ARSAdvances in Radio ScienceARSAdv. Radio Sci.1684-9973Copernicus PublicationsGöttingen, Germany10.5194/ars-15-269-2017Design of a carrier-depletion Mach-Zehnder modulator in 250 nm
silicon-on-insulator technologyFélix RosaMaríamaria.felix-rosa@int.uni-stuttgart.deRathgeberLotteElsterRaikHoppeNiklashttps://orcid.org/0000-0001-8818-3144FöhnThomasSchmidtMartinVogelWolfgangBerrothManfredUniversity of Stuttgart, Institute for Electrical and Optical
Communications Engineering, Stuttgart, GermanyMaría Félix Rosa (maria.felix-rosa@int.uni-stuttgart.de)5December20171526928115January201718September201719October2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://ars.copernicus.org/articles/15/269/2017/ars-15-269-2017.htmlThe full text article is available as a PDF file from https://ars.copernicus.org/articles/15/269/2017/ars-15-269-2017.pdf
We present the design of a single-drive Mach-Zehnder modulator for amplitude
modulation in silicon-on-insulator technology with 250 nm active layer
thickness. The applied RF signal modulates the carrier density in a reverse
biased lateral pn-junction. The free carrier plasma dispersion effect in
silicon leads to a change in the refractive index. The modulation efficiency
and the optical loss due to free carriers are analyzed for different doping
configurations. The intrinsic electrical parameters of the pn-junction of the
phase shifter like resistance and capacitance and the corresponding RC-limit
are studied. A first prototype in this technology fabricated at the IMS CHIPS
Stuttgart is successfully measured. The structure has a modulation efficiency
of VπL=3.1 V⋅cm at 2 V reverse bias. The on-chip insertion loss is
4.2 dB. The structure exhibits an extinction ratio of around 32 dB. The
length of the phase shifter is 0.5 mm. The cutoff frequency of the entire
modulator is 30 GHz at 2 V. Finally, an optimization of the doping
structure is presented to reduce the optical loss and to improve the
modulation efficiency. The optimized silicon optical modulator shows a
theoretical modulation efficiency of VπL=1.8 V⋅cm at 6 V bias and
a maximum optical loss due to the free carrier absorption of around
3.1 dB cm-1. An ultra-low fiber-to-fiber loss of approximately 4.8 dB
is expected using the state of the art optical components in the used
technology.
Scheme of the designed Mach-Zehnder modulator.
Introduction
Backhaul nets rely on custom made high-speed electro-optical components. The
ever increasing data rates and associated rising complexity and costs are
the main driver for the integration of complete optical systems on a single
die. One of the key components of such a system is the optical modulator.
High modulation efficiency, small size, low driving voltage, high extinction
ratio (ER), low optical loss and wide bandwidth are the figures of merit of
the modulators to be optimized.
During the last years our group has presented CMOS compatible grating
couplers (GC) with a record coupling efficiency of η=-0.62 dB
(Zaoui et al., 2014) in a 250 nm silicon-on-insulator (SOI) platform
fabricated at the Institut für Mikroelektronik Stuttgart (IMS CHIPS).
The low losses of the fiber-to-chip coupling (Zaoui et al., 2014) or
polarization splitting (Zaoui et al., 2013) are an important benefit to
reduce the total loss of the optical modulator. Due to this fact a first
design of a silicon optical modulator utilizing this technology is realized
in this work serving as a preparative step for the fabrication of a low loss
and highly efficient modulator in a CMOS compatible technology.
The influence of the doping concentration and the geometry of the phase
shifter on the modulator performance for different technologies are
investigated in the literature (e.g., Petousi et al., 2013; Goykhman et
al., 2013). Based on these works we present the study of the influence of
the most important design parameters of the modulator in the novel
technology developed by IMS CHIPS using 250 nm active Si instead of the
standard 220 nm. First, the geometry of the waveguide is calculated for a
single mode propagation and low loss. Then, an analysis of the doping
influence on the modulation efficiency performance and optical loss is done
for the fabrication of a prototype. The measurement results of the
fabricated device are presented in this work as a validation. Furthermore,
an optimization of the doping is realized to improve the modulation
efficiency and optical loss of the structure. Finally, the results are
compared with the work of other research groups.
Design of the device
In this work a silicon optical modulator is simulated for fabrication in the
IMS CHIPS technology for the first time. The used SOI-wafer has a 625 µm
thick silicon substrate with a 3 µm thick buried oxide (BOX) layer. On
top is a 250 nm thick active silicon layer in which the components are
structured. The SOI-wafer is passivated with a 1 µm thick SiO2
layer. A 500 nm thick aluminum metal layer is added and structured on top of
the processed wafer. The active silicon is connected to the top metal
through vias.
