systems (MEMS) fabrication. We will describe the modeling and the design of an acoustic device represented here by a condenser microphone with a perforated ...
11-13 May 2011, Aix-en-Provence, France
Capacitive Microphone fabricated with CMOS-MEMS Surface-Micromachining Technology Josué Esteves, Libor Rufer, Gustavo Rehder TIMA Laboratory (CNRS, G-INP, UJF) 46 Avenue Félix Viallet, Grenoble, France Abstract- This paper presents a standard complementary metal– oxide–semiconductor (CMOS) technology combined with sacrificial layers etching used for micro-electro-mechanical systems (MEMS) fabrication. We will describe the modeling and the design of an acoustic device represented here by a condenser microphone with a perforated diaphragm. Models based on the electromechanical analogy and on the finite element analysis (FEA) have been used to predict the behavior of the microphone. These models have taken into account material constants and dimensions of the AMS 0.35 μm CMOS technology. An effect of etch holes in the microphone diaphragm on the dynamic response of the structure was studied and an optimization study has been done to determine the sensor lateral dimensions and the position of these holes. We will show simulation results, the microphone design and the final layout of the structure.
range. Different MEMS microphones have been developed by different groups and some designs, using dedicated technology process, have been commercialized until now. Most of the designs consist of a movable diaphragm and a perforated fixed electrode, called the backplate, separated by an air gap (see Fig. 1). Below the backplate, there is a back-chamber that makes the evacuation of air from the air gap easier.
Fig. 1. Schematic structure of a conventional MEMS condenser microphone.
I. INTRODUCTION Several studies have been carried out since last two decades with the aim to use a standard CMOS process to fabricate micro-electro-mechanical systems [1], [2]. This, so called, CMOS-MEMS process was originally introduced as a technique using back-side bulk micro-machining (BSBM), and later front-side bulk micro-machining (FSBM) of a silicon wafer, thus allowing to free-up layers deposited on the silicon wafer during the CMOS process. The technologies based on the bulk etch of silicon made possible to design different devices with movable elements made of a stack of several layers deposited on top of silicon wafer during a CMOS process. Different realizations using this approach can be found in [3], [4]. More recently, another approach to a CMOS-based MEMS fabrication was proposed [5]. This technique is based on surface micromachining applied on specific layers issued from CMOS process. Thus metal layers can be considered as sacrificial and can be removed for instance with PAN etch (Phosphoric, acetic and nitric acids). Remaining structure can be then composed of silicon nitride, silicon oxide and polysilicon layers [5]. In some cases, it is more convenient to keep metal layers for device design. In this case, silicon oxide is chosen as a sacrificial layer and is removed for example with buffered oxide etch (BOE) saturated with aluminum (silox vapox III – transene) [6]. Further, the silicon oxide can also be etched by vapor HF, which does not attack the aluminum layers and prevents inter-layers stiction. Advantages of this new CMOS-MEMS fabrication technique are easy execution, low-cost maskless etching and the possibility to integrate the electronic circuit and MEMS device together on the same chip. We have considered to use this CMOS-MEMS technology to fabricate a condenser microphone for the audible frequency
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In this work, we have studied and developed a model of a condenser microphone with a different structure. Our microphone structure does not contain a back-chamber, and is composed of a movable perforated electrode and a fixed electrode (without holes), separated by an air gap. This kind of structure allows using of a standard CMOS process with only one additional post-process step to etch sacrificial layers to realize the MEMS device. Similar microphone structure with perforated movable electrode was recently described in [7]. In this article, a specific dedicated technology was used to create an aluminum diaphragm, and the modeling does not take into account the air gap effect that is very important for the frequency response of the microphone. The paper is structured as follows. In Section 2, we will describe the microphone structure and propose an equivalent circuit model with lumped-parameters for the microphone modeling taking into account the effect of etch holes on the microphone behavior. In Section 3, simulations with CoventorWare, commercial FEA simulation software for MEMS, are performed in order to determine different parameters of the equivalent circuit and to estimate the microphone performance. Next, Section 4 will present the fabrication using AMS 0.35 µm CMOS standard process. Finally, Section 5 will provide some conclusions and directions on our future research. II.
