*2.2. Nanospectrometers*

To significantly reduce the number of required fabrication steps by consolidating them into a single step, nanoimprint is used to define all required different cavity heights for a complete FP filter array [11,32–34]. Thus, nanoimprinted cavities are used with precisely defined heights between the two identical highly reflecting DBRs. From the usage of nanoimprint technology in their fabrication, we were introducing the term nanospectrometers—a combination of an FP filter array and its corresponding detector array—as shown in Figure 4a with a selection of four FP filters out of the whole array. The filter array comprises of two DBRs (shown in gray) and the cavities (shown in orange). The cavities were fabricated in a single nanoimprint step. Each individual filter cavity height defines the wavelength of a characteristic different narrow filter line. One option is to directly deposit the filter array on a detector array (black and magenta). In Figure 4a, each FP filter has one detector, constituting one pixel. However, each filter can also correspond to many detector pixels (e.g., 4, 9, 16, etc.). In Figure 4a, the right part displays the spectral transmission spectra of these four FP filters. Since they have the same DBR, they reveal the same spectral stopband widths (i.e., same spectral width of minimum transmission). However, the spectral positions of the filter lines vary due to the tailored different cavity heights. Within a single step, 3D nanoimprint allows fabrication of all different cavities (even 100,000 or more, theoretically). In the following, the static FP filter arrays are discussed in Sections 2–7 (fixed, i.e., static cavity heights), and the variable MEMS tunable FP filter arrays are considered in Sections 8 and 9.

Applying a single 3D nanoimprint step, 192 unequal cavity heights are defined with a single nanoimprint step, generating 192 pixels. This 3D nanoimprint does not require time-consuming digital etching [28,29] or digital deposition [31]. Since the nanoimprint template can be reused many times, this technology is cost-efficient. The digital etching is only used once to fabricate the 3D nanoimprint template, and not permanently during cavity fabrication.

Figure 4b illustrates the sequence of main fabrication steps from top to bottom. It starts with the deposition of the bottom DBR on the detector array. Next, the liquid cavity material (orange) is deposited by spin-coating. Subsequently, the 3D cavity structure is defined using a transparent 3D stamp (light blue) which is pressed into the cavity material and hardened via UV light. After lifting the stamp, the top DBR is deposited.

Nanoimprint is a process of shaping deformable materials by means of molding technology. Presently, many variants of nanoimprint technologies [81–84] are used to generate high resolution 2D structures. On the contrary, 3D nanoimprint is less common but essential for our nanospectrometer. It is challenging to accurately control the vertical dimension (3D) in addition to the lateral dimension. For mass production, a master template (as a positive), including in our case the checkerboard-type arranged mesa structures (various cavity structure heights), is replicated into many identical stamps (as a negative). The 3D nanoimprint is performed using one of these replicated stamps, generating the orange 3D cavity structures (again positive) simultaneously in a single step (Figure 4). Please note that the process described in Figure 4 is involving only a single DBR, thus, revealing a single stopband.

In the following section, three bottom DBR stacks which reveal different heights are imprinted in a single step to produce 192 different FP filters as a proof-of-principle. This imprints over the vertical steps located at the lateral borders of the DBR stacks, each of which has a different vertical extension.

#### **3. Static FP Filter Array Fabrication in the VIS Spectral Range Demonstrating a Single Nanoimprint over 3 DBR Stacks of Different Height**

#### *3.1. DBR Mirrors: Materials and Geometrical Issues*

Before fabrication, the filter array design has to be performed. The individual cavity heights were identified via simulations using "OpenFilters" [85] in the range of 26–215 nm. However, nanoimprint process is often associated with residual layers that has to be considered in the design. To keep the residual layer constant in lateral directions despite the different mesa volumes, four adjoining mesa heights are laterally grouped in a 2 × 2 submatrix consistently, where all sub-matrices of four mesas have the same combined volume. Thus, the lateral positioning of these cavities is done applying the volumeequalized design methodology [86] to ensure that the residual layer thickness is as constant as possible.

Since DBRs are used as highly reflecting mirrors, the cavity heights have to be designed in such a way that the transmission lines are within the spectral stopbands of the DBRs. If a DBR with a 100 nm stopband width is used, the different filter transmission lines must be spectrally located inside the stopband width of 100 nm. In that case, the detectable range is a bit smaller than 100 nm. As already mentioned, the DBR stopband width depends on the refractive index contrast of the used materials, which can be deposited for example via Plasma Enhanced Chemical Vapor Deposition (PECVD) or ion beam sputter deposition (IBSD) [34]. In the VIS spectral range, SiO2/Si3N4 DBRs allows about 100 nm stopband width, and a TiO2/SiO2 DBR enlarges the spectral stopband to about 200 nm. It is important to mention that the interface quality of cavity and DBR mirror as well as the steadiness of the periods within a DBR are important for high optical quality of the sensor, by ensuring high filter line transmissions and low linewidths.

#### *3.2. Definition of 3D Nanoimprint Templates Using Digital Etching and Digital Deposition*

The fabrication of the 3D templates (corresponding to the design) is the most important part of 3D nanoimprint lithography. Since many different mesa height levels are required with height differences located in nm range and accuracies in sub-nm range, the fabrication of 3D templates is a challenge of enabling multiple mesa heights and accurate height differences in the nm range combined with accuracies in the sub-nm range. In comparison, it is by far less challenging to define 2D templates. A single step in e-beam lithography and subsequent etching are enough to fabricate 2D structures with a complex lateral pattern since a constant height can be obtained throughout the imprint area. However, fabricating

3D templates is by far more challenging since the key requirements for the sensors are determined by the third dimension (height). The number of lithography and etching steps can be dramatically reduced if the heights are arranged in a digital way, allowing application of digital masking [34] during lithography, followed by a tailored etching step, respectively. More details can be found in [11], in which the fabrication of the master template (made of Si or GaAs in our case) is described.

The accuracy demand for the FP filter arrays is very low in lateral resolution and contrarily very high in vertical direction. A highly accurate etch depth control is required in the use of digital etching and lithography methodology for the 3D nanoimprint templates.

The digital lithography and etching methodology is used to define all the different checkerboard-like arranged mesa of different heights in the master template. As already mentioned, the master template is replicated to create stamps, thus transforming the different mesa into the required different cavity dimensions. Nanoimprinting with the stamps translates the stamp with its checkerboard-like cavities of different depths again into the different checkerboard-like arranged mesa morphology of different mesa heights.

As a comparison, Correia et al. [28,29] applied digital etching to directly fabricate the checkerboard mesa structure and Wang et al. [31] applied digital directly to deposit the checkerboard mesa structure. Such approach works as an initial demonstration of the principle; however, this would be not desirable for industrial production. A more efficient approach is using digital lithography and etching only to define the nanoimprint master template, which can be reused (replicated) multiple times; therefore it is well applicable for future mass production.

#### *3.3. Combining Three DBR Stopbands in the Fabrication Process of an FP Filter Array*

Often, the width of a single DBR stopband is not broad enough. In this case, combining several stopbands to extend to the usable total spectral range of the nanospectrometer is required. A proof-of-principle is demonstrated for this purpose, in which three spectrally neighboring stopbands are combined. 3D nanoimprint was performed across these three DBR stacks of different heights, and filter arrays were fabricated. In Figure 5, only three different FP filters out of many are depicted for each of three DBRs (with different stopbands). This results in nine individual cavities, displayed here as a part of a whole sensor device. Since the lower DBRs can be directly defined on a detector chip, expensive micro-mounting at later fabrication stage can be avoided.

For a DBR, the central wavelengths of the DBR stopbands are defined by the thicknesses of the thin quarter-wave films. A proof-of-concept with SiO2/Si3N4 DBRs fabricated by PECVD is shown, in which less than 120 min is required to deposit a single 9.5-period DBR in this material system. Structuring of the DBRs is performed by means of lithography, lift-off, and an etching process as described in detail in [11]. If the application requires more stopbands to enhance the total spectral range, this is also possible with additional lithography steps. The important point in fabricating sensors with multiple DBRs is simply to maintain a high fabrication quality of the devices even after repeating the process cycle several times.

According to Figure 5, the three bottom-DBRs with spectrally neighbored stopbands provide different vertical total heights of 224 nm and 188 nm for the step height (height difference) between bottom DBR 1 and bottom DBR 2 and the step height between bottom DBR 2 and bottom DBR 3, respectively. Using Substrate Conformal Imprint Lithography (SCIL) with flexible stamps, we performed 3D nanoimprint across these vertical steps. The flexible stamp combines hard-PDMS (polydimethylsiloxane) to ensure structure conformity and soft-PDMS connecting it to a flexible transparent carrier (i.e., thin glass or polymer), thus providing the large scale conformal property. In general, nanoimprint lithography enables large area imprinting up to 12 inch, and SCIL reaches 8 inch with resolutions below 10 nm [84]. The SCIL stamp can be reused for 500 prints using hard-PDMS and 600 prints using X-PDMS [84]. The tricky masking before depositing the next DBR is described in [11,37] in detail.

**Figure 5.** Cross section a nanospectrometer combining three different, spectrally neighbored DBRs in an FP filter array with a sensor array in CMOS or CCD technology. The definition of the blue cavity layer is achieved in just one nanoimprint step. The inclusion of nanoimprint for this sensor provides the term nanospectrometer, which we introduced for this sensor device. Shown here is the first option, namely by placing the FP filter array directly on the photodetector array including the processing integrated electronics. Reprinted with permission from ref. [11]. Copyright 2021 MDPI.

#### *3.4. The Complete Array: Lateral Arrangement of the FP Filters*

All FP filters of each of the three arrays are organized in a formation of 12 × 12 (144) checkerboard. The central 64 (8 × 8) filters comprise 64 different cavity heights, while the residual 80 filters surrounding the central part are used as control elements for the nanoimprint quality and the residual layer thickness, only for research purposes. More details on this subject is provided in [11]. To estimate the minimum required space in Section 11, the lateral size of each mesa is considerably minimized. Each filter array containing 64 different cavity heights reveals 64 distinct transmission lines per array. A total of 192 different transmission lines were obtained by combining three stopbands. Please note that each of the 192 cavities has different heights and they were imprinted altogether via a single 3D nanoimprint process step. This enormously simplifies the fabrication process.

