\int_0^\pi {S({\beta - {k_0}{n_2}\cos \theta } )} d\theta, $$

where φ(h/2) is the surface mode field of the waveguide, and S(σ) is used to describe the roughness of the side wall of the waveguide. The roughness of the sidewall of the waveguide is generally exponential or Gaussian. Scattering losses owing to the roughness of sidewall interfaces for the Si/Si₃N₄ waveguide are plotted for different core geometries in Fig. 7. The roughness parameters at opposite sidewalls and at the top and bottom interfaces are assumed to be equal, and only the results obtained from core geometries operating in the single-mode regime are shown. The typical sidewall roughness correlation lengths, owing to the planar waveguide fabrication processes, range approximately from 10⁰ to 10¹ nm.

Fig. 7. Simulated sidewall scattering losses for the fundamental TE mode of the (a) Si and (b) Si₃N₄ core waveguides with roughness (σ) profiles (1550 nm).

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From Fig. 7, it can be observed that the scattering loss decreases with the increase in the waveguide width. Increasing the core width causes the mode size to increase, thereby decreasing the fraction of mode power at the interface and yielding a corresponding decrease in scattering loss. Alternatively, increasing the width of the waveguide will decrease the intensity of the E-field at the rough sidewall and reduce the relative amount of scattered light. However, this latter approach is often not feasible as increasing w past the second mode cut-off width will cause multi-mode operation in the waveguide.

The top and bottom surface scattering loss can be defined simply and accurately by using the formula proposed by [29].

(6)$${\alpha _{{top}/bottom}} = \frac{{{{\cos }^3}\theta }}{{2\sin \theta }}{\left( {\frac{{4\pi {n_{core}}\sqrt {\sigma_{top}^2 + \sigma_{bottom}^2} }}{{{\lambda_0}}}} \right)^{2}}\frac{1}{{h + \frac{1}{{{k_{yt}}}} + \frac{1}{{{k_{yb}}}}}}, $$

where k_yt and k_yb are the attenuation constants of the upper and lower cladding layers of the waveguide, respectively. Therefore, the top and bottom surface scattering loss of the TE₀ mode can be calculated as 0.18 dB/cm (for the Si waveguide) and 0.1 dB/cm (for the Si₃N₄ waveguide) for a roughness of 1 nm using the above formula. The total loss can be calculated as α = α_sidewall + α_top/bottom.

In addition, the deposition of the Er gain layer will also cause surface scattering losses. Based on the experiments on the deposition of erbium films [19], the surface roughness of an erbium film with an optimal thickness of 1 µm after high temperature annealing is approximately 40 nm, which corresponds to a scattering loss of 3 dB/cm.

Figure 8 presents the simulated bend loss for the Si waveguide versus the core thickness for various bend radii. It can be observed that the larger bending radius of the curved waveguide results in a smaller waveguide bending loss. When the bending radius is less than approximately 6 µm (for Si) and 2 mm (for Si₃N₄), the bending loss is significantly affected by the bending radius and exponentially decreases with the increase in the bending radius. The bending loss of the waveguide tends to be the same when the radius exceeds a certain value. Beyond this value, increasing the bending radius has little effect on the bending loss. Thus, the bending radius is chosen in this range.

Fig. 8. Bend loss versus core thickness of the (a) Si and (b) Si₃N₄ waveguides for various bend radii. The widest possible single-mode core width is used for each thickness. (λ₀ = 1550 nm)

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The low-loss optical waveguides were designed considering their mode distribution (single-mode transmission) and their propagation loss (mainly including the sidewall, top/bottom scattering loss, and bend radiation loss). The optimized core geometry design parameters of the low-loss Si/Si₃N₄ waveguides and their propagation losses are tabulated in Table 1.

Table 1. optimized parameters of the low-loss waveguides.

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To achieve higher on-chip gain, more signal light propagating under the gain region needs to be coupled to the gain medium. Therefore, a gradually tapering structure is used to couple the optical field in the transmission SOI waveguide to the gain layer above to obtain as much amplification as possible. The key parameter of this coupling structure is the design of the waveguide width in the coupling zone, as shown in Fig. 9(a). When the waveguide width is narrowed down and the field is delocalized, it should be distributed more or less equally between the top (erbium-doped) and bottom (DBR) layers. An approximate equivalent refractive index (calculated as 1.62 in COMSOL) is introduced as a bottom cladding to evaluate this effect. Importantly, a relative thick SiO₂ layer can be used as a top layer in the multilayer SiN/SiO₂ stack to reduce the bottom cladding’s influence. And the bottom DBR also provides certain bottom reflectivity for the signal propagation. Therefore, the bottom DBR has little influence on the whole light field distribution. When the waveguide width is narrowed down and the field is delocalized, the light field will not leak toward the substrate, but instead diffuses through the gain layer, the optical mode will be confined well in the top erbium-doped layer. Figure 9(b) depicts the confinement factor changes for signal light (1535 nm) in both SOI waveguide and gain layer along the propagation direction. It can be observed that the signal light propagates as a single mode along the waveguide. The optical field is initially concentrated on the lower SOI waveguide transmission (82%) and gradually coupled into the upper gain layer during the chip transmission process. The confinement factor in the gain layer is calculated as 92%, and the signal light is significantly amplified. As a result, the optimized width of the waveguide region is approximately 220 nm. In addition, different taper lengths will lead to different effective refractive index distributions along the waveguide, which has a direct impact on the coupling loss. It can be calculated that the coupling loss tends to be stable when the length of the taper is greater than 200 µm, and at this time the length of the taper at both ends has little influence, thus the length can be set around 200 µm to reduce the coupling length. This structure couples most of the optical field in the waveguide to the gain layer, which results in effective amplification of the optical field.

