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A high sensitivity and high linearity pressure sensor based on a peninsula-structured diaphragm for low-pressure ranges
Accepted Manuscript Title: A High Sensitivity and High Linearity Pressure Sensor Based on a Peninsula-Structured Diaphragm for Low-Pressure Ranges Author: Xian Huang Dacheng Zhang PII: DOI: Reference:
S0924-4247(14)00283-0 http://dx.doi.org/doi:10.1016/j.sna.2014.05.031 SNA 8818
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
17-2-2014 28-5-2014 29-5-2014
Please cite this article as: X. Huang, D. Zhang, A High Sensitivity and High Linearity Pressure Sensor Based on a Peninsula-Structured Diaphragm for Low-Pressure Ranges, Sensors and Actuators: A Physical (2014), http://dx.doi.org/10.1016/j.sna.2014.05.031 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A High Sensitivity and High Linearity Pressure Sensor Based on a Peninsula-Structured Diaphragm
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for Low-Pressure Ranges
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Xian Huang1,2 and Dacheng Zhang2,* 1 Shenzhen Graduate School, Peking University, Shenzhen, P. R. China 2 Institute of Microelectronics, Peking University, Beijing, P. R. China [email protected], [email protected]
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Abstract
The trade-off between sensitivity and linearity has been the major problem in
problem,
a
novel
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designing the piezoresistive pressure sensors for low pressure ranges. To resolve the peninsula-structured
diaphragm
with
specially
designed
d
piezoresistors was proposed. Finite element method (FEM) was adopted for analyzing
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the sensor performance as well as comparisons with other sensor structures. In
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comparison to flat diaphragm, the proposed sensor design could achieve a sensitivity increase by 11.4 %, nonlinearity reduction of 60 % and resonance frequency increase of 41.8 %. In addition, the modified peninsula-structured diaphragms featuring a center boss have been optimized to achieve ultra-low nonlinearities of 0.018 %FFS and 0.07 %FFS for the 5 KPa and 3 KPa pressure ranges respectively with higher sensitivities as compared to the CBM (cross beam membrane) and hollow stiffening structures. In accordance with the FEM results, the fabricated pressure sensor with the peninsula-structured diaphragm showed a sensitivity of 18.4 mV/V full-scale output and a nonlinearity error of 0.36 %FSS in the pressure range 0 ~ 5 kPa. The proposed sensor structure is potentially a better choice for designing low pressure sensors.
Page 1 of 41
Keywords: MEMS pressure sensor, Peninsula-structured diaphragm, Sensitivity and
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Linearity, FEM, Sensor fabrication
to
the
simple
and
low-cost
fabrication
process,
MEMS
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Attributed
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1. Introduction
(Micro-Electro-Mechanical systems) piezoresistive pressure sensors have been in
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mass production for over three decades. Normally, the sensor is fabricated by bulk silicon micro-machining processing technique. The key component of the sensor is a
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thin square diaphragm which deflects when pressure is applied. Four Piezoresistors configured in a Wheatstone bridge are placed near the center of the diaphragm edge.
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d
The bridge converts the stress in the deflected diaphragm to an electrical signal. By adjusting the dimensions of the diaphragm, a wide measurement range of pressure can
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be obtained. Piezoresistive pressure sensors have been used in a wide range of applications, for instance, the automobiles [1] and process control [2]. Recently, there is a rapid growth in demand for the ultra-low pressure measurement in fields like biomedical (invasive measurements) [3], smart homes such as HVAC (heating, ventilation and air conditioning) controls [4] and aerodynamics such as wall/wing pressure measurement [5,6]. In order to apply for ultra-low pressure (for example ≤ 5 KPa) measurement, the sensitivity should be significantly improved to maintain an appropriate sensor output (for example ≥ 15 mV/(V FFS)) for signal processing. Based on the mechanical behavior of the flat square diaphragm, sensitivity is
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proportional to the square of the ratio of diaphragm width to diaphragm thickness. Thus, sensitivity can be increased by a larger width / thickness ratio. Unfortunately, the nonlinearity error increases with this ratio at a much faster rate [3], a non-tolerable
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nonlinearity error (for example > 1.0 %FFS) may be occurred during the sensitivity
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optimization process. Therefore, the nonlinearity problem involved in the low
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pressure sensors should be solved to open the new areas of applications.
Various types of modified diaphragms for the fabrication of low pressure sensors
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have already been reported to resolve the nonlinearity problem. In order to increase the stiffness of the diaphragm, center bosses were often added to the diaphragm [7,8].
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It was an effective method to reduce the nonlinearity error. However, the reduction of nonlinearity error was achieved at the expense of sensitivity or sensor size. Besides,
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d
the additional center mass would increase the acceleration sensitivity of the diaphragm, which was detrimental for the stability of the sensor for high sensitivity
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and accuracy applications. To tackle this problem, P.K. Kinnell [9] introduced a novel hollow stiffening structure to replace the solid center boss and a 30 mbar (3 KPa) full-scale differential pressure sensor with the hollow stiffening structure was fabricated. The sensor had perfect performances with a sensitivity of 18 mV/V full-scale output and linearity < 0.4 %FSS. The sensor allowed the advantages gained by a stiffening boss in terms of sensor linearity without either the negative effects of acceleration sensitivity or unnecessary increase in die size. Based on the electrochemical etch-stop technology, the hollow stiffen structure also had the advantages of high precision diaphragm thickness / sensor performance control.
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Nevertheless, the fabrication process for the hollow stiffening structure was relatively complicated and the key processes (including electrochemical etch-stop and fusion bonding process) require specialized production facilities which have not been widely
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adopted in foundries yet. The front-side beam diaphragm first proposed by M.H. Bao
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[10] has also been widely adopted for low pressure sensor design. Recently, a novel
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front-side cross beam membrane (CBM) structure was proposed by B. Tian [11] and further developed by Z. L. Yu [12] for micro pressure measurement. Tian’s CBM
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structure exhibited perfect linearity and stability performance, but the sensitivity was relatively low (7.081 mV/kPa, DC power 4.57 V) for measuring 5 KPa pressure. Yu
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combined the CBM structure with a double-side center boss for measuring absolute micro pressure lower than 500 Pa. High sensitivity and high overload resistance were
te
d
achieved, but the nonlinearity problem (3.046 %FSS) remained unsolved. Many factors that influence the nonlinearity performance of the low pressure
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sensors have also been reported. Matsuda [13] presented the nonlinear piezoresistance effects in silicon. Lin [14] studied the sensitivity and nonlinearity issue on the pressure sensors with a half Wheatstone bridge configuration by characterizing the diaphragm thickness and the length of sensing resistors. Chiou [15] discussed the linearity performance of the pressure sensor under high residual stress induced by passivation films and anodic bonding. However, in previous works that applied structured diaphragm for pressure sensor design, only limited discussion concerned the influence of pattern and positioning of piezoresistors on sensor’s nonlinearity performance. Despite the growing achievements in low pressure sensor design and
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fabrication, additional research and considerable progress are still needed to further improve the performances of the pressure sensor such as the increasing of sensor output and stability, the decreasing of nonlinearity error, chip size and fabrication
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cost.
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In our study, a novel high sensitivity and high linearity pressure sensor based a
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peninsula-structured diaphragm for low pressure ranges was proposed. The proposed sensor structure could have the advantages of low fabrication cost, high sensitivity,
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good linearity and diaphragm stability over other existing structures. In the following sections, stress distribution characteristics for the proposed diaphragm under pressure
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loading were studied in detail by FEM analysis. The influences of the pattern and positioning of piezoresistors as well as the lithography alignment errors on sensor’s
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d
performance were discussed. Comparisons with other sensor structures with typical flat, center-bossed diaphragm and recently proposed CBM, hollow stiffen structure
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were carried out respectively in terms of sensitivity and linearity to demonstrate the superiority of the sensor structure. Moreover, modified peninsula-structured diaphragms featuring a center boss have been optimized to achieve ultra-low nonlinearity errors with higher sensitivities. A fabrication process for the proposed sensor with the peninsula diaphragm was presented in detail. Finally, the fabricated sensor devices were tested and compared with the FEM result, which verified the accuracy of the FEM simulation.
2. Background
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2.1 Sensor output Diaphragm type piezoresistive pressure sensors are usually arranged into a full
on the diaphragm, and
and
and
) loaded
) loaded transversely. When the pressure is applied will have the same positive increment
. Due to different patterning and
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will have the same negative increment
, while
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longitudinally and two (
and
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Wheatstone bridge configuration with two piezoresistors (
positioning of the piezoresistors, the resistance increment
normally differs to
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. Based on the Wheatstone bridge circuit, the correlation between the output voltage and the resistance can be described as
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(1)
d
where Vin is the source DC power and Vout is the output voltage. R is the resistance of the
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piezoresistors. Since the resistance change is proportional to the mechanical stress, for
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low doped P-type piezoresistors along <110> direction: represents the shear piezoresistance coefficients and
(
represents the average stress
difference between longitudinal and transverse directions within the resistor) [16]. Then the correlation between the output voltage and the mechanical stress can be obtained as
(2)
where
and
are average stress for resistor
and
respectively.
2.2 Nonlinearity error The terminal based nonlinearity error of the pressure sensor is defined as [15]
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(3) where Delt is the voltage output difference between the real voltage output and the
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ideal linear output. The full-scale span (FSS) is the voltage range of the full pressure range. NL is the terminal based nonlinearity error.
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There are two major sources for the nonlinearity error of a diaphragm type
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piezoresistive pressure sensor with the Wheatstone bridge configuration [17]. The first source is the nonlinear dependence of the stress with the applied pressure when large
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deflection of the diaphragm occurs (balloon effect). The second source is the unbalanced stress (
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in equation (2)) among piezoresistors in the and
, the stress term
d
Wheatstone bridge. If a stress unbalance appears between
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would have a non-zero value, the sensor output would not be proportional
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to the applied stress even if all the stress terms in equation (2) change linearly under small deflection.
For flat diaphragm, the trade-off between sensitivity and linearity will become
irreconcilable when designing sensors for very low pressure measurement as discussed in the introduction. In our case, for the 5 KPa full range pressure sensor designed based on the flat diaphragm with a thickness of 10 μm, the output voltage
could reach 100 mV (the source voltage is 5 V and the doping concentration of piezoresistors is 2.5e18 /cm-3) by adjusting the diaphragm’s width. However, the nonlinearity error would exceed 1.2 %FFS at the same time.
In order to meet
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simultaneously the NL design criteria within 0.5 % and the output beyond 100 mV for
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measuring the 5 kPa pressure, the flat diaphragm of the sensor must be modified.
3. Sensor Design
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A novel sensor structure featuring a peninsula-structured diaphragm was proposed
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to solve the abovementioned contradiction between the nonlinearity and sensitivity as shown in Fig. 1. The peninsula structures were located near the diaphragm edge with
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narrow beams connecting to the Si pedestal. Four piezoresistors on the narrow beams
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connected with each other to form the Wheatstone bridge. The side length of the diaphragm was 1900 μm. The thickness of the diaphragm was 10 μm while the extra
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are 3600 × 3600 × 400 μm³.
d
thickness of the peninsular structure was designed to be 9 μm. The device dimensions
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Through the application of the peninsula structure, on the one hand, the effect of local stiffening of the diaphragm was realized which could reduce the axial stress induced by large deflection effect and thereby decrease the mechanical nonlinearity error; on the other hand, the linear bending stress would be concentrated at the narrow beam of the peninsula which ensured a high sensitivity of the sensor. Besides, since the peninsula were located at the diaphragm edge, the influence brought by the mass of the peninsula on acceleration sensitivity was much less compared with the diaphragms with the center bosses. The peninsula stiffened the diaphragm and concentrated stress in regions with piezoresistors during pressure loading, which makes it possible to achieve high sensitivity, good linearity and diaphragm stability
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simultaneously. Stress distribution characteristics for the peninsula structure will be discussed in detail for optimization of the sensor performance.
