1. Introduction

Complementary metal-oxide-semiconductor (CMOS)-compatible silicon electro-optical (EO) modulators are basic building blocks for optoelectronic systems [1]. Recently developed Si modulators typically rely on electrically altering the Si refractive index through mechanisms such as carrier injection, accumulation, or depletion in either a PN diode or a metal-oxide-semiconductor (MOS) capacitor, and converting the phase variation into the optical intensity variation through a Mach-Zehnder interferometer (MZI) or a ring resonator [2, 3]. Due to the weak plasma dispersion effect of Si and the diffraction limit of the Si waveguides, the Si MZI modulators suffer from large footprints of ~10³–10⁴ μm². The ring modulators have compact footprints of ~10²–10³ μm², but at a price of higher temperature sensitivity and lower optical bandwidth. Ultra-compact modulators with μm² footprint and even higher performance (i.e., higher speed and lower energy consumption) are highly desired for further high-density Si electronic photonic integrated circuits (Si-EPICs). On the other hand, optical circuits based on deposited materials such as amorphous-Si and Si₃N₄ are emerging recently for three-dimensional (3D) integration of multiple photonic layers on Si electronic circuits [4, 5] or for flexible photonics [6]. Modulators which can be integrated with these deposited waveguides are needed.

Plasmonis provides an approach to miniaturize optical devices beyond the diffraction limit [7]. Several ultra-compact plasmonic modulators have been reported, but they usually rely on non-CMOS-compatible materials or processes, making it difficult to integrate them into the existing Si-EPICs [8, 9]. A fully CMOS-compatible plasmonic modulator utilizing Si as the active material is demonstrated recently [10, 11]. However, it requires a very large modification of the Si electron concentration to reach a realistic modulation depth. This is because Si is not a good active material for plasmonic modulator, as will be explained in this paper. Moreover, it limits the modulator on the single-crystal Si layer.

Recently, transparent conductor oxides (TCOs) such as indium tin oxide (ITO) are emerging as an attractive active material for new concept optical modulators because of its unique property such as epsilon-near-zero (ENZ) in the near infrared regime and electrically-tunable permittivity [12–20]. Based on the Drude model, the real part of the ITO’s permittivity can be tuned between positive and negative by varying its electron concentration (N_ITO). As a result, its optical property changes dramatically between dielectric-like and metal-like [12, 13]. Since ITO can behave as a highly-doped n-type semiconductor, its N_ITO can be electrically changed through mechanisms such as accumulation or depletion in a MOS capacitor. In order to form the MOS capacitor and also to enhance the overlap between the optical mode and the thin active ITO layer, the ITO layer together with a gate oxide layer is usually sandwiched between two Si layers to form a slot waveguide [14], or a Si and a metal layer to form a metal-dielectric-Si hybrid plasmonic waveguide (HPW) [15], or two metal layers to form a metal-dielectric-metal (MDM) plasmonic waveguide [16–18]. The first two configurations can be easily integrated with conventional Si waveguides with high coupling efficiency because Si is utilized as both the waveguide material and the electrode. However, the Si layer needs to be highly doped and a rib waveguide structure is required for serving as the electrode. Moreover, it limits the modulator on the single-crystal Si layer. The third configuration can be integrated with any kind of waveguide in principle. However, it usually has a large insertion loss because the MDM waveguide has large propagation loss and also large coupling loss to the dielectric waveguide when the sandwiched dielectric layer is very thin. Moreover, these three configurations work only for one polarization mode whose dominate electric field is perpendicular to the ITO/Si or ITO/metal interfaces.

In this paper, a new design of ITO-based plasmonic modulator is proposed, which is comprised of a Cu/ITO/HfO₂/TiN stack deposited on a stripe waveguide. The stack itself forms a MOS capacitor where ITO behaves as a semiconductor, HfO₂ serves as a high-κ gate dielectric, and Cu and TiN serve as electrodes. The top Cu layer is much thicker and the bottom TiN layer is much thinner than the light penetration depth in a metal (~26 nm), so that the stack together with the beneath stripe waveguide form a hybrid plasmonic waveguide. The stack can be deposited on either high-index-contrast waveguide such as Si or low-index-contrast waveguide such as Si₃N₄ to form an EA modulator for both transverse electric (TE) and transverse magnetic (TM) modes. Since the thin TiN, HfO₂, and ITO layers can be conformally deposited on the waveguide layer-by-layer using the well-developed atomic-layer-deposition (ALD) method at low temperature (e.g., less than 400°C) [21], the proposed modulator is CMOS backend-compatible.