MICROPHONE STRUCTURE
The microphone is fabricated with the AMS 0.35 µm CMOS back-end process resulting in a passivation layer, four metal layers, three via layers and several silicon dioxide layers. In our design, we can create the diaphragm and the backplate of the microphone with metal layers, the air gap between the electrodes can be realized by etching the sacrificial silicon dioxide layer through small holes in the
ISBN:978-2-35500-013-3
11-13 May 2011, Aix-en-Provence, France microphone diaphragm. The chosen CMOS technology imposes the vertical structure dimensions i.e. the air gap and the diaphragm thicknesses. Fig. 2 shows different views of the microphone structure and the corresponding dimensions are listed in Table I.
Fig. 2. Microphone cross-sectional view (a), top view of the diaphragm (b). TABLE I DIMENSIONS OF THE MICROPHONE ELEMENTS Elements Dimension (µm) Diaphragm side length (Lmem) 500 Diaphragm thickness (tmem) 1 Arm length (Larm) 71 Arm width (Warm) 141 Big hole side length (Lhole1) 5 Big hole pitch (Pitch1) 10 Small hole side length (Lhole2) 1 Small hole pitch (Pitch2) 5 Air gap thickness (ha) 2.64
We have considered a diaphragm supported by four beams anchored by the oxide layer in order to obtain an optimum stiffness and thus acceptable sensitivity. The air gap thickness that was taken into account in this design corresponds to the distance between the metal layers M4 and M2 of the CMOS process. Two sets of holes are designed in the microphone diaphragm. Small holes with the sides of 1 µm are densely distributed on the diaphragm surface with the aim to allow fast sacrificial layer etching. Larger holes with the sides of 5 µm disposed on the diaphragm have the important role of controlling the diaphragm damping and their dimensions were optimized in order to obtain flat frequency response close the resonance. The microphone must work in the audible frequency range from 20 Hz to 20 kHz. The required capacitance variation of the microphone was obtained through the analysis of the expected noise of the electronic circuit. For a minimum signalto-noise ratio of 40 dB, the microphone capacitance variation must be at least 60 fF. In this section, we will describe the microphone equivalent circuit with lumped parameters. We present the effect of holes on the mechanical parameters and on the electrostatic field distribution, as well as their influence on the mechanical damping. A. Equivalent circuit Lumped parameters equivalent circuit (Fig. 3) is used to
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study the frequency response of the microphone. An analogy between the acoustic, mechanical, fluidic and electrical domains is used to build the equivalent circuit. To characterize the mechanical and fluidic part behavior of the MEMS microphone, an equivalent spring-mass-damper system under harmonic excitation is considered. The total stiffness of the system is given by the rigidity of the diaphragm and the spring effect of the air gap, kmem and kairgap respectively. The resistance Rairgap represents the damping caused by the viscous losses in the air gap and Mmem is the effective diaphragm mass. In the acoustic domain, a sound pressure (Pg) is applied to the diaphragm through the radiation impedance composed of the radiation resistance Rrad, representing the frictional force, and by the radiation mass Mrad, representing the mass of the air close to the diaphragm that is vibrating in phase with the plate. In the electrical domain, the capacitance of the microphone is represented by C0 and the parasitic capacitance, due to the electric field in the oxide (anchor of the microphone) is Cp. The link between the acoustic and mechanical domain is modeled by the mechano-acoustic transformer with the ratio Amem, representing the diaphragm area. The second transformer represents the coupling between electrical and mechanical domain with the ratio Γ.
Fig. 3. Microphone equivalent circuit.
