Fully etched diffraction grating couplers

In this section, we extensively study the fully etched diffraction grating coupler as in our fabrication facilities at NTRC, we only have 1 etching step. Even though it may be possible to use two etching steps, it is the objective of this thesis to fabricate sensors as quickly, as cheap and as simple as possible to be disposable. Now, if we take the same design as the shallow etch case, but let the shallow parts be completely etched, the contrast between air and silicon is too high, and a large percentage of a wave would be propagated

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backwards and thus, the efficiency of the DGC is too low as the grating coupler looks more like a reflecting mirror.

Some applications have been found for this kind of high contrast gratings (HCG) [52], and in recent years, they have been proposed to be used as diffraction gratings when the lightwave is travelling below this structure [53]. So, in order to reduce this contrast or refractive indices, the usage of subwavelength size structures has been suggested [54].

That name is adopted because these structures are smaller in comparison to the wavelength. The shape of the structures is not fixed and the most common are geometrical shapes such as squares or circles [55]. In this thesis, we study the case of square-shaped subwavelength structure. A schematic of a subwavelength fully etched DGC is shown in Figure 2-9.

Figure 2-9 (Left) 3D Schematic of a fully etched DGC (Right) 2D Schematic

From the 3D schematic, it is seen that now we have one more spatial direction to consider. The period in the Z direction is still present, but now, we have another period and etch factor in the X direction. Although it is possible to simulate such a 3D structure with 3D FDTD, we would like to be able to use the same methodology as the shallow etched case. From the previous section of shallow etched DGC we know the diffraction equation. In order to use that equation, we need to take additional steps into account to convert the 3D problem into a 2D problem. As for fully-etched DGC the X-direction geometry cannot be ignored, we need to account for that variation using the following equation for the TE mode to transform it in a 2D problem [55].

1

𝑛_𝐻−2𝐷 = [ 𝑒𝑓_𝑥

𝑛_ℎ−3𝐷² +(1 − 𝑒𝑓_𝑥) 𝑛_{𝑆𝑖−3𝐷}² ]

1/2 (2.3)

And for the TM mode we have the following equation

2 2 1/2

3 (1 )

TM

x h D x Si

n ef n_  ef n  (2.4)

Then, we are able to use the same procedure as the case of a shallow etched grating coupler. When the shape is not a rectangle, a previous step is needed that consists in obtaining the equivalent area of that shape with rectangular dimensions to then be treated as a 2D problem. In summary, we need to get an equivalent refractive index that takes into account the variations in all directions. First we get an equivalent refractive index for one direction and then the total equivalent effective refractive index for the second direction.

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In order to design the grating coupler, we used a similar graphical procedure as the shallow etched case beginning by solving the equivalent refractive index of the X holes taking into account the dispersion of silicon. Then, we applied the same methodology as described in the previous section. Following this procedure, we were able to approximate the Bragg wavelengths as shown in Figure 2-10 for different periods in the Z direction (650 nm, 700 nm, 750 nm) and a constant period in the X direction of 600 nm. From the figure, we can see that a period of 700 nm would give us the best results, so we chose this design to be the main one. We did the same procedure for the TM polarization and are shown in the Bottom of the figure with the main difference being the larger periods required to get a Bragg wavelength around 1550 nm.

Figure 2-10 (Top) TE Fully etched grating coupler design for different periods in nm (Bottom) TM polarization

Obtaining a full characterization of this kind of device is more complicated as we have many degrees of freedom in comparison to the shallow etched version. For the fully-etched version, we can tune the period in the X and Z direction. Also, we can tune the fill factor in the X and Z directions. Moreover, we have to adjust the parameters for each polarization. Therefore, from the main design, we varied some parameters to experimentally analyze their effects. Our main design is summarized in Table 2-2.

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Table 2-2 Design Parameters for the fully etched DGC

We characterized the devices in terms of the following parameters: Si thickness, cladding, period, hole size, polarization and fiber tilt angle. The parameter that was not modified is the BOX thickness, but we tried to remove the second order reflections by tilting the fiber in a small angle. It is important to say that the BOX size can be optimized to obtain better efficiencies. The results are shown in Figure 2-11.

Silicon thickness

It is important to study the variations in the silicon thickness as they greatly affect the performance of the system. As the wafers are not precisely flat, there are some variations from chip to chip according to the wafer position of the chip. Central chips have a Si height closer to the nominal value of the datasheet. Thus, the first study we did was regarding the top silicon thickness and we found that a thicker silicon achieves a better performance in comparison to a thinner one in terms of coupling power and bandwidth.

We increased the efficiency by 5 dB and extended the bandwidth to 70 nm by using a Si thickness of 250 nm instead of 220 nm. Although this thickness is beneficial for DGC, it is detrimental for the Bragg gratings filters when used as narrowband filters because the stop band is increased in tenths of nanometers as it will be shown in the next chapter.