2. Device structure

Figure 1 shows schematic of the proposed modulator integrated with a conventional stripe waveguide. The whole structure is embedded in a thick cladding SiO₂ layer. The thin TiN layer is much wider than the Cu/ITO/HfO₂ stack. One electrode is connected on Cu and the other is connected on the thin TiN layer. The dielectric core has width of W and height of h. The TiN, HfO₂, and ITO layers are first set to have thickness of 5, 5, and 3 nm, respectively. The influence of these thicknesses on the modulator’s performance will be discussed in Section 5. The refractive indices of Si, Si₃N₄, SiO₂, HfO₂, TiN [22], and Cu [23] at 1.55-μm wavelength are set to 3.45, 2.0, 1.44, 1.87, 0.9 + 4.18j, and 0.282 + 11.048j, respectively. The permittivity of ITO is defined by the Drude mode as $\epsilon ={\epsilon }_{\infty }-\frac{N_{ITO}{e}^2}{{\epsilon }_0{m}^{*}}\cdot \frac{1}{{\omega }^2+i\omega \Gamma }$, where ε_∞ is the high-frequency permittivity, Γ is the electron damping factor, ω is the angular frequency of light, N_ITO is the electron concentration, m* is the effective mass, and e and ε₀ are the electron charge and the permittivity of free space, respectively. We set ε_∞ = 3.9, Γ = 1.8 × 10¹⁴ s⁻¹, and m* = 0.35m_e (where m_e is the electron mass) for ITO [17]. Figure 2 plots the calculated real part and imaginary part of the ITO’s permittivity as a function of N_ITO at 1.54, 1.55, and 1.56-μm wavelengths. One sees that the real part of the permittivity crosses zero at a certain N_ITO, which is defined as the ENZ point. The ENZ point is 6.5 × 10²⁰ cm⁻³ at 1.55 μm and becomes smaller at longer wavelength. The ITO’s optical property is dielectric-like when its real part of permittivity is positive and is metal-like when its real part of permittivity is negative.

 

Fig. 1 (a) 3D view and (b) cross-sectional view of the proposed EA modulator integrated with a stripe dielectric waveguide.

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Fig. 2 The calculated real part and imaginary part of the ITO’s permittivity as a function of electron concentration in ITO, the real part of the permittivity crosses zero at a certain N_ITO, which is defined as the ENZ point.

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3. Electrical simulation

The stack forms a MOS capacitor where a voltage is applied between the TiN and Cu layers. For electrical simulation, the 3D structure shown in Fig. 1 can be simplified to the 2D structure shown in Fig. 3(a). A semiconductor device simulation software MEDICI [24] is used to calculate the 2D electron distribution N_ITO(x, y) in the thin ITO layer under different voltages. The electron concentration in the as-deposited ITO, which is defined as N₀, is typically in the range of ~10²⁰−10²¹ cm⁻³, depending on the deposition condition. Here, we assume N₀ = 3.5 × 10²⁰ cm⁻³. The mobility and work function of ITO are set to 50 cm²⋅V⁻¹⋅s⁻¹ and 0.5 eV, respectively, and the resistivity of TiN is set to ~300 μΩ⋅cm. Auger recombination, Shockley-Hall-Read recombination, surface recombination, Fermi-Dirac statics, and the modified local density approximation (MLDA) method are included. We find N_ITO(x, y) keeps almost unchanged along the x-coordinate (not shown here). Therefore, the 2D distribution N_ITO(x, y) can be further reduced to the 1D distribution N_ITO(y), as plotted in Fig. 3(b) under different voltages. One sees that electrons near the ITO/HfO₂ interface are depleted under the negative voltages and are accumulated under the positive voltages. The concentration of accumulated electrons maximizes at the ITO/HfO₂ interface and decreases to N₀ quickly with the distance from the interface increasing. As a first approximation, the distribution can be approximated to a step function, i.e., N_ITO(y) = N_AcL at (t_ITO – t_AcL) < y < t_ITO and N_ITO(y) = N₀ at 0 < y < (t_ITO – t_AcL), where t_ITO is the ITO thickness and t_AcL is the accumulation layer (AcL) thickness in the case of V > 0. In the case of V < 0, a depletion layer is formed, which is also represented as AcL for simplification. N_AcL can be roughly estimated as $N_{AcL}=N_0+\frac{{\epsilon }_0\cdot {\epsilon }_{HfO2}}{e\cdot t_{HfO2}\cdot t_{AcL}}(V-V_{FB})$, where ε_HfO2 ( = 25) is the dielectric constant of HfO₂, t_HfO2 is the HfO₂ thickness, and V_FB is the flat-band voltage. Based on Thomas-Fermi screening theory, t_AcL is ~1 nm [18]. But in [12], t_AcL is reported to be 5 ± 1 nm. Here we simply assume t_AcL = t_ITO = 3 nm. N_AcL is plotted in Fig. 3(c) as a function of V. One sees that the required voltage swing for N_ITO modification from 2 × 10²⁰ to 7 × 10²⁰ cm⁻³ is ~-2−4 V in the case of t_AcL = 3 nm. The influence of t_AcL and t_ITO on the modulator’s performance is discussed in Section 5.1.

 

Fig. 3 (a) A simplified 2D structure for electrical simulation. (b) 1D election concentration distribution along y coordinate in the 3-nm ITO layer under different voltages, obtained from the MEDICI simulation. The dashed lines represent the average concentrations in the 3-nm ITO layer. (c) Average N_ITO in the accumulation layer versus voltage in the case of t_AcL = 1, 2, or 3 nm.

