A method for improving the drop test performance of a MEMS microphone Matthias Wintera*, Seifeddine Ben Aounb, Gregor Feiertagc, Anton Leidlc, Patrick Scheelec**, Helmut Seidela a
Universität des Saarlandes, LMM, Saarbrücken, Germany; b TU München, TEP, Arcisstraße 21, Munich, Germany; c EPCOS AG, Anzinger Straße 13, Munich, Germany
ABSTRACT Most micro electro mechanical system (MEMS) microphones are designed as capacitive microphones where a thin conductive membrane is located in front of a rigid counter electrode. The membrane is exposed to the environment to convert sound into vibrations of the membrane. The movement of the membrane causes a change in the capacitance between the membrane and the counter electrode. The resonance frequency of the membrane is designed to occur above the acoustic spectrum to achieve a linear frequency response. To obtain a good sensitivity the thickness of the membrane must be as small as possible, typically below 0.5 µm. These fragile membranes may be damaged by rapid pressure changes. For cell phones, drop tests are among the most relevant reliability tests. The extremely high acceleration during the drop impact leads to fast pressure changes in the microphone which could result in a rupture of the membrane. To overcome this problem a stable protection layer can be placed at a small distance to the membrane. The protective layer has small holes to form a low pass filter for air pressure. The low pass filter reduces pressure changes at high frequencies so that damage to the membrane by excitation in resonance will be prevented. Keywords: MEMS, microphone, frequency response, drop test, low pass, CSMP
1. INTRODUCTION Nowadays on the mobile phone market electret condenser microphones (ECMs) [1] are more and more replaced by silicon micro electro-mechanical condenser microphones, because ECMs have the disadvantage of loosing charge and therefore electrical performance by environmental effects like high temperature or humidity. MEMS microphones have a very high long-term stability. A further advantage is that MEMS microphones can be mounted using the surface mount technology and furthermore they can be designed smaller than ECMs. To the authors´ knowledge the smallest fully packaged MEMS microphone these days has been developed by G. Feiertag et al [2]. The microphone MEMS chip and the ASIC are integrated in a chip scale microphone package (CSMP). Figure 1 shows a drawing of the package, a cross-section is shown in figure 2. The MEMS chip, as well as the ASIC, is flipchip bonded on a HTCC ceramic substrate which offers small sound holes which have a diameter of 100 µm. The back volume of the MEMS is closed by a rigid polymer foil and protected by a thick copper layer. The sound travels through the holes in the ceramic layer and the highly perforated counter electrode until it reaches the circular membrane. The membrane is nearly closed, only some small vent holes permit static pressure compensation. The acoustic behaviour of this microphone system is described in this paper using an electro-mechanical-acousticalanalogous circuit [3]. The aim of this model is to predict both the acoustical performance as well as the quality performance in regard to a fast pressure change, e.g. which occurs when the mobile device with microphone is dropped on the floor. *
[email protected]; phone +49 89 636 23840; epcos.com **Patrick Scheele is now with EADS, Ulm
Smart Sensors, Actuators, and MEMS IV, edited by Ulrich Schmid, Carles Cané, Herbert Shea Proc. of SPIE Vol. 7362, 736214 · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.821187
Proc. of SPIE Vol. 7362 736214-1
Fig. 1. Drawing of the packaged MEMS microphone (left: top view; right: bottom view), size 2.05 x 2.8 x 0.95 mm³
Back volume
MEMS Chip
ASIC
Membrane with vent holes
Metallization Bump
HTCC substrate
Small sound holes Sound port
Perforated counter electrode
Fig. 2. Cross-section of the chip scale microphone package (CSMP)
2. MEASUREMENTS 2.1 Frequency response The acoustical measurements were focussed on the frequency response of various microphone package designs. The different designs have a different number of small sound holes (see figure 2 and figure 1 on the right side) in the HTCC substrate. The total number of small sound holes was either 1, 2, 4 or 15. The frequency response was measured in a pressure chamber. The sound pressure was monitored by a reference microphone by Brüel & Kjaer, type 4938. Since the pressure chamber shows resonant behaviour at frequencies above 6 kHz the sensitivity could not be measured in absolute values. So the different designs were measured successively and afterwards the offsets were calculated. Figure 3 shows the change in the frequency response of the designs with 1, 2 and 4 holes in comparison to the design with 15 holes. It can be seen that the number of sound holes has a strong influence on the frequency response and acts as a low pass filter. A smaller number of holes leads to a lower cut-off frequency and a stronger suppression. The unsteadiness in the high frequency range is caused by the measurement setup.