Fig. 9. (a) Structure of the gradually tapering waveguide. (b) Confinement factor changes for signal light (1535 nm) in both SOI waveguide and gain layer along the propagation direction. The optical field distribution of the signal light (1535 nm) in the waveguide simulated by COMSOL. (c) Coupling losses versus width of different taper tips. The inset shows the coupling situation of light fields between different layers.

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The finite difference time domain algorithm is used to simulate the transmission of light in a conical coupled structure. Figure 9(c) depicts the influence of the taper width on the field coupling. It can be observed that the coupling loss is large (the coupling efficiency is low) when the taper width is large. The light field energy in the passive waveguide cannot be transferred to the gain layer very well because the waveguide still has a large limiting effect on the optical field. The restriction of the waveguide on the optical field is gradually weakened with the decreasing cone width, and the light field is gradually transferred to the gain layer above. However, when the taper width is too small, the mode mismatch increases, and the coupling efficiency will decrease. Finally, the vertical coupling loss is calculated to be approximately 0.87 dB, with taper width of approximately 220 nm.

The pump mode in the vertical cavity must satisfy the resonance condition, that is, the pump light at any position in the cavity should have the same phase (coherence) as the reflected pump light. Thus, the thickness of Er-based films is optimized to an integral multiple of the half wavelength (980 nm/2 = 490 nm) based on the pump resonance condition. The pump has a standing wave in the vertical DBR cavity, and the light intensity is periodically distributed in the cavity. Therefore, the gain layer can also be designed periodically, following the position with strong and weak pump intensity in the cavity, to ensure the best use of the pump intensity. Figure 10 depicts the standing wave of the pump light in the vertical DBR cavity. The Er gain layer will not play a good role in amplification because of weak pump intensity in the troughs. Thus, low-loss silicon nitride layers are added in these positions. These layers reduce the transmission loss of the film without reducing the gain. In addition, although the resonant wavelength of the proposed vertical cavity is depended on the thickness of the different embedded between the DBRs, the large reflectance bandwidths of the top and bottom reflectors result in a high tolerance to variations of their position.

Fig. 10. Design of the periodical gain layer: based on the standing wave effect of the pump intensity in the vertical DBR cavity.

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Moreover, additional coupling losses exist in the interface between the Er gain layer (1.65) and the top higher index pump layer (3.23), which mainly affect the pump transmission in the vertical direction. This interface coupling can be approximately regarded as vertical incidence. The generated Fresnel reflection losses can be approximately fitted via the Fresnel formula, as follows:

(7)$$\alpha (dB) = 10{\log _{10}}\left[ {\frac{1}{{1 - {{\left( {\frac{{n_{bonding}^2 - {n_{pump - layer}} \cdot {n_{gain - layer}}}}{{n_{bonding}^2 + {n_{pump - layer}} \cdot {n_{gain - layer}}}}} \right)}^2}}}} \right]. $$

From the above equation, it can be observed that the greater the refractive index difference between the two layers, the greater the reflectivity, and the greater the coupling loss. In this structure, the bonding layer (1.8) between the erbium gain layer and the high refractive index pump active layer not only plays the role of bonding integration but also acts as a transition region between the layers, which can effectively reduce the interface loss caused by Fresnel reflection. To improve the transmission efficiency from the pump layer to the erbium layer and to reduce the intensity of the end reflection, the thickness of the bonding layer can be optimized to an odd number of times of the pump wavelength to ensure the interference cancellation of the reflected light. The interface loss is approximately 0.27 dB.

