Defects found in macroporous silicon.
Macroporous silicon (MPS) has been shown to be a promising material in many areas of technical interest. In particular, MPS has been applied for electronic devices and microfluidic applications. One of the most promising features of MPS is that it enables the development of optical applications using simple and cost-effective technology, compatible with MEMS fabrication processes and suitable for mass production. This chapter describes the application of MPS structures fabricated using electrochemical etching (EE) for the detection of gases of environmental concern in the wavelength range comprising 4 μ m to 15 μ m , such as C O 2 . Vertical-modulated MPS structures are reported, whose photonic bandgaps can be placed at different wavelengths depending on the application needs. These structures have been applied to the quantification of C O 2 , and these results are summarised here. Detection is performed by the direct measure of absorption, obtaining promising results with short optical paths.
- macroporous silicon
- photonic crystal
- electrochemical etching
- non-dispersive infrared
- gas sensing
Macroporous silicon (MPS) has been shown to be a versatile material with a broad spectrum of promising applications . MPS was first described by Lehmann in the early 1990s [2, 3, 4] and has since attracted great interest among researchers. Of the initial works in MPS development, it is also worth mentioning those from Zhang , Propst , and Parkhutik . Of particular interest is the
Thanks to the existence of PBGs, photonic crystals have been used for advanced applications in optical communications , photovoltaics , photonics , light emission , anti-reflection/blackbody emitters , and gas sensing [15, 16]. Particularly, in this field, the peculiar functionalities of PCs make these structures very attractive for their use in chemical sensing: gas detection [15, 17, 18] and bio-sensing . The main advantage of using PCs for these areas is their potential to design and fabricate very compact and cheap photonic devices [20, 21]. Furthermore, the possibility of integration into large-scale circuits or microelectronic fabrication processes [21, 22] opens up vast opportunities for novel devices.
In particular, in this chapter, we focus on the use of MPS PCs for the optical detection and quantification of gases. More specifically, the characteristic
2. Sensing application: gas detection
Sensor demand for everyday applications is rapidly growing. The areas of use are many and multidisciplinary [23, 24]—to name a few: environmental [25, 26], safety , security , health, transportation, and wearables. Market research shows that gas sensor segment has strong growth  (forecast to achieve $765 M in 2020 ). Furthermore, climate change concerns is making governments and other agencies push the research and deployment of
2.1. Detection strategies: optical
Optical gas detection provides very desirable advantages over other methods. In first place, pure optical methods like spectroscopy have exceptionally fast response times to changes in mixture concentration. Furthermore, the spectroscopic optical systems are highly selective: they permit identifying a target gas by its
Traditional optical-based measuring is based on the direct measurement of optical power. One of its main drawbacks is that the equipment is large and expensive. Indeed, one has to trade-off space for detection limit. Some applications require several centimetres or even metres of optical path to reach the required sensitivity. Furthermore, spectroscopic systems are energy limited, thus they require stable and high power light sources such as lasers or thermal radiators. Spectroscopic systems also require additional complex mechanical and electronic equipment for the signal conditioning and processing. On the other hand, non-spectroscopic optical systems impose less strict requirements on some of these aspects. However, reducing the optical path length has not found a good solution until recently with the advent of PCs.
Other optical systems exist that use alternative detection strategies. Nevertheless, these alternative systems lose some of the more desirable traits of optical detection, like response time and selectivity. Special mention has to be done with respect to
2.2. Gases of environmental concern
The growing global consciousness in environmental preservation and climate change has driven the research and development of sensing devices. In particular, monitoring the environment for pollution control [25, 31] is one of the most important applications. Gas sensors are also significant for health  and indoor air quality assessment .
Air pollutants and greenhouse gases are primarily related to the exhaust gases of combustion processes. Major air pollutants are carbon monoxide ( ), ground-level ozone ( ), nitrogen dioxide ( ), and sulphur dioxide ( ). Greenhouse gases are carbon dioxide ( ), methane ( ), and nitrous oxide ( ) . There are many other toxic air pollutants such as nitric oxide ( ), ammonia ( ), and hydrocarbons.