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2
Delta sensitivity / dBV/Pa
0
−2
1 sound hole 2 sound holes 4 sound holes
−4
−6
−8
−10 2 10
3
10
4
10
Frequency / Hz Fig. 3. Shift in the frequency response of the microphone dependent on the number of small sound holes through the HTCC substrate normalized to 15 holes. 2.2 Drop tests For every package type, 20 samples were dropped. For this test the microphone units were soldered on special drop test boards conform to JEDEC standard JESD22-B111. These boards were mounted on an aluminium carrier. The carrier was dropped on a concrete floor from a height of 1.50 m. Each board was dropped 40 times varying the impact direction. After the dropping the membranes were examined and the number of cracks was counted for every design. The number of destroyed membranes can be seen in table 1.
Table 1. Drop test results.
Number of holes 15 4 3 2 1
Drop test results Number of ruptured membranes 6 0 0 0 0
The results indicate an improvement in drop test performance with a reduced number of small sound holes, hence lower cut-off frequency. In the case of a lower cut-off frequency the excitation of the membrane caused by the forces of the drop impact is lower, especially in its resonance frequency. So the mechanical stability of the MEMS microphone can be improved by choosing a clever package design.
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3. SYSTEM DESCRIBING MODEL For further optimization of the package design without cost and time consuming hardware processing a theoretical model was created to predict changes in the frequency response, and hence in the mechanical stability, by changing package parameters. This model is based on the description of the air flow in the system. The air flow is simulated by an analogues electrical circuit. For different parts of the microphone unit various analogues equations were used. The parts are separated into mechanical and acoustical components. The simulation model was verified as an equivalent circuit in SPICE and for faster calculation analytical calculations were done in Matlab. 3.1 Mechanical components The mechanical elements of the circuit include the description of the membrane which can be described by its compliance C m
A2 = Cp ⋅ A k
Cm =
(1)
where k is its spring constant and A its effective area. C p can be calculated for a circular plate by
⎛ ⎞ ⎜ ⎟ 1 R ⎜ ⎟ Cp ≈ ⋅⎜ 2 ⎟ 8 ⋅ t ⋅σ 2⋅ E ⋅t ⎜⎜ ⎟⎟ + 1 2 2 ⎝ 1 −υ ⋅σ ⋅ R ⎠ 2
(
where R is the radius of the membrane, t its thickness, Poisson ratio [4].
(2)
)
σ
the mechanical tension, E the Young´s modulus and
υ
the
The membrane also acts as an inductance caused by its mass. This can be described by
Mm =
t ⋅ ρ Si ⋅ f mass A
(3)
with ρ Si as the density of the silicon and f mass a mass factor. The mass factor is about 1.5 [5]. The counter electrode can be described similar to the membrane. 3.2 Acoustical components The acoustical components can be divided into resistances, inductors and capacitances. Resistances occur in small holes, e.g. the perforations of the counter electrode, and can be calculated in the case of laminar flow by [6]
Rh =
8 ⋅η ⋅ l π ⋅r4
(4)
where η is the viscosity of the fluid, l the length of the hole and r the radius of the hole. Another acoustical resistance occurs when the movement of the membrane causes the air in the narrow gap between the two electrodes to flow with one electrode strongly perforated. This phenomenon was described by Z. Skvor [7]. The resulting resistance is given by
R gap
12 ⋅ η ⋅ X 02 ⎡ 1 ⎛ X 0 ⎞ 3 1 r 2 1 r 4 ⎤ = ⋅ ⎢ ln⎜ − ⋅ ⎟− + ⋅ ⎥ 3 ⋅ A ⎣ 2 ⎝ r ⎠ 8 2 X 02 8 X 04 ⎦ d air
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(5)
In this formula, X 0 stands for the effective distance between the holes in the perforated counter electrode and r is the radius of the perforation holes. d air describes the gap between the electrodes. Inductive acoustical components occur when air has to be accelerated. In our model this happens in the cylindrical tubes. It can be described by the following equation [3]:
Mh =
ρ ⋅ (1 + 0.8 ⋅ 2 ⋅ r ) r 2 ⋅π
(6)
In this equation ρ represents the density of air, r the radius of the tube and l its length. Capacitive elements are present when the air flow works against big volumes [3]:
CV =
V ρ ⋅ c2
(7)
Here V is the air volume and c is the velocity of sound. 3.3 Radiation impedance The acoustic impedance of the air in contact with the vibrating diaphragm is represented by a radiative resistance and mass [8]:
Z rad = In this formula
ω
π ⋅ ρ ⋅ R4 2⋅c
8 ⋅ω 2 + ρ ⋅ R3 3
(8)
is the angular vibration frequency.
