Design of a 90 GHz SOI Fin Electro-Optic Modulator for High-Speed Applications

: Introducing high speed networks, such as the ﬁfth generation of mobile technology and related applications including the internet of things, creates a pressing demand for hardware infrastructure that provides su ﬃ cient bandwidth. Here, silicon-based microwave-photonics presents a solution that features easy and inexpensive fabrication through a mature platform that has long served the electronics industry. In this work, the design of an electro-optic modulator is proposed where the ‘ﬁn’ structure is adopted from the domain of electronics devices, with emphasis on the high speed of operation. The proposed modulator is customized to provide a bandwidth of 90 GHz with a small phase shifter length of 800 µ m and an optical insertion loss of 4 dB. With such a speed, this proposed modulator ﬁts high-speed applications such as modern tele-communications systems.


Introduction
Optical interconnects demonstrate core advantages over their traditional electrical counterparts in many aspects such as immunity to electromagnetic interference, high data transfer rates, and low losses [1,2]. Having integrated systems with such characteristics will be also very advantageous if the systems are complementary metal-oxide semiconductor (CMOS) compatible. Such compatibility adds compactness, low-cost and ease of fabrication to the previous list of advantages. This concept gave a big momentum for silicon photonics for almost three decades. Currently, with many components being mature enough [3][4][5][6][7][8][9][10][11][12], silicon photonics stands ready to serve in many speed-demanding applications, such as 5G networks [13], central processing unit (CPU)-memory interconnects [14] and radio-over-fiber (RoF) [15]. A key device in such applications is the electro-optic modulator where electrical data converts into optical data [16], before commencing its trip over low-loss optical fibers.
The main method to modulate laser in a silicon waveguide is the plasma dispersion effect which was quantitatively described by Soref about three decades ago [17]. This technique is the practical way to get around the small electro-optic coefficient of silicon. In this method, the modulating voltage manipulates the charge carrier concentration in doped silicon. The result is the variation of both parts of the effective refractive index, the real, n e , which is responsible for the mode phase shift and the imaginary, k, which is responsible for the optical power loss. Based on this idea, two families of modulators can be studied. The first family, which includes carrier-injection modulators, is the one that grabbed attention earlier. Here, electric current flows through the waveguide leading to an increase in the charge concentration, which decreases n e but increases k. Although this current flow results in a big change in n e and hence enables a relatively short phase shifter length, the speed is limited A cross section of the phase shifter is shown in Figure 1a. The shifter consists of a rectangular waveguide of silicon core and silicon dioxide cladding. The width of the core is W and its height is H. Three rectangular pieces of aluminum are placed around the core to form the electrodes. The top and right pieces are electrically connected to the modulating voltage while the left is grounded. The silica layer between the core and the right or left electrodes has a thickness denoted by y o . A silica layer of thickness z o separates the core from the top electrode.
The proposed modulator employs the Mach-Zender interferometer (MZI) structure where light propagates through two arms, as shown in Figure 1b. Each arm possesses a phase-shifter as the one just described. When the applied modulating voltage, V, is zero on both arms, the two modes in the MZI arms are in phase and the output power is high, P H . Applying a voltage difference to the arms, the output optical power is then low, P L . The extinction ratio, ER, in dB is given by ER = 10 log P H P L [40]. If the input optical power is P o , then the insertion loss, IL, in dB is given by IL = 10 log P o P H . One goal in such designs is to maximize ER and minimize IL. The voltage difference is applied to the arms in the form of positive voltage, V 1 , on one arm and negative voltage, V 2 , on the other. This technique is known as the push-pull technique [41] and is useful to decrease the voltage applied to an arm. See Figure 1b. The phase shifter length is denoted by L. If this length is enough to produce a π phase-shift between the two arms, then the length is called the 'effective length', denoted by L π . This length is calculated from L π = λ o 2∆n e , where λ o is the free-space wavelength of the light and ∆n e is the difference in the effective index, ∆n e , between the propagating modes in the two arms. The required voltage difference to induce this phase shift is denoted by V π . In such a case, ER is at its absolute maximum since P L is at its absolute minimum. The reason for why P L cannot go down to zero is that the two arms do not possess the same optical loss, since the optical loss due to plasma dispersion is function of the applied voltage, which inherently is not the same for the two arms. Hence, ER cannot be infinity. Still, due to small differences in the optical loss values in the two arms and also due to the short arm length, very high ER values can be achieved as will be discussed later. A trade-off exists, on the other hand, between the aforementioned parameters. The device size can be reduced, to enable higher fabrication density, lower IL, and lower C and hence higher f 3dB , at the expense of the phase shift between the arms, which results in a decrease in ER. technique is known as the push-pull technique [41] and is useful to decrease the voltage applied to an arm. See Figure 1b. The phase shifter length is denoted by . If this length is enough to produce a phase-shift between the two arms, then the length is called the 'effective length', denoted by .
