Delphine Marris-Morini
1
, Laurent Vivien
1
, Gilles Rasigade
1
, Jean-Marc Fédéli
2
, Eric Cassan
1
,
Xavier Le Roux
1
, Paul Crozat
1
, Sylvain Maine
1
, Anatole Lupu
1
, Philippe Lyan
2
,
Pierrette Rivallin 2 , Mathieu Halbwax 1 , Suzanne Laval 1 .
[1] Institut d’Electronique Fondamentale, Université Paris-Sud XI-CNRS, Bât. 220, F-91405 ORSAY cedex –
France
[2] CEA-LETI, Minatec, 17 rue des Martyrs, F-38054 GRENOBLE cedex 9, France
The evolution of silicon optical modulators is recalled, from the first effect demonstrations to the characterisation of high performance devices integrated in optical waveguides. Among possibilities to achieve optical modulation in silicon-based materials, the carrier depletion effect has demonstrated good capacities. Carrier depletion in Si and SiGe/Si structures has been theoretically and experimentally investigated. Large phase modulation efficiency, low optical loss, and large cut-off frequency are obtained by considering simultaneously optical and electrical structure performances. Integrated Mach Zehnder interferometers and resonators are compared to convert phase modulation into intensity modulation. Finally, recent results on high speed and low loss silicon optical modulator using an asymmetric Mach
Zehnder interferometer are presented. It is based on a p-doped slit embedded in the intrinsic region of a lateral pin diode integrated in a SOI waveguide. This design allows a good overlap between the optical mode and carrier density variations. An insertion loss of 5 dB has been measured with a -3 dB bandwidth of 15 GHz.
Silicon microphotonics has generated an increasing interest in the recent years, as it can profit from mature CMOS technology with high production volume. Furthermore the integration of optics and electronics on a same chip would allow the enhancement of integrated circuit (IC) performances. Optical telecommunications can benefit from the development of low cost and high performance solutions for high-speed optical links. As an example, 4×10 Gbit/s silicon based optical transceivers have been recently demonstrated [1]. In microelectronic chips, with the extreme miniaturization of transistors, performance limitations come more and more from electrical interconnects, which suffer from RC delay, signal distortion, and power consumption [2-4]. The replacement of global electrical wiring by optical interconnects can overcome some of theses limitations, as negligible signal distortion even for high frequencies
(> 10 GHz) and long distances (> 1cm) is obtained with optical interconnects, with reduced latency, skew, and jitter [4]. With the development of multi-core processors, high data rate transmission between different cores is also required [2]. Optical wavelength multiplexing is a way to increase data rate on a single waveguide. Two possible examples are illustrated in
1/26

figure 1. In figure 1a, a global signal (e.g., the clock signal) is distributed to different points on a chip. The optical signal is detected using photodetectors situated in different sub-regions loaded by CMOS transistor blocks. In figure 1b a dual-core processor is schematically depicted, with input/output wavelength multiplexed optical communications (WDM) using different optical sources at different wavelengths, followed by modulators to encode information. The different communications can travel between both cores on the same waveguide. Multiplexers (MUX) and demultiplexers (DEMUX) are then required. fig 1: Examples of optical interconnect links: (a) distribution of a global signal (e.g., clock signal) and (b) point to point communications between 2 cores using wavelength multiplexing.
For all these applications, high speed silicon-based optical links require different building blocks: optical sources, modulators, and passive circuits to distribute light on the silicon chip and photodetectors are needed.
The use of silicon-on-insulator (SOI) substrates for silicon-based photonics and optoelectronics presents several advantages. SOI is compatible with low cost CMOS technology and large wafer diameters up to 300 mm are commercially available. Another advantage is the strong light confinement in submicron waveguides due to the large refractive index difference between silicon and buried silicon oxide (
 n~2). Strip or rib waveguides on
SOI wafers can be realized by using a standard optical lithography process followed by full or partial etching of the silicon film, respectively [5-7]. Slightly etched single-mode SOI rib microwaveguides are a promising solution for photonic integrated circuits. The scattering losses induced by the side-wall roughness can be lower than 0.4 dB/cm [7]. Compact 90°turns and beam splitters to distribute light from one input to one or several outputs anywhere on the chip have been successfully integrated in slightly etched waveguides [7-8].
Active photonic devices are required at the optical link inputs and outputs. Different ways are possible to get a light source in or on silicon, among them the use of erbium doped silicon [9-
10], the Raman effect in silicon [11-12], or III-V integration [13-14] have been particularly investigated.
A photodetector is required to detect the optical signal and to convert it into an electrical one.
Within the group IV materials, pure germanium is a promising candidate as a broadband photodetector and it is compatible with the CMOS technology. Despite the large lattice mismatch between silicon and germanium, specific growth techniques have been developed, and impressive results on germanium on silicon photodetectors have been achieved in the last
2/26

few years [15-22]. A 42 GHz waveguide integrated germanium-on-silicon PIN photodetector, has been recently demonstrated [22], with a large responsivity ~1A/W at 1.55µm wavelength.
A high speed optical modulator integrated in a SOI waveguide is the last fundamental building block, essential for the development of silicon microphotonics. As illustrated in figure 2, an optical modulator is an optoelectronic device that provides modulated optical signal at the output driven by an electrical command, when a continuous input beam is provided at the input. fig 2: Optical modulator operating principle
Performances of different optical modulators can be compared in terms of insertion loss and extinction ratio, given by the following relations, I
IN
, I
ON
and I
OFF
being defined in figure 2:
IL

