NL2019631B1 - Method for Fabrication of Large-Aspect-Ratio Nano-Thickness Mirrors - Google Patents

Abstract

The present invention is in the field of photonic crystal mirrors, which have a relatively large size, are extremely thin, have a low weight, have a large aspect ratio, a very good reflectance, and a high strength, as well as a method for 5 fabrication of such a device, and a product comprising said device, such as a lightsail.

Description

Title: Method for Fabrication of Large-Aspect-Ratio Nano-Thickness Mirrors

FIELD OF THE INVENTION

The present invention is in the field of photonic crystal mirrors, which have a relatively large size, are extremely thin, have a low weight, have a large aspect ratio, a very good reflectance, and a high strength, as well as a method for fabrication of such a device, and a product comprising said device.

BACKGROUND OF THE INVENTION

Photonic crystal mirror systems are considered to focus on the interaction between light and mechanical motion on low energy scales. In order to have enhanced capabilities one needs a high reflectivity, a low dissipation and a small mass. Achieving all of these in one relatively large device has been a challenge up to now.

Various investigations have been done on optomechanical systems .

Makles et al. in "2D photonic-crystal optomechanical nano resonator" Opt. Lett.40, 174-177 (2015), describes photonic crystal mirrors. Therein photonic crystal have also been fabricated on fully clamped square membranes which are not tethered to the substrate. While these are highly reflective (exceeding 99%), they do not exhibit the same mechanical isolation observed in trampoline structures. It is noted that clamping can reduce the mechanical quality factor.

Another recent research focuses on an optomechanical system combining a tethered trampoline membrane and photonic crystal arrays of holes. Norte et al. in "Mechanical resonators for quantum optomechanics experiments at room temperature" describes that despite having a high reflectivity, the mentioned optomechanical system, with photonic crystal arrays of holes does not exhibit a high mechanical dissipation.

Photonic crystal (optomechanical) mirror systems may be used in several applications, such as for testing macroscopic quantum physics, high precision sensors, e.g. chemical sensors, or accelerometers.

The present invention relates also to light sails. A light sail (also referred to as solar sail or photon sail) may be used for propulsion in space. It uses radiation pressure exerted by light on large mirrors. The light may originate from a star, such as the sun, or even a man-made external source, such as a laser. High-energy laser beams could be used as an alternative light source to exert much greater force than would be possible using sunlight, a concept known as beam sailing. The light exerts a force on the mirrors when reflected. It is therefore important to have a highly reflective mirror .

An advantage of a space craft having a light sail is a relatively low-cost operations and long operating lifetimes; in principle the source of light is of infinite nature. As light sails are relatively simple structures, they can be used often without deterioration.

In practice it has been found that solar pressure indeed affects spacecrafts. For long distance travelling a spacecraft will be displaced thousands of kilometres by solar pressure. Also an orientation of a space craft may be influenced.

For specific examples, such as light sails, relatively large mirrors are required. Prior art mirrors are limited in size to typically less than 1 cm2. To give some idea about forces, in an example of a huge 1000 by 1000 meter mirror the force is only about 8 Newtons (at a distance of 150*106 km to the sun). It is noted that electric engines provide similar forces .

The present invention therefore relates to an improved optomechanical system, which solves one or more of the above problems and drawbacks of the prior art, providing reliable results, without jeopardizing functionality and advantages.