These gases have simple molecular composition with strong light absorption in the medium infrared wavelength range. The absorption spectrum of a gas at these light frequencies is caused by the different vibrational and rotational modes of the atomic bonds in the molecules . The absorption coefficient spectra for several of the environmental concern gases are plotted in Figure 1. Absorption data of several gases can be found on the freely available HiTRAN database . Each vibrational-rotational mode of a gas corresponds to an absorption line. These modes are narrow and close together3. However, at atmospheric pressure
From the data shown in Figure 1, it is clear that is potentially the largest contributor to greenhouse effect. In addition, its absorption band is clearly separated from other strong absorbers, making this gas easy to detect and quantify in an unknown mixture.
2.3. Non-dispersive infrared detection of gases
Non-dispersive infrared (NDIR) detection relies on the fact that certain absorption lines of gases are “isolated” and their wavelengths have little overlap with other gases, as seen in Figure 1. This is profited to simplify the design of a gas detector reducing cost, complexity, space requirements, and power . Identification and quantification of a certain gas can be done looking at a narrowband region of the spectrum. This can be done using optical filters or selective light sources, or a combination. At the other end, the detector (a photodiode: PD) will give a measure of the optical power received, directly corresponding to the concentration of the gas. When light passes through a gas mixture, some wavelengths will be absorbed following the Beer–Lambert (B-L) law
where is the optical intensity of the source (or the reference value), is the received optical power, is the optical path, is the gas concentration, and is the absorption coefficient of the gas; source intensity and absorption coefficient depend on wavelength . An optical filter thus selects the absorption lines to measure. This allows for a multigas detection scheme using different filters for each gas . Alternatively, the absorption can be measured as follows: (where is the absorption, and the transmission). This is valid under the assumption that no light reflection occurs at the gas interfaces4.
The simplest NDIR system is depicted in Figure 2a. A sample of the unknown gas mixture is placed in a gas cell. Light is then passed through the cell from a source to a detector. From Eq. (1), it is clear that optical path length is critical for the performance of the system. The necessary optical length to achieve a desired detection limit can be several meters. Such long paths are highly impractical. Typical commercial products employ special cells (e.g., a Harriot cell) or optical systems using several mirrors to extend the effective optical path keeping a small volume.
To remedy the need of complex, bulky, and fragile optical systems to achieve the long optical paths required, a PC can be used as proposed in Figure 2b. PCs-based sensors are projected to require very small footprints, a few centimetres at most. The idea is to take advantage of the special features that PCs exhibit. One of such is the existence of propagation modes with extremely slow group velocity
3. Macroporous silicon applied to gas detection
Macroporous silicon is a
3.1. Seminal works
One of the first uses of MPS for gas sensing is in the work by Geppert . From the analysis of the photonic band structure5 of the PCs, they observe that some bands are very flat at certain wave vectors, thus the group velocity
reduces to values about
, the speed of light). The slow propagating light has more time to interact with the media making possible to reduce the physical path length while maintaining an acceptable interaction time. It is also observed that some bands have the maximum field intensity located in the high dielectric region (
Some of the described devices are three-dimensional (3-d) PCs made of MPS. For these devices, light is shone normal to the surface, propagating parallel to the pores’ axis. The devices were used to detect ammonia ( ) and sulphur hexafluoride ( ). Transmitted light was measured through the PC and a small cavity of depth filled with gas. They show promising results, but they argue that the small figures obtained are due to the low coupling efficiency of the PC. Furthermore, no enhancement was observed by the presence of the PC. This is also attributed to the large change in the effective refractive index6 ( ) as for high contrast materials the transmittance , thus reducing the coupling efficiency. In , it is also discussed a simple way to compensate for deviations in the bandgap due to fabrication tolerances: tilting the sample , a shift as large as of the PBG (about ) can be achieved.