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For the transient state simulation, the gate voltage is increased from −2 to 4 V with a ramp time of 10 fs. Figure 4 plots variation of the average N_ITO in the 3-nm-thick ITO layer with time. The sum of the rise time and the fall time (τ_s) for 10%-90% N_ITO variation is ~31 ps. The cut-off frequency estimated as $\raisebox{1ex}{$0.35$}\!\left/ \!\raisebox{-1ex}{${\tau }_s$}\right.$ is ~11 GHz. The device in accumulation has capacitance $C=A\cdot \frac{{\epsilon }_0\cdot {\epsilon }_{HfO2}}{t_{HfO2}}$, where A is the area. For a 1-μm-long modulator with a 400-nm × 340-nm Si core, A is ~1.1 μm² and C is ~48 fF. The resistance R mainly comes from the thin TiN layer. R = ~300 Ω when the lateral distance between the Cu/ITO/HfO₂ stack and the Al contact on the TiN layer is 0.5 μm, as shown in Fig. 3(a). Then, the cutoff frequency defined by $f_{\max }=\frac{1}{2\pi \times R\cdot C}$ is estimated to ~11 GHz, close to that read from Fig. 4. It indicates that the modulation speed is mainly limited by the RC delay. It is reported that the resistivity of TiN depends on the deposition conditions [25]. If the resistivity is improved to ~65 μΩ⋅cm, τ_s reduces to ~6.5 ps and the cutoff frequency increases to ~54 GHz, as shown by the red curve in Fig. 4. Other methods to reduce R include increasing the TiN layer thickness and/or shortening the lateral distance between the Cu/ITO/HfO₂ stack and the Al contact on the TiN layer. However, the insertion loss may be degraded, as will be discussed in Section 5.2. The switching energy per bit can be estimated as $E=\frac{1}{2}{C}_{on}\cdot V_{on}{}^2+\frac{1}{2}{C}_{off}\cdot V_{off}{}^2$ [26]. For the above 1-μm-long modulator, V_on = −2 V and V_off = 4 V, thus E = ~0.4 pJ/bit.

 

Fig. 4 The transient response of the electron concentration in the 3-nm-thick ITO layer under a gate voltage variation between −2 and 4 V. The rise time and fall time are defined as the time period for 10% to 90% N_ITO variation. The red curve represents the device with a reduced R, which can be achieved by reducing TiN resistivity, increasing TiN layer thickness, and/or shortening the lateral distance of two electrodes.

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4. Optical simulation

4.1 Integration with high-index-contrast waveguides

The modulator integrated with a high-index-contrast stripe waveguide such as Si is first investigated. The mode properties of Cu/3-nm-ITO/5-nm-HfO₂/5-nm-TiN/Si HPWs are calculated using the eigen-mode expansion (EME) method [27]. The HPW may contain many modes, depending on the size of the Si core. Among them two fundamental plasmonic modes can be distinguished: one is the quasi-TE mode whose dominate electric field component is along the x axis (E_x) and the other is the quasi-TM mode whose dominate electric field component is along the y axis (E_y). Figure 5 plots propagation loss (α), its differentiation (dα/dN_ITO), real part of the effective mode index (n_eff), and ratio of electric intensity in the ITO layer (which is defined as the electric field confinement factor) of these two fundamental plasmonic modes as a function of N_ITO for HPWs with different Si core sizes. One sees that the propagation loss and the ratio of electric field in the ITO layer increase with N_ITO increasing, reach maximum at a certain N_ITO, and then decrease with N_ITO further increasing. N_ITO for the maximum ratio of electric intensity in the ITO layer is very near the ENZ point (which is indicated by the dash lines in the figure), whereas N_ITO for the maximum α is slightly larger the ENZ point. Meanwhile, n_eff reaches minimum near the ENZ point and increases quickly with N_ITO further increasing. The value of this certain N_ITO is almost independent on the Si core size and the polarization. For EA application, the condition when the maximum α is reached can be defined as the “OFF”-state, and the condition when α is much smaller can be defined as the “ON”-state. Here we assume N_ITO = 7 × 10²⁰ cm⁻³ for the “OFF”-state whereas N_ITO for the “ON”-state can be either >> 7 × 10²⁰ cm⁻³ or << 7 × 10²⁰ cm⁻³. Accordingly, the modulator works on either the accumulation mode, i.e., varying N_ITO from << 7 × 10²⁰ cm⁻³ to 7 × 10²⁰ cm⁻³, or the depletion mode, i.e., varying N_ITO from >> 7 × 10²⁰ cm⁻³ to 7 × 10²⁰ cm⁻³. From Fig. 5, one sees that the absolute value of dα/dN_ITO in the smaller N_ITO side is slightly larger than that in the larger N_ITO side. More importantly, α at (7 × 10²⁰ cm⁻³ − ΔN_ITO) is slightly smaller than α at (7 × 10²⁰ cm⁻³ + ΔN_ITO), where ΔN_ITO is the voltage induced modification of N_ITO. It indicates that the accumulation mode is more effective and also has smaller insertion loss than the depletion mode. Here we simply assume N_ITO = 2 × 10²⁰ cm⁻³ for the “ON”-state.

 

Fig. 5 The mode properties, i.e., the propagation loss α, the α differentiation dα/dN_ITO, the real part of the effective mode index n_eff, and the ratio of electric field intensity in the ITO layer, of the Cu/3-nm-ITO/5-nm-HfO₂/5-nm-TiN/Si HPWs versus the electron concentration N_ITO in the 3-nm ITO layer for (a) quasi-TE mode and (b) quasi-TM mode. The dash lines represent the ENZ point.

