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Advances in Optical Technologies

Volume 2008 (2008), Article ID 678948, 10 pages

http://dx.doi.org/10.1155/2008/678948

## Developments in Gigascale Silicon Optical Modulators Using Free Carrier Dispersion Mechanisms

^{1}Intel Corporation, 2200 Mission College Blvd, SC12-326, Santa Clara, CA 95054, USA^{2}Intel Corporation, S. B. I. Park Har Hotzvim, Jerusalem 91031, Israel

Received 6 December 2007; Accepted 15 April 2008

Academic Editor: Graham Reed

Copyright © 2008 Juthika Basak et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper describes the recent advances made in silicon optical modulators employing the free carrier dispersion effect, specifically those governed by majority carrier dynamics. The design, fabrication, and measurements for two different devices are discussed in detail. We present an MOS capacitor-based modulator delivering 10 Gbps data with an extinction ratio of 4 dB and a pn-diode-based device with high-speed transmission of 40 Gbps and bandwidth greater than 30 GHz. Device improvements for achieving higher extinction ratios, as required for certain applications, are also discussed. These devices are key components of integrated silicon photonic chips which could enable optical interconnects in future terascale processors.

#### 1. Introduction

Over the past few years, the demands for high-performance computers, ever increasing instructions per cycle and high-energy efficiency, have fuelled the rapid development of multicore and many core microprocessors. With the recent advent of quad-core processors into the market [1, 2], coupled with the laboratory demonstration of a teraflop processor containing 80 cores [3], the need for interconnects supporting gigascale and terascale I/O has become imperative. Although present implementations of chip to chip copper interconnects are being pushed to deliver gigascale bandwidths with the design of transceivers that use active or passive equalizers [4, 5], this is unlikely to be a frequency scalable option.

On a parallel front, optical technology has been successfully deployed in long-haul fiber communications for more than two decades now. Individual components targeted toward these applications have been developed to the extent of delivering bandwidths as large as 40 Gbps [6, 7]. Multiple channels of such high bandwidth transmitted together using wavelength division multiplexing (WDM) is capable of terascale data rates. It would therefore seem intuitive to extensively employ similar optical technology in short reach applications such as rack to rack and board to board communications. However, this approach has not gathered momentum and the primary reason has been the high costs of materials such as III-V semiconductors and lithium niobate, which are inherently suited for photonic applications. Thus, developing a cost-effective optical technology has become essential for its adoption in the computer industry.

Interest in silicon photonics has been spurred predominantly by the low cost of silicon. In addition, its high volume manufacturability and the potential of electronics and photonics integration in the all pervasive microelectronics applications have added a further boost to this field. Silicon photonics is now being enabled by the successful demonstration of the requisite building blocks on silicon such as fast silicon optical modulators [8–13], SiGe photodetectors [14–16], silicon Raman lasers [17, 18], silicon optical amplifiers [19–22], silicon wavelength converters [23–25], and hybrid silicon lasers [26]. A high speed silicon photonic transceiver circuit which monolithically integrates all of these functionalities would be the ultimate culmination point expected to provide a low-cost solution for future optical interconnects.

Silicon optical modulators are one of the key building blocks which have been extensively studied. High-speed data transmission at 10 Gb/s [9–11], 30 Gb/s [12], and 40 Gb/s [13] has been demonstrated using silicon modulators with different device configurations. Combining these gigascale silicon modulators with recently developed hybrid silicon lasers [26] and using WDM, one could create a single chip that can transmit data at Tb/s data rate for future high performance computing applications and mega data centers.

Unlike today’s commercially available optical modulators
which use III-V semiconductors [27] or LiNbO_{3} [28], achieving
modulation in crystalline silicon is challenging due to the fact that it
exhibits no linear electro-optic (Pockels) coefficient and has a very weak
Franz-Keldysh effect [29, 30]. It has been very recently shown that strained
silicon possesses the Pockels effect [31], but the measured electro-optic
coefficient is relatively small (an order of magnitude smaller than that for
LiNbO_{3}). It has also been shown that strained Ge/SiGe quantum well structures
have relatively strong electro-optic absorption due to the quantum-confined
Stark effect [32], making it possible for optical modulation. However, critical
strain engineering is needed and high-speed optical modulator performance has
yet to be demonstrated for the Ge quantum well system. Silicon also exhibits an appreciable
thermo-optic efficient (~2 × 10^{−4}/K) [33]. However, the thermo-optic
modulator is not suitable for high-speed applications because of its inherently
slow response.