10

Log


I
I
ON
IN

 (1)
ER

10

Log


I
ON
I
OFF

 (2)
High performance optical modulator should present low insertion loss, large extinction ratio, and high frequency operation, at least 10 Gbit/s. Furthermore to benefit from high production volume and mature technology, optical modulators should be compatible with silicon technology.
Several ways have been investigated to get silicon-based modulators. Electro-optical effects in strained silicon [23], in bulk silicon-germanium [24], or quantum-confined Stark effect in
SiGe/Ge quantum wells [25] have been recently demonstrated, but at the moment, most of the fast modulators integrated on silicon are based on free carrier concentration variations [26-
33].
The first modulator achieving a 1 GHz bandwidth was demonstrated in 2004, and was based on carrier accumulation on a Metal-Oxide-Semiconductor capacitor [26]. With improvements in device design, material quality, and by using a custom driver to distribute the global capacitance in eleven smaller sections, 10 Gbit/s data transmission was obtained [27].
Carrier injection in a PIN diode has been for a long time thought to be limited to a few hundreds of Mbit/s, due to carrier recombination lifetime in the intrinsic region. However, bit rates up to 18 Gbit/s have recently been obtained in ring resonators [28] and up to 10 Gbit/s using a Mach Zehnder interferometer (MZI) [29]. In both cases pre-emphasis of the electrical signal was used, to assure rapid injection and then depletion of carriers by using pulses at rising and falling edges.
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Carrier concentration variation can also be obtained by depletion, which is intrinsically a high speed process and does not require a complex electrical supply. Carrier depletion can be obtained in a reverse biased PN or PIN diodes. The very low electrical current going through a reverse-biased diode ensures low power dissipation. Recent experimental results using carrier depletion in a doped slit inserted in a lateral PIN diode have shown a 15 GHz 3dBbandwidth with an insertion loss smaller than 5dB [30-31]. Other depletion-based devices have been reported in the literature: 10 GHz-bandwidth with low loss (3dB) has been reported in a lateral PN diode [32], and depletion in a vertical PIN diode has also been reported, showing an impressive 30 GHz bandwidth [33], but with a reduced active length and so a reduced modulation depth (1dB).
The recently reported performances of silicon-based optical modulators are summarized in table 1.
Ref 27 28 29 32 33
Carrier density variation by :
Accumulation in a MOS capacitor injection + electrical signal pre-emphasis injection + electrical signal pre-emphasis
Depletion in a lateral PN diode
Depletion in a vertical PIN diode
30-31
Depletion in a doped slit in a lateral PIN diode
Interferometric structure
Insertion loss
MZI
10 dB
ring resonator
-
MZI
12 dB
MZI or ring resonator
3 dB
MZI
7 dB
MZI
5 dB
3 dB bandwidth - - 10 GHz 30 GHz 15 GHz
Transmission rate / RF extinction ratio
10 Gbit/s
(extinction ratio of 3.8 dB)
18 Gbit/s
(extinction ratio of 3dB)
10 Gbit/s 10 Gbit/s
(extinction ratio of 6 dB)
40 Gbit/s
(extinction ratio of 1 dB) table 1: Recently reported silicon-on-insulator integrated optical modulators
-
In the following, SiGe/Si and all-silicon phase shifters based on carrier depletion are presented and theoretically compared. Optical modulation is experimentally demonstrated using both structures. In section 3 the integration of both phase shifters in SOI rib waveguides is investigated, and section 4 is devoted to integrated interferometer properties. The last section deals with the demonstration of an integrated high speed modulator.
In pure crystalline silicon, the optical properties can be varied by either the thermal effect [34-
35] or free carrier concentration variations [36-37], both are responsible for refractive index variations. The thermal effect is slow (~ ms) and cannot be used for high speed modulators, but it can appear as a parasitic effect. Free carrier concentration variations are then used to achieve optical modulation. Carrier depletion has been considered first in SiGe–Si multiple quantum wells integrated in a SOI waveguide [38-40] and then in an all-silicon structure
[41,43].
A.
SiGe/Si modulator
1.
Design
The SiGe/Si modulator is based on a stack of Si
1-x
Ge x
/ Si heterostructures. To avoid optical absorption, the germanium fraction has to be kept low enough to insure a bandgap larger than the incident photon energy. Furthermore due to the lattice mismatch difference between Ge and Si, the stack thickness has to be kept lower than a critical thickness, which depends on x, the Ge fraction in Si
1-x
Ge x
layers. Low x fractions are then used. In this case, the conduction
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band discontinuity between Si and Si
1-x
Ge x
is negligible, and the valence band discontinuity ensures hole confinement in Si
1-x
Ge x
wells. Thin p-doped Si layers are located in the middle of the Si barriers. At equilibrium, holes coming from these p-doped layers are confined in the
Si
1-x
Ge x
wells. The stack is embedded in the intrinsic region of a PIN diode, as represented in figure 3. When a reverse bias is applied on the diode, holes are depleted. Free-carrier concentration variations are responsible for refractive index (
 n) and absorption coefficient
(

