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Performance of Fabry–Perot microcavity structures with corrugated diaphragms
Sensors and Actuators 79 Ž2000. 162–172 www.elsevier.nlrlocatersna
Performance of Fabry–Perot microcavity structures with corrugated diaphragms Jaeheon Han a
a,)
, Jiyoung Kim b, Tae-Song Kim c , Jeong-Seog Kim
d
Department of Electronic Engineering, Kangnam UniÕersity, San 6-2 Kukal-Ri, Kiheung-Eup, Yongin City, Kyunggi-do 449-702, South Korea b Department of Materials Engineering, Kookmin UniÕersity, Seoul, South Korea c Thin Film Technology Research Center, KIST, Seoul, South Korea d Department of Materials and Mechanical Engineering, Hoseo UniÕersity, Chungnam, South Korea Received 9 February 1999; received in revised form 26 July 1999; accepted 29 July 1999
Abstract A Fabry–Perot microcavity structure with a corrugated diaphragm as a deflecting diaphragm has been fabricated successfully. The composite dielectric layers of movable top and stationary bottom diaphragm of Fabry–Perot microcavity are optimized to have proper mechanical stability and optical response. Deflection behavior and device characteristics of a corrugated diaphragm case are compared with those of a planar diaphragm case. Output signal degradation as a function of pressure, ‘‘signal averaging effect’’, is reduced using corrugated top diaphragm structures over planar top diaphragm structures. This is achieved by improving the flatness of the deflecting diaphragm in the optically sampled area of the microcavity structures. However, the corrugated structure shows a static deflection of the diaphragm without applying pressure due to the localized internal stress generated by the asymmetry of the corrugation on the diaphragm, ‘‘zero-pressure offset effect’’. The existence and the influence of these parasitic effects have been observed by both real-time measurement and analytical simulation of the diaphragm. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Fabry–Perot microcavity structure; Corrugated diaphragm; Signal averaging effect; Zero pressure offset effect; Confocal scanning laser microscope
1. Introduction Fabry–Perot cavity-based structures have been widely used for their versatility and tunability such as pressure sensors, temperature sensors, chemical sensors, and tunable optical filters and amplifiers w1–4x. This kind of sensor detects changes in optical path length induced by either a change in the refractive index or a change in physical length of the cavity. Conventionally, these Fabry–Perot-based sensors have been manufactured by using a hybrid two-wafer assembly technique that requires an expensive and difficult fusion bonding process w4,5x. The fusion bonding process limits the flexibility and the accuracy of the dimensions of the device structures. Silicon Very Large Scale Integration ŽVLSI. fabrication technology-based micromachining techniques have recently
)
Corresponding author. Tel.: q82-331-280-3806; fax: q82-331-2803750; E-mail: [email protected]
adopted to build miniature Fabry–Perot sensors w6x. Micromachining techniques make Fabry–Perot sensors more attractive by reducing the size and the cost of the sensing element. Another advantage of the miniature Fabry–Perot sensors is that low coherence light sources, such as light emitting diodes ŽLEDs., can be used to generate the interferometric signal, since the optical length of the miniature cavity is of the same order as the wavelength of the light, and shorter than the coherence length of a typical LEDs. Also, remote sensing and signal acquisition can be achieved without loss of ratio of signal to noise ŽSrN ratio. in harsh environments, by using the Fabry–Perot cavity and optical fiber as the sensing element and interconnect, respectively. One of the major obstacles to commercialization of the miniature Fabry–Perot cavity-based sensors is the degradation of device performance due to non-planar deflection of a deflecting diaphragm. In this paper, we demonstrate how the deflection behavior of a diaphragm and performance of Fabry–Perot microcavity systems are improved by adding a corrugation ring in a planar, circular diaphragm as a deflecting top diaphragm.
0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 9 . 0 0 2 6 7 - 8
J. Han et al.r Sensors and Actuators 79 (2000) 162–172
2. Fabrication of a corrugated top diaphragm structure A schematic fabrication procedure of Fabry–Perot microcavity structure with a corrugated top diaphragm as a deflecting diaphragm is shown in Fig. 1. Fabry–Perot microcavity having the size of several hundreds microns is embedded between one movable and one static diaphragms. Each diaphragm consists of multiple film stacks having two silicon nitride layers cladding a silicon dioxide layer. These dielectric films are deposited using Low Pressure Chemical Vapor Deposition ŽLPCVD.. The thickness of each layer is chosen in such a way that the Fabry–Perot microcavity is mechanically stable and must also have optimal optical response w8,9x. Total residual stress of the stack should be weak tensile to allow the diaphragm to remain flat and total reflectance of Fabry– Perot microcavity can be adjusted between 0.1 and 0.5 to obtain maximum variation of an amplitude and optimal range of a linearity of the measured optical response. Taking both the mechanical stability and the optical response into account, optimal film thickness ratio of the silicon dioxide to the silicon nitride is determined to be 3 to 3.5 experimentally. It is observed that with this ratio, the measured tensile residual stresses of the stacked layers of a top and a bottom diaphragm are between 0.1 and 0.2 GPa by using beam curvature method w10x. The first step of fabrication is to deposit sacrificial ˚ thick silicon nitride and 5000 A˚ dielectric layers, 300 A
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thick silicon dioxide stack. These are deposited by the ˚ silicon dioxide is the main LPCVD method. The 5000 A ˚ silicon nitride is the sacrificial layer. The thin 300 A barrier layer to protect the main sacrificial layer from overetching damage of the KOH wet anisotropic silicon substrate etching step. Then the bottom diaphragm dielectric stack is deposited directly on top of the sacrificial dielectric layers. The bottom diaphragm consists of two ˚ thick silicon nitride layers and a 4500-A˚ thick 750-A silicon dioxide layer deposited by the LPCVD method. The following step is the patterning and plasma etching of the dielectric stack deposited on the backside of the double-side polished wafer. Then, by using the patterned back side dielectric layers as masking layers, the silicon substrate is anisotropically etched with 40% KOH solution at 808C from the back-side of the wafer to form the square dielectric bottom diaphragm on the front side of the wafer. At this stage, the defined bottom diaphragm is the combined dielectric stack of both sacrificial and bottom diaphragm layers. The next step is to form the etch windows on the bottom diaphragm using plasma etching process from the front side of the wafer. The etch windows allow access to the sacrificial polysilicon layer to form an air gap between top and bottom diaphragm in the final stage of the fabrication. The etching should stop at approximately onehalf of the total thickness of the sacrificial silicon dioxide layer after the complete removal of the bottom diaphragm dielectric layers inside the patterned etch window area.
Fig. 1. Schematics of fabrication procedure of a corrugated Fabry–Perot cavity device. Ža. Formation of bottom membrane layers and etch windows. Žb. Patterning of a sacrificial polysilicon and a corrugation. Žc. Deposition of top membrane layers. Žd. Removal of the backside stacked layers and a sacrificial polysilicon.
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Fig. 2. Schematic views of cross-sections and optical micrographic top views of a planar and a corrugated top diaphragm Fabry–Perot cavity devices.