SUMMARY OF THE INVENTION

It is an object of the invention to overcome one or more limitations of the devices of the prior art and at the very least to provide an alternative thereto. In a first aspect, the invention relates to a photonic Large-Aspect-Ratio Nano-Thickness Mirror assembly according to claim 1. The present invention relates to an optomechanical system with a low mass, a high mechanical quality factor. A photonic crystal mirror assembly (see fig. 1; 100) comprising a 2-2000 nm thin film membrane 12, which may be tethered, comprising a material with a tensile strength > 0.5 GPa. The membrane is connected to a substrate frame 17. The mirror is a patterned photonic crystal array having at least one array with reflective holes 14. A typical membrane window cross-sectional dimension A-A' is 10 mm to 300 mm; however larger areas can be made with the present method without any issue, such as up to a few meters. In an alternative an assembly of the present mirrors may be provided, such as an assembly of 2-210 mirrors. The surface area 5 of the holes is adapted for reflecting light, which acts as a high reflectivity mirror for impinging light, e.g. a free space laser or the sun. The array of holes is preferably periodical in at least one dimension, preferably in two dimensions, i.e. forming a regular row or column and preferably regular rows and columns. The membrane is relatively thin and preferably as thin as possible, having a thickness of 3-250 nm, preferably 4-100 nm, more preferably 5-50 nm, such as 10-20 nm. The system comprises a thin film membrane with a material with a high tensile strength >0.5 GPa. A high tensile strength material is found to improve the mechanical quality factor. The system comprises a patterned photonic crystal array functioning as a mirror, which is typically in a central location of the mirror or all over the mirror. For some applications the membrane comprises holes over substantially (90— 99.9%) all of its surface, such as to have an as high as possible reflective area. Such a photonic crystal array is made of holes together forming a combined mirror. The holes preferably have a circular i.e. cylindrical shape to have minimized scattering and losses, but may also be square, rectangular, or multigonal, such as hexagonal. The holes preferably also have a contracting characteristics, meaning that they relax in such a way that they contract (diminish in size) slightly and thereby increase the stress.

The membrane in the present invention could be as thin as 2-500 nm, but typically is 2-100 nm in thickness, such as 50 nm. In order to have a high reflectiveness the holes are adapted, typically in their top surface area (per hole); it is noted that formally a hole can not have a surface; a reference to such a surface is then regarded to be a virtual surface of the hole. By optimally adapting the holes it has been found that almost every photon (99,99%) can be reflected. In order to suspend the membrane a frame is provided. The frame is preferably as thin and as small as possible, in view of weight. In view of strength, the frame is preferably not too small/thin. It has been found that a substrate frame with a height h of 10-500 pm, preferably 50-100 pm, and a frame lower width fw of < 10% of a width of the membrane mw performs well. It is preferred to have a high aspect ratio frame. A second aspect the invention relates to a product comprising at least one present mirror assembly. A third aspect the invention relates to a light sail. A fourth aspect the invention relates to a method of making the present photonic crystal mirror assembly comprising various steps, e.g. of providing a substrate, such as Si, and glass. The Si substrate thickness is in range of 10 pm-20 mm, preferably 50 pm-2 mm, more preferably 100 pm-1 mm, such as 200 pm-500 pm. The substrate is preferably pre-etched to reduce its thickness. Thereafter a step of depositing a high tensile stress layer, such as a SiN layer. It is preferred to use a very accurate ratio of chemical precursors: for instance when NH3 and S1H2CI2 are used a ratio of 3:1 is used, and it is preferred to use a ratio in between 310.2:1, preferably 310.1:1, more preferably 310.05:1. Such may be achieved by limiting variations in the respective gas flows accordingly over a time of deposition. More in general, for a given stoichiometry relative variations should be in the same order or less, i.e. less than about 6%, preferably less than about 3%, more preferably less than about 1.5%, such as less than 1%.

The stress layer may have a thickness of 2-2000 nm. The high stress layer is thereafter patterned to form holes, such as by using an electron beam resist for the holes. The Electron beam resist used in the present invention may be a standard E-beam resist, i.e. ZEP. The resist is patterned using electron beam lithography to define various elements of the present system, such as a window. A system used may be EBPG 5000 or EBPG 5200 (of Raith). It has been found that by using a smaller wavelength of electrons, compared to the wavelength of light used in photo-lithography, a higher resolution compared to photolithography is obtained. Photo-lithography could also be used, but such would imply a need of more time and additional calibration. After patterning the resist is developed and rinsed. Then directional plasma etching is performed to form the array of holes, e.g. by using CHF3, or C4F8/SF6. In view of time needed for etching it is noted that an etching rate of a material such as S13N4 is around 1 nm/sec. For releasing the membrane a wet etch or a dry etch process may be used; said dry etch release could be performed in space. Prior to releasing the membrane a part of the substrate under a to be formed membrane is pre-etched to a thickness of 1-50 pm, preferably 2-10 pm, such as 3-5 pm. This etching of a part of the substrate can be done in an initial stage of the present method, such as at the beginning, or just before releasing the membrane. For this pre-etch typically a wet etch is used. The remainder of the substrate is found to provide a good stability, which is important when forming large mirrors. The remainder of the substrate under the to be formed membrane is then etched, therewith releasing the membrane. For the wet etch a KOH solution may be used. The dry etch can use similar chemicals as above. A temperature used for wet etching is found to be not very critical and could therefore be from room temperature up to 80 °C, e.g. 75 °C. Wet etching can be used in this step due to higher aspect ratio achieved by wet etching compared to dry etching. By using this release step it has been found that the stress can be engineered, i.e. the stress is increased up to values well above 1 GPa, such as > 5GPa.