The following paragraphs discuss the different parameters of the equivalent circuit taking into account the effect of etch holes. B. Mechanical behavior with holes The analytic description of the microphone mechanical behavior is quite complex and difficult to solve because of the diaphragm geometry (arms, holes). For this reason, an approach using finite element simulations and reduced elements approximation is used. Indeed, we can determine the mechanical parameters of the equivalent circuit that represents the diaphragm, namely its spring coefficient kmem and effective mass Mmem, with FEA performed in CoventorWare and consider the diaphragm as a spring-mass system governed by the well-known relations: (1) F = PA = k mem wmax
k mem (2) M mem Simulations can calculate the resonant frequency (f0) and the maximum displacement (wmax) of the structure when we applied a uniform force F corresponding to a pressure P on the diaphragm. From wmax and knowing the diaphragm area (A), we can calculate the spring coefficient of the diaphragm with (1). From the resonant frequency and the calculated spring f0 =
ISBN:978-2-35500-013-3
11-13 May 2011, Aix-en-Provence, France coefficient, we can calculate the effective mass of the diaphragm with (2). However, the mechanical properties, namely the effective Young’s modulus and the internal stress of a MEMS structure, are influenced by its perforation [8]. We have performed estimations of this effect and confirmed with CoventorWare the results of [9] showing the stress concentration in the proximity of holes (see Fig. 4). Simulations for several diaphragms with different holes configurations have shown that the resonant frequency for a perforated diaphragm (f0WithHole) can be approximately estimated with the following relation: f0WithoutHole
AWithHole ≤ f0WithHole ≤ f0WithoutHole AWithoutHole
(3)
where AWithHole is the perforated diaphragm area, AWithoutHole is the entire diaphragm area and f0WithoutHole is the resonant frequency of the diaphragm without holes. According to these different observations, we have to consider the etch holes in the calculation of kmem and Mmem.
Fig. 4. Simulation showing the stress on the diaphragm with holes.
The simulations of the microphone were performed on the quarter of the structure using symmetry plane conditions (Fig. 5) because of the high number of etch holes (several thousands) that demands intensive computational resources . CoventorWare calculates the resonant frequency and the maximum displacement of the structure, and with (1) and (2), we can calculate the spring coefficient kmem and the effective mass Mmem of the perforated diaphragm (Table II).
viscous flow of air, pressure in the air gap changes and creates forces against the diaphragm movement. This phenomenon called squeeze film damping is accompanied with two kinds of forces. One is the damping force, caused by the viscous flow of air, and the other is the elastic force due to the compression of the air gap. The squeeze film can be described by the Navier-Stokes and Reynolds equations taking into account some effects that are specific to the small film dimensions, like air rarefaction, compressibility and inertia effects, and air flow through the holes of a perforated plate. The squeeze film damping is very important for the microphone operation, in particular in the high frequencies, in the vicinity of its resonance [8]. The air gap stiffness kairgap and the damping Rairgap are proportional to the elastic and damping forces respectively. Several analytic models have been proposed to calculate the elastic and damping forces and so the corresponding elements of the model ([10]-[14]). These models take into account rarefaction, compressibility and inertia effects as well as the effect of etch holes and are a helpful alternative to the microphone FEM simulations that can have constraints in computational requirements. Although it exists several similar models, we have decided to choose the model described in [13]. This model provides relations for damping force (Fdamp) and stiffness force for perforated plate taking into account rarefaction, compressibility effects and also inertia effects (Fstiff+iner). (4) Fdamp = {ℑ( Fnet )}Pa r02
Fstiff +iner = {ℜ( Fnet )}Pa r02
(5)
where Pa is the atmospheric pressure, r0 is the outer radius of a pressure cell (proportional to the pitch), Fnet is the real complex force acting on the diaphragm due to the squeeze film given by the following expression:
[
Fnet = Fsq1 + Fsq2 + Fh
(6)
]
⎡ 2R I ( jΓ )K1( jΓRi ) − I1( jΓRi )K1( jΓ ) ⎤ −(1− Ri2 )⎥e jτ (7) Fsq1 = πξ0 ⎢ i 1 ⎣⎢ jΓ I0( jΓRi )K1( jΓ )+ I1( jΓ )K0( jΓRi ) ⎦⎥
[
]