This will prevent any void or discontinuity of the subsequently deposited layers in the etch window while the bottom diaphragm is still continuous due to the remaining sacrificial dielectric layer. Then, 0.7 mm thick LPCVD undoped polysilicon layer is deposited and patterned as the air gap portion of the Fabry–Perot microcavity. The next step is defining corrugation ringŽs. by patterning and plasma-etching the sacrificial polysilicon layer. After stopping plasma polysilicon etching at about one-half of the total thickness of the deposited polysilicon with corrugation patterning, another ˚ thick silicon nitride layers dielectric stack of two 1750-A ˚ and 10,500-A thick silicon dioxide layer is overcoated to form a corrugated top diaphragm with sealed microcavity. Single or multiple circular corrugations on a top diaphragm are implemented on the outside of the optically sampled area defined by a bottom diaphragm Žan outer corrugation ring scheme.. This is to avoid the unwanted interference of optical response by the corrugation region having different microcavity gap spacing compared with the rest of planar region in the top diaphragm and is to make the corrugation contribute solely to affect mechanical properties of a deflecting top diaphragm. The bottom diaphragm area of the top diaphragm microcavity structure is considered as the active area, in other words, the optically sampled area, since the bottom diaphragm area defines the transmitted beam area. If the corrugation ring is placed in the portion of the top diaphragm coupled with the underneath bottom diaphragm, this scheme Žan inner corrugation ring scheme. will have an influence on both the flexibility of the diaphragm and the change in Fabry– Perot microcavity gap spacing.
The stacked dielectric layers, and sacrificial silicon nitride and silicon dioxide buffer layers on the backside of the wafer are removed by the combination of blanket wet and plasma etching methods. This reveals the sacrificial polysilicon through the etch windows on the bottom diaphragm to be seen from the backside of the wafer. The sacrificial polysilicon is etched off using KOH solution through these etch windows. Both the top and the bottom diaphragms are freed to form microcavity structure after removing the sacrificial polysilicon layer. For the fabrication of a planar Fabry–Perot microcavity structure, the corrugation masking step is skipped from the above-described fabrication procedure. Fig. 2 shows the schematic views of the cross-sections and the optical microscopic top views of a planar and a corrugated top diaphragm Fabry– Perot microcavity structures.
3. Experimental analysis Optical response is measured by using a 2 = 2 optical fiber directional coupler setup shown in Fig. 3Ža.. A 633-nm He–Ne laser is focused to the one end of input ports of the directional coupler and a reflected intensity is measured from the other end of input ports. One end of output ports is connected to a Fabry–Perot cavity device placed in a sample chamber. The transmitted intensity is obtained by a photodetector placed right after the sample chamber that is connected to a compressed dry air pressure line and a pressure controller. The other end of output ports is dumped into index matching liquid to avoid any reflected light at the end of the unused port of the direc-
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Fig. 3. Schematic view of an optical measurement setup. Ža. Overall scheme; Žb. configuration of a sample chamber for the alignment of an optical fiber.
tional coupler. For high signal-to-noise ratio a chopper and lock-in amplifiers are used. The optical fiber consists of a 100-mm diameter core coated with a 45-mm thick cladding layer. The optical fiber is aligned to the Fabry–Perot microcavity by adjusting the micro XYZ translation stage while monitoring the transmitted intensity detected from the photodetector through the sample as shown in Fig. 3Žb.. The measured transmittance is obtained from the measured transmitted intensity by comparing a Fabry–Perot microcavity and a pinhole Žno Fabry–Perot microcavity. structure having the same size of optical beam transmission area. This is reasonable because the measured transmitted intensity of the pinhole corresponds to the transmittance of unity. The pinhole structure is obtained by removing the fabricated Fabry–Perot cavity structure off from the device using ultrasonic treatment. This leaves opening pinhole structure and the size of the pinhole is equal to the size of the bottom diaphragm Žoptical beam transmission area, which is named optically sampled area. of the fabricated Fabry–Perot cavity device. Fig. 4 shows pressure vs. transmittance plot of a planar and a corrugated device having 300 mm diameter top diaphragm as a deflecting diaphragm. A corrugated device has single 30-mm width corrugation ring placed on the
outside of the optically sampled area of a top diaphragm. For the case of a planar top diaphragm ŽFig. 4Ža.., the signal averaging effect of optical response prevails as the applied pressure increases. The signal averaging effect, that is, pressure-dependent degradation of output optical response, is caused by variation in the amount of deflection over the optically sampled area due to the bowing nature of the boundary cramped deflecting diaphragm. Since it is impossible to build an unclamped, free-standing, planar-moving diaphragm in the real world, the focus is to minimize the non-planarity of the deflection under the applied external load. The first approach is to control the active device area, i.e., the ‘‘optically sampled area’’, by maximizing the area ratio of a moving top diaphragm to a stationary bottom diaphragm w7x. As shown in Fig. 5, the optically sampled area, the active area in the device, is defined by the minimum transmitting area throughout the entire path of the optical beam from the optical fiber to the photodetector via the cavity structure in case of the transmitted intensity measurement. This is equivalent to the area of a bottom diaphragm in our top diaphragm device. Fig. 5 also shows that the difference in Fabry–Perot cavity gap spacing between the center position A and the edge position B of the optically sampled area becomes larger
Fig. 4. Transmittance as a function of pressure of Fabry–Perot cavity devices having a 300-mm diameter Ža. planar top diaphragm and Žb. corrugated top diaphragm.
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Fig. 5. Schematic view showing the ‘‘optically sampled area’’ of the transmitted intensity measurement.
and subsequently, the variation of the resultant transmitted intensity as a function of the edge-to-center distance of the optically sampled area Žfrom B to A. becomes greater with increasing deflection of the moving top diaphragm. Since sinusoidal nature of a Fabry–Perot cavity optical response causes possible cancellation of positive and negative transmitted intensity values from the different positions in the optically sampled area of a diaphragm, the detected transmitted intensity with actual bowed diaphragm can be lower than the expected one with ideal planar diaphragm with no bowing. This explains why signal averaging effect occurs, especially with increasing deflection of a movable diaphragm. The degree of the parasitic signal averaging effect becomes larger with increasing the degree of the curvature of a deflecting diaphragm within the optically sampled area. The curvature becomes smaller by increasing the area ratio of a moving top diaphragm to a stationary bottom diaphragm. This suggests that the larger the size of a moving top diaphragm with constant size of a stationary bottom diaphragm becomes, the lesser the signal averaging effect occurs. The second approach is to add corrugation on the deflecting diaphragm. For a corrugated top diaphragm case shown in Fig. 4Žb., transmittance increases steadily with
pressure until it reaches a maximum and then decreases with further increase in the applied pressure. This result suggests that at zero pressure the corrugated top diaphragm is already deflected, concave in our case, due to the non-uniformly distributed out-of-plane internal stress induced by the asymmetry of the corrugated structure with respect to the horizontal plane of the diaphragm. This behavior of change in transmittance can be explained as follows: Transmittance increases until reaching the maximum as the corrugated diaphragm becomes flat from initial concave shape. This follows degradation of transmittance due to signal averaging effect as the shape of the deflected diaphragm changes from flat to convex with further increase in pressure. This internal film stress induced deflection of a diaphragm without external load is called ‘‘zero pressure offset effect’’, and had been previously suggested through simulation works using finite element method w8,11x. Fig. 6 shows transmittance behavior of a Fabry–Perot cavity structure having 200 mm diameter top diaphragm with and without a 30-mm width corrugation ring. Comparison of a 200-mm ŽFig. 6Žb.. and a 300-mm ŽFig. 4Žb.. diameter corrugated top diaphragm device confirms zero pressure offset effect while varying the compliance of a diaphragm depending on the size of a diaphragm. This comparison also shows that transmittance plot of 200 mm corrugated top diaphragm device has no degradation region caused by signal averaging effect contrary to that of 300 mm corrugated top diaphragm device, for the pressure ranging to 12 psi. This is because smaller diaphragm has better stiffness and moves shorter distance under the same applied pressure. In addition, the parasitic signal averaging effect of 200 mm diaphragm device is larger than that of 300 mm diaphragm device for both planar and corrugated cases. This is because the degree of flatness of a deflecting diaphragm within the optically sampled area is enhanced by increasing the area ratio of a moving top diaphragm to a stationary bottom diaphragm in case of larger top diaphragm device while having the same size of a bottom diaphragm Ž120 mm for planar device.. For corrugated devices, the size of a bottom diaphragm is 60 mm. The
Fig. 6. Transmittance as a function of pressure of Fabry–Perot cavity devices having 200 mm diameter Ža. planar top diaphragm and Žb. corrugated top diaphragm.