#### **4. Experimental Results of Static FP Filter Arrays in the VIS Range**

#### *4.1. Transmission Spectra of Static FP Filter Arrays*

Optical spectra of all FP filter lines were recorded using a microscope spectrometer setup which includes a confocal microscope (Imager D1m Zeiss), a lateral active aperture manipulation, a halogen lamp, a photodetector, a lateral active aperture manipulation and a commercial grating spectrometer (HR 2000 Ocean Optics) with a resolution of 0.5 nm [35]. Figure 6 displays spectra of 192 filter lines of the FP filter array consisting of three DBRs (spectrally neighbored). The 192 filter lines cover a total spectral range of 163 nm (i.e., 507–670 nm) with spectral increments of about 1 nm or below and without any gaps. The transmission intensities of the different filter lines vary due to an interplay between material absorption, linewidth variation, reflectivity changes, and further effects. The material absorption is higher for shorter wavelengths than that for longer wavelength since the strong material absorption of glass in the UV region is approached. This explains the strongly reduced transmission intensities with decreasing wavelength for each stopband. In addition, stopbands with larger central wavelength have thicker DBR stacks and thus suffer more from absorption. In contrast, stopbands with smaller central wavelength suffer less from absorption. This explains the trends measured in Figure 6. For details see [11,37].

**Figure 6.** (**Top**) optical micrograph displaying three FP filter arrays and (**bottom**) related optical transmission spectra. Reprinted with permission from ref. [37]. Copyright 2018 Springer Applied Nanoscience.

#### *4.2. Interpretation of Experimental Results Concerning Linewidths*

The experimental linewidths (FWHM) presented in Figure 5 of [11] were measured in the FP filter array, as shown in Figure 6 in this review. The measured FWHM are found to be between 1.7 and 5 nm. The closer we come to the borders of the stopbands, the higher the measured values. This observed strong variation of the FWHM as a function of wavelength is due to an interplay of many effects: reflectivity changes, spectral variation of material absorption interface roughness, and further effects.

The spectral reflectivity of each DBR is dependent on the precise spectral position inside its stopband, which is strongly influencing the dependence of FWHM on wavelength. The highest reflectivity exists at the center of the spectral stopband, leading to smallest FWHM at these spectral positions. As the filter lines come closer to the stopband borders, the lower the reflectivity, and thus the higher the FWHMs of the filter transmission lines. This is by far the most dominating effect and explains the main FWHM features that were observed experimentally.

Next, the role of interface roughness is discussed, first by considering one stopband in the VIS range. Assuming that the same interface roughness is occurring at the two interfaces between cavity and DBR for all the FP filters, the influence of interface roughness Δ*l* has a stronger influence on smaller cavity lengths *L*. For *L*1 *< L*2, a larger relative cavity length fluctuation is obtained for smaller cavities Δ*L*1 *= L*1 ± Δ*l* than for longer cavities Δ*L*2 *= L*2 ± Δ*l*. Increasing FWHM of a transmission line automatically leads to a reduction of the peak intensity. Since this effect is not clearly visible in the experiments, we conclude that the interface roughness is not very pronounced in our case. In addition, another effect is involved: the scattering probability increases with decreasing wavelength, since the averaging over interface roughness is more pronounced for larger wavelengths.

In our experiments, the lowest FWHM value of 1 nm [33,34] are observed; however, not in FP arrays as depicted in Figure 6, but in an FP filter processed individually. We estimate that smaller values down to 0.5 nm should be possible with 15.5 periods of SiO2/TiO*<sup>2</sup>*, using ultrapure Si and Ti targets and extended vacuum pumping.

#### **5. Static FP Sensor Array in a Fiber Technology System**

In our previous paper [11], a laboratory demonstrator is presented as a proof-ofprinciple. In the demonstrator, an FP filter array with optical bandpass filters was integrated into a commercial grayscale CCD camera and equipped with a telecentric lens. To

implement the signal processing, a procedure similar to that described by Emadi et al. [87] is used. In [11], free beam optics was involved in remote sensing of fruit on a tree or bread inside an oven, whereas the focus in this review is on sensing integrated in fiber technology. Figure 7 presents the schematic design of a sensing system consisting of a nanospectrometer (FP filter array plus detector array), bandpass filters, and fiber input. The divergent light leaving the fiber is parallelized by an achromatic lens system. The bandpass filters block the spectral light outside the FP stopbands, which otherwise would also transmit, reach the Si detector array and increase the noise level. The electrical output and signal processing is not shown here. This was presented in our previous paper [11].

**Figure 7.** Schematic cross section of an FP filter array mounted parallel and in close vicinity of the Si detector array (CCD or CMOS). The divergent light of the fiber is made almost parallel by the lens system. In this option, the FP filter array is defined on a glass substrate which is aligned here in a bottom-up way on the CCD or CMOS photodiode array. As a comparison, in the first option shown previously in Figure 4 the FP filter array is defined directly on the detector array.

#### **6. Laboratory Demonstration of Efficiency Boosting by Spectral Preselection**

The benefits of the FP filter-based sensor concepts are their compactness with further miniaturization potential and their ability to detect a broad spectral range with high resolution. However, one considerable drawback of filter-based systems is their very low detection efficiency. Notwithstanding, this disadvantage is also typical for other interferometric or plasmonic sensor principles (Figures 1 and 3). This chapter presents a methodology for boosting the efficiency (making full use of available light), demonstrated for FP filter sensors. Moreover, it can also be applied to all methodologies suffering from the abovementioned disadvantage. In our previous paper [11], it was demonstrated in free beam optics methodology for remote optical sensing. In this paper, it is presented for fiber-based sensing systems.

The reason for this disadvantage is visualized in Figure 8a. The available "white" light to be analyzed is delivered by an optical fiber, where a parallel light bundle is subsequently produced by collimation optics. To record a complete spectrum, the light must be distributed over the entire area covered by the filters or filter arrays. Finally, the light arrives at the filter arrays or filter array groups (depicted as 1 to *N*). In this case, each narrowband filter receives the entire broadband spectrum, but only a small fraction of the incident light is transmitted through it and can be used for detection. This means that most of the analyzed light is reflected and lost for application. The narrower the transmission line of the filter, the greater the loss. As one solution to drastically improve the efficiency of filter-based systems, the spectral preselection concept was proposed [88]. Figure 8b demonstrates the basic principle of the preselection concept that comprises the spectral and spatial separation of the highly concentrated incoming light. In particular, the resulting partial spectra (subbands) are spatially separated and delivered to the corresponding filter arrays which only cover a limited spectral range. Each single filter acquires the increased intensity because the spectral preselection method concentrates the necessary wavelength region there, where it is most needed. As an example, Figure 8c shows the photo of the FP filter array [37] as one of the suitable filters for the described concept.

**Figure 8.** Basic principle of efficiency enhancement of filter-based spectrometers. (**a**) Typical case without spectral preselection: filter arrays are illuminated with broadband light. (**b**) Special optics "spectrally preselects" the incoming light to illuminate correspondent filter arrays. Thus, efficiency increase is achieved, and the filters transmit more light. (**c**) Photo of illuminated FP filter arrays (with scale bar of 200 μm, in gray).

In principle, there are various methods to achieve a spectral preselection, e.g., employing micro prisms, Köster prisms or dichroic beam splitters [88], which significantly differ in their complexity and spatial expansion. A suitable method ensures an optimized compromise between efficiency enhancement and minimum increase in complexity.

A very simple approach of the preselection concept can be realized using multiple dichroic longpass beam splitters arranged successively in a row and aligned to the filter arrays for the respective spectral subbands [89]. Figure 9a shows a photo of the manufactured preselection module superimposed with the schematic beam path. At first, the incoming light, provided by an optical fiber and collimated by appropriate optics, hits a deflecting prism which aligns the ray bundle with respect to the subsequent optical components. In more detail, the prism is equipped with a shortpass dichroic layer acting as a beam splitter that reflects longer wavelengths and transmits shorter wavelengths. The dichroic filter serves to separate the light that falls within the sensitivity range of the subsequent filter arrays from the wavelengths outside the stopband. In our case, wavelengths longer than 491 nm are reflected, which comprises all spectral ranges of the following FP filter arrays with dissimilar DBRs (521–571 nm, 576–630 nm, and 628–685 nm). Each of these applied dichroic splitter elements have a longpass characteristic. These beam splitters reflect the desired wavelength range toward the suitable filter array and transmit the residual wavelengths used for the subsequent splitters and filter arrays. The last element is also a dichroic mirror that transmits all wavelengths longer than the upper limit of the corresponding stopband.

The preselection module with the integrated FP filter arrays is combined to a mechanical adapter that allows for a connection to a CCD camera. Figure 9b shows a photo of the front side of the preselection module and the mechanical adapter with all optical elements clearly visible. The comparison with the 1 Euro coin substantiates the compactness of the module (17.5 × 17.5 × 7.8 mm3). Figure 9c demonstrates the back side of the module with FP filter arrays. Figure 9d shows a photograph of the final measurement setup with the closed module connected to a CCD camera and fed by the input light delivered by an optical fiber. With this approach, an efficiency enhancement by a factor larger than four compared to the used reference system [11,89] was experimentally demonstrated.

As already mentioned, the example presented serves exclusively as a proof-of-concept. A sensor that is simultaneously optimized in terms of compactness, efficiency and spectral properties can be achieved through a joint, tailored development of detector, filter arrays and preselection setup. Although the introduction of preselection module moderately increases the overall effort for the spectral sensor, a good compromise between efficiency enhancement and increase in complexity is achieved.

**Figure 9.** Efficiency increased module comprising dichroic beam splitters and FP filter arrays. (**a**) Photo of the preselection module with schematic beam path. (**b**,**<sup>c</sup>**) Photos of the module integrated in a housing. (**b**) Front side of the module displayed together with a coin (1EUR ) for size comparison. (**c**) Back side of the module, where the three glass substrates carrying FP filter arrays are visible. (**d**) Measurement setup: closed module connected to a CCD camera is illuminated by an optical fiber.