The present invention provides a solution to one or more of the above mentioned problems and overcomes drawbacks of the prior art.

Advantages of the present description are detailed throughout the description.

DETAILED DESCRIPTION OF THE INVENTION

In an exemplary embodiment of the present photonic mirror assembly, for a given wavelength or range of wavelengths it has been found that the best results in terms of reflectance (%) is when the radius or cross-sectional length of the holes is about 0.25-0.5* of a wavelength to be reflected, preferably 0.3-0.45, more preferably 0.33-0.40 of said wavelength. For instance for a wavelength of 1550 nm the height is at least 150 nm, preferably 200 ran or more. Likewise, if a wavelength range is provided, such as from 360-600 nm with a weighted mean of 480 nm the height is preferably 160 nm. For some applications such lower reflectance could still be acceptable. Suitable mirrors can be made for optical wavelength in a range of 210-3000 nm. For each wavelength a suitable reflective material can be selected.

In an exemplary embodiment of the present photonic mirror assembly for a given wavelength or range of wavelengths the holes have a cross-sectional length 7 which is 0.25-0.50 * wavelength or 0.25-0.50 * weighted mean of said range of wavelengths, respectively.

The space area 8 between the holes (i.e. total mirror area minus the sum of hole areas) is in a range of 35-97% of a surface area 13 of the mirror, preferably 50-80%, such as 60-75%, and the remainder of the surface area of the mirror is thus being formed by the holes. In a similar approach a lattice constant may be used as a reference, the lattice constant being a distance between two adjacent or periodical holes for one dimension. The radius of the holes is preferably selected such that it falls in the range of 0.1-0.45 * lattice constant, preferably 0.12-0.4, more preferably 0.15-0.35, such as 0.2-0.3 * lattice constant.

To reduce losses and scattering and to have a high reflectivity, the width of the preferably circular holes are substantially the same and tuned to be around 0.25-0.50 * wavelength, typically 0.33-0.4*wavelength. The said holes may be ordered periodically. The photonic crystal mirrors made by using holes are able to achieve a reflectivity exceeding 99.9% without the need to fabricate expensive and complicated multilayer stacks of dielectrics.

In an exemplary embodiment of the present photonic mirror assembly the frame has an upper width fu of 1-2 times of a lower width fw, preferably of 1.001-1.1 * fw, more preferably of 1.002-1.05 * fw, such as 1.005-1.02 * fw. By making such width good properties are obtained.

In an exemplary embodiment of the present photonic mirror assembly the height h of the substrate is 10-300 pm, preferably 20-250 pm, more preferably 50-200 pm, such as 100-170 pm.

In an exemplary embodiment the present photonic mirror assembly comprises ie[2,210] arrays with holes, preferably 4-512 arrays, more preferably 4-256 arrays, wherein m and mi of each array i are chosen independently. So large mirrors, or combined mirrors can be made with a large flexibility in design .

In an exemplary embodiment of the present photonic mirror assembly the thin film membrane 12 has a thickness of 3-300 nm, preferably 5-200 nm, more preferably 10-100 nm, such as 20-50 nm. The membrane is preferably as thin as possible. In view of strength a smallest thickness is limited somewhat.

The present system has improved characteristics, i.e. a good reflectivity (> 99.99%), a low mass, a low noise, and a low dissipation, compared to the prior art.

In an exemplary embodiment of the present photonic mirror assembly the membrane is formed of a material selected from S13N4, S1O2, SiC, InGaP, Si, and combinations thereof. It is found that by depositing a layer, such as S13N4, by low pressure chemical vapour deposition (LPCVD) with high (silicon) substrate temperatures (300 - 700 °C) and preferably a low deposition rates (0.5-5 nm/min.) increased condensation reactions during film growth and high stress film are obtained. In this respect also a gas ratio of chemicals used is controlled.