The most effective way of performing fast optical
modulation in silicon is via the free carrier plasma dispersion effect. This effect
relates the variation in the concentration of electrons (Δ*N _{e}*) and holes (Δ

*N*) in a semiconductor to changes in the absorption coefficient (Δ

_{h}*) and refractive index (Δ*

*α**n*). This effect has been mathematically described by the Drude-Lorenz equations [33] and further refined experimentally to give the following empirical relation at the wavelength of 1.55

*μ*m:

The performance of modulators using free carrier
plasma dispersion is determined by the speed and efficiency of carrier density
modulation in the region of the traveling optical mode. Various device
configurations have so far been proposed to achieve carrier density modulation
in silicon. The first and most extensively investigated device configuration is
the forward biased p-i-n diode modulator [34]. In this device, the free carrier
density change in silicon is achieved through current injection and is
primarily governed by minority carrier dynamics. The forward biased p-i-n diode
approach in a resonant ring structure implementation has been demonstrated to
give high modulation efficiency and, in turn, compact device sizes of ~12 *μ*m [35].
However, modulation speed in these devices is usually limited by the slow
carrier generation and/or recombination processes, unless the carrier lifetime
can be significantly reduced [36]. It is to be noted that a reduction in the
carrier lifetime also results in a reduction in current injection as well as phase
modulation and these tradeoffs need to be considered based on specific
applications.

Contrary to the forward biased diode, the MOS capacitor [8, 9] and reverse biased pn junction [10, 12, 13, 37] based modulators rely on electric field-induced majority carrier dynamics and do not suffer from inherent bandwidth limitations. However, the phase modulation in these devices is not as efficient due to smaller overlap between the charge modulation area and the optical mode. In addition, since these devices are limited by their resistance-capacitance (RC) time constants, reducing device parasitic effects is critical to exploit their high bandwidth characteristics.

This paper describes our efforts progressively toward developing a high-speed silicon optical modulator. We focus on the investigation of the phase modulator or phase shifter, as it is the key element of modulators that can be constructed based on various implementation configurations such as Mach-Zehnder interferometer (MZI) and microring resonators. Since the MZI modulator has a broad operation wavelength range and provides a good vehicle for the modulator characterization, we adopted the MZI configuration in all our approaches [33]. In addition, our devices were designed to operate in the push-pull configuration in order to achieve higher power efficiency. This paper is organized as follows. In Section 2, we present details of the MOS capacitor-based silicon modulator and demonstrate 10 Gbps operation with an extinction ratio of 4 dB. Section 3 describes further device development to achieve bandwidths greater than 10 Gbps and discusses the implementation of the silicon modulator based on a pn-diode. Here, we present experimental results of data transmission at 40 Gbps with a 3 dB bandwidth of >30 GHz. Section 4 concludes this paper.

#### 2. MOS Capacitor-Based Silicon Modulator

Carrier density modulation is obtained by driving an MOS capacitor into the accumulation mode of operation. A voltage applied across the capacitor can induce an accumulation of charges in the doped silicon near the center dielectric. This modifies the refractive index profile of silicon in the waveguide region and ultimately the optical phase of light passing through it, thus acting as a phase modulator. When placed in one or both arms of an MZI, this phase modulator(s) can change the relative phase difference between the light passing through the two paths. Interference of the outputs from the two arms causes the phase modulation to be converted into the desired optical intensity modulation.

##### 2.1. Design and Structure

Figure 1(a) shows the schematic of the cross-section
of the designed silicon waveguide-based MOS capacitor phase shifter. It
comprises of a 1.0 *μ*m *n*-type-doped crystalline silicon layer (the epitaxial silicon
layer of the SOI wafer) at the bottom and a 0.55 *μ*m *p*-type-doped crystalline silicon
on the top with a gate dielectric separating them. The 10.5 nm gate dielectric consists
of a multilayer stack of silicon dioxide and nitride. A process called
epitaxial lateral overgrowth (ELO) is used to grow the crystalline silicon on
top of the gate dielectric [38]. This use of single crystalline silicon was a
significant development toward reducing device transmission loss from its prototype
version which had a polysilicon layer that gave much larger optical loss due to
defects in the material lattice [39]. The p-doping concentration in the ELO-silicon
is 1 × 10^{18}/cm^{3}, while the n-dopant concentration in the SOI
silicon is 2 × 10^{17}/cm^{3}. These doping concentrations were
chosen to ensure high bandwidth performance but were not strictly optimized for
minimum resistance.