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To understand the basis for this huge variation in the HPW’s optical property induced by N_ITO variation, 2D distributions of the dominant electric field component (i.e., E_x for the TE mode and E_y for the TM mode) are depicted in Figs. 6(a)–6(d) for a HPW with 400-nm × 340-nm Si core at the “ON” and “OFF” states. One sees E_x of the TE mode is confined at the two sidewalls of the Si core and E_y of the TM mode is confined at the top of the Si core. This is because the plasmonic mode has its dominant electric field perpendicular to the metal/dielectric interface and the electric field intensity in a thin layer is inversely proportional to its absolute permittivity value due to the continuity of electric displacement normal to the interfaces. For both TE and TM modes, the electric field in the Si core at the “OFF”-state is much weaker than that at the “ON”-state. To see the electric field distributions more clearly, Fig. 6(e) plots normalized E_x taken along the a-a’ lines and Fig. 6(f) plots normalized E_y taken along the b-b’ lines, respectively. The corresponding electric field distribution in the 400-nm × 300-nm Si stripe waveguide is also shown for comparison. At the “ON”-state, ITO has positive real part of ε_ITO and its |ε_ITO| (2.7) is close to that of HfO₂ (3.5), thus it plays a similar role as the dielectric HfO₂. As a result, the HPW is similar to the previously reported Cu/insulator/Si/insulator/Cu waveguide for the TE mode [28] or the Cu/insulator/Si waveguide for the TM mode [29], which has a relatively small α. Here, the insulator layer is the sum of the ITO layer and the HfO₂ layer. The thin TiN layer plays a minor role on the HPW’s optical property because the electric field intensity in the TiN layer is very small. With N_ITO increasing, |ε_ITO| decreases and the imaginary part of ε_ITO increases, thus both the electric field intensity in the ITO layer and α of HPW increase. At the “OFF”-state, ITO has ε_ITO of −0.3 + 0.62j, the electric field in the ITO layer is dramatically enhanced due to its small |ε_ITO| of 0.69. As a result, the HPW has very large α. With N_ITO further increasing, |ε_ITO| increases again, making both the electric field intensity in the ITO layer and α of HPW decrease. The property of HPW approaches again to that of the Cu/insulator/Si/ insulator/Cu (for the TE mode) or Cu/insulator/Si waveguide (for the TM mode). Here, the insulator layer is only the HfO₂ layer and the thin ITO layer behaves as the thin TiN layer.

 

Fig. 6 2D electric field distribution in the Cu/3-nm-ITO/5-nm-HfO₂/5-nm-TiN/400-nm × 340-nm-Si: (a) TE mode, E_x at “ON”-state, (b) TM mode, E_y at “ON”-state, (c) TE mode, E_x at “OFF”-state, and (d) TM mode, E_y at “OFF”-state. Normalized 1D distributions near the ITO interface: (e) along the a-a’ line for the TE mode and (f) along the b-b’ line for the TM mode, the inset are the distributions in the whole structure as well as the distributions in the 400-nm × 340-nm Si waveguide.

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Although N_ITO for the maximum α is almost independent on the Si core size, α at the “ON”-state (α_on) and “OFF”- state (α_off) depend on the Si core size. To reveal the influence of the Si core size on the modulator’s performance, a figure of merit defined as $FoM=\frac{{\alpha }_{off}-{\alpha }_{on}}{{\alpha }_{on}}$ is plotted in Fig. 7 as a function of the Si core’s size, which reflects a tradeoff between the modulation depth and the insertion loss. For the TE mode, FoM depends on W weakly since α_off increases approximately FoM-times larger than α_on with W decreasing, whereas FoM increases with h increasing since α_on decreases while α_off keeps almost the same with h increasing. This is because with h increasing the effect of the top stack layers becomes smaller and the HPW approaches to the standard horizontal Cu/dielectric/Cu structure. For the TM mode, FoM depends on h weakly when h is larger than ~220 nm and FoM increases with W increasing. This is because with W increasing the effect of the sidewall stack layers becomes smaller and the HPW approaches to the standard vertical Cu/insulator/Si/insulator/Si structure. If h is too small, the fundamental TE mode is difficult to be excited, and if W is too small, the fundamental TM mode is difficult to be excited. Instead, modes whose electric field is not confined in the Cu/dielectric interface may be excited. One of such modes is shown by the dashed curves in Fig. 5(b) for example. The propagation loss of this mode depends on N_ITO weakly, thus it does not contribute to the EA modulation. It indicates that a larger Si core is benefit for our EA modulator, in contrast to the previously reported Cu/insulator/Si/insulator/ Si or Cu/insulator/Si waveguide where a small Si core is preferred to confine the optical mode tightly. Therefore, the Si core of the EA modulator can be set to be the same as that of the input/output Si waveguides. Here we set W = 400 nm and h = 340 nm, which is typical for a single-mode Si stripe waveguide.

 

Fig. 7 FoM of HPWs with different Si core sizes for (a) quasi-TE mode and (b) quasi-TE mode.

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The 3D finite-difference time-domain (FDTD) method [27] is used to simulate a 1-μm-long EA modulator inserted in the 400-nm × 340-nm Si stripe waveguide. A 1.55-μm TE or TM light is launched into the left Si waveguide, propagating through the modulator, and then being monitored in the right Si waveguide. Figure 8(a) shows the absolute value of Poynting vector along the Y-cut at the center of the Si waveguide under the TE excitation at “ON” and “OFF”-states. The output power is 51% (−2.9 dB) at the “ON”-state and is 0.53% (−22.8 dB) at the “OFF”-state, indicating that the modulator has insertion loss of 2.9 dB and modulation depth of 19.9 dB. The mode profiles (i.e., the E_x distributions) in the input Si waveguide, the middle of the modulator, and the output waveguide at the “ON”-state are depicted in Fig. 8(b). The output light keeps the same TE polarization as the input light. The mode profile in the modulator shows a clear E_x enhancement in the ITO/HfO₂ layer at both sides, indicating the excitation of the plasmonic TE mode. However, the E_x profile differs slightly from that shown in Fig. 6(a) probably because of excitation of other modes besides the fundamental TE mode in the modulator. At the “OFF”-state, the plasmonic mode excited in the modulator is quickly attenuated.