(a) Scheme of the silicon ridge waveguide with the contact
regions. (b) Calculated total resistance (in Ωcm) of the slabs
depending on the thickness hsl and the length of the slabs s for two
different doping concentrations. Na (acceptors) and Nd(donors). (c) Simulation of the loss depending on the distance s for
different slab thicknesses hsl (h=250 nm, w=400 nm).
The design consists of a single-drive Mach-Zehnder modulator (MZM) for
amplitude modulation (Fig. 1). Two transversal electric (TE) mode grating
couplers followed by a linear taper couple the light between single mode
fibers and the 400 nm wide waveguides. A 1×2 multimode interference coupler
(MMI) splits the light uniformly in both interferometer arms. Two branches
of doped waveguides, one of them connected to an RF coplanar line through
vias, perform the modulation. Another 2×1 MMI acts as power combiner. Both
waveguides are doped to get similar optical loss in both branches and hence
to maximize the ER of the modulator. Only one arm is driven during
modulation for an easier characterization and comparison with the
simulations. A delay line is added in one branch to increase the optical
path difference (OPD) resulting in a reduction of the free spectral range in
the optical transmission spectrum. Hence, the phase shift produced by the
modulator section can be easily observed by analyzing a small wavelength
range. The modulation relies on the free carrier plasma dispersion effect: a
pn-junction allows to modulate the free carrier density locally in the
waveguide core with an external DC or RF voltage. A change in the density of
free carriers leads to a change in the refractive index Δn, but also
to a change in the attenuation Δα (Soref and Bennett, 1987).
Estimation of the ridge waveguide geometry
The research on the geometric dimensions is carried out by simulating the
mode profiles in a ridge waveguide for a wavelength of 1550 nm. In Fig. 2a
the most important geometric parameters are described. The height
h=250 nm is determined by the thickness of the silicon layer of the
wafer. For the optimization of the waveguide width, it is considered that
only the fundamental TE mode should be guided in the core in order to avoid
multimode interference. For narrow waveguides the mode is not well confined
in the silicon waveguide core. Therefore, the attenuation α is high
if additional absorption due to highly doped Si or metal regions occurs.
Hence, the waveguide core should be designed as wide as possible. However,
for a core width of 420 nm and above, the second order TE mode can propagate
as well. Thus, the waveguide width is set to w=400 nm.
The RF metal lines are connected through metal vias to a 250 nm thick highly
doped Si region for a better ohmic contact. The height of the silicon
underneath the metal contact should not be too small, particularly if the
height hsl is very small. Then, the contact resistance between metal and
the doped silicon is much lower and the influence of process variations is
minimized.
The distance s between the metal vias and the silicon waveguide core has a
huge influence on the attenuation of the optical signal, since the highly
doped Si (∼ 1020 cm-3) and the metal, with a
complex refractive index n=n+iκ,
strongly attenuate the optical modes. This means, on the one hand, that the
distance s should be chosen to be as large as possible. On the other hand, it
has to be taken into account that for a greater distance s, the electrical
resistance also increases weakening the electrical performance of the
device. In Fig. 2b the calculated total resistance R in Ωcm (to
calculate the resistance in Ω, the resistance R has to be divided by
the phase shifter length L) of the slabs is plotted for different slab
thickness hsl depending on the distance s. Rn and Rp are the
resistances in Ωcm of the n- and p-doped slabs.
R=Rn+Rp=s⋅ρnhsl+s⋅ρphsl
The resistance (if the slabs are lowly doped) is analytically calculated for
two different doping densities, being Na and Nd the doping
concentration of the p- and n-doped regions. The parameters ρn
and ρp are the resistivity of the n- and p-doped silicon.
In addition, the attenuation is significantly greater at the same distance
s, if a higher proportion of the electric field of the propagation light is
present in the region of the metal contact. Therefore, the ratio
hsl/h should be as small as possible to keep the optical mode confined in
the waveguide core. Figure 2c shows the attenuation over the distance s (of
the structure with intrinsic Si core and slabs as shown in Fig. 2a) for
different slab thicknesses hsl. As the heighthsl increases, the
distance in which the metal should be positioned to obtain the same
attenuation shifts to larger values.
The slab thickness hsl=50 nm is chosen to keep the optical mode
confined in the core of the waveguide. That maximizes the modulation due to
the carrier-depletion in the core of the waveguide. Hence, the minimum
spacing of the metal chosen in the following is s=1.25µm to
minimize the optical loss.
Scheme of the different parameters regarding the geometry and
doping of the modulator. Three variants of the doping profile are simulated
(pn-, n- and p-doped core). The values of the parameters h,hsl, w and s are
fixed.