To form the rib waveguide, the entire ELO-silicon,
gate dielectric, and ~0.1 *μ*m of the SOI silicon are etched. This results in a
waveguide rib height of 0.65 *μ*m and waveguide slab thickness of 0.9 *μ*m. The rib
width is 1.6 *μ*m (measured at the middle of the rib height), and since the sidewalls
of the waveguide rib are not entirely vertical, the gate dielectric width is
1.9 *μ*m. This yields a 1.6 *μ*m by 1.6 *μ*m waveguide with single-mode operation. In
order to minimize the metal contact loss, it is necessary to place the contacts
outside of the optical mode. To meet this requirement, two ~3 *μ*m wide polysilicon
sections with high p-doping concentration and a 0.3 *μ*m overlap with the top
corners of the ELO-silicon rib (Figure 1(a)) are grown. Aluminum for contacting
the p-region is subsequently placed on top of the polysilicon. This design ensures
an Ohmic contact between the metal and the polysilicon as well as electrical connectivity
between the polysilicon and the rib. The 1 *μ*m wide oxide region between the two
polysilicon regions shown in Figure 1(a) serves to isolate the contact metal
from the rib as well as push the optical mode downwards, away from the lossy polysilicon.
The aluminum contacts to the n-region are deposited on the slab, also far from
the waveguide. The oxide regions underneath the polysilicon and on both sides
of the rib ensure optical confinement and prevent optical field from penetrating
into the contact areas. The scanning electron microscope (SEM) cross-sectional
image of the fabricated device is shown in Figure 1(b).

The overall length of the MZI modulator is 15 mm, which includes the input and output waveguides, 3 dB directional coupler-based splitters, and two arms of straight waveguides of a nominally equal length of 13 mm. Each arm comprises of a 3.45 mm long high-doping, high-speed RF MOS capacitor phase shifter section, and two ~4.75 mm long lightly-doped, low-speed phase shifters that are driven with DC voltages to electrically bias the MZI at quadrature.

##### 2.2. Optical Performance

As mentioned earlier, the MOS capacitor device
operates in accumulation mode, where the *n*-type silicon slab is grounded and a
positive drive voltage, *V _{D}*, is applied to the

*p*-type ELO-silicon causing a thin charge layer to accumulate on both sides of the gate dielectric. The resulting change in free carrier density causes a change in refractive index (

*n*) of silicon in accordance with (1), which is manifested as a change in the effective refractive index of the optical mode (Δ

*n*). The optical phase shift at the end of the capacitor depends on the magnitude of this voltage-induced Δ

_{ eff }*n*, the device length

_{ eff }*L*, and the optical wavelength

*and can be calculated as [33]*

*λ*The Δ*n _{
eff
}* is governed by device design
parameters such as the waveguide dimensions and the position of the gate
dielectric as they determine how effectively the accumulated charges overlap
with the optical mode [8]. As a figure of merit for phase efficiency, the
product

*V*can be determined from the measured phase shift, where

_{π}L_{π}*V*and

_{π}*L*are the voltage swing (beyond the flat-band voltage of 1.25 V) and device length required to achieve

_{π}*π*radian phase shift. The goal is to minimize the

*V*product to lower the required voltage drive and shorten the device length for a given phase shift. Smaller waveguide dimensions, though harder to fabricate, ensure stronger mode-charge interaction and hence higher phase efficiency. As an example, the phase shifter design of Figure 1 with waveguide dimensions of 1.6

_{π}L_{π}*μ*m × 1.6

*μ*m gives

*V*of 3.3 V-cm, which is 50% smaller than the prototype of this device which had waveguide dimensions of 2.5

_{π}L_{π}*μ*m × 2.3

*μ*m and gave

*V*of 7.8 V-cm.

