High-Bandwidth Silicon Strip Waveguide-Based Electro-Optical Modulator in Series Push–Pull Configuration

Abstract

Silicon modulators operating at high speeds are crucial for contemporary optical communication systems; nevertheless, their performance is limited by the resistance–capacitance (RC) time constant. This research introduces a modulator based on a silicon strip waveguide, also known as a capacitively coupled silicon modulator (CC-Si), arranged in a series push–pull (SPP) configuration, which effectively addresses the constraints imposed by the RC time constant. The modulator demonstrates a consistent electro-optic (EO) response that extends to 68 GHz. Furthermore, it achieves a phase shift of 0.022 radians for a C-band optical wave when exposed to a 15 GHz radio frequency (RF) modulation signal with an amplitude of 2.45 V.

1. Introduction

Optical fiber communication presents considerable benefits compared to conventional techniques such as copper wiring, chiefly owing to its superior bandwidth, resistance to electromagnetic interference, and capacity to convey data over extended distances with reduced signal degradation. These attributes render it particularly suitable for scenarios that require rapid, dependable, and secure data transmission, encompassing high-speed internet services, telecommunications, and datacenter operations [1]. Optical modulators serve as essential elements in modern optical communication systems, facilitating the transformation of electrical message signals into optical signals by modulating the phase, intensity, or both of a monochromatic light, either in free space or within an integrated waveguide. Integrated modulators are designed to control light within integrated waveguides, functioning at reduced voltage levels and increased bandwidth while exhibiting significantly lower optical loss in comparison to traditional bulk or free space optical modulators. These devices are particularly essential for short-reach optical communications, such as those occurring within and between datacenters [2,3,4]. Silicon-on-insulator (SOI)-based integrated modulators are attractive for their CMOS (complementary metal-oxide semiconductor) compatibility, high bandwidth, and low insertion loss. Among the different types of silicon modulators, the depletion type silicon modulator is the most popular in the field of optical communications because of its high-speed operation. In most cases, the depletion type silicon modulator consists of a rib waveguide with a lightly doped lateral PN (P-type/N-Type) diode in the core region and metal electrodes placed on the highly doped silicon slabs on either side of the waveguide core region. For high-speed operation, such modulators are operated in the reverse bias regime [5]. The bandwidths of these modulators are limited to ∼40 GHz because of the RC time constant which comes from the highly doped silicon slabs [6]. Although the bandwidth of silicon modulators has been enhanced using travelling wave electrodes (TWE) [7], segmented TWEs [8], and slow light effects [9], very few approaches have been made to remove the RC time limitation. In our previous reports, we have demonstrated a novel approach to enhance the bandwidth by coupling the electrical signal to the waveguide core capacitively. We also demonstrated a silicon strip waveguide-based silicon modulator or a capacitively coupled silicon (CC-Si) Mach–Zehnder interferometer (MZI) modulator in single drive configuration [10,11].

In this paper, we present a CC-Si MZI modulator configured in a series push–pull (SPP) arrangement, which was fabricated in a multi-project wafer (MPW) run at the Advanced Micro Foundry (AMF). The EO characterization of the modulator reveals the capability to generate sidebands reaching frequencies of up to 68 GHz around a continuous wave (CW) optical carrier in the C-band, with a flat EO response observed across this frequency range. Notably, for an RF modulation signal of 15 GHz, a linear correlation was established between the phase shift of the C-band optical carrier and the amplitude of the RF modulation signal. Specifically, the phase shift of the optical signal was observed to increase from 0.014 radians to 0.022 radians in a linear manner as the RF signal amplitude was elevated from 1.35 V to 2.45 V.

