Design and experimental results of small silicon

Invited Paper

Design and experimental results of small silicon-based optical modulators C. E. Pnga, G. T. Reeda*, W. R. Headleya, K. P. Homewooda, A. Liub, M. Panicciab, R. M. H. Attac, G. Ensellc, A. G. R. Evansc, D. Hakd, O. Cohend a

School of Electronics and Physical Sciences, University of Surrey, Guildford, UK b Intel Corporation, San Jose, CA 95134, USA c Department of Electronics and Computer Science, University of Southampton, UK d Intel Corporation, Jerusalem S.B.I. Park Har Hotzvim, Jerusalem 91031, ISRAEL ABSTRACT In silicon based photonic circuits, optical modulation is usually performed via the plasma dispersion effect or via the thermo-optic effect, both of which are relatively slow processes. Until relatively recently, the majority of the work in Silicon-on-Insulator (SOI) was based upon waveguides with cross sectional dimensions of several microns. This limits the speed of devices based on the plasma dispersion effect due to the finite transit time of charge carriers, and on the thermo-optic effect due to the volume of the silicon device. Consequently moving to smaller dimensions will increase device speed, as well as providing other advantages of closer packing density, smaller bend radius, and cost effective fabrication. As a result, the trend in recent years has been a move to smaller waveguides, of the order of 1 micron in cross sectional dimensions. In this paper we discuss both the design of small waveguide modulators (of the order of ~1 micron) together with a presentation of preliminary experimental results. In particular two approaches to modulation are discussed, based on injection of free carriers via a p-i-n device, and via thermal modulation of a ring resonator. Keywords: grating coupler, phase modulator, thermo-optic effect, photonic circuits, integrated optics, optical coupling, optical waveguides, silicon-on-insulator

1. INTRODUCTION Most of the SOI modulators that have been reported in the literature have been based upon relatively large optical waveguides, of several microns in cross sectional dimensions. This was primarily to take advantage of relatively straightforward optical coupling to and from such devices via a 9µm communications optical fibre. However, in recent years there has been a trend to fabricate smaller devices, to maximise the benefits of closer packing density, smaller bend radius, and cost-effective fabrication. An additional benefit of smaller dimensions is the improved speed and efficiency of active silicon devices, in particular optical phase modulators [e.g. 1]. This paper considers the design of such modulators and the potential improvement in performance gained in moving to smaller waveguide dimensions, as well as presenting progress in fabrication and some preliminary experimental results. In particular, examples are given based on silicon waveguide heights of just above and just below 1µm. The modulators discussed are of two types. The first comprises a p-i-n structure around a rib waveguide, and the second is based upon modulation of a ring resonator. In passing we note that one very serious difficulty emerges from the move to smaller dimensions, which is the problem of coupling from an optical fibre to small optical waveguides. This is a particular problem in silicon, since the refractive index of the silica fibre (~1.45) is very different from that of the silicon waveguide (~3.5). Furthermore, unlike the III-V compounds, there is a lack of suitable materials with refractive indices between 1.45 and 3.5 with which to fabricate a mode converter, that are both compatible with silicon and convenient for processing. Consequently, a low-loss coupler between an optical fibre and the waveguide is crucial for successful implementation of small silicon photonic circuits in optical fibre communication systems. Some potential solutions have been discussed elsewhere (e.g. [2, 3]). *[email protected]; fax ++ 44 (0)1483 689404; School of Electronics and Physical Sciences, University of Surrey, Guildford, Surrey, GU2 7XH, UK

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Optoelectronic Integrated Circuits VI, edited by Louay A. Eldada, Proceedings of SPIE Vol. 5356 (SPIE, Bellingham, WA, 2004) 0277-786X/04/$15 · doi: 10.1117/12.529385

2.