#### **7. Static FP Filter Arrays for the NIR: Fabrication and Characterization**

The near-infrared (NIR) spectral range is very interesting for sensing, e.g., for chemical analytics. This range was also considered in our previous paper [11] and is repeated briefly in this review. For the NIR spectral range, the FP filter arrays were designed in the 1.4–1.5 μm wavelength range, and 9.5 periods of Si3N4/SiO2 were deposited by PECVD for the top and bottom DBR at 120 ◦C temperature. This avoids degradation of the polymeric cavity layer due to higher process temperatures. The mr-NIL210 resist was used to obtain cavity heights much larger than those used in Sections 3 and 4 fabricated for the VIS spectral range. Each filter element here is 40 × 40 μm<sup>2</sup> in lateral dimensions, and the vertical height of the imprinted cavities ranges between 365 and 530 nm. The experimental characterization [11] reveals high maximum transmission values up to 90% and average transmissions well above 70%. The smallest FWHM (4.7 nm) is achieved at 1450 nm. This provides an FP filter resolution *λ/*Δ*λ* of 300, defined as filter transmission wavelength divided by the FWHM. Again, a comparison of experimental and simulated FWHMs had been performed. The description of the theoretical model calculations and the discussion of the FWHM variations were already described in Section 4.2. The surface roughness of layered heterostructures on the very thick resist mr-UVCur06 was investigated by an atomic force microscopy (AFM), revealing rms-values of <4 nm for a single layer and <8 nm for a double layer. This agrees with our FWHM observations since in layered heterostructures, this measured surface roughness is embedded in the heterostructure and transformed into interface roughness.

Finally, the influence of temperature changes on the structure and heat distribution is discussed. Having more interfaces in the heterostructure will shrink the overall thermal conductivity vertical to the interfaces. For more details see [36,90]. A good heat transfer to the heat sink is desirable since the ensemble of filter line wavelengths will shift with changing temperature. The dominating effect in the shifts results from the temperature dependence of the refractive indices of all involved materials. A much smaller effect is the influence of thermal expansion of all the layers in vertical direction. Such temperature changes for interferometric sensing application can be substantially suppressed either by implementation of Peltier elements that are commonly used in fiber optical communication

systems, or using temperature sensors and data processing software to execute correction of temperature shifts, since this information will be captured in any case by the arrays of spectrally neighboring filters with a wide spectral span. Figures of spectra and FWHM can be found in [11].

Contrary to the static FP filter arrays in Sections 3–7, the MEMS tunable FP filters in the following sections are considered to have a single air-gap (Section 8) or multiple air-gaps (Section 9).

#### **8. MEMS Tunable FP Filters with a Single Air-Gap for the VIS and NIR Spectral Range**

In the range 300–1100 nm, Si enables cheap and reliable detectors which can be integrated to powerful arrays in CCD or CMOS photodetector technology. Due to different designs, e.g., different channel geometries, they have a different spectral sensitivity. For sensorics in VIS spectral range, the combination of Si as detector material and static FP filter arrays (Sections 4 and 5) is a good and cheap solution. Therefore, MEMS tunable FP sensors in the VIS range are not as urgently required as in the NIR spectral range.

However, CMOS photodetector arrays or CCD arrays based on Silicon cannot be applied for the NIR spectral range of >1.2 μm, since Si becomes transparent and is no longer sensitive for light in that range. Therefore, detector arrays such as InGaAs have to be used for the NIR instead. Considering the aspect of cost reduction of IR spectrometers, MEMS tunable spectral sensors are very attractive in the NIR applications. A large spectral range of 1.15–1.8 μm (650 nm span) can be spanned using only three InGaAs photodiodes (an array of three photodiodes) and three related MEMS tunable filters that are neighbored in the spectrum. If each MEMS filter can be tuned over 220 nm, three of them are enough to cover 650 nm, with overlap. In the literature, various MEMS tunable filter designs were demonstrated in different material systems [38–58]. However, this review focuses on two MEMS concepts, namely the actuation of a single or several air-gaps.

Figure 10 depicts a MEMS tunable FP filter including a single air-gap. The lower DBR is directly connected to the substrate (not shown), which means that it remains flat and unactuated. The electrostatic actuation is displacing only the top DBR and varies the air-gap cavity height. All the incident wavelengths are reflected, except those which are able to constitute a standing wave in the cavity, and only this standing wave is allowed to transmit the filter. As already mentioned above, the following FP condition is only an approximation: The cavity height is a multiple of half of the wavelength in the cavity medium. Details on why it is only an approximation are given in Section 10.

However, this design has some disadvantages: (i) limited stopband widths and (ii) the rather bulky and stiff DBR stacks which require relatively long suspensions. The required large membrane displacements to allow large tuning ranges are only possible with such extended suspensions. If semiconductor DBRs (e.g., GaAs/AlAs) are used, the most elegant option is to n- and p-dope each of the two DBRs and to use electrostatic tuning by varying the applied voltage, as shown in Figure 10. Increasing the tuning voltage leads to a decreasing air-gap and decreasing filter wavelength (blue-shift).

If dielectric DBRs (SiO2/Si3N4 or SiO2/TiO2) are used, electrostatic actuation can also be applied, but this requires the specific definition of additional electrode layers since the light transmissive part of the filter must stay metal-free. In case dielectric mirrors thermal tuning is preferred, thin-film heaters are defined only on the suspensions. Increasing the tuning current through the thin-film heaters leads to increase of air-gap, thus increasing filter wavelength (red-shift).

**Figure 10.** Single air-gap MEMS tunable FP filters with four times half-a-wavelength cavity (4·*λ*/2) and semiconductor DBRs.

Figure 11a depicts a cross section of a single air-gap FP filter with two SiO2/Si3N4 DBRs, each with 12 periods of quarter-wave layers. The white part in between the two DBRs is the air-gap cavity with a thickness of *L* = 800 nm. The absolute value of the electrical field (black line), shown as an overlay, is depicted on this multilayer structure. This visualizes the standing fundamental mode inside the interferometer for an air-gap cavity of *L* = 800 nm thickness. The electrical field clearly visualizes that all dielectric layers in the DBRs are quarter-wave layers. For the same cavity thickness of *L* = 800 nm, the corresponding reflectance spectrum is displayed in Figure 11b (also in black color). Since the mirrors are dielectric and not conductive, thermal MEMS tuning is applied here. Figure 11b displays corresponding reflectance spectra for different air-gap cavities of width *L*. In Figure 11b, a red-shift is observed with increasing tuning current, in accordance to electrostatic MEMS tuning methodology.

**Figure 11.** MEMS tunable FP filters with half-a-wavelength cavity and SiO2/Si3N4 DBRs. (**a**) Cross section of the cavity embedded by dielectric DBRs together with the absolute value of the standing electrical field (black profile). (**b**) Corresponding reflectance spectra for different air-gap cavity widths *L* addressed by MEMS tuning.

#### **9. MEMS Tunable FP Filter Sensors in the NIR Range with Multiple Air-Gaps: Methodology, Simulations, Fabrication and Characterization**

The abovementioned disadvantages resulting from thick DBR layer stacks and limited stopband widths can be overcome in the second airgap-based option. The second option uses multiple air-gap FP filters and is visualized in Figure 12. The cross section of the multiple air-gap FP filter is shown in Figure 12a, in which the larger central air-gap has the width *L*. In the DBRs, the blue InP layers are three-quarter-wave in optical thickness, and the white air-gaps in between are quarter-wave layers. This can be clearly seen from the absolute value of the standing electrical field, displayed in black. Figure 12b depicts corresponding reflectance spectra for different central air-gap widths *L* addressed by MEMS tuning. A blue-shift is observed with increasing tuning voltage, in accordance to electrostatic MEMS tuning methodology.

**Figure 12.** MEMS tunable InP multiple air-gap FP filter with half-a-wavelength central cavity. (**a**) Cross section of an InP multiple air-gap FP filter including the larger central air-gap of width *L*. The absolute value of the standing electrical field is displayed in black. (**b**) Corresponding reflectance spectra for different central air-gap widths *L*, which is obtained by MEMS tuning. In this case only *L* is varied, all the *λ*/4 air-gaps remain unchanged.

This multiple air-gap design enables large tuning ranges with a slim design and the resulting wide stopband widths, thus overcoming the disadvantages mentioned for the single air-gap design (Figure 10). Actuation of the mirrors and hence varying the cavity length is accomplished by p-doping the top DBR, n-doping the bottom DBR and applying a reverse bias. Including us, four groups have investigated vertical-cavity tunable filters based on micromachined InP/air-gap DBR using different approaches [42,45–57]. Each DBR consists of 3*λInP*/4 InP membranes and two *λ*/4 air-gaps. The left part of Figure 13 shows a top view on an InP filter element with four supporting posts, four suspensions and the central top membrane. The right part of Figure 13 displays a cross section which is orientated according to the white broken line (left). Within the membrane and suspension posts, InGaAs served as sacrificial layers and is replaced by air upon removal. However, InGaAs within the supporting posts still remains as substantial layers.

**Figure 13.** (**Left**) top view on an InP filter element showing four supporting posts with four contact

pads (yellow), four suspensions and the top membrane (the topmost one out of the six membranes). The orientation of cross section on the right is indicated by the white broken line. (**Right**) cross section of the MEMS multilayer structure. InGaAs exists only inside the supporting posts. Between the suspensions and central membranes, InGaAs was serving as a sacrificial layer and had been selectively removed and replaced by air. The bottom contacts are shown in orange.

Doping of the DBRs considerably increases the tuning efficiency. Charging capabilities of metals is larger than that of semiconductors. The higher the doping level of semiconductors, the closer the semiconductor resembling a metal. Therefore, doped semiconductors are more suitable for electrostatic tuning than undoped. Reverse biasing is only shifting charges, and the current through the supporting posts is very small due to both very small areas and reverse biasing.

Metal organic chemical vapor epitaxy (MOCVD) is applied to grow the required latticematched multi heterostructure on [100] n-InP substrates: *λair*/4 InGaAs layers alternating in the stack with 3*λInP*/4 InP membranes. The *λair*/4 InGaAs layers act as sacrificial layers and are eventually etched, transforming into air-gaps. The top DBR located above the air-gap cavity is p-doped, and the bottom DBR layers located below the air-gap cavity is n-doped. First, the contacts are defined by lithography, evaporation and lift-off directly on the epitaxial structure. Then, Si3N4 is deposited by PECVD, and lithography and reactive ion etching (5.1 sccm Ar, 3.5 sccm CHF3, 6.7 Pa, 100 W) is used to generate the Si3N4 etch mask. Only the uncovered parts of the semiconductor surface are dry-etched in vertical direction using reactive ion etching (20 sccm CH4, 70 sccm H2, 4.7 Pa, 200 W) to achieve an etch depth down to ~5.5 μm. Use of a Si3N4 mask instead of a resist mask reveals improved selectivity in the dry-etching process and avoids polymer deposition which is highly unsought on the side walls of the mesa. This process is non-selective and provides vertical side walls, and sharp edges. Then, the etch mask is removed by wet-chemical etching (HF/H2O), producing pure semiconductor mesa. The supporting posts are masked by a protective layer to avoid underetching. To underetch the InP membranes, FeCl3/H2O is used to selectively remove the InGaAs sacrificial layers with an excellent selectivity of about 1000. The precise value depends on doping and temperature. This provides very smooth semiconductor/air interfaces. An etching time of 35 minutes at a temperature of 21 ◦C is used. It is important that the membranes and suspensions are underetched completely to ensure free vertical motion. The final structure after critical point drying and removal of the protection mask is depicted in Figure 13. A total of 500 filter elements were fabricated simultaneously on a wafer area of 1 cm2. The chance was used to fabricate multiple design variants differing in suspension lengths and membrane diameters on the same wafer. The filter variants have membrane diameters of 15–40 μm with three or four suspensions of 10–80 μm length and 10 μm width connecting the membrane to the supporting posts. Straight or bent suspensions and circular or square membranes were implemented.