⎡ 2R I ( jΓ )K1 ( jΓ Ri ) − I 1 ( jΓ Ri )K1 ( jΓ ) ⎤ jτ Fsq 2 = πΦ b ⎢ i 1 ⎥e ⎢⎣ jΓ I 0 ( jΓ Ri )K1 ( jΓ ) + I 1 ( jΓ )K 0 ( jΓ Ri ) ⎥⎦
[
]
F h = ( π R i2 ) Φ b e Fig. 5. Simulation structure: quarter model of the microphone using symmetry planes. TABLE II MICROPHONE MECHANICAL PARAMETERS Simulation results Calculated parameters f0 = 13491 Hz kmem = 3.8 N/m wmax = 88 nm at 1 Pa Mmem = 5.3x10-10 kg
It can be noticed that the resonant frequency of the perforated structure obtained from the FEA (13491 Hz) corresponds to the relation (3). C. Air gap modeling When the diaphragm oscillates normally to the backplate, the air gap between the diaphragm and the backplate is squeezed causing a lateral fluid motion in the gap. Due to the
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jτ
(8) (9)
where Fsq = Fsq1 + Fsq2 is the complex force due to the squeeze-film, Fh is the force acting on the hole surface, ξo is the non-dimensional amplitude, Фb is the non-dimensional pressure at the hole/air gap interface, Г is a non-dimensional complex number that includes the compressibility, inertia and gas rarefaction effects, Ri and R0 are respectively the nondimensional inner and outer radii of a pressure cell, In is the Modified Bessel function of nth order, Kn is the Macdonald’s function of nth order and τ is the non-dimensional time. Knowing that Fdamp and Fstiff.+iner. are respectively the imaginary and real parts of Fnet, we can calculate the air gap stiffness kairgap and the damping Rairgap. In order to respect the requirements on the microphone performance, we must achieve a negligible spring effect and low damping due to the air gap. The size of the holes and the pitch have been chosen taking into account the etch time, low
ISBN:978-2-35500-013-3
11-13 May 2011, Aix-en-Provence, France damping and negligible spring effect in the frequency range of interest. So, a non-staggered configuration with 5 x 5 µm² square holes and 10 µm pitch is used. Air gap damping coefficient The damping coefficient, Rairgap, can be determined from (4): Fdamp (10) R airgap = ha ω First, we compare FEM and lumped-model results for various configurations. For simulations, we use CoventorWare which provides the damping force and coefficient for squeezefilm. Next, we apply the lumped-model on the chosen configuration. Considering possible device applications, simulations were performed up to 100 kHz. Table III shows the air gap damping coefficient error between the FEM and the lumped-model results for different diaphragm sizes and thus for different number of holes. We have compared several diaphragm configurations. In this table, the air gap value similar to that of the designed microphone was fixed and we have used the non-staggered (matrix) hole configuration with 10 µm pitch for each diaphragm.
Air gap
2 µm
TABLE III MODEL/SIMULATION ERRORS Diaphragm size Damping coefficient (kg/s) (µm²) (number Simulation Analytical of holes) -6 2.6x10-6 100x100 (100) 2.1x10 200x200 (400) 9.4x10-6 1.0x10-6 -5 300x300 (900) 2.1x10 2.3x10-5 400x400 (1600) 3.9x10-5 4.1x10-5 -5 500x500 (2500) 6.2x10 6.5x10-5 600x600 (3600) 9.0x10-5 9.3x10-5 700x700 (4900) 1.2x10-4 1.2x10-4
Error (%) 22.2 10.7 7.2 5.6 4.6 3.9 3.5
In the considered frequency range, the damping coefficient Rairgap is constant and the agreement between simulated and calculated values varies from 22 % to 3.5 %. We have found similar results when using the analytical model of the squeeze-film for the microphone as when performing the FEA with CoventorWare. Fig. 6 shows the damping force simulated with CoventorWare and using (10). We have obtained Rairgap = 5.4x10-5 kg/s, which is within 10 % of the simulated value (6.1x10-5 kg/s).
Air gap spring coefficient The air gap spring coefficient, kairgap, can be calculated from (5): Fstiff + iner (11) k airgap = ha In a similar way, we compare FEM and lumped-model results for various configurations, but there were important errors (more than 80%). Even if this model is not accurate enough to calculate the air gap spring coefficient, according to the simulation result for the microphone case, in the audio frequency range, the air gap spring coefficient, kairgap = 0.006 N/m (at 20 kHz), is very low comparing to the diaphragm spring coefficient kmem (Table II). Therefore, the air gap stiffness can be neglected. Indeed, according to the obtained air gap spring value, we can suppose a condition of incompressible fluid. This can be also confirmed by the squeeze number σ estimation, which characterizes the compressibility effect for a perforated diaphragm: 12 μω r02 (12) σ = Pa h a2 Where μ is the fluid viscosity, ha is the air gap thickness and ω is the pulsation. If σ
