1. Introduction

Arrayed Waveguide Gratings (AWGs) have increasingly become more important in Wavelength Division Multiplexing (WDM) systems. An AWG in silicon-on-insulator (SOI) is of particular interest because of both its technological and material advantages. The high index contrast in the SOI optical system results in a smaller device and better optical confinement within the waveguide as compared to low index contrast systems. Also, the mature microelectronic fabrication technology can be easily transferred to most of the SOI photonic devices. The spectral response of a typical SOI AWG exhibits a Gaussian profile, which restricts the wavelength selectivity of the devices due to wavelength drift caused by the laser diode and the AWG. Therefore, a flat spectral response is desirable to ease the wavelength selectivity of the WDM system. Various methods have been proposed and demonstrated in different material systems and each has its own advantages and disadvantages [1–4]. In this paper, we take an alternative approach by presenting the design methodology of achieving a flat spectral response AWG via ion implantation. This approach uses standard process fabrication steps and is highly repeatable, whilst allowing flat spectral response to be achieved.

2. Theoretical model

In order to put forward the main ideology of the design method, we designed the AWG to operate at a centre wavelength λ₀ of 1.55µm and a grating order m of 52 with a path length difference ΔL of 23.62µm. The rib waveguides are designed according to the criteria of singlemode and zero-birefringence conditions [5] with the aid of the BEAMPROP [6] simulation package. Thus, a rib width of 1.1µm with an etch depth of 880nm were chosen. Subsequently, we determined the remaining AWG parameters following the approach of Amersfoort [7]. The parameters for both the input and output star coupler should be identical for self consistency purposes and for most AWG designs. Hence by default, the two star couplers are identical except for the number of input and output ports.

The principle of this methodology is the introduction of free carriers via ion implantation, to selected regions of the array waveguides to induce absorption of the optical field propagating along the respective array waveguide. Implantation offers clear advantages for such a selective doping strategy; as it allows precise control of the concentration of implanted dopant atoms and the dopant depth distribution profiles. The implanted ions are used to modify the shape of the optical field distribution across the array waveguides from a Gaussian to a SINC function and hence obtain a flat spectral response at the output of the devices. This is possible because the focused beam profile at the output waveguides is the spatial Fourier transform of the optical field profile at the output array/star coupler interface [1]. Illustrative examples are included specifically using both n-types and p-types dopants at concentration levels in the range 1e17cm^-3 to 1e20cm^-3 and the effect of different net concentrations on the design are compared.

2.1. Optical field distribution

The optical field progression across the star coupler from the input waveguide can be regarded as a Gaussian distribution. This spatial distribution in the focal plane can be obtained by the spatial Fourier transform of the paraxial approximation method [8]. The fundamental mode profile of the centre input waveguide can be approximated as a normalised power Gaussian function. Hence, the spatial light distribution impinging on the array waveguides is given as [9]:

where w_i is mode field radius with respect to the waveguide in question, x_i is the distance away from the origin from the star coupler and σ is the focal length product in Fourier optics propagation which is given as in [8]. If the focused beam profile at the output waveguides is the spatial Fourier transform of the optical field profile at the output array-slab interface, then by discretising the optical wavelengths as proposed in [1] we can rewrite the transmission function of the AWG as:

where M is the number of array waveguides, q is the spatial harmonics from q=1, 2, … …, M, and λ _o is the center wavelength and FSR is the free spectral range, Δλ is the channel spacing, β_aw is the propagation constant of the array waveguides and L_c is the fixed optical path length with the AWG. Hence g(p) indicates the optical field distribution across the arrayed waveguides, which is described by the inverse discrete Fourier transform of the output field.