Figure 14 displays the scanning electron microscope (SEM) images of filters with four suspensions. The optical quality of the two surfaces of each membrane is guaranteed by the high quality of the epitaxial heterointerfaces which is preserved in the selective chemical etching step, providing very low optical roughness. Our surface micromachining fabrication process demands no micro-mounting since the entire structure is fabricated in a sequence of process steps. Furthermore, a monolithic integration is obtained within the GaInAsP/InP material system, allowing the integration of photodiodes and verticalcavity surface emitting lasers. The central, light gray circular areas in Figure 14a–c show unprotected regions to allow underetching of membranes and suspensions. The dark gray areas outside of the circular areas show protected regions. Figure 14d provides a closer look on the suspension region, especially through the wider central air-gap that allows a view through the structure to the ground behind, marked with "\*". The ground level in front is marked with "\*\*". A single suspension has a width of 10 μm (light blue). The top DBR consists of the layers 1, 2, and 3 and the bottom DBR is made of layers 4, 5 and 6. At the central area, a view on top of suspension 4 is possible (marked with number 4 in white).

**Figure 14.** SEM micrographs of InP/InGaAs multiple air-gap MEMS tunable FP filters. Each DBR consists of three InP layers and two air-gaps. (**a**) 60 μm long suspensions and a circular membrane with 40 μm diameter. (**b**) Square membranes. (**c**) Short suspensions and small membranes. (**d**) Details of the suspension region. It allows a view through the structure to the ground behind marked with "\*". The ground level in front is marked with "\*\*".

Figure 15a displays an SEM micrograph top view of an InP multiple FP filter prior to the wet-chemical under-etching. The light gray circular region allows the etching solution to remove the sacrificial layers therein. The dark gray region outside prevents the underlying structures from being etched. Figure 15b shows a detailed close-up image of the suspension and membrane region, allowing a view through the central air-gap. Figure 15c displays the filter line wavelength as a function of actuation voltage, and the corresponding reflectance spectra is shown in the inset. A very wide tuning range of 221 nm [56] for a variation of the actuation voltage of 0–28 V is measured for our MEMS filters. To the best of our knowledge, this is the largest tuning range measured for any InP/multiple air-gap DBR-based verticalcavity filter. The FWHM is very narrow (about 1 nm) at lower actuation voltages; however, it broadens with increasing actuation voltage due to buckling of the membranes.

MEMS tunable filters were also fabricated using nanoimprint technology, successfully reducing the sacrificial layer to zero. A methodology proposed by Cheng et al. [91] was selected and adapted using selective curing in silica template. It was modified and transformed into our hybrid SCIL stamps [92]. Using UV-blocking metal layers in the otherwise transparent stamps, areas with non-cured nanoimprint resist could be generated. Therefore, cured hard resist remains only in the area of supporting posts, while other areas with non-cured resist show non-existent residual layers during resist removal. Being able to avoid residual layers was an important step forward for our SCIL 3D nanoimprint technology [92].

Figure 16 presents a 3D perspective view of the whole sensor attached to a fiber. A MEMS tunable FP filter is integrated with an InGaAs photodiode. The MEMS filter and the photodiode were grown within the same MOCVD epitaxial run on InP substrate.

**Figure 15.** (**a**) SEM image in tilted top view on an InP multiple air-gap MEMS tunable FP filter with InP/InGaAs supporting posts with contacts on top; (**b**) SEM image in tilted side view, enabling a look through the central airgap between the suspensions; (**c**) Tuning characteristic showing the filter peak wavelength as a function of the actuation voltage. A selection of experimental reflection spectra *R*(*λ*) is displayed in the inset. Various spectra are shown for different actuation voltages *U*. Reprinted with permission from ref. [11]. Copyright 2021 MDPI.

**Figure 16.** Interferometric sensor for the NIR spectral range, consisting of a MEMS tunable filter and

a photodiode. The actuation voltage will be applied between the rectangular and triangular contact pads. The photodiode is biased via the two highly doped semiconductor layers PD1 and PD4, and the sensor signal is also picked off between PD1 (triangular contact pad) and PD4 (substrate contact). To allow light incidence only on the white area, the rest of the PD top is covered by light protection layers. The rectangular contact pads correspond to the round contact pads in Figures 13 and 15, as well as to the rectangular contact pads in Figure 14.

The InP material system enabling monolithic integration with InGaAs photodiodes is not only beneficial for NIR sensorics, but also very favorable for receiver systems to be used for NIR wavelengths tailored for telecommunication requirements of low fiber dispersion and low fiber absorption. Our lab demonstrator including MEMS tunable FP filters and InGaAs photodiodes in monolithic integration was working well in the laboratory practice. In addition, a packaged MEMS tunable filter with two fiber pigtails was demonstrated using the InP/multiple air-gap material system.

#### **10. Limits of Semiconductor and Dielectric Material Systems for MEMS-Based Sensorics: Geometry, FWHM, Tuning and Stopband Width**

In this section, further conceptional facts and details are presented as a continuation to Sections 8 and 9. A separate Section 10 was chosen for this purpose to avoid overloading and interruption of the common thought in the previous two sections.

The first question is, how do the membranes of the top and bottom DBR move under electrostatic actuation? Figure 17a shows the InP multiple air-gap FP filter without applied voltage (unactuated), and Figure 17b displays the real situation when an actuation voltage is applied (actuated state). Because of applied voltage, charges are shifted. The charges accumulate mainly at the inner surfaces of the two central membranes. Therefore, the two central membranes are mainly actuated. Consequently, the outer membranes stay nearly uncharged and remain nearly unactuated. The outer membranes remain nearly unaffected due to shielding effects. Figure 17c displays a hypothetic situation, in which all the membranes of the top DBR are actuated in the same way and the whole bottom DBR moves in unity.

In Figure 18a,b the difference in tunability between the two cases shown in Figure 17b,c are investigated. Performing detailed theoretical model calculations using the Transfer-Matrix method the respective spectra, tuning ranges and FWHM have been calculated. The comparison starts from the same unactuated situation (blue spectrum) and studies different actuation states Δ*L* = 50 nm, 100 nm and 150 nm (the remaining central air-gap is *L* − Δ*L*). The spectra corresponding to these tuning conditions are displayed in different colors. The hypothetic case is shown in Figure 17c actuating all membranes, and the realistic cases is displayed in Figure 17b actuating only the central membranes.

For the two cases, the wavelength tuning Δ *λ* of the filter line is plotted as a function of the central air-gap height difference Δ*L* in Figure 19. Moving all the membranes of each DBR leads to a higher MEMS tunability.

The tuning efficiency is Δ *λ/*Δ*L* = 0.92 if all membranes are actuated, and it is otherwise Δ *λ/*Δ*L* = 0.8 if only central membranes are actuated. In comparison, the obtained tuning efficiency in Figure 11b is much smaller, i.e., Δ *λ/*Δ*L* = 0.56 for SiO2/Si3N4 DBRs. The multiple air-gap InP methodology is not only much better in MEMS tuning but also much more compact. The InP multiple air-gap FP filter reveals the smallest extension of the whole multilayer unit in the literature, with exception to photonic crystal membranes. Please note that the length scales of the two FP filters in Figures 11a and 12a are not identical.

**Figure 17.** Schematic of MEMS tunable FP filters including multiple air-gaps and membranes and suspensions made of InP. The supporting posts are built of the complete InP/InGaAs multilayer stack, as grown by epitaxy. (**a**) Unactuated state; (**b**) Actuated state where only the two central membranes of the DBRs are actuated; (**c**) Actuation of all membranes (i.e., actuating the whole two DBR stacks). This tuning configuration is shown in Figures 12 and 18a. The meaning of - *λ* used in (**<sup>a</sup>**–**<sup>c</sup>**) is explained hereinafter in this section.

**Figure 18.** Electrostatic MEMS tuning of InP multiple air-gap filters, (**a**) actuating all membranes of the DBRs and (**b**) actuating only the two central membranes.

**Figure 19.** Electrostatic MEMS tuning of InP multiple air-gap filters with two different cases: Actuating all membranes of the DBRs (lower curve) and actuating only the two central membranes (upper curve). The colors of the symbols correspond to those used in Figure 18.

It is also worth noting that many misunderstandings are related to the often and commonly used term "half-a-wavelength cavity". The FP condition for two metallic mirrors states reads: the cavity length *L* is a multiple of half of the wavelength in the medium. Figures 11a, 12a and 17a show half-a-wavelength cavities. Since the electromagnetic wave penetrates into the DBR mirrors, the figures show a feature which looks like half a wavelength inside the mode (Eigenfunction), but that is an effective wavelength - *λ* and not the half vacuum wavelength. It is not the same, and it depends on the DBR mirrors. During the tuning of the length *L*, the nodes are no longer located at the interfaces between the layers as shown in Figures 11a and 12a. Considering the insufficient idea of half of the vacuum wavelength inside the cavity, the tuning efficiency Δ*λ*/Δ*L* should be 1, independent of the materials of the DBR. A detailed explanation can be found in one of our doctorate dissertations [93].

The FWHM are nearly identical in both cases compared in Figure 18. A possible explanation could be that the FWHM is dominantly related to the number of periods. Since the number of periods is equal in both cases in Figure 18, the FWHM remain nearly identical.

Figure 19 reveals that the difference in tuning of the two cases is 13%. The wavelength tuning is dominantly related to changes in the airgap thicknesses. Therefore, the differences between the two cases are more pronounced in tunability rather than in the FWHM. However, quantifying 13%, the difference is still relatively small. This might be due to the fact that the mode shapes adapt not only to the changes in the central air-gap but also to the changes of the two other air-gaps which are located next to the central air-gap. For the complex localization of nodes and interfaces during the tuning, please refer to [93].