3. Modeling

The performance of MQW vertical-cavity-emitting pump laser can be predicted using the P-I model. The relationship between the working current and the emitting power of MQW can be expressed as follows [30,31]:

(8)$${{P}_{out}} = \eta (I - {I_{th}}(N,T)) = \eta (I - {I_{th0}} - {I_{off}}(T)), $$

where η is the conversion efficiency, which is least affected by temperature and can be approximated as a constant, N is the concentration of carriers, and T is the temperature of the device. I_th (N, T) is the threshold current for the normal working of the pump device. It can be divided into a temperature-independent constant, I_th0, and a temperature-dependent empirical thermal bias current, I_off (T). The thermal bias current can be expressed as a polynomial function of temperature, as follows:

(9)$${{I}_{off}}(T) = \sum\nolimits_{n = 0}^\infty {{a_n}} {T^n} \approx {a_0} + {a_1}T + {a_2}{T^2} + {a_3}{T^3} + {a_4}{T^4}. $$

The temperature, T, of the pump device is determined by the temperature of the external environment, T₀, and the self-heating effect of the device. The self-heating effect is related to the instantaneous power, IV, generated by the device, where V is the working voltage. The formula can be expressed as follows [30]:

(10)$${T} = {T_0} + (IV - {P_0}){R_{th}} - {\tau _{th}}\frac{{dT}}{{dt}}, $$

where R_th is the thermal impedance, and τ_th is the thermal time constant. Assuming that the V-I relationship of the device does not change significantly at different operating temperatures, the V-I relationship can be expressed as follows [30]:

(11)$${V} = I{R_s} + {V_T}\ln (1 + I/{I_s}), $$

where R_s is the series impedance, V_T is the diode thermal voltage, and I_s the diode saturation current. These parameters need to be fitted according to the experimental values. To keep numerical stability, the sub-relaxation method is used to set the weighted average of the updated value and the old value as the initial value of the iteration, until the relative error of the two adjacent values is less than the given error limit. The optimized modeling parameters of the pump device are shown in Table 2. The pump emission characteristics can be obtained by using these parameters.

Table 2. optimized modeling parameters of the pump device.

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The equivalent modeling of the whole Er-based waveguide amplifier with heterogeneous integrated III-V semiconductor vertical-cavity-emitting pump laser is demonstrated in Fig. 11, using the finite element analysis method.

Fig. 11. Equivalent model of whole Er-based waveguide amplifier with heterogeneous integrated III-V semiconductor vertical-cavity-emitting pump laser.

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The two directions of the model are (1) signal transmission (z direction) and (2) pump absorption (x direction). The population dynamics of Er³⁺ and the propagation power of pump/signal are distributed uniformly in the transverse direction of the waveguide (y direction). In this case, they can be approximately simplified into two-dimensional distributions. In every waveguide block, the population dynamics of Er³⁺ (N(x,z)) on each energy level can be calculated using the rate equation, while the evolution of propagating components of signal and pump (P_s,p(x,z)) along the waveguide can be calculated using the propagation equation [12,18,32]. To start from the first block (1,1,1) according to the boundary input conditions, the adjacent blocks (1,1,2) in the z direction and the adjacent blocks (2,1,1) in the x direction are calculated according to the two-dimensional rate equation and the propagation equation, as follows:

(12)$$\left\{ {\begin{array}{l} {{ - }\left[ {\frac{{{\sigma_{13}}{P_p}(x,z)}}{{{A_{yz}}h{\nu_p}}} + \frac{{{\Gamma _s}{\sigma_{12}}{P_s}(x,z)}}{{{A_{xy}}h{\nu_s}}}} \right]{N_1}(x,z) + \left[ {{A_{21}} + \frac{{{\Gamma _s}{\sigma_{21}}{P_s}(x,z)}}{{{A_{xy}}h{\nu_s}}}} \right]{N_2}(x,z) + {C_2}N_2^2(x,z) + {C_3}N_3^2(x,z)}\\ { - {C_{14}}{N_1}(x,z){N_4}(x,z) - {K_{tr}}N_2^{Yb}(x,z){N_1}(x,z) = 0}\\ {\frac{{{\Gamma _s}{\sigma_{12}}{P_s}(x,z)}}{{{A_{xy}}h{\nu_s}}}{N_1}(x,z) - \left[ {{A_{21}} + \frac{{{\Gamma _s}{\sigma_{21}}{P_s}(x,z)}}{{{A_{xy}}h{\nu_s}}}} \right]{N_2}(x,z) + {A_{32}}{N_3}(x,z) - 2{C_2}N_2^2(x,z) + 2{C_{14}}{N_1}(x,z){N_4}(x,z) = 0}\\ {\frac{{{\sigma_{13}}{P_p}(x,z)}}{{{A_{yz}}h{\nu_p}}}{N_1}(x,z) - {A_{32}}{N_3}(x,z) - 2{C_3}N_3^2(x,z) + {A_{43}}{N_4}(x,z) + {K_{tr}}N_2^{Yb}(x,z){N_1}(x,z) = 0}\\ {\frac{{\sigma_{12}^{Yb}{P_p}(x,z)}}{{{A_{yz}}h{\nu_p}}}N_1^{Yb}(x,z) + \frac{{\sigma_{21}^{Yb}{P_p}(x,z)}}{{{A_{yz}}h{\nu_p}}}N_2^{Yb}(x,z) + A_{21}^{Yb}N_2^{{Yb}}(x,z) + {K_{tr}}N_2^{Yb}(x,z){N_1}(x,z) = 0} \end{array}} \right.$$