3.1.1
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3.1 Finite element method analysis Stress distribution characteristics for the diaphragm
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The sensor performances were predicted by the non-linear static analysis and
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modal analysis by the ANSYSTM software. Owing to the symmetry, only a quarter of the finite element model of the pressure sensor was established. Figure. 2(a) shows
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the stress intensity distribution for the peninsula-structured diaphragm under 5 kPa uniform pressure loading. In accordance with the previous discussion, the mechanical
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stress concentrated at the narrow beam of the peninsula structure. For the P-type
d
<110> oriented piezoresistors, the resistance change and the sensitivity of the sensors =Sx-Sy) between
te
are actually determined by the magnitude of the stress difference (
the longitudinal and transverse direction. The curves in Fig. 2(b) represent the
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distribution of the stress Sx-Sy from the central point to the diaphragm edge for the flat (10 μm and 19 μm thick) and peninsula-structured diaphragms (flat area 10 μm thick and peninsula area 19 μm thick). It is evident that the mechanical stress for each diaphragm reached its maximum at the center of the diaphragm edge. The maximum stress in peninsula-structured diaphragm was increased up to 350 % compared with flat diaphragm with the thickness of 19 μm, whereas it slightly reduced compared with flat diaphragm with the diaphragm thickness of 10 μm. 3.1.2
Stress distribution characteristics for the narrow beam of the peninsula
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The
stress
distribution
characteristics
near
the
narrow
beam
of
the
peninsula-structured diaphragm were studied in detail as shown in Fig. 3. The distributions of stress Sx-Sy along the path that parallels to the diaphragm edge for the
ip t
peninsula-structured diaphragm (black curve) and flat diaphragm (10 μm thick, red
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curve) are plotted in Fig. 3(a). The distance of the analyzed path to the diaphragm
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edge was 25 μm. For the case of peninsula-structured diaphragm, from the beam center to the beam edge, the stress Sx-Sy monotonically increased from 28.3 MPa to
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41.8 MPa with an increment of nearly 48 %. The distributions of stress Sx and Sy are plotted in Fig. 3(b) and 3(c) respectively. Since there’s no constrains on the beam edge
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in the Y direction, from beam center to beam edge, the tensile stress Sy would decrease monotonically to zero (see Fig. 3(c)). Meanwhile, the decreased constrains in
te
d
Y direction would contribute to the deformation in X direction, which in turn induced a slight increase in tensile stress Sx (see Fig. 3(b)). In summary, the increase of tensile
Ac ce p
stress Sx, coupled with the decrease of tensile stress Sy led to the increase of Sx-Sy from the beam center to beam edge shown in Fig. 3(a). As for flat diaphragm, the stress Sx-Sy slightly reduced along the same path, which is a widely known result. Remarkably, though for peninsula-structured diaphragm the stress Sx-Sy at the beam center was smaller compared with that of the 10 μm thick flat diaphragm (see Fig. 2(b) and Fig. 3(a)), the stress at the beam edge is about 25 % larger than the maximum stress in flat diaphragm (see Fig. 3(a)). For the purpose of maximizing sensitivity of the sensor, the sensing piezoresistors should be placed at regions of maximum stress Sx-Sy. For peninsula-structured
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diaphragm, piezoresistors should be placed close to the corner formed by the diaphragm edge and the beam edge. However, the stress was non-uniform and rapidly changing in these regions, just as shown in Fig. 3(a). Therefore, the risk of severe
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performance degradation in case that lithography alignment error occurs during
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fabrication process should be evaluated and the pattern of the piezoresistors should be
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properly designed. 3.2 Piezoresistor design
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The sensor performance is closely related to the pattern and positioning of the piezoresistors. For comparison and optimization, four candidate designs for the
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piezoresistors were proposed as shown in Fig. 4. The configurations for the
d
piezoresistors are listed in table 1. All resistors were along the <110> direction. The
te
total length and width of the resistors were fixed at 200 μm and 12 μm respectively. Design I~III were commonly applied in flat diaphragms [18], they were arranged at
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the center of the beam with different turns. Design IV was specially designed for the peninsula-structured diaphragm. Based on the analysis of stress distribution characteristics, the piezoresistors in design IV were positioned at regions of maximum stress Sx-Sy, therefore it would achieve the largest sensitivity among the four candidate designs.
After obtain the average stress for each piezoresistor by FEA non-linear static analysis, the output voltage could be calculated by applying equation (1) and the nonlinearity error could be calculated based on equation (3). The source power Vin in equation (1) was set at 5 V. The dependence of the output voltage and nonlinearity
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error on the loading pressure for different piezoresistor designs are shown in Fig. 5. It was observed that both sensitivity and nonlinearity differed as the positioning of resistors changed. Among these four candidate designs, a maximum sensitivity of 22.4
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mV/kPa was obtained in design IV as expected, while sensitivities around
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19.06~19.13 mV/kPa were obtained for the others (see Fig. 5(a)). Besides high
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sensitivity, low nonlinearity error is also a very attractive sensor characteristic. Figure. 5(b) shows the terminal based nonlinearity error of each piezoresistor design. Design I
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and II had the best nonlinearity error of 0.46 %FSS, design IV had a moderate nonlinearity error of 0.48 %FFS and design III showed a worst nonlinearity error of
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0.53 %FSS. As discussed before, unbalanced stress between
and
was
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designs.
d
responsible for the variations of the nonlinearity errors for different piezoresistor
From the above discussion, the piezoresistor design IV exhibited the largest
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sensitivity and a moderate nonlinearity error. In addition, since both
and
were symmetric positioned to the beam center (see Fig. 4), the sensor performance degradation induced by alignment errors between the piezoresistor layer and the peninsula layer could be reduced. Therefore, the non-uniform and rapidly changing stress in regions of piezoresistors in design IV will have little influence on the fabrication tolerance. Simulation results from FEM indicated that an alignment error of ± 2 μm (the maximum possible alignment error in our laboratory) had a negligible influence on the sensor performance with piezoresistor design IV, which demonstrated a good fabrication tolerance of the piezoresistor design IV. In summary,
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the largest sensitivity and moderate nonlinearity error, together with a good fabrication tolerance, make the piezoresistor design IV the best choice for application.
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3.3 Geometrical optimization process for the 5 KPa pressure sensor The optimization process of the peninsula diaphragm for the 5 KPa pressure sensor
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including the proposal of the peninsula structure, the influences of peninsula height
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and diaphragm thickness was discussed with reference to the sensor outputs and nonlinearity errors. Peninsula structure
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3.3.1
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Figure 6 shows the optimization process of the structured diaphragm for the 5 KPa pressure sensor. The piezoresistor design III was applied in the optimization process was set to 1.28e-9 /Pa corresponding to a doping concentration of
d
for simplicity.
te
2.5e18 /cm-3. The sensor with 100 mV full range output was first designed based on
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the conventional flat diaphragm with a thickness of 1900 μm and width of 10 μm (see Fig. 6 (a) 1-flat diaphragm). The nonlinear static simulation indicated that large
deflection of the diaphragm occurred: the deflection at the diaphragm center was 4.9 μm (see Fig. 6 (b)), the ratio of deflection to thickness reached 0.49 and the maximum
nonlinearity error exceeded 1.2 %FFS (see Fig. 6 (d)). In order to stiffen the diaphragm and reduce the nonlinearity errors, four relatively large rectangular bosses with a thickness of 5 μm were added to the diaphragm (see Fig. 6 (a) 2-large rectangular structure). It is noted that the diaphragm deflection was greatly reduced (see Fig. 6 (b)) as well as the nonlinearity errors of the sensor (see Fig. 6 (d)). However, the bending stress of the diaphragm (see Fig. 6 (c)) and the sensitivity of the
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sensor (see Fig. 6 (e)) were also reduced. For the purpose of concentrating the bending stress, the width of the rectangular structure was narrowed from 600 μm to 220 μm to form the small rectangular structure (see Fig. 6 (a) 3-small rectangular
ip t
structure). It is found that bending stress around the diaphragm edge was increased to
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the same value as the flat diaphragm (see Fig. 6 (c)) and a highest sensitivity of 20.74
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mV/KPa was achieved (see Fig. 6 (e)). However, the nonlinearity error was also increased up to 1.03 %FFS (see Fig. 6 (d)). The simulation results clearly indicate that
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the large rectangular structure had advantage of relatively good linearity and disadvantage of relatively low sensitivity; while the small rectangular structure had
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advantage of relatively high sensitivity and disadvantage of relatively poor linearity performance. In order to allow for the nonlinearity error reduction by the large
te
d
rectangular boss without sensitivity loss, the width of the large rectangular boss was partially narrowed in regions of piezoresistors to form the peninsula structure (see Fig.
Ac ce p
6 (a) 4-peninsula structure). It is noted that a sensitivity of 20.11 mV/KPa (the same as the flat diaphragm) and nonlinearity error of 0.75 %FFS (decreased by 37.5% compared with the flat diaphragm) were achieved. If the piezoresistor design III was replaced by design IV, the sensitivity of the sensor with the peninsula structure would be further increased to 23.61 mV/KPa. The results indicated that the peninsula structure had both the advantage of the large rectangular structure in terms of low nonlinearity error and the advantage of the small rectangular structure in terms of high sensitivity. 3.3.2
Peninsula height
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In order to further reduce the nonlinearity error, the influence of peninsula height was studied. The dimensions of the peninsula-structured diaphragm were the same as shown in Fig. 6 (a), piezoresistor design IV was applied for all sensors. When the
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peninsula height increased from zero (flat diaphragm) to 20 μm, Fig. 7 (a) shows the
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corresponding simulation results. It is observed that when the peninsula thickness
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increased from 0 to 5 μm, the sensor output increased from 100 mV to the maximum value 118 mV; then the sensor output would decrease gradually as the peninsula
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thickness continued to increase. While the nonlinearity error reduced monotonically from 1.2 %FFS to about 0.2 %FFS. Considering the design constrains of nonlinearity
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error (< 0.5 %FSS), the trade-off between sensitivity and linearity finally made the
Diaphragm thickness
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3.3.3
d
peninsula height to be 9 μm.
If the peninsula thickness was fixed at 9 μm and the diaphragm thickness
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increased from 5 μm to 15 μm, Fig. 7 (b). shows the corresponding simulation results.
It is observed that both the sensor outputs and the nonlinearity errors decreased monotonically as the diaphragm thickness increased. It is also noted that if the diaphragm thickness was designed to be 10 μm with the fabrication tolerance of ± 1
μm, the linearity errors would vary between 0.30 ~ 0.81 %FFS and the sensor outputs between 96.5 ~ 131.8 mV. 3.4 Comparisons with other types of diaphragms 3.4.1
Comparisons with center-bossed and flat diaphragms
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As a basic comparison, the static performance of peninsula structure were first compared with typical ones with center-bossed and flat diaphragm as shown in Fig. 8 (a). They had the same diaphragm thickness of 10 μm and size of 1900 μm. The
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simulated sensor outputs and nonlinearity errors versus pressure loading were plotted
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in Fig. 8 (b) and (c). Compared with the flat diaphragm, the sensitivity of the sensor
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with peninsula-structured diaphragm was increased about 11.4 % while the maximum nonlinearity error was reduced by 60.0 %. By introducing the solid center-boss
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structure to the flat diaphragm, the nonlinearity error could also be reduced to the same as the peninsula-structured diaphragm (see Fig. 8 (c)). However, the sensitivity
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of the sensor was also reduced by 8.5 % compared to the sensor with flat diaphragm. In other words, the reduction of the nonlinearity error by introducing the center-boss
3.4.2
te
d
was achieved at the expense of sensitivity loss. Comparisons with the CBM structure
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As for comparisons with Tian’s CBM structure [11], the peninsula-structured
diaphragm was redesigned to have the same diaphragm thickness (20 μm) and lateral dimension (2900 μm). The peninsula thickness was also the same as the beam thickness (20 μm) in CBM structure. The optimized geometry size of the peninsula
structure was plotted in Fig. 9 (a).