Next, the limits of FWHM are studied for multiple air-gap InP filters and displayed in Figure 20. Theoretical model calculations based on the transfer-matrix method are used to simulate the spectra of InP multiple air-gap FP filter lines. Measured data for the spectral InP absorption coefficient is given as *αInP* = 3.43 cm<sup>−</sup>1. The DBRs consist of 357 nm InP (3*λInP*/4) and 3675 nm air (*λair*/4) which are embedding the central air-gap of *L* = 815 nm (0.53 *λair*). The red curve is simulated for DBRs with three InP membranes, resulting in FWHM of 1.01 nm and dip reflectance of 0.00043 at a dip wavelength of 1562.995 nm. The black curve is simulated for DBRs with four InP membranes, resulting in FWHM of 0.112 nm and dip reflectance of 0.028 at a dip wavelength of 1562.906 nm.

**Figure 20.** Transfer-matrix model calculations of InP multiple air-gap FP filter line spectra with DBRs including 3 and 4 InP membranes each.

These low values could be confirmed experimentally with four InP membranes, in which a FWHM of 0.1 nm was measured at 1.55 μm. However, such a low value was only measured once from a single sample. Such linewidth broadening can only be avoided if the non-bending (buckling) of the central membrane areas is completely absent. Notwithstanding, the simulations and measurements showed what is possible. The optical resolution of the FP filter methodology is predicted to be around 15,000 in the best case.

Next, the maximum potential DBR characteristics are reviewed and shown in Figure 21. Applying transfer-matrix model calculations, transmission and reflectance spectra are calculated for different numbers of periods *p* and the appropriate material absorption coefficients *α*. The spectral variation of absorption *α = α*(*λ*) is taken from experimental results. In the inset of Figure 21a, the spectral reflectance is shown for a Si3N4/SiO2 DBR (*p* = 12, *λi*/4 layers, *α* = 0). The maximum spectral reflectivity *Rmax* for *λ* = 1.55 μm (see arrow) is extracted from all the spectra which were calculated for Si3N4/SiO2 and InP/air-gap DBRs. *Rmax* for *λ* = 1.55 μm is plotted in Figure 21a as a function of the number of periods *p*. Numerous spectra ranging the absorption loss *α* = 0, 0.1, 0.3, 1, 3, 10, 20, and 100 cm<sup>−</sup><sup>1</sup> were calculated for Si3N4/SiO2 DBR's. Please note that the values of *α* are determined by the technological fabrication and the appropriate process parameters. However, for ultra-pure semiconductor material, the optical loss dominantly is related only to the band structure in defect-free crystalline material of high quality. Therefore, low material loss can be guaranteed, and it is understood well in these crystalline materials. Figure 21a reveals that *Rmax* of a DBR strongly grows with increasing *p*, but it saturates for higher values of *p*. The level of *Rmax* saturation is strongly decreased with growing loss. As already mentioned, the extended spectral region of high reflectivity (i.e., the spectral plateau in the center, as shown in the inset of Figure 21c) represents the stop-band.

According to Figure 21a, the dielectric Si3N4/SiO2 system (*λ* = 1.55 μm, Δ*n* = 0.47, *n*Si3N4 = 1.94, *α*Si3N4 = *α*SiO2 both varied, *n*SiO2 = 1.47) yields *Rmax* > 0.998 already for *p* ≥ 12 if loss is neglected. For *α*Si3N4 = *α*SiO2 = 15 cm<sup>−</sup>1, a reflectivity of 99.8% is exceeded for *p* > 14. In contrast, 99.8% reflectivity cannot be reached for *α*Si3N4 = *αSiO2* = 20 cm<sup>−</sup><sup>1</sup> since *Rmax* saturates at *Rmax,sat* = 0.997. Please note that Δ*n* is much larger for InP/air-gap structures on InP substrates which was the motivation to use and study this system (*λ* = 1.55 μm, Δ*n* = 2.167, *nInP* = 3.167, *nAir* = 1, *αInP* = 3.4 cm<sup>−</sup>1) which provides a maximum reflectance *Rmax* of 0.9998 for *p* = 4 and yields *Rmax* exceeding 99.8% if *p* ≥ 3. To share further values, three InP/air-gap membranes embedded in air on both sides (in contrast to the previous structure no InP substrate is considered) reveal *Rmax* = 0.99993 for *p* = 4.5 and 0.9996 for *p* = 3.5. This demonstrates that using an air "substrate" instead of an InP substrate reveals a much larger *Rmax* already for smaller *p* due to a larger refractive index contrast at the

exterior ends of the DBR mirror. In summary, type and presence of a substrate strongly influence the optical data, especially for smaller number of periods *p*.

**Figure 21.** (**a**) Calculated maximum spectral reflectance *Rmax* for Si3N4/SiO2 DBRs (orange) as a function of the number of periods *p* showing the absorption coefficient *α* as a variation parameter. In the case of the InP multiple air-gap DBRs (blue), *αInP =* 3.43 cm<sup>−</sup>1. The inset displays the calculated reflectance spectrum indicating the spectral position of the maximum spectral reflectance *Rmax*. (**b**) Transmission spectra for InP multiple air-gap DBRs. The dotted line shows a DBR structure including thinner InP layers (*λInP*/4) revealing a huge stopband of 1500 nm. The full line shows a structure including thicker InP layers (3*λInP*/4) revealing a smaller stopband of 500 nm. (**c**) Reflectance spectra for Si3N4/SiO2 DBRs and InP multiple airgap DBRs.

In Figure 21b, the benefit is seen resulting from a very large refractive index contrast between 1 (air) and 3.167 (InP) existing between the two DBR materials for *λ* = 1.55 μm. This high contrast enables very large stopbands: 500 nm for the combination of *λair*/4 with 3*λInP*/4, and 1500 nm for the combination of *λair*/4 with *λInP*/4. Even the 3*λInP*/4 InP membranes is already sufficient to produce the stopband width exceeding the values of Si3N4/SiO2 by far (Figure 21c).

Notwithstanding, none of the four groups fabricating InP multiple air-gap DBRs has achieved to successfully fabricate *λInP*/4 suspended InP membranes up until now. The main issue lies in the breaking of the suspensions and membranes during the drying process after selectively removing the InGaAs sacrificial layers. For this reason, the dotted profile in Figure 21b remains a dream. Hopefully, improved future fabrication technologies with solvents implying less turbulences and improved drying processes can enable further progress on this challenging field. Thus, the full line in Figure 21b dealing with *3λInP*/4 thick membranes is the state-of-the-art in the present times.

Due to the arsenic carry-over in the epitaxial growth of the ... InP/InGaAs/InP ... heterostructure layer, the two interfaces are not identical. After finishing the InGaAs growth and switching to InP, traces of arsenic are still in the MOCVD reactor and are incorporated into the InP close to the interface. In contrast: after finishing the InP growth and switching to InGaAs, no arsenic can be carried back into the already finished InP layer. This arsenic carry-over leads to small stress gradients and subsequently buckling (bending) of the membranes and suspensions after removal of the InGaAs sacrificial layers. Completely flat membranes were obtained in our epitaxial growth after additional doping of arsenic in the opposite interface, and thus creating symmetric structures: arsenic-doped InP/undoped InP/arsenic-doped InP.

#### **11. Further Concepts for Miniaturization Based on Plasmonics, Ring Resonators, Quantum Dots, Spatial Heterodyning, and Photonic Crystals on Fiber Tips and in MEMS Membranes**

Beside the widely applied concepts of interferometric sensors beeing discussed in the previous sections, further options for miniaturization of sensors exist. In some of them, DBRs or even a complete FP filter are replaced by a single layer with 1D or 2D periodic patterns. Other concepts make use of different interaction effects such as plasmonic

resonances or Raman scattering. In the following section, a short overview to examples of all these approaches is given.

#### *11.1. Sensors Based on Photonic Crystals in MEMS Membranes*

As already covered in the introduction, guided mode resonances allow either broador narrowband resonances by coupling a wave in and out of a slab waveguide, and then superimpose this resonant mode with the directly reflected and transmitted continuous mode, respectively. The result is a Fano shaped resonance line in the spectrum, where bandwidth and line shape are given by the coupling condition. The basic concept of coupling resonant and continuous modes is shown In Figure 22a, and an example of a single InP MEMS membrane with a square lattice of elliptical holes can be seen in Figure 22b.

**Figure 22.** (**a**) Principle of a guided mode resonance. The incident wave (blue) is partly transmitted and reflected in form of continuous modes (green) and partly couples in and out the slab in form of a resonant mode (red). Superposition of both parts leads to the typical Fano line shape. (**b**) A MEMS membrane with elliptical air holes as base elements in a 2D square lattice, breaking the symmetry and leading to polarization dependent reflection and transmission.

Zobenica et al. [77] applied two parallel membranes including photonic crystals (PCs) and quantum dots (QDs), which were coupled evanescently. In this case, a single DBR is replaced by two PC layers. This idea was shown first in [62,73]. The graph in the third column from the right-hand side in Figure 3 depicts the design of the MEMS PC membrane. These devices reveal a very low FWHM of 0.08 nm for central wavelength at 1319 μm. The spectral filter lines could be tuned in the experiments across 30 nm by electrostatic MEMS actuation. However, it is challenging to adjust position and size of the QD for distinct wavelengths.

Using PC structures with MEMS tunable narrowband filters, polarization selectivity can be additionally implemented. This maintains the compactness of MEMS devices by introducing holes with pronounced elliptical symmetry in the PC structure of the top membrane in the top DBR [64]. Here, most commonly guided mode resonance structures [63,66] or structural birefringence [67] are applied. In both cases, the selective behavior of the filter device regarding electric field orientation of the incident wave is based on disturbing the 90◦-symmetry by either line gratings or introducing elliptical base elements in a 2D PC.

#### *11.2. Nano-Optical Sensor Concepts*

A spectroscopic MEMS sensor using the excitation of surface plasmon-polariton (SPP) resonance on a cantilever was reported by Oshita et al. [68]. The device is fabricated from a SOI wafer, and a metallic grating is applied on top to provide the excitation condition for SPPs. In operation, the cantilever is oscillating at resonance frequency close to 400 Hz and provides the largest angular stroke. As the coupling condition for SPP to the metallic grating is strongly angle dependent, the signal recorded for half an oscillation period can be evaluated to ge<sup>t</sup> the spectral information. In the cited work, a spectral scanning range of 300 nm was achieved with a FWHM of approximately 10 nm or more. The spectral range

is mainly limited by the properties of the materials and the grating. Further data are given in Figure 3 in the second column from the right-hand side.