Here, A_ij describes spontaneous emission and nonradiative relaxation probability between levels i and j. C₂ and C₃ are the first-order and second-order cooperative up conversion coefficients, respectively, C₁₄ is the Er³⁺ cross relaxation coefficient, K_tr is the Yb³⁺ to Er³⁺ energy-transfer coefficient, N_Er and N_Yb are the Er³⁺ and Yb³⁺ concentrations, respectively. W₁₂/W₂₁ represents stimulated emission and absorption transition rate of signal light. R₁₃/R₃₁ represents stimulated emission and absorption transition rate of pump light. A_xy and A_yz are the waveguide-core cross-sectional area (xy plane) and the pump absorption area (yz plane), respectively. h is the Planck’s constant. σ represents the absorption and emission cross sections for Er³⁺ and Yb³⁺. The whole gain material system is based on two kinds of Er-based materials, Er³⁺:Al₂O₃ and Er silicate thin films. The corresponding parameters of these films are extracted from previous reports [12,32–34], as shown in Table 3.

Table 3. Parameters of Al₂O₃:Er³⁺ and Er silicate thin films used for modeling.

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According to the energy level equation, the transmission equation of the transmission signal can be obtained as follows:

(13)$$\left\{ {\begin{array}{l} {\frac{{\partial {P}_p^ \pm (x,z)}}{{\partial x}} ={-} {g_p}(x,z){P}_p^ \pm (x,z)}\\ {\frac{{\partial {P}_p^ \pm (x,z)}}{{\partial z}} = 0}\\ {{P_p}(x,z) = P_p^ + (x,z) + P_p^ - (x,z)}\\ {\frac{{\partial {P_s}(x,z)}}{{\partial z}} = {\Gamma _s}[{\sigma_{21}}{N_2}(x,z) - {\sigma_{12}}{N_1}(x,z)]{P_s}(x,z) - {\alpha_s}{P_s}(x,z)}\\ {\frac{{\partial {P_s}(x,z)}}{{\partial x}} = 0} \end{array}} \right.. $$

The boundary conditions are as follows:

(14)$$\left\{ {\begin{array}{l} {{P_s}(x,0) = {{P}_{sin}}}\\ {P_p^ + (0,z) = {{P}_{pin}}}\\ {P_p^ + (0,z) = {R_1}P_p^ - (0,z)}\\ {P_p^ - ({L_{eff}},z) = {R_2}P_p^ + ({L_{eff}},z)} \end{array}} \right., $$

where P_sin and P_pin are the input power of pump and signal, respectively; R₁ and R₂ are the reflectivity of the bottom and top DBRs, respectively; L_eff is the effective cavity length; and α(ν_s) is the propagation loss per unit length at the signal frequency, which is discussed in section 2.

The coupling relationship between the Er-based gain layer and the III-V layer can be calculated using coupling theory [35], and the pump coupling and absorption in the direction perpendicular to the waveguide can be measured using the pump coupling absorption coefficient. The expression considering the sensitization and vertical-cavity loss is as follows:

(15)$${{g}_p}(x,z) = {\eta _p}[{\sigma _{13}}{N_1}(x,z) + \sigma _{12}^{Yb}N_1^{Yb}(x,z) - \sigma _{21}^{Yb}N_2^{Yb}(x,z)] - \alpha ({\nu _p}), $$

where α(ν_p) is the propagation loss per unit length at the pump frequency. η_p is the vertical coupling efficiency, which can be fitted using the electrical-optical conversion efficiency of the active layer: the number of photons produced by each pair of composite carriers beyond the threshold current. This parameter reflects the quality of the laser, and it can be calculated as follows:

(16)$${\eta _{p}} = {\eta _i}\frac{{\ln (1/{R_1}{R_2})}}{{2\alpha ({\nu _p})L + \ln (1/{R_1}{R_2})}}, $$

where η_i is the internal quantum efficiency of the MQW. The coupling efficiency of the pump and the lower gain layer is mainly related to the internal quantum efficiency of the pump material, pump transmission loss, and reflectance of the DBR at both ends. A pump coupling efficiency of approximately 95% can be calculated, considering the interface loss described in section 2. Subsequently, the pump transmission equations in the vertical direction are established to describe the pump absorption effects more accurately. The signal power of all the units is iterated until the boundary conditions are met. It is presupposed that the Er³⁺ concentration and signal power density are consistent within the same row of z coordinates (same xy plane). After this two-dimensional modeling and iteration, the signal amplification of the entire waveguide can be fitted.