They also present an alternative structure, refined in later works [17, 42], which uses two-dimensional (2-d) MPS structures. These are easier to fabricate and tolerances are better. As the structure is two-dimensional, the photonic band structure exists only for
3.2. Structure design
From the possible strategies when using MPS structures as gas sensors, 2-d crystals impose the need to inject the light from the sides. In this way is easy to obtain long optical paths along the samples, but light coupling is complicated. However, from a practical standpoint, a system based on the normal incidence on the sample, using 3-d PCs, is easier to assemble, align, and calibrate7. In this chapter we expose results based in this option with PCs produced with macroporous silicon.
The designed MPS silicon structures are simulated using a simplified model by the finite-difference time-domain (FDTD) numerical method. Some MPS structures will be used as reflectors, while others will be used as filters. Reflection design requires a PBG encompassing just the absorption region of the desired gas. On the other hand, transmission design needs a PGB as wide as possible, with some crystal defects to block all light but the corresponding to the gas absorption line. The largest PBGs are obtained with an opal like PC . As the samples will be illuminated from the top8, the horizontal pore arrangement is not as important. Our samples pore disposition is a square array. The EE of silicon does not allow getting perfect spherical shapes (opals), but the actual pore profile has a sinusoidal-like shape, or
To place the PBG at the absorption line, the vertical period is calculated to be around . As a rule of thumb, in a silicon PC, optical bandgaps can be found at about four times the pitch. Therefore, to have a PBG at , . Considering the MPS porosity9 is about , the effective refractive index , where . This gives that the vertical period has to be .
The FDTD simulations show that in the vertical direction there is a narrow PBG (
For MPS fabrication, the EE method is one of the most versatile, and one of the preferred for three-dimensional structure definition. A general description of the method is the dissolution of silicon by an electrically promoted reduction–oxidation chemical process (
The etching setup places the patterned face to be etched in contact with the electrolyte, opposing to the cathode. The back-face (i.e., the other side) is contacted electrically to close the electrochemical circuit. The illumination can be provided from either the front or back surfaces. For practicality reasons, it is simplest to irradiate from the backside. Our etching setup follows these principles, plus the IR light is provided by IR LEDS with , and is continuously pumped through the etching cell at a controlled temperature.
The pore growth and morphology depend on several factors of the etching process. The pore front (i.e., the
The MPS photonic crystals developed in this work have all been fabricated using the light assisted EE of silicon using n-type substrates. Having pores arranged in an
After the porosification, some samples were post-processed to create a membrane. The membrane is done by anisotropic etching of the back face. For gas measurements, an open membrane is the best option: gas can flow freely through the MPS sample, solving any issues with gas trapping or residence time for the sensors.
3.3.1. Fabrication quality
In general, the EE of silicon produces good quality porous silicon. What is “good quality” with respect to MPS? In a minimal sense, macroporous silicon is of “good quality” if pores are of the same shape and have grown uniformly. Of course this does not provide much information whether the “quality” is acceptable for the intended application. In particular, for photonic applications, the requirements can be very strict. Fabrication imperfections arise due to numerous reasons: wafer crystalline defects, crystal alignment, and local dopant distribution; but also the etching process itself can account for some variability, and lithography errors will also cause flaws in the grown pores. The common fabrication defects one can encounter in a MPS structure fabricated by EE are summarised in Table 1.
From Table 1, the defects that are of greater concern are the ones classified as “large optical influence.” Here
The abovementioned discussion was made considering the local effect of perturbations in the pore shape and outcome of the etching process. Nonetheless, the uncertainties of etching, the inhomogeneity of the substrate, and the flaws in lithography can be considered on a larger scale or
3.4. Absorption and losses of macroporous silicon
One important concern is determining how absorption and fabrication tolerances will affect the performance of the detection system. Intrinsic silicon absorbs light at wavelengths shorter than , approximately, however when silicon is doped with impurities, strong absorption may be observed in the MIR range. Several papers report on the absorption dependence with doping level in silicon . Interestingly, for the doping concentrations used in the fabrication of optical gas sensors working in the middle infrared ( ), it is found that material absorption is negligible [54, 55].