2. Device Structure

The CC-Si modulator was fabricated on a standard SOI wafer with a 220 nm thick silicon device layer (${\mathrm{h}}_{\mathrm{Si}}$) on a 2 µm thick buried oxide (BOX) layer (${\mathrm{h}}_{\mathrm{BOX}}$) and 725 µm thick silicon substrate (${\mathrm{h}}_{\mathrm{Sub}}$). Figure 1a shows the cross-sectional view of the modulator in the SPP configuration. Each arm of the MZI consists of a 650 nm wide (${\mathrm{w}}_{\mathrm{WG}}$) silicon strip waveguide to ensure single mode operation for the fundamental transverse electric (TE) optical mode. The lightly doped PN junction is in the center of the waveguide. A highly P-doped (P++) silicon slab and a highly N-doped (N++) silicon slab with a thickness (${\mathrm{h}}_{\mathrm{Slab}}$) of 90 nm (${\mathrm{h}}_{\mathrm{Slab}}$) are placed 500 nm away from the P side and the N side of the waveguide, respectively. There are two aluminum metal layers (Mt1 and Mt2) used for DC (direct current) bias and RF transmission lines. There are two aluminum vias (Via1 and Via2) which establish electrical connections between the highly doped silicon slab layer and the Mt1 layers and between the Mt1 and the Mt2 layers, respectively. All layers are covered with a ∼3 µm (${\mathrm{h}}_{\mathrm{Clad}}$) silicon dioxide upper cladding. The bond pad opening layer exposes the Mt2 layer at the contact pad area for external DC and RF electrical connections. To enhance the electric field inside the waveguide, the Mt1 layer of the DC contact is extended above the strip waveguide and the Via1 layer of the signal and ground contacts are pushed away from the waveguide sufficiently to avoid electrical field confinement between two Mt1 layers. A Lumerical Device was used to perform electrostatic simulations by applying a different DC bias voltage, ${\mathrm{V}}_{\mathrm{DC}}$, between –3 V and −30 V while maintaining the signal terminal voltage, ${\mathrm{V}}_{\mathrm{sig}}$ = 0 V. For these simulations, we considered Mt1 layer thickness, ${\mathrm{h}}_{\mathrm{Mt}1}$ = 50 nm, Mt2 layer thickness, ${\mathrm{h}}_{\mathrm{Mt}2}$ = 100 nm, Via-1 layer thickness, ${\mathrm{h}}_{\mathrm{Via}1}$ = 750 nm, and Via-2 layer thickness, ${\mathrm{h}}_{\mathrm{Via}2}$ = 2 µm. We also considered the P, N, P++, and N++ doping concentrations to be ∼3.5 × 10¹⁷ cm⁻³, ∼5 × 10¹⁷ cm⁻³, ∼1.8 × 10²⁰ cm⁻³, and ∼8.7 × 10¹⁹ cm⁻³, respectively. Due to the absence of an ohmic contact between the PN diode and the electrodes, the variation in carrier concentrations surrounding the PN diode is influenced by the electric field present within the waveguide core. The capacitive reverse bias configuration of the PN diode facilitates the electric field in the waveguide core to further displace the electrons and holes apart in the depletion region. Figure 1b,c show the electron concentrations and Figure 1d,e show the hole concentrations in the waveguide region of the left arm of the MZI for the abovementioned ${\mathrm{V}}_{\mathrm{DC}}$, respectively. We notice a change in carrier concentrations when ${\mathrm{V}}_{\mathrm{DC}}$ is reduced from −3 V to −30 V, which seems quite small since the electrical field confinement within the waveguide core was very small. Figure 1f,g show the electron field distribution in the waveguide core and in the surrounding cladding region for the abovementioned ${\mathrm{V}}_{\mathrm{DC}}$, respectively. However, we obtain a change in effective refractive index, $\Delta {\mathrm{n}}_{\mathrm{eff}}$. An estimation of $\Delta {\mathrm{n}}_{\mathrm{eff}}$ (≈−1.23 × 10⁻⁴) has been calculated in [10,11] using Lumerical Mode Solver. In both the Lumerical Device and Mode Solver, we used perfectly matched layer (PML) boundary conditions, considering the cross-sectional area shown in Figure 1f,g. We use this change in effective index, combined with an asymmetric bias between the two signal and ground electrodes to produce the push–pull modulator. The RF modulation signal is applied between the signal and the ground contacts of the device. A negative DC bias is applied at the central electrical contact. For fast operation, the PN diode in both arms of the MZI must be at reverse bias all the time. Therefore, the magnitude of the DC bias voltage must be at least equal to the amplitude of the RF signal. This is how a differential push–pull operation is achieved by an MZI modulator in SPP configuration.