Simulations of (a) the change of the effective refractive index,
(b) the attenuation, (c) modulation efficiency and VπL⋅α
depending on the reverse bias voltage for different doping profiles in the
waveguide core (sp=sn=s=1.25µm;
hsl=50 nm; Na=Nd=1× 1017 cm-3).
Doping profile
The next step in the design of the modulator is to optimize the doping
profile. The result of the calculated parameters Δneff and
α depends on the doping of the waveguide. The simulations are
realized with the commercial software RSoft from Synopsys®.
The finite element method (FEM) is used to simulate the propagating and
leaky modes of the doped waveguide cross section. The carrier effect is
included in the simulations by utilizing the Multi-Physics Utility of the
software. The change of the optical refractive index and the absorption
generated by the free carrier distributions is determined from the model
described in Soref and Bennett (1987).
The influence of the doping concentration requires a balancing between these
parameters: a higher doping concentration allows for a higher change of the
effective refractive index Δneff, but the optical loss increases
with the free carrier density. The distance from the p+- and
n+-type doped regions to the waveguide core is sp and sn,
respectively. For a good ohmic contact, the high doping concentration is
determined as Na+,d+=1×1020 cm-3.
Three different doping profiles of the waveguide core are depicted in
Fig. 3. The doping concentration for the lowly doped regions is
Na,d=1× 1017 cm-3. In this section the distances
sn and sp are the same as s=1.25µm to analyze the loss
caused only for the carrier absorption of the low doping. In Sect. 7 these
distances are varied to optimize the structure. The attenuation α is
always given at 0 V since for higher bias voltages the free carrier density
in the waveguide core is lower. The simulation results of the different
doping profiles are presented in Fig. 4.
(a) Doping profile of a p-doped (left) and pn-doped (right)
waveguide (Na=Nd=1× 1017 cm-3). (b) Free
carrier concentration for the applied reverse bias voltage of 0 V, (c) 3 V
and (d) 6 V.
3-D view of the phase shifter. Analysis of the intrinsic RC-limit
caused by the electrical properties of the depletion region in the optical
waveguide.
A purely p-doped core is compared to a purely n-doped core. For p-type
doping a Δneff more than three times higher than for n-type
doping is obtained at the same voltage (Fig. 4a). Besides, the attenuation
is lower for p-type doping (Fig. 4b). The results for the pn-doped core
(p/n doped-curve) are analyzed in detail. In this case the change of the
effective refractive index Δneff rises with the reverse voltage
faster than for the purely p-doped core, but it flattens for higher reverse
voltages (Fig. 4a). The attenuation is lower than for the purely p- or
n-doped core from 0 to 6 V and also decreases with the reverse voltage
until the curve flattens (Fig. 4b). The effect of charge carrier-depletion
is therefore significantly greater than for purely p-type doping. Figure 4c
shows a comparison of the modulation efficiency (VπL) and the figures
of merit that combine the modulation efficiency with the respective optical
loss due to the free carrier absorption (VπL⋅α) of the two
doping profiles (pn- and p-doped cores). The modulation efficiency is calculated
as
VπL=λ⋅V2⋅Δneff=λ⋅V2(neffV-neffV=0V),
being λ=1550 nm the wavelength, V the reverse bias voltage,
neff(V) the effective index at the applied bias voltage V and
neff(V=0V) the effective index at the voltage V=0 V.
The pn-doped core exhibits a better performance in the modulation efficiency
till 5.5 V with respect to the p-doped core design. For higher bias voltages
the p-doped core design has a better modulation efficiency (i.e., lower
VπL). The VπL⋅α is noticeably lower for the pn-doped due
to the reduction in the loss caused by the decrease of free carriers in the
core of the waveguide because of the depletion (see Fig. 5). The simulations
show a VπL=1.9 V⋅cm and approximately VπL⋅α=1 V⋅dB at 2 V for the pn-doped core and VπL=2.9 V⋅cm and around VπL⋅α=7 V⋅dB at 2 V for
the p-doped core. At the bias voltage of 6 V compared to 2 V the simulation
results show for the pn-doped core design a stronger change in figure of
merit: VπL=3.9 V⋅cm and VπL⋅α=0.6 V⋅dB. The p-doped
core changes significantly less in the values obtained: VπL=3.7 V⋅cm and VπL⋅α=6.5 V⋅dB.
(a) Total resistance in Ωcm (normalized with the phase
shifter length) of the symmetrically p- and n-doped slabs with
hsl=50 nm for different doping concentrations and slab lengths. (b)
Junction capacitance per unit length of the phase shifter and (c) cutoff
frequency depending on the doping concentration and reverse bias voltage for
a pn-junction in the center of the waveguide core for a length of the phase
shifter of L=1 mm and sn,p=1.25µm.