On the other hand, fabrication tolerances definitively do have an impact on optical performance. For instance, in , it is reported that a variation of the pore radius attenuates the transmitted light. This is further studied in , global pore diameter fluctuation of was caused by the spatial variation of dopant. They further claim that, for a better than transmission in a thick PC, the pore position should change less than and diameter has to be within . A systematic study of the effect of in-plane disturbances in electrochemically etched MPS is presented in . Some interesting conclusions extracted from this work are that ellipsoid perturbation up to has little impact on the PBG if the porosity is maintained near its optimum, and that a small variation of the air fraction of just is enough to shift a narrow PBG ( ) out of the designed central gap frequency . Similar conclusion was found in the work by our group , where the effect of vertical period variation in 3-d MPS was analysed. Wide PBGs were designed for the samples used in this work, but noticeable narrowing and shift could be observed with periodicity variations above . Furthermore, it was found that the PBG became more transparent allowing light transmission higher than a in the forbidden band.
4. Measurements and results
Samples of MPs photonic crystals were fabricated with a lattice pitch of 700 nm and modulated pore profile. The fabrication conditions were the ones described earlier in Section 3.3—using the EE method. The modulation profiles for the 3-d PCs were programmed to generate a “strong”12 profile having a vertical period, the same as the lattice pitch. The samples were initially characterised to obtain their optical spectrum in the MIR range using a Vertex 70 Fourier-Transform Infrared Spectrometer (FT-IR) from Bruker Optics. Also some of the structures were cleaved and latter inspected by SEM to determine the pore morphology and actual etched profile. After the samples were analysed, the valid samples were used in a dedicated gas measuring system also using FT-IR spectrometers to measure the performance of the PCs in sensing carbon dioxide.
4.1. Fabrication, sample characterisation, and morphological study
The fabricated samples were etched using a silicon substrate with
crystal orientation. For the 700 nm period MPS structures, substrates of the appropriate resistivity were used. The pores are arranged in a square pattern. This pattern is transferred to the substrate surface using nano-imprint lithography (NIL). The etching temperature was set to
. The resulting PCs are to be used with light coming from the top, aligned to the pores’ axis, with normal or quasi-normal angle of incidence (
). The actual modulation waveforms depend whether the samples will be used for reflectance or transmittance. For the samples used in transmission gas measurements, membranes were made. However, the structure resilience is critical given the thin porous layer, so membranes are
4.1.1. Morphological analysis
The morphological analysis of some samples shows, as seen in Figure 5, that the etched profiles of the MPS structures have some imperfections. The observed flaws are mainly small variations in pore radius between adjacent pores, pore “wiggling”, skew, and pore death. On the surface of the pores, a rough finish due to microporous silicon can be appreciated (see Figure 5). Pore radius variation is small—less than —for the samples used here. This has a small impact on the optical response of the PC as has demonstrated by our works  and others [58, 59]. Skew is generally not an issue. Some extreme cases have shown up to of crystal misalignment from the direction (see Figure 5b), but otherwise pores grow fine. Some pore “wiggling” can be observed in the fabricated samples (see Figure 5a). As a consequence, there is some decrease of the optical performance of the PC. In general, the degree of wiggling in our samples is small.
The fabrication process for the MPS samples has been optimised to obtain structures virtually free from dead pores. In general, optical performance is preserved if dead pores are few, or if pores die late during etching. To avoid pore death in the initial samples, the lower current limit was increased, so dynamic range was reduced and modulation could not be as strong as desired (compare Figure 5a and b).