3. Experimental Demonstration

To demonstrate the EO response of the CC-Si MZI modulator in the SPP configuration, we built an experimental setup in Figure 1f. A high-power RF signal generator which can generate sinusoidal signal up to 70 GHz with +25 dBm power was used. The RF signals are applied between the signal and ground terminal of one end of the the MZI. A 67 GHz RF probe configured in a Ground–Signal (GS) arrangement was employed to deliver the RF signal. To mitigate signal reflection, a GS bond pad fabricated using the Mt2 layer was optimized to achieve a 50 Ω impedance at this end of the MZI. An out-of-chip 50 Ω termination load is employed to terminate the other end of the RF transmission line of the modulator, utilizing another 67 GHz RF probe in a GS configuration. A negative DC bias should be applied to the DC bias contact; however, the RF signal generator is very sensitive to the DC voltages and therefore, for the safety of the instrument, we avoid applying any DC bias. We use a tunable laser source (TLS) to generate a +9 dBm CW optical carrier at a 1550.31 nm wavelength, which is near the quadrature point of the MZI. The extinction ratio of the MZI around this carrier wavelength is around ∼37.4 dB and the estimated optical propagation loss of the active part of the MZI around this wavelength for different applied voltages has been reported in ref. [11]. The optical carrier is coupled to the chip using a grating coupler after passing through a polarization controller (PC). The grating coupler is derived from the process design kit (PDK) of AMF and has been optimized to maximize the transmission at a wavelength of 1550 nm, with an angle of incidence of 10°. The coupled optical carrier signal is split into two MZI arms using a 1 × 2 multimode interference (MMI) coupler. Afterward, phase modulation optical signals from both arms are combined using a 2 × 2 MMI coupler. These modulated optical signals are coupled out of the chip using two other grating couplers. One of the modulated signals is detected by a high-resolution optical spectrum analyzer (OSA). In this way, we can generate sidebands up to 68 GHz, which can be seen from Figure 2a. The frequency-dependent modulation indices, $\mathrm{m}\left({\mathrm{f}}_{\mathrm{m}}\right)$, are calculated from the carrier–sideband power ratio expressed by Equation (1) [12].

$${\mathrm{R}}_{1,0}={\displaystyle \frac{{\mathrm{J}}_1^2\left(\mathrm{m}\right)}{1+{\mathrm{J}}_0^2\left(\mathrm{m}\right)+2{\mathrm{J}}_0\left(\mathrm{m}\right)\cos \mathrm{\varphi }}}={\displaystyle \frac{\mathrm{I}\left({\mathrm{\omega }}_0+{\mathrm{\omega }}_{\mathrm{m}}\right)}{\mathrm{I}\left({\mathrm{\omega }}_0\right)}}$$

(1)

Here, ${\mathrm{\omega }}_0$ and ${\mathrm{\omega }}_{\mathrm{m}}$ (=$2\mathrm{\pi }{\mathrm{f}}_{\mathrm{m}}$) are the optical carrier frequency and the frequency of the modulation RF signals, respectively. ϕ is the constant phase difference between two arms of the unbalanced MZI. ${\mathrm{J}}_0$ and ${\mathrm{J}}_1$ are the Bessel functions of the first kind for orders 0 and 1, respectively. Carrier nulling is difficult to achieve in this case due to the distortions of the ${\cos }^2$ function of an unbalanced MZI CC-Si modulator and noise. To reduce the relevant uncertainties, the normalized transmission spectrum of the unbalanced MZI modulator is measured over a wider spectral range that includes the current operating optical carrier. In order to estimate the exact phase shift, ϕ, a fit of a model function of an unbalanced MZI modulator shown in Equation (2) is performed with the experimental data.