2.2. Optical model–free carrier absorption

As mentioned previously, control of the amplitude is via ion implantation, the introduction of free carriers into silicon will affect both the real and imaginary refractive indices. The changes in refractive index and absorption coefficient due to free electrons and holes at the communication wavelength of 1.55µm are given as [10]:

where Δn_e is the change in refractive index resulting from the change in electron carrier concentration, Δn_h is the change in refractive index resulting from the change in hole carrier concentration, Δα_e is the change in absorption resulting from the change in electron carrier concentrations and Δα_h is the change in absorption resulting from the change in free hole carrier concentrations. Three different net concentration; 9e17 cm^-3, 1e18 cm^-3 and 2e18 cm^-3 are investigated in this work.

2.3. Design methodology

The first step in the design methodology is to obtain the intensity difference between the spatial field distribution in the focal plane and the spatial field transform at the output array-slab interface. This intensity difference is evaluated at each individual array waveguide as shown in Fig. 1, together with the field distribution and field transform in both the focal plane and output array-slab interface respectively. This intensity difference is used to gauge the concentration and type of dopant required for introducing adequate absorption to transform the gaussian distribution to a SINC distribution. The concentration of free carriers to be introduced into each array waveguide (AW) can be calculated based on Eq. (4), and for a particular dopant type. Each individual AW will require a different doping length, since the intensity required in each AW is unique. Thus, the doping length, L_doping is given as:

 

Fig. 1. Field distribution and intensity difference plot between the Gaussian and sin(x)/x function Since the phase of the optical field in the AWs is dependent upon the refractive index of the material, one would expect a phase change resulting from the doping concentration. These phase changes are evaluated approximately from:

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It is important to note the phase caused by a change in Δn for the individual AW, since a 2mπ phase difference is still required between the adjacent waveguides to enable constructive interference at the 2nd star coupler. Since the phase change is negative in silicon Eq. (3), to ensure this occurs, an additional optical path length for each AW is required to maintain the desired phase difference. These excess optical path lengths are then calculated using Eq. (7).

2.4. Numerical results

For the intended absorption to be introduced as shown in Fig. 1, the maximum loss factor is around 40 dB which could prove to be a critical aspect in terms of the doping length L_doping. In order to maintain the compactness of the AWG, herein, we investigated this parameter with respect to the dopant concentration level at different absorption intensities. In Fig. 2, L_doping is plotted against dopant concentration at an absorption level of 10 dB to 40 dB. The curves in Fig. 2 all exhibit decreasing doping length with increasing dopants concentration. If we examine each dopant type at a specific concentration, for example at 1e19 cm^-3, we observe the significance of choosing a particular n-type or p-type dopant becomes clear. For n-type dopants at concentration level of 1e19 cm^-3, the required L_doping for introducing 10dB, 20dB, 30dB and 40dB are 271µm, 542µm, 813µm and 1084µm respectively, in comparison to a ptype dopants at the same concentration level result in a significantly decreased L_doping of 112µm, 226µm, 339µm, 451µm respectively. N-type dopants will result in a shorter L_doping. However, for this work, we examine the usage of each dopant type, either holes or electrons, for comparison purposes.

 

Fig 2. Variation in (a) electrons and (b) holes net concentration with different absorption factors to evaluated the intended doping length.

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Another important aspect to be investigated is the phase change induced by the each dopant type and the variation in doping concentration level as described in Eq. (3) and Eq. (6). These phase changes vary across the grating arms, hence creating phase perturbations, because of the sensitivity of the phase condition. These phase conditions have to be maintained multiples of 2π to sustain constructive interference at the output. A general trend can be clearly seen from Fig. 3 regardless of the dopant types, that is, an increase in phase with an increase in absorption factors, as defined by Eq. (3) and Eq. (4). Figure 3(a) shows a constant relationship between carrier concentration and phase, as well as a constant relationship between carrier concentration and compensation length for different absorption factors. This implies that for different carrier concentrations, a similar change in phase and compensation length result due to the linear relationship in electron concentration and refractive index change in Eq. (3).