In an exemplary embodiment of the present photonic mirror assembly the tensile stress is >1 GPa, preferably > 2 GPa. Maximum values that were obtained are in the order of 4-5 GPa, i.e. close to rupture of the layers. Such high values are obtained by not relaxing the layers deposited and optionally also further increasing the stress, especially of the tethers. It has been found that in high stress membranes mechanical frequencies are achieved which are independent of thickness and are stress dominated. It is noted that an ultimate yield strength of a S13N4 thin films is about 6 GPa, which may be a result of the present processing.

In an exemplary embodiment of the present photonic mirror assembly a surface area of the crystal array is in a range 10 cm2-10 m2, hence relatively big. The surface area of the crystal array may depend on a final application and an amount of power and frequency that is needed to be generated. For instance to be used as a chemical sensor, or a light sail, a higher surface area for the photonic mirror assembly could be used.

In a further aspect the present invention relates to a product comprising the present mirror assembly, such as a light sail, a deformable mirror, a Quantum transducer, a sensor, such as a chemical sensor, an accelerometer, preferably comprising an optical read out system, wherein the read out system is capable of detecting or measuring at least one of a change in frequency, a change in amplitude, and a change in damping. The present invention can be used in high precision measurements, ultra-high resolution force and mass sensors, and optical sensors. Optical sensors can be used in very sensitive conditions.

In a further aspect the present invention relates to a light sail, wherein the light sail is deployable. As such the sail can be brought into space and deployed.

In an exemplary embodiment the present light sail comprises tethers (11) and wherein the light sail comprises two or more mirror assemblies, preferably 5-10 assemblies.

In an exemplary embodiment the present light sail comprises two or more mirror assemblies, preferably 5-100 assemblies .

In an exemplary embodiment the present light sail has a regular shape, such as circular, ellipsoidal, square, rectangular, triangular, and multigonal, such as hexagonal and octagonal .

In an exemplary embodiment the present light sail comprises a means for deploying the sail.

In an exemplary embodiment the present method comprises a step of reducing of the stress at the central part of the mirror .

In an exemplary embodiment, method of producing a photonic mirror comprises the steps of providing a substrate, such as Si, depositing a high stress layer, and forming the array of holes.

The high stress layer could be S13N4 deposited by low pressure chemical vapour deposition (LPCVD) on <100> Silicon wafer substrates, or other high stress layers such as S1O2,

SiC, InGaP and Si. Precursors used to deposit S13N4 are di-chlorosilane (S1H2CI2) (DCS) and ammonia (NH3) . It is found that S13N4 layers deposited by LPCVD at 300-700 °C have few impurities (impurities are annealed at high temperature) and low optical absorptions, which is found crucial for minimizing optical losses. The higher the deposition temperature of S13N4, the higher stress is obtained (100 MPa-1.5 GPa). The deposition rate is around 1 nm/min, and a typical thickness of S13N4 layers in this invention is 15 nm. The surface area roughness of the S13N4 layers is better than 2 nm as can be measured by light scattering (e.g. Semilab SRP-2100); hence a very smooth surface is obtained.

The invention will hereafter be further elucidated through the following examples which are exemplary and explanatory of nature and are not intended to be considered limiting of the invention. To the person skilled in the art it may be clear that many variants, being obvious or not, may be conceivable falling within the scope of protection, defined by the present claims.

SUMMARY OF THE FIGURES

Figures la,b-3 show certain aspects of the present assembly .

Figures 4 shows schematics of a light sail. DETAILED DESCRIPTION OF FIGURES In the figures: 100 mirror assembly 200 light sail 5 surface area hole 7 cross-sectional length hole 8 space area between holes 9 array of holes 11 tether 12 membrane 13 surface area mirror 14 hole 17 substrate/frame A-A' cross section membrane fu frame upper width fw frame lower width m„ membrane width

Figure la shows a fabricated device 100. Therein a Si substrate 17 is partly etched in a central part thereof. A central membrane 12 is provided.

Figure la shows the membrane 12 having a certain width mw. The frame 17, supporting the membrane, has a height h, an upper width fu, and a lower width fw.

Figure 2 shows a schematic layout of the membrane 12.

Four optional tethers 11 are shown attached to the membrane 12. In a central part a mirror 13 is provided with a regular two-dimensional array of holes 14. Each hole has a surface area 5. Typically the surface areas (and likewise heights) of the holes are substantially the same or equal with respect to one and another (90-110% relative, preferably 99-101% relative, with respect to a mean surface area/height). A dotted line A-A' is indicated. Further a width 7 of holes is indicated .