was set to 1.0e-9 /Pa corresponding to a
doping concentration of 7.5e18 /cm-3. The formerly discussed piezoresistor design IV and III were applied for both sensor structures. The distribution of the stress Sx-Sy from the central point to the diaphragm edge for both sensor under 5 KPa uniform pressure loading is plotted in Fig. 9 (b). The
Page 16 of 41
maximum value of Sx-Sy in the peninsula-structured diaphragm (27.6 MPa) was increased by 42.3 % compared with CBM structure (19.4 MPa). The simulated sensor outputs and nonlinearity errors versus pressure loading were plotted in Fig. 9 (c) and
ip t
(d). First, for both sensors, piezoresistor design IV exhibited larger sensor outputs
cr
with an increment of 6.6 % ~ 10.0 % compared with piezoresistor design III. The
us
results indicated that the optimized piezoresistor design IV also applied for the CBM structure for sensitivity optimization. Second, the largest sensitivity of the sensor with
an
peninsula diaphragm (14.81 mV/KPa) was increased about 41.3 % compared with CBM structure (10.48 mV/KPa). Third, it is noted that these two sensors had very
M
close absolute values of nonlinearity errors but with different signs: - 0.13 %FFS in CBM structure versus + 0.16 % FFS in peninsula structure. As discussed by Lin, for
te
d
conventional sensors with flat diaphragm the sign of the nonlinearity error was related to the diaphragm dimensions, resistor design and it might even go from negative to
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positive as the applied pressure changes [14]. Based on the non-linear simulation of these two structured diaphragms, we conclude that the sign of the nonlinearity error can also be changed with different shapes of the diaphragm structure, even if all other parameters (diaphragm dimensions, resistor designs and pressure ranges) are the same. 3.4.3
Modified peninsula structure with a center boss
The conclusion also suggests that it’s possible to achieve a level of close to zero nonlinearity error by adjusting the shapes of the diaphragm structure. To achieve the goal, a possible diaphragm structure was proposed as shown in Fig. 10 (a), which was
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formed by adding an extra center boss to the peninsula-structured diaphragm. It is observed that as the side length of the center boss increased from 400 to 1200 μm, the nonlinearity error reduced and changed signs from positive to negative (see Fig. 10
ip t
(c)). The minimum absolute nonlinearity error (< 0.02 %FFS) was achieved when the
cr
size of the center boss was about 800 μm. The simulation results confirmed the
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prediction that a level of close to zero nonlinearity error could be achieved by adjusting the shapes of the diaphragm structure. The conclusion offers a new approach
an
to design low pressure sensors (≤ 5 KPa) with ultra-low nonlinearity error (< 0.1 %FFS) and appropriate sensor output. In addition to the nonlinearity error reduction,
M
the sensitivity was also decreased by 6.9 % compared with the peninsula diaphragm without the center boss (but it’s still 31.6 % larger compared with the CBM structure).
te
d
The results suggested that the trade-off between sensitivity and linearity still existed during the optimization of the diaphragm. Comparisons with the hollow stiffening structure
Ac ce p
3.4.4
For comparisons with Kinnell’s 3 KPa pressure sensor with the novel hollow
stiffening structure [9], the modified peninsula diaphragm with a center boss was also optimized based on the dimensions of Kinnell’s structure, which had a thickness of 5 μm and width of 1550 μm as shown in Fig. 11 (a).
was set to the maximum value
1.38e-9 /Pa corresponding to a relatively low doping concentration. Since the detailed side length of the three bosses were not provided in [9], the test results were adopted for comparisons with the peninsula structure as shown in Fig. 11 (b) and 11 (c). It is noted that compared with the hollow stiffening structure, a higher sensitivity of 37.5
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mV/KPa and a lower nonlinearity of 0.07 %FFS could be achieved for the modified peninsula structure with a center boss in the pressure range of 0 ~ 3 KPa. It should be noted that the sensitivity of the sensor was also related to the doping concentration of
ip t
the piezoresistors, it would decrease as the doping concentration increased. Moreover,
cr
since the hollow stiffening structure applied the electrochemical etch-stop method to
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fabricate the diaphragm, the hollow stiffening structure had the advantage of high precision diaphragm thickness / sensor performance control which were very
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important for yield improvement in mass production. Based on the simulation results, when the diaphragm thickness had variations of ± 1μm, the proposed sensor structure
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would have sensor outputs between 88.9 ~ 137.4 mV and nonlinearity errors between - 0.16 %FFS ~ + 0.31 %FFS. For better uniformity of the sensor’s performance, SOI
te
d
(silicon on insulator) wafer or EPI (epitaxial) wafer with electrochemical etching technology would be an appropriate choice for sensor fabrication. Dynamic behavior comparisons
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3.4.5
Besides the sensitivity and linearity performance, the mechanical stability of the
diaphragm is also of particular importance for ultra-high sensitive pressure sensors used in high accuracy measurement. Mechanical stability of the diaphragm is dominated by the first resonance frequency of the diaphragm. In order to stabilize the diaphragm, normally a higher first resonance frequency is preferred. As shown in Fig. 12, the dynamic behavior analysis indicated that for sensors of case 1 (Fig. 8) the highest first resonance frequencies of 58.0 kHz was achieved for the peninsula-structured diaphragm with an increment of 121 % and 42 % compared with
Page 19 of 41
the center-bossed diaphragm and flat diaphragm respectively; while for sensors in case 2 and 3 (Fig.9 and 10) the first resonance frequencies almost equaled with each other. The results indicated that the peninsula-structured diaphragm and the modified
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peninsula diaphragm with a center boss were as good as the CBM structure in terms
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of diaphragm stability and were much better as compared with the center-bossed and
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flat diaphragms.
In this section, structured diaphragm was applied to improve the characteristics of
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a standard flat square diaphragm. After the geometrical optimization process, the novel peninsula-structured diaphragm was proposed. Comparisons with typical sensor
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structures were conducted and summarized in terms of sensitivity, maximum
d
nonlinearity error and first resonant frequency as shown in table 2. With the same
te
diaphragm dimensions and piezoresistor designs, the proposed sensor structures could achieve the highest sensitivity, good nonlinearity and mechanical stability
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performance as compared to the alternatives. In particular, ultra-low nonlinearity performance was achieved by the modified peninsula-structured diaphragms for the pressure range of 5 KPa and 3 KPa respectively with different diaphragm dimensions. It is concluded that our present sensor structures have the best overall performance among these sensor structures.
4. Fabrication Process A fabrication process for the proposed sensor with the peninsula structured diaphragm will be presented in detail. An overview of the process is shown in Fig. 13,
Page 20 of 41
it mainly consisted of four process steps. The first step was the fabrication of piezoresistors and heavily doped section (Fig. 13 (a) and (b)). The 4 inch n-type (100) oriented Si wafer was chosen as the substrate. After the thermal oxidization process,
ip t
photo lithography and Boron implantation was employed to pattern and form the
cr
piezoresistors and the heavily doped contact sections on the front side of the silicon
wafer. After the final thermal activation process, a sheet resistance of 243 Ω/□ was
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achieved for the piezoresistors with a surface doping concentration of 2.5e18/cm-3.
an
The second step was the KOH (potassium hydroxide) solution anisotropy etching process (Fig. 13 (c)). The passivation films of SiO2 and Si3N4 were deposited by
M
means of low pressure chemical vapor deposition (LPCVD) process. After patterning, cavity etching was conducted at a constant temperature of 80 ± 1 °C. The etching
te
d
solution was pure aqueous KOH solution with a KOH content of 30 wt%. The solution was agitated at a relatively low speed by a stirrer with three large blades
Ac ce p
turning at around 50 rpm. With the etching depth of nearly 380 μm, the variations of the etching depth within a wafer could be decreased from larger than ± 5 μm (without stirring) to less than ± 1 μm for more than 85 % of the cavities. Considering the thickness variation of the Si wafer (± 1 μm), the diaphragm thickness of 19 ± 2 μm
could be achieved. The third step was the metallization process (Fig. 13 (d)). It began with the contact hole etching, followed by Al (aluminum) sputtering with a thickness of 1 μm. Then lithography and Al etching process were conducted to form the electrode. After a sintering process low resistance ohmic contact was formed between the heavily doped section and Al pad. The last step was ASE (advanced silicon
Page 21 of 41
etching) process on the front side to form the peninsula structure with a depth of 9 μm (Fig. 13 (e)). The fabricated pressure sensor is shown in Fig. 14, where the SEM
ip t
images of the piezoresistors are displayed in detail.
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5. Experimental results
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The schematic diagram of packaged pressure sensor structure is shown in Fig. 15(a). After dicing, the sensor chip was assembled on a gold-plated Kovar base
an
through adhesive. Wire bonding process using gold wire was implemented to realize the connection between the pressure chip and the pins. A via hole existed at middle of
M
the Kovar base, so differential pressures could be loaded on the sensor’s diaphragm.
d
In order to test the sensor performance with pressure loadings, a special nut-screw
te
structure was designed and applied, as shown in Fig. 15(b). The packaged sensor was assembled in the nut with the pins of the sensor connected with the signal wire from
Ac ce p
the backside of the nut. Anti-leak rubber was used to prevent pressure leakage from the nut during the test. When the screw with a PVC hose and the nut with the packaged sensor were screwed together, pressure ranging from 0 to 5 kPa could be applied to the sensor chip from the PVC hose using the PPC2+ gas pressure controller.
Three sensor devices from different regions of the same wafer were measured. The measured voltage outputs and calculated nonlinearity errors are shown in Fig. 16. The average sensitivity of the three devices was 19.9 mV/V full-scale output with the average maximum nonlinearity error of 0.42 %FSS. The realistic performances of
Page 22 of 41
these sensors are well within the simulation with diaphragm thicknesses of 10.2 ~ 10.8 μm in the tolerance range of 10 ± 2 μm. The zero offset voltages for the three devices ranged between 2.2 ~ 9.1 mV. During pressure cycling from 0 to 5 kPa and 5
ip t
kPa to 0, there was no indication of pressure hysteresis. The detailed technical data of
cr
the device 3 at 21 °C is listed in Tab. 3. In particular, the tested burst pressure of
us
device 3 was 57 kPa, a factor of 10 larger than the full pressure range (5 kPa).
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6. Summary and Conclusion
A highly sensitive, linear and stable pressure sensor featuring the novel
M
peninsula-structured diaphragm was proposed. Based on detailed study of the stress distribution characteristics for the diaphragm, a special piezoresistor design was
te
d
evaluated and adopted for sensor performance optimization. Utilizing the mature technologies of KOH and ASE etching, the proposed sensor structure was
Ac ce p
manufactured based on the cost-effective silicon wafer, which was particularly important for low-cost mass production. In comparison to typical sensors with center-bossed, CBM structure, hollow stiffening structure and flat diaphragm, the FEM simulation indicated that by proper geometrical optimization the proposed sensor with peninsula structured diaphragm could achieve the best overall performance among these sensors. In particular, ultra-low nonlinearity performance could be achieved by the modified peninsula-structured diaphragm. In accordance with the FEM results, the fabricated pressure sensor showed that a sensitivity of 18.4 mV/V full-scale output and nonlinearity of 0.36 %FSS were achieved for the full
Page 23 of 41
pressure range of 5 kPa with no indication of pressure hysteresis. It is concluded that the proposed sensor has excellent sensitivity, linearity, diaphragm stability and the most important feature low cost. The proposed sensor structure with the
ip t
peninsula-structured diaphragm is potentially a better choice for designing low
cr
pressure sensors in fields like biomedical, smart homes and aerodynamics.
us
Acknowledgment
This work was financed by 863 Program (Grant No. 2011AA040401) and 973
an
Program (Grant No. 2011CB309502). The sensor fabrication and measurement were supported by National Key Laboratory of Science and Technology on Micro/Nano
M
Fabrication, Institute of Microelectronics, Peking University.
References[1] W.J. Fleming, Overview of Automotive Sensors, IEEE Sensors Journal, 1 (4)
d
(2001) 296-308.
[2] W. P. Eaton, J. H. Smith, Micromachined pressure sensors: review and recent developments,
te
Smart Mater. Struct. 6 (1997) 530–539
[3] S. Marco, J. Samitier, O. Ruiz, J.R. Morante, J.E. Steve, High performance piezoresistive
Ac ce p
pressure sensors for biomedical applications using very thin structured membranes, Meas. Sci. Technol. 7 (1996) 1195–1203
[4] D. Ding, R.A. Cooper, P.F. Pasquina, L.F. Pasquina, Sensor technology for smart homes, Maturitas, 69 (2011) 131-136.
[5] J. Hurault, S. Kouidri, F. Bakir, Experimental investigations on the wall pressure measurement on the blade of axial flow fans, Experimental Thermal and Fluid Science, 40 (2012) 29-37
[6] H. Takahashi, K. Matsumoto, I. Shimoyama, Differential pressure distribution measurement of a free-flying butterfly wing, Transducers, 2011, pp. 2022-2025.