variations, following these equations [36-37]:
At

=1.3 µm:
 n  
6
,
2
.
10

22  N
  
6
,
0
.
10

18  N

6
,
0
.
10

18  P 0
,
8

4
,
0
.
10

18  P
(3)
At

=1.55 µm:
 n
 
8 , 8 .
10

22 
N
  
8 , 5 .
10

18 
N

8 , 5 .
10

18 
P
0 , 8

6 , 0 .
10

18 
P
(4) where

N and

P are respectively the electron and hole concentrations, expressed in cm
-3
. It is worth noting that doping increases the absorption coefficient. Doped regions should then be limited to avoid large optical loss.
Device simulations were performed to optimize the SiGe/Si stack for optical modulation [38].
After device optimization, three Si
0.8
Ge
0.2
quantum wells of 10 nm are separated by 20-nmthick Si layers. 5 nm-thick, 10×10
18
cm
-3
boron-doped layers are located in the middle of Si barriers. An effective index variation around 2.10
-4
for -6V reverse bias is predicted with this structure for TE polarization at 1.31 µm-wavelength. As the refractive index variation with free-carrier concentration variations is proportional to
 2 , an effective index variation around
2.8.10
-4
can be predicted at 1.55 µm. fig 3: SiGe/Si modulator cross section
2.
Experimental demonstration
A device was fabricated to experimentally demonstrate the optical modulation effect in
SiGe/Si heterostructures. It is represented in figure 4. The principle was to demonstrate the effect of phase modulation by converting the induced phase shift into an intensity modulation by using a Fabry Perot resonator as an interferometric structure.
5/26

fig 4: SiGe/Si modulator test device
The device was fabricated on an 8 inch undoped SOI substrate, with a 0.7 µm-thick buried oxide layer. The upper crystalline silicon layer was etched down to 50 nm, and a 50 nm-thick growth was performed to obtain a phosphorus doped silicon layer, forming the bottom contact. The doping level was 2.10
18 cm
-3
. A 500 nm – thick silicon dioxide (SiO
2
) layer was then deposited onto the wafer using plasma-enhanced chemical vapour deposition (PECVD).
Lithography was performed, and BHF used to etch apertures in the silica. The SiGe/Si modulation-doped stack was then grown by Ultra High Vacuum Chemical Vapour Deposition
(UHV-CVD). A second lithography and oxide-etching was performed to define metal contacts: 30 nm-thick titanium and 300 nm-thick aluminium was used. The interferometric structure used was the Fabry Perot cavity obtained by the cleaved facets of the sample.
The experiments consisted of measuring the shift of Fabry Perot resonance fringes as a function of the applied bias, in a 2.3 mm long modulator waveguide cavity. The wavelength positions for Fabry Perot resonance maxima are related to the cavity length L and the effective index n eff
:
2 Ln eff
 p

, (5) where p is a positive integer.
The carrier-induced index variation shifts by

the wavelength of a given resonance maximum. As a first order approximation, the effective index variation
 n eff
is given by the following relation:
 n ef f

 
 n g
, (6) where n g
is the guided mode group index, and is given by: n g
  p

 2 p
, (7)
2 L
  p where
 p
is the experimental wavelength difference between two successive resonance peaks.
The experimental set-up used a tuneable laser in the 1550 nm range. A linearly polarized light beam was coupled into the waveguide using a polarization maintaining lensed fiber. The output light was collected by an objective and was measured with an infrared detector.
Electrical probes were used to bias the diode. The effective index variation with applied voltage, ranging from 0 to -10 V was deduced using equation 6. The experimental results are plotted in figure 5.
6/26

The measured effective index variation increases as the reverse bias increases. It may have two contributions: the first one is due to hole depletion in the structure, and the second one to a thermal effect related to the electrical power dissipated in the device, which becomes more important as the reverse bias increases (figure 6).
To realize a high speed modulator, the thermal contribution cannot be used and it acts as a parasitic effect. Thermal and carrier-depletion contributions have thus been dissociated [40].
The thermal effect is proportional to the electrical dissipated power, which is deduced from experimental current/voltage measurements (figure 6). The carrier-depletion is in a first approximation expected to be proportional to the absorption variation, via Kramers-Krönig relations. Using experimental data, a fitting procedure using optimization algorithms was used, and both contributions are reported in figure 5. It can be noted that the thermal effect was negligible for a reverse bias lower than -4V. The carrier-depletion induced effective index variation reached 2×10
-4
at -6V. fig 5: Experimental effective index variation as a function of applied voltage fig 6: Experimental current/voltage characteristic of the device
To evaluate the modulation phase efficiency a figure of merit is usually defined as the product
V  L  , where V  and L  are the applied voltage and the length required to obtain a

phase shift of the guided wave respectively. The lower the product V  L  the more efficient the phase
7/26

shifter. L  can be directly deduced from the
 n eff
(V) measurement for each value of the bias considering only the carrier-depletion contribution to the effective index variation:
L


2
 n
 ef f
 
(8)
At -6V, the experimental value of V  L  was then 2.3 V×cm
3.
Intrinsic speed
The response time of SiGe/Si modulation-doped multiple quantum well (MQW) modulators has been theroretically investigated [41]. Under a reverse bias, the hole transport in the MQW stack depends on the carrier capture/escape processes and drift-diffusion transport across the
Si barrier layers. Both tunnelling and thermo-ionic emission have been taken into account, to evaluate the time needed for the free carriers to escape from and be captured into the wells.
Transient simulations have been performed, assuming a reverse-bias step from 0 to -6V with a rise time lower than 1fs applied on the diode. The hole density distributions obtained at several times until a new equilibrium was achieved are reported in figure 7.
At the beginning of the simulation (fig 7.a), holes are initially confined in the three SiGe quantum wells. When time increases, holes begin to drift, due to the electrical field, and then escape from the first quantum well, to be capture by the following ones. After 10 ps, the first well is emptied, but the hole concentration is still large in the second and the third ones. 50 ps after the bias step, the hole distribution is very close to the equilibrium one, under -6V reverse bias. fig 7: Numerical calculation of the hole concentration in the direction perpendicular to the
SiGe/Si layers, for different times after a bias step is applied on the device.
8/26