 

Fig. 8 (a) The absolute value of Poynting vector along the Y-cut at the center of the Si waveguide under the TE excitation at the “OFF” and “ON” states, (b) E_x distributions in the input Si waveguide, the middle of modulator, and the output Si waveguide, (c) The absolute value of Poynting vector along the X-cut at the center of the Si waveguide under the TM excitation at the “OFF” and “ON” states, (d) E_y distributions in the input Si waveguide, the middle of modulator, and the output Si waveguide.

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The modulator under the TM excitation exhibits similar property. Figure 8(c) shows absolute value of Poynting vector along the X-cut at the center of the Si waveguide at “ON” and “OFF”-states. The output power is 48% (−3.2 dB) at the “ON”-state and is 1.5% (−18.4 dB) at the “OFF”-state, corresponding to insertion loss of 3.2 dB and modulation depth of 15.2 dB. Figure 8(d) shows mode profiles (i.e., the E_y distributions) in the input Si waveguide, the middle of the modulator, and the output waveguide at the “ON”-state. The output light keeps the same TM polarization as the input light. Again, the mode profile in the modulator differs slightly from that shown in Fig. 6(b) probably due to the excitation of other modes besides the fundamental plasmonic TM mode.

The transmission powers through the EA modulators with different lengths (L) at the “ON” and “OFF”-states are plotted in Fig. 9. The transmission at the “ON”-state, which is defined as the insertion loss, increases with L increasing. From linearly fitting, the propagation loss is extracted to ~1.9 (~1.3) dB/μm for the TE (TM) mode, close to that obtained from the EME calculation (Fig. 5). The coupling loss between the modulator and the Si waveguide is extracted to be ~0.8 (~1.1) dB/fact for the TE (TM) mode, which is determined by the mode-index difference and the mode overlap between the modulator and the input/out waveguide. The modulator also shows a weak Fabry-Perot resonance due to weak reflection at the waveguide/modulator facets, which deviates the insertion loss from the exactly linear dependence on L. At the “OFF”-state, the output power decreases quickly with L increasing and then depends on L weakly with L further increasing, which may be attributed to the excitation of low-loss modes besides the fundamental TE/TM plasmonic mode in the modulator, as observed in Figs. 8(b) and 8(d). As a result, the modulator has large modulation depth of ~15 dB/μm at the small L region while the modulation depth maximizes when L becomes longer. For the TE mode, the maximum modulation depth is ~32 dB when L ≥ ~2 μm, and for the TM mode, the maximum modulation depth is ~15.2 dB when L ≥ ~1 μm.

 

Fig. 9 Transmitted powers of an EA modulator inserted in a 400-nm × 340-nm Si stripe waveguide at the “ON” and “OFF”-states as a function of the modulator’s length. The EA modulator has the same dimension of Si core as the input/output Si waveguide.

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Large modulation depth is also observed for other TCO-based EA modulators reported in literature. For example, a vertical Si/SiO₂/TCO/Si EA modulator reported in [14] exhibits modulation depth of 3 dB when L = 0.25 μm. However, the vertical Au/SiO₂/ITO/Si EA modulator reported in [15] has a relatively low modulation depth of ~1 dB/μm. The difference can be attributed to the variation range of the TCO property between the “ON” and “OFF” states. In both ours and [14], the TOC property is changed through the ENZ point between the “ON” and “OFF” states, whereas in [15], the TCO property at the “OFF”-state is still far from the ENZ point. Form Fig. 5, one sees that a large dα/dN_ITO is obtained only near the ENZ point.

4.2 Integration with low-index-contrast waveguides

As the above-mentioned, the Cu/ITO/HfO₂/TiN stack can be deposited on a low-index-contrast waveguide such as Si₃N₄ to form an EA modulator. Passive Cu-Si₃N₄-Cu or Cu-SiO₂-Si₃N₄-SiO₂-Cu plasmonic waveguide components for CMOS backend integration has been demonstrated [30], but Si₃N₄ waveguide-based active devices are missing. The optical properties of Cu/3-nm-ITO/5-nm-HfO₂/5-nm-TiN/Si₃N₄ HPWs are shown in Fig. 10 as a function of N_ITO. Similar to the Si-core counterparts, the propagation loss and the ratio of electric field intensity in the 3-nm ITO layer increases with N_ITO increasing, reaches maximum near the ENZ point, and then decreases with N_ITO further increasing. Meanwhile, n_eff shows large variation near the ENZ point. N_ITO for the maximum α and that for the maximum ratio of electric field in the ITO layer are similar to the Si-core counterparts. Therefore, we still define “ON” state at N_ITO = 2 × 10²⁰ cm⁻³ and “OFF”-state at N_ITO = 7 × 10²⁰ cm⁻³.

 

Fig. 10 The mode properties (i.e., the propagation loss α, the real part of the effective mode index n_eff, and the ratio of electric field intensity in the ITO layer) of the Cu/3-nm-ITO/5-nm-HfO₂/5-nm-TiN/Si₃N₄ HPWs as a function of average electron concentration N_ITO in the 3-nm ITO layer for (a) quasi-TE mode and (b) quasi-TM mode. The dash lines represent the ENZ point.