_{π}L_{π}The optical
loss of the phase shifters is measured to be 10 dB/cm for the high-speed sections and 5.2 dB/cm for
the low-speed sections. Optical measurements on the MZI
modulator gives a total insertion loss of 19 dB comprising of 9 dB coupling loss and 10 dB on-chip loss, when the MZI is in the “on” state, which is defined here as
the maximum optical output intensity of the MZI. Of the 10 dB on-chip loss, 3.5 dB is due to the high-speed (RF) sections,
2.5 dB due to the low-speed (bias) sections, and the remaining 4 dB is
estimated to be due to a combination of voltage-induced free carrier absorption
[40] and the unoptimized design of the splitters and bends. Optical coupling to
the 1.6 *μ*m × 1.6 *μ*m waveguides is done using a lensed single-mode fiber with
approximately 3.3 *μ*m spot size. The total coupling loss of 9 dB can be
significantly reduced using one of the known waveguide mode converter
techniques [41–43]. Although mode converters were not implemented with the MOS capacitor-based
devices, we have extensively studied their performance and have achieved
coupling loss as low as ~1.5 dB/facet for similar waveguide thickness [44].

##### 2.3. High-Speed Performance

The intrinsic bandwidth of the modulator was expected
to be limited by the RC time constant. Since the capacitance of the device is
proportional to its length, a shorter device would have a larger bandwidth.
Therefore, in order to maintain the same phase shift as a 3.45 mm long RF phase
shifter but simultaneously enhancing the bandwidth, the phase shifter is
divided into eleven equal segments of 315 *μ*m each and every segment driven by
the same signal with a phase correlation determined by the group velocity of
light. The impedance of these sections is measured as a function of frequency
and is plotted in Figure 2. The reactance is modeled to be from a capacitance
of 2.4 pF, while the resistance is measured as 6.5 Ω. The RC cutoff frequency,
(2*π*RC)^{−1}, can therefore be calculated to be 10.2 GHz.

High-speed operation of the modulator required the use of a low-impedance driver circuit. A custom IC was designed and manufactured using a 70 GHz-F_{
T
} SiGe HBT process, details of which can be found in [9]. It employs a
push-pull
emitter-coupled logic (ECL) output stage which is wire-bonded directly to each
of the 11 segments of the RF phase-shifter on each arm and has been indicated
schematically in Figure 3. The driver operates from a single-ended power supply
in the range from 3.3 to 3.9 V and is targeted to deliver up to 1.6 V_{
pp
} (3.2 V_{
pp
} differential) to each phase-shifter when operating at 8 Gbps. The data pulses delivered to each of the segments are delayed using internal
transmission lines to match the optical group velocity across the modulator. A
number of control settings are available to trade performance for power
dissipation (from 2.7 W to 3.9 W depending on supply voltage, output swing, bit
rate, and edge rate). Of this power, approximately 10% is dissipated in the
modulator. Improved driver design and improved phase-shifter efficiency will
lead to reduced power dissipation.

To characterize data transmission
performance, a DC voltage of −3.3 V is applied to the *n*-type silicon slab. A DC voltage applied to the ELO-silicon rib
of the low-speed phase sections sets the MZI at quadrature bias. The DC bias is
chosen such that the entire AC swing of 1.4 V_{
pp
}
applied to the RF phase shifters
is above the flat-band voltage [8]. This voltage swing, based on calculations
for the device in Figure 3, should yield 0.15 *π* radian phase shift in each MZI
arm, enough to give a modulation extinction ratio (ER) of 4.2 dB. The modulator
was tested at several data rates with a maximum at 10 Gbps. The resulting eye
diagram for a 10 Gbps [2^{32} – 1] pseudorandom bit sequence (PRBS) input
gives an ER of 3.8 dB and is shown in Figure 4.
The 20–80% rise/fall
time is measured to be ~55 ps and is not found to vary too much from
measurements at lower data rates such as at 6 Gbps. Combined with the fact that
the inherent bandwidth of the modulator was earlier estimated to be ~10 GHz
from measurements of capacitance and resistance, it is evident that the inherent
modulator bandwidth is not the limitation in these measurements. On the
contrary, it is the ~0.7 nH inductance of the wirebonds and the slower slew rate of the driver circuit,
corresponding only to 8 Gbps, that limit the demonstrated device bandwidth.