[7] A. Yasukawa, M. Shimazoe, Y. Matsuoka, Simulation of circular silicon pressure sensors with
a center boss for very low pressure measurement, IEEE Trans. Electron Devices, 36 (1989) 1295-1301.
[8] H. Sandmaier and K. Kuhl, A square-diaphragm piezoresistive pressure sensor with a rectangular central boss for low-pressure ranges, IEEE Trans. Electron Devices 40 (1993)1754-1759.
[9] P.K. Kinnell, J. King, M. Lester, R. Craddock, A hollow stiffening structure for low-pressure sensors, Sens. Actuators A 160 (2010) 35-41.
[10] M.H. Bao, L.Z. Yu, Y. Wang, Micromachined beam-diaphragm structure improves performances of pressure transducer, Sens. Actuators A 21-A23 (1990) 137-141.
[11] B. Tian, Y. L. Zhao, Z. D. Jiang, B. Hu, The design and analysis of beam-membrane structure
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sensors for micro-pressure measurement, Rev. Sci. Instrum. 83 (2012) 045003.
[12] Z. L. Yu, Y. L. Zhao, L. Sun, B. Tian, Z.D Jiang, Incorporation of beams into bossed diaphragm for a high sensitivity and overload micro pressure sensor, Rev. Sci. Instrum. 84 (2013) 015004.
[13] K. Matsuda, K. Suzuki, K. Yamamura, Y. Kanda, Nonlinear piezoresistance effects in silicon, J Appl. Phys. 73 (1993) 1838-1847; piezoresistive pressure sensors, J. Microelectromech. Syst. 8(4) (1999) 514-522.
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[14] L.W. Lin, H.C. Chu, Y.W. Lu, A simulation program for the sensitivity and linearity of
[15] J.A. Chiou, S. Chen, Pressure nonlinearity of micromachined piezoresistive pressure sensors
cr
with thin diaphragms under high residual stresses, Sens. Actuators A 147 (2008) 332-339.
[16] C.S. Smith, Piezoresistance effect in germanium and silicon, Phys. Rev. 94 (1954) 42-49. [17] S. Marco, J. Samitier, O. Ruiz, J. R. Morante, J. Esteve, High-performance piezoresistive
us
pressure sensors for biomedical applications using very thin structured membranes, Meas. Sci. Technol. 7 (1996) 1195-1203.
[18] H.S. Hsieh , H.C. Chang , C.F. Hu, C.P. Hsu, W. Fang, Method for sensitivity improvement
Ac ce p
te
d
M
an
and optimal design of a piezoresistive pressure sensor, IEEE Sensors Conference, 2010, pp. 1799-1802.
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Figure 1 Proposed sensor structure.
ip t
Figure 2 Stress distribution characteristics for the diaphragm under uniform 5 kPa pressure loading. (a) The stress intensity distribution for a 1/4 model of the sensor (flat area 10 μm thick and peninsula area 19 μm thick). (b) The stress difference (Sx-Sy) between longitudinal and transvers direction along the path that goes from the central point to diaphragm edge for the peninsula-structured and flat diaphragms (10 μm and 19 μm thick) respectively.
an
us
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Figure 3. Stress distributions along the path that parallels to the diaphragm edge with a distance of 25 μm, the background is the stress distributions around the narrow beam of the peninsula structure. (a) Stress Sx-Sy along the path for peninsula-structured diaphragm (black curve) and flat diaphragm (10 μm thick, red curve). The background is the stress intensity distribution. (b) Stress Sx along the path. The background is the distribution of the stress Sx. (c) Stress Sy along the path. The background is the distribution of the stress Sy.
Figure 4 Schematic illustration of four candidate designs for the piezoresistors.
M
Figure 5 Simulated sensor output (a) and nonlinearity error (b) versus pressure loading of each candidate design shown in Fig. 4.
Ac ce p
te
d
Figure 6 Optimization process for the peninsula structure (a) four sensors with flat diaphragm, large rectangular structure, small rectangular structure and peninsula structure (b) diaphragm deflections from the diaphragm center to the middle of the diaphragm edge under 5 KPa pressure loading (c) stress distributions from diaphragm center to the middle of the diaphragm edge under 5 KPa pressure loading (d) nonlinearity error versus pressure loading (e) sensor output versus pressure loading.
Figure 7 Diaphragm optimization in terms of peninsula height and diaphragm thickness. (a) Sensor outputs and nonlinearity errors with respect to peninsula height (b) sensor outputs and nonlinearity errors with respect to diaphragm thickness.
Figure 8 Comparisons with the center-bossed and flat diaphragms. (a) Three sensor structures (b) sensor outputs versus pressure loading (c) nonlinearity errors versus pressure loading.
Figure 9 Comparisons with the CBM structure. (a) Geometry of the CBM and peninsula structures (b) stress distributions from the diaphragm center to the middle of the diaphragm edge (c) sensor outputs versus pressure loading (d) nonlinearity errors versus pressure loading.
Figure 10 Modified peninsula structure with a center boss to achieve the close to zero nonlinearity error. (a) Geometry of the sensor structure (b) sensor outputs versus
Page 26 of 41
pressure loading (c) nonlinearity errors versus pressure loading.
Figure 11 Comparisons with the hollow stiffening structure. (a) Geometry of the sensor structures (b) sensor outputs versus pressure loading (c) nonlinearity errors versus pressure loading.
cr
ip t
Figure 12 Dynamic behavior of the sensors with different types of diaphragm. (a)~(c) first resonance mode of the peninsula diaphragm, center-bossed diaphragm and flat diaphragm of case 1; (d)~(f) first resonance mode of the CBM structure, peninsula diaphragm and modified peninsula diaphragm with a center boss of case 2 and 3.
Figure 13 Overview of the fabrication process.
us
Figure 14 SEM images of the pressure sensor and the piezoresistors.
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Figure 15 Package of the pressure sensor (a) schematic diagram of packaged pressure sensor structure (b) packaged sensor and the designed nut-screw structure for sensor measurement.
Ac ce p
te
d
M
Figure 16 Measured sensor outputs (a) and nonlinearity errors (b) versus pressure loading for three sensor devices.
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Xian Huang was born in 1988. He is from the Shenzhen Graduate School of Peking University, Shenzhen, China. He has been working toward the Ph.D degree in the Institute of Microelectronics since 2010, Peking University, Beijing, China. His main research interests include micro/nano fabrication technology and MEMS piezoresistive devices.
Ac ce p
te
d
M
an
us
cr
ip t
Dacheng Zhang, received the Ph.D. degree from the Institute of Microelectronics, Peking University in 2005, Beijing, China. He is currently a professor in the Institute of Microeletronics, Peking University. His main search is about micro/nano fabrication technology, mechanics properties analyzing of micro-structure and MEMS devices.
Page 28 of 41
Ac ce p
te
d
M
an
us
cr
ip t
Highlights • A peninsula-structured diaphragm was proposed in pressure sensor design. • The resistor design was optimized to improve the sensor performance. • The new sensor design has been compared with other typical sensors. • Ideal results were obtained after fabrication and test of the proposed sensor.
Page 29 of 41
us
cr
ip t
Figures
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Figure 1 Proposed sensor structure
Ac ce p
te
d
M
Figure 2 Stress distribution characteristics for the diaphragm under uniform 5 kPa pressure loading. (a) The stress intensity distribution for a 1/4 model of the sensor (flat area 10 μm thick and peninsula area 19 μm thick). (b) The stress difference (Sx-Sy) between longitudinal and transvers direction along the path that goes from the central point to diaphragm edge for the peninsula-structured and flat diaphragms (10 μm and 19 μm thick) respectively.
Page 30 of 41
ip t cr us an M d te Ac ce p
Figure 3. Stress distributions along the path that parallels to the diaphragm edge with a distance of 25μm, the background is the stress distributions around the narrow beam of the peninsula structure. (a) Stress Sx-Sy along the path for peninsula-structured diaphragm (black curve) and flat diaphragm (10 μm thick, red curve). The background is the stress intensity distribution. (b) Stress Sx along the path. The background is the distribution of the stress Sx. (c) Stress Sy along the path. The background is the distribution of the stress Sy.
Page 31 of 41
ip t cr
te
d
M
an
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Figure 4 Schematic illustration of four candidate designs for the piezoresistors
Ac ce p
Figure 5 Simulated sensor output (a) and nonlinearity error (b) versus pressure loading of each candidate design shown in Fig. 4.
Page 32 of 41
ip t cr us an M
Ac ce p
te
d
Figure 6 Optimization process for the peninsula structure (a) four sensors with flat diaphragm, large rectangular structure, small rectangular structure and peninsula structure (b) diaphragm deflections from the diaphragm center to the middle of the diaphragm edge under 5 KPa pressure loading (c) stress distributions from diaphragm center to the middle of the diaphragm edge under 5 KPa pressure loading (d) nonlinearity error versus pressure loading (e) sensor output versus pressure loading.
Figure 7 Diaphragm optimization in terms of peninsula height and diaphragm thickness. (a) Sensor outputs and nonlinearity errors with respect to peninsula height (b) sensor outputs and nonlinearity errors with respect to diaphragm thickness.
Page 33 of 41
ip t cr us an M
Ac ce p
te
d
Figure 8 Comparisons with the center-bossed and flat diaphragms. (a) Three sensor structures (b) sensor outputs versus pressure loading (c) nonlinearity errors versus pressure loading.
Page 34 of 41
ip t cr us an M d te Ac ce p
Figure 9 Comparisons with the CBM structure. (a) Geometry of the CBM and peninsula structures (b) stress distributions from the diaphragm center to the middle of the diaphragm edge (c) sensor outputs versus pressure loading (d) nonlinearity errors versus pressure loading.
Page 35 of 41
ip t cr us an M d te
Ac ce p
Figure 10 Modified peninsula structure with a center boss to achieve the close to zero nonlinearity error. (a) Geometry of the sensor structure (b) sensor outputs versus pressure loading (c) nonlinearity errors versus pressure loading.
Page 36 of 41
ip t cr us an M d
Ac ce p
te
Figure 11 Comparisons with the hollow stiffening structure. (a) Geometry of the sensor structures (b) sensor outputs versus pressure loading (c) nonlinearity errors versus pressure loading.
Page 37 of 41
ip t cr us an M
Ac ce p
te
d
Figure 12 Dynamic behavior of the sensors with different types of diaphragm. (a)~(c) first resonance mode of the peninsula diaphragm, center-bossed diaphragm and flat diaphragm of case 1; (d)~(f) first resonance mode of the CBM structure, peninsula diaphragm and modified peninsula diaphragm with a center boss of case 2 and 3.
Figure 13 Overview of the fabrication process
Page 38 of 41
ip t
cr
Figure 14 SEM images of the pressure sensor and the piezoresistors
te
d
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an
us
Ac ce p
Figure 15 Package of the pressure sensor (a) schematic diagram of packaged pressure sensor structure (b) packaged sensor and the designed nut-screw structure for sensor measurement
Figure 16 Measured sensor outputs (a) and nonlinearity errors (b) versus pressure loading for three sensor devices.