The same simulations have been performed for a reverse-bias step from -6V to 0V. To evaluate the intrinsic speed of the modulator, the local refractive index variations were deduced from the hole distribution calculations, using equation 4. The local refractive index variations were then introduced in an optical mode solver [42]. The evolution of the effective index variation as a function of time, assuming a 20 Gbit/s square signal applied on the diode is reported in figure 8. fig 8: Numerical calculation of the effective index variation with time, assuming an electrical 20 Gbit/s square signal.
For both rising and falling times, effective index variation evolutions can be fitted by exponential time (t) evolutions.
 n ef f

A

B
 exp



 t



(9)

=
 down
=7.2 ps when the bias voltage decreases, and

=
 up
=9.5 ps when it increases. A cut-off frequency can be defined as f max

2
 
Max

1
 up
,
 dow n
 (10)
In this configuration the cut-off frequency f max
is 16 GHz. This is the intrinsic limitation, due to the time needed for a carrier to be swept out and to come back into the active region. In fact, other effects will limit the device rapidity, especially RC time constants. This means that the bias step applied on the active region, which was ideal in the simulations, will not be so ideal in practical issues. This will be discussed in the following.
However, the maximum operation frequency of this device is 16 GHz, and is limited by tunnelling and thermo-ionic emission at the SiGe/Si barriers. This can be avoided using an allsilicon structure.
B.
Si modulator
1.
Design and experimental demonstration
An all silicon modulator has been made, still based on carrier depletion in a PIN diode [41].
As the bandwidth of the SiGe/Si MQW modulator was limited by the SiGe/Si barrier, SiGe quantum wells have been removed. The active region of the derived structure is schematically
9/26

shown in figure 9. The modulator was based on a doped P
+
silicon layer, introduced as a source of free holes in the core of a non-intentionally doped Si region. This structure was placed between P
+
and N
+
regions, which form the N and P part of the diode. Devices have been fabricated using the same process as described in section 2.A for the SiGe/Si modulator.
The P
+
layer in the middle of the structure was 150 nm-thick, with a doping level larger than
5×10 18 cm
-3
. The P and N part of the diode were 50 nm thick, with a doping concentration of
10 18 cm -3 . The overall sample thickness was 500 nm, which is compatible with the integration in a rib SOI waveguide. fig 9: Silicon modulator cross section
The effective index variations with bias voltage ranging from 0 to -6V have been deduced from experimental measurements similar to the previously described ones and results are reported in figure 10. Thermal and carrier-depletion contributions have been separated. No significant thermal contribution occurred from 0 to -2V, and it still represented a minor part up to -6V. The electrical contribution to the index variation due to carrier depletion in the diode reached 1×10
-4
at -4V. V  L  was then 3.1 V×cm. fig 10: Experimental effective index variation versus applied voltage
10/26

Carrier depletion in an all-silicon device using a p-doped layer in the middle of a PIN diode was thus successfully demonstrated.
2.
Intrinsic speed
The Si modulator allows a higher speed to be achieved than with the SiGe/Si structure.
Transient simulations were performed to evaluate the intrinsic speed limitation of this device
[43]. The numerical simulation principle was the same as for the SiGe/Si modulator. The evolution of the effective index variation as a function of time is plotted in figure 11 when an ideal bias step from 0 to -6V (fig 11a) and from -6V to 0V (fig11b) is applied. For both rise and fall times, effective index variation evolutions can be fitted by exponential curves, with

=
 down
=
 up
=1.1 ps. The intrinsic maximum frequency is then around 150 GHz, meaning that carrier drift times will not limit the modulator speed. fig 11: Numerical calculation of the effective index variation with time, after an ideal bias step applied on the device: (a) from 0 to -6V ; (b) from -6 to 0V
The temperature sensitivity of the modulator performances can be a key parameter depending on the targeted application. Especially in the case of on-chip optical interconnects, microprocessors can suffer from large temperature variations. To evaluate the temperature influence on the modulator operation, transient simulations were performed at 400 K instead of 300 K as usually. It was shown that the same value of the effective index variation is achieved between 0 and -6 V The time evolution of the effective index variation was still well fitted by an exponential function with an increase in the response time from 1.1 to 1.4 ps, which is explained by the hole mobility reduction when the temperature varies from 300 K to
400 K. However the maximum available modulation frequency due to carrier movements in the active region is still larger than 100 GHz at T = 400 K. Despite the temperature increase, the modulation bandwidth is again not be limited by carrier transport in the active region.
In conclusion, both SiGe/Si and Si modulators have been experimentally demonstrated. In both cases, at equilibrium, holes are located in a middle of the intrinsic part of a PIN diode, thanks to p-doped layers. A reverse bias is used to induce carrier depletion without requiring large currents, which is advantageous for low power dissipation
To achieve high speed modulation, the active regions have to be integrated in small foot-print waveguides. Electrical and optical considerations need to be taken into account, in order to optimize the modulation characteristics (mainly the extinction ratio and insertion loss), and to maximize the modulator bandwidth.
11/26