In Fig. 3(b), the graph indicates a decrease in phase and compensation length with increase concentration level for holes; this is caused by the sub-linear dependence on the holes concentration as discussed in Eq. (3). By comparing both plots in Figs. 3, it can be noted that for the same concentration level of 1e19cm^-3, we expect an 82% decrease in compensation length for electrons with reference to holes. This reduction in compensation length will have a significant impact on device footprint.

Clearly it is possible to define a theoretical model with any doping variety and concentration. However, to develop such model effectively, one major factor to consider is the resultant doping length based on a particular dopant type. From Fig. 2, it is obvious that an ntype dopant provides a significant improvement in reducing L_doping, also Fig. 3(a) indicated a linear relation between the variation of dopant concentration and Δφ. This means the relationships between the concentration level, the change in phase and compensation length is constant for a particular absorption factor.

 

Fig 3. Left: Phase change induced by changing of refractive index due to (a) electrons net concentration and (b) holes net concentration; Right: Compensation length required to maintain constructive interference at the output of the AWG.

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Based on the above findings, we have optimised the device model to produce the best performance, based upon the parameters investigated. The device should use an n-type dopant and the net doping concentration should not exceed the equilibrium solubility limits of silicon [11]. Thus, an ideal net concentration is approximately 1e20 cm^-3. By referring to the intensity difference as shown in Fig. 1, and evaluating the doping length for such device, we predicted L_doping (max) at around 100µm as shown in Fig. 4. This is not an unreasonable length for such a device, since ΔL is approximately 25% of L_doping (max). For most practical AWG, usually a large number of grating arms are required, for example in this work 100 grating arms are used. Hence to sustain constructively interference at the output of the AWG, an increment of 2mπ at each consecutive grating arm is required, therefore, the total path at the 100^th grating arms, required for maintaining the phase condition exceeds L_doping (max) by 95%, which can be calculated by multiplying ΔL by a hundred. Hence the device dimension is not affected by L_doping (max). The doping length has to be evaluated for each array waveguide since the absorption coefficient is unique. Based upon this modelling, we can predict Δφ and the necessary compensation length due to the effect of ion implantation as shown in Fig. 5. As an example, we compared L_doping of the intended net concentration of 1e20 cm-3 for n-type dopant to the compensation length, as shown in Fig. 5. It can be clearly seen that from Fig. 5 the maximum compensation length required to maintain the 2mπ phase condition is approximately 3µm, which constitutes 0.12% of the total path length of the array waveguide. Thus, it can be concluded that this methodology is viable without degrading the compactness of the SOI AWG.

 

Fig. 4. Doping length evaluated across the grating arms based on 1e20 cm^-3 n-type dopant.

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Fig. 5. Evaluating the phase condition and compensation length based on the resultant doping length.

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3. Experimental results

The SOI AWG is fabricated using standard CMOS technology. The fabrication is conducted in two stages; (1) implantation and (2) patterning of AWG. The mask of the implantation uses negative resist and the intended areas of the wafer are implanted with n-type dopants. Ion implantation is performed in 6 steps; two low energy implants at Southampton University using the 200keV Danfysik A/S implanter and four high energy implants at University of Surrey using 2MeV implanter. The implantation profiles before and after annealing can be simulated using the process simulator ATHEN by SILVACO [12] and is shown in Fig. 6.

This recipe is predicted to show a relatively uniform profile at 1e18cm^-3 net concentration. Two low energy implants; at 70keV with fluences of 0.2 × 10¹⁴cm^-2 and 150 keV with fluence of 0.3×10¹⁴cm^-2 are required for shallow depth at 100nm and 300nm respectively. Subsequent high energy implants are conducted to allow a uniform profile reaching 1.5µm as shown by the grey lines in Fig. 6. Annealing process is performed using the AG RTA 210 annealer. Rapid thermal annealing consists of a 6 seconds ramp up from initial 700°C to 1000°C, followed by 60 seconds anneal and 9 seconds cool down. The post annealing profile is shown in Fig. 6 as the solid line sit on top of the implanted profiles. This clearly demonstrated that dopants are electrically activated and the lattice structure is restored. As the dopants are fully activated, there are no more extra implanted carriers available to cause unwanted additional optical attenuation. The flat-top AWG has been successfully patterned and fabricated in a 1.5 µm silicon overlayer UNIBOND SOI wafers using positive resist by the Leica-Cambridge 10.5 electron beam direct write lithographer and the anisotropic Oxford RIE80 etcher. The wafers were then diced and the end facet polished. Coupling dependent loss at the input/output facet was removed by normalising the measured data to a straight waveguide fabricated under similar conditions.