This MOS capacitor-based modulator is the first silicon modulator to reach
the 10 GHz bandwidth milestone. In addition, further improvements in phase
efficiency, optical loss, as well as bandwidth are possible with optimization. Modeling and experimental studies
show that reducing the waveguide dimensions and thinning down the gate
dielectric could greatly improve the phase efficiency [45, 46]. A waveguide
with dimensions of 1 *μ*m × 1 *μ*m and a gate dielectric of 6 nm is expected to give
a *V _{π}L_{π}* product as low as 0.68 V-cm. Such a device would facilitate
the use of a CMOS-based driver with drive
voltages <1 V

_{ pp }to obtain an ER as high as 12 dB for a 0.25 cm long phase shifter length. By optimizing the doping profiles as well as the MZI splitter design, this small cross-section device can achieve 10 GHz modulation bandwidth with >12 dB ER and on-chip loss as little as 2 dB.

While the MOS capacitor-based modulator has the potential to realize several GHz of intrinsic bandwidth with reasonably low-optical loss, the device operation speed that can be experimentally demonstrated depends on the electrical drive design. As the capacitance of the MOS capacitor modulator is large (6–8 pF/mm), it requires very short device segments for high data rates if lumped drive is used. An alternative approach would be to use a traveling-wave electrode (transmission line) design. This approach not only addresses the RC speed limitation of lumped devices but also significantly reduces the frequency dependence of the power dissipation of the modulator. For the MOS capacitor-based modulator, however, its high capacitance makes matching the RF phase velocity and optical group velocity more challenging for high-speed operations. In addition, the RF loss of the transmission line would be large at high frequencies because of the large capacitance per unit length. Therefore, from the electrical drive circuitry point of view, it is critical to reduce device capacitance. With this in mind and with the aim of pushing up modulation speeds higher, we started exploring the pn-diode-based optical modulator design, which can potentially have a smaller capacitance. The following section describes the design and performance of the pn-diode-based modulator.

#### 3. Pn Diode-Based Silicon Modulator

This implementation of the modulator, also based on free carrier dispersion, produces a carrier modulation by operating a pn diode in reverse bias and hence in the carrier depletion mode. This modulator is also built in an MZI configuration but is an improvement over the MOS capacitor-based device in a couple of different ways. The dielectric layer between the two doped sections in the MOS capacitor is now replaced by the depletion width of the pn junction, and this leads to a reduction in the modulator capacitance and hence improved bandwidth. At the same time, the metal electrodes are now designed to operate as traveling wave electrodes and this eliminates the dependence of bandwidth on the RC time constant. Processing of this modulator also employs a simpler and more standard nonselective epitaxial silicon growth process instead of the ELO growth step required for the demonstrated version of the MOS capacitor-based device.

##### 3.1. Design and Structure

The phase shifter components of this silicon modulator
are the reverse biased pn diodes embedded in the MZI arms. Figure 5(a) shows a
schematic of the cross-sectional view of the phase shifter. It comprises of a
*p*-type-doped crystalline silicon rib waveguide having a rib width of ~0.6 *μ*m and a rib height of ~0.5 *μ*m with an *n*-type-doped silicon cap layer. This thin cap layer
which is 0.1 *μ*m thick and ~1.8 *μ*m wide is formed using a nonselective epitaxial silicon
growth process and is used for pn junction formation and electrical contact. Both
modeling and experiments confirm that the 0.6 *μ*m by 0.6 *μ*m waveguide can support only a single TE mode for wavelengths
around 1.55 *μ*m.

The p-doping concentration is ~1.5 × 10^{17} cm^{−3},
and the n-doping concentration varies from ~3 × 10^{18} cm^{−3} near the top of the cap layer to ~1.5 × 10^{17} cm^{−3} at the pn
junction. To ensure good Ohmic contact between silicon and metal contacts, two
slab regions ~1 *μ*m away from both sides of the rib edge and part of the thin
cap layer starting ~0.3 *μ*m away from the rib edge are heavily doped with a
concentration of ~1 × 10^{20} cm^{−3} of *p*- and *n*-type dopants,
respectively. The process parameters described above have been designed to
target the pn junction at approximately 0.4 *μ*m above the buried oxide to enable optimal mode overlap with
the depletion region. As the n-doping concentration is much higher than the
p-doping concentration, carrier depletion under reverse bias occurs mainly in
the *p*-type-doped region. This leads to better phase modulation efficiency
because the hole density change results in a larger refractive index change as
compared to the electron density change as indicated by (1).