4. Discussion

4.1 Gain characteristics

Figure 12 shows the output pump emitting power of the designed heterogeneous integrated III-V MQW vertical-cavity-emitting pump laser. A threshold input current for DBR vertical resonators exists owing to the photon steady-state oscillation condition. It was observed that the threshold current is approximately 2.5 mA at room temperature, and the threshold current increases with the increase in environment temperature. It was found that the output pump emitting power increases with the increase in the input current. However, when the input current exceeds a certain value, the output power decreases with increasing input current. Hence, the output power exhibits an extreme response to the saturation current. The P-I relationship of pump emission displays the same general trend with the change in environment temperature, but there exists a large gap. The leakage current increases with the rise in temperature, and the threshold current I_th (N, T) = I_th0 + I_off (T) also increases, resulting in a drop in the output power. The performance of the laser deteriorates thereafter, and the thermal saturation occurs at a smaller current than that before. Resultantly, the maximum output power of the pump emission corresponds to an optimum input current. The maximum output pump emitting power can reach 12 mW for an input current of 44 mA at room temperature.

Fig. 12. Output pump emitting power versus input current (0–50 mA) at different environment temperatures (15–65 °C) of the designed heterogeneous integrated III-V MQW vertical-cavity-emitting pump laser.

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Figure 13 shows the signal gain characteristics of the integrated Er-based waveguide amplifiers, for both Er³⁺:Al₂O₃ and the Er silicate gain layer. The speculative modeling and theory of this proposed amplifier can be applied with the experimental SiN-Er³⁺:Al₂O₃ waveguide structure reported earlier [36–41]. In this hybrid structure, any additional optical intensity localized in the SiN waveguide may introduce detrimental intracavity losses owing to scattering of the Er³⁺:Al₂O₃ material and SiN waveguide, as described in section 2. The corresponding loss data can be extracted from Table I, while the experimental data of Er³⁺:Al₂O₃ films are shown in Table 2. It can be seen that the amplifier gain increases with the increase in input current injected in the MQW and gradually saturates. This result occurs because an increase in signal power further enhances Er³⁺ stimulated radiation, thus causing more rapid reduction in the Er³⁺ concentration in the excited state. This reduction in turn restrains further amplification of the signal, resulting in gain saturation that slows down as the input current increases. The pump power changes little along the waveguide transmission because of its vertical incidence. Consequently, there is no pump-over-absorption effect in the amplifier, and the absorption efficiency of the Er-based material with respect to the pump light is greatly improved. According to the calculation of Fig. 13(a), the maximum saturated gain is approximately 35 dB/cm when the input current is 45 mA at room temperature.

Fig. 13. Signal gain of (a) Er³⁺:Al₂O₃ and (b) Er silicate waveguide amplifiers with designed heterogeneous integrated III-V MQW vertical-cavity-emitting pump laser versus waveguide length (0–8 mm) with different electric-injected current (20–45 mA).

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To further improve the gain, the Er-Yb silicate material is selected to replace the Er-doped gain material. The Er-Yb silicate material has a high Er concentration and presents no problem regarding insolubility. The Er³⁺ concentration (∼10^21∼22 cm⁻³) of this material is higher than that of other Er-doped materials by two to three orders of magnitude, while Yb cations are added to act as sensitizers for pump absorption. The Er silicate compound itself has a high gain of ∼10¹ to 10² dB/cm, according to recent research results pertaining to both film [19,34,42–46] and nanowire [47–51] structures. Top-down CMOS technology can be also employed to fabricate high-quality Er silicate structures for amplifier application [18]. Therefore, Er silicate compounds are more favorable candidate materials for use in the proposed pump-integrated waveguide amplifier. The corresponding parameters of Er-Yb silicate films are shown in Table II. According to the calculation relating to Fig. 13(b), the maximum saturated gain is approximately 42.5 dB/cm when the input current is 45 mA at room temperature, which is about 21% higher than that of the Er³⁺:Al₂O₃ gain layer. The proposed high-gain silicon-based waveguide amplifiers with electric-injected pumps can better solve the problem pertaining to electrical-driving of EDWAs for on-chip silicon photonics systems.

4.2 Frequency response

Normally the proposed amplifier is considered to have stable gain at high signal frequencies because of the long upper state lifetime, and one would not consider modulating the pump source. However, when applied to the light source (such as lasers when introducing resonant cavity structure), the high speed modulation of the device is indirectly limited by the electrical modulation of the pump source. In this application scenario, the frequency response characteristics of the device directly determine the device transmission bandwidth, which holds important research significance. The frequency response of the designed waveguide amplifier is primarily decided by the integrated MQW vertical-cavity-emitting pump laser, because the lifetime of the upper level carrier in the III-V MQW material is shorter than the excited state ion lifetime in the Er silicate material. The frequency response characteristics of the device reflect the relationship between the output and the input at different operating frequencies. The device frequency response can be theoretically calculated via modification of the compound equivalent circuit model, which shows good agreement with the actual device for a wide range of currents and signal amplitudes. The signal bandwidth can be optimized, and the data transmission speed can be improved. The photo-electric conversion characteristics of the device are described by the rate equation in the large signal mode, and the frequency response function of this composite equivalent circuit is as follows [25,31]:

(17)$$H(f) = \frac{{f_r^2}}{{f_r^2 - {f^2} + 2j\gamma (f/2\pi )}} \cdot \frac{1}{{1 + jf/{f_p}}}, $$

where f_p is the cut-off frequency, and f_r is the relaxation oscillation frequency, which can be calculated as follows:

(18)$${{f}_{r}} = \sqrt {\frac{{\Gamma {G_0}(I - {I_{th}})}}{{4{\pi ^2}qV}}}, $$

where Γ is the confinement factor, and G₀ is the gain coefficient. γ is the damping factor, which can be expressed as:

(19)$$\gamma = 4{\pi ^{2}}({\tau _{p}} + \varepsilon /{G_0}), $$

where τ_p is the photon lifetime, and ɛ is the gain compression factor. These parameters can also be optimized iteratively using experimental data. Figure 14(a) shows the calculated frequency response of different bias currents at room temperature for the designed Er silicate waveguide amplifier. First, the response amplitude increases with the frequency of the input signal and subsequently decreases, when the same bias current is injected. The corresponding input signal frequency at a -3 dB response amplitude is defined as the device bandwidth. Secondly, the peak value of the response amplitude moves to the right to a higher frequency with increase in the bias current at low levels, and it moves to the left to a lower frequency with a further increase in bias current. This indicates that the amplifier transmission characteristics correspond to the changes in pump emitting output power, with the increase in bias current. A maximum bandwidth of approximately 42 GHz is calculated for the bias current of 30 mA at room temperature. The large-bandwidth feature allows for the high-speed modulation of the device. Figure 14(b) shows the relationship between the device bandwidth and the bias current at different environment temperatures. It can be observed that the bandwidth first increases and subsequently decreases with the increase in bias current; this variation is the same as that of the saturation of the pump emitting output power shown in Fig. 12. In addition, the initial turning point of the bandwidth decreases with the increase in temperature; moreover, the saturation decreasing point also decreases with the increase in temperature. This is similar to the change in saturation decreasing point shown in Fig. 12. Importantly, it can be concluded that the frequency response of the amplifier corresponds to the P-I variations of the MQW pump laser. The physical explanation for this is that the increase in injected current results in the rise in device temperature. The carriers obtain more energy to break through the quantum well barrier, which leads to increased leakage. Hence, the device photo-electric modulation characteristics progressively worsen. Therefore, the bandwidth characteristics of the amplifier can be improved from the standpoint of temperature control.

Fig. 14. (a) Calculated frequency response of different bias currents at room temperature and (b) bandwidth versus bias current at different environment temperatures for the designed Er silicate waveguide amplifier.

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4.3 Fabrication

Waveguide fabrication (shown in Fig. 15) commences with a silicon substrate and SiO₂/Si₃N₄ dielectric films constituting the bottom DBR layer. As per the traditional CMOS process, SiO₂/Si₃N₄ DBR structures can be prepared via plasma enhanced chemical vapor deposition (PECVD). The reaction gas is ionized using radio frequencies and other methods, and plasma is formed locally. High-quality SiO₂ and Si₃N₄ films can be alternately grown on the substrate at a lower temperature, because of the spontaneous reaction via the relatively strong activity of plasma. Following this, low-pressure chemical vapor deposition (LPCVD) is used to deposit a thick stoichiometric Si/Si₃N₄ film, resulting in a fixed index contrast of approximately 23% with the substrate layers. Lithography is performed, and the developed photoresist is then reflowed on a hotplate to reduce the line edge roughness before etching. Reactive ion etching is subsequently used to etch through the Si/Si₃N₄ film, whereby the waveguide core width is defined. Following this, 100-nm-thick SiO₂ layers are deposited via TEOS-based LPCVD. After several hours of annealing, the resulting protrusion of SiO₂ above the waveguide cores is removed through chemical mechanical polishing. After the polishing, sputtering is used to deposit microns of the Er-based gain layer as the waveguide upper coupling layer, and the finished wafer is finally annealed at over 750 °C for an additional hour. Such back-end-of-line deposition of the Er-doped Al₂O₃ or silicate film is well performed on the chip level [17,41]. These gain devices can be integrated with other active silicon photonic devices and have good fabrication compatibility with SOI platform [16,17].

Fig. 15. Schematic overview of the processes used to fabricate the ultra-low-loss Si/Si₃N₄ waveguides.