Page 39 of 41
Tables
200
12
12
5
Ac ce p
te
d
M
an
us
Table 3 Technical data of the device 3 at 21 °C Full range pressure (kPa) 5 Full range output (mV) 92.1 Wheatstone bridge resistance (Kohm) 3.9 Supply voltage (V) 5 Zero output (mV) 2.2 Sensitivity (mV/kPa) 18.4 Nonlinearity error (%FFS) 0.36 Burst pressure (kPa) 57 Die size (mm) 3.6*3.6*0.4
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3.9
Distance d (μm)
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Table 1 Configuration for the piezoresistors Piezoresistor (PZR) Total Length Width Space Resistance (μm) (μm) (μm) ( )
Page 40 of 41
Table 2 Performance comparisons of different sensor structures. Performance comparisons
Case 2
Center-boss ed
18.40
0.48
Flat diaphragm
20.10
CBM structure Peninsula-st ructure
Ac ce p Case 3
Modified peninsula-st ructure with a center boss
Case 4* Hollow stiffening structure Case 4
Modified peninsula-st ructure with a center boss
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0.48
58.0
cr
22.40
te
Case 2
Peninsula-st ructure
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Case 1
(mV/KPa)
Nonlinearity First resonant error frequency (|%FFS|) (KHz)
an
Case 1
Sensitivity
26.2
1.20
40.9
10.48
0.13
44.5
14.81
0.16
44.2
13.79
0.018
43.5
30.0
0.35
——
37.5
0.07
55.3
M
Case 1
Sensor structures
Diaphragm types
d
Group
* The data of the hollow stiffening structure was from the test results in reference [9]
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S0924-4247(14)00283-0 http://dx.doi.org/doi:10.1016/j.sna.2014.05.031 SNA 8818
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
17-2-2014 28-5-2014 29-5-2014
Please cite this article as: X. Huang, D. Zhang, A High Sensitivity and High Linearity Pressure Sensor Based on a Peninsula-Structured Diaphragm for Low-Pressure Ranges, Sensors and Actuators: A Physical (2014), http://dx.doi.org/10.1016/j.sna.2014.05.031 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A High Sensitivity and High Linearity Pressure Sensor Based on a Peninsula-Structured Diaphragm
ip t
for Low-Pressure Ranges
us
cr
Xian Huang1,2 and Dacheng Zhang2,* 1 Shenzhen Graduate School, Peking University, Shenzhen, P. R. China 2 Institute of Microelectronics, Peking University, Beijing, P. R. China [email protected], [email protected]
an
Abstract
The trade-off between sensitivity and linearity has been the major problem in
problem,
a
novel
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designing the piezoresistive pressure sensors for low pressure ranges. To resolve the peninsula-structured
diaphragm
with
specially
designed
d
piezoresistors was proposed. Finite element method (FEM) was adopted for analyzing
te
the sensor performance as well as comparisons with other sensor structures. In
Ac ce p
comparison to flat diaphragm, the proposed sensor design could achieve a sensitivity increase by 11.4 %, nonlinearity reduction of 60 % and resonance frequency increase of 41.8 %. In addition, the modified peninsula-structured diaphragms featuring a center boss have been optimized to achieve ultra-low nonlinearities of 0.018 %FFS and 0.07 %FFS for the 5 KPa and 3 KPa pressure ranges respectively with higher sensitivities as compared to the CBM (cross beam membrane) and hollow stiffening structures. In accordance with the FEM results, the fabricated pressure sensor with the peninsula-structured diaphragm showed a sensitivity of 18.4 mV/V full-scale output and a nonlinearity error of 0.36 %FSS in the pressure range 0 ~ 5 kPa. The proposed sensor structure is potentially a better choice for designing low pressure sensors.
Page 1 of 41
Keywords: MEMS pressure sensor, Peninsula-structured diaphragm, Sensitivity and
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Linearity, FEM, Sensor fabrication
to
the
simple
and
low-cost
fabrication
process,
MEMS
us
Attributed
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1. Introduction
(Micro-Electro-Mechanical systems) piezoresistive pressure sensors have been in
an
mass production for over three decades. Normally, the sensor is fabricated by bulk silicon micro-machining processing technique. The key component of the sensor is a
M
thin square diaphragm which deflects when pressure is applied. Four Piezoresistors configured in a Wheatstone bridge are placed near the center of the diaphragm edge.
te
d
The bridge converts the stress in the deflected diaphragm to an electrical signal. By adjusting the dimensions of the diaphragm, a wide measurement range of pressure can
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be obtained. Piezoresistive pressure sensors have been used in a wide range of applications, for instance, the automobiles [1] and process control [2]. Recently, there is a rapid growth in demand for the ultra-low pressure measurement in fields like biomedical (invasive measurements) [3], smart homes such as HVAC (heating, ventilation and air conditioning) controls [4] and aerodynamics such as wall/wing pressure measurement [5,6]. In order to apply for ultra-low pressure (for example ≤ 5 KPa) measurement, the sensitivity should be significantly improved to maintain an appropriate sensor output (for example ≥ 15 mV/(V FFS)) for signal processing. Based on the mechanical behavior of the flat square diaphragm, sensitivity is
Page 2 of 41
proportional to the square of the ratio of diaphragm width to diaphragm thickness. Thus, sensitivity can be increased by a larger width / thickness ratio. Unfortunately, the nonlinearity error increases with this ratio at a much faster rate [3], a non-tolerable
ip t
nonlinearity error (for example > 1.0 %FFS) may be occurred during the sensitivity
cr
optimization process. Therefore, the nonlinearity problem involved in the low
us
pressure sensors should be solved to open the new areas of applications.
Various types of modified diaphragms for the fabrication of low pressure sensors
an
have already been reported to resolve the nonlinearity problem. In order to increase the stiffness of the diaphragm, center bosses were often added to the diaphragm [7,8].
M
It was an effective method to reduce the nonlinearity error. However, the reduction of nonlinearity error was achieved at the expense of sensitivity or sensor size. Besides,
te
d
the additional center mass would increase the acceleration sensitivity of the diaphragm, which was detrimental for the stability of the sensor for high sensitivity
Ac ce p
and accuracy applications. To tackle this problem, P.K. Kinnell [9] introduced a novel hollow stiffening structure to replace the solid center boss and a 30 mbar (3 KPa) full-scale differential pressure sensor with the hollow stiffening structure was fabricated. The sensor had perfect performances with a sensitivity of 18 mV/V full-scale output and linearity < 0.4 %FSS. The sensor allowed the advantages gained by a stiffening boss in terms of sensor linearity without either the negative effects of acceleration sensitivity or unnecessary increase in die size. Based on the electrochemical etch-stop technology, the hollow stiffen structure also had the advantages of high precision diaphragm thickness / sensor performance control.
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Nevertheless, the fabrication process for the hollow stiffening structure was relatively complicated and the key processes (including electrochemical etch-stop and fusion bonding process) require specialized production facilities which have not been widely
ip t
adopted in foundries yet. The front-side beam diaphragm first proposed by M.H. Bao
cr
[10] has also been widely adopted for low pressure sensor design. Recently, a novel
us
front-side cross beam membrane (CBM) structure was proposed by B. Tian [11] and further developed by Z. L. Yu [12] for micro pressure measurement. Tian’s CBM
an
structure exhibited perfect linearity and stability performance, but the sensitivity was relatively low (7.081 mV/kPa, DC power 4.57 V) for measuring 5 KPa pressure. Yu
M
combined the CBM structure with a double-side center boss for measuring absolute micro pressure lower than 500 Pa. High sensitivity and high overload resistance were
te
d
achieved, but the nonlinearity problem (3.046 %FSS) remained unsolved. Many factors that influence the nonlinearity performance of the low pressure
Ac ce p
sensors have also been reported. Matsuda [13] presented the nonlinear piezoresistance effects in silicon. Lin [14] studied the sensitivity and nonlinearity issue on the pressure sensors with a half Wheatstone bridge configuration by characterizing the diaphragm thickness and the length of sensing resistors. Chiou [15] discussed the linearity performance of the pressure sensor under high residual stress induced by passivation films and anodic bonding. However, in previous works that applied structured diaphragm for pressure sensor design, only limited discussion concerned the influence of pattern and positioning of piezoresistors on sensor’s nonlinearity performance. Despite the growing achievements in low pressure sensor design and
Page 4 of 41
fabrication, additional research and considerable progress are still needed to further improve the performances of the pressure sensor such as the increasing of sensor output and stability, the decreasing of nonlinearity error, chip size and fabrication
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cost.
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In our study, a novel high sensitivity and high linearity pressure sensor based a
us
peninsula-structured diaphragm for low pressure ranges was proposed. The proposed sensor structure could have the advantages of low fabrication cost, high sensitivity,
an
good linearity and diaphragm stability over other existing structures. In the following sections, stress distribution characteristics for the proposed diaphragm under pressure
M
loading were studied in detail by FEM analysis. The influences of the pattern and positioning of piezoresistors as well as the lithography alignment errors on sensor’s
te
d
performance were discussed. Comparisons with other sensor structures with typical flat, center-bossed diaphragm and recently proposed CBM, hollow stiffen structure
Ac ce p
were carried out respectively in terms of sensitivity and linearity to demonstrate the superiority of the sensor structure. Moreover, modified peninsula-structured diaphragms featuring a center boss have been optimized to achieve ultra-low nonlinearity errors with higher sensitivities. A fabrication process for the proposed sensor with the peninsula diaphragm was presented in detail. Finally, the fabricated sensor devices were tested and compared with the FEM result, which verified the accuracy of the FEM simulation.
2. Background
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2.1 Sensor output Diaphragm type piezoresistive pressure sensors are usually arranged into a full
on the diaphragm, and
and
and
) loaded
) loaded transversely. When the pressure is applied will have the same positive increment
. Due to different patterning and
us
will have the same negative increment
, while
cr
longitudinally and two (
and
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Wheatstone bridge configuration with two piezoresistors (
positioning of the piezoresistors, the resistance increment
normally differs to
an
. Based on the Wheatstone bridge circuit, the correlation between the output voltage and the resistance can be described as
M
(1)
d
where Vin is the source DC power and Vout is the output voltage. R is the resistance of the
te
piezoresistors. Since the resistance change is proportional to the mechanical stress, for
Ac ce p
low doped P-type piezoresistors along <110> direction: represents the shear piezoresistance coefficients and
(
represents the average stress
difference between longitudinal and transverse directions within the resistor) [16]. Then the correlation between the output voltage and the mechanical stress can be obtained as
(2)
where
and
are average stress for resistor
and
respectively.
2.2 Nonlinearity error The terminal based nonlinearity error of the pressure sensor is defined as [15]
Page 6 of 41
(3) where Delt is the voltage output difference between the real voltage output and the
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ideal linear output. The full-scale span (FSS) is the voltage range of the full pressure range. NL is the terminal based nonlinearity error.
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There are two major sources for the nonlinearity error of a diaphragm type
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piezoresistive pressure sensor with the Wheatstone bridge configuration [17]. The first source is the nonlinear dependence of the stress with the applied pressure when large
an
deflection of the diaphragm occurs (balloon effect). The second source is the unbalanced stress (
M
in equation (2)) among piezoresistors in the and
, the stress term
d
Wheatstone bridge. If a stress unbalance appears between
te
would have a non-zero value, the sensor output would not be proportional
Ac ce p
to the applied stress even if all the stress terms in equation (2) change linearly under small deflection.
For flat diaphragm, the trade-off between sensitivity and linearity will become
irreconcilable when designing sensors for very low pressure measurement as discussed in the introduction. In our case, for the 5 KPa full range pressure sensor designed based on the flat diaphragm with a thickness of 10 μm, the output voltage
could reach 100 mV (the source voltage is 5 V and the doping concentration of piezoresistors is 2.5e18 /cm-3) by adjusting the diaphragm’s width. However, the nonlinearity error would exceed 1.2 %FFS at the same time.
In order to meet
Page 7 of 41
simultaneously the NL design criteria within 0.5 % and the output beyond 100 mV for
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measuring the 5 kPa pressure, the flat diaphragm of the sensor must be modified.
3. Sensor Design
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A novel sensor structure featuring a peninsula-structured diaphragm was proposed
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to solve the abovementioned contradiction between the nonlinearity and sensitivity as shown in Fig. 1. The peninsula structures were located near the diaphragm edge with
an
narrow beams connecting to the Si pedestal. Four piezoresistors on the narrow beams
M
connected with each other to form the Wheatstone bridge. The side length of the diaphragm was 1900 μm. The thickness of the diaphragm was 10 μm while the extra
te
are 3600 × 3600 × 400 μm³.
d
thickness of the peninsular structure was designed to be 9 μm. The device dimensions
Ac ce p
Through the application of the peninsula structure, on the one hand, the effect of local stiffening of the diaphragm was realized which could reduce the axial stress induced by large deflection effect and thereby decrease the mechanical nonlinearity error; on the other hand, the linear bending stress would be concentrated at the narrow beam of the peninsula which ensured a high sensitivity of the sensor. Besides, since the peninsula were located at the diaphragm edge, the influence brought by the mass of the peninsula on acceleration sensitivity was much less compared with the diaphragms with the center bosses. The peninsula stiffened the diaphragm and concentrated stress in regions with piezoresistors during pressure loading, which makes it possible to achieve high sensitivity, good linearity and diaphragm stability
Page 8 of 41
simultaneously. Stress distribution characteristics for the peninsula structure will be discussed in detail for optimization of the sensor performance.