$${\mathrm{T}}_{\mathrm{UMZI}}(\mathrm{\omega })={\mathrm{A}}_0+{\mathrm{A}}_1{\cos }^2\left({\displaystyle \frac{1}{2}}\left({\mathrm{B}}_0+{\mathrm{B}}_1\left(\mathrm{\omega }-{\mathrm{\omega }}_{\mathrm{c}}\right)+{\mathrm{B}}_2{\left(\mathrm{\omega }-{\mathrm{\omega }}_{\mathrm{c}}\right)}^2\right)\right)$$

(2)

In Equation (2), ${\mathrm{B}}_0={\mathrm{\beta }}^{\left(0\right)}\Delta \mathrm{L}$, ${\mathrm{B}}_1={\mathrm{\beta }}^{\left(1\right)}\Delta \mathrm{L}$, and ${\mathrm{B}}_2={\displaystyle \frac{1}{2}}{\mathrm{\beta }}^{\left(2\right)}\Delta \mathrm{L}$, where $\Delta \mathrm{L}$ is the path length difference between the two arms of the MZI, and ${\mathrm{\beta }}^{\left(0\right)}$, ${\mathrm{\beta }}^{\left(1\right)}$ and ${\mathrm{\beta }}^{\left(2\right)}$ are the propagation constant, being the first and the second order derivatives of the propagation constant, respectively. ${\mathrm{\omega }}_{\mathrm{c}}$ is the center frequency of the frequency range of the unbalanced MZI spectrum. The fitting parameters ${\mathrm{A}}_0$, ${\mathrm{A}}_1$, ${\mathrm{B}}_0$, ${\mathrm{B}}_1$, and ${\mathrm{B}}_2$ are determined using the least-square fit method. The phase shift, ϕ, of an unbalanced CC-Si MZI modulator can be calculated from Equation (3).

$$\mathrm{\varphi }={\displaystyle \frac{1}{2}}\left({\mathrm{B}}_0+{\mathrm{B}}_1\left(\mathrm{\omega }-{\mathrm{\omega }}_{\mathrm{c}}\right)+{\mathrm{B}}_2{\left(\mathrm{\omega }-{\mathrm{\omega }}_{\mathrm{c}}\right)}^2\right)$$

(3)

After eliminating the effect of the grating couplers, the measured transmission spectrum is shown by the blue circles in Figure 2b. The fit to the measured data using Equation (2) is shown by the red line in Figure 2b and the operating optical carrier is pointed out with a green circle in Figure 2b. The phase shift value, ϕ, and the carrier to sideband ratio, ${\mathrm{R}}_{1,0}$, are used to calculate the $\mathrm{m}\left({\mathrm{f}}_{\mathrm{m}}\right)$ using Equation (1), shown as the blue line of Figure 2c. The signal generator can generate a power of +25 dBm for all frequencies. However, the losses of the RF probes and the RF cable are frequency-dependent. Hence, the RF power, which is actually applied at the modulator terminal, is microwave frequency-dependent. We measure the RF power for different frequencies using an RF power meter. The associated frequency-dependent peak voltages, $\mathrm{V}\left({\mathrm{f}}_{\mathrm{m}}\right)$, based on these RF power measurements, are plotted in the red line of Figure 2c. It is observed that the curve of $\mathrm{m}\left({\mathrm{f}}_{\mathrm{m}}\right)$ follows the curve of $\mathrm{V}\left({\mathrm{f}}_{\mathrm{m}}\right)$. Later, the $\mathrm{m}\left({\mathrm{f}}_{\mathrm{m}}\right)$ curve is normalized with respect to a frequency independent +2 dBm RF power, which is plotted in Figure 2d. A liner fit of the normalized $\mathrm{m}\left({\mathrm{f}}_{\mathrm{m}}\right)$ is also shown in Figure 2d, which shows that the the CC-Si MZI modulator has a very flat frequency response.