Figure 3 shows a schematic representation of the present mirror. Also the array of holes 9 is indicated.

Figure 4 shows a light sail 200, with some mirror assembly with arrays of holes 9 indicated therein. Typically most or the whole area of the sail would be covered with mirrors. The light sail may comprise a large number of present assemblies, together forming one sail.

Experiment A substrate, typically a Si wafer, is provided, on which 250 nm S13N4 is grown using an LPCVD technique with S1H4, NH4+ at about 10 kPa at a growth rate of 50 nm in 13 min. In a subsequent step a resist is spun on both sides. An optical lithographic step is used to define a window on a top part of the product. The window is then developed and rinsed thereby defining a frame. The exposed silicon is removed by a KOH etch step. On a top side a second resist is spun and a mask is used to define holes. The holes are exposed in a subsequent lithographic step, typically using an E-beam (EBPG6-5000 system) and "ZEP" E-beam resist. The holes in the silicon nitride are formed by C4F8/SF6 plasma etch. Thereafter the remaining resist on the top and bottom side are removed, such as by a wet etch.

In a next step the substrate (Si) is etched through using 30% KOH or TMAH, at an etch rate of about 1 pm/min, leaving behind the suspended structure, a frame, and holes together forming a mirror. Likewise a dry etch may be used.

For the purpose of searching the following section is added, of which the last section represents a translation into Dutch. 1. A photonic Large-Aspect-Ratio Nano-Thickness Mirror assembly (100) having a size > 1*1 cm2 and a weight of < 1 g/m2, comprising a 2-2000 nm thin film membrane (12) comprising a material with a tensile strength > 0.5 GPa, wherein the membrane is a patterned photonic crystal array having at least one n*m array (9) with holes, wherein a surface area of the holes (5) and array of holes are adapted for reflecting light, wherein the membrane is provided on a substrate frame (17), wherein the substrate frame has a height h of 10-500 pm, and a frame lower width f„ of < 10% of a width of the membrane mw. 2. Photonic mirror according to any of the preceding embodiments, wherein for a given wavelength or range of wavelengths the holes have a cross-sectional length (7) which is 0.25-0.50 * wavelength or 0.25-0.50 * weighted mean of said range of wavelengths, respectively, 3. Photonic mirror according to any of the preceding embodiments, wherein a space area (8) between the holes is in a range of 35-97% of a surface area of the mirror (13), the remainder of the surface area of the mirror being formed by top surfaces of the holes. 4. Photonic mirror according to any of the preceding embodiments, wherein the frame has an upper width fu of 1-2 times of a lower width fw, preferably of 1.001-1.1 * fw, more preferably of 1.002-1.05 * fw, such as 1.005-1.02 * fw. 5. Photonic mirror according to any of the preceding embodiments, wherein the height h of the substrate is 10-300 pm, preferably 20-250 pm, more preferably 50-200 pm. 6. Photonic mirror according to any of the preceding embodiments, comprising ie[2,210] arrays with holes, wherein ni and mi of each array i are chosen independently. 7. Photonic mirror according to any of the preceding embodiments, wherein the thin film membrane (12) has a thickness of 3-300 nm, preferably 5-200 run, more preferably 10-100 run, such as 20-50 nm. 8. Photonic mirror according to any of the preceding embodiments, wherein the membrane is formed of a material selected from S13N4, S1O2, SiC, InGaP, Si and combinations thereof. 9. Photonic mirror according to any of the preceding embodiments, wherein the tensile stress is >1 GPa, preferably > 2 GPa . 10. Photonic mirror according to any of the preceding embodiments, wherein a surface area of the crystal array is in a range 10 cm2-10 m2. 12. Product comprising at least one mirror assembly according to any of the preceding embodiments, wherein the product is selected from a light sail, a deformable mirror, a Quantum transducer, a sensor, such as a chemical sensor, an accelerometer, preferably comprising an optical read out system, wherein the read out system is capable of detecting or measuring at least one of a change in frequency, a change in amplitude, and a change in damping. 13. LightSail according to embodiment 12, wherein the light sail is deployable. 14. LightSail according to embodiment 12 or 13, wherein the light sail comprises tethers (11) and wherein the light sail comprises two or more mirror assemblies, preferably 5-100 assemblies . 15. LightSail according to any of embodiments 12-14, wherein the light sail has a regular shape, such as circular, ellipsoidal, square, rectangular, triangular, and multigonal, such as hexagonal and octagonal. 16. LightSail according to any of embodiments 12-15, wherein the light sail comprises a means for deploying the sail. 17. Method of producing a photonic crystal mirror according to any of the preceding embodiments, comprising providing a substrate, providing a high tensile strength material on the substrate, patterning the high tensile strength material, etching holes in the high tensile strength material, pre-etching a part of the substrate under a to be formed membrane to a thickness of 1-50 pm, preferably 2-10 pm, and under etching substrate under the high tensile strength material thereby forming the membrane. 18. Method according to embodiment 17, wherein under etching is performed in space.