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corrugated top diaphragm devices have a smaller bottom diaphragm than the planar top diaphragm devices, because we designed the corrugation region to be placed at the outside of the optically sampled for a corrugated device. In this way, the Fabry–Perot cavity gap spacing in the optically sampled area is not interrupted by the topographical change in corrugation region. Because of different size of the bottom diaphragm, the absolute magnitude of the measured transmitted intensity should be different for both planar and corrugated device. However, the transmittance, as an intrinsic parameter, converted from the measured transmitted intensity is still not affected because it is obtained by comparing a Fabry–Perot cavity and its corresponding pinhole structure both having the same size of
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the optically sampled area Žbottom diaphragm.. Therefore, transmittance plots of planar and corrugated devices with same top diaphragm and different bottom diaphragm in size can be compared with each other. In our case, which is probably the first experimental demonstration of zero pressure offset effect, this effect is also graphically demonstrated with real-time, three-dimensional images by using confocal scanning laser microscope. Fig. 7 shows the real-time, 3-D images at 0 and 15 psi for the Fabry–Perot microcavity structures having 200 mm diameter top diaphragm with and without a 30-mm width corrugation ring. The obtained real-time, 3-D image is a quarter piece of a circular top diaphragm device. These images are generated by scanning a He–Ne laser beam
Fig. 7. Real-time, 3-D confocal scanning laser micrograph of 200 mm diameter top diaphragm devices. The 2-D cavity gap spacing Ž2-D height. is also shown through the radius Žedge-to-center distance. of the deflecting top diaphragm. The 2-D height measurement lines ŽW1-to-W2, X1-to-X2, Y1-to-Y2 and Z1-to-Z2. are crossing the etch-window-induced irregular area in topography. Ža. Planar device at 0 psi. Žb. Planar device at 15 psi. Žc. Corrugated device at 0 psi. Žd. Corrugated device at 15 psi.
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Fig. 7 Žcontinued..
with varying focal planes on the device placed on the sample stage of the microscope while supplying the pressure. In Fig. 7, the shape of the diaphragm is slightly concave at 0 psi and near flat at 15 psi for the corrugated device, while flat at 0 psi and convex at 15 psi for a planar device. This observation of a deflecting diaphragm is in good agreement with the characteristics of the transmittance plots shown in Fig. 6. This behavior can be described in detail from the real-time, 2-D cavity gap spacing plots as a function of the edge-to-center distance of a top diaphragm, Fig. 8, which is obtained from the corresponding 3-D images in Fig. 7. For the planar device, the gap
spacing increases proportionally with pressure, suggesting the uniform bowing of the diaphragm. However, for the corrugated device, while the gap spacing changes from concave at 0 psi to approximately flat with increasing pressure at the inner region of the top diaphragm. The optically sampled area, which is bottom diaphragm area in this case, is within the inner region, as shown in Fig. 8. The deflection, which started from the edge of the moving top diaphragm, seems to be mainly propagated into the outer region of the top diaphragm and confined in the corrugation region, while maintaining deflection-free movement in the inner region. This result suggests that the
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Fig. 8. Real-time, 2-D cavity gap spacing plot of Fabry–Perot cavity having 200 mm diameter Ža. planar top diaphragm and Žb. corrugated top diaphragm devices, with varying pressure. The measurement line is the radius Žedge-to-center distance. of a top diaphragm without crossing the etch-window-induced irregular area in topography in this case.
corrugation region behaves as a stress concentrator and buffer for the moving diaphragm. This is because the corrugation region behaves like a flexible hinge, changing its own shape rather than the shape of the entire diaphragm while absorbing the external load. It is also shown that the etch-window-induced non-uniformity in topography at the top diaphragm is localized and the overall deflection behavior of the top diaphragm is not significantly affected by this topographical non-uniformity. The magnitude of the zero pressure effect seems to be proportional to the size of a corrugated top diaphragm. This can be explained by the increase in the out-of-plane internal stress induced momentum with decreasing stiffness Žincreasing size and decreasing thickness. of the diaphragm. Extreme case of zero pressure offset effect can be a multiple corrugation top diaphragm device showing complete sticking of a multiple-corrugated top diaphragm to a bottom diaphragm without applying pressure. This is due to the excessive deflection of a diaphragm caused by the large downward out-ofplane internal stress of multiple corrugation rings. These above-observations suggest that it is possible to fabricate Fabry–Perot cavity structures with completely planar moving diaphragm in their useful operating input ranges by optimizing the stiffness of a diaphragm Žto prevent zero pressure offset. while adopting corrugation scheme Žto improve planar movement in the optically sampled area.. 4. Theoretical analysis Theoretical calculation of the deflection behavior of a diaphragm was performed for both planar and corrugated diaphragms. The modeling uses the following specific
parameters. The thickness for Si 3 N4 Ž h1 . and SiO 2 Ž h 2 . is ˚ respectively. Young’s modulus for 1500 and 10,500 A, Ž . Si 3 N4 E1 and SiO 2 Ž E2 . is 380 and 75 GPa, respectively. Residual stress for Si 3 N4 Ž s 1 . and SiO 2 Ž s 2 . is 1.1 and y0.1 GPa, respectively. Poisson’s ratio Žy . for both Si 3 N4 and SiO 2 is 0.2. The residual stresses, s 1 and s 2 , were measured using the beam curvature method with the film samples prepared on the same wafers where the real devices were being fabricated. Young’s modulus, E1 and E2 , are taken from the literature w12x. The detailed analytical modeling of a planar circular diaphragm case was described in our previous publication w7x. The deflection of a corrugated diaphragm with initial stress can be approximated by means of an analytical expression; a superposition of the linear model of a corrugated diaphragm without internal residual stress and of the non-linear model of the planar diaphragm with a large internal residual stress. The superposition is based on the assumption that the corrugated diaphragm can be modeled as a fictitious planar diaphragm, which locally has the same radial and tangential flexural rigidity as the corrugated diaphragm w13x. The behavior of a corrugated diaphragm with internal residual stress is described using superposition of a stressfree corrugated diaphragm and a planar diaphragm with internal residual stress, a planar diaphragm with an internal residual stress of s Bpr2.83 instead of s should be considered w14,15x. Thus, the following equation is obtained: ps4
h2 y A p E h2 2
a h
4
a
2
q
s Bp 2.83
Ž 1.
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where Ap s
2 Ž q q 1. Ž q q 3.
y2
ž
3 1y
/
q2
and Bp s 32
1yy 2 1
3yy
.
y
2
Ž q y y . Ž q q 3.
q y9 6
Also, the corrugation profile factor q can be represented as: 2
q s
S l
1 q 1.5
H2 h2
,
Ž 2.
where H is the depth of the corrugations, l is the corrugation spatial period and S is the corrugation arc length ŽFig. 9.. The q is equal to 1 for flat diaphragms Ž H s 0. and is larger than 1 for corrugated diaphragms. The above-equations show that the effect of internal residual stress is much smaller for corrugated diaphragms than for planar diaphragms, although it is still not negligible. By using the equivalent thickness Ž h., Young’s modulus Ž E ., and residual stress Ž s . of the composite films, distributed uniformly throughout the entire diaphragm, Wps Ž r ., WplŽ r ., and Wm Ž r . are defined as small pure plate, large pure plate, and pure membrane deflection distance as a function of the distance from the center of the diaphragm, respectively, while compensating for the effect of a corrugation. The corrugation compensation factors, A p and Bp , are added to the formula for the planar circular diaphragm case as follows: Wps Ž r . s
pa4
ž / ½ A p Eh3
Wpl Ž r . s p
Wm Ž r . s
1y
Ž 1 y y 2 . a4
2.83 p Bp s h
Bp hE
ž
a2 y r 2 4
r
ž / a
1y
/
.