SILICON OPTICAL MODULATORS

In this section the design of two optical modulators is discussed. The first is the design of a small geometry (0.98µm waveguide height) optical phase modulator based on the plasma dispersion effect, and the second is an optically controlled intensity modulator based upon a ring resonator, both are potentially high speed optical modulators. 2.1 Plasma dispersion phase modulator A plasma dispersion device is shown in figure 1. We have previously presented results of an alternative design [4] with a modelled modulation bandwidth in excess of 1GHz. However, due to fabrication limitations we have designed a series of devices with more modest bandwidths that will both validate our modelling and should produce significantly faster devices than previously realised experimentally. The devices were designed using commercial simulators to study the electrical and optical characteristics of the device. Electrical modelling was performed using the two-dimensional semiconductor simulator from SILVACO [5]. Anode 0.5 µm

y (µm) 1.38

1 = 0.58µm 2 = 0.75µm 3 = 0.79µm 4 = 0.84µm 5 = 0.90µm

1.13

x

p+

n+ 1020 cm-3

Cathode

0.9

y

1

Cathode

2

n+ 1020 cm-3

Si

3 4

0.34µm 0.4µm 0.44µm

5

0.48µm

n-intrinsic 1015 cm-3 0.4

SiO2

0

x (µm) 0

11.15

12.05

12.55

13.45

24.6

Fig. 1: Geometry of the p-i-n phase modulator with the optimised doping profile at the n+ regions

Figure 1 shows a schematic of the 3-terminal device structure to be discussed in this paper. It is a lateral optical phase modulator integrated into a low loss SOI rib waveguide. The device has a symmetrical p-i-n structure where two n+ regions are joined as a common cathode. Both n and p regions were modelled as highly doped regions. The profile used in the n and p regions was established by modelling a fabrication process using SILVACO [5]. The p+ region was modelled as a solid epitaxially grown layer with a doping concentration of 1019 atoms/cm3 which was subsequently subjected to an ion implantation step to increase the doping concentration to 1020 atoms/cm3. The doping of the n regions was modelled as a series of ion implantation steps to achieve a pre-determined doping profile, with a concentration of 1020 atoms/cm3 at the surface, falling to a concentration of approximately 1016 atoms/cm3 at the buried oxide, as depicted schematically by the contours in figure 1. The device is based around an overall silicon guiding layer thickness of 0.98µm, etched rib waveguides 0.5µm wide with an etch depth of 0.48µm in order to satisfy the single-mode condition [6]. The oxide thickness was modeled as 0.4µm, although we actually used 0.67µm, which ensures sufficiently good optical confinement. The device relies on the principle of the free-carrier plasma dispersion effect to produce a refractive index change in the waveguiding region of the rib. When the anode is biased positively with respect to the cathode, such that the p-i-n diode structure is forward biased, both electrons and holes are injected into the guiding region, and hence the resultant phase of a propagating optical mode is altered by the associated change in refractive index. 2.1.1 The p-i-n device simulation The device was modelled for both its static and dynamic behaviour using the device simulation package from SILVACO [5]. The simulator is a physically based simulator which predicts the electrical characteristics associated with physical structures by solving the equations which describe semiconductor physics such as Poisson’s equation and the charge

Proc. of SPIE Vol. 5356

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continuity equations for holes and electrons. The simulator has been used to predict the injected free carrier concentrations in the intrinsic region of the devices for both dc and transient biasing conditions. The concentration of free carriers is then converted to refractive index change in the device by using the relations determined by Soref and Bennett [7]. To determine the voltage associated with a π-phase shift, the concentration of free carriers must be known. From the change in refractive index, the active device length required to produce the refractive index change associated with a π-phase shift is obtained from the relation between phase change and change in propagation constant: ∆φ = ∆βL

(1)

where L is the active length of the device. If such a phase shift is introduced into an optical waveguide, this can readily be translated into an intensity change via a Mach Zehnder interferometer. For small changes in refractive index, the change in effective refractive index ∆N≈∆n. Therefore, ∆φ, is approximately: ∆φ =

2π

λ

∆nL

(2)

Soref and Bennet [7] determined the refractive index change and absorption change in silicon as a function of carrier concentration. At a wavelength of 1.55µm, the refractive index change (∆n) is given by:

(

∆n = ∆ne + ∆nh = − 8.8 × 10 −22 (∆N e ) + 8.5 × 10 −18 (∆N h ) 0.8

)