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Figure 16 shows the feasible fabrication of the electrically driven, position-adapted, fully integrated Er-based waveguide amplifier. The processes involved in the fabrication of the Er-based waveguide can be compatible with traditional CMOS processes, as described in Fig. 15. The high-quality MQW pump source is prepared on an InP substrate using epitaxial growth. It is worth noting that a 1.5-µm high reflective coating needs to be deposited after the fabrication of the pump source (not included in Fig. 15 for simplification) to reducing the leakage of signal light in the lower waveguide to the pump layer. The key process, being the integration of the Er-based film and the III-V pump source, mainly involves the method of wafer bonding. As shown in Fig. 15, the PECVD method is used to deposit a SiO₂/SiN film as the bonding medium layer on both the Er silicate film and the III-V pump source. Chemical mechanical polishing is subsequently conducted to smoothen the surface roughness of the bonding medium to meet the bonding requirements. To improve the bonding quality, the contents of hydrogen and water in the bonding medium are reduced via thermal annealing. The surface is activated using reactive ion etching followed by bonding to complete the integration of Er silicate thin film and III-V pump source. Following this, the original substrate of the III-V pump source is removed via mechanical thinning and chemical etching. Traditional methods such as photolithography and etching are used for the subsequent manufacturing of other layers; the process thereof is shown in Fig. 15.

Fig. 16. Fabrication process of the device, including the fabrication of Er-based gain layer, III-V pump source, bonding technology, and subsequent processing.

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The designed Er waveguide amplifier involves straightforward, monolithic fabrication that yields high gain amplification with an electric pump. Although it is difficult to achieve electroluminescence in the Er-based material itself, the proposed novel amplifier structure with reliable design, modeling and experimental feasibility paves the way forward for the development of electric-pumped high-gain, large-bandwidth silicon-based waveguide amplifiers in the future.

5. Conclusion

In this study, we proposed a novel on-chip, electrically driven, position-adapted, fully integrated erbium-based waveguide amplifier for silicon photonics. The III-V MQW vertical-cavity-emitting pump laser was heterogeneously integrated on an Er-based hybrid waveguide amplifier, using hybrid or heterogeneous bonding technology. The vertical pump resonant cavity, MQW active layer, and the amplifier waveguide structure were designed and modeled. A maximum saturated gain of approximately 42.5 dB/cm was predicted for an injected current of 45 mA at room temperature, and a modulation bandwidth of ∼42 GHz could be achieved for an incident pump power of ∼10 mW. This device structure presents a new technical scheme for electrically pumped Er-based waveguide amplifiers. Overall, these results indicate that the proposed high gain Er-based waveguide amplifier with an integrated electric pump has the potential to satisfy on-chip amplification requirements.

Funding

State Key Laboratory of Advanced Optical Communication Systems and Networks. (2018GZKF11); National Natural Science Foundation of China (61635001).

Acknowledgements

The authors acknowledge funding from the National Natural Science Foundation of China Grant No. 61635001 and acknowledge the State Key Laboratory of Advanced Optical Communication Systems Networks, China, under the contract No. 2018GZKF11.

Disclosures

The authors declare no conflicts of interest.

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Parameters	Si waveguide	Si₃N₄ waveguide
Thickness	220 nm	100 nm
Width	450 nm	2.8 µm
Bend radius	>6 µm	>2 mm
Thickness of the Er gain layer	1 µm	1 µm
Total scattering loss of waveguide	0.28–1.48 dB/cm	0.15–1.1 dB/cm
Surface scattering loss of gain layer	∼3 dB/cm	∼3 dB/cm
Bend loss	<0.01 dB/cm	<0.01 dB/cm

Parameters	Symbol	Values for Er³⁺:Al₂O₃ from [12]	Values for Er-Yb silicate from [32–34]
Er³⁺ concentration (cm^-3)	$N_{E r}$	3×10²⁰	3.3×10²¹
Yb³⁺ concentration (cm^-3)	$N_{Y b}$	0	1.7×10²²
Er³⁺ emission cross section at 1532 nm (cm²)	$σ_{21}$	4.2×10⁻²¹	1.24×10⁻²⁰
Er³⁺ absorption cross section at 1532 nm (cm²)	$σ_{12}$	5.65×10⁻²¹	1.24×10⁻²⁰
Er³⁺ absorption cross section at 980 nm (cm²)	$σ_{13}$	2.58×10⁻²¹	2.58×10⁻²¹
Yb³⁺ emission cross section at 980 nm (cm²)	$σ_{21}^{Y b}$	-	1.2×10⁻²⁰
Yb³⁺ absorption cross section at 980 nm (cm²)	$σ_{12}^{Y b}$	-	1.2×10⁻²⁰
Er³⁺ emission lifetime at ⁴I_13/2 level (ms)	$τ_{21}$	7.6	7.8
Er³⁺ nonradiative lifetime at ⁴I_11/2 level (µs)	$τ_{32}$	60	100
Er³⁺ radiative lifetime at ⁴I_11/2 level (µs)	$τ_{31}$	100	100
Er³⁺ nonradiative lifetime at ⁴I_9/2 level (µs)	$τ_{43}$	1	1
Er³⁺ radiative lifetime at ⁴I_9/2 level (µs)	$τ_{41}$	1	1
Yb³⁺ emission lifetime at ²F_5/2 level (ms)	$τ_{21}^{Y b}$	-	2
1^st cooperative upconversion coefficient of Er³⁺ (cm³/s)	$C_{2}$	8×10⁻¹⁸	5×10⁻¹⁷
2^nd cooperative upconversion coefficient of Er³⁺ (cm³/s)	$C_{3}$	8×10⁻¹⁸	5×10⁻¹⁷
Er³⁺ cross relaxation coefficient (cm³/s)	$C_{14}$	8×10⁻¹⁸	3.5×10⁻¹⁷
Yb³⁺-to-Er³⁺ energy-transfer coefficient (cm³/s)	$K_{t r}$	-	2.3×10⁻¹⁶