In order to integrate the active region into a SOI waveguide, a rib waveguide was preferred to make easier the integration of electrical contacts. The first configuration consisted in using epitaxial growth of the active region. In this case all the layers were parallel to the SOI substrate and the PIN diode was vertical. Both SiGe/Si and all-silicon modulator can be integrated in the vertical diode. The optimization was performed in the SiGe/Si case, and a
RC cut-off frequency equal to the intrinsic maximum frequency was obtained. To benefit from the larger intrinsic frequency of the all-silicon modulator, a second version was proposed, where the P and N parts of the diode were placed on both sides of the rib waveguide, with the active region in the middle of the waveguide. This configuration was called the lateral diode, and it allowed an increase in the RC cut-off frequency.
A.
Vertical diode
SiGe/Si and all-silicon modulators can be integrated in a rib waveguide using a vertical diode.
(figure 12). Optimization is required in both cases and it has been detailed in the case of the
SiGe/Si modulator [44].
A rib waveguide is considered with a total thickness fixed at 380 nm. The SiGe/Si modulation doped structure is embedded in the rib waveguide, and a bottom p-doped contact and a top ndoped contact are considered, as reported in figure 12. fig 12: Schematic view of the vertical diode cross-section.
The device characteristics have been simulated both electrically and optically. ISE software was used for the electrical numerical simulations [45]. Poisson’s equations coupled to continuity equations for holes and electrons were solved using standard drift-diffusion modelling. The doping dependant mobility was used, and the recombination was evaluated using Schokley-Read-Hall and Auger models. Free carrier concentrations in the device were then obtained, for different bias voltages applied to the diode. From these free-carrier concentration variations, the variation of the refractive index and absorption coefficient were estimated using equations 3-4. An optical mode solver was then used to calculate the effective index and absorption coefficient of the guided mode in the waveguide. The loss calculation took into account the contribution of the doped regions and the metal contacts.
The effective index variation has to be maximized, to ensure good modulation properties. This means that the overlap between the guided mode and the regions where refractive index
12/26

variations occur has to be optimized. Rib waveguide geometrical parameters (rib width and etching depth) were tuned to obtain a highly confined optical mode, while keeping single mode operation. The SiGe/Si modulator based on a vertical PIN diode was optimized at a wavelength of 1.3 µm [44]. The optimal device had a rib width of 650 nm, and the etching depth was 110 nm. The SiGe/Si period was 30 nm, and the distance between the P
+
layer and the first SiGe well was 15 nm.
To achieve high frequency operation it is important to evaluate the small-signal equivalent model of the device. It consists of the capacitance C of the reverse biased PIN diode in series with an access resistance R due to the doped silicon regions between the metal and the active region.
The device is electrically equivalent to a low pass filter, with a cut-off frequency defined by: f max

1
2
 
RC
(11)
The modulator capacitance is directly proportional to the active region surface, which is the product between the phase shifter length L and the active region width W. The cut-off frequency is then inversely proportional to the active region width, which has to be reduced.
The capacitance per surface unit is C/(W×L). It was calculated and is reported in figure 13. It decreases from 1.09 fF/µm² to 0.87 fF/µm² when the bias goes from 0 to -6V. fig 13: Small-signal capacitance per surface unit
To ensure that the optical mode propagates without perturbations (and without additional loss), the minimal value of W is a few microns. The optimal device had a width W=1.65 µm,
To get the top contact, the easiest way consists in depositing the metal directly on top of the doped region, on the rib waveguide. However this introduces very strong light absorption.
The upper contact was then moved to one side of the waveguide (the left side in figure 12), above the SiO
2
passivation layer. The N
+
layer needed to be deposited after the waveguide definition. Such a layer is monocrystalline when epitaxially grown on silicon, and polycrystalline on silica.
Doped layers between the active region (under the rib waveguide) and metal contacts are responsible for access resistances. To decrease resistance values, the doping level or the
13/26

doped layer thickness should be increased. However this is responsible for an optical loss enhancement. To decrease access resistances while keeping optical loss low, a compromise between high speed operation and low optical loss has to be fulfilled.
Finally, the N
+
doping level was 4×10
18
cm
-3
, and the P
+
doping level was 7.5×10
18 cm
-3
. The cut-off frequency was 16 GHz, i.e., the RC constants were reduced enough so that the intrinsic speed was not altered. The figure of merit V  L  equalled 1.8 V×cm. Th optical loss was 9 dB for a device length of 3 mm.
The optimization has been done at 1.3 µm, but the same device has been simulated at 1.55µm.
The cut-off frequency was still 16 GHz. As the effective index variation increases with
 2 , L  decreased down to 2.55 mm, and optical loss was 8.4 dB for a device length of 2.55mm.
Finally, the figure of merit V  L  equalled 1.5 V×cm. This value can be favourably compared with published silicon modulator results [26-27, 32].
B.
Lateral diode
To increase the cut-off frequency of the modulator, and decrease the optical loss, a new integration scheme has been developed. It is based on a lateral diode, as described in figure
14. The P and N doped regions of the diode are on each side of the waveguide, and a p-doped slit is inserted in the middle of the waveguide, to bring holes at equilibrium in the center of the waveguide. The n-doped region slightly overlaps the guided mode, to ensure an efficient depletion of the thin p-doped slit. fig 14: Schematic view of the lateral diode cross-section.
The lateral diode configuration has some advantages when compared to the vertical diode geometry.
The small-signal capacitance of the device is proportional to the diode area, which in this case is the product of the device length and the rib waveguide height. The rib waveguide height is typically 400 nm or lower. The capacitance per phase shifter unit length is then reduced. It has been calculated by electrical simulations, and ranges typically from 0.3 to 0.2 fF/µm. A reduction of the capacitance by a factor of 6 is thus obtained when compared with the vertical modulator structure.
Regarding the access resistances, the lateral diode also offers advantages. The doped region thickness can be greatly increased, when compared with the 50 nm-thick doped layer in the case of the vertical PIN diode, thus leading to much smaller resistances. Furthermore, the doped regions for the P and N parts of the diode do not overlap the guided mode at its maximum, leading to optical loss reduction.
14/26