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However, α_off of the Si₃N₄-based HPWs is much smaller than that of the Si-based HPWs because of the low index contrast of Si₃N₄/SiO₂. For the TE mode, α_off is 3.3 dB/μm for the 800-nm × 600-nm Si₃N₄ core HPW and is 5.1 dB/μm for the 400-nm × 600-nm Si₃N₄ core HPW. Thus, a narrower Si₃N₄ core is preferred to reach a larger modulation depth for the TE mode. For the TM mode, however, the Si₃N₄ core is required to be wide enough to excite the fundamental plasmonic TM mode. Otherwise, modes other than the fundamental plasmonic TM mode may be excited, as shown by the dashed curves in Fig. 10(b). It indicates a wider Si₃N₄ core is preferred for the TM mode. Here, the input/output Si₃N₄ stripe waveguide is set to W = 800 nm and h = 600 nm, which is typical for a single-mode Si₃N₄ stripe waveguide. We design the modular for the TE mode has the Si₃N₄ core of 400-nm × 600-nm, inserted in the 800-nm × 600-nm Si₃N₄ stripe waveguide through two 1-μm-long tapered couplers, as shown in Fig. 11(a). The tapered coupler has the same Cu/ITO/HfO₂/TiN stack as the main body of the modulator, thus they can be regarded as a part of the modulator. For the TM mode, we design the modulator has the same size Si₃N₄ core of 800-nm × 600-nm as the input/output Si₃N₄ waveguide.

 

Fig. 11 (a) The absolute value of Poynting vector along the Y-cut at the center of the Si₃N₄ waveguide under the TE excitation at the “OFF” and “ON” states, the modulator has a 400-nm × 600-nm Si₃N₄ core inserted in the 800-nm × 600-nm stripe Si₃N₄ waveguide through 1-μm-long tapered couplers. (b) E_x distributions in the input Si₃N₄ waveguide, the middle of modulator, and the output Si₃N₄ waveguide, (c) The absolute value of Poynting vector along the X-cut at the center of the Si₃N₄ waveguide under the TM excitation at the “OFF” and “ON” states, the modulator has the same 800-nm × 600-nm Si₃N₄ core as the input/output Si₃N₄ stripe waveguide. (d) E_y distributions in the input Si₃N₄ waveguide, the middle of modulator, and the output Si₃N₄ waveguide.

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3D FDTD simulation results for such 3-μm-long Si₃N₄ EA modulators are shown in Fig. 11. At the “ON”-state, the output power is −5.1 (−3.7) for the TE (TM) mode, and at the “OFF”-state, the output power is −13.0 (−18.5) dB for the TE (TM) mode. The mode profiles in the input Si₃N₄ waveguide, the middle of the modulator, and the output S₃N₄ waveguide at the “ON”-state are shown in Figs. 11(b) and 11(d) for the TE and TM modes, respectively. Similar to the Si-core counterpart, the output light keeps the same polarization as the input light for both TE and TM modes.

Figure 12 shows 3D FDTD simulation results for the Si₃N₄ EA modulators whose top views are shown in the inset schematically. The transmission at the “ON”-state decreases with L increasing. From linearly fitting, the propagation loss is extracted to 0.77 (0.32) dB/μm for the TE (TM) mode, close to that obtained from the EME calculation (Fig. 10). The coupling loss between the modulator and the Si₃N₄ waveguide is extracted to 1.5 (1.2) dB/facet for the TE (TM). At the “OFF”-state, the output power decreases quickly with L increasing first and then depends on L weakly with L further increasing, which can be attributed to the excitation of modes other than the fundamental plasmonic mode, as observed in Figs. 11(b) and 11(d) for the TE and TM modes, respectively. One sees from Fig. 12 that the optimal length for the TE modulator is ~4 μm (including two 1-μm-long coupler and 2-μm-long main body), which provides insertion loss of 6.3 dB and modulation depth of 16.5 dB, and the optimal length for the TM modulator is ~3 μm, which provides insertion loss of 3.7 dB and modulation depth of 14.8 dB. As compared with the Si counterpart, the Si₃N₄ modulator has poor performance in the viewpoint of the insertion loss, modulation depth, footprint, and the energy consumption (since the energy ∝ L), while, it has similar speed as the Si counterpart (since the speed is limited by the RC delay and C ∝ L, R ∝ 1/L). Nevertheless, our design provides an approach, for the first time to our best knowledge, to directly modulate light propagating along the Si₃N₄ waveguide.

 

Fig. 12 Transmitted powers of Si₃N₄ EA modulators inserted in the 800-nm × 600-nm Si₃N₄ stripe waveguide at the “ON” and “OFF”-states as a function of the modulator’s length. The TE modulator has 400-nm × 600-nm Si₃N₄ core and two 1-μm-long tapered couplers, and the TM modulator has 800-nm × 600-nm Si₃N₄ core, as shown schematically in the right.

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5. Influence of the stack’s parameters and processing tolerance

In the above analysis, the thicknesses and optical properties of the ITO, TiN and HfO₂ layers are set to certain values without optimization. The layers’ thicknesses can be precisely controlled by ALD and their properties may be slightly tuned by the deposition conditions. The influences of these parameters on the modulator’s performance are discussed in this section, which can be used to guide the optimization route for the layers’ deposition conditions. Moreover, the influence of possible misalignment during fabrication is also discussed. For simplification, the beneath dielectric core is fixed to the 400-nm × 340-nm Si core. The results are applicable for the Si₃N₄ core EA modulators.