Figure 5 is shown as example of the working principle of the simulated p- and
pn-doped waveguide core for a better understanding of the simulation results
of Fig. 4. A comparison of the free carrier distribution of both structures
is depicted for different reverse bias voltages. In the p-doped case, which
is shown in the left column of the figure, the free charge carriers are
present in the core and migrate with the voltage. The depletion region is
formed at the edge of the core. However, the maximum of the optical electric
field lies in the center of the waveguide and only a small portion overlaps
with the region of the charge carrier-depletion. The situation is different
in the pn-doped waveguide, shown on the right column of Fig. 5. Here, there
is a depleted region at 0 V in the center of the waveguide, where the
maximum of the electric field is placed. Thus, the attenuation is smaller
than in the p-doped case. When the voltage is applied, electrons and holes
move and the depletion region expands. For a reverse bias voltage between
0 and 3 V (Fig. 5b, c) the high change in the free carrier
concentration occurs in the waveguide core. Here, the optical field is
confined, therefore the Δneff is large and also the modulation
efficiency. When the applied reverse voltage exceeds 4 V the depletion
region is wider than the waveguide core (Fig. 5d) and the Δneff starts to flatten (Fig. 4a), since almost all free carriers are
removed.
The modulation performance could be improved by further optimization of the
doping concentration. That is realized for the case of the p-doped waveguide
core in Sect. 7. The fabrication of the pn-doped core is a technological
challenge because misalignments could produce a wide undoped region. That
results in a significant deterioration of the modulation efficiency of the
device. Therefore, for our first prototype the p-doped core type is chosen.
Analysis of the RC-limit of the modulator
The high-speed performance of the optical modulator depends on factors like:
bandwidth and loss of the transmission lines (TLs), similar velocity of the
optical and electrical signal for long phase shifters, loss of the optical
waveguides, a good matching between the characteristic impedance of the TL
and the modulator driver or the termination impedance (in this work we
measure the device on wafer with a termination impedance of 50 Ω)
and the intrinsic RC-limit caused by electrical properties of the depletion
region in the optical waveguide.
The total resistance per unit length R of the slabs of the optical waveguide
symmetrically doped are calculated using Eq. (1) for different lengths of
the lowly doped region in the slabs with hsl=50 nm. As expected the
resistance is reduced for higher doping concentrations and increases with
the lowly doped slab length (Fig. 7a). The contribution of the p-doped
region in the total resistance is higher than the n-doped due to the
resistivity of p-doped is around twice higher than for n-doped for the same
doping concentration.
The junction capacitance of the modulator Cj per unit length of the
phase shifter is calculated by
Cj=AL⋅qε0εrSiNaNd2Na+Nd(Vbi-V)
where A=h⋅L is the cross section area of the pn-junction. The
thickness of the cross section is h= 250 nm since the pn-junction is formed
in the waveguide core and the depletion width is smaller than the waveguide
core width w. L is the length of the phase shifter, ε0 and
εrSi are the permittivity of the free space and the
dielectric constant of silicon, q is the elementary charge, Vbi is the
built-in potential voltage and V is the applied voltage. The junction
capacitance is calculated for the pn-junction in the center of the waveguide
depending on the applied reverse bias voltage. In Fig. 7b Cj is
plotted for the applied voltages (1–6 V) varying the acceptor
concentration for fixed donor concentration of Nd=1× 1017 cm-3 (blue curves) and
Nd=1× 1018 cm-3 (red curves). The intrinsic 3 dB bandwidth (cutoff
frequency fc) is calculated according to
fc=12πRsC
for the reverse bias voltages 2 and 6 V, being C the junction capacitance
in pF (C=Cj⋅L). The donor concentration is the same as
in Fig. 7b and the corresponding value of the Cj of this figure is
used for the calculation of the cutoff frequency of Fig. 7c. The series
resistance Rs is calculated using Eq. (1) by
Rs=RL+50Ω=Rn+RpL+50Ω=sn⋅ρnhsl+sp⋅ρphslL+50Ω
for a phase shifter length of L=1 mm and a slab length of
s=sn=sp=1.25µm. The 50 Ω load impedance is
added in the calculation of Rs. For a donor concentration of
Nd=1× 1017 cm-3 the cutoff frequency shows
only a weak dependence on the acceptor concentration. At 6 and 2 V reverse
bias voltages cutoff frequencies of 23 GHz (C=0.0826 pF and
Rs=82.5Ω) and 15 GHz (C=0.128 pF and
Rs=82.5Ω) are achieved for a phase shifter length
L=1 mm, sn,p=1.25µm, Nd=1× 1017 cm-3 and Na=10× 1017 cm-3. For a
higher donor concentration of Nd=1× 1018 cm-3 the increase of the junction capacitance due to the higher doping does not
compensate the decrease in the resistance and therefore lower values of
fc are achieved.
