Operation and Optimization of Silicon-Diode-Based
Optical Modulators
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Spector, S.J. et al. “Operation and Optimization of Silicon-DiodeBased Optical Modulators.” Selected Topics in Quantum
Electronics, IEEE Journal Of 16.1 (2010) : 165-172. © 2010 IEEE
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http://dx.doi.org/10.1109/jstqe.2009.2027817
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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 16, NO. 1, JANUARY/FEBRUARY 2010
165
Operation and Optimization of Silicon-Diode-Based
Optical Modulators
Steven J. Spector, Cheryl M. Sorace, Michael W. Geis, Matthew E. Grein, Jung U. Yoon,
Theodore M. Lyszczarz, Member, IEEE, Erich P. Ippen, Life Fellow, IEEE, and Franz X. Kärtner, Fellow, IEEE
(Invited Paper)
Abstract—An optical modulator in silicon based on a diode structure has been operated in both forward and reverse bias. This modulator achieves near state-of-the-art performance in both modes,
thereby making this device ideal for comparing the two modes of
operation. In reverse bias, the device has a Vπ L of 4.0 V·cm and a
bandwidth of 26 GHz. In forward bias, the device is very sensitive,
a Vπ L as low as 0.0025 V·cm has been achieved, but the bandwidth is only 100 MHz. A new geometry for a reverse-bias device
is proposed, and it is predicted to achieve a Vπ L of 0.5 V·cm.
Index Terms—Diodes, integrated optics, optical communication,
optical modulation, silicon-on-insulator (SOI) technology.
I. INTRODUCTION
NE of the critical components for many silicon photonics applications is an electrooptical modulator. A large
amount of research has been done investigating the use of various optical effects to achieve electrooptic modulation in silicon.
The optical effects used in pure silicon systems include thermal [1], plasma dispersion [2], and the linear electrooptic effect
in strained silicon [3]. Hybrid devices involving other active materials besides silicon have also been employed. These include
modulators based on germanium/silicon heterostructures using
the quantum confined Stark effect [4], and the Franz–Keldysh
effect [5], III–V material bonded to silicon [6], and electrooptic
polymer applied to a silicon slot-waveguide [7]. A large number
of modulators using plasma dispersion have been demonstrated,
and this is perhaps the most mature of these technologies. To use
plasma dispersion for a modulator, a mechanism is necessary to
affect the concentration of free carriers in a waveguide. This has
been achieved in a number of ways. In a p-n diode under reverse
bias, the depletion width can be modulated [8]–[11], removing
free carriers. In a p-i-n diode, free carriers can be injected under
O
Manuscript received May 12, 2009; revised July 2, 2009. Current version
published February 5, 2010. The work of S. J. Spector, M. W. Geis, M. E. Grein,
J. U. Yoon, and T. M. Lyszczarz was supported by the Electronic and Photonic
Integrated Circuit (EPIC) Program of the Defense Advanced Research Projects
Agency (DARPA) under Air Force Contract FA8721-05-C-0002. The work of
C. M. Sorace, E. P. Ippen, and F. X. Kärtner was supported by the DARPA EPIC
Program under Contract W911NF-04-1-0431. The work of C. M. Sorace was
supported by an Ida Green fellowship and by a National Science Foundation
(NSF) graduate research fellowship.
S. J. Spector, M. W. Geis, M. E. Grein, J. U. Yoon, and T. M. Lyszczarz are
with the Lincoln Laboratory, Massachusetts Institute of Technology (MIT),
Lexington, MA 02420 USA (e-mail: spector@ll.mit.edu; geis@ll.mit.edu;
megrein@ll.mit.edu; yoon@ll.mit.edu; lyszczarz@ll.mit.edu).
C. M. Sorace, E. P. Ippen, and F. X. Kärtner are with the Department
of Electrical Engineering and Computer Science, Massachusetts Institute of
Technology (MIT), Cambridge, MA 02139 USA (e-mail: ch20117@mit.edu;
ippen@mit.edu; kaertner@mit.edu).