2 2
, r
ž / a
Ž 3. 2 2
1r3
5
,
Ž 4. Ž 5.
Then, individual deflection distance as a function of the
Fig. 10. Calculated Wave as a function of pressure Žline: calculated data, dot: measured data. for the planar and the corrugated Fabry–Perot microcavity structure.
radius of a diaphragm, W Ž r ., can be obtained from Eqs. Ž3. – Ž5. as follows: WŽ r. s
1 1
1 q
Wps Ž r .
1
,
Ž 6.
q Wpl Ž r .
Wm Ž r .
And, average deflection distance, Wave , is defined by averaging W Ž r . throughout the entire area of a diaphragm. The calculated W Ž r . and Wave also require compensation to accommodate for the zero pressure offset effect in our case, since the calculation is assumed to have no deflection at zero pressure. This is done by offsetting the initial calculated W Ž r . and Wave with the deflection distance measured by confocal scanning laser microscope. Fig. 10 shows the final calculated Wave as a function of pressure for the corrugated Ž30 mm corrugation ring width. and the planer top diaphragm devices with 300 mm top and 110 mm bottom diaphragm. For both cases, the measured Wave , which is extracted from the transmitted intensity measurements, matches to the calculated Wave fairly well. It is also shown that the corrugated diaphragm has larger average deflection distance than the planar diaphragm as the applied pressure increases.
5. Conclusions
Fig. 9. Schematic view of characteristic parameters of a corrugated diaphragm.
A Fabry–Perot microcavity structure with a corrugated diaphragm as a deflecting diaphragm has been fabricated and characterized. Corrugation ring on a deflecting top
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diaphragm is implemented into the outside of the optically sampled area of a Fabry–Perot microcavity structure. It is found from the transmittance measurement that without external load, a corrugated diaphragm is already deflected, concave in our case, due to the non-uniformly distributed out-of-plane internal stress induced by the asymmetry of the corrugated structure with respect to the horizontal plane of the diaphragm. This is called ‘‘zero pressure offset effect’’, which is probably the first experimental demonstration in Fabry–Perot microcavity structure. The pressure-dependent degradation of optical response due to non-uniform deflection of a diaphragm, ‘‘signal averaging effect’’, is also shown. Influence of the zero pressure offset effect and the signal averaging effect on device performance is described with the comparison of transmittance and real-time, 3-D imaging results between a planar and a corrugated device. For a planar device, the signal averaging effect is prevailing throughout the entire range of pressure as the shape of deflected diaphragm changes initially from flat to curved uniformly Žconvex, in our case.. However, for a corrugated device, the zero pressure offset effect is predominant initially and then the signal averaging effect becomes more significant with further increase in pressure, as the shape of deflected diaphragm changes initially from concave to flat and then finally to convex. The actual cavity gap spacing of the deflecting diaphragm as a function of pressure was also investigated experimentally through the real-time 3-D images. The deflection characteristics of a diaphragm by the measured transmittance result matched fairly well with those by the real-time, 3-D images and the analytical simulation results. This investigation suggests that Fabry–Perot microcavity structures and their application devices with completely planar moving diaphragm in their useful operating ranges can be accomplished by the optimal combination of the stiffness of a diaphragm and the incorporation of corrugation structure.
Acknowledgements The author wishes to thank Professor Dean P. Neikirk of the University of Texas at Austin for the diverse supports and the helpful discussions in this project.
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w3x J.H. Jerman, D.J. Clift, S.R. Mallinson, A Miniature Fabry–Perot Interferometer with a Corrugated Silicon Diaphragm Support, Tech. Digests IEEE Soild-State Sensor and Actuator Workshop, 1990, pp. 140–144. w4x P.M. Sarro, A.W. Herwaarden, W. Vlist, A silicon–silicon nitride membrane fabrication process for smart thermal sensors, Sens. Actuators, A 41r42 Ž1994. 666–671. w5x M.A. Chan, S.D. Collins, R.L. Smith, A micromachined pressure sensor with fiber-optic interferometric readout, Sens. Actuators, A 43 Ž1994. 196–201. w6x K. Aratani, P.J. French, P.M. Sarro, D. Poenar, R.F. Wolffenbuttel, S. Middelhoek, Surface micromachined tunable interferometer array, Sens. Actuators, A 43 Ž1994. 17–23. w7x J. Han, Novel fabrication and characterization method of Fabry–Perot microcavity pressure sensors, Sens. Actuators, A 75 Ž1999. 168–175. w8x S.T. Cho, K. Najafi, K.D. Wise, Internal stress compensation and scaling in ultrasensitive silicon pressure sensors, IEEE Trans. Electron Devices 39 Ž4. Ž1992. 836–842. w9x M. Mehregany, R. Howe, S. Senturia, Novel structures for the in-situ measurement of mechanical properties of thin films, J. Appl. Phys. 62 Ž1987. 3579. w10x G. Stoney, The tension of metallic films deposited by electrolysis, Proc. R. Soc. 82 Ž1989. 172. w11x Y. Zhang, S. Crary, K. Wise, Pressure Sensor Design and Simulation using the CAEMEMS-D Module, Dig. IEEE Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1990, pp. 32–35. w12x K.E. Peterson, Silicon as a mechanical material, Proc. IEEE 70 Ž1982. 420–457. w13x M. Di Giovanni, Flat and Corrugated Diaphragm Design Handbook, Marcel Dekker, New York, 1982. w14x Y. Zhang, K.D. Wise, Performance of non-planar silicon diaphragms under large deflections, J. Microelectromech. Syst. 3 Ž2. Ž1994. 59–68. w15x P.R. Scheeper, W. Olthuis, P. Bergveld, The design, fabrication, and testing of corrugated silicon nitride diaphragms, J. Microelectromech. Syst. 3 Ž1. Ž1994. 36–42.
Jaeheon Han received his BS and MS degrees in Materials Science from Korea University, Seoul, Korea, and Korea Advanced Institute of Science and Technology, Seoul, Korea, in 1982 and 1984, respectively. He received his MS and PhD degrees in Electrical and Computer Engineering from Arizona State University and The University of Texas at Austin in 1989 and 1996, respectively. From 1984 to 1987, he was employed as a Member of Technical Staff at Semiconductor R&D center, Hyundai Electronics, Korea. He worked also at Integrated Device Technology, USA and National Semiconductor, USA, during 1990 and 1993, as a senior engineer. From 1996 to 1997, he was a Member of Technical Staff at VLSI Technology Labs., Bell Laboratories, Lucent Technologies, Orlando, FL. In 1997, he became an assistant professor of Electronic Engineering at Kangnam University, Korea. His research interests are in the areas of MEMS based sensors, and VLSIrULSI semiconductor processes and devices.