Finally, the lateral diode fabrication is CMOS compatible. Epitaxial growths are not required, as the doped regions can be obtained by ion implantation.
In conclusion we have compared two integration schemes in a rib waveguide. First, both
SiGe/Si and all-silicon modulators can be integrated in a vertical PIN diode. This structure has been extensively simulated. The influence of geometrical parameters on electrical and optical performances has been studied, and an optimized structure has been defined. The main limitation of this modulator comes from the RC/optical loss compromise. As the SiGe/Si structure has an intrinsic frequency limitation of 16 GHz, there is no way to achieve higher frequency operation, and thus the device has been optimized to achieve an RC-cut-off frequency of 16 GHz. For the all-silicon structure, the RC cut-off frequency has to be put higher to benefit from the larger intrinsic frequency limitation. In the vertical diode configuration this can be done, but at the expense of larger optical loss. A solution to increase cut-off frequency without increasing the optical loss is to use a lateral PIN diode. In this case, both capacitance and access resistances are reduced, leading to an easier optimization of the phase shifter for improved performance.
Once the phase shifter is correctly designed, a waveguide integrated interferometer is required to convert the phase modulation into intensity modulation.
An integrated interferometer is required to convert phase variation into intensity modulation.
According to the application, the interferometer requirements are different. For example, in a microprocessor the modulator should have a very low temperature dependence, as large temperature variations can occur on a chip. Resonant interferometers seem difficult to use in this case. Different requirements on the size, optical bandwidth, etc., will also be determined by the application. Two well-known interferometers are presented and compared next.
A.
Mach Zehnder interferometer
A Mach Zehnder-based modulator consists of an input waveguide, a splitter, two waveguide integrated phase shifters, and an output combiner, as illustrated in fig 15. The optical beam is split off into both arms of the modulator. When the light is recombined at the output combiner, the ON state is achieved when there is no phase difference between the two signals; the OFF state is achieved when there is a differential phase shift of

radians. fig 15: Schematic view of a Mach Zehnder interferometer
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Although a bias is generally applied only in one arm, the phase shifter is integrated into both arms, in order to obtain similar optical losses. When the beams have

phase difference, the output intensity is zero only if both beam amplitudes are equal. Assuming identical waveguides, with the same length and losses, and assuming an ideal splitter and combiner, the
Mach-Zehnder intensity transmission is then given by:
T
 e
 
0
L  cos
2
  n ef f
 
L


, (12) where L is the phase shifter length and

0
is the absorption coefficient in the phase shifter.
The absorption coefficient variation with bias voltage due to free carrier depletion is neglected.
Using those assumptions, transmission varies from T max
= e
 
0
L to 0, when a

phase shift is obtained in one arm of the Mach Zehnder.
V  and L  are simultaneously defined by the following relation:
L


2
  n
 ef f
  (13)
As the achievable effective index variation is a few 10
-4
for a bias of a few volts, typical values of L  are of a few millimetres. The relatively large phase shifter length required in a
Mach Zehnder based silicon modulator is the main drawback. However, this interferometer has some advantages, particularly related to temperature sensitivity. Indeed, as it is based on a phase difference measurement, if an external thermal effect is responsible for index variation, it will be the same for both arms so that no influence occurs on the modulation properties.
Furthermore this device presents a large optical bandwidth, which is limited only by the splitter and combiner performances.
An asymmetric Mach-Zehnder modulator can also be used. The length of the passive waveguide in one arm is increased by

L, leading to a wavelength-dependant transmission when no modulation is applied, given by the following equation:
  e
 
0
L  cos
2

 n ef f

L
When index modulation is achieved in one arm, the transmission spectrum is shifted according to:
  e
 