Digital Object Identifier 10.1109/JSTQE.2009.2027817
forward bias [12]–[14]. In a MOS capacitor, the field effect can
alter the accumulation of free carriers under a gate oxide [15].
The critical characteristics for a modulator are its sensitivity to
applied voltage and high-frequency response. The measurement
and optimization of these characteristics as well as the optical
loss will be discussed for a diode-based modulator.
Table I summarizes the results of the best diode-based carrierdispersion devices currently demonstrated in the literature.
Some devices employ phase shifters in either resonant rings [12]
or disks [10], and some devices use phase shifting waveguides
in a more traditional Mach–Zehnder interferometer arrangement. Modulators using slow-wave structures have also been
demonstrated [16], but these have not yet achieved the performance of the devices listed in the table. For Mach–Zehnderinterferometer-based devices, the standard figure of merit of
Vπ L is listed. Since forward-bias diodes are current driven devices, this figure of merit is only a gauge for comparison with
reverse-bias diodes. Nevertheless, the low Vπ L of the forwardbias devices does reflect the much greater sensitivity of these
devices relative to reverse-bias devices. For devices that use resonant enhancement, a standard figure of merit is not available.
The voltage required to switch the devices is listed, as defined by
the respective authors. This voltage is determined by a number
of characteristics of the device, including device quality factor
(Q), ring diameter, and the performance with respect to carrier
injection of the phase shifter.
For some devices in the literature, the speed or bandwidth
has been directly measured, and the measured value is listed in
the table. Often authors focus on digital performance, and in
those cases only the speed of the device in bits per second is
stated. This performance parameter is listed in the table, when
the bandwidth of the device is unavailable. Often the bandwidth
can be estimated to be greater than half the bit rate, for the
nonreturn-to-zero (NRZ) scheme used in all the devices listed
here. However, in many of these examples, in particular, for
those devices that use forward-bias approaches, preemphasis is
used to compensate for the bandwidth limitations of the device.
The bandwidths of these devices are not simple to estimate from
the available data. Note that the voltages listed are the peak-topeak voltages of the signal into the device after preemphasis.
Because of the different metrics used by different authors, it
is challenging to directly compare the different performance of
the devices. The last two rows in the table represent the results of
this paper’s authors, i.e., a single device that is operated in both
forward and reverse bias. This device has achieved performance
1077-260X/$26.00 © 2010 IEEE
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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 16, NO. 1, JANUARY/FEBRUARY 2010
TABLE I
SUMMARY OF PREVIOUSLY DEMONSTRATED SILICON DIODE MODULATORS
roughly equivalent to that of the best devices in the current literature, for both modes of operation. Analysis of this modulator
will provide a detailed and direct comparison between these two
modes of operation. In forward bias, a Vπ L of 0.0025 V·cm was
achieved with 100 MHz of bandwidth. In reverse bias, Vπ L was
4 V·cm with 26 GHz of bandwidth. Although this is very good
performance for a p-n diode modulator under reverse bias, further optimizations of the design are possible. An improvement
to the design is proposed that is projected to achieve 7× better
sensitivity and a Vπ L of 0.5 V·cm.
II. METHOD
A. Device Description
The modulators are fabricated using Unibond silicon-oninsulator (SOI) wafers with a 0.22-µm-thick layer of silicon
above a 3-µm buried oxide. Fig. 1(a) schematically shows the
top view of the modulator. The active areas of the device are
p-n diode phase shifter sections in the arms of the modulator.
By employing a relatively short interaction length (typically
0.5 mm), a simple lumped element electrode can be used. The
modulator can be operated in a push–pull configuration by driving the center electrode (as shown), or a single arm can be driven.
An additional thermal phase shifter (not shown) is fabricated on
one arm to allow the modulator to be driven at quadrature, regardless of the bias on the diodes.