The most significant defect found in the samples here used was vertical period variation13. As seen from Figure 5, for neighbouring pores, the beginning and ending of each vertical period is slightly different. As shown in our previous work , this variation has a noticeable influence on the PC optical response. In general, the 700 nm samples fabricated with our equipment show about variation in periodicity which results in about PBG narrowing from the ideal and nearly minimum transmittance 14.
Two types of PC structures were fabricated for this work. Samples used for reflectance measurements are regular 3-d structures with a continuous sinusoidal-like profile for the pores. Such samples are shown in Figure 5 along with an example of current waveform used to generate them. The cross section images reveal that the modulation is slightly skewed to the beginning of the modulation. The vertical period is measured to be which is the desired length. Total etched depth is and the mean pore diameter is . The programmed “modulation index” 15 is about , but results in . Despite this, this structure has good enough optical performance.
Comparing the etched pore profile from the input waveform (Figure 5c), it can be seen that during the high plateau portion of the profile, once the pore has reached its maximum diameter, it slowly starts narrowing as the pore front advances. Presently, this can only be “corrected” by trial and error and judicious changes to the current and potential waveforms. For example, a second profile was designed with smoother transitions and “pre-skewing” resulting however in the PC of Figure 5b. Better modulation index was obtained ( ) but the skewing did not improve. In addition, the vertical period increased to , which corresponds to a PBG centred at .
Samples used for transmittance measurements include one or more defects, as shown in Figure 6. These structures have been fabricated using a refined profile. As seen on the SEM cross-section micrograph, the modulation skew is still present16, but the vertical period length is better adjusted. Otherwise, the quality of the fabricated structures is maintained. The modulation index has been increased, with pores having a smaller diameter at the necks. This greatly improves the PBG (both width and transmittance blocking) of the PC compared to the first structures depicted in Figure 5. The vertical period of the PC used for these samples is . These samples have at least one planar defect in the regular PC profile to define a resonant cavity. These cavities have a diameter , and length was varied around , to place the resonance at .
4.1.2. Optical response
Samples were optically characterised after fabrication to ensure the adequacy to sensing . This was done in a FT-IR spectrometer in reflection mode with light incident at a quasi-normal angle of . Also some samples were analysed in transmission mode with light illuminating in normal angle of incidence. The wavelength range of the analysis extends the MIR and some of the NIR regions from to .
Samples used for reflectance gas measurements, such as the one in Figure 5a, have a single PBG in the optical response. The morphological analysis shows that, as the modulation index is small, the PBG will be relatively narrow. This is confirmed in the measurement shown in Figure 7. The results confirm that as expected by the criteria given above, the PBG of a 3-d PC with a vertical period of is centred at . PC quality and modulation index limit the reflectance to about . In spite of these shortcomings, the obtained response is good enough to be used for the sensing of carbon dioxide.
The samples for transmission measurements have different responses according to the number of PC defects placed. As seen in Figure 8a, b, placing two defects gives rise to two resonant states, and three states if three defects are used. Coupling between resonant cavities induce the appearance of several resonances in the optical spectra even if all cavities are of the same dimensions. The placement of the defect along the PC depth also influences the coupling efficiency and quality factor of the resonance. The creation of a membrane also improves the transmitted signal, compare Figure 8c and d where the transmitted peak is almost to the of the non-membrane sample.
4.2. Gas measurement system
After the devices were characterised, they were measured under different atmospheres consisting of diluted in pure nitrogen. The amount of carbon dioxide was controlled using a two gas mixer in which one line is pure nitrogen as the carrier gas, and the process gas ( is this case) is connected to the second line. Each line is controllable separately: shutting, pressure, and flow. Both gas lines are then mixed in a manifold and the mixture is then output to the gas cell. The gas cell is sealed with one input port and one exhaust port. The flow control is performed using mass flow controllers (MFCs) of different range: the carrier gas controller (MFC1) is full scale (FS), and the process gas controller (MFC2) is FS. Both MFCs are calibrated for , so for the process gas a correction factor is used. For the measurements, a constant flow rate of for the mixture is used. In these conditions, the minimum gas concentration goes from to . Given the performance data of the MFCs, the concentration uncertainty is given by , where is the gas concentration, and and are the flow rates of carrier and gas, respectively. Note that .