Jiyoung Kim received his BS and MS degrees in Metallurgical Engineering from Seoul National University, Korea, in 1986 and 1988, respectively. He received his PhD degree in Materials Science and Engineering from the University of Texas at Austin, USA, in 1994. From 1994 to 1996, he worked as a process integration engineer at Texas Instruments, Dallas, TX. Since 1996, he has been an assistant professor at the Department of Materials Engineering in Kookmin University, Seoul, Korea. His research interests are in the areas of ferroelectric thin film applications, alternative CMOS dielectrics, CMOS interconnections and sensor applications.
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Tae-Song Kim received his BS in Ceramic Engineering from Yonsei University, Seoul, Korea in 1982, and his MS and PhD in Materials Science from KAIST ŽKorea Advanced Institute of Science and Technology. in 1984 and 1993. From 1994, he has been a senior research scientist in KIST ŽKorea Institute of Science and Technology.. His major research area is the ferroelectric thin film deposition and their application to micro-devices, MEMS devices, and sensing film deposition for gas sensor.
Jeong-seok Kim received his BS from Korea University in 1980, MS from KAIST in 1982 and PhD from the University of Texas at Austin in 1990 all in Materials Science. He had been a research scientist in KIST during 1982 and 1986. Currently, he is an associate professor at the Department of Materials and Mechanical Engineering in Hoseo University, Korea.
Performance of Fabry–Perot microcavity structures with corrugated diaphragms Jaeheon Han a
a,)
, Jiyoung Kim b, Tae-Song Kim c , Jeong-Seog Kim
d
Department of Electronic Engineering, Kangnam UniÕersity, San 6-2 Kukal-Ri, Kiheung-Eup, Yongin City, Kyunggi-do 449-702, South Korea b Department of Materials Engineering, Kookmin UniÕersity, Seoul, South Korea c Thin Film Technology Research Center, KIST, Seoul, South Korea d Department of Materials and Mechanical Engineering, Hoseo UniÕersity, Chungnam, South Korea Received 9 February 1999; received in revised form 26 July 1999; accepted 29 July 1999
Abstract A Fabry–Perot microcavity structure with a corrugated diaphragm as a deflecting diaphragm has been fabricated successfully. The composite dielectric layers of movable top and stationary bottom diaphragm of Fabry–Perot microcavity are optimized to have proper mechanical stability and optical response. Deflection behavior and device characteristics of a corrugated diaphragm case are compared with those of a planar diaphragm case. Output signal degradation as a function of pressure, ‘‘signal averaging effect’’, is reduced using corrugated top diaphragm structures over planar top diaphragm structures. This is achieved by improving the flatness of the deflecting diaphragm in the optically sampled area of the microcavity structures. However, the corrugated structure shows a static deflection of the diaphragm without applying pressure due to the localized internal stress generated by the asymmetry of the corrugation on the diaphragm, ‘‘zero-pressure offset effect’’. The existence and the influence of these parasitic effects have been observed by both real-time measurement and analytical simulation of the diaphragm. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Fabry–Perot microcavity structure; Corrugated diaphragm; Signal averaging effect; Zero pressure offset effect; Confocal scanning laser microscope
1. Introduction Fabry–Perot cavity-based structures have been widely used for their versatility and tunability such as pressure sensors, temperature sensors, chemical sensors, and tunable optical filters and amplifiers w1–4x. This kind of sensor detects changes in optical path length induced by either a change in the refractive index or a change in physical length of the cavity. Conventionally, these Fabry–Perot-based sensors have been manufactured by using a hybrid two-wafer assembly technique that requires an expensive and difficult fusion bonding process w4,5x. The fusion bonding process limits the flexibility and the accuracy of the dimensions of the device structures. Silicon Very Large Scale Integration ŽVLSI. fabrication technology-based micromachining techniques have recently
)
Corresponding author. Tel.: q82-331-280-3806; fax: q82-331-2803750; E-mail: [email protected]
adopted to build miniature Fabry–Perot sensors w6x. Micromachining techniques make Fabry–Perot sensors more attractive by reducing the size and the cost of the sensing element. Another advantage of the miniature Fabry–Perot sensors is that low coherence light sources, such as light emitting diodes ŽLEDs., can be used to generate the interferometric signal, since the optical length of the miniature cavity is of the same order as the wavelength of the light, and shorter than the coherence length of a typical LEDs. Also, remote sensing and signal acquisition can be achieved without loss of ratio of signal to noise ŽSrN ratio. in harsh environments, by using the Fabry–Perot cavity and optical fiber as the sensing element and interconnect, respectively. One of the major obstacles to commercialization of the miniature Fabry–Perot cavity-based sensors is the degradation of device performance due to non-planar deflection of a deflecting diaphragm. In this paper, we demonstrate how the deflection behavior of a diaphragm and performance of Fabry–Perot microcavity systems are improved by adding a corrugation ring in a planar, circular diaphragm as a deflecting top diaphragm.
0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 9 . 0 0 2 6 7 - 8
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2. Fabrication of a corrugated top diaphragm structure A schematic fabrication procedure of Fabry–Perot microcavity structure with a corrugated top diaphragm as a deflecting diaphragm is shown in Fig. 1. Fabry–Perot microcavity having the size of several hundreds microns is embedded between one movable and one static diaphragms. Each diaphragm consists of multiple film stacks having two silicon nitride layers cladding a silicon dioxide layer. These dielectric films are deposited using Low Pressure Chemical Vapor Deposition ŽLPCVD.. The thickness of each layer is chosen in such a way that the Fabry–Perot microcavity is mechanically stable and must also have optimal optical response w8,9x. Total residual stress of the stack should be weak tensile to allow the diaphragm to remain flat and total reflectance of Fabry– Perot microcavity can be adjusted between 0.1 and 0.5 to obtain maximum variation of an amplitude and optimal range of a linearity of the measured optical response. Taking both the mechanical stability and the optical response into account, optimal film thickness ratio of the silicon dioxide to the silicon nitride is determined to be 3 to 3.5 experimentally. It is observed that with this ratio, the measured tensile residual stresses of the stacked layers of a top and a bottom diaphragm are between 0.1 and 0.2 GPa by using beam curvature method w10x. The first step of fabrication is to deposit sacrificial ˚ thick silicon nitride and 5000 A˚ dielectric layers, 300 A
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thick silicon dioxide stack. These are deposited by the ˚ silicon dioxide is the main LPCVD method. The 5000 A ˚ silicon nitride is the sacrificial layer. The thin 300 A barrier layer to protect the main sacrificial layer from overetching damage of the KOH wet anisotropic silicon substrate etching step. Then the bottom diaphragm dielectric stack is deposited directly on top of the sacrificial dielectric layers. The bottom diaphragm consists of two ˚ thick silicon nitride layers and a 4500-A˚ thick 750-A silicon dioxide layer deposited by the LPCVD method. The following step is the patterning and plasma etching of the dielectric stack deposited on the backside of the double-side polished wafer. Then, by using the patterned back side dielectric layers as masking layers, the silicon substrate is anisotropically etched with 40% KOH solution at 808C from the back-side of the wafer to form the square dielectric bottom diaphragm on the front side of the wafer. At this stage, the defined bottom diaphragm is the combined dielectric stack of both sacrificial and bottom diaphragm layers. The next step is to form the etch windows on the bottom diaphragm using plasma etching process from the front side of the wafer. The etch windows allow access to the sacrificial polysilicon layer to form an air gap between top and bottom diaphragm in the final stage of the fabrication. The etching should stop at approximately onehalf of the total thickness of the sacrificial silicon dioxide layer after the complete removal of the bottom diaphragm dielectric layers inside the patterned etch window area.