Fig. 1(b) shows schematically the cross section of the waveguide in the active area of the modulator. The central region, or
core of the waveguide is 220 nm thick, 500 nm wide, and lightly
n-type-doped to a concentration of 2 × 1017 cm−3 . The sidewalls are moderately doped, n-type on one side and p-type on
the other, to a concentration of 1018 cm−3 and an approximate
depth of 50 nm. When a reverse bias is applied, a depletion region forms at the p-n junction on one side of the waveguide. This
depletion region’s size increases into the center of the waveguide
as the bias is increased, thus creating a change in the refractive
index of the waveguide. Under forward bias, carriers are injected
Fig. 1. (a) Top-view layout of the dual-output Mach–Zehnder modulator.
(b) Schematic view of the cross section of one of the phase shifters (all dimensions are in micrometers).
from both sides of the diode, increasing the number of carriers in
the lightly doped n-region in the center. The device acts nearly
identically to a p-i-n diode under forward bias; the lightly doped
n-region in the center has little effect. To make electrical contact
to the core of the waveguide, 50-nm-thick slab regions (heavily
doped, 1019 cm−3 concentration), the waveguide is connected
to metal contacts located 1 µm away. To ensure good ohmic
contact, the silicon slab under the metal contacts is degenerately
doped to a concentration of 1021 cm−3 . The parasitic resistance
of the diodes including ohmic contacts and the resistance of the
doped Si is usually <0.3 Ω·cm.
An adiabatic output coupler [11], [17], instead of the more
standard y-coupler, is used to combine the two arms of the
Mach–Zehnder interferometer. This type of output coupler provides low loss, broadband functionality, and two complementary
outputs (channels 1 and 2) from the modulator. The two complementary outputs can be used in analog applications to linearize
the transfer function of the modulator and to compensate for
fluctuations external to the modulator [18], [19]. To provide
SPECTOR et al.: OPERATION AND OPTIMIZATION OF SILICON-DIODE-BASED OPTICAL MODULATORS
Fig. 3.
Fig. 2.
bias.
167
Response of a 5-mm-long modulator under reverse bias.
Response of the two channels of the 0.5-mm-long modulator in forward
efficient coupling on and off the wafer, reverse taper couplers
combined with lower index oxynitride waveguides [20] are used.
B. Testing Method
For the frequency response measurements, the modulator is
driven in a push–pull configuration. A 1550-nm laser beam
generated by a laser diode with maximum optical power of
∼10 mW is coupled into the modulator via a lensed fiber. A
fiber polarization controller is used to match the polarization of
the input laser to the silicon waveguide. After coupling losses
and other losses, about 1 mW of optical power is estimated to
enter the modulator. The RF signal is generated by a network
analyzer and connected to the modulator chip through a bias tee.
RF powers of approximately 1 mW were used. The output beam
from the modulator chip is collected by an aspheric lens, goes
through a fiber preamplifier, a 2-nm bandpass filter, another fiber
amplifier, and is then finally detected with an ∼50-GHz InGaAs
photodetector. The configuration used to make dc measurements
is similar, but a number of modifications are made. For the
dc measurements, the modulator is driven using a single arm.
Instead of the network analyzer and bias tee, a dc power supply
is used to operate the modulator. The fiber amplifier was no
longer used, and an optical power meter replaced the high-speed
photodetector.