∆α = ∆α e + ∆α h = 8.5 × 10−18 (∆N e ) + 6.0 ×10 −18 (∆N h )

(3) (4)

where ∆ne and ∆αe are the changes in refractive index and absorption coefficient resulting from the change in free electron concentration, ∆Ne; ∆nh and ∆αh are the changes in refractive index and absorption coefficient resulting from the change in free hole concentration ∆Nh. All the device simulations shown here were based upon a device interaction length of 500µm and operation at a wavelength of 1.55µm. Fig. 2 shows the simulation results for an applied dc injection current. Three curves are shown in figure 2, for different carrier lifetimes. The solid curve uses lifetimes that we have used previously in larger devices, that give good agreement with experimental results [9]. However, for smaller devices with more surfaces in proximity to the lifetime may change. Therefore we have also modeled devices with shorter lifetimes. This will be discussed further in association with experimental results.

Fig. 2: Predicted dc performance for the modulator of figure 1, with different intrinsic region carrier lifetimes

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A typical figure of merit for such devices is based on the drive current Iπ or current density Jπ required to achieve π radian phase shifts. From Figure 2, the predicted drive currents for this device represented by the solid line is approximately 2.3mA. Fig. 3 shows the transient results for the same devices. For the transient solutions, the device anode and cathode were first zero biased for 10ns, followed by a step increase to Vπ for 200ns, and finally a step decrease to 0V. Vπ is the voltage corresponding to a π radian phase shift. The rise time tr is defined as the time required for the induced phase shift to change from 10% to 90% of the maximum value, and the fall time tf is defined as the time required for the induced phase shift to change from 90% to 10% of the maximum value. The rise time is used to calculate the device speed, as it is slower than the fall time and hence the limiting transition. From figure 3, the predicted rise time for the device represented by the solid line is 6.8ns, corresponding to a bandwidth of approximately 70MHz. Devices with shorter lifetimes exhibit faster responses as expected (100MHz and 175MHz), but at the expense of higher drive current as shown in figure 2. Whilst these responses represent changes of π radians, the small signal bandwidth can be greater, if the device is pre-biased to the linear region of its characteristic.

Fig. 3: Predicted transient performance for modulator of figure 1, with different intrinsic region carrier lifetimes

Whilst this predicted bandwidth is significantly smaller than the 1GHz devices we have previously discussed [4], the limitation is simply due to fabrication restrictions. Nevertheless, this is still significantly faster than devices of this type that have been reported previously, having bandwidths limited to approximately 10-20MHz [8, 9]. 2.2 Ring-resonator modulator A modulator can also be based upon a single input/output ring resonator. The operation of the ring resonator is well known, but it is worth briefly reviewing it here to demonstrate the operation of a modulator. Following the approach of Yariv [10], we can describe the ring resonator depicted in figure 4. Two assumptions are made about the coupling region of the ring resonator: 1) coupling is limited to waves travelling in only one direction (i.e. no reflections) and 2) the coupler is lossless. Whilst these assumptions are not strictly accurate, in a high quality coupler they approximate reality. We can now describe the coupler using two constants via the unitary scattering matrix:


47

b1 t κ = * b2 κ − t*

a1 a2

(5)

where a1, a2 are the coupler input amplitudes of the input waveguide and ring respectively, t is the transmission coefficient, κ is the coupling coefficient, and b1, b2 are the amplitudes in the output waveguide and ring respectively.

Κ1 represents ring loss

ring waveguide

L = ring circumference a2 input waveguide

b2

a1

b1

output waveguide

coupling region Fig. 4: Schematic of a single input/output ring resonator

The coefficients of the matrix are related by: 2

t +κ

2

=1

(6)

Finally propagation around the ring is represented as: a2 = K1b2exp(jθ)

(7)

Hence Κ1 represents the proportion of the power transmitted around the ring (and hence the loss) and θ is the phase shift per circulation around the ring. Combining equations (5), (6), and (7), and solving for b1 gives:

b12 a12

2

=

K12 + t − 2 K1 t cosθ 2

1 + K12 t − 2 K1 t cosθ

(8)