This length is calculated from = , where is the free-space wavelength of the light and Δ is the difference in the effective index, Δ , between the propagating modes in the two arms. The required voltage difference to induce this phase shift is denoted by . In such a case, is at its absolute maximum since is at its absolute minimum. The reason for why cannot go down to zero is that the two arms do not possess the same optical loss, since the optical loss due to plasma dispersion is function of the applied voltage, which inherently is not the same for the two arms. Hence, cannot be infinity. Still, due to small differences in the optical loss values in the two arms and also due to the short arm length, very high values can be achieved as will be discussed later. A trade-off exists, on the other hand, between the aforementioned parameters. The device size can be reduced, to enable higher fabrication density, lower , and lower and hence higher , at the expense of the phase shift between the arms, which results in a decrease in .

Optimizing the Modulator Parameters
In this section, the dimensions of the waveguide cross section, the silica thickness and the core doping, are optimized in order to achieve the best performance of the modulator in terms of losses, speed and size. In this work, the mode profile and the effective index are found using the commercially available software, MODE, while the plasma dispersion is simulated using DEVICE, both from Lumerical [42]. The simulation settings are shown in Appendix A. Three waveguide cross sections are tested. The heights are taken as = 150 nm, 220 nm, and 300 nm with the corresponding width values = 600 nm, 450 nm, and 400 nm , respectively. Those dimensions ensure single mode operation at = 1.55 μm. The mode of interest in this work is the transverse electric field like (TE-like) mode which has its major electric field component parallel to the substrate. The electric field intensity, for the mode supported by each of the three different waveguides, is shown in Figure 2. In this design, acceptors are chosen for the doping, since holes have a stronger effect on the change of than electrons [17]. The doping concentration, , is varied from 1 × 10 cm to 3 × 10 cm .

Optimizing the Modulator Parameters
In this section, the dimensions of the waveguide cross section, the silica thickness and the core doping, are optimized in order to achieve the best performance of the modulator in terms of losses, speed and size. In this work, the mode profile and the effective index are found using the commercially available software, MODE, while the plasma dispersion is simulated using DEVICE, both from Lumerical [42]. The simulation settings are shown in Appendix A. Three waveguide cross sections are tested. The heights are taken as H = 150 nm, 220 nm, and 300 nm with the corresponding width values W = 600 nm, 450 nm, and 400 nm, respectively. Those dimensions ensure single mode operation at λ o = 1.55 µm. The mode of interest in this work is the transverse electric field like (TE-like) mode which has its major electric field component parallel to the substrate. The electric field intensity, for the mode supported by each of the three different waveguides, is shown in Figure 2. In this design, acceptors are chosen for the doping, since holes have a stronger effect on the change of n e than electrons [17]. The doping concentration, N A , is varied from 1 × 10 16  The insertion loss for this device comprises four mechanisms. Three loss mechanisms are related to the propagation through the waveguide. First, the free carrier absorption loss, which depends on and . Second, the optical absorption due to the overlap between the optical mode and the metallic electrodes. The total of the two losses is found through DEVICE and MODE simulations, in dB/cm, and is given the symbol . Third, the passive waveguide scattering losses, taken here as 1 dB/cm [43]. This loss is to be added to to give the total phase shifter loss, which is designated by , in dB/cm . The fourth loss mechanism is the insertion loss due to the two Y-junctions of the MZI, which is taken here as 0.3 dB for each junction, totalling 0.6 dB of optical losses for the MZI [44].