(a) Modification of the lateral pn-junction. (b) Relative
capacitances for the simplification of the calculation of the total junction
capacitance.
(a) Layout of a MZM with a phase shifter length of 500 µm,
(b) MZM micrograph.
Cross section of the fabricated phase modulator.
Measurement of the optical transmission of the MZM for different
reverse bias voltages.
Measurement of the transmission (a) and reflection (b) of
the TL and the TWEs of the modulator with same dimensions for different
applied voltages.
(a) Layout MZM. Position 1: Symmetric CPW. Position 2: Start of
the phase shifter, the CPW is not symmetric along the phase shifter because
of the diode (pn-junction) under the metal lines. (b) Asymmetric and
symmetric CPW.
Scheme of the measured aluminum coplanar waveguide.
Measurement results of the (a) transmission and (b)
reflection vs. frequency for the structure in Fig. 14.
Scheme of the simulated structure.
sp=sn=0.5µm, s=1.25µm, hsl=50 nm, Na+,d+=1×1020 cm-3.
Simulations of (a) the change of the effective refractive index
at 6 V, (b) the attenuation at 0 V, (c) modulation efficiency and VπL⋅α of the structure shown in Fig. 16 varying the acceptor doping
density Na for two donor doping densities Nd.
Scheme of the simulated structure. The distance sp,n is
varied. Na=9×1016 cm-3,
Nd=1×1018 cm-3, Na+,d+=1×1020 cm-3, s=1.25µm, hsl=50 nm.
Simulation of (a) the optical loss regarding the free carrier
absorption at 0 V and (b)VπL⋅α vs. the distance from the core
to the area with high doping concentration for the structure in Fig. 18.
The analytical calculation of the junction capacitance for the waveguide
with p-doped core (Fig. 5a left) is more complicated because of the
different heights of the p- and n-doped regions. To simplify the calculation
a conversion of the pn-junction is realized, where the height of the p-side
is adapted as shown Fig. 8a and the doping of the p-side is transformed by
N′a=Nahhsl.
The relative width of the depletion region depending on the newly adapted
doping is calculated as
dn=wdepN′aNd+N′aanddp=wdepNdNd+N′a.
The depletion width wdep is
wdep=2qε0εr(Na+Nd)(Vbi-V)qNaNd.
Then, the total junction capacitance is divided into three new capacitances
as shown Fig. 8b and calculated by
Cj=11Cj1+1Cj2+Cj3.
The numeric expressions for the relative capacitances Cj1, Cj2 and
Cj3 are calculated using the method of conformal mapping as described by
(Yu and Bogaerts, 2012) including the effect of the electrical field out of
the pn-junction (Cch) described in Chang (1976)
Cj1=CCh1-ε0εr,Sihdpεr,SiO2εr,Si+ε0εr,Sihdp,Cj2=CCh2-ε0εr,Sihdnεr,SiO2εr,Si+ε0εr,Sihdn
and
Cj3=12CCh3-ε0εr,SiO2hslwdep/2.
At 0 V bias voltage the total junction capacitance of the fabricated device
described in the next section (Fig. 10) is
Cj=119.19pFcm+11.078pFcm+0.076pFcm≈1.04pFcm.
The same cross section is simulated using the software CST-Microwave Studio
with a result of 1.01 pFcm for an ideal pn-junction of the
structure. This matches well with the analytical model. The series
resistance is Rs=79Ω (sn,p=400 nm;
hsl=80 nm). Therefore, the expected cutoff frequency at 0 V bias
voltage is 39 GHz. For higher bias voltages the junction capacitance is
reduced (Cj (2 V) = 0.65pFcm and
Cj (6 V) = 0.49pFcm) and the calculated cutoff frequencies
are fc (2 V) = 62 GHz and fc (6 V) = 82 GHz.
Fabricated structure and measurement results
First designed optical modulator in IMS CHIPS technology is successfully
measured. The device is fabricated as a prototype to prove the accuracy of
the simulations and the functionality of the used technology. The layout and
micrograph of the complete MZM with a 500 µm long phase shifter is
shown in Fig. 9. The cross-section of the phase modulator is presented in
Fig. 10.
The target doping concentrations in the p- and n-doped regions are
1 × 1017 cm-3. In this design the distances
s= 0.7 µm and sp,n= 0.4 µm are smaller the optimum
dimensions shown in the previous simulations (Fig. 4). Besides, instead of
the target slab thickness hsl= 50 nm, the fabricated structure has a
slab thickness of 80 nm due to fabrication deviations during the silicon
etching process. Therefore, higher optical loss is expected for this device
(see Fig. 2b and Fig. 4b).