III. EXPERIMENTAL RESULTS
A. DC Characteristics
The dc response of a 0.5-mm-long modulator operated in
forward bias is plotted in Fig. 2. The response is plotted as a
function of the current in the device. The output of channel 1
has a decaying sinusoidal response, with the first peak occurring at a voltage of 0.9 V and 1 mA, and the first minimum
occurring at 1.0 V and 5.5 mA. This gives a Vπ of 0.1 V, or
a Vπ L of 0.005 V·cm. Although Vπ L is a standard metric for
comparing phase shifters, Vπ L is not a good metric for characterizing phase shifter performance when operating in forward
bias. A good universal metric should treat changes in device
length or applied voltage equivalently. However, in forward
bias, the number of free carriers in the device depends primarily on the current in the device and the voltage is clamped
at the knee voltage of the diode. Because the I–V curve for a
diode in forward bias is exponential, a small change in V has a
much larger impact on Vπ L than a small change in L. One can
then lower Vπ L significantly by making the device as short as
possible and making the incremental increase in V necessary to
compensate. This works over the exponential range of the I–V
characteristic until the series resistance in the diode starts to
dominate. A device 0.25 mm long was tested and had roughly
the same performance as the 0.5 mm device giving a Vπ L of
0.0025 V·cm. A better metric for the performance is the signal power required to drive the device between minimum and
maximum transmission. In this case, the average power for a
50% duty cycle square-wave signal is (Vπ /2)(5.5–1) mA =
0.22 mW. It also should be noted that the response (i.e., the
amount of index change) of the device is not linear with current or voltage. The spacing between subsequent maxima and
minima increases with current. Both complementary outputs are
shown in Fig. 2, and the second channel has the expected inverted shape of the first channel, i.e., the second channel goes
low, when the first channel goes high, and vice versa. Both channels show a decaying signal as the current increases due to the
increased absorption from the greater number of free carriers in
the device. The best extinction achieved is 20 dB.
The dc response of a 5-mm-long modulator operated in reverse bias is plotted in Fig. 3 with the response plotted as a
function of voltage. Unlike the shorter device shown earlier,
the extinction achieved is only 4 dB. The poor extinction may
indicate that there is uneven loss in the two long arms of the
modulator. The spacing between the first peak at 3 V and the
minimum at 11 V give a Vπ of 8 V, or a Vπ L of 4 V·cm. As in
the forward-bias case, the response of the device is not linear
(with voltage). This is expected, since the width of the depletion region scales roughly as the square root of voltage. Very
little dc current is needed to operate the device in reverse bias.
There is a small amount of dc current (about 1 µA) that depends
on the intensity of light in the waveguide. This is believed to
be photocurrent generated by defects states, most likely in the
sidewalls of the waveguide [21].
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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 16, NO. 1, JANUARY/FEBRUARY 2010
Fig. 4. Frequency response of the device in forward and reverse bias. The
modified device had its carrier lifetime reduced by Si ion implantation.
B. RF Characteristics
The ac response of the same 0.5-mm-long device operated in
forward and reverse bias is shown in Fig. 4. The bias voltage in
forward bias is 1 V, and the bias voltage in reverse bias is 16 V.
As can be seen from the graph, forward-bias operation is much
more sensitive than reverse bias at lower frequencies. However, the forward-bias operation is limited by the carrier lifetime [14]. Its 3 dB response point is near 100 MHz. Conversely,
reverse-bias operation, which is not limited by the carrier lifetime, has excellent bandwidth with a 3 dB point near 26 GHz.
At smaller reverse biases, the response changes only a little. At
a reverse bias of 2 V, the bandwidth decreases to 20 GHz, due to
an increase in the capacitance, but the sensitivity increases by
2.5 dB. The response curves of the forward and reverse bias (at
16 V) modes of operation cross at 13 GHz. It has been shown
that reducing the carrier lifetime can improve the bandwidth of
the device when operated in forward bias [14]. The response of
a similar device that had its carrier lifetime reduced, by silicon
implantation (with an area dose of 1 × 1014 cm−2 and energy of
190 keV) is also plotted in Fig. 4. Although the implantation did
improve the bandwidth of the device to 1 GHz, this increase in
bandwidth was at the expense of the sensitivity at lower frequencies. At frequencies above 5 GHz the devices with and without
the Si implantation perform nearly identically. The silicon implantation also increases the loss of the waveguide by about
100 dB/cm. It may be possible to reduce the carrier lifetime
without such losses by tailoring the energy of the implant [22].