With all of the dimensions and the doping dose combinations, a selection criterion is necessary to pick the desired device. First, the results are filtered for the smallest at each doping concentration when = 0. This selection criterion simply picks the configurations with maximum silica thickness in the range of this study, = = 500 nm, because the overlap of optical mode with the electrodes is minimal. According to this criterion, the phase shifter loss, , when = , is plotted versus the doping concentration in Figure 3a. In Figure 3b, the corresponding effective length, , is plotted versus the doping concentration. The insertion loss for this device comprises four mechanisms. Three loss mechanisms are related to the propagation through the waveguide. First, the free carrier absorption loss, which depends on N A and V. Second, the optical absorption due to the overlap between the optical mode and the metallic electrodes. The total of the two losses is found through DEVICE and MODE simulations, in dB/cm, and is given the symbol α o . Third, the passive waveguide scattering losses, taken here as 1 dB/cm [43]. This loss is to be added to α o to give the total phase shifter loss, which is designated by α, in dB/cm . The fourth loss mechanism is the insertion loss due to the two Y-junctions of the MZI, which is taken here as 0.3 dB for each junction, totalling 0.6 dB of optical losses for the MZI [44].
With all of the dimensions and the doping dose combinations, a selection criterion is necessary to pick the desired device. First, the results are filtered for the smallest IL at each doping concentration when V = 0. This selection criterion simply picks the configurations with maximum silica thickness in the range of this study, y o = z o = 500 nm, because the overlap of optical mode with the electrodes is minimal. According to this criterion, the phase shifter loss, αL, when L = L π , is plotted versus the doping concentration in Figure 3a. In Figure 3b, the corresponding effective length, L π , is plotted versus the doping concentration.
The first remark here is that the waveguide with H = 300 nm, which has the largest cross-sectional area, is the one that shows the largest L π at all concentrations. This finding follows from the fact that a larger cross section means more charge resides inside the phase shifter. Hence, manipulating the charge density with the modulating voltage is less effective. This results in a smaller change of the effective index and consequently a longer L π . The insertion loss for this device comprises four mechanisms. Three loss mechanisms are related to the propagation through the waveguide. First, the free carrier absorption loss, which depends on and . Second, the optical absorption due to the overlap between the optical mode and the metallic electrodes. The total of the two losses is found through DEVICE and MODE simulations, in dB/cm, and is given the symbol . Third, the passive waveguide scattering losses, taken here as 1 dB/cm [43]. This loss is to be added to to give the total phase shifter loss, which is designated by , in dB/cm . The fourth loss mechanism is the insertion loss due to the two Y-junctions of the MZI, which is taken here as 0.3 dB for each junction, totalling 0.6 dB of optical losses for the MZI [44].
With all of the dimensions and the doping dose combinations, a selection criterion is necessary to pick the desired device. First, the results are filtered for the smallest at each doping concentration when = 0. This selection criterion simply picks the configurations with maximum silica thickness in the range of this study, = = 500 nm, because the overlap of optical mode with the electrodes is minimal. According to this criterion, the phase shifter loss, , when = , is plotted versus the doping concentration in Figure 3a. In Figure 3b, the corresponding effective length, , is plotted versus the doping concentration.
(a) The first remark here is that the waveguide with = 300 nm, which has the largest crosssectional area, is the one that shows the largest at all concentrations. This finding follows from the fact that a larger cross section means more charge resides inside the phase shifter. Hence, manipulating the charge density with the modulating voltage is less effective. This results in a smaller change of the effective index and consequently a longer .