For normalisation purposes, the input power |a1|2 can be set to unity. If the phase shift, θ, is expressed as the product of the propagation constant and the ring circumference, L, then equation (8) becomes:

b1

2

 2π  2 K12 + t − 2 K1 t cos NL   λ  =  2π  2 2 1 + K1 t − 2 K1 t cos NL  λ  

(9)

where L is the optical path length around the ring, N is the effective index of the waveguide. Thus we have an expression for the output power of the ring resonator. We can plot equation (9), and we see that the result is the well known characteristic of the ring resonator (figure 5). Figure 5 is plotted for a ring resonator with the following parameters: Optical path length around the ring, L = 3.513mm, K1 = 0.95 (95% transmission, corresponding to a waveguide loss of 0.22 dB, i.e. 0.63dB/cm in this case), effective Index, N = 3.47.

48


It can be seen from figure 5 that the theoretical characteristic of such a ring resonator has the potential of acting as a modulator if we can switch between regions of high throughput and low throughput. One way to achieve such switching is via changes in effective index. In silicon we can typically achieve this either by injection of free carriers as described in section 2.1, above, or by thermal tuning. In the case of carrier injection, the refractive index of silicon is reduced, as described by equation (3). However, carrier injection also introduces loss via absorption, as described by equation (4). This is demonstrated in figure 6, by plotting equation (9) for modified values of effective index and ring loss. In figure 6, the effective index is modulated by an amount ∆N = 10-3. If we make the simplifying assumption that ∆N ≈ ∆n, the change in refractive index, then from equation (3), this corresponds to a level of injected carriers of approximately 3 × 1017cm-3.

Fig. 5: Modelled Ring Resonator response

The corresponding absorption loss can be calculated from equation (4), as a change in absorption coefficient of 4.35. This corresponds to a change in the transmission parameter K1 of 0.217, resulting in a revised value of K1’ = 0.733. Hence considerable addition loss is introduced. The additional loss accounts for the change in shape of the characteristic in figure 6, and the change in refractive index accounts for the shift in wavelength. It can be seen from figure 6 that the additional loss of the ring significantly impairs the response of the resonator, primarily because the width of the troughs is increased (i.e. the finesse of the ring is reduced). However, the nature of the transfer function is such that at high transmission, the throughput is still very high. Hence if we switch from a high transmission point on the carrier injection shifted curve, to a low (resonant) point on the unshifted curve, the modulation depth we can achieve will still be large. We have seen from the previous section on phase modulators that in principle, the response time of carrier injection can be high. Therefore the ring resonator presents an alternative means of developing a fast optical modulator. However, if the absorption loss is too problematic for a given application, an alternative modulation mechanism exists in silicon, the thermo optic effect, although this effect is limited to much slower response times, typically of the order of a few 10s of kHz. The thermo-optic coefficient in silicon is [11]: dn = 1.86 × 10 − 4 / K dT

(10)


49

In this case the change in refractive index is positive, but will still facilitate switching between high and low throughput parts of the characteristic. If we again assume ∆N ≈ ∆n = 1×10-3, then a temperature change of only 5.4K is required over the whole ring. Alternatively the temperature change can be localized to part of the ring, and a larger temperature change imposed. This has been the approach of typical thermo-optic modulators in silicon [e.g. 11].

Fig. 6: Unshifted and shifted (Carrier Injection) responses of the Ring Resonator