IV. MODELING AND OPTIMIZATION
A. Forward Bias
The forward-bias response of the device was modeled
previously in [14]. In that work, a numerical model using
SENTAURUS (Synopsys) software was used to predict the performance of the device, and the predictions showed very good
agreement with the experimental performance. There is little
that can be done to further improve the performance of the
device in forward-bias operation. Modeling and experiments
have both shown that decreasing the carrier lifetime improves
the bandwidth, but the sensitivity at higher frequencies does
not actually increase. Fundamentally, the phase change in the
modulator depends on the carriers being driven into the device
and the time it takes for the carriers to leave. At frequencies
slower than the carrier lifetime, the carrier concentration can
reach steady state. At these frequencies, the maximum number
of carriers in the device will depend on the carrier lifetime. A
shorter lifetime will lead to a smaller number of carriers, thereby
reducing sensitivity. However, a shorter lifetime will improve
the bandwidth, because the carriers can reach steady state at a
higher frequency. At frequencies much faster than the carrier
lifetime, the carrier lifetime has no effect on the forward-bias
response.
Small gains can be made by further shrinking the cross section of the device, so that less total charge is necessary for the
same modal index change. There is a limit to how compact the
mode can be before the index of silicon can no longer confine
it. A simple model, where the charge injection is considered be
constant over the cross-sectional area of the device, shows that
a waveguide with dimensions of 400 nm × 150 nm is nearly
optimal. The improvement is only modest, with 17% less charge
necessary for the same modal index change compared to the fabricated device. Shrinking the device also may have the advantage
of decreasing the carrier lifetime without greatly changing the
loss of the device. Carrier lifetime generally scales with the size
of a structure, because much of the carrier recombination occurs
at the surface.
B. Reverse Bias
The dc response of the device in reverse bias has been modeled by solving Poisson and carrier continuity equations [11],
and the model and measurements are in fairly good agreement.
Although this device performs well, further optimizations to improve the sensitivity are possible. Replacing the n-type carriers
with p-type in the center of the waveguide should improve the
device response by nearly a factor of 2 due to the greater index
change caused by p-type carriers at these concentrations [2].
A further improvement can be made by having a horizontal
p-n junction rather than a vertical junction. Previously fabricated designs that use a waveguide with horizontal junction
require an epitaxial overgrowth [8]. Another device has been
demonstrated that has a horizontal junction in a disk [10]. In
this device, the whispering gallery mode of the disk is used,
allowing contact to be made in the center of the disk away from
the mode. Fig. 5 shows a device that is simple to fabricate and
use in a standard Mach–Zehnder and uses a primarily horizontal
junction, and arrangement similar to [23], and [24]. To fabricate
this device, the entire waveguide is doped p-type, and then the
appropriate top part of the waveguide is counter doped n-type at
a higher concentration. (The n-type doping does not extend over
the entire top of the waveguide to allow for realistic alignment
tolerances).
To optimize this device, different thicknesses and different
p-type doping concentrations were modeled. Fig. 6 shows the
performance as the rib height h is changed. To gauge the performance of the device, the index change when the voltage goes
from 0 to 2 V was used as a metric. The optimal rib height
SPECTOR et al.: OPERATION AND OPTIMIZATION OF SILICON-DIODE-BASED OPTICAL MODULATORS
169
Fig. 5. Schematic view of the cross section of a reverse-bias-type device with
a primarily horizontal junction. This device is similar to the device in Fig. 1,
with two important differences: 1) the main part of the waveguide is doped
p-type and 2) the n-type region (doped at 10 1 8 cm−3 ) extends over the top of
the waveguide. This region is 50 nm thick at the side and top of the waveguide.
Fig. 7. Modeled response of the modulator as the p-type doping concentration
in the waveguide is changed. The rib height was held at 100 nm for this set of
modeling data.