5.1 The ITO layer

The most important parameter for our EA modulator is the ITO layer and the accumulation layer in this layer. In the above analysis, we simply assume t_AcL = t_ITO = 3 nm. Here we vary the ITO thickness from 3 to 10 nm and assume AcL has thickness of 1, 2, or 3 nm, respectively, i.e., N_ITO in the AcL region will be changed from 2 × 10²⁰ cm⁻³ at the “ON”-state to 7 × 10²⁰ cm⁻³ at the “OFF”-state while N_ITO out the AcL region keeps 3.5 × 10²⁰ cm⁻³. Figure 13 plots α_on and (α_off – a_on) as a function of t_ITO with different t_AcL values. One sees that α_on increases slightly and (α_off – a_on) decreases significantly with t_ITO increasing. It indicates that increasing t_ITO will degrade both the insertion loss and the modulation depth, which can be attributed to the fact that the ITO layer out the AcL region does not contribute to the EA modulation. Due to the same reason, (α_off – a_on) depends on t_AcL more significantly. In the case of t_ITO = 3 nm, (α_off – a_on) decreases from ~22 dB/μm to ~7 dB/μm when t_AcL decreases from 3 nm to 1 nm. By increasing the modulator length from ~1 μm (in the case of t_AcL = 3 nm) to ~3 μm (in the case of t_AcL = 1 nm), the similar modulation depth can be obtained, however, at a price of increasing the insertion loss from ~3.0 dB to ~7.4 dB. But, the required voltage swing is reduced to ~-0.6–1.2 V if t_AcL = 1 nm, as read from Fig. 3(c). As a result, the switching energy per bit is reduced to ~0.1 pJ/bit. On the other hand, the RC-limited modulation speed keeps similar since C ∝ L and R ∝ 1/L.

 

Fig. 13 (a) α_on and (b) the difference of α_off and α_on of the Cu/ITO/5-nm-HfO₂/5-nm-TiN/400-nm × 340-nm-Si HPWs at the “ON” and “OFF”-states as a function of t_ITO by assuming the AcL thickness t_AcL of 1, 2, or 3 nm, respectively. N_ITO inside AcL is 2 × 10²⁰ cm⁻³ at the “ON”-state and 7 × 10²⁰ cm⁻³ at “OFF”-state whereas N_ITO outside AcL is 3.5 × 10²⁰ cm⁻³.

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Other TCOs such as ZnO:Al can also be used as the active material. Their permittivities also obey the Drude model but having different values of ε_∞, Γ, and N₀ [31]. For example, ZnO:Al has ε_∞ of 3.5 and Γ of 2.3 × 10¹⁴ s⁻¹ [32]. Here we still assume t_ITO = t_AcL = 3 nm and N_ITO at “ON”-state = 2 × 10²⁰ cm⁻³ while the values of ε_∞ and Γ are changed to investigate their effect on the modulator’s performance. In one case, ε_∞ varies from 3.1 to 4.1 while keeping Γ = 1.8 × 10¹⁴ s⁻¹. In the other case, Γ varies from 1.2 × 10¹⁴ s⁻¹ to 2.6 × 10¹⁴ s⁻¹ while keeping ε_∞ = 3.9. The simulation results are plotted in Fig. 14. One sees from Fig. 14(a) that N_ITO for the maximum α_off (i.e., the required N_ITO for the “OFF”-state) decreases with ε_∞ decreasing. This is because the ENZ point decreases with ε_∞ decreasing according to the Drude mode. The reduction of the required N_ITO for the “OFF”-state can reduce the operating voltage, thus reduce the consumption energy per bit. Meanwhile, both α_on and (α_off – α_on) increase slightly with ε_∞ decreasing, thus the modulator length can be slightly shortened to keep certain insertion loss and the modulation depth. For comparison, Si has large ε_∞ of ~11.7. Its ENZ point is ~1.2 × 10²¹ cm⁻², much larger than that for ITO (~6.5 × 10²⁰ cm⁻²). As a result, a large voltage is required to reach the sufficient modulation depth for the Si-based plasmonic modulator [10]. It indicates that Si is not a good active material for the plasmonic EA modulator due to its large ε_∞ value. On the other hand, Fig. 14(b) shows that the variation of Γ has no influence on N_ITO for the maximum α, whereas α_on decreases and (α_off – α_on) increases with Γ decreasing, indicating that both the insertion loss and the modulation depth are improved with Γ decreasing. Overall, we can conclude that a TCO material for the EA modulator requires its ε_∞ and Γ values as smaller as better. The small ε_∞ value is more critical because it determines the required ΔN_ITO (i.e., the required voltage swing) for modulation between “ON” and “OFF” states.

 

Fig. 14 α_on (at N_ITO = 2 × 10²⁰ cm⁻³), α_on – α_off, and N_ITO for the maximum propagation loss of the Cu/ITO/5-nm-HfO₂/5-nm-TiN/400-nm × 340-nm-Si HPWs as a function of ε_∞ and Γ of ITO: (a) ε_∞ varies from 3.1 to 4.1 while Γ = 1.8 × 10¹⁴ s⁻¹ and (b) Γ varies from 1.2 to 2.6 while ${\epsilon }_{\infty }$ = 3.9.