The second remark is that the waveguide with the largest exhibits the lowest optical losses at low levels of doping concentrations, despite the previous finding. This can be explained by the small carrier absorption loss which allows the electrode absorption to be the dominant loss. Using MODE, the waveguide with = 300 nm has a confinement factor, defined as the ratio of the core power to the total mode power, Γ = 84%. This is the largest amongst the three and hence its mode has the least overlap with the electrodes at the same and . The waveguide with = 220 nm has Γ = 77% and the one with = 150 nm has Γ = 60% . However, as the doping dose increases, apparently, the carrier absorption loss becomes the dominant and hence the waveguide with = 300 nm becomes the most lossy.
Based on the previous discussion, the device that shows the lowest is found from Figure 3a This device is referred to as 'Modulator A' in the next discussion. Next, the selection criterion could be altered to target a higher speed of modulation, at the expense of the insertion loss. With closer electrodes at = 300 nm and = 500 nm and for = 150 nm, = 600 nm and = 2 × 10 cm we get = 1.6 mm, = 6.9 + 0.6 = 7.5 dB, = 26.7 dB = 40 Volt, = 0.044 , and = 44 GHz. This interesting case has its main device parameters shown in Figure 4. As the modulating voltage, , increases above zero, the holes deplete and therefore the effective index increases and the phase shifter loss decreases [17]. With depletion, the capacitance decreases in value since the charge inside the silicon waveguide moves away from the silicon edges which effectively enlarges the capacitor width [45]. With negative , the hole concentration increases which results in a decrease in and increase in . The charge accumulating at the silicon edge makes the effective thickness of the capacitor determined by the oxide thickness [45]. Therefore, the capacitance is higher in the accumulation regime. To account for the slowest response, this value is used in the 3 − dB bandwidth calculations, although the The second remark is that the waveguide with the largest H exhibits the lowest optical losses at low levels of doping concentrations, despite the previous finding. This can be explained by the small carrier absorption loss which allows the electrode absorption to be the dominant loss. Using MODE, the waveguide with H = 300 nm has a confinement factor, defined as the ratio of the core power to the total mode power, Γ = 84%. This is the largest amongst the three and hence its mode has the least overlap with the electrodes at the same y o and z o . The waveguide with H = 220 nm has Γ = 77% and the one with H = 150 nm has Γ = 60%. However, as the doping dose increases, apparently, the carrier absorption loss becomes the dominant and hence the waveguide with H = 300 nm becomes the most lossy.
Based on the previous discussion, the device that shows the lowest IL is found from Figure 3a, as the one with H = 300 nm, W = 400 nm, L = L π = 3 mm, N A = 3 × 10 16 cm −3 , IL = 0.75 + 0.6 = 1.35 dB. The other parameters for this design are V π = 30 Volt and ER = 29.5 dB. Using DEVICE, we find the capacitance per micrometer of the propagation path, C = 0.04 f F µm . Then, the total device capacitance C = C L = 121 f F which gives f 3dB = 1 2πRC = 26 GHz. Note that in the bandwidth calculations we employ the commonly used value of contact resistance R = 50 Ω. This design shows a small IL and a very high ER. This device is referred to as 'Modulator A' in the next discussion.