Claims (17)

A photonic nano-thick mirror structure (100) with a large aspect ratio with a size of 1 x 1 cm 2 and a weight of <1 g / m2, comprising a thin film membrane (2) of 2-2000 nm comprising a material with a tensile strength > 0.5 GPa, wherein the membrane comprises a patterned photonic crystal array with at least one n * m array (9) with holes, a surface of the holes (5) and array of holes being adapted to reflect light, wherein the membrane is mounted on a substrate frame (17), the substrate frame having a height h of 10-500 µm, and a frame lower width fw of <10% of a width of the membrane mw. Photographic mirror according to one of the preceding claims, wherein the holes for a given wavelength or range of wavelengths have a cross-sectional length (7) of 0.25-0.50 * wavelength or 0.25-0.50 * respectively weighted average of the wavelength range. A photographic mirror according to any one of the preceding claims, wherein a space region (8) is between the holes in a range of 35-97% of an area of the mirror (13), the remainder of the surface of the mirror being formed through upper surfaces of the holes. A photographic mirror according to any one of the preceding claims, wherein the frame has an upper width fu of 1 to 2 times a lower width fw, preferably of 1, 001-1, 1 * fw, more preferably 1, 002-1.05 * f ", such as 1,005-1.02 * f". A photographic mirror according to any one of the preceding claims, wherein the height h of the substrate is 10-300 µm, preferably 20-250 µm, more preferably 50-200 µm. A photographic mirror according to any one of the preceding claims, comprising ie [2,210] arrays with holes, wherein m and mi of each array i are independently selected. A photographic mirror according to any of the preceding claims, wherein the thin film membrane (12) has a thickness of 3-300 nm, preferably 5-200 nm, more preferably 10-100 nm, such as 20-50 nm. A photographic mirror according to any one of the preceding claims, wherein the membrane is formed from a material selected from S13 N4, SiCb, SiC, InGaP, Si and combinations thereof. A photographic mirror according to any one of the preceding claims, wherein the tensile strength is> 1 GPa, preferably> 2 GPa. The photographic mirror of any one of the preceding claims, wherein a surface of the crystal array is in a range of 10 cm 2 - 10 m 2. 12. Product comprising at least one mirror assembly according to one of the preceding claims, wherein the product is selected from a light sail, a deformable mirror, a quantum transducer, a sensor, such as a chemical sensor, an accelerometer, preferably comprising an optical read-out system wherein the readout system is capable of detecting or measuring at least one of a change in frequency, an amplitude change, and a change in attenuation. A light sail according to claim 12, wherein the light sail is foldable. A light sail according to claim 12 or 13, wherein the light sail comprises connections (11) and wherein the light sail comprises two or more mirror compositions, preferably 5-100 compositions. A light sail according to any one of claims 12-14, wherein the light sail has a regular shape, such as circular, elliptical, square, rectangular, triangular and multi-angular, such as hexagonal and octagonal. A light sail according to any one of claims 12-15, wherein the light sail comprises means for unfolding the sail. A method for manufacturing a photonic crystal mirror according to any one of the preceding claims, comprising providing a substrate, providing a material with a high tensile strength on the substrate, patterning the material with a high tensile strength, etching holes in the high-tensile material, pre-etching a portion of the substrate under a membrane to be molded to a thickness of 1-50 ym, preferably 2-10 ym, and under-etching substrate under the high tensile material through which the membrane is being formed. The method of claim 17, wherein the under-etching is performed in the space.