For DC measurements a DC voltage source is connected through a bias-T to a
ground-signal-ground (GSG) probe. The optical transmission spectrum for
different reverse bias voltages is plotted in Fig. 11. The fiber-to-fiber
insertion loss (IL) of the entire MZM, that includes the losses of the
gratings, tapers and MMIs, is 12.5 dB for λ= 1550 nm. The GC
used for this design is a standard one, therefore the total loss could be
reduced by using the high efficient couplers (η=-0.74 dB at
λ= 1550 nm) developed by our group in the same technology
(Zaoui et al., 2014) reducing the total loss of the modulator by
approximately 6 dB. The IL on-chip is 4.2 dB for 0 V bias. The loss of the
phase shifter is about 2 dB mm-1. The passive ER is around 32 dB and the
modulation efficiency is VπL=3.1 V⋅cm
at 2 V reverse bias voltage. The simulated modulation efficiency for this
structure is VπL=2.87 V⋅cm with a loss of
1 dB mm-1. The difference with the measured one is probably caused by
irregularities in the doping or misalignment of the doping masks during
fabrication. Same simulations are realized with a horizontal shift of
∼ 150 nm of the highly doping mask and similar results as the
measured ones are demonstrated.
The frequency response of the MZM is examined. High frequency measurements
of the coplanar waveguides (CPW) working as traveling wave electrodes (TWEs)
of the modulator are realized for different bias voltages. The measurements
of the TWEs are compared in Fig. 12 with the response of the TL with the
same dimensions (Wm= 7.9 µm and sm= 2.2 µm)
without the MZM under the RF coplanar lines. The TL shows a similar
transmission than the TWEs of the optical modulator. The difference is the
resonance of the TWEs around 30 GHz. The doped silicon ridge waveguide used
to modulate the light using the plasma dispersion effect works as a diode.
In the core of the waveguide there is a depletion region caused by the
reverse bias voltage applied to the waveguide through the TWEs. By
increasing the supply voltage, the depletion region becomes wider.
Consequently, the variable junction capacitance decreases and the electrical
transmission of the modulator improves. In addition, the asymmetric
configuration of the modulator favors the mode conversion of the CPW mode
(in Fig. 13a position 1 with symmetric CPW) to the unwanted
coupled-slotline (CSL) mode (in Fig. 13a position 2 with asymmetry because
of the diode under the CPW). That also explains that in the case of the TL
without modulator under the lines, therefore symmetric, the resonance is not
observed. To suppress this CSL mode, air-bridges could be used to flatten
the frequency response curve and thus increase the bandwidth (Jongjoo Lee
et al., 1999; Hao Xu et al., 2014). Therefore, the bandwidth of the device
calculated in Sect. 5 could be achieved if this undesired effect is
diminished. This is difficult because the ground lines have a width smaller
than 8 µm. That is too small for the use of bond wires to minimize
this effect. Nevertheless, in future designs this fact should be taken into
account to avoid undesirable effects using symmetric CPW as presented in
Fig. 13b.
If the velocities of the driving electrical signal and optical wave match
perfectly, the 6.4 dB-electrical bandwidth of the TWEs corresponds to the
3 dB-electro-optical bandwidth of the modulator. The 6.4 dB-electrical
bandwidth of the modulator for the voltage range from 0 to 2 V is 30 GHz.
However, for higher voltages like 8 V (green curve) a bandwidth higher than
50 GHz can be reached. The reflection of the TWEs keeps below -10 dB up to
50 GHz.
New dimensions of the transmission lines are simulated to improve the
performance with respect to the bandwidth and loss by using the software
Momentum of Advance Design System (ADS). The dimensions are based on the
previous simulations of the optical doped waveguide, since the distance
between the metal lines depends on the length of the slabs
(s= 1.25 µm). Therefore, the space between the metal lines
sm is kept lower than 2.9 µm. The optimized coplanar line is
fabricated and measured on wafer using RF-probes with a pitch of 100 µm. The new transmission line is also designed as an L-shape line (Fig. 9 and
Fig. 14), based on the measurement setup used. In Fig. 15 the measurement
results are compared with the dimensions of the coplanar TL presented before
(Fig. 12). With a line width of Wm= 16.7 µm and a distance
between the metal lines of sm= 2.8 µm the loss of the line is at
50 GHz less than 3.2 dB and approximately 0.5 dB at low frequencies. Both
lines have a 3 dB bandwidth greater than 50 GHz. The new design offers a
better frequency response with a lower loss in the whole measured spectrum
and the reflection is kept lower than -20 dB up to 50 GHz.