Modeling shows that the high-speed performance of a
pn-diode modulator is limited by the pn junction capacitance, silicon
resistances, and the metal contact parasitics, and not by the carrier dynamics.
To minimize the RC limitation of the frequency response of the modulator [47, 48],
we designed a traveling wave electrode based on a coplanar waveguide structure
as shown in Figure 5(a). The “signal” metal layer is ~6 *μ*m wide and is connected to the heavily doped *n*-type silicon
region through a 1 *μ*m contact. The separation between the signal and ground metal
layers is ~3 *μ*m and the metal thickness is ~1.5 *μ*m. The RF traveling wave coplanar waveguide and modulator
optical waveguide are carefully designed so that both electrical and optical
signals copropagate along the length of the phase shifter with similar speeds.
In addition, it is necessary to keep the electrode capacitance small so that
the RF loss of the electrodes is minimal. The single-sided asymmetric silicon
cap layer design, also shown in Figure 5(a), is used to reduce the capacitance
of the phase shifter. The transmission line loss, impedance, and phase velocity
are calculated using a commercial software package HFSS, and details on this
can be found in [49]. These parameters strongly depend on the metal trace
dimensions as well as silicon doping concentration and profile. The
cross-section SEM image of a fabricated pn diode phase shifter waveguide is
shown in Figure 5(b).

##### 3.2. Optical Performance

As in the MOS capacitor-based modulator, the phase
shift in the reverse biased pn junction is also given by (3). By changing the
applied reverse bias voltage *V* across
the diode, we can obtain a change in depletion width (*W _{D}*) according to the following equation [50]:
where the condition of an
asymmetrically doped pn junction has been assumed with the n-doping
concentration much higher than the p-doping concentration.
Here, is the low-frequency relative
permittivity of silicon,

*N*is the acceptor concentration, and

_{A}*V*is the built-in voltage. Changing the depletion width of a pn junction is equivalent to changing the free carrier density, and hence a change in the refractive index Δ

_{ Bi }*n*. Because the depletion width is usually smaller than the waveguide height, the phase modulation efficiency strongly depends on the pn junction location relative to the guided mode center.

_{ eff }Similar to the MOS capacitor-based modulator, we define
the figure of merit for phase efficiency as the *V _{π}L_{π}* product, where

*V*and

_{π}*L*are the reverse bias voltage and device length required for achieving

_{π}*π*-radian phase shift, respectively. The

*V*dependence on junction position location is modeled to show that at 3.5 V drive, junction depths of 0.1, 0.2, and 0.3

_{π}L_{π}*μ*m from the top of the waveguide rib yield

*V*values of 5.2, 3.1, and 2.8 V-cm, respectively. This marked dependence proves the importance of optimizing the p- and n-doping profiles to get maximum overlap between the free carrier density change and the optical mode. Figure 6 also shows the modeled phase shift versus the reverse bias for the device with a junction depth of 0.3

_{π}L_{π}*μ*m and with a length of 5 mm. It is clear from Figure 6 that the phase efficiency is not linearly dependent upon the voltage, and this is in accordance with the nonlinear dependence of

*W*on the bias, as indicated in (4). A better phase efficiency is obtained for a smaller drive voltage. For example,

_{D}*V*= 2.16 V-cm for 1 V drive, while it is 2.8 V-cm for 3.5 V drive and 3.5 V-cm for 7 V drive.

_{π}L_{π}Figure 7 shows the measured phase shift of the pn
junction phase shifter as a function of the drive voltage for different phase
shifter lengths. As the data shows, * π*/2 phase shift is achieved at 4 V bias for a phase shifter
length of 5 mm, and hence the
measured

*V*is ~4 V-cm. This measured phase efficiency is much smaller than the modeled results shown in Figure 6. We suspect this is mainly due to process variations in the pn junction location, causing it to be nonoptimal. We can also see that the measured phase shift is not linearly dependent on the drive voltage, which is qualitatively in agreement with our modeling. Figure 7 also shows the phase shift versus drive voltage for 1 mm and 3 mm phase shifters. As expected, they have the same phase efficiency of ~4 V-cm.