3.1.1
ip t
3.1 Finite element method analysis Stress distribution characteristics for the diaphragm
cr
The sensor performances were predicted by the non-linear static analysis and
us
modal analysis by the ANSYSTM software. Owing to the symmetry, only a quarter of the finite element model of the pressure sensor was established. Figure. 2(a) shows
an
the stress intensity distribution for the peninsula-structured diaphragm under 5 kPa uniform pressure loading. In accordance with the previous discussion, the mechanical
M
stress concentrated at the narrow beam of the peninsula structure. For the P-type
d
<110> oriented piezoresistors, the resistance change and the sensitivity of the sensors =Sx-Sy) between
te
are actually determined by the magnitude of the stress difference (
the longitudinal and transverse direction. The curves in Fig. 2(b) represent the
Ac ce p
distribution of the stress Sx-Sy from the central point to the diaphragm edge for the flat (10 μm and 19 μm thick) and peninsula-structured diaphragms (flat area 10 μm thick and peninsula area 19 μm thick). It is evident that the mechanical stress for each diaphragm reached its maximum at the center of the diaphragm edge. The maximum stress in peninsula-structured diaphragm was increased up to 350 % compared with flat diaphragm with the thickness of 19 μm, whereas it slightly reduced compared with flat diaphragm with the diaphragm thickness of 10 μm. 3.1.2
Stress distribution characteristics for the narrow beam of the peninsula
Page 9 of 41
The
stress
distribution
characteristics
near
the
narrow
beam
of
the
peninsula-structured diaphragm were studied in detail as shown in Fig. 3. The distributions of stress Sx-Sy along the path that parallels to the diaphragm edge for the
ip t
peninsula-structured diaphragm (black curve) and flat diaphragm (10 μm thick, red
cr
curve) are plotted in Fig. 3(a). The distance of the analyzed path to the diaphragm
us
edge was 25 μm. For the case of peninsula-structured diaphragm, from the beam center to the beam edge, the stress Sx-Sy monotonically increased from 28.3 MPa to
an
41.8 MPa with an increment of nearly 48 %. The distributions of stress Sx and Sy are plotted in Fig. 3(b) and 3(c) respectively. Since there’s no constrains on the beam edge
M
in the Y direction, from beam center to beam edge, the tensile stress Sy would decrease monotonically to zero (see Fig. 3(c)). Meanwhile, the decreased constrains in
te
d
Y direction would contribute to the deformation in X direction, which in turn induced a slight increase in tensile stress Sx (see Fig. 3(b)). In summary, the increase of tensile
Ac ce p
stress Sx, coupled with the decrease of tensile stress Sy led to the increase of Sx-Sy from the beam center to beam edge shown in Fig. 3(a). As for flat diaphragm, the stress Sx-Sy slightly reduced along the same path, which is a widely known result. Remarkably, though for peninsula-structured diaphragm the stress Sx-Sy at the beam center was smaller compared with that of the 10 μm thick flat diaphragm (see Fig. 2(b) and Fig. 3(a)), the stress at the beam edge is about 25 % larger than the maximum stress in flat diaphragm (see Fig. 3(a)). For the purpose of maximizing sensitivity of the sensor, the sensing piezoresistors should be placed at regions of maximum stress Sx-Sy. For peninsula-structured
Page 10 of 41
diaphragm, piezoresistors should be placed close to the corner formed by the diaphragm edge and the beam edge. However, the stress was non-uniform and rapidly changing in these regions, just as shown in Fig. 3(a). Therefore, the risk of severe
ip t
performance degradation in case that lithography alignment error occurs during
cr
fabrication process should be evaluated and the pattern of the piezoresistors should be
us
properly designed. 3.2 Piezoresistor design
an
The sensor performance is closely related to the pattern and positioning of the piezoresistors. For comparison and optimization, four candidate designs for the
M
piezoresistors were proposed as shown in Fig. 4. The configurations for the
d
piezoresistors are listed in table 1. All resistors were along the <110> direction. The
te
total length and width of the resistors were fixed at 200 μm and 12 μm respectively. Design I~III were commonly applied in flat diaphragms [18], they were arranged at
Ac ce p
the center of the beam with different turns. Design IV was specially designed for the peninsula-structured diaphragm. Based on the analysis of stress distribution characteristics, the piezoresistors in design IV were positioned at regions of maximum stress Sx-Sy, therefore it would achieve the largest sensitivity among the four candidate designs.
After obtain the average stress for each piezoresistor by FEA non-linear static analysis, the output voltage could be calculated by applying equation (1) and the nonlinearity error could be calculated based on equation (3). The source power Vin in equation (1) was set at 5 V. The dependence of the output voltage and nonlinearity
Page 11 of 41
error on the loading pressure for different piezoresistor designs are shown in Fig. 5. It was observed that both sensitivity and nonlinearity differed as the positioning of resistors changed. Among these four candidate designs, a maximum sensitivity of 22.4
ip t
mV/kPa was obtained in design IV as expected, while sensitivities around
cr
19.06~19.13 mV/kPa were obtained for the others (see Fig. 5(a)). Besides high
us
sensitivity, low nonlinearity error is also a very attractive sensor characteristic. Figure. 5(b) shows the terminal based nonlinearity error of each piezoresistor design. Design I
an
and II had the best nonlinearity error of 0.46 %FSS, design IV had a moderate nonlinearity error of 0.48 %FFS and design III showed a worst nonlinearity error of
M
0.53 %FSS. As discussed before, unbalanced stress between
and
was
te
designs.
d
responsible for the variations of the nonlinearity errors for different piezoresistor
From the above discussion, the piezoresistor design IV exhibited the largest
Ac ce p
sensitivity and a moderate nonlinearity error. In addition, since both
and
were symmetric positioned to the beam center (see Fig. 4), the sensor performance degradation induced by alignment errors between the piezoresistor layer and the peninsula layer could be reduced. Therefore, the non-uniform and rapidly changing stress in regions of piezoresistors in design IV will have little influence on the fabrication tolerance. Simulation results from FEM indicated that an alignment error of ± 2 μm (the maximum possible alignment error in our laboratory) had a negligible influence on the sensor performance with piezoresistor design IV, which demonstrated a good fabrication tolerance of the piezoresistor design IV. In summary,
Page 12 of 41
the largest sensitivity and moderate nonlinearity error, together with a good fabrication tolerance, make the piezoresistor design IV the best choice for application.
ip t
3.3 Geometrical optimization process for the 5 KPa pressure sensor The optimization process of the peninsula diaphragm for the 5 KPa pressure sensor
cr
including the proposal of the peninsula structure, the influences of peninsula height
us
and diaphragm thickness was discussed with reference to the sensor outputs and nonlinearity errors. Peninsula structure
an
3.3.1
M
Figure 6 shows the optimization process of the structured diaphragm for the 5 KPa pressure sensor. The piezoresistor design III was applied in the optimization process was set to 1.28e-9 /Pa corresponding to a doping concentration of
d
for simplicity.
te
2.5e18 /cm-3. The sensor with 100 mV full range output was first designed based on
Ac ce p
the conventional flat diaphragm with a thickness of 1900 μm and width of 10 μm (see Fig. 6 (a) 1-flat diaphragm). The nonlinear static simulation indicated that large
deflection of the diaphragm occurred: the deflection at the diaphragm center was 4.9 μm (see Fig. 6 (b)), the ratio of deflection to thickness reached 0.49 and the maximum
nonlinearity error exceeded 1.2 %FFS (see Fig. 6 (d)). In order to stiffen the diaphragm and reduce the nonlinearity errors, four relatively large rectangular bosses with a thickness of 5 μm were added to the diaphragm (see Fig. 6 (a) 2-large rectangular structure). It is noted that the diaphragm deflection was greatly reduced (see Fig. 6 (b)) as well as the nonlinearity errors of the sensor (see Fig. 6 (d)). However, the bending stress of the diaphragm (see Fig. 6 (c)) and the sensitivity of the
Page 13 of 41
sensor (see Fig. 6 (e)) were also reduced. For the purpose of concentrating the bending stress, the width of the rectangular structure was narrowed from 600 μm to 220 μm to form the small rectangular structure (see Fig. 6 (a) 3-small rectangular
ip t
structure). It is found that bending stress around the diaphragm edge was increased to
cr
the same value as the flat diaphragm (see Fig. 6 (c)) and a highest sensitivity of 20.74
us
mV/KPa was achieved (see Fig. 6 (e)). However, the nonlinearity error was also increased up to 1.03 %FFS (see Fig. 6 (d)). The simulation results clearly indicate that
an
the large rectangular structure had advantage of relatively good linearity and disadvantage of relatively low sensitivity; while the small rectangular structure had
M
advantage of relatively high sensitivity and disadvantage of relatively poor linearity performance. In order to allow for the nonlinearity error reduction by the large
te
d
rectangular boss without sensitivity loss, the width of the large rectangular boss was partially narrowed in regions of piezoresistors to form the peninsula structure (see Fig.
Ac ce p
6 (a) 4-peninsula structure). It is noted that a sensitivity of 20.11 mV/KPa (the same as the flat diaphragm) and nonlinearity error of 0.75 %FFS (decreased by 37.5% compared with the flat diaphragm) were achieved. If the piezoresistor design III was replaced by design IV, the sensitivity of the sensor with the peninsula structure would be further increased to 23.61 mV/KPa. The results indicated that the peninsula structure had both the advantage of the large rectangular structure in terms of low nonlinearity error and the advantage of the small rectangular structure in terms of high sensitivity. 3.3.2
Peninsula height
Page 14 of 41
In order to further reduce the nonlinearity error, the influence of peninsula height was studied. The dimensions of the peninsula-structured diaphragm were the same as shown in Fig. 6 (a), piezoresistor design IV was applied for all sensors. When the
ip t
peninsula height increased from zero (flat diaphragm) to 20 μm, Fig. 7 (a) shows the
cr
corresponding simulation results. It is observed that when the peninsula thickness
us
increased from 0 to 5 μm, the sensor output increased from 100 mV to the maximum value 118 mV; then the sensor output would decrease gradually as the peninsula
an
thickness continued to increase. While the nonlinearity error reduced monotonically from 1.2 %FFS to about 0.2 %FFS. Considering the design constrains of nonlinearity
M
error (< 0.5 %FSS), the trade-off between sensitivity and linearity finally made the
Diaphragm thickness
te
3.3.3
d
peninsula height to be 9 μm.
If the peninsula thickness was fixed at 9 μm and the diaphragm thickness
Ac ce p
increased from 5 μm to 15 μm, Fig. 7 (b). shows the corresponding simulation results.