 

Fig. 6. Implantation profilea: gray kines indicated implanted profiles of respective energy and fluence and black line indicates post anneal profile

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The experimental setup for measuring the AWG is shown in Fig. 7. We used a tunable laser covering both C and L bands. The wavelengths are scanned and the maximum output power is recorded with no device present. The output power with device under test (DUT) is then recorded with the similar range of wavelengths. The output is first directed towards the MicroPhysic viewer with its output fed to a monitor to display the detected image. Fine adjustment of the fibre and DUT is performed using the micropositioner until the maximum output power is observed on the detector. When optimum waveguiding is achieved, the focusing lens is replaced by a lens fibre as shown in Fig. 7 and the true output power is recorded for a range of wavelength. To improve accuracy and maintain consistency in the measurement, the experimental is conducted at least ten times and average result is noted. This output power is normalised to the laser power recorded

 

Fig. 7. The experimental setup to measure the AWG; detection of light from output waveguides through lensed fiber with spot size of 2.5µm.

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Figure 8(a) shows that, at 1549.3nm, the responses clearly exhibit a sharp peak for both the Gaussian AWG and the flat-top AWG. The peak of the Gaussian deviated from the designed wavelength by 1nm. This could be the result of fabrication tolerances, since the physical character of the AWG is strongly dependent on the fabrication precision of the waveguide and any small deviation from the design value will result in additional phase errors which might cause the peak of the response to steer either left or right of the spectrum. Active tuning such as thermal effect could be added to compensate for such shifting. The broadened passband is measured to be 0.5nm, a 5 times broadening from the Gaussian peak. The adjacent response is measured as shown in Fig. 8(b), showing a flat response from 1550.6 to 1551.1 nm, giving a broadening factor of approximately 0.5nm. This result shows a consistency with the previous channel. The channel spacing Δλ also agrees well with our model at 1.6nm.

 

Fig. 8. (a). Measured response of a flat-top SOI AWG. Peak at 1549.3nm with broadening factor of 0.5nm. (b). Measured response of a flat-top SOI AWG. Peaks at 1549.3nm and 1550.8nm with broadening factor of 0.5nm and channel spacing of 1.6nm

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4. Conclusion

We have presented and demonstrated experimentally a flat-top response SOI AWG via ion implantation. The analysis indicated that the use of n-type dopant provides a convenient method to design a flat-top response without sacrificing the compactness of the AWG. The measured result shows an improvement of 80% of the passband flatness compared to the gaussain peak and clearly exhibited a passband width of 0.5nm. We fabricated our example in Silicon-on-Insulator (SOI) because this material is useful in the field of optical communications. However, our design can be applied to other semiconductor materials. We can also include materials that are insulators such as silica (glass), or Lithium Niobate (LiNbO₃) in which we can introduce absorption either through doping or crystal damage. In either case the doping can be performed by ion implantation, or some other doping mechanism and the principles of the design procedure still hold. This method gives the robustness of tailoring the optical field distribution across the array waveguides by the appropriate choice of net doping concentration, and hence gives room for design flexibility without increasing the physical dimension of the AWG significantly. This potentially creates the opportunity for achieving a smaller SOI AWG device with the use of higher net dosage and the realisation of achieving a uniformity doping concentration through multiple implantations. This experiment result validates the design methodology which could be useful for future development of a low cost, small scale flat-top AWG in SOI.