Optimization using different doping concentrations for p- and n-doped
regions – influence in the modulation performance and optical loss of the
distance from waveguide core to the highly doped regions
For the optimization of the structure new simulations are realized varying
the doping concentration and the distance sn and sp to the highly
doped regions. In the new design this distance is reduced to
sn=sp= 0.5 µm and the distance to metal contacts is
s= 1.25 µm (Fig. 16). So, the highly doped regions are present in the
slabs. The Δneff and the optical loss α of the structure
are simulated depending on the acceptor concentration Na of the p-doped
region for two different donor concentrations (Nd= 1 × 1017 cm-3 and Nd= 1 × 1018 cm-3) of
the n-doped region. The highly doped regions have concentrations of
Na+,d+= 1 × 1020 cm-3. The simulation results
are plotted in Fig. 17. The change of the effective index is similar for a
low acceptor doping concentration (Na= 5 × 1016 cm-3). However, for the case of
Nd= 1 × 1018 cm-3 the Δneff increase till around twice the
value for the Nd= 1 × 1017 cm-3 curve achieving
a Δneff of around 2.5 × 10-4 (Fig. 17a). The
loss regarding the free carrier absorption increases with the doping
concentration as expected. The offset between both curves is kept constant
for the simulated range of Na (Fig. 17b). As comparison, the
modulation efficiency and the figure of merit VπL⋅α are plotted
in Fig. 17c. Looking at this plot an optimal doping concentration can be
chosen taking into account the modulation efficiency and loss. For example,
a promising configuration is Nd= 1 × 1018 cm-3
and Na= 9 × 1016 cm-3 since a low VπL of
around 1.8 V⋅cm at 6 V is achieved with a VπL⋅α≈6 V⋅dB.
Finally, the distance from the waveguide core to the highly doped regions
sp and sn is examined. Simulations to determine the optimum value
for these parameters are realized for the optimized doping
Na= 9 × 1016 cm-3 and Nd= 1 × 1018 cm-3. The scheme of the simulated structure is presented in
Fig. 18. With these simulations (Fig. 19) it is proven that the distance
sp,n= 0.5 µm taken in Fig. 16 is a good value. But still a small
improvement could be achieved by increasing this distance to
sp,n= 0.6 µm. The loss is α= 0.31 dB mm-1. This small
difference in the sp,n distance has not a notable influence in the
modulation efficiency (VπL=1.8 V⋅cm) and a value of VπL⋅α≈5.8 V⋅dB is obtained. However, the
bandwidth is slightly reduced for short modulators due to the increase of
the series resistance of the device. For sp,n= 0.5 µm, the
calculated bandwidth for a phase shifter length of 0.5 mm is fc (2 V) = 27 GHz and fc (6 V) = 39 GHz. For the case of
sp,n= 0.6 µm the bandwidth is 25 and 36 GHz at 2 and 6 V,
respectively. For modulators with long phase shifters (∼ 3 mm)
the difference in the bandwidth due to this fact is negligible.
Thus, the final structure has a waveguide core width of w= 400 nm and is
p-doped. The slabs have a width of s= 1.25 µm and a thickness of
hsl= 50 nm. The highly doped regions are separated from the waveguide
core at a distance of sp,n= 0.6 µm. The doping concentrations
are Na+,d+= 1020 cm-3,Na= 9 × 1016 cm-3 and Nd= 1 × 1018 cm-3. For a 6 V
reverse bias voltage the change of the effective refractive index is
Δneff= 2.5 × 10-4. Therefore, a phase shift
Δφ=π is obtained for a phase shifter length of
Lπ=λ2Δneff≈3.1mm
Thus, the modulation efficiency of the modulator is VπL= 1.8 V⋅cm. The calculated cutoff frequency of the modulator with a
phase shifter length of 3.1 mm is 7 and 10 GHz at 2 and 6 V. The
calculated optical loss of the phase shifter for the length Lπ is
0.97 dB at 0 V. The fiber-to-fiber loss of the modulator is determined as
the sum of the calculated phase shifter loss and the losses of the
previously designed and measured optical components (i.e., grating couplers,
MMIs, waveguides and tapers) in the used technology. The measured loss at
λ=1.55µm of the grating couplers is 0.74 dB/coupler and
0.05 dB/MMI. The coupling loss between the 400 nm width strip waveguide and
the ridge waveguide of the phase shifter is 0.05 dB/coupling. The linear
taper with a length of 400 µm has a loss of 0.4 dB and the waveguide
loss due to the roughness and other imperfections during the fabrication
process is 3.3 dB cm-1. Considering a phase shifter length of 3.1 and 1 mm
of additional undoped waveguides an ultra-low fiber-to-fiber loss of
approximately 4.8 dB is expected for the complete modulator fabricated in
this technology.