Fig. 1. Schematics of fabrication procedure of a corrugated Fabry–Perot cavity device. Ža. Formation of bottom membrane layers and etch windows. Žb. Patterning of a sacrificial polysilicon and a corrugation. Žc. Deposition of top membrane layers. Žd. Removal of the backside stacked layers and a sacrificial polysilicon.
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Fig. 2. Schematic views of cross-sections and optical micrographic top views of a planar and a corrugated top diaphragm Fabry–Perot cavity devices.
This will prevent any void or discontinuity of the subsequently deposited layers in the etch window while the bottom diaphragm is still continuous due to the remaining sacrificial dielectric layer. Then, 0.7 mm thick LPCVD undoped polysilicon layer is deposited and patterned as the air gap portion of the Fabry–Perot microcavity. The next step is defining corrugation ringŽs. by patterning and plasma-etching the sacrificial polysilicon layer. After stopping plasma polysilicon etching at about one-half of the total thickness of the deposited polysilicon with corrugation patterning, another ˚ thick silicon nitride layers dielectric stack of two 1750-A ˚ and 10,500-A thick silicon dioxide layer is overcoated to form a corrugated top diaphragm with sealed microcavity. Single or multiple circular corrugations on a top diaphragm are implemented on the outside of the optically sampled area defined by a bottom diaphragm Žan outer corrugation ring scheme.. This is to avoid the unwanted interference of optical response by the corrugation region having different microcavity gap spacing compared with the rest of planar region in the top diaphragm and is to make the corrugation contribute solely to affect mechanical properties of a deflecting top diaphragm. The bottom diaphragm area of the top diaphragm microcavity structure is considered as the active area, in other words, the optically sampled area, since the bottom diaphragm area defines the transmitted beam area. If the corrugation ring is placed in the portion of the top diaphragm coupled with the underneath bottom diaphragm, this scheme Žan inner corrugation ring scheme. will have an influence on both the flexibility of the diaphragm and the change in Fabry– Perot microcavity gap spacing.
The stacked dielectric layers, and sacrificial silicon nitride and silicon dioxide buffer layers on the backside of the wafer are removed by the combination of blanket wet and plasma etching methods. This reveals the sacrificial polysilicon through the etch windows on the bottom diaphragm to be seen from the backside of the wafer. The sacrificial polysilicon is etched off using KOH solution through these etch windows. Both the top and the bottom diaphragms are freed to form microcavity structure after removing the sacrificial polysilicon layer. For the fabrication of a planar Fabry–Perot microcavity structure, the corrugation masking step is skipped from the above-described fabrication procedure. Fig. 2 shows the schematic views of the cross-sections and the optical microscopic top views of a planar and a corrugated top diaphragm Fabry– Perot microcavity structures.
3. Experimental analysis Optical response is measured by using a 2 = 2 optical fiber directional coupler setup shown in Fig. 3Ža.. A 633-nm He–Ne laser is focused to the one end of input ports of the directional coupler and a reflected intensity is measured from the other end of input ports. One end of output ports is connected to a Fabry–Perot cavity device placed in a sample chamber. The transmitted intensity is obtained by a photodetector placed right after the sample chamber that is connected to a compressed dry air pressure line and a pressure controller. The other end of output ports is dumped into index matching liquid to avoid any reflected light at the end of the unused port of the direc-
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Fig. 3. Schematic view of an optical measurement setup. Ža. Overall scheme; Žb. configuration of a sample chamber for the alignment of an optical fiber.
tional coupler. For high signal-to-noise ratio a chopper and lock-in amplifiers are used. The optical fiber consists of a 100-mm diameter core coated with a 45-mm thick cladding layer. The optical fiber is aligned to the Fabry–Perot microcavity by adjusting the micro XYZ translation stage while monitoring the transmitted intensity detected from the photodetector through the sample as shown in Fig. 3Žb.. The measured transmittance is obtained from the measured transmitted intensity by comparing a Fabry–Perot microcavity and a pinhole Žno Fabry–Perot microcavity. structure having the same size of optical beam transmission area. This is reasonable because the measured transmitted intensity of the pinhole corresponds to the transmittance of unity. The pinhole structure is obtained by removing the fabricated Fabry–Perot cavity structure off from the device using ultrasonic treatment. This leaves opening pinhole structure and the size of the pinhole is equal to the size of the bottom diaphragm Žoptical beam transmission area, which is named optically sampled area. of the fabricated Fabry–Perot cavity device. Fig. 4 shows pressure vs. transmittance plot of a planar and a corrugated device having 300 mm diameter top diaphragm as a deflecting diaphragm. A corrugated device has single 30-mm width corrugation ring placed on the
outside of the optically sampled area of a top diaphragm. For the case of a planar top diaphragm ŽFig. 4Ža.., the signal averaging effect of optical response prevails as the applied pressure increases. The signal averaging effect, that is, pressure-dependent degradation of output optical response, is caused by variation in the amount of deflection over the optically sampled area due to the bowing nature of the boundary cramped deflecting diaphragm. Since it is impossible to build an unclamped, free-standing, planar-moving diaphragm in the real world, the focus is to minimize the non-planarity of the deflection under the applied external load. The first approach is to control the active device area, i.e., the ‘‘optically sampled area’’, by maximizing the area ratio of a moving top diaphragm to a stationary bottom diaphragm w7x. As shown in Fig. 5, the optically sampled area, the active area in the device, is defined by the minimum transmitting area throughout the entire path of the optical beam from the optical fiber to the photodetector via the cavity structure in case of the transmitted intensity measurement. This is equivalent to the area of a bottom diaphragm in our top diaphragm device. Fig. 5 also shows that the difference in Fabry–Perot cavity gap spacing between the center position A and the edge position B of the optically sampled area becomes larger
Fig. 4. Transmittance as a function of pressure of Fabry–Perot cavity devices having a 300-mm diameter Ža. planar top diaphragm and Žb. corrugated top diaphragm.
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Fig. 5. Schematic view showing the ‘‘optically sampled area’’ of the transmitted intensity measurement.
and subsequently, the variation of the resultant transmitted intensity as a function of the edge-to-center distance of the optically sampled area Žfrom B to A. becomes greater with increasing deflection of the moving top diaphragm. Since sinusoidal nature of a Fabry–Perot cavity optical response causes possible cancellation of positive and negative transmitted intensity values from the different positions in the optically sampled area of a diaphragm, the detected transmitted intensity with actual bowed diaphragm can be lower than the expected one with ideal planar diaphragm with no bowing. This explains why signal averaging effect occurs, especially with increasing deflection of a movable diaphragm. The degree of the parasitic signal averaging effect becomes larger with increasing the degree of the curvature of a deflecting diaphragm within the optically sampled area. The curvature becomes smaller by increasing the area ratio of a moving top diaphragm to a stationary bottom diaphragm. This suggests that the larger the size of a moving top diaphragm with constant size of a stationary bottom diaphragm becomes, the lesser the signal averaging effect occurs. The second approach is to add corrugation on the deflecting diaphragm. For a corrugated top diaphragm case shown in Fig. 4Žb., transmittance increases steadily with
pressure until it reaches a maximum and then decreases with further increase in the applied pressure. This result suggests that at zero pressure the corrugated top diaphragm is already deflected, concave in our case, due to the non-uniformly distributed out-of-plane internal stress induced by the asymmetry of the corrugated structure with respect to the horizontal plane of the diaphragm. This behavior of change in transmittance can be explained as follows: Transmittance increases until reaching the maximum as the corrugated diaphragm becomes flat from initial concave shape. This follows degradation of transmittance due to signal averaging effect as the shape of the deflected diaphragm changes from flat to convex with further increase in pressure. This internal film stress induced deflection of a diaphragm without external load is called ‘‘zero pressure offset effect’’, and had been previously suggested through simulation works using finite element method w8,11x. Fig. 6 shows transmittance behavior of a Fabry–Perot cavity structure having 200 mm diameter top diaphragm with and without a 30-mm width corrugation ring. Comparison of a 200-mm ŽFig. 6Žb.. and a 300-mm ŽFig. 4Žb.. diameter corrugated top diaphragm device confirms zero pressure offset effect while varying the compliance of a diaphragm depending on the size of a diaphragm. This comparison also shows that transmittance plot of 200 mm corrugated top diaphragm device has no degradation region caused by signal averaging effect contrary to that of 300 mm corrugated top diaphragm device, for the pressure ranging to 12 psi. This is because smaller diaphragm has better stiffness and moves shorter distance under the same applied pressure. In addition, the parasitic signal averaging effect of 200 mm diaphragm device is larger than that of 300 mm diaphragm device for both planar and corrugated cases. This is because the degree of flatness of a deflecting diaphragm within the optically sampled area is enhanced by increasing the area ratio of a moving top diaphragm to a stationary bottom diaphragm in case of larger top diaphragm device while having the same size of a bottom diaphragm Ž120 mm for planar device.. For corrugated devices, the size of a bottom diaphragm is 60 mm. The
Fig. 6. Transmittance as a function of pressure of Fabry–Perot cavity devices having 200 mm diameter Ža. planar top diaphragm and Žb. corrugated top diaphragm.