Fig. 6. Modeled response of the modulator as the rib height (h in Fig. 5) is
changed. The change in the modal index is plotted as the voltage is changed
from 0 to −2 V.
is found to be 150 nm (for a p-type carrier concentration of
6 × 1017 cm−3 ). This height gives the best performance because
the optical mode overlaps best with the depletion region.
Fig. 7 shows the performance as the p-type doping concentration is altered (with a rib height of 100 nm). For the range of
p-type concentration modeled, the performance improves with
increasing p-type concentration. This is expected, because the
amount of depleted charge in a junction at a given voltage scales
as the square root of the doping concentration [25]. However, as
will be discussed in the next section, optical loss also increases
with carrier concentration. For a reasonable tradeoff, a carrier
concentration of 6 × 1017 cm−3 was chosen for an optimum.
Fig. 8 shows the comparative responses of three modeled devices: the device shown in Fig. 1 (fabricated and tested above),
a similar device with p-type carriers in the center, and an optimized version of the device shown in Fig. 5. The optimized
device is much more sensitive particularly at low voltages. This
device (with a rib height of 150 nm and a p-type doping concentration of 6 × 1017 cm−3 ) achieves a Vπ L of 0.5 V·cm at low
bias voltages. This is a 7× improvement over the original device
that has a modeled Vπ L of 3.5 V·cm at low-bias voltages.
The capacitance of the device was modeled (also using SENTAURUS software) to be 4.9 pF/cm compared to
1.9 pF/cm for the older design. With a 50 Ω impedance from a
power supply and a 700 µm device (necessary to achieve a π
phase shift in a push–pull configuration with ±3 V), the RC time
Fig. 8. Modeled response of three types of modulators under reverse bias.
The old designs are shown in Fig. 1 and can have the center of the waveguide
doped either p-type or n-type. The optimized design is shown in Fig. 5, with a
rib height (h) of 150 nm, and p-type carrier concentration of 6 × 10 1 7 cm−3 in
the center of the waveguide.
constant (τR C = RC) is 17 ps, and the RC-limited bandwidth
(BWR C = (2πτR C )−1 ) is nearly 10 GHz. To achieve higher
bandwidth, a shorter device could be used, but less modulation
depth would be achieved. Traveling-wave electrodes could also
be employed to reduce the RC time constant limitation [26].
C. Optical Loss
The device described previously was optimized for sensitivity, but for some applications low loss may be more important.
Because the same carriers that are necessary for index change
cause absorption, any modulator that relies on plasma dispersion will intrinsically have some optical loss. The formulas used
to relate carrier concentration to index change and optical loss
at a wavelength of 1.55 µm are
∆n = ∆ne + ∆nh = −8.8 × 10−22
∆Ne − 8.5 × 10−18 (∆Nh )0.8
(1)
∆α = ∆αe + ∆αh = 9.1 × 10−22
∆Ne1.22 + 2.5 × 10−20 ∆Nh1.13
(2)
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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 16, NO. 1, JANUARY/FEBRUARY 2010
anisms, such as sidewall scattering, which will also limit how
low the achievable optical loss is.
V. CONCLUSION
Fig. 9.
Length and loss for a π phase shift with p-type carriers in bulk silicon.
where ∆ne is the change in refractive index resulting from the
change in free electron carrier concentrations, ∆Ne , ∆nh is the
change in refractive index resulting from the change in free hole
carrier concentrations, ∆Nh , ∆αe and ∆αh are the changes in
absorption resulting from ∆Ne and ∆Nh , respectively, and ∆n
and ∆α are the net changes in refractive index and absorption,
respectively. The earlier modeling of the modulators used (1),
which is a commonly used approximation to the data of Soref
and Bennet [2]. It should be noted that (2) differs from the commonly used approximation for the optical absorption, because
in this case, the approximation can result in substantial error.
The nonlinear equation (2) is a power law fit to the data in [2]
and follows the experimental data in [2] much more accurately.