Followed by the EO measurement, we measure transmission spectra of different modulated optical signals for 15 GHz RF sinusoidal signals with different powers, i.e., different peak voltage, ${\mathrm{V}}_{\mathrm{m}}$. The measured transmission spectra are shown in Figure 2e. The laser operated at an elevated power level of +9 dBm, resulting in thermal drift at the carrier wavelength. Furthermore, the OSA has a resolution of 20 pm, equivalent to 1.25 GHz, when centered at a wavelength of 1550 nm, which constrains the precision of the peak power measurements for GHz-level sidebands. Consequently, sidebands corresponding to varying amplitudes of 15 GHz RF signals manifest at slightly distinct wavelengths. Before applying the 15 GHz RF signals, we measure the powers of different RF signals using an RF power meter. Thus, we determine the phase shift, ϕ$\left({\mathrm{V}}_{\mathrm{m}}\right)$ for 15 GHz RF-signal which is voltage dependent. Figure 2f shows the phase shifts for different RF powers, i.e., different ${\mathrm{V}}_{\mathrm{m}}$ of 15 GHz signals. We observe a linear relationship between ${\mathrm{V}}_{\mathrm{m}}$ and ϕ$\left({\mathrm{V}}_{\mathrm{m}}\right)$. ϕ increases from 0.014 radians to 0.022 radians almost linearly as the amplitude of the 15 GHz RF signal is raised from 1.35 V to 2.45 V. These devices are expected to have comparatively lower phase shifts, since we use silicon dioxide cladding with low dielectric constant which reduces the electrical field confinement within the waveguide region [10].

4. Conclusions

To summarize, we have demonstrated a CC-Si modulator which can enhance the bandwidth of silicon devices by eliminating the RC time limitation. Lumerical Device simulations were performed to show the working principle of the CC-Si modulator. We performed the EO measurement of a CC-Si MZI modulator in SPP configuration and observe a flat EO frequency response of up to 68 GHz which proves the broadband nature of this device. RF modulation signals of 15 GHz with different amplitudes were used to calculate the voltage-dependent phase shift of ϕ$\left({\mathrm{V}}_{\mathrm{m}}\right)$. We observed an almost linear relationship between the phase shift of a C-band optical carrier and the amplitude of the RF modulation signal. The phase shift of the optical signal increased from 0.014 radians to 0.022 radians almost linearly while the RF signal amplitude was elevated from 1.35 V to 2.45 V.

The EO response of the CC-Si modulator clearly shows that it will be flat beyond 68 GHz. We are currently limited by the RF power and the maximum frequency provided by the signal generator. The ${\mathrm{V}}_{\mathrm{\pi }}\mathrm{L}$ of this modulator is high due to the low dielectric constant silicon dioxide (${\mathrm{ϵ}}_{{\mathrm{SiO}}_2}$ = 3.9) cladding [13] around a comparatively higher dielectric constant silicon (${\mathrm{ϵ}}_{\mathrm{Si}}$ = 11.9) waveguide [14] which results in a greater electrical field drop outside of the waveguide core. This limitation can be improved by replacing the silicon dioxide cladding with a very high dielectric constant material like barium titanate which has been found effective in different platforms like a silicon–organic hybrid (SOH) platform [15,16,17] and a lithium niobate-on insulator (LNOI) platform [18,19,20]. However, the deposition of a high dielectric constant material is not a standard for existing silicon photonic foundries. But we are currently investigating this approach by doing back-end-of-line (BEOL) post-fabrication processes. Moreover, due to the resolution of the OSA, we chose a sideband at a comparatively higher frequency (15 GHz) of RF signal, where other differing factors such as impedance mismatch, microwave propagation loss, and velocity mismatch between the optical and the RF mode play a significant role. Thus, the voltage-dependent phase shift, ϕ$\left({\mathrm{V}}_{\mathrm{m}}\right)$, in such high frequency will be much lower compared to the phase shift values measured at kHz range frequencies. Also, for the safety of the signal generator, no DC bias is applied, which leads to higher chirping by generating positive $\Delta {\mathrm{n}}_{\mathrm{eff}}$ in both MZI arms. As a result, the differential phase shift between two arms is smaller than the phase shift with a negative DC bias. Thus, the absence of negative DC bias leads to lower phase shifts. Additionally, without any DC bias for the half-cycle of an RF modulation sinusoidal signal, the PN diode will be in forward bias, which can potentially limit the bandwidth of the device. Nevertheless, with progress in characterization and fabrication techniques, we believe that these challenges can be solved, which will enable the creation of high-performance devices.