Cladding

Then, tetraethoxysilane (TEOS) was deposited as cladding. This material is one of the most popular claddings in silicon photonics, as it can be deposited on the waveguides using low pressures and with high precisions. This means that the waveguides are not destroyed by the TEOS cladding and the thickness can be controlled. Also, it has the same refractive index of the SiO2 substrate, being 1.444 at 1550 nm wavelength. Usually, the minimum size that is required for TEOS to enter the hole without any air bubble formation is around 300 nm diameter. Our structures are in the limit of this condition as the holes are 300 nm × 250 nm. The results show that an increase in the refractive index is translated into a longer Bragg wavelength and we go from 1530 nm to 1580 nm confirming that the cladding is indeed entering the holes. However, theoretically, there should be a shift of about 90 nm, and we only see a shift of 50 nm. This may be due to the fact that the holes are not completely filled with TEOS, and only a portion is. It is also here that we restate that our designs are mostly for air cladding.

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Figure 2-11 Experimental results for the shallow etched DGC for TE polarization (Top Left) Silicon thickness (Top Right) Different cladding (Bottom Left) Period (Bottom Right) Dimensions

Period

The modification of the period in the propagation direction of light matches our equation, meaning that longer periods results in longer Bragg wavelengths with a 𝜕𝜆_𝐵/𝜕Λ of 1.6 [nm/nm]. The efficiency remains relatively constant with a 1 dB variation, but the main difference is the reduced bandwidth of the system. This is the parameter that has the biggest impact on the Bragg wavelength and is probably the most important because after we fabricate the devices, we cannot change it and it has a heavy impact.

Shape

Next, we changed the dimensions and area of the etched hole. The motivation to study this parameter is that the most common problem we encountered during the EBL fabrication process was that the stigma and focus conditions were difficult to optimize, and sometimes, we ended up producing rounded versions of the square, or much bigger versions of the intended shape. Thus, we would like to investigate what is the best shape to use to obtain good and reproducible results. To do this, we designed different dimensions of the rectangle. The result is that the shape of the transmission spectra is modified, and in the case where the rectangle is too long and too narrow 200 × 300 μm, there seems to be a split in resonances but the bandwidth is larger if we gather both of them.

Tilt angle

With our experimental setup, we are able to change the tilt angle of the fiber from 20 degrees to 0 degrees that correspond to a vertically placed fiber on top of the chip. We analyzed the effects the angle has on the transmission spectrum and the results are shown in Figure 2-12. From the results we can obtain a slope of 𝜕𝜆_𝐵/𝜕° = -6.02 [nm/degree] and the bandwidth is also modified as 𝜕𝐵𝑊/𝜕° = 1.35 nm/degree.

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Figure 2-12 Fiber Tilt effect on the transmission of a DGC

Polarization

As we also design devices that operate with TM polarization, we fabricated a DGC with a similar methodology as the TE case and similar structures but for TM. The biggest difference, as the case of the shallow etched DGC, is the longer period required for the same Bragg wavelength due to the fact that the refractive index for TM is smaller. Since a similar discussion applies for both polarizations in terms of bandwidth, and losses, we are just going to show the best design. In Figure 2-13 we show the SEM image for a TE polarized fully etched DGC and for a TM polarized fully etched DGC as well as their characteristic transmission spectrum. The transmission graphs include two DGC insertion losses and the waveguide loss. As we can see, the maximum power we can receive is up to -10 dBm when the input is 0 dBm and minimum of -40 dBm which is well above the noise level of the photodiode. Thus, our DGC scheme is adequate for input and output light from an external laser source into the chip and we can correctly measure and characterize the optical response of the device. Lastly, it is important to say that as the wavelength increases, so does the fluctuations in power, especially for the TE case, so these noise fluctuations are also seen when evaluating the devices.

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Figure 2-13 SEM image and transmission spectrum for the (Top) TM DGC and (Bottom) TE DGC

The SEM image for each DGC and their respective transmission spectrum is shown in Figure 2-13 and their design values are summarized in Table 2-3.

Si h [nm] ΛZ [nm] HoleZ

[nm] ΛX [nm] HoleX

[nm] λB [nm]

TE 250 700 250 600 300 1550

TM 250 940 430 650 350 1570

Table 2-3 Design parameters for the TE and TM fully etched DGC

For the rest of the thesis these parameters are used and are they are our main work-horse to couple light. Additionally, for the case when we required to do sensitivity experiments, we had to fabricate long waveguides to being able to manually place a microfluidic channel on top of the chip. Those long waveguides were 6 mm in length.

When we wanted to characterize the different parameters of a device, we used 600 μm long devices as we can produce many of them because we can save EBL exposing time and chip space, so we could place many designs in the same chip, in the order of 100.

This is the main advantage of fully etched DGC over SCC and as we showed, the efficiency is adequate and we are able to detect and characterize our devices.

Next, we will introduce the two devices that are the main topic of this thesis so that we thoroughly characterized, which are the Bragg grating and the rectangular resonator.

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