It is observed that both the sensor outputs and the nonlinearity errors decreased monotonically as the diaphragm thickness increased. It is also noted that if the diaphragm thickness was designed to be 10 μm with the fabrication tolerance of ± 1
μm, the linearity errors would vary between 0.30 ~ 0.81 %FFS and the sensor outputs between 96.5 ~ 131.8 mV. 3.4 Comparisons with other types of diaphragms 3.4.1
Comparisons with center-bossed and flat diaphragms
Page 15 of 41
As a basic comparison, the static performance of peninsula structure were first compared with typical ones with center-bossed and flat diaphragm as shown in Fig. 8 (a). They had the same diaphragm thickness of 10 μm and size of 1900 μm. The
ip t
simulated sensor outputs and nonlinearity errors versus pressure loading were plotted
cr
in Fig. 8 (b) and (c). Compared with the flat diaphragm, the sensitivity of the sensor
us
with peninsula-structured diaphragm was increased about 11.4 % while the maximum nonlinearity error was reduced by 60.0 %. By introducing the solid center-boss
an
structure to the flat diaphragm, the nonlinearity error could also be reduced to the same as the peninsula-structured diaphragm (see Fig. 8 (c)). However, the sensitivity
M
of the sensor was also reduced by 8.5 % compared to the sensor with flat diaphragm. In other words, the reduction of the nonlinearity error by introducing the center-boss
3.4.2
te
d
was achieved at the expense of sensitivity loss. Comparisons with the CBM structure
Ac ce p
As for comparisons with Tian’s CBM structure [11], the peninsula-structured
diaphragm was redesigned to have the same diaphragm thickness (20 μm) and lateral dimension (2900 μm). The peninsula thickness was also the same as the beam thickness (20 μm) in CBM structure. The optimized geometry size of the peninsula
structure was plotted in Fig. 9 (a).
was set to 1.0e-9 /Pa corresponding to a
doping concentration of 7.5e18 /cm-3. The formerly discussed piezoresistor design IV and III were applied for both sensor structures. The distribution of the stress Sx-Sy from the central point to the diaphragm edge for both sensor under 5 KPa uniform pressure loading is plotted in Fig. 9 (b). The
Page 16 of 41
maximum value of Sx-Sy in the peninsula-structured diaphragm (27.6 MPa) was increased by 42.3 % compared with CBM structure (19.4 MPa). The simulated sensor outputs and nonlinearity errors versus pressure loading were plotted in Fig. 9 (c) and
ip t
(d). First, for both sensors, piezoresistor design IV exhibited larger sensor outputs
cr
with an increment of 6.6 % ~ 10.0 % compared with piezoresistor design III. The
us
results indicated that the optimized piezoresistor design IV also applied for the CBM structure for sensitivity optimization. Second, the largest sensitivity of the sensor with
an
peninsula diaphragm (14.81 mV/KPa) was increased about 41.3 % compared with CBM structure (10.48 mV/KPa). Third, it is noted that these two sensors had very
M
close absolute values of nonlinearity errors but with different signs: - 0.13 %FFS in CBM structure versus + 0.16 % FFS in peninsula structure. As discussed by Lin, for
te
d
conventional sensors with flat diaphragm the sign of the nonlinearity error was related to the diaphragm dimensions, resistor design and it might even go from negative to
Ac ce p
positive as the applied pressure changes [14]. Based on the non-linear simulation of these two structured diaphragms, we conclude that the sign of the nonlinearity error can also be changed with different shapes of the diaphragm structure, even if all other parameters (diaphragm dimensions, resistor designs and pressure ranges) are the same. 3.4.3
Modified peninsula structure with a center boss
The conclusion also suggests that it’s possible to achieve a level of close to zero nonlinearity error by adjusting the shapes of the diaphragm structure. To achieve the goal, a possible diaphragm structure was proposed as shown in Fig. 10 (a), which was
Page 17 of 41
formed by adding an extra center boss to the peninsula-structured diaphragm. It is observed that as the side length of the center boss increased from 400 to 1200 μm, the nonlinearity error reduced and changed signs from positive to negative (see Fig. 10
ip t
(c)). The minimum absolute nonlinearity error (< 0.02 %FFS) was achieved when the
cr
size of the center boss was about 800 μm. The simulation results confirmed the
us
prediction that a level of close to zero nonlinearity error could be achieved by adjusting the shapes of the diaphragm structure. The conclusion offers a new approach
an
to design low pressure sensors (≤ 5 KPa) with ultra-low nonlinearity error (< 0.1 %FFS) and appropriate sensor output. In addition to the nonlinearity error reduction,
M
the sensitivity was also decreased by 6.9 % compared with the peninsula diaphragm without the center boss (but it’s still 31.6 % larger compared with the CBM structure).
te
d
The results suggested that the trade-off between sensitivity and linearity still existed during the optimization of the diaphragm. Comparisons with the hollow stiffening structure
Ac ce p
3.4.4
For comparisons with Kinnell’s 3 KPa pressure sensor with the novel hollow
stiffening structure [9], the modified peninsula diaphragm with a center boss was also optimized based on the dimensions of Kinnell’s structure, which had a thickness of 5 μm and width of 1550 μm as shown in Fig. 11 (a).
was set to the maximum value
1.38e-9 /Pa corresponding to a relatively low doping concentration. Since the detailed side length of the three bosses were not provided in [9], the test results were adopted for comparisons with the peninsula structure as shown in Fig. 11 (b) and 11 (c). It is noted that compared with the hollow stiffening structure, a higher sensitivity of 37.5
Page 18 of 41
mV/KPa and a lower nonlinearity of 0.07 %FFS could be achieved for the modified peninsula structure with a center boss in the pressure range of 0 ~ 3 KPa. It should be noted that the sensitivity of the sensor was also related to the doping concentration of
ip t
the piezoresistors, it would decrease as the doping concentration increased. Moreover,
cr
since the hollow stiffening structure applied the electrochemical etch-stop method to
us
fabricate the diaphragm, the hollow stiffening structure had the advantage of high precision diaphragm thickness / sensor performance control which were very
an
important for yield improvement in mass production. Based on the simulation results, when the diaphragm thickness had variations of ± 1μm, the proposed sensor structure
M
would have sensor outputs between 88.9 ~ 137.4 mV and nonlinearity errors between - 0.16 %FFS ~ + 0.31 %FFS. For better uniformity of the sensor’s performance, SOI
te
d
(silicon on insulator) wafer or EPI (epitaxial) wafer with electrochemical etching technology would be an appropriate choice for sensor fabrication. Dynamic behavior comparisons
Ac ce p
3.4.5
Besides the sensitivity and linearity performance, the mechanical stability of the
diaphragm is also of particular importance for ultra-high sensitive pressure sensors used in high accuracy measurement. Mechanical stability of the diaphragm is dominated by the first resonance frequency of the diaphragm. In order to stabilize the diaphragm, normally a higher first resonance frequency is preferred. As shown in Fig. 12, the dynamic behavior analysis indicated that for sensors of case 1 (Fig. 8) the highest first resonance frequencies of 58.0 kHz was achieved for the peninsula-structured diaphragm with an increment of 121 % and 42 % compared with
Page 19 of 41
the center-bossed diaphragm and flat diaphragm respectively; while for sensors in case 2 and 3 (Fig.9 and 10) the first resonance frequencies almost equaled with each other. The results indicated that the peninsula-structured diaphragm and the modified
ip t
peninsula diaphragm with a center boss were as good as the CBM structure in terms
cr
of diaphragm stability and were much better as compared with the center-bossed and
us
flat diaphragms.
In this section, structured diaphragm was applied to improve the characteristics of
an
a standard flat square diaphragm. After the geometrical optimization process, the novel peninsula-structured diaphragm was proposed. Comparisons with typical sensor
M
structures were conducted and summarized in terms of sensitivity, maximum
d
nonlinearity error and first resonant frequency as shown in table 2. With the same
te
diaphragm dimensions and piezoresistor designs, the proposed sensor structures could achieve the highest sensitivity, good nonlinearity and mechanical stability
Ac ce p
performance as compared to the alternatives. In particular, ultra-low nonlinearity performance was achieved by the modified peninsula-structured diaphragms for the pressure range of 5 KPa and 3 KPa respectively with different diaphragm dimensions. It is concluded that our present sensor structures have the best overall performance among these sensor structures.
4. Fabrication Process A fabrication process for the proposed sensor with the peninsula structured diaphragm will be presented in detail. An overview of the process is shown in Fig. 13,
Page 20 of 41
it mainly consisted of four process steps. The first step was the fabrication of piezoresistors and heavily doped section (Fig. 13 (a) and (b)). The 4 inch n-type (100) oriented Si wafer was chosen as the substrate. After the thermal oxidization process,
ip t
photo lithography and Boron implantation was employed to pattern and form the
cr
piezoresistors and the heavily doped contact sections on the front side of the silicon
wafer. After the final thermal activation process, a sheet resistance of 243 Ω/□ was
us
achieved for the piezoresistors with a surface doping concentration of 2.5e18/cm-3.
an
The second step was the KOH (potassium hydroxide) solution anisotropy etching process (Fig. 13 (c)). The passivation films of SiO2 and Si3N4 were deposited by
M
means of low pressure chemical vapor deposition (LPCVD) process. After patterning, cavity etching was conducted at a constant temperature of 80 ± 1 °C. The etching
te
d
solution was pure aqueous KOH solution with a KOH content of 30 wt%. The solution was agitated at a relatively low speed by a stirrer with three large blades
Ac ce p
turning at around 50 rpm. With the etching depth of nearly 380 μm, the variations of the etching depth within a wafer could be decreased from larger than ± 5 μm (without stirring) to less than ± 1 μm for more than 85 % of the cavities. Considering the thickness variation of the Si wafer (± 1 μm), the diaphragm thickness of 19 ± 2 μm
could be achieved. The third step was the metallization process (Fig. 13 (d)). It began with the contact hole etching, followed by Al (aluminum) sputtering with a thickness of 1 μm. Then lithography and Al etching process were conducted to form the electrode. After a sintering process low resistance ohmic contact was formed between the heavily doped section and Al pad. The last step was ASE (advanced silicon
Page 21 of 41
etching) process on the front side to form the peninsula structure with a depth of 9 μm (Fig. 13 (e)). The fabricated pressure sensor is shown in Fig. 14, where the SEM
ip t
images of the piezoresistors are displayed in detail.
cr
5. Experimental results
us
The schematic diagram of packaged pressure sensor structure is shown in Fig. 15(a). After dicing, the sensor chip was assembled on a gold-plated Kovar base
an
through adhesive. Wire bonding process using gold wire was implemented to realize the connection between the pressure chip and the pins. A via hole existed at middle of
M
the Kovar base, so differential pressures could be loaded on the sensor’s diaphragm.
d
In order to test the sensor performance with pressure loadings, a special nut-screw
te
structure was designed and applied, as shown in Fig. 15(b). The packaged sensor was assembled in the nut with the pins of the sensor connected with the signal wire from
Ac ce p
the backside of the nut. Anti-leak rubber was used to prevent pressure leakage from the nut during the test. When the screw with a PVC hose and the nut with the packaged sensor were screwed together, pressure ranging from 0 to 5 kPa could be applied to the sensor chip from the PVC hose using the PPC2+ gas pressure controller.
Three sensor devices from different regions of the same wafer were measured. The measured voltage outputs and calculated nonlinearity errors are shown in Fig. 16. The average sensitivity of the three devices was 19.9 mV/V full-scale output with the average maximum nonlinearity error of 0.42 %FSS. The realistic performances of
Page 22 of 41
these sensors are well within the simulation with diaphragm thicknesses of 10.2 ~ 10.8 μm in the tolerance range of 10 ± 2 μm. The zero offset voltages for the three devices ranged between 2.2 ~ 9.1 mV. During pressure cycling from 0 to 5 kPa and 5
ip t
kPa to 0, there was no indication of pressure hysteresis. The detailed technical data of
cr
the device 3 at 21 °C is listed in Tab. 3. In particular, the tested burst pressure of
us
device 3 was 57 kPa, a factor of 10 larger than the full pressure range (5 kPa).
an
6. Summary and Conclusion
A highly sensitive, linear and stable pressure sensor featuring the novel
M
peninsula-structured diaphragm was proposed. Based on detailed study of the stress distribution characteristics for the diaphragm, a special piezoresistor design was
te
d
evaluated and adopted for sensor performance optimization. Utilizing the mature technologies of KOH and ASE etching, the proposed sensor structure was
Ac ce p
manufactured based on the cost-effective silicon wafer, which was particularly important for low-cost mass production. In comparison to typical sensors with center-bossed, CBM structure, hollow stiffening structure and flat diaphragm, the FEM simulation indicated that by proper geometrical optimization the proposed sensor with peninsula structured diaphragm could achieve the best overall performance among these sensors. In particular, ultra-low nonlinearity performance could be achieved by the modified peninsula-structured diaphragm. In accordance with the FEM results, the fabricated pressure sensor showed that a sensitivity of 18.4 mV/V full-scale output and nonlinearity of 0.36 %FSS were achieved for the full
Page 23 of 41
pressure range of 5 kPa with no indication of pressure hysteresis. It is concluded that the proposed sensor has excellent sensitivity, linearity, diaphragm stability and the most important feature low cost. The proposed sensor structure with the
ip t
peninsula-structured diaphragm is potentially a better choice for designing low
cr
pressure sensors in fields like biomedical, smart homes and aerodynamics.
us
Acknowledgment
This work was financed by 863 Program (Grant No. 2011AA040401) and 973
an
Program (Grant No. 2011CB309502). The sensor fabrication and measurement were supported by National Key Laboratory of Science and Technology on Micro/Nano
M
Fabrication, Institute of Microelectronics, Peking University.
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d
(2001) 296-308.