3. EXPERIMENTAL RESULTS Having demonstrated the two methods of implementing optical modulation, this section provides preliminary experimental results of the two variants. 3.1 Plasma dispersion phase modulator The plasma dispersion modulators described in section 2.1 has been fabricated in a CMOS compatible process that has been described elsewhere [12]. Figure 7a shows an electron micrograph of the end facet of the 0.5 micron rib waveguide upon which the modulator is based. However, so far the only functional modulators that have been characterised have rib widths of 0.75µm. The electrical diode characteristic of the p-i-n diode is shown in figure 7b. The device was characterized optically by applying an ac voltage to the device, as well as a dc bias to enable the device to switch between a high and low level of carrier injection. Light was coupled to the device via a 60× objective lens, and detected using a commercial detector, with a bandwidth of 10MHz. Due to the small size of the waveguide, coupling efficiency was poor, resulting in a poor signal to noise ratio at the detector, which has restricted our ability to produce high speed data. However, there is no reason to believe that the modulator will not respond at much higher frequencies. The coupling efficiency problem, and hence the signal to noise problem would be overcome in a real device by utilizing a more efficient coupling technique (e.g. [2]). Figure 8 shows oscilloscope traces representing the drive signal (a), the current in the device (b), and the received optical signal (c). This data is captured at a convenient modulation speed of 100kHz. Clearly the optical signal faithfully reproduces the drive data, indicating that the device successfully modulates the optical beam. However, the modulation as recorded is absorption based, because the poor signal to noise ratio

50


precludes the use of a Mach-Zehnder interferometer. The phase shift of the optical signal is merely an artifact of the detector, present at all frequencies.

Fig. 7a: Rib waveguide facet of phase modulator

Fig. 7b: I/V traces of both side contacts (cathode) with respect to the waveguide rib (anode) of the phase modulator

Fig. 8: Oscilloscope traces of applied modulating signal, device current, and detected optical signal

We can analyse the data a little further to infer reliable operation of the phase modulator. This result represents a modulation depth of 26% for an applied current of 23mA (rms). However, to compare this to the modelling results we must take account of the different rib width. For the same density of carriers in each modulator, the current in the 0.75µm rib will be approximately 1.5 times larger than in a 0.5µm, hence this would be 15.3mA. The modulation depth is associated with the definition of the loss coefficient, α:


51

I = e −αL I0

(11)

A modulation depth of 26% corresponds to a change in loss coefficient of ∆α = 6.02. From equation (4), this corresponds to a carrier injection level of N = 4.2 × 1017, or 2.1 × 1017 electrons/cm3 and 2.1 × 1017 holes/cm3. In turn this corresponds to a phase shift (from equations (1) – (3)) of : ∆φ = 0.51π radians

(12)

Therefore a phase shift of π radians corresponds to an approximate current of 28.5mA for the 0.5µm rib, which is approximately an order of magnitude larger than the modelled value. This can be due in part to incorrect assumptions about the lifetime of the carriers used in the modelling, as discussed previously, as well as more obvious omissions from the model such as contact resistance. However, the issue of carrier lifetime is significant. If we now revisit the data of figures 2 and 3, we can see that very small lifetimes, of the order of 3ns are required to result in such large driving currents. Data exists in the literature suggesting values of average carrier lifetimes between 100ns and 600ns (e.g. [13]), more consistent with the solid curves in figures 2 and 3. Therefore it is unlikely that incorrect assumptions about carrier lifetime fully explain the device behaviour, but that contact resistance is also partly responsible. Since this is only preliminary data, more complete analysis of a range of devices is expected to clarify the situation. Furthermore we have every expectation that these devices will respond at much higher frequencies when the coupling efficiency is improved. 3.2 Ring resonator modulator Ring resonators with target specifications as given in section 2.2 have also been fabricated in a CMOS compatible process. Figure 9a shows a photograph of example devices in plan view. The rings were illuminated with light from a tunable laser, and the wavelength scanned over the range 1550nm to 1570nm. A proportion of the resulting characteristic is shown in figure 9b. The waveguides used to fabricate the rings are somewhat different to those of the carrier injection phase modulator above, but are still close to 1µm in cross sectional dimensions. The silicon guiding layer height is 1.33µm, whilst the rib width is approximately 1µm. The etch depth was varied but was typically of the order of 0.8µm.

Fig. 9a: Photograph of the SOI ring resonator structures

52


Fig. 9b: Optical response of the optical ring resonator

The resonators have been modulated by illuminating the ring with a visible red, 670nm semiconductor laser beam. The red laser was biased to a linear part of its characteristic, and modulated by a signal generator. This enabled us to test the ring resonator modulator with both analogue and digital signals. Whilst being modulated by the red laser the ring resonator was simultaneously passing longer wavelength light (λ ≈ 1.56µm). Figures 10a and 10b show oscilloscope traces representing the drive signal and the detected optical signal for analogue and digital signals respectively.