The gas mixture is fed to a gas cell purposely built where the MPS photonic crystal is placed. The gas flows continuously through the cell. For the measurements, a broadband infrared light source is used. This light is directed to the cell and then collected by a photodetector (PD). In the work here presented, the MPS structures were characterised by FT-IR spectrometry. The expected response of an autonomous NDIR measuring device can be then extrapolated from the spectroscopic gathered data in the characterisation of the PCs.
4.2.1. Principle of detection and method
The basic idea here proposed for an NDIR system is to use a MPS photonic crystal with a PBG wide enough to comprise one of the gas absorption
From the characterisation measurements, it is straightforward to approximate the expected response of the NDIR system. The spectra can be any of the reflectance, transmittance or absorbance, as these are proportional to the power of the electromagnetic wave: , and so on. Now it is possible to define the quantity as the normalised optical power received at the PD from the reflectance data. is thus proportional to the gas concentration and estimates the actual output of a PD. Equivalent power quantities and can be defined for the transmittance and absorbance spectra respectively. A second measuring criteria is simply evaluating the reflectance spectrum at a given wavelength (equivalent quantities are defined for transmittance and absorbance). Such wavelength is chosen to be where absorption is the greatest. The relation of this quantity with an actual output of a PD is less clear but serves to evaluate the performance of the gas cell and PC.
4.3. Reflection measurement
Reflection measurement of uses a PC as a selective reflector. The reflection spectra are obtained from which the absorbance spectra are calculated as ; where is the measured spectrum at some gas concentration, and is the reference spectrum (only ). The “optical power” is then . Using a reference spectrum removes any effect of the optical system, such as reflectance at optical interfaces.
The measurement setup consists of the gas mixer connected to a specifically built gas cell. A schematic view of the cell design is shown in Figure 9 alongside the actual built device. The cell consists of two plates separated with an O-ring such that the cell is made airtight. The top plate has one port for gas input and another for output, and a central opening where a potassium bromide ( ) window is placed and held in place by a sealant. When assembled, the two plates are held by several screw ensuring mechanical stability and airtightness, with the PC underneath the IR window. The gap from the sample to the window is about , resulting in a total17 light path of .
The cell is then placed in the spectrometer to make the gas concentration readings. In particular, a Renishaw Raman microscope equipped with Smiths IlluminatIR FT-IR module is used to take reflectance measurements at normal incidence, . The aperture sizes used in the optical setup was . The wavelength range extends from ( ) to ( ). Resolution is .Each spectrum at a given concentration was averaged over scans.
Reflectance spectra were measured for at concentrations from to , the results summarised in Figure 10. Lower concentrations were tested but for concentrations below changes are very small and difficult to discriminate. This effect is then observed in the “optical power” signal at the output (Figure 10b) calculated as mentioned above. Figure 10b also shows that the Beer–Lambert law is closely followed by the measured data for concentrations above . From the fitted B-L model, it is possible to extract the exponential term (where is the optical path length, and the absorption coefficient). From the HiTran data for carbon dioxide, at and instrument resolution, . This gives that the effective path length is . Measurement uncertainty is dominated by the mixer uncertainty, as seen in Figure 10b, as power measures are averaged over a large number of scans. This results in a fairly constant uncertainty across the full measurement range about .