[2] W. P. Eaton, J. H. Smith, Micromachined pressure sensors: review and recent developments,
te
Smart Mater. Struct. 6 (1997) 530–539
[3] S. Marco, J. Samitier, O. Ruiz, J.R. Morante, J.E. Steve, High performance piezoresistive
Ac ce p
pressure sensors for biomedical applications using very thin structured membranes, Meas. Sci. Technol. 7 (1996) 1195–1203
[4] D. Ding, R.A. Cooper, P.F. Pasquina, L.F. Pasquina, Sensor technology for smart homes, Maturitas, 69 (2011) 131-136.
[5] J. Hurault, S. Kouidri, F. Bakir, Experimental investigations on the wall pressure measurement on the blade of axial flow fans, Experimental Thermal and Fluid Science, 40 (2012) 29-37
[6] H. Takahashi, K. Matsumoto, I. Shimoyama, Differential pressure distribution measurement of a free-flying butterfly wing, Transducers, 2011, pp. 2022-2025.
[7] A. Yasukawa, M. Shimazoe, Y. Matsuoka, Simulation of circular silicon pressure sensors with
a center boss for very low pressure measurement, IEEE Trans. Electron Devices, 36 (1989) 1295-1301.
[8] H. Sandmaier and K. Kuhl, A square-diaphragm piezoresistive pressure sensor with a rectangular central boss for low-pressure ranges, IEEE Trans. Electron Devices 40 (1993)1754-1759.
[9] P.K. Kinnell, J. King, M. Lester, R. Craddock, A hollow stiffening structure for low-pressure sensors, Sens. Actuators A 160 (2010) 35-41.
[10] M.H. Bao, L.Z. Yu, Y. Wang, Micromachined beam-diaphragm structure improves performances of pressure transducer, Sens. Actuators A 21-A23 (1990) 137-141.
[11] B. Tian, Y. L. Zhao, Z. D. Jiang, B. Hu, The design and analysis of beam-membrane structure
Page 24 of 41
sensors for micro-pressure measurement, Rev. Sci. Instrum. 83 (2012) 045003.
[12] Z. L. Yu, Y. L. Zhao, L. Sun, B. Tian, Z.D Jiang, Incorporation of beams into bossed diaphragm for a high sensitivity and overload micro pressure sensor, Rev. Sci. Instrum. 84 (2013) 015004.
[13] K. Matsuda, K. Suzuki, K. Yamamura, Y. Kanda, Nonlinear piezoresistance effects in silicon, J Appl. Phys. 73 (1993) 1838-1847; piezoresistive pressure sensors, J. Microelectromech. Syst. 8(4) (1999) 514-522.
ip t
[14] L.W. Lin, H.C. Chu, Y.W. Lu, A simulation program for the sensitivity and linearity of
[15] J.A. Chiou, S. Chen, Pressure nonlinearity of micromachined piezoresistive pressure sensors
cr
with thin diaphragms under high residual stresses, Sens. Actuators A 147 (2008) 332-339.
[16] C.S. Smith, Piezoresistance effect in germanium and silicon, Phys. Rev. 94 (1954) 42-49. [17] S. Marco, J. Samitier, O. Ruiz, J. R. Morante, J. Esteve, High-performance piezoresistive
us
pressure sensors for biomedical applications using very thin structured membranes, Meas. Sci. Technol. 7 (1996) 1195-1203.
[18] H.S. Hsieh , H.C. Chang , C.F. Hu, C.P. Hsu, W. Fang, Method for sensitivity improvement
Ac ce p
te
d
M
an
and optimal design of a piezoresistive pressure sensor, IEEE Sensors Conference, 2010, pp. 1799-1802.
Page 25 of 41
Figure 1 Proposed sensor structure.
ip t
Figure 2 Stress distribution characteristics for the diaphragm under uniform 5 kPa pressure loading. (a) The stress intensity distribution for a 1/4 model of the sensor (flat area 10 μm thick and peninsula area 19 μm thick). (b) The stress difference (Sx-Sy) between longitudinal and transvers direction along the path that goes from the central point to diaphragm edge for the peninsula-structured and flat diaphragms (10 μm and 19 μm thick) respectively.
an
us
cr
Figure 3. Stress distributions along the path that parallels to the diaphragm edge with a distance of 25 μm, the background is the stress distributions around the narrow beam of the peninsula structure. (a) Stress Sx-Sy along the path for peninsula-structured diaphragm (black curve) and flat diaphragm (10 μm thick, red curve). The background is the stress intensity distribution. (b) Stress Sx along the path. The background is the distribution of the stress Sx. (c) Stress Sy along the path. The background is the distribution of the stress Sy.
Figure 4 Schematic illustration of four candidate designs for the piezoresistors.
M
Figure 5 Simulated sensor output (a) and nonlinearity error (b) versus pressure loading of each candidate design shown in Fig. 4.
Ac ce p
te
d
Figure 6 Optimization process for the peninsula structure (a) four sensors with flat diaphragm, large rectangular structure, small rectangular structure and peninsula structure (b) diaphragm deflections from the diaphragm center to the middle of the diaphragm edge under 5 KPa pressure loading (c) stress distributions from diaphragm center to the middle of the diaphragm edge under 5 KPa pressure loading (d) nonlinearity error versus pressure loading (e) sensor output versus pressure loading.
Figure 7 Diaphragm optimization in terms of peninsula height and diaphragm thickness. (a) Sensor outputs and nonlinearity errors with respect to peninsula height (b) sensor outputs and nonlinearity errors with respect to diaphragm thickness.
Figure 8 Comparisons with the center-bossed and flat diaphragms. (a) Three sensor structures (b) sensor outputs versus pressure loading (c) nonlinearity errors versus pressure loading.
Figure 9 Comparisons with the CBM structure. (a) Geometry of the CBM and peninsula structures (b) stress distributions from the diaphragm center to the middle of the diaphragm edge (c) sensor outputs versus pressure loading (d) nonlinearity errors versus pressure loading.
Figure 10 Modified peninsula structure with a center boss to achieve the close to zero nonlinearity error. (a) Geometry of the sensor structure (b) sensor outputs versus
Page 26 of 41
pressure loading (c) nonlinearity errors versus pressure loading.
Figure 11 Comparisons with the hollow stiffening structure. (a) Geometry of the sensor structures (b) sensor outputs versus pressure loading (c) nonlinearity errors versus pressure loading.
cr
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Figure 12 Dynamic behavior of the sensors with different types of diaphragm. (a)~(c) first resonance mode of the peninsula diaphragm, center-bossed diaphragm and flat diaphragm of case 1; (d)~(f) first resonance mode of the CBM structure, peninsula diaphragm and modified peninsula diaphragm with a center boss of case 2 and 3.
Figure 13 Overview of the fabrication process.
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Figure 14 SEM images of the pressure sensor and the piezoresistors.
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Figure 15 Package of the pressure sensor (a) schematic diagram of packaged pressure sensor structure (b) packaged sensor and the designed nut-screw structure for sensor measurement.
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Figure 16 Measured sensor outputs (a) and nonlinearity errors (b) versus pressure loading for three sensor devices.
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Xian Huang was born in 1988. He is from the Shenzhen Graduate School of Peking University, Shenzhen, China. He has been working toward the Ph.D degree in the Institute of Microelectronics since 2010, Peking University, Beijing, China. His main research interests include micro/nano fabrication technology and MEMS piezoresistive devices.
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Dacheng Zhang, received the Ph.D. degree from the Institute of Microelectronics, Peking University in 2005, Beijing, China. He is currently a professor in the Institute of Microeletronics, Peking University. His main search is about micro/nano fabrication technology, mechanics properties analyzing of micro-structure and MEMS devices.
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Highlights • A peninsula-structured diaphragm was proposed in pressure sensor design. • The resistor design was optimized to improve the sensor performance. • The new sensor design has been compared with other typical sensors. • Ideal results were obtained after fabrication and test of the proposed sensor.
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Figures
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Figure 1 Proposed sensor structure
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Figure 2 Stress distribution characteristics for the diaphragm under uniform 5 kPa pressure loading. (a) The stress intensity distribution for a 1/4 model of the sensor (flat area 10 μm thick and peninsula area 19 μm thick). (b) The stress difference (Sx-Sy) between longitudinal and transvers direction along the path that goes from the central point to diaphragm edge for the peninsula-structured and flat diaphragms (10 μm and 19 μm thick) respectively.
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Figure 3. Stress distributions along the path that parallels to the diaphragm edge with a distance of 25μm, the background is the stress distributions around the narrow beam of the peninsula structure. (a) Stress Sx-Sy along the path for peninsula-structured diaphragm (black curve) and flat diaphragm (10 μm thick, red curve). The background is the stress intensity distribution. (b) Stress Sx along the path. The background is the distribution of the stress Sx. (c) Stress Sy along the path. The background is the distribution of the stress Sy.
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Figure 4 Schematic illustration of four candidate designs for the piezoresistors
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Figure 5 Simulated sensor output (a) and nonlinearity error (b) versus pressure loading of each candidate design shown in Fig. 4.
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Figure 6 Optimization process for the peninsula structure (a) four sensors with flat diaphragm, large rectangular structure, small rectangular structure and peninsula structure (b) diaphragm deflections from the diaphragm center to the middle of the diaphragm edge under 5 KPa pressure loading (c) stress distributions from diaphragm center to the middle of the diaphragm edge under 5 KPa pressure loading (d) nonlinearity error versus pressure loading (e) sensor output versus pressure loading.
Figure 7 Diaphragm optimization in terms of peninsula height and diaphragm thickness. (a) Sensor outputs and nonlinearity errors with respect to peninsula height (b) sensor outputs and nonlinearity errors with respect to diaphragm thickness.
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Figure 8 Comparisons with the center-bossed and flat diaphragms. (a) Three sensor structures (b) sensor outputs versus pressure loading (c) nonlinearity errors versus pressure loading.
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Figure 9 Comparisons with the CBM structure. (a) Geometry of the CBM and peninsula structures (b) stress distributions from the diaphragm center to the middle of the diaphragm edge (c) sensor outputs versus pressure loading (d) nonlinearity errors versus pressure loading.
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Figure 10 Modified peninsula structure with a center boss to achieve the close to zero nonlinearity error. (a) Geometry of the sensor structure (b) sensor outputs versus pressure loading (c) nonlinearity errors versus pressure loading.
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Figure 11 Comparisons with the hollow stiffening structure. (a) Geometry of the sensor structures (b) sensor outputs versus pressure loading (c) nonlinearity errors versus pressure loading.
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Figure 12 Dynamic behavior of the sensors with different types of diaphragm. (a)~(c) first resonance mode of the peninsula diaphragm, center-bossed diaphragm and flat diaphragm of case 1; (d)~(f) first resonance mode of the CBM structure, peninsula diaphragm and modified peninsula diaphragm with a center boss of case 2 and 3.
Figure 13 Overview of the fabrication process
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Figure 14 SEM images of the pressure sensor and the piezoresistors
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Figure 15 Package of the pressure sensor (a) schematic diagram of packaged pressure sensor structure (b) packaged sensor and the designed nut-screw structure for sensor measurement
Figure 16 Measured sensor outputs (a) and nonlinearity errors (b) versus pressure loading for three sensor devices.
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Tables
200
12
12
5
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Table 3 Technical data of the device 3 at 21 °C Full range pressure (kPa) 5 Full range output (mV) 92.1 Wheatstone bridge resistance (Kohm) 3.9 Supply voltage (V) 5 Zero output (mV) 2.2 Sensitivity (mV/kPa) 18.4 Nonlinearity error (%FFS) 0.36 Burst pressure (kPa) 57 Die size (mm) 3.6*3.6*0.4
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Table 1 Configuration for the piezoresistors Piezoresistor (PZR) Total Length Width Space Resistance (μm) (μm) (μm) ( )
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Table 2 Performance comparisons of different sensor structures. Performance comparisons
Case 2
Center-boss ed
18.40
0.48
Flat diaphragm
20.10
CBM structure Peninsula-st ructure
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Modified peninsula-st ructure with a center boss
Case 4* Hollow stiffening structure Case 4
Modified peninsula-st ructure with a center boss
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58.0
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Peninsula-st ructure
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(mV/KPa)
Nonlinearity First resonant error frequency (|%FFS|) (KHz)
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Case 1
Sensitivity
26.2
1.20
40.9
10.48
0.13
44.5
14.81
0.16
44.2
13.79
0.018
43.5
30.0
0.35
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37.5
0.07
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Sensor structures
Diaphragm types
d
Group
* The data of the hollow stiffening structure was from the test results in reference [9]
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