_{π}L_{π}The phase modulation is accompanied by optical absorption
modulation, as can be seen in (2). Therefore, we expect a voltage induced gain
in the phase shifter transmission which can introduce an optical field amplitude
imbalance between the two arms of the MZI and potentially degrade the
extinction ratio of the device. To quantify this effect, we measure the change
in transmission for a straight phase shifter for different bias voltages and
plot the optical transmission versus the phase shift. The results are given in
Figure 8 which shows that the measured VDG is ~1.43 dB/*π*. This is in excellent agreement with our modeling. Inspite
of the VDG-induced arm imbalance, the DC extinction ratio of the MZI is measured
to be >20 dB, as can be seen in Figure 9.

The total length of the MZI modulator is 8.25 mm. This includes the input and output waveguides, 2 MMI splitters, and the two straight arms of the MZI, each ~3 mm long, inclusive of a 1 mm long phase shifter. 1 × 2 multimode interference (MMI) couplers are used as the splitters in the MZI because the directional coupler-based splitter (used for the MOS capacitor device) for the small waveguide size used here requires very fine lithography resolution to keep excess optical loss at a minimum. The on-chip insertion loss is ~4 dB, when the MZI is in the “on” state, which is defined here as the maximum optical output intensity of the MZI. This on-chip insertion loss (excluding coupling loss) includes ~1 dB passive waveguide transmission loss, ~0.5 dB MMI coupler loss, and ~2.5 dB phase shifter loss, which can be attributed primarily to the dopants. The passive waveguide and phase shifter losses are measured using the well-known cutback method [33], and the MMI coupler loss is determined by comparing its transmission to that of straight reference waveguides.

##### 3.3. High-Speed Performance

As described in Section 3.1, the metal electrodes have been designed to give high-bandwidth performance. Both modeling and measurements show that the capacitance of this device is an order of magnitude smaller than the MOS capacitor-based modulator. However, it is imperative to ensure proper termination of the modulator transmission line in order to suppress the RF signal reflection from the end of the traveling-wave electrode. In our experiment, we have used two different approaches for device termination. One approach is to flip-chip bond the silicon MZI modulator chip to a printed circuit board (PCB) and surface mount external resistors on the PCB traces that are connected to the output end of the modulator electrode. The PCB is designed for high-speed performance with PCB traces having ~0.3 dB/cm RF loss and 50 ohm impedance at 40 GHz and is used with low RF loss connectors. The other approach for terminating the device is to monolithically integrate a thin-film resistor with the silicon modulator die. For our MZI devices, we used titanium nitride (TiN) as the resistor material.

The high-frequency performance of the silicon
modulator has been characterized by measuring both its 3 dB frequency roll-off
and data transmission capability. The MZI silicon modulator used for the high-speed
experiments contains a 1 mm long phase shifter in each arm. The RF signal from
either a signal generator or a pseudorandom bit sequence (PRBS) generator is
amplified using a commercially available modulator driver. For single-ended drive, the amplified output
of 6.2 V_{
pp
} is combined with 3.1 V_{
DC
} using a bias tee to
ensure reverse bias operation for the entire AC voltage swing. (For dual drive,
we use an RF signal of ~7.6 V_{
pp
} differential with each arm biased at
~2 V_{
DC
}.) This DC-coupled signal is connected to the input of the
traveling-wave electrode of one of the phase shifters via the PCB connector or
a GSG probe with RF insertion loss of <1 dB up to
50 GHz. The output of the electrode is terminated with a 14 Ωload. A
continuous-wave laser beam at ~1550 nm is coupled into the silicon modulator
via a lensed fiber. The modulated optical output is collected using another
lensed fiber and is connected to a 53 GHz digital communications analyzer (DCA)
optical module.