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5.2 The TiN layer

The difference between our modulator and that reported in [15] is that our modulator has a thin TiN layer to serve as the bottom electrode. Figure 15(a) plots α_on, (α_off – α_on) and FoM of Cu/3-nm-ITO/5-nm-HfO₂/TiN/Si HPWs as a function of t_TiN. Although both α_on and (α_off – α_on) increase with t_TiN increasing, FoM decreases significantly with t_TiN increasing. It indicates that t_TiN is as thinner as better in the viewpoint of the insertion loss. On the other hand, t_TiN is as thicker as better in the viewpoint of the RC-limited modulation speed, as observed from Fig. 4. The insertion loss is contributed by the propagation loss ( = α_on⋅L, where L is the modulator length) and the coupling loss between the modulator and the input/output waveguides. The coupling loss (including two facets) is ~1.6 (~2.2) dB for the TE (TM) mode and depends on t_TiN weakly (not shown here). To balance the insertion loss and the resistance, an optimal t_TiN may be set when the propagation loss equals the coupling loss because for the TiN layer thinner than this optimal value, the insertion loss depends on t_TiN weakly as the coupling loss dominates. The optimal t_TiN is ~5 nm for our 1-μm-long Si EA modulator, as read from Fig. 15(a). A method to reduce the resistance (hence increase the modulation speed) without degrading the insertion loss is to improve the mobility of the TiN layer, which may be achievable by optimization of the TiN deposition condition. Another method is to reduce the lateral distance between the Al contact on the TiN layer and the Cu/ITO/HfO₂ stack. However, it may increase the fabrication difficulty.

 

Fig. 15 The influence of the thin TiN layer on the modulator’s performance: (a) TiN has permittivity of −16.66 + 7.52j while its thickness ranges from 0 to 10 nm, (b) TiN has thickness of 5 nm while different permittivity values.

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The values of TiN permittivity reported in literature are diverse, for example, −16.66 + 7.52j in [22], −83.3 + 21.3j in [20], and −20 + 21j in [31]. We name them as TiN-1, TiN-2, and TiN-3, respectively. Moreover, we assume TiN-4 having the same permittivity as Ag (−86.64 + 8.74j). Figure 15(b) shows α_on and (α_off – α_on) of HPWs with the above four kinds of TiN layers. One sees that the larger |ε_TiN| (e.g. the better plasmonic material) results in a slightly smaller α_on. However, the dependence of α_on and (α_off – α_on) on ε_TiN is relatively weak. Therefore, the optimization for the TiN layer can be focused on its conductivity rather than its permittivity.

5.3 The HfO₂ layer

For conventional MOS transistors, the gate dielectric is preferred to have high dielectric constant and thin thickness to reduce the operating voltage. The influence of the HfO₂ layer on the optical properties of our EA modulator is plotted in Fig. 16. In one case t_HfO2 varies from 1 to 11 nm while its refractive index n_HfO2 keeps 1.87. In the other case, n_HfO2 varies from 1.44 to 2.4 while t_HfO2 keeps 5 nm. One sees that both α_on and (α_off – α_on) increase with t_HfO2 decreasing or with n_HfO2 increasing. This is because the optical power contained in the HfO₂ layer, which does not contribute to the modulation, decreases with t_HfO2 decreasing or with n_HfO2 increasing. For the TE mode, FoM is almost independent on t_HfO2 and n_HfO2, whereas for the TM mode, FoM decreases slightly with t_HfO2 decreasing or with n_HfO2 increasing. It indicates that the influence of the HfO₂ layer on the modulator’s optical property is weak. Therefore, the optimization of the HfO₂ layer can be focused on its electrical property.

 

Fig. 16 The influence of the HfO₂ layer on the modulator’s performance: (a) HfO₂ has refractive index of 1.87 while its thickness ranges from 1 to 12 nm. (b) The gate oxide has thickness of 5 nm while its refractive index ranges from 1.44 to 2.4.

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5.4. Fabrication tolerances

The proposed modulator can be fabricated using the standard CMOS backend technology, somewhat similar to that for the Si-based plasmonic modulators except ALD of the ultrathin layers [28–30]. After the Si (or Si₃N₄) core formation, a thin TiN layer is deposited and patterned. Then, a thick SiO₂ layer is deposited and a window is opened to define the plasmonic area. HfO₂, ITO, and Cu are deposited sequentially, followed by chemical mechanical polishing (CMP) to remove the Cu/ITO/HfO₂ stack outside the window. In this fabrication flow, a possible misalignment (ΔL) may exist between the TiN layer and the Cu/ITO/HfO₂ stack, as shown in Fig. 17(a) schematically. The influence of such a misalignment is studied using the 3D FDTD method and the results are plotted in Fig. 17(b). One sees that both the insertion loss and the modulation depth depend on ΔL weakly. It indicates the device has large processing tolerance. The insertion loss even becomes slightly smaller when ΔL is negative. Therefore, the length of the TiN layer can be designed to be slightly smaller than that of the SiO₂ window in which the Cu/ITO/HfO₂ stack is filled.

 

Fig. 17 (a) Schematic top view of the modulator, showing a possible misalignment of ΔL between the TiN layer and the Cu/ITO/HfO₂ stack, (b) Insertion loss and modulation depth of the 1-μm-long Si EA modulator as a function of the misalignment ΔL.

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6. Conclusion

An EA modulator applicable for both TE and TM modes is proposed and investigated theoretically. The modulator offers various advantages including ultra-compact size (~1 μm²), high speed (>10 GHz), low energy consumption (~0.4 pJ/bit), broad optical bandwidth (originated from the nature of EA modulation), integration with all kinds of waveguides, large processing tolerance, and backend CMOS compatibility. It is almost ideal for seamless integration in the existing EPICs, especially the 3D integrated EPICs where multiple photonic layers are stacked above the electric layer. A key challenge to realize such an “ideal” modulator is optimization of the atomic layer deposited ITO layer. The electron concentration of the as-deposited ITO should be about half of the ENZ point (here, ~3.5 × 10²⁰ cm⁻³) and its ε_∞ and Γ values are as smaller as better.