0
L  cos
2



 n ef f
 
L
 n ef f

L




The transmission of an asymmetric Mach Zehnder as a function of wavelength is plotted in figure 16. The absorption coefficient is assumed to be negligible. With no bias, the transmission presents maxima and minima due to the length difference between both arms
(
 L=40µm in this case). When V
 reverse bias is applied on one arm, the transmission spectrum is shifted. At a given wavelength, a large transmission variation is obtained.
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fig 16: Transmission spectrum of an asymmetric Mach Zehnder (
 L=40µm) with: a) no bias, b)V  bias applied.
The transmission of this device as a function of the bias is reported in figure 17, at several wavelengths.
At a wavelength of 1.5555 µm, the transmission varies from 1 to 0. The evolution is the same as for a symmetric Mach Zehnder, with no arm length difference. At a wavelength of 1.5534
µm, a large transmission variation can be obtained, from 0.85 to 0.15 with a bias from 0 to
V  /2. It is also possible to achieve transmission equal 0 with no bias, and transmission equal to 1 for an applied bias equals to V  , at a wavelength of 1.5470 µm. fig 17: Transmission of an asymmetric Mach Zehdner (
 L=40µm) as a function of the bias at different wavelength.
The advantages of this interferometer is that with the wavelength dependence of the transmission, it is possible to chose a wavelength in a linear part of the spectrum, where small index variations (meaning small bias) are responsible for large transmission variations.
For both kinds of Mach Zehnder modulators, a waveguide splitter and combiner are required.
An ultracompact splitter for submicrometer rib waveguides based on a star coupler has been reported [46]. It has been successfully compared with Multi Mode Interference (MMI) couplers and Y-junctions in terms of wavelength sensitivity, influence of process variation, and required surface (area <<100 µm²). An optical microscope view of such a rib waveguide star coupler splitter is shown in fig 18 (a), while the results of an FDTD calculation are reported in figure 18 (b). It is based on an input waveguide, an enlarged region where light diffracts, and two output waveguides well positioned to collect the light. A transmission larger than 48 % is obtained in each output waveguide.
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fig 18: (a) optical microscope view of rib waveguide star-coupler splitter
(b): FDTD calculation of the splitter
B.
Resonant structures: ring resonators
To achieve compact devices, resonant structures can be used at the price of a higher temperature sensitivity and lower optical bandwidth. Fabry Perot cavities can be shorter but require the realization of Bragg mirrors integrated within SOI waveguides. Bragg mirrors with low losses have been demonstrated in strip waveguides [47,48], but their integration in rib waveguides is more difficult. Light leakages due to the low lateral confinement of light limit the performance of such mirrors.
A ring resonator can be used as an alternative solution, as it does not require the integration of
Bragg mirrors.
A passive ring resonator is reported in figure 19. It is based on a ring waveguide near a straight waveguide. To realize an optical modulator, the phase shifter has to be inserted in the ring. fig 19: Scanning electron microscope view of a rib waveguide integrated ring resonator
Light coming from the straight waveguide is coupled into the ring. The coupling properties depend on the waveguide geometry and on the gap d between both waveguides. After propagation in the ring, light is coupled back to the straight waveguide.
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The device transmission as a function of the wavelength was calculated and is plotted in figure 20. When no bias is applied on the phase shifter integrated in the ring, the transmission presents sharp minima, which correspond to destructive interferences between light coming from the straight waveguide, and from the ring. When a bias is applied on the active region in the ring, the phase shift that is encountered by the optical mode propagating in the ring varies, and the resonance is shifted. At a wavelength near the peaks, the intensity can be greatly modified by a small effective index variation. fig 20 : Theoretical transmission of a ring resonator modulator as a function of the wavelength, for different bias voltages.
Passive ring resonators (i.e., without phase shifter) have been realized and characterized. The devices were fabricated on SOI wafers with a 400 nm thick silicon layer and a 1 µm thick buried silicon oxide (BOX) layer. The thickness of the silicon layer was decreased to 380 nm by thermal oxidation. Oxide was deposited to form a hard mask. Electron-beam lithography with a negative resist was used. The hard mask was etched down to the silicon layer, followed by a partial etching to define the rib waveguide. Structures were encapsulated by 500 nm of
SiO
2
. The ring radius was 50 µm, and different coupling gaps d have been chosen to reach critical coupling (200, 300, and 450 nm). For each device, the output power has been recorded for wavelengths ranging from 1520 nm to 1525 nm, and the results are reported in figure 21. fig 21: Measured transmission spectra of ring resonators for d equal 200, 300, and 450nm.
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The mean transmission has been normalized to separate the three results on the same graph.
The small oscillations visible over the whole spectrum are due to Fabry Perot resonances between the sample cleaved facets.
The evolution of the extinction ratio is due to the variation of the coupling constant with d. As the gap widens, the field transmission coefficient varies and the extinction ratio increases. At a 450 nm gap, the measured passive ring contrast is larger than 10dB.
The performances of an optical modulator based on such a ring resonator with SiGe/Si or allsilicon phase shifter integrated in the ring were investigated. An ultra-low insertion loss of around 1 dB is achievable with this interferometric structure, as in the ‘ON’ state the light does not go across the large phase shifter region where doped regions are responsible for optical loss. A large contrast ratio up to 10 dB was predicted, with the application of a few volts reverse bias.
In conclusion, two different interferometric structures were compared for the integration of
SiGe/Si or all-silicon phase shifters to achieve a high performance optical modulator. Mach
Zehnder interferometers lead to a large extinction ratio and a large optical bandwidth with low temperature sensitivity, while ring resonators can be very useful to achieve low loss and ultra compact devices.
A.
Design and fabrication
An all-silicon optical modulator based on a lateral PIN diode as described in figure 14
(described in sub-section 3B) has been fabricated. It has some advantages in comparison with other depletion devices, based on more conventional vertical or lateral PN diodes. Indeed, optical loss is reduced as a large part of the waveguide does not include any doped regions and metallic contacts are deposited on both sides of the waveguide, just a few microns apart.
Moreover, this design is quite favorable for high speed operation, as the capacitance and the access resistances are reduced.
The silicon rib waveguide width was 660 nm, the rib height was 400 nm, and the etching depth was 100 nm, leading to a single mode propagation of the guided mode at a wavelength of 1.55 µm. A 100 nm-wide p-doped slit, with a doping concentration of 10
18
cm
-3
was inserted in the intrinsic region of the lateral PIN diode. The doping concentration in the p- and n-doped regions of the PIN diode were 10
18
cm
-3
. The silicon modulator was based on an asymmetric Mach-Zehnder interferometer. The phase shifter was inserted in both arms over a length of 4 mm, and electrodes were used to bias one arm.
Intrinsic rapidity and RC time constants have been studied previously but another limitation came from the RF electrode. Indeed, it was important to correctly bias the 4-mm long phase shifter all along the structure. Coplanar waveguide electrodes were used in a ground – signal – ground (GSG) configuration. Design parameters were W, the width of the signal electrode, and G, the gap between both the signal and ground electrodes. Two different designs have been used, as shown in figure 22. In a first case, the width of the signal electrode was 5 µm and the gap between the signal and ground electrode was 25 µm to obtain a characteristic impedance around 50 ohms, taking into account the capacitance of the PIN diode. In the second configuration, the width of the signal electrode was 40 µm and the gap between signal and ground electrodes was 20 µm to reduce the RF propagation loss.
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fig 22: Optical microscope view of the modulator with electrodes:
(a) W = 5µm, G = 25 µm, and a taper is used to apply the RF probes on both sides and (b) W = 40µm and G = 20µm.
The optical modulator was fabricated on an undoped 8 inch SOI substrate with a 1 µm-thick
BOX layer and a 400 nm-thick crystalline silicon film. A silicon dioxide (SiO
2
) cap layer was first deposited onto the wafer using low pressure chemical vapor deposition (LPCVD). A 100 nm-wide slit was defined using 193 nm deep-UV (DUV) lithographic patterning followed by a reactive ion etching of silicon dioxide. Double ion implantation was performed to obtain a thin doped layer over the whole Si layer thickness. Waveguides were then patterned, using classical technological processes, i.e., DUV optical lithography and reactive ion etching. P and N doped regions were obtained by ion implantation, followed by thermal annealing.
Finally, a Ti/TiN/AlCu/Ti/TiN metal stack was deposited onto the wafer and electrodes were patterned and etched down to the SiO
2
film. The entire process was fully compatible with SOI
CMOS technology and could be transferred to high-volume microelectronic manufacturing.
B.
Experimental results:
The experimental set-up used a tuneable laser centered at a wavelength of 1550 nm. A linearly TE polarized light beam was coupled into the waveguide using a polarizationmaintaining lensed-fiber. The output light was collected by an objective and focused on an infrared detector. Electrical probes were used to bias the diode. Very low values of the reverse current (-2 µA at -10 V) were measured, which ensures low electrical power dissipation in DC configurations.
The output spectra of the modulator were recorded for different bias from 0 to -10 V bias
(fig 23). The measured spectra were normalized with the transmission of straight waveguides without phase shifters. The effective index variation in the phase shifter due to hole depletion created a red-shift of the spectrum. Due to the very small overlap of the guided mode with doped regions, the measured insertion loss was as low as 5 dB. At a given wavelength, for example 1530 nm, a large transmission variation was obtained as a function of the bias. The
DC extinction ratio was larger than 11 dB from 0 to -10 V.
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fig 23: Experimental transmission of the modulator as a function of the wavelength, for different reverse bias voltages.
At -10 V,