Fig. 10a: Optical response of the optical ring resonator under an analogue modulation at a frequency of 1.8MHz

Fig. 10b: Optical response of the optical ring resonator under a digital modulation at a frequency of 12kHz

For the analogue signal we have plotted a conventional bandwidth plot, shown in figure 11. The gain has been normalized to the low frequency gain. This diagram shows that the 3dB bandwidth is approximately 70kHz, but also that the device is still responding well at 2MHz and beyond. In fact the data in figure 10a was recorded at 1.8MHz. The fact that the modulation signal is produced via a laser at a visible wavelength means that silicon will absorb the light. Hence the modulation may be produced either by introduction of free carriers or by thermal changes. However, we have seen from section 2.1.2 of this paper that carrier injection should in principle be a relatively fast modulation mechanism, as compared to thermal modulation. Hence a bandwidth of only 70kHz suggests that the dominant modulation mechanism in the current device is a thermal mechanism. This has been verified experimentally in the following procedure. The wavelength of the tunable laser was adjusted until it was at a null in the ring resonator characteristic in figure 9b. The resonator was then illuminated with the 670nm laser, and consequently the null of the resonator characteristic was shifted to another wavelength. In particular, at very small shifts in the characteristic, it is possible to determine the direction of the shift by retuning the tunable laser to the same null of the characteristic. The resulting shift in wavelength was always to a longer wavelength. We can see from equation (9) that if the effective index at resonance goes up slightly, then the wavelength of light must also rise to maintain resonance. A rise in effective index results from the thermo-optic effect rather than carrier injection, hence confirming that this is the dominant mechanism. Nevertheless it is clear that the principle of tuning an optical modulator based upon a silicon ring resonator has been demonstrated. Alternatively, if we use carrier injection to modulate the ring resonator, it is anticipated that this type of device will operate to frequencies in excess of those of the phase modulator based upon carrier injection, because a lower level of injection is required in the ring resonator to shift from a high throughput state to a low throughput state. Therefore these devices have the potential to operate at high modulation frequencies, at low drive power.


53

Fig. 11: Frequency response of the Ring Resonator

4. CONCLUSION In this paper we have discussed the operation of two types of small optical modulators in SOI optical devices. For an optical phase modulator based on the injection of free carriers, a design was presented, together with modelling data, and preliminary experimental data demonstrating the viability of the device. The experimental results demonstrate the functionality of the device but the phase efficiency data is approximately an order of magnitude smaller than predicted by modelling. Unknown variations in carrier lifetime may contribute to increased drive current but do not fully explain it. Unwanted contact resistance is a more likely explanation. More thorough characterisation of numerous devices should clarify the situation. Nevertheless we expect these devices to respond at much higher frequencies, as predicted by the modeling data. (b) A second modulator based upon an optical ring resonator has also been discussed, and further preliminary data has demonstrated the viability of the device. The ring resonator has been modulated by illumination with a modulated 670nm laser. The dominant modulation mechanism in this experimental arrangement has been shown to be due to the thermooptic effect. Neither device has yet been evaluated at high modulation speeds. The carrier injection modulator has been predicted to operate at approximately 70MHz, but the small size of the device meant that poor device coupling efficiency has resulted in a poor signal to noise ratio at the detector. This will be resolved in future by using an alternative coupling mechanism. The ring resonator device also has the potential for high frequency modulation. So far the device has been modulated to in excess of 2MHz via the thermo-optic effect, but we expect to achieve much faster modulation by injection of free carriers.

ACKNOWLEDGEMENTS The authors are grateful to the Intel Corporation, EPSRC and Bookham Technology plc for funding. The authors are also grateful to Mr. C. Murray and Dr. S Sweeney from the University of Surrey for help with experimental equipment. W. R. Headley is grateful to the Royal Academy of Engineering, UK for assistance with travel and subsistence costs.

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