Next, the selection criterion could be altered to target a higher speed of modulation, at the expense of the insertion loss. With closer electrodes at z o = 300 nm and y o = 500 nm and for H = 150 nm, W = 600 nm and N A = 2 × 10 17 cm −3 we get L π = 1.6 mm, IL = 6.9 + 0.6 = 7.5 dB, ER = 26.7 dB V π = 40 Volt, C = 0.044 f F µm , and f 3dB = 44 GHz. This interesting case has its main device parameters shown in Figure 4. As the modulating voltage, V, increases above zero, the holes deplete and therefore the effective index increases and the phase shifter loss decreases [17]. With depletion, the capacitance decreases in value since the charge inside the silicon waveguide moves away from the silicon edges which effectively enlarges the capacitor width [45]. With negative V, the hole concentration increases which results in a decrease in n e and increase in α o . The charge accumulating at the silicon edge makes the effective thickness of the capacitor determined by the oxide thickness [45]. Therefore, the capacitance is higher in the accumulation regime. To account for the slowest response, this value is used in the 3-dB bandwidth calculations, although the maximum change of the capacitance is approximately 2% over the entire range of the modulating voltage. maximum change of the capacitance is approximately 2% over the entire range of the modulating voltage.   Then, a modification can be adopted to push the speed up. By shortening the phase shifter length to L = 0.8 mm = 800 µm, the speed goes up to 90 GHz, the insertion loss goes down to IL = 3.4 + 0.6 = 4 dB while the extinction ratio decreases to ER = 3 dB. Although being much smaller, this ER value is widely reported in literature as an acceptable value [22,[46][47][48][49][50]. This design is referred to as 'Modulator B'.
A third alternative is a design with low modulation voltage. We find that the device with H = 150 nm, W = 600 nm, N A = 10 16 cm −3 , z o = 400 nm, y o = 500 nm has the following: V π = 22 Volt, L π = 3 mm, IL = 3 + 0.6 = 3.6 dB, ER = 28 dB, f 3dB = 24 GHz. The depletion reaches its maximum when the applied voltage to one arm is 2 Volt only. The rest of the V π which is 20 Volt are employed in the accumulation regime for the other arm. Seeking a low voltage of operation, this device can be operated between V = 0 and V = 2 Volt, sacrificing the accumulation contribution to ∆n e . Along with L = 7.5 mm, we get IL = 7.5 + 0.6 = 8.1 dB, ER = 3 dB, and f 3dB = 10 GHz. This design is called 'Modulator C'.
Looking into the former range of results, 'Modulator B', with f 3dB = 90 GHz, can be employed in the backhaul truck circuits of the 5G networks with a speed of 100 Gbps of non-return-to-zero (NRZ) coding [13], where also high voltage can be provided. 'Modulator C', which exhibits much lower bandwidth but also much lower voltage of operation, is then more suitable for the end user applications of the 5G systems where the speed of operation is 1-10 Gbps [13], which can be easily supported by a bandwidth of 10 GHz. A summary of the proposed variants of this modulator is given in Table 1.

Comparison with Other Devices
Many modulator structures have been proposed in the literature. The most important of which are summarized in Table 2. -Data is not available. * The speed is related to the 3 dB bandwidth using the relation Speed = 2 × (3 dB bandwidth), where the non-return-to-zero modulation is assumed.
Looking into the previous performance metrics, the proposed modulator in this work features the simplest fabrication process, especially if compared to complicated PN junction designs in [20] and [46]. The reason is that this modulator is based on the 'fin' structure which is a standard structure in the electronics industry. This feature enables easy and inexpensive fabrication of the proposed modulator through, for example, the multi-project-wafer (MPW) prototyping service from IMEC [62]. 'Modulator B' features a very high bandwidth of 90 GHz which can accommodate up to 180 Gbps of NRZ signal. Also, it possesses a competitive phase shifter length and an acceptable insertion loss and extinction ratio, compared to the modulators in Table 2. However, with the high voltage of operation, this modulator is more suitable for backbone circuits. For the end user device, the alternative is given as 'Modulator C'.

Conclusions
In this work, a MOS-based modulator has been proposed. The modulator employs a standard structure from the electronics domain, the 'fin' gate structure. This makes the modulator easy and inexpensive to fabricate. We showed how the design parameters-such as the doping concentration, the waveguide dimensions, and the silica thickness-can be altered to get different variants of the proposed modulators. The performance metrics such as the insertion loss, the extinction ratio, the modulation speed and the voltage of operation can then be customized to make the modulator suitable at different points of a communications network. The very high bandwidth of 90 GHz is introduced to match the 5G network requirements at the backhaul truck. This way, silicon photonics can be easily integrated with the prospective networks for high speed communications and the internet of things.