For the optical frequency roll-off measurement, the signal generator is swept from 100 MHz to 44 GHz. The input drive signal is first measured as a function of frequency using a DCA electrical module with 63 GHz bandwidth. This DC-coupled RF signal is then applied to the modulator and the modulated optical signal is also measured as a function of frequency. To obtain the frequency response of the MZI modulator for a constant input drive voltage, the optical output is normalized by the measured input drive voltage for all frequencies. The results for the frequency roll-off measurements for both the devices packaged on a PCB as well as that with on-chip resistors are plotted in Figure 10, where we can see that both the devices have a 3-dB roll-off frequency of >30 GHz.

The high-speed data transmission performance of the MZI
modulator was measured using a PRBS source with [2^{31}–1] pattern
length as the RF input. The MZIs have been designed such that both arms can be
driven in a push-pull configuration but can be driven more simply in the single-ended
configuration as well. The high-speed testing of the device on the PCB was
performed using a single-ended drive scheme, while the device with the on-chip
termination was driven differentially. Figure 11(a) shows the eye diagram of
the modulator optical output at a bit rate of 40 Gb/s. The ER is measured to be
1.1 dB with a rise/fall time of ~14 ps. The open eye diagram proves that the
modulator is capable of transmitting data at 40 Gb/s, which is consistent with
the 3 dB roll-off frequency of >30 GHz.

Demonstration of such high-speed data transmission represents a significant leap in silicon modulator performance and is a testament to the success of the steps taken to extend the bandwidth beyond 10 Gbps. However, the demonstrated performance above is, by no means, the fundamental limit and there is a lot of room for improvement. For example, the ER can be significantly improved by optimizing the pn-junction location, which alone can lead to ~30% improvement in phase efficiency based on our simulation results.

Another approach toward increasing the ER is to
increase the length of the phase shifter contained in the MZI. However, this
comes with the trade-off of a larger RF signal attenuation, which limits the
data rate to a lower value. Figure 11(b) shows the measured eye diagram at 10 Gbps for an MZI with a 3 mm phase shifter section, which gives an ER of ~5.2 dB
for a 7.6 V_{
pp
} differential drive with each arm biased at 2 V_{
DC
}.
Increasing the data rate beyond 10 Gbps rapidly closes the eye due to
insufficient bandwidth. One way to overcome the bandwidth limitation would be
to break up the 3 mm phase shifter into three smaller segments of 1 mm each and
drive every segment with the same signal. This configuration can be expected to
give an ER of ~5 dB even for ~40 Gbps
since the bandwidth is now determined by that of a 1 mm device, which has
already been shown to be >30 GHz. This is identical to the approach taken
for the MOS capacitor which has already been successfully demonstrated.
Analogously, the total phase shifter length in the MZI can be further increased
to 5 or even 10 mm to give larger extinction ratios, while still maintaining
individual segment length at 1 mm. The limitations now become the optical loss,
and the increase in driver and packaging complexity.

#### 4. Conclusions

In this paper, we have presented two implementations of silicon optical modulators, both based on the free carrier plasma dispersion effect. One of them is based on an MOS capacitor operating in the accumulation mode, while the other incorporates a pn-diode operating in the carrier depletion mode. The MOS capacitor-based device was the world’s first silicon optical modulator to give data transmission at 10 Gbps. Transmission line implementation of the pn-diode-based modulator helped us push the bandwidths even higher to demonstrate 40 Gbps data transmission and provide a more frequency scalable option for optical modulators. Several straightforward options have been suggested for improving the performance further in terms of the phase efficiency and the achievable extinction ratio. The developments in the silicon optical modulator described in this paper indicate that reaching the performance levels demonstrated so far by other materials is now a forthcoming reality, thus providing a huge impetus toward driving optical interconnects in future terascale microprocessors.

#### Acknowledgments

The authors thank K. Callegari, J. Ngo, and J. Tseng for sample preparation; T. Luo for early work on RF characterization; Ulrich D. Keil and Thorkild Franck for driver circuit development for the MOS capacitor device; D. Li for data collection software; R. Gabay, A. Ugnitz, and G. Nutrica for device fabrication assistance; L. Kulig for material analysis; and M. Morse, T. Mader, S. Q. Shang, G. Sarid, T. Franck, R. Jones, D. D. Lu, H. Braunisch, G. T. Reed, and J. E. Bowers for useful discussions.

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