4. GENERATING THE SIMULATION MODEL 4.1 Membrane model The mechanical behaviour of the MEMS chip and its geometry has been described in [5]. At first the correctness of the formulas and the parameters describing the membrane were evaluated. Therefore the membrane was assumed to consist of a mechanical spring and a mechanical mass. The geometric and material data were entered into equations (2) and (3). To check if the value of the mechanical compliance C p is valid the pull-in voltage was measured (figure 4). The membrane and the counter electrode are seen as a plate capacitor. A pull-in occurs when the voltage between the membrane and the counter electrode is so high that the membrane collapses onto the counter electrode. This occurs at around 2/3 of the distance between the membrane and the counter electrode, called d air [9]. Measuring the pull-in voltage can be done by slowly increasing the voltage.
UP =
3 8 ⋅ d air 27 ⋅ ε 0 ⋅ C p
(9)
From the theoretical calculation a pull-in voltage of 13.6 V was predicted which is in good agreement with the measurement result shown in figure 4.
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5
4.5
C s/ pF
4
3.5
3
2.5 11
11.5
12
12.5
13
13.5 14 Voltage / V
14.5
15
15.5
16
Fig. 4. Measurement of the pull-in voltage. Since the resonance frequency of a LC resonant circuit appears at
f0 =
1 1 ⋅ 2 ⋅π M m ⋅ Cm
(10)
the value for the mechanical mass could be evaluated by measuring the resonance frequency of the membrane and using the before determined value for C m . The membrane model was simulated in SPICE (see Figure 5). 30
Compliance/ nm/Pa
25
20
15
10
5
0 0 10
10
1
2
10
3
10 Frequency / Hz
4
10
Fig. 5. Membrane model in SPICE.
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5
10
6
10
4.2 Model of the MEMS with enclosed back volume As next step the whole MEMS microphone was simulated in SPICE using the equivalent circuit shown in figure 6. A closed back volume was assumed. The package was still neglected. In this model p~ is the external sound pressure, electrode,
M p the acoustic mass of the air in the perforations of the counter
R p the acoustic resistance through the perforations, C ce and C m the mechanical compliances of the counter
electrode and membrane,
M ce and M m the mechanical masses of the counter electrode and membrane, R gap the
acoustical resistance of the air gap between counter electrode and membrane, between counter electrode and membrane,
C gap the capacitance due to the volume
C bv the capacitance caused by the closed back volume and Z rad the
radiation impedance caused by the movement of the membrane. The sensitivity of the system can be determined by regarding the voltage drop
p m at the membrane. To compare the
simulation results with measurements the power amplifier has to be taken into consideration. The power amplifier was considered to be linear over the whole frequency range with an amplification factor of 4 dB.
DdLI VOIU1I1
Ivent Mvent
P
fZrad
Counter el eetrncl
Membrane
1Mm
Air gap
R gap
UUUI
Cgap
'CceURp
T
T....
U - U-U -I IMce - -liMp - - -
Fig. 6. Equivalent circuit diagram of the MEMS model (not to scale).
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For the first approach to calculate the circuit SPICE was applied. After verifying the SPICE model a simplified analytical model was created to perform faster calculations with the help of Matlab. Figure 7 shows that the analytical model as well as the SPICE simulation is in very good accordance with the acoustic measurement.
−25 −30
Matlab SPICE Measurement
Sensitivity / dBV/Pa
−35 −40 −45 −50 −55 −60 −65 −70 0 10
1
10
2
10
3
10 Frequency / Hz
10
4
5
10
6
10
Fig. 7. MEMS model in SPICE and Matlab compared to measurement. The high pass behaviour at 3 Hz shown in figure 7 is caused by the vent holes in the membrane. 4.3 Model of the packaged MEMS In the last step, the acoustic influence of the package was also taken into consideration. The equivalent circuit of the whole system is shown in figure 8. Three further circuit elements were added. C in is generated by the air volume between the HTCC substrate and the MEMS and ASIC respectively caused by the bumps (see figure 2).
Rin and M in
describe the acoustical resistance and inductance in both the small sound holes and the sound port through the HTCC substrate.
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DCK voiuiiie
CbV
Membrane
Mvent Z
Rgap
T
Counter
Air gap
. .. IM1IIUU .k
I
+CCURP
.----- 1-u-I--c---. I
I
R,
HTCC substrate M
Fig. 8. Equivalent circuit diagram of the packaged MEMS (not to scale). Figure 9 shows the comparison between the simulation model calculated in Matlab and the measurement results that have already been shown in figure 3. Since the small sound holes tend to be larger than the assumed diameter of 100 µm we added a 5% failure tolerance for the diameter in the simulation. To obtain a good agreement of the simulation model with the measurements we used in the simulation higher values than the theoretical values for Rin and M in . The used value for M in was 2.5 times higher than theoretically predicted. This circumstance can be explained by the measurement setup. In the measurement setup the sound is carried from the pressure chamber to the microphone unit through a micro-tube. This micro-tube adds another inductive reactance in series with M in . Implicating this micro-tube in the calculations results in a 2.5 times higher theoretical value for M in in good agreement with the measurement.