Another approach, presented by Faraji-Dana et al., applies tailored dispersion properties of diffractive elements using a folded beam path in a thin glass plate where light is reflected at three specifically designed metasurfaces [94]. The authors showed a spectrometer covering 100 nm spectral range with 1.2 nm resolution and device volume of 7 mm3.

#### *11.3. Sensors with Links to Telecom Devices*

Strong ties exist between spectroscopic sensors and devices used in multiplexing systems of optical telecommunication systems. In both cases, the goal is to analyze spectrally encoded information, but the focus for telecommunication is mostly on spectral linewidth, whereas in spectroscopy a broad spectral range is often required as well. Transfer of concepts from one field to the other is generally beneficial, and the most common device types such as FP or AWG are frequently found in both fields. Two examples of spectroscopic sensors derived from telecom concepts are presented in the following.

Filters with extremely small FWHM were demonstrated by Li et al. [78] and are included in Figure 1 at the right-hand side. This device is based on a fiber Bragg grating (FBG) with linear chirp. Local heating at a defined position of the FBG introduces a change in refractive index and therefore a phase shift in the grating period. Phase shifts in periodic patterns lead to resonant conditions and high transmission for a certain wavelength. Such behavior can also be understood by looking at the cavity of a DBR FP filter in the same way. A *λ*/2 layer in a periodic sequence of *λ*/4 layers represents a phase shift in the layer structure as well. The device presented by Li et al. is tunable for 16.5 nm in the spectral range around 1.55 μm, with a FWHM of only 0.007 nm.

The application of ring resonators is another path to achieve sub-nm spectral resolution. These devices are commonly used in telecom systems and are known to have very high Q factors of more than 100,000, but also small free spectral ranges as they work in a high order. Nitkowski et al. showed such a spectrometer integrated to a microfluidic chip [95]. From the same group, an improved device combining a ring resonator, a diffraction grating and a waveguide array was presented later, with 0.05 nm FWHM in the near IR spectral range and a footprint of 2 mm<sup>2</sup> [96]. Smooth sidewalls of the stripe waveguides and accurate dimensions of the ring structures are crucial, but the planar technology is well understood and commercially applied in the telecom field for many years already.

#### *11.4. Sensors with Computational Signal Evaluation*

For several recently developed spectrometer devices, such as the plasmonic MEMS sensor shown by Oshiita et al., computational post-processing of the acquired data are an essential part of the sensing principle. A very interesting and compact example in this direction is the nanowire-based spectrometer of Yang et al. [97]. The II-VI semiconductor of the nanowire is grown with gradually varying composition along the length of the wire, leading to a varying band gap. By choosing the appropriate base material, several spectral ranges can be addressed. An array of small electrodes is contacted to the nanowire and allows the measurement of a locally generated photocurrent. Evaluation of the signals is based on a pre-calibrated response function and an algorithm to extract the spectral data. The authors show results over a spectral range of 130 nm with FWHM of approximately 8 nm in the visible range. The device size is determined by the length of the nanowire and the dimension of the electrode array, both being on the order of 100 μm or less.

#### *11.5. Sensors on the Fiber Tip*

A highly efficient way to integrate optical measurement methods with fiber systems is to use the optical fiber itself as sensor. Beside the small size given by the fiber diameter, the typical advantages of fiber optics, namely its mechanical flexibility and immunity to electromagnetic interference, make this type of sensors interesting for measurements in difficult locations and harsh environments. However, most of the sensors are not tunable

or require additional electrical components at the opposite end of the fiber, thus increasing the overall size of the system again. Furthermore, the fabrication of fiber-based sensors can be quite challenging and will be addressed at the end of this discussion. Interaction with light waves can occur inside the fiber based on structures such as fiber Bragg gratings or on evaluation of scattering effects. In the following overview, a different approach where the sensor is fabricated on the tip of an optical fiber will be covered. In such a configuration, interaction with light waves occurs locally at the tip, and the fiber is merely used for guiding the wave to a detector.

As previously introduced, guided mode resonances (GMR) in 1D or 2D photonic slab waveguides enable very compact filter elements on MEMS devices. Tailoring the coupling strength between resonant and continuous mode allows for narrowband spectral properties, whereas breaking symmetries will lead to polarization dependent behavior. In a similar way, GMR filter elements can be implemented on the tip of optical fibers, as shown in Figure 23. A high refractive index thin film of ZrO2 was deposited by ion beam sputter deposition on the fiber tip and acts as a slab waveguide with SiO2 and air as surrounding materials. The periodic pattern, centered at the core of the single-mode fiber, was fabricated by FIB milling lithography. Nanoimprint lithography on a fiber tip is another possible fabrication method, in which the whole facet is covered and patterned in a single process step as shown by Tabassum et al. [98]. The fabrication is far simpler to implement than using sputter deposition and focused ion beam (FIB) milling, but it lacks the precise control of layer thickness or alignment to the fiber core.

**Figure 23.** Tip of an optical fiber with GMR structure aligned to the core. The inset shows an FIB cross section of the ZrO2 slab waveguide layer deposited by ion beam sputter deposition and the 1D periodic pattern fabricated by FIB milling. The dark bar covering a part of the pattern is a locally deposited protection layer to avoid damage of the pattern during preparation of the cross section and to enhance contrast for imaging.

Several research groups showed FP filters on fiber tips, mainly for sensing applications in gases and liquids. Mostly, air cavities are implemented by splicing a short section of multi-mode fiber or capillary to a single-mode fiber. Ma and Wang showed that fabricating a MEMS mirror on the spliced segmen<sup>t</sup> by sputter coating and FIB milling and subsequent selective underetching leads to an FP with the single-mode fiber facet being the second mirror. Target application of this sensor was detection of H2 in gas atmospheres [99]. The combination of a single-mode fiber and a short photonic crystal fiber (PCF) segmen<sup>t</sup> with high index core and large surrounding air holes as fiber tip sensor was presented by Zhu et al. [100]. An FP cavity forms by reflections due to the mode mismatch at the splice and at the PCF to air interface and was applied to measure temperatures by tracing the optical path length variation resulting from thermal expansion and effective refractive

index change. A similar pressure sensor fabricated of a short capillary spliced to a singlemode fiber and covered by a few-layer graphene sheet as flexible membrane and FP mirror was shown by Ma et al. [101]. Kilic et al. [102] presented an acoustic sensor working on the FP principle as well, but first they fabricated a PC mirror on a released MEMS membrane using the GMR effect with a broadband resonance. The silicon on insulator chip was then mounted with high-viscosity epoxy to the fiber tip, forming an air cavity between silicon membrane and a metal layer coated on the fiber facet. Monolithic fabrication of an FP cavity by FIB milling was reported by Alberts et al. [103] using an off-centered, partly metal coated reflector for application as refractometer in liquids.

Beside the interferometric principles for sensors, plasmonic fiber tip devices are also a viable option. Still, using surface plasmon polariton resonances is difficult due to the required excitation condition. De Maria et al. [104] showed, however, that polishing the fiber tip under the excitation angle and coating the surface with silver is a possible solution for this problem. More common is the application of localized plasmon polariton (LPP) resonance by exciting free electron oscillations in nano-sized particles or structures [105,106]. Since excitation of LPP resonances can be accomplished by free space modes, no extra preparation is required. A typical application is the enhancement of weak intensity signals in Raman spectroscopy using the local field enhancement around the metallic nano structures, known as surface enhanced Raman spectroscopy (SERS) [107]. Kostovski et al. showed that this method can be integrated into a fiber tip sensor using nanoimprint lithography and subsequent deposition of a metal layer [108]. Probes based on nanoscale fiber tips and with additional metallization [109] are applied widely for scanning near field optical microscopy. Plasmonic effects or optical antennas are used to characterize optical properties which are not accessible to other methods. For example, Burresi et al [110] report on probing the magnetic field of an optical wave by applying a metallic split ring aperture at a tapered fiber tip.

Further implementations of sensor on fiber tips exist. In some, the optical fiber is only used as signal path, whereas the interaction with a sample is based on non-optical effects. The fiber tip atomic force microscope, presented by Iannuzzi et al. is an example from this group of sensors [111]. As mentioned, the technology required for the fabrication of fiber tip devices can be challenging. This is due to the small and not perfectly flat surface of a fiber facet, which makes resist coating or lithography quite difficult. Nevertheless, several routes for possible processes have already been shown [112]. These include FIB milling, nanoimprint lithography, align & shine photo lithography, two photon polymerization lithography, or mounting of chips fabricated by conventional methods.

#### *11.6. Spatial Heterodyne Sensors*

As a complement to the different, mainly FP-based sensor concepts discussed so far, the Spatial Heterodyne Spectrometer (SHS) is considered in the following section. The attractiveness of the SHS concept is based on the possibilities for tailoring its optical properties to specific user requirements in combination with its significant potential for miniaturization.

Essentially, the SHS is based on the configuration of a Michelson interferometer, where the mirrors in each arm are substituted by diffraction gratings [113]. The gratings are fixed in a tilted mount and do not require moving parts.

The basic working principle of SHS is schematically shown in Figure 24 (according to [114]). The incoming polychromatic wavefronts are separated by the beam splitter into two partial wavefronts, each striking on a respective grating. The orientation of the grating determines the Littrow wavelength, whose wavefront is diffracted exactly backward to the incident direction. All other wavelengths have different diffraction angles and propagation directions. At the detector, the superimposed light from both gratings is recorded. In detail, the periodicity of the interference pattern Λ for a specific wavelength *λ* depends on the half angle between intersecting wavevectors *θ* and the refractive index *n* of the ambient medium. The entire recorded interferogram is composed by the contribution of all involved wavelengths. Finally, the interferogram must be converted to a conventional

spectrum by Fourier transformation. The working principle allows very high spectral resolution for a small spectral bandwidth.

Applications for SHS range from space born projects e.g., satellite-based atmospheric temperature measurements [115] to Raman Spectroscopy of minerals [114]. Particularly impressive are the small dimensions that can be achieved. A SHS system was presented in [115], operating between 761.9 nm and 765.3 nm with a resolving power of about 8000, and requiring only a volume of 38 × 38 × 27 mm<sup>3</sup> in size. In the meantime, progress has also been made in the production technology of SHS. Yi et al. [116] reported on the fabrication procedure of monolithic interferometers for SHS systems with ultraviolet curing adhesive and commercial optical elements, which may open the door to high volume manufacturing.