was 6 nm. The phase shift was then about 0.75
 
for a 4 mm-long phase shifter. The deduced value of V  L  was 5 V.cm.
Numerical simulations made for this device are given in figure 24. A very good agreement can be seen between both experimental and theoretical DC results. Waveguide optimization would increase the optical mode confinement in the rib region and the overlap between the guided mode and the doped slit. A V  L  value as low as 2 V.cm can be predicted for an optimized configuration. fig 24: Numerical calculation of the modulator transmission as a function of the wavelength for several reverse bias voltages.
The frequency response of the modulator was measured using an AC signal generated by an opto-RF vector network analyser (Agilent 86030A) coupled to the DC bias, using a bias tee.
The RF signal was coupled to the coplanar electrodes from the optical input side and a 50
 termination load was added at the output side. The modulated optical signal was coupled back
22/26

to the opto-RF vector network analyser. The normalized optical response as a function of the frequency is given in figure 25 for both electrode designs, which are specified in table 2. fig 25: Experimental normalized optical response of the modulator as a function of the RF signal frequency for both electrode designs.
Electrode design:
W (µm) G (µm) Impedance
Design 1 5 25 50

Design 2 40 20 < 50

Table 2: Ground-signal-ground coplanar waveguide electrode geometries.
A 3 dB cut-off frequency of ~ 10 GHz was measured for the 1 matched), and ~15 GHz was measured for the 2 nd st
electrode design (50

electrode design, which was not 50
 matched, but with a larger signal electrode width.
This result shows the importance of the RF design, to ensure a high quality propagation of the RF signal all along the entire length of the phase shifter. The device speed limitation was not due to carrier transport mechanisms, but rather to the electrical supply.
The device rapidity can also be increased by an optimization of the RF traveling wave coplanar electrodes so that both electrical and optical signals propagate along the phase shifter with similar velocities. Furthermore, optimization of the phase modulation efficiency will reduce the phase shifter length, which will be favorable for increasing the bandwidth of the device.
In summary, important progress in silicon-based modulators has been obtained in the last 5 years. A SiGe structure has been proposed to achieve refractive index modulation, and a V  L  of 2.3 V.cm has been experimentally demonstrated at 1.55µm. Theoretical investigations of device speed has shown an intrinsic limitation, around 16 GHz, due to the time required for the carriers to escape out of the SiGe wells. A new all-silicon structure has then been
23/26

proposed, to increase the intrinsic frequency to around 100 GHz. An experimental V  L  of 3.1
V.cm has been obtained. The integration of these active regions in rib waveguides has been investigated, using both vertical and lateral PIN configurations. The devices have been optimized in terms of geometry, doping levels, etc., to achieve a large modulation efficiency, low optical loss, and large bandwidth. Integrated waveguide interferometers have been studied and compared. These previous works have allowed the final realization of a high speed and low loss silicon integrated optical modulator based on a p-doped slit embedded in the intrinsic region of a lateral PIN diode. An asymmetric Mach Zehnder has been used, with
4 mm-long phase shifters. The importance of the RF electrode has been emphasized, and experimental results have been reported: an insertion loss of 5 dB has been measured for a 3 dB optical bandwidth of 15 GHz.
Acknowledgements : The research leading to these results has received funding from the
French RMNT program "CAURICO" (Ultra-high speed optoelectronic devices for optical interconnects) and from the European Community's Seventh Framework Programme
(FP7/2007-2013) under grant agreement n° 224312 HELIOS. The authors acknowledge the staff of the 200 mm clean room of the LETI and MINERVE / CTU University Technological
Facilities center for the fabrication of high quality optical structures.
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