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2
Delta sensitivity / dBV/Pa
0
−2
−4
−6
−8
1 sound hole with 0% tolerance (Simulation) 1 sound hole with 5% tolerance (Simulation) 2 sound holes with 0% tolerance (Simulation) 2 sound holes with 5% tolerance (Simulation) 4 sound holes with 0% tolerance (Simulation) 4 sound holes with 5% tolerance (Simulation) 1 sound hole (Measurement) 2 sound holes (Measurement) 4 sound holes (Measurement)
−10 2 10
3
4
10
10
Frequency / Hz Fig. 9. Simulation model of the packaged MEMS microphone compared to measurement. The shift in the frequency response is plotted dependent on the number of holes normalized to 15 holes. Because the small sound holes tend to have a bigger diameter than the proposed 100 µm we added a 5% tolerance plot for the diameter as well.
The value for
Rin used in the simulations was 10 times higher than the predicted value from equation (4). This huge
disagreement is not fully understood yet. A slightly higher value for the resistance was expected because the sound holes in the HTCC ceramic have a very rough surface. This roughness was expected to lead to a higher resistance in the order of 1.5 [10]. One possible explanation for the high resistance is the appearance of turbulences. Since the Reynolds number in tubes is defined as [6]
Re =
d ⋅v
η
(11)
with d = 100 µm as the diameter of the tube, v as the flow velocity and η as the dynamic viscosity of air, it can be calculated to be Re ≈ 2000 when the flow velocity is assumed to be similar to the sound velocity. Wu et al. [11] foresee turbulent flow in micro-tubes already at a Reynolds number greater than 500. So the resistance of the sound holes in the package cannot be described by equation (4) since this equation assumes laminar flow. To adjust the formula of the resistance a friction factor is introduced. For laminar flow the friction factor is λ = 64 /Re [6]. For turbulent flow a lot of different values for the friction factor can be found in literature, depending on the diameter, fluid and roughness of the wall [11, 12, 13]. With rough walls the friction factor can be more than 12 times higher than in laminar flow [14].
Proc. of SPIE Vol. 7362 736214-10
To obtain more reliable measurement results it would be better to measure the frequency response of the different microphone package designs in free-field, because the sound guide in the pressure chamber influences the measurement. These free-field measurements are ongoing.
−10 −15 −20
Sensitivity / dBV/Pa
−25 −30 −35 −40 −45 −50 −55 −60 −65 0 10
Microphone chip with closed back volume, without package Microphone chip in standard package Microphone chip in CSMP (4 small sound holes) 10
1
2
10
3
10 Frequency / Hz
4
10
5
10
Fig. 10. Simulated frequency response of an unpackaged MEMS, a MEMS in a standard microphone package and a MEMS packaged with our CSMP technology Figure 10 shows a comparison of the frequency response between different microphone package designs. Just regarding the pure MEMS chip with a closed back volume only one resonance in the high frequency range occurs caused by the mechanical mass and compliance of the membrane. Integrating the MEMS in a package generates a second resonance, because a front volume generated thereby acts like a Helmholtz resonator. Standard microphone packages have one large sound hole and a big front volume [15]. In the simulation shown in figure 10 the front volume of the standard package was assumed to be 5 mm³ and the sound hole was assumed to have a diameter of 1 mm. This leads to a high second resonance, at worst in the acoustic frequency range. By decreasing the front volume and increasing the resistance by decreasing the size of the sound hole the second resonance frequency gets dampened. In the case of our CSMP a linear frequency response in the acoustic range is achieved.
5. CONCLUSION In this paper it is shown that a chip scale package can have a huge influence on the acoustic performance of a MEMS microphone chip. Small sound holes in the substrate layer may act as a low pass filter.
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The design of a low pass can be used to optimize the performance of the mechanical robustness of the MEMS chip itself. Dropping microphones in different package designs showed that an added low pass filter can increase the mechanical stability by suppressing excitation of the resonance frequency. A model for simulating the acoustical performance of a packaged MEMS microphone is described. The simulations of the analogues circuit were performed with SPICE. Furthermore analytical calculations were done in Matlab. The simulation model was built step by step. First the pure membrane was investigated and the simulation parameters of the membrane were proven. As next step the counter electrode was added to the simulation model and the back volume was assumed to be closed. The simulation model was verified by measurement results. Therefore a linear amplifier was added to the model, too. As last step the simulation model was completed by adding the package design as well. A discrepancy between the theoretically calculated value of the resistance through the small sound holes occurred. This discrepancy may be explained by appearance of turbulent flow. A comparison between our chip scale microphone package and a standard microphone package shows a strong reduction of the resonance caused by the small front volume in the package. As a result we achieve a linear frequency response in the acoustic range. To clearly verify the simulation model for the CSMP, free-field measurements of microphones with the different package designs will be conducted.
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