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corrugated top diaphragm devices have a smaller bottom diaphragm than the planar top diaphragm devices, because we designed the corrugation region to be placed at the outside of the optically sampled for a corrugated device. In this way, the Fabry–Perot cavity gap spacing in the optically sampled area is not interrupted by the topographical change in corrugation region. Because of different size of the bottom diaphragm, the absolute magnitude of the measured transmitted intensity should be different for both planar and corrugated device. However, the transmittance, as an intrinsic parameter, converted from the measured transmitted intensity is still not affected because it is obtained by comparing a Fabry–Perot cavity and its corresponding pinhole structure both having the same size of
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the optically sampled area Žbottom diaphragm.. Therefore, transmittance plots of planar and corrugated devices with same top diaphragm and different bottom diaphragm in size can be compared with each other. In our case, which is probably the first experimental demonstration of zero pressure offset effect, this effect is also graphically demonstrated with real-time, three-dimensional images by using confocal scanning laser microscope. Fig. 7 shows the real-time, 3-D images at 0 and 15 psi for the Fabry–Perot microcavity structures having 200 mm diameter top diaphragm with and without a 30-mm width corrugation ring. The obtained real-time, 3-D image is a quarter piece of a circular top diaphragm device. These images are generated by scanning a He–Ne laser beam
Fig. 7. Real-time, 3-D confocal scanning laser micrograph of 200 mm diameter top diaphragm devices. The 2-D cavity gap spacing Ž2-D height. is also shown through the radius Žedge-to-center distance. of the deflecting top diaphragm. The 2-D height measurement lines ŽW1-to-W2, X1-to-X2, Y1-to-Y2 and Z1-to-Z2. are crossing the etch-window-induced irregular area in topography. Ža. Planar device at 0 psi. Žb. Planar device at 15 psi. Žc. Corrugated device at 0 psi. Žd. Corrugated device at 15 psi.
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Fig. 7 Žcontinued..
with varying focal planes on the device placed on the sample stage of the microscope while supplying the pressure. In Fig. 7, the shape of the diaphragm is slightly concave at 0 psi and near flat at 15 psi for the corrugated device, while flat at 0 psi and convex at 15 psi for a planar device. This observation of a deflecting diaphragm is in good agreement with the characteristics of the transmittance plots shown in Fig. 6. This behavior can be described in detail from the real-time, 2-D cavity gap spacing plots as a function of the edge-to-center distance of a top diaphragm, Fig. 8, which is obtained from the corresponding 3-D images in Fig. 7. For the planar device, the gap
spacing increases proportionally with pressure, suggesting the uniform bowing of the diaphragm. However, for the corrugated device, while the gap spacing changes from concave at 0 psi to approximately flat with increasing pressure at the inner region of the top diaphragm. The optically sampled area, which is bottom diaphragm area in this case, is within the inner region, as shown in Fig. 8. The deflection, which started from the edge of the moving top diaphragm, seems to be mainly propagated into the outer region of the top diaphragm and confined in the corrugation region, while maintaining deflection-free movement in the inner region. This result suggests that the
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Fig. 8. Real-time, 2-D cavity gap spacing plot of Fabry–Perot cavity having 200 mm diameter Ža. planar top diaphragm and Žb. corrugated top diaphragm devices, with varying pressure. The measurement line is the radius Žedge-to-center distance. of a top diaphragm without crossing the etch-window-induced irregular area in topography in this case.
corrugation region behaves as a stress concentrator and buffer for the moving diaphragm. This is because the corrugation region behaves like a flexible hinge, changing its own shape rather than the shape of the entire diaphragm while absorbing the external load. It is also shown that the etch-window-induced non-uniformity in topography at the top diaphragm is localized and the overall deflection behavior of the top diaphragm is not significantly affected by this topographical non-uniformity. The magnitude of the zero pressure effect seems to be proportional to the size of a corrugated top diaphragm. This can be explained by the increase in the out-of-plane internal stress induced momentum with decreasing stiffness Žincreasing size and decreasing thickness. of the diaphragm. Extreme case of zero pressure offset effect can be a multiple corrugation top diaphragm device showing complete sticking of a multiple-corrugated top diaphragm to a bottom diaphragm without applying pressure. This is due to the excessive deflection of a diaphragm caused by the large downward out-ofplane internal stress of multiple corrugation rings. These above-observations suggest that it is possible to fabricate Fabry–Perot cavity structures with completely planar moving diaphragm in their useful operating input ranges by optimizing the stiffness of a diaphragm Žto prevent zero pressure offset. while adopting corrugation scheme Žto improve planar movement in the optically sampled area.. 4. Theoretical analysis Theoretical calculation of the deflection behavior of a diaphragm was performed for both planar and corrugated diaphragms. The modeling uses the following specific
parameters. The thickness for Si 3 N4 Ž h1 . and SiO 2 Ž h 2 . is ˚ respectively. Young’s modulus for 1500 and 10,500 A, Ž . Si 3 N4 E1 and SiO 2 Ž E2 . is 380 and 75 GPa, respectively. Residual stress for Si 3 N4 Ž s 1 . and SiO 2 Ž s 2 . is 1.1 and y0.1 GPa, respectively. Poisson’s ratio Žy . for both Si 3 N4 and SiO 2 is 0.2. The residual stresses, s 1 and s 2 , were measured using the beam curvature method with the film samples prepared on the same wafers where the real devices were being fabricated. Young’s modulus, E1 and E2 , are taken from the literature w12x. The detailed analytical modeling of a planar circular diaphragm case was described in our previous publication w7x. The deflection of a corrugated diaphragm with initial stress can be approximated by means of an analytical expression; a superposition of the linear model of a corrugated diaphragm without internal residual stress and of the non-linear model of the planar diaphragm with a large internal residual stress. The superposition is based on the assumption that the corrugated diaphragm can be modeled as a fictitious planar diaphragm, which locally has the same radial and tangential flexural rigidity as the corrugated diaphragm w13x. The behavior of a corrugated diaphragm with internal residual stress is described using superposition of a stressfree corrugated diaphragm and a planar diaphragm with internal residual stress, a planar diaphragm with an internal residual stress of s Bpr2.83 instead of s should be considered w14,15x. Thus, the following equation is obtained: ps4
h2 y A p E h2 2
a h
4
a
2
q
s Bp 2.83
Ž 1.