For p-type dopants, the ratio of index change to loss
(∆nh /∆αh ) is not constant with changes in ∆Nh . As a first
step in estimating the loss in a modulator, consider a phase
shifter in bulk silicon with only p-type carriers. p-Type carriers are chosen because they give greater index change and less
absorption than n-type carriers. The absorption versus carrier
concentration in bulk p-type silicon is plotted in Fig. 9. This
figure shows the amount of loss versus carrier concentration
in enough silicon thickness for the carriers to cause a π phase
shift. Also plotted in this figure is the thickness of the silicon
that gives a π phase shift. As the concentration is lowered, the
ratio of ∆nh /∆αh improves and the optical loss goes down, but
the length of the device required for a π phase shift increases.
In general, the optimization of loss will lead to less sensitive,
longer devices with lower carrier concentrations. This is true
even for devices that reach full depletion (i.e., no carriers within
the mode at maximum reverse bias) during operation. Although
full modeling of the losses in the devices described earlier has
not been done, the best-performing devices have the highest
carrier concentration and can be expected to have the highest
optical losses.
Fig. 9 also provides an estimate of the minimum loss that can
be achieved in a modulator. Lengths greater than a few centimeters are likely impractical for high-speed devices, limiting the
loss to around 0.2 dB. Real devices will have other loss mech-
A modulator has been demonstrated that can be operated
in forward and reverse bias, with performance similar to the
best devices that have been demonstrated using either mode
of operation. This device is ideally suited for making a direct
comparison between these two modes of operation. In forward
bias, the device is very sensitive (Vπ L = 0.0025 V·cm) but
has low bandwidth (∼100 MHz). In reverse bias, the device is
much less sensitive (Vπ L = 4 V·cm), but has higher bandwidth
(∼26 GHz). The response curves of the two modes of operation
cross at 13 GHz; below 13 GHz forward bias is more sensitive,
while above 13 GHz reverse bias is more sensitive. For lower
speed applications, a device that operates in forward bias may be
preferred. The bandwidth of the forward-biased device can be
extended by using a high-pass, preemphasis filter, or by lowering
the carrier lifetime in the device. Both of these techniques create
a flatter response by lowering the low-frequency response of the
system.
Forward-bias phase shifters are already close to their fundamental limit in performance. Small improvements can be made
by changing the geometry of the device, but dramatic improvements are unlikely. There is, however, room for improvement
in reverse-bias devices. A new geometry for reverse-bias operation, using a horizontal junction, was proposed and optimized,
and this device is modeled to have a 7× improvement in sensitivity. This improved reverse-biased device may be preferable over
a forward-bias device for all but the lowest speed applications.
To achieve low optical loss in a modulator, a device that relies
on p-type carriers at relatively low concentrations is best. Lower
carrier concentrations, however, reduce sensitivity and increase
device length. When designing a device, it may be necessary to
tradeoff sensitivity for optical loss.
ACKNOWLEDGMENT
The authors would like to thank the assistance of D. Lennon,
J. Knecht, D. Yost, R. Schulein, F. Gan, and G.-R. (Rona) Zhou.
The authors also would like to thank M. Popović for the design
of the adiabatic output coupler, and discussions with M. Watts.
Opinions, interpretations, conclusions, and recommendations
are those of the authors, and do not necessarily represent the
view of the United States Government.
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Steven J. Spector received the Ph.D. degree in physics from the State University of New York at Stony Brook, Stony Brook, NY, in 1997.
From 1997 to 1999, he was a Postdoctoral Member of staff at Bell Laboratories, Lucent Technologies. In 1999, he joined the Lincoln Laboratory,
Massachusetts Institute of Technology (MIT), Cambridge, as a staff member.