**Figure 24.** Illustration of the basic principle of spatial heterodyne spectroscopy (SHS).

#### **12. Estimation of Potential Space Requirement after Utmost Miniaturization**

Concerning grating spectrometers, the company Hamamatsu and Ibsen Photonics most probably came close to the miniaturization limits defined by such an optical resolution, which is still sufficient for some applications. In the case of our VIS and NIR FP filter arrays, the miniaturization potential in lateral direction was not used in our proof-of-principle. With 40 × 40 μm<sup>2</sup> in lateral direction, the mesa is considerably very big, and therein lies a high miniaturization potential to make them smaller. In this section, the potential limits for miniaturization of all six sensor principles are estimated: AWG, static FP filter array, MEMS tunable FP filter arrays, plasmonic sensors, MEMS tunable PC filters, and chirped fiber Bragg gratings. To identify the miniaturization limits, best case scenarios (ideal conditions) and optimum vertical light incidence are considered. For the static arrangements (FP filter array, AWG), Δ*λ* = 2 nm in the VIS range was chosen for the spectral step size (channel spacing) between spectrally neighboring transmission lines; and in the NIR range, a channel spacing of Δ*λ* = 4 nm. A spectral span of 400 nm in the VIS range and a spectral span of 500 nm in the NIR range has to be covered. Although a preliminary estimation was already performed in [11], here it is further complemented with inclusion of two additional sensor concepts and supplementary figures visualizing the lateral arrangements.

#### *12.1. Static FP Filter Arrays Covering 400 nm in the VIS Spectral Range*

In Figure 25a, the minimum space requirements for a static FP filter array for the VIS spectral range is shown. To eliminate effects from borders within a single pixel, the lateral size of the square optically active mesa (orange) has to be approximatively 8*λ* × 8*λ* or larger, which was derived from experiments and simulations. This means that 6 μm side dimensions of the square mesa are sufficient for the wavelength range *λ* = 400–800 nm. Choosing a spatial spacing of 4 μm between the square mesa, results in a period of 10 μm and reveals an area of 10 × 10 μm<sup>2</sup> for each pixel. The material system TiO2/SiO2 for the DBRs allows stopband widths of 200 nm, thus, 100 spectrally adjacent filter lines in each stopband are required. Two neighboring stopbands are required to span 400 nm (Figure 25a). To be on the safe side for mounting issues, empty frames of 50 μm width surrounding both arrays are chosen. A space of 204 × 358 μm<sup>2</sup> is required, resulting in a chip size of about 0.07 mm2. This is well compatible with commercial Si CCD detector arrays or Si CMOS detector arrays. All signal recording and processing electronics are located behind the layer containing the filters as depicted in Figure 25a, leading to a very compact layout.

**Figure 25.** Space requirement to cover 400 nm in the VIS spectral range using two neighboring TiO2/SiO2 stopbands for the DBRs and PDs/CCDs in the Si material system. (**a**) Static FP filter array. (**b**) MEMS tunable FP filters.

#### *12.2. Static FP Filter Arrays Covering 500 nm in the NIR Spectral Range*

Since Si cannot be used for this purpose, other detector material such as InGaAs is required. However, photodiodes in the InGaAs material system are by far more expensive than Si CCD or CMOS detector arrays. The company Hamamatsu offers linear InGaAs photodiode arrays which have stripe-like active areas (orange in Figure 26) of 15 × 100 μm<sup>2</sup> which are followed by stripes of 10 × 100 μm<sup>2</sup> as spacers (white in Figure 26). Therefore, the period of the spacer/stripe arrangemen<sup>t</sup> is 25 μm. For *λ* = 1500 nm, this also fulfills the required 8*λ* minimum pixel size. A minimum of 125 pixels are required for one DBR in the TiO2/SiO2 material system with a stopband of 500 nm, which translates to 100 × 3125 μm<sup>2</sup> (Figure 26). Considering an empty frame of 100 μm width around the linear array, 300 × 3325 μm<sup>2</sup> space are required, resulting in 1 mm<sup>2</sup> chip size. Such approximated size excludes any signal processing electronics that still have to be integrated in this commercial solution.

**Figure 26.** Space requirement to cover 500 nm in the NIR spectral range using commercial InGaAs PDs. Please note that this array is considerably scaled down in size compared to Figures 25 and 27.

> This requires a huge amount of space. However, if tailored square photodiodes would be used, the required space would shrink considerably. However, this technology is not ye<sup>t</sup> available on the market. Figure 27a displays an estimate for the required space for that case. To avoid border effects within a single pixel, the lateral size of the square optically active mesa (orange in Figure 27a) should also be approximately 8 *λ* × 8*λ* or larger, known from experiments and simulations. Thus, 13 μm for both sides of the squares are sufficient for the wavelength range of *λ* = 1500 nm. Using 4 μm spatial spacing between the mesa, the period is 17 μm in length. Thus, an area of 17 × 17 μm<sup>2</sup> are required for each pixel. A single TiO2/SiO2 DBR with a stopband of 500 nm already covers the required spectral range. Since the required 125 pixels are not practical for a rectangular array, 130 pixels are chosen (Figure 27a) and arranged in a 10 × 13 array. Applying empty frames of 50 μm width surrounding arrays, a total of 274 × 325 μm<sup>2</sup> space is required. This results in a chip size of about 0.09 mm2. For a very compact design, the complete signal processing electronics should be placed behind the sensor part as depicted in Figure 27a. However, such technology (corresponding to Si CCD or Si CMOS) has not ye<sup>t</sup> been developed in the InGaAs/InP-based material system. Nevertheless, a hybrid solution with a Si CMOS chip behind the InP chip is also possible, as shown in Figure 5.

**Figure 27.** Space requirement to cover 500 nm in the NIR spectral range using tailored InGaAs PDs, not ye<sup>t</sup> available on the market. (**a**) Static FP filter array with a single TiO2/SiO2 DBR. (**b**) MEMS tuneable FP filters in the InP multiple airgap system. (**c**) 1 × 3 splitter, schematically aligned to the 3 MEMS membranes.

#### *12.3. MEMS Tunable FP Filter Arrays Covering 500 nm in the NIR Spectral Range*

The InP/multiple airgap material system allows DBRs with a stopband width between 500 nm and 1500 nm, depending on the InP layer thicknesses (3 *λInP*/4 or *λInP*/4), respectively. Therefore, a single stopband is already enough to cover the required 500 nm wavelength span in the NIR spectral range. In the experiment, a tuning range of 221 nm was obtained. To be on the safe side, three MEMS tunable filters are used to cover the

required 500 nm. For our minimum space estimation, the following required elements are arranged according to Figure 27b: supporting posts spanning a lateral area of 40 × 40 μm2, suspensions with 35 μm lengths, and circular membranes with 15 μm diameters. The 15 μm diameter is fully sufficient to cover the wavelength range between 1.2–1.7 μm. As shown in Figure 27b, the central filter is sharing its supporting posts with the two neighboring filters. Applying empty frames of 20 μm all around the three filters ensures that the optically active membrane (orange) is at least 50 μm apart from the chip borders. This requires 340 × 140 μm<sup>2</sup> space and reveals a chip size of 0.05 mm2. As demonstrated, the advantage in this concept is that the InGaAs Photodiode can be fabricated together with the MEMS filter within the same epitaxial step (monolithic integration), as depicted in Figure 16. Concerning fiber and waveguide optics, a 1 × 3 integrated waveguide splitter (Figure 27c) could be used to divide the light from the fiber and to guide it to the three active regions (shown in orange). Please note that the plane spanned in Figure 27c is perpendicular to the plane spanned in Figure 27b, and the three ends of the splitter are ending centrally to the three orange membranes. This is indicated by the two dotted lines relating Figure 27b,c. The fiber would be coupled to the right-hand side waveguide end of Figure 27c.

#### *12.4. MEMS Tunable FP Filter Arrays Covering 400 nm in the VIS Spectral Range*

The material system TiO2/SiO2 is chosen for the DBRs, allowing stopband widths of about 200 nm. According to Figure 25b, the required elements are supporting posts with an area of 40 × 40 μm2, four suspensions with lengths of 35 μm, and circular membranes (orange) of 10 μm diameter. This diameter is sufficient for application at *λ* = 400 ... 800 nm. Please note that the dielectric material system exhibits much smaller tuning ranges due to the single air-gap MEMS in comparison to the slim InP multiple airgap system. Although they have 200 nm wide stopbands, four tunable FP filters (each with 100 nm tuning range) are required to cover the targeted 400 nm (Figure 25b). Neighboring filters share supporting posts which are located in between. As in Section 12.3, applying empty frames of 20 μm all around the four filters ensures that the optically active membrane (orange) is at least 50 μm apart from the chip borders. This requires 240 × 240 μm<sup>2</sup> space and results in a chip size of 0.06 mm2. Similar to previous cases, the complete signal processing electronics is placed behind the sensor part depicted in Figure 25b to make it very compact. Concerning fiber and waveguide optics, a linear arrangemen<sup>t</sup> of the four MEMS filters would be a better option (like in Figure 27b), and a 1 × 4 integrated waveguide splitter should be used to divide the light from the fiber to the four active regions (orange) as in Figure 27c.

It is important to note that in Sections 12.1–12.4, the photodetectors and the electronics are hidden behind the filters elements and not visible in Figures 25–27.

#### *12.5. MEMS Tunable PC Filter to Cover a Spectral Span of 500 nm in the NIR Range*

Zobenica et al. [77] measured a tuning range of 30 nm (1308–1338 nm) and pointed out that there is a potential to extend it to 40 nm. A wavelength span of 500 nm can be covered by combining 15 spectrally neighbored filters, supporting posts of 15 × 50 μm2, PC membranes with suspensions requiring in total an area of 15 × 15 μm2, and additionally the electronics. As discussed in Sections 12.3 and 12.4 the filters are considered with overlapping tuning ranges, just to ensure reliable operation. Similar to previous cases, here the neighboring MEMS filters share their supporting posts in between the filters. Considering the additional space for contacts of sensing and actuation diodes, the estimate yields 0.33 mm<sup>2</sup> for the total chip size. The papers do not provide enough information concerning space for signal processing, electronics and contacts. However, extrapolating from what is visible in Figure 1c in [77], we assume that there might be a miniaturization potential of a factor of 6, which is considered in our estimation.