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170
where Ap s
2 Ž q q 1. Ž q q 3.
y2
ž
3 1y
/
q2
and Bp s 32
1yy 2 1
3yy
.
y
2
Ž q y y . Ž q q 3.
q y9 6
Also, the corrugation profile factor q can be represented as: 2
q s
S l
1 q 1.5
H2 h2
,
Ž 2.
where H is the depth of the corrugations, l is the corrugation spatial period and S is the corrugation arc length ŽFig. 9.. The q is equal to 1 for flat diaphragms Ž H s 0. and is larger than 1 for corrugated diaphragms. The above-equations show that the effect of internal residual stress is much smaller for corrugated diaphragms than for planar diaphragms, although it is still not negligible. By using the equivalent thickness Ž h., Young’s modulus Ž E ., and residual stress Ž s . of the composite films, distributed uniformly throughout the entire diaphragm, Wps Ž r ., WplŽ r ., and Wm Ž r . are defined as small pure plate, large pure plate, and pure membrane deflection distance as a function of the distance from the center of the diaphragm, respectively, while compensating for the effect of a corrugation. The corrugation compensation factors, A p and Bp , are added to the formula for the planar circular diaphragm case as follows: Wps Ž r . s
pa4
ž / ½ A p Eh3
Wpl Ž r . s p
Wm Ž r . s
1y
Ž 1 y y 2 . a4
2.83 p Bp s h
Bp hE
ž
a2 y r 2 4
r
ž / a
1y
/
.
2 2
, r
ž / a
Ž 3. 2 2
1r3
5
,
Ž 4. Ž 5.
Then, individual deflection distance as a function of the
Fig. 10. Calculated Wave as a function of pressure Žline: calculated data, dot: measured data. for the planar and the corrugated Fabry–Perot microcavity structure.
radius of a diaphragm, W Ž r ., can be obtained from Eqs. Ž3. – Ž5. as follows: WŽ r. s
1 1
1 q
Wps Ž r .
1
,
Ž 6.
q Wpl Ž r .
Wm Ž r .
And, average deflection distance, Wave , is defined by averaging W Ž r . throughout the entire area of a diaphragm. The calculated W Ž r . and Wave also require compensation to accommodate for the zero pressure offset effect in our case, since the calculation is assumed to have no deflection at zero pressure. This is done by offsetting the initial calculated W Ž r . and Wave with the deflection distance measured by confocal scanning laser microscope. Fig. 10 shows the final calculated Wave as a function of pressure for the corrugated Ž30 mm corrugation ring width. and the planer top diaphragm devices with 300 mm top and 110 mm bottom diaphragm. For both cases, the measured Wave , which is extracted from the transmitted intensity measurements, matches to the calculated Wave fairly well. It is also shown that the corrugated diaphragm has larger average deflection distance than the planar diaphragm as the applied pressure increases.
5. Conclusions
Fig. 9. Schematic view of characteristic parameters of a corrugated diaphragm.
A Fabry–Perot microcavity structure with a corrugated diaphragm as a deflecting diaphragm has been fabricated and characterized. Corrugation ring on a deflecting top
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diaphragm is implemented into the outside of the optically sampled area of a Fabry–Perot microcavity structure. It is found from the transmittance measurement that without external load, a corrugated diaphragm is already deflected, concave in our case, due to the non-uniformly distributed out-of-plane internal stress induced by the asymmetry of the corrugated structure with respect to the horizontal plane of the diaphragm. This is called ‘‘zero pressure offset effect’’, which is probably the first experimental demonstration in Fabry–Perot microcavity structure. The pressure-dependent degradation of optical response due to non-uniform deflection of a diaphragm, ‘‘signal averaging effect’’, is also shown. Influence of the zero pressure offset effect and the signal averaging effect on device performance is described with the comparison of transmittance and real-time, 3-D imaging results between a planar and a corrugated device. For a planar device, the signal averaging effect is prevailing throughout the entire range of pressure as the shape of deflected diaphragm changes initially from flat to curved uniformly Žconvex, in our case.. However, for a corrugated device, the zero pressure offset effect is predominant initially and then the signal averaging effect becomes more significant with further increase in pressure, as the shape of deflected diaphragm changes initially from concave to flat and then finally to convex. The actual cavity gap spacing of the deflecting diaphragm as a function of pressure was also investigated experimentally through the real-time 3-D images. The deflection characteristics of a diaphragm by the measured transmittance result matched fairly well with those by the real-time, 3-D images and the analytical simulation results. This investigation suggests that Fabry–Perot microcavity structures and their application devices with completely planar moving diaphragm in their useful operating ranges can be accomplished by the optimal combination of the stiffness of a diaphragm and the incorporation of corrugation structure.
Acknowledgements The author wishes to thank Professor Dean P. Neikirk of the University of Texas at Austin for the diverse supports and the helpful discussions in this project.
References w1x J.P. Dakin, C.A. Wade, P.B. Withers, An Optical Fiber Pressure Sensor, SPIE Fiber optics ’87: 5th International Conference on Fiber optics and Opto-electronics, Vol. 734, 1987, pp. 194–201. w2x J. Han, Fabry–Perot chemical sensors by silicon micromachining techniques, Appl. Phys. Lett. 74 Ž3. Ž1999. 445–447.
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Jaeheon Han received his BS and MS degrees in Materials Science from Korea University, Seoul, Korea, and Korea Advanced Institute of Science and Technology, Seoul, Korea, in 1982 and 1984, respectively. He received his MS and PhD degrees in Electrical and Computer Engineering from Arizona State University and The University of Texas at Austin in 1989 and 1996, respectively. From 1984 to 1987, he was employed as a Member of Technical Staff at Semiconductor R&D center, Hyundai Electronics, Korea. He worked also at Integrated Device Technology, USA and National Semiconductor, USA, during 1990 and 1993, as a senior engineer. From 1996 to 1997, he was a Member of Technical Staff at VLSI Technology Labs., Bell Laboratories, Lucent Technologies, Orlando, FL. In 1997, he became an assistant professor of Electronic Engineering at Kangnam University, Korea. His research interests are in the areas of MEMS based sensors, and VLSIrULSI semiconductor processes and devices.
Jiyoung Kim received his BS and MS degrees in Metallurgical Engineering from Seoul National University, Korea, in 1986 and 1988, respectively. He received his PhD degree in Materials Science and Engineering from the University of Texas at Austin, USA, in 1994. From 1994 to 1996, he worked as a process integration engineer at Texas Instruments, Dallas, TX. Since 1996, he has been an assistant professor at the Department of Materials Engineering in Kookmin University, Seoul, Korea. His research interests are in the areas of ferroelectric thin film applications, alternative CMOS dielectrics, CMOS interconnections and sensor applications.
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Tae-Song Kim received his BS in Ceramic Engineering from Yonsei University, Seoul, Korea in 1982, and his MS and PhD in Materials Science from KAIST ŽKorea Advanced Institute of Science and Technology. in 1984 and 1993. From 1994, he has been a senior research scientist in KIST ŽKorea Institute of Science and Technology.. His major research area is the ferroelectric thin film deposition and their application to micro-devices, MEMS devices, and sensing film deposition for gas sensor.
Jeong-seok Kim received his BS from Korea University in 1980, MS from KAIST in 1982 and PhD from the University of Texas at Austin in 1990 all in Materials Science. He had been a research scientist in KIST during 1982 and 1986. Currently, he is an associate professor at the Department of Materials and Mechanical Engineering in Hoseo University, Korea.