Macroporous silicon is a versatile material that has shown to be a good candidate for the obtainment of PCs for gas sensing applications. Using fabrication methods such as EE opens up the possibility of obtaining high-quality photonic filters, in large quantities, and economically competitive. Furthermore, this fabrication technique is very flexible allowing creating customised designs with little effort. Using silicon as the base material has other benefits, such as the reutilisation of the existing manufacturing tooling and the reuse of process flows. Moreover, EE is compatible with microfabrication technology and might be incorporated in VLSI designs to build complete sensing devices. This will result in more compact and integrated system design lowering the bill of materials, costs, and improving manufacturability.
Here we demonstrate one possible way to use MPS PCs for gas sensing: as selective filters. Carbon dioxide has been detected and quantified using NDIR reflectance measurements. It has been found the MPS crystal has also an effect in the measured absorption. This is due to the very nature of the PC, slowing the group velocity of the incident light and enhancing the interaction time—increasing the effective optical path length—with the gas mixture. The inclusion of resonant cavities further enhances light absorption by inducing resonant states and spatially confining the IR radiation.
The PCs here shown, prove that a compact sensor using MPS technology is feasible, achieving a detection range near to that of commercial optical devices based on IR PD/LED. The devices shown here have room for improvement in particular regarding the fabrication, and progress is steadily being made in this area.
This work has been funded by the Spanish
Conflict of interest
The authors declare that there is no conflict of interest.
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- Nonetheless, MPS is not the only material nor technology in which PCs can be devised and fabricated.
- The chemical composition of a gas compound has specific vibrational (atomic bonds; from MIR to VIS) and electronic (electron excitation; from VIS to X-Ray) resonances that result in particular absorption frequencies unique for such gas.
- An ideal vibration-rotation mode has a single frequency. However, the actual line profile of a mode depends on external factors such as the gas pressure, velocity, temperature, etc. Typical line profiles are Gaussian (Doppler broadening), Lorentzian (pressure broadening), and Voigt (mixture of the previous). In standard conditions, ideal gas line profile separation is around Δ k = 2 cm − 1 , and full-width half-maximum approximately FWHM = 0.2 cm − 1 .
- The construction of a gas cell as well as other optical elements existing in the light path introduces several reflections. However, all of them are accounted when measuring the reference value I 0 .
- The band structure is the reciprocal of the dispersion diagram, thus the slope of the band represents the group velocity v g = ∂ ω / ∂ k , where ω is the wave frequency and k the wave vector in the reciprocal lattice of the PC, for a plane wave propagating through the media .
- There exist several methods to find the effective refractive index of a PC. The simplest one for low frequencies is calculating the average of the different materials that compose the PC. To obtain the n eff at higher frequencies, a theoretical study of the photonic band structure is needed, from it, n eff can be derived from the group velocity.
- Indeed, using 3-d PCs, the light can be launched into free space and coupled into the crystal from the top or bottom surface, which are much larger than the sides of the MPS structure.
- Concretely, the “top” surface is the surface from where the pores are etched. This surface has the initial pattern of the pore sites. For prime quality wafers, this face is polished and the incident light will have little scattering.
- Porosity is defined as the ratio of air to silicon volume in the unit-cell.
- A porous media is termed microporous for pore diameters less than 5 nm , mesoporous for 50 nm > d pore > 5 nm , and macroporous if pores are larger than 50 nm wide.
- For example, a scratch on the back-surface or shadow of the illumination will cause the shape of such scratch or shadow to be transferred to the pores grown at the front surface: the affected area will have smaller diameter pores or, in extreme cases, dead pores and branching.
- This profile tries to obtain a spherical shape as close as possible.
- That is for the current way the PCs are being used: with light coming from the “top” along the pores’ axis.
- These performance figures were achieved with the latter fabricated samples, with an optimised EE process.
- The input waveform is a square signal, so the concept of modulated index in AM is extended here as m = max r t ∕ min r t , where r t is the radius of the poresuperfluous.
- However for this particular instance, the asymmetric modulation was actually designed.
- This figure may change due to uncertainty. For example MPS sample thickness or tightening of the screws can change the gap as much as 0.2 mm . It must be remarked that this is a proof-of concept cell.