He was a Program Co-Chair in 2007 and a General Co-Chair in 2008 for the
Optical Society of America (OSA) Topical Meeting on Integrated Photonics and
Nanophotonics Research and Applications. He previously was engaged in the
fabrication of high-resolution zone plates for soft X-ray microscopy, and also
involved in EUV mask blank inspection. His current research interests include
the development of silicon photonic devices.
Dr. Spector is a member of the OSA.
Cheryl M. Sorace received the B.S. degree in engineering physics from Cornell
University, Ithaca, NY, in 2008. is a first-year graduate studen in the Optics and
Quantum Electronics Group, Massachusetts Institute of Technology (MIT),
Cambridge..
She is a first-year Graduate Student in the Optics and Quantum Electronics
Group, Massachusetts Institute of Technology (MIT), Cambridge. She is a
National Science Foundation Graduate Research Fellow. Her current research
interests include integrated photonics and the interaction between light and
matter.
Ms. Sorace was awarded the Ida Green Fellowship by MIT in 2008. She is a
Student Member of the Optical Society of America (OSA).
Michael W. Geis received the B.A. degree in physics, the M.S. degree in electrical engineering in 1970, and the Ph.D. degree in space physics and astronomy
in 1976 from Rice University, Houston, TX.
During his graduate work, he studied atomic and molecular physics with
emphasis on charge exchange reactions. From 1976 to 1978, he was a Postdoctoral Student in the Chemistry Department, Rice University, where he
was engaged in laser-driven chemical reactions between molecular beams. In
1978, he joined the Submicrometer Technology Group, Lincoln Laboratory,
Massachusetts Institute of Technology (MIT), Cambridge. He has been involved
with semiconductor-on-insulator technology using zone-melting recrystallization, submicrometer structure fabrication, dry etching with reactive ion etching
and ion-beam-assisted etching, diamond growth and devices. He has authored or
coauthored more than 100 journal papers. He is currently engaged in developing
cold cathodes, signal processing using optics, and liquid crystal optical shutters.
Matthew E. Grein, photograph and biography not available at the time of
publication.
172
IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 16, NO. 1, JANUARY/FEBRUARY 2010
Jung U. Yoon, photograph and biography not available at the time of publication.
Theodore M. Lyszczarz (M’79), photograph and biography not available at the
time of publication.
Erich P. Ippen (S’66–M’69–SM’81–F’84–LF’06), photograph and biography
not available at the time of publication.
Franz X. Kärtner (S’87–M’89–SM’04–F’09) received the Diploma and
Ph.D. degrees in electrical engineering from Technische Universität München,
Munchen, Germany, in 1986 and 1989, respectively, and the Habilitation degree
in experimental physics from the Swiss Federal Institute of Technology (ETH),
Zurich, Switzerland, in 1997.
From 1991 to 1993, he was a Feodor-Lynen Fellow of the Alexander von
Humboldt Stiftung at Massachusetts Institute of Technology (MIT). From 1993
to 1997, he was a Research Scientist at the ETH. He was a Visiting Professor
at MIT. In 1998, he joined the Electrical Engineering Department, Universität
Karlsruhe (TH), Karlsruhe, Germany, where he was the Head of the High Frequency and Quantum Electronics Laboratory. In 2001, he returned to MIT,
where he is currently a Professor in the Department of Electrical Engineering and Computer Science. His current research interests include classical and
quantum noise in electronic and optical devices; femtosecond lasers and their
applications in frequency metrology, precision timing distribution, high-speed
signal processing and attosecond science.
Dr. Kärtner was a Program Co-Chair and a General Co-Chair for the IEEE
Photonics Society [formerly known as the IEEE Laser and Electro-Optics Society (LEOS)] Annual Meetings 2002 and 2004, the Conference on Lasers and
Electro-Optics 2007 and 2009, and is currently the Chair of Ultrafast Optical
Phenomena Technical Group of OSA 2008–2010 and the Chair of the Commission D, Electronics and Photonics, International Union of Radio Scientists
(URSI) 2008–2011. He is a Fellow of the Optical Society of America.