#### *12.6. AWG Covering 500 nm in the NIR Spectral Range*

During his time at the company NTT, Japan, Y. Yoshikuni et al. [24] performed pioneering work on arrayed waveguide gratings (AWGs). His team demonstrated 64 channels with 50 GHz frequency spacing for fiberoptic long-haul telecommunication at 1.55 μm. The corresponding sample was already downscaled and had lateral dimensions of 7 × 3.6 mm<sup>2</sup> [22–24]. At the time of publication, they also implemented the most complex InP photonic device integration in the world, including semiconductor optical amplifiers, photodiode arrays and several AWGs. On the basis of these early and also recent publications, a space requirement of 50 mm<sup>2</sup> including 125 channels was estimated for the NIR spectral range.

#### *12.7. Plasmonic MEMS Cantilever Covering 500 nm in the NIR Spectral Range*

The device presented by Oshita et al. already shows a very broad tuning range of 300 nm in the NIR spectral range [68]. Increasing this parameter could be accomplished by a larger stroke of the deflection angle, but this will be limited by several constraints. Flatness of the cantilever during actuation is crucial as the coupling condition to a SPP is angle dependent and bending of the grating would lead to increased FWHM. Reducing this cantilever size will decrease the efficiency of light coupling to the grating considerably. There may be some room for improvement based on optimization of the geometric shape of the device. In the end, using a second device with different spectral tuning range to reach 500 nm spectral span seems to be the more promising option. In such implementation, two identical MEMS cantilevers would be fabricated, but different grating structures and possible different metals would lead to SPP resonance excitation in different spectral ranges for the same deflection angle. The required space of such a sensor system would be around 20 mm<sup>2</sup> if no reduction in size of the single devices is considered.

#### *12.8. Locally Heated Chirped FBG to Cover a Spectral Span of 500 nm in the NIR Spectral Range*

Tunable filters based on a chirped FBG as reported by Li et al. [78] work only for a limited spectral span of 15–20 nm. Therefore, tuning over a range of 500 nm would require at least 30 individual chirped fibers. Since the outer diameter of a conventional single-mode fiber is only 125 μm, even an array of 30 fibers, positioned for example in a template of etched channels on a silicon substrate, would only require 5 mm in width. The length of the chirped FBG is given by the required number of periods and is in this case in the range of 50 mm. The presented sensor is not ye<sup>t</sup> optimized for miniaturization since the thermal actuation is based on a heating wire attached to a very bulky linear positioning stage. A possible approach that will not lead to any further increase of the device size would be to integrate an array of heater elements into the silicon wafer template. This would finally lead to a space requirement of 250 mm<sup>2</sup> for the sensor alone, excluding other elements such as a photodiode, any further optical fibers for wave transport, coupling elements or control of the heater array.

#### **13. Where Are the Minimum Structure Size Limits in 3D Nanoimprint Lithography?**

The potential of 2D nanoimprint lithography for replication of extremely small structures was demonstrated by patterns with 5 nm lateral half-pitch [117], and most recently, even a reduction to 2 nm was reported [118]. The 5 nm dimension were imprinted with a III/V semiconductor stamp. It was grown by molecular beam epitaxy, subsequently cleaved and selectively etched on the cleaved side. Finally, the cleaved side represented the nanoimprint stamp [117]. An even more exotic stamp is a substrate with carbon nanotubes on top. 2 nm in lateral direction were demonstrated by imprinting with these carbon nanotubes [118]. In addition to experimental investigations, theoretical studies have also been performed by modeling the stamp-resist interface. The most relevant forces between the stamp surface and the nanoimprint resist surface, considering the individual atoms of both surfaces, were studied in sub-nanoscale using theoretical model calculations [119,120]. The result shown that the stamp could not be released from the cured and hardened imprint resist if lateral structure dimensions are below 0.5 nm. This represents a theoretical limit for minimum lateral size dimensions for nanoimprint lithography. In general, the smaller the molecules used in the nanoimprint resist, the smaller the minimum structure dimensions

which are obtainable via nanoimprint lithography. Typically, a monomer has a size of 1–2 nm, i.e., even for short-chained polymers, only a small space is remaining in the structure.

Many different template materials are possible, such as glass, Si or III/V semiconductors. Imprints can be directly performed using the template, as what was done in our experiments using GaAs templates. Alternatively, the master template (mother-structure) has also been replicated into polydimethylsiloxane (PDMS) serving as a daughter-structure which is used for the subsequent imprinting in mr-UVcur06. This resist is cured with UV light.

In the following discussion, an intuitive visualization is made in Figure 28 to illustrate the vertical mesa height differences in the sub-nm range in relation to the scale of resist molecules. For the purpose of simplicity, the influence of surface roughness is not included.

**Figure 28.** Cross sections of schematic surface profiles. The crystalline structure of the Si master template is visualized by the periodic honey-comb structure (**top**). The master template is replicated in PDMS and rotated by 180◦, as shown in green (**center**). The schematic includes a possible arrangemen<sup>t</sup> of organic molecules in the PDMS. Subsequently, 3D nanoimprints were performed using this PDMS stamp. After imprinting the resist, hardening the resist and releasing the stamp the blue schematic surface is resulting (**bottom**). The figures do not have the same scale in vertical and lateral direction: differences exist in vertical mesa heights between *a* = 0.2 nm and 1 nm, lateral mesa widths between 6 μm and 40 μm, and vertical mesa heights between 10 nm and 300 nm.

Our smallest height difference which was measured with an interference microscopy was *a* = 0.2 nm [33,34]. On a first glance, this result might be in contradiction to the smallest lateral structure sizes of 0.5 nm which were predicted in the abovementioned theoretical model calculations [119,120]. However, there is no contradiction since the lateral dimensions of our mesa are in the range of >6 μm (see Section 12) or even 40 μm in our proof-of-principle (Sections 2–4). The chains of the nanoimprint resist molecules will spread in lateral directions. This means that a very high vertical accuracy can be obtained if comparably large lateral dimensions can be tolerated or are even required as in our case. Furthermore, very high vertical resolution can be obtained if larger residual layers are acceptable or reservoir for excess resist are included in the design. Even if our technology which enables zero-residual layers is used [92], these reservoir technologies and volume equalizing technologies [86] have to be applied.

Measuring *a* = 0.2 nm [33,34] using an interference microscopy is executed by averaging over an area containing many polymer chains (diffraction-limited focal diameter). Please note that the exact same approach is applied in the optical sensor, therefore, this is a relevant value for the height differences.

A schematic FP array structures with two different mesa heights is displayed in Figure 25 to envisage vertical resolution limits in 3D nanoimprint lithography. The polymer chains of the nanoimprint resist reveal different lengths and shape, and they have a lateral thickness of approximatively 0.2 nm. In lateral directions, the molecules can easily migrate and spread during the filling of the stamp (mold) with imprint resist. Due to these microfluidic aspects, our 3D nanoimprints could reveal vertical mesa height differences down to 0.2 nm since the lateral dimension is large enough to allow material migration and spreading. In summary, 2D nanoimprint technology uses constant vertical step heights and the smallest structure sizes in lateral directions were 2–5 nm in the experiments [117,118] and 0.5 nm in theoretical model calculations [119,120], as already mentioned. In our 3D nanoimprint experiments, 0.2 nm in mesa height difference was obtained in structures with rather large lateral sizes in the range of several μm, due to viable allow material migration and spreading. At the moment, it is hard to estimate the limits for 3D nanoimprint if ultra-small variations are involved in vertical and lateral dimension simultaneously, but it could be in the sub-nm range in all combined three directions.

#### **14. Can Nanoimprint Be Applied to Fabricate the Seven Sensor Types Compared Here?**

Today, a variety of molding technologies exist, such hot embossing, nanoimprint, injection molding and LIGA. The acronym LIGA consist of the German words **Li**thographie, **G**alvanik, **A**bformung, which means (X-ray) lithography, electroplating, molding [121] and is used worldwide. In nanoimprint technology, structures are replicated using a stamp with structure sizes between a few nm up to several μm. In contrast, LIGA technology is replicating structures from a stamp generating structures between a few μm to several mm [121]. Even larger objects are replicated by injection molding ranging in size between several μm to the range of a few meters.

Using molding technologies, miniaturized grating spectrometers [72] can be generated to define curved mirrors, grating, cavities to insert detector arrays, guide elements and housing parts in a single step. To lower fabrication cost, molding is always a very good strategy. Micro-grating spectrometers were also replicated applying LIGA processes [122]. Using InGaInAs, waveguide structures were lithographically treated and etched to define transmission grating, curved mirrors and trenches for optical fibers [123].

In this last section, the question is raised whether nanoimprint can be applied in the fabrication of AWG sensors, miniaturized spectrometers, plasmonic MEMS sensors, static FP filter array sensors, MEMS tunable FP array, tunable chirped fiber Bragg gratings, and MEMS tunable PC arrays, all of which are shown in Figure 1. Several advantages of nanoimprint concerning cost, time, and effort were already presented and confirmed by results presented in the previous sections. The lithography included in manufacturing can be replaced by nanoimprint lithography in five out of the seven sensor types. However, in cannot be used in the fabrication of the classical grating spectrometers and the chirped fiber Bragg gratings. Moreover, nanoimprint might not be ideal for the precise positioning of the QDs within the PC structure [77]. We expect that the positioning of the QD would be arduous and might require, e.g., electron or ion beam lithography. Thus, nanoimprint lithography might not reveal clear advantages in manufacturing of MEMS tunable PC structures. However, it is highly desirable to use nanoimprint lithography for the fabrication of AWGs since it has clear advantages in replacing optical lithography in large scale production. Furthermore, nanoimprint is very desirable, but not absolutely necessary, in manufacturing MEMS tunable FP filter arrays. Most essential is it for static FP filter arrays. Using nanoimprint technology, the whole cavity structure including millions of FP filters (pixels) can be imprinted in a single step. Furthermore, the stamp/mold is reusable for many times. Theoretically, there is no limit in the number of FP filters (pixels) which can be defined within a single imprint step that generates all the different 3D cavities altogether [33–37]. Alternative methodologies have to use many more fabrication steps [28–31], which limits the number of pixels which can be manufactured in a realistic way. Among all the considered sensor types, the static FP filters make the most of the advantages of 3D nanoimprint lithography. Many FP filter arrays can be imprinted in a batch process at the same time, potentially resulting in a significant cost reduction. For

repetitive processes in large scale (mass production), nanoimprint lithography reveals its characteristic superiority in saving time, cost and effort.