Comparison with other technologies
Silicon optical modulators based on the carrier-depletion effect have been
developed by different research groups in the last years. High-speed
modulations up to 60 Gbit s-1 have been demonstrated (Xiao et al.,
2013) by properly choosing the doping concentration and precisely locating
the junction. Modulators based on the slow light effect can be integrated on
a very small area and exhibit a very low VπL of 0.85 V⋅cm (Brimont
et al., 2012; Akiyama et al., 2012). However, the loss is higher than for
other modulators of the same length. Some of the device developed during the
last years are presented as a comparison in Table 1 based on the publication
(Azadeh et al., 2015a). Different doping profiles and
concentrations are used. The pn-diode in the optical waveguide can be
designed in vertical direction (Liao et al., 2007; Azadeh et al., 2015b),
lateral direction (Samani et al., 2015; Tu et al., 2014; Wang et al., 2013)
or with interdigitated doping patterns (Xu et al., 2012; Hao Xu et al., 2014;
Giesecke et al., 2016). Some important figures of merit of the modulator and
geometry dimensions of the published devices are presented in Table 1 and
compared with the results of this work.
State of the art of carrier-depletion phase shifter designs
on different SOI technologies for λ=1550 nm.
Typeh[nm]L [mm]hsl [nm]sn,p [µm]α[dB mm-1]Optical loss [dB]VπL[V⋅cm]fc[GHz] (bias V)ReferenceLateral2202.5 1.25900.826.55/15.57 4.55/13.572 (2 V) 2.25 (2 V)17 (2 V) 23 (2 V)Azadeh et al. (2014)Lateral2201100–2.83.961.72 (2 V)30 (2 V)Wang et al.(2013)Lateral2205.5100–0.945.262.2 (4 V)24 (5 V)Tu et al.(2014)Lateral2200.5100sp= 0.5 sn= 0.5510650.85 (5 V)Data rate: 40 Gbit s-1Brimont et al. (2012)Lateral2204.2900.951.14.56/14.773.15 (7.5 V)35 (3 V)Samani et al.(2015)Lateral22202.4100–7.11760.97(0–2 V)61 (1 V)4Azadeh et al.(2015a)Interd.13400.758011261.62 (2 V)20 (3 V)Xu et al.(2012)Interd.12201900.62.83.852.2 (2 V)30 (3 V)Hao Xu et al. (2014)Interd.1220245–1.1 0.652.26 1.360.6 (2 V) 0.74 (2 V)5 (2 V) 3 (2 V)Giesecke et al. (2016)Vertical2901.8–0.84.26.760.74(0–2 V)48 (1 V)4Azadeh et al. (2015a)Vertical5001–11.8< 45/107< 430 (3 V)Liao et al.(2007)Lateral2500.5800.424.25/12.573.1 (2 V)30 (2 V); > 50 (6 V)This workLateral22503.1500.60.3134.871.8 (6 V)10 (6 V)4This workLateral22500.5500.60.3133.171.8 (6 V)36 (6 V)4This work
1 Interdigitated. 2 Simulated/calculated.
3 Only free carrier absorption at 0 V. 4 Intrinsic cutoff frequency.
5 On-chip loss. 6 Insertion loss. 7 Fiber-to-fiber loss.
Conclusions
The design and simulations of a single-drive carrier-depletion MZM in a
250 nm SOI technology with a modulated phase shifter in one branch of the
device is presented. The influences of the ridge waveguide dimensions and
the doping of the device are studied. An analysis of the RC-limit of the
modulator for different doping profiles is described. A MZM is fabricated
and measured showing a modulation efficiency of 3.1 V⋅cm with an optical loss
of α= 2 dB mm-1. The length of the phase shifter is 0.5 mm. The
on-chip insertion loss of the modulator is 4.2 dB. The electrical bandwidth
of the modulator is 30 GHz. RF coplanar lines with a 3 dB bandwidth higher
than 50 GHz are designed and measured. Finally, simulations to optimize the
modulation efficiency and optical loss are realized achieving a theoretical
modulation efficiency of VπL=1.8 V⋅cm and a maximum optical loss due
to the free carriers of α=0.31 dB mm-1. The expected fiber-to-fiber
loss of a MZM with a phase shifter length of 3.1 mm is approximately 4.8 dB.
The measurement data and simulation data that support the
findings of this study are available in Zenodo with the identifier
10.5281/zenodo.1037908 (Félix Rosa et al., 2017).
The authors declare that they have no conflict of
interest. Edited by: Dirk
Killat Reviewed by: three anonymous referees
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