Parameters	Si waveguide	Si₃N₄ waveguide
Thickness	220 nm	100 nm
Width	450 nm	2.8 µm
Bend radius	>6 µm	>2 mm
Thickness of the Er gain layer	1 µm	1 µm
Total scattering loss of waveguide	0.28–1.48 dB/cm	0.15–1.1 dB/cm
Surface scattering loss of gain layer	∼3 dB/cm	∼3 dB/cm
Bend loss	<0.01 dB/cm	<0.01 dB/cm

Parameters	Symbol	Values for Er³⁺:Al₂O₃ from [12]	Values for Er-Yb silicate from [32–34]
Er³⁺ concentration (cm^-3)	$N_{E r}$	3×10²⁰	3.3×10²¹
Yb³⁺ concentration (cm^-3)	$N_{Y b}$	0	1.7×10²²
Er³⁺ emission cross section at 1532 nm (cm²)	$σ_{21}$	4.2×10⁻²¹	1.24×10⁻²⁰
Er³⁺ absorption cross section at 1532 nm (cm²)	$σ_{12}$	5.65×10⁻²¹	1.24×10⁻²⁰
Er³⁺ absorption cross section at 980 nm (cm²)	$σ_{13}$	2.58×10⁻²¹	2.58×10⁻²¹
Yb³⁺ emission cross section at 980 nm (cm²)	$σ_{21}^{Y b}$	-	1.2×10⁻²⁰
Yb³⁺ absorption cross section at 980 nm (cm²)	$σ_{12}^{Y b}$	-	1.2×10⁻²⁰
Er³⁺ emission lifetime at ⁴I_13/2 level (ms)	$τ_{21}$	7.6	7.8
Er³⁺ nonradiative lifetime at ⁴I_11/2 level (µs)	$τ_{32}$	60	100
Er³⁺ radiative lifetime at ⁴I_11/2 level (µs)	$τ_{31}$	100	100
Er³⁺ nonradiative lifetime at ⁴I_9/2 level (µs)	$τ_{43}$	1	1
Er³⁺ radiative lifetime at ⁴I_9/2 level (µs)	$τ_{41}$	1	1
Yb³⁺ emission lifetime at ²F_5/2 level (ms)	$τ_{21}^{Y b}$	-	2
1^st cooperative upconversion coefficient of Er³⁺ (cm³/s)	$C_{2}$	8×10⁻¹⁸	5×10⁻¹⁷
2^nd cooperative upconversion coefficient of Er³⁺ (cm³/s)	$C_{3}$	8×10⁻¹⁸	5×10⁻¹⁷
Er³⁺ cross relaxation coefficient (cm³/s)	$C_{14}$	8×10⁻¹⁸	3.5×10⁻¹⁷
Yb³⁺-to-Er³⁺ energy-transfer coefficient (cm³/s)	$K_{t r}$	-	2.3×10⁻¹⁶

Design of an on-chip electrically driven, position-adapted, fully integrated erbium-based waveguide amplifier for silicon photonics

Abstract

1. Introduction

2. Design

2.1 General structure

2.2 Vertical pump resonant cavity

2.3 III-V active layer

2.4 Hybrid waveguide and loss analyses

3. Modeling

4. Discussion

4.1 Gain characteristics

4.2 Frequency response

4.3 Fabrication

5. Conclusion

Funding

Acknowledgements

Disclosures

References

Cited By

Figures (16)

Tables (3)

Equations (19)

OSA Continuum

Parameters	Symbol	Values	References
conversion efficiency	η	7.38%	[22]
threshold current constant	I_th0	-21.58 mA	[24]
thermal impedance	R_th	-11.87 °C/W	[24]
1^st temperature coefficient	a₁	1.547×10⁻² mA/K	[24]
2^nd temperature coefficient	a₂	2.047×10⁻⁴ mA/K²	[24]
3^rd temperature coefficient	a₃	1.578×10⁻⁸ mA/K³	[24]
4^th temperature coefficient	a₄	-5.837×10⁻¹² mA/K⁴	[24]
series impedance	R_s	149.8 Ω	[24]
thermal voltage	V_T	0.937 V	[25]
saturation current	I_s	7.918×10⁻² mA	[25]