Particulate Failures for Surface-Micromachined MEMS'

Tao Jiang and R. D. (Shawn) Blanton

Center for Electronic Design Automation ECE Department

Carnegie Mellon University Pittsburgh, PA 15213-3890

ABSTRACT We investigate the -failure modes of a comb-drive

surface-micromachined microresonator that are caused by particulate 'contaminations. The microresonator structure is chosen as our research vehicle because it pdssesses all the primitive components found in many capacitive-based MEMS sensors and actuators. Process simulation is used to create the full-spectrum of defective structures caused by foreign particles. The generated defective structures are then classified based on their geometrical properties. Finite element anaIysis is used to understand the impact of these defects on the mechanical frequency. response of the microresonator while HSPICE simulations are performed to determine the corresponding electrical misbeha viors within an acceleration measuring application. Simulation results show that particles can cause unwanted anchors, broken beams and welded comb fingers. However, the most interesting defects are broken comb fingers and lateral finger protrusions that only affect sensing capacitance. These defects lead to a very small increase or decrease in the shuttle mass. The mass change is so small that the mechanical frequency response of the resonator is virtualIy unchanged. However, the HSPICE simulations show that the change in output sensing voltage can be catastrophic.

1 INTRODUCTION

Advances in manufacturing have made the use of MEMS-based devices commercially viable in products that include pressure sensors, automotive inertial sensors, ink- jet printer heads, optical and RF networks, and disposable chemical analysis systems. The high-volume production of these MEMS-based systems, usually on the order of tens of millions or higher, will require cost-effective testing techniques to screen defective devices from good ones. Most current industrial practice relies on characterization and design validation tests for this purpose. This may be problematic since:

1. characterization/validation tests target only portions of the functionality and hence may miss specific failure modes,

2. are applicable only for a specific design and,

3. may be inefficient in that simpler, less expensive tests may be sufficient.

We are developing generic fault models for capacitive inertial sensors and actuators that are fabricated using surface-micromachined technologies [ 1-31. Generic fault models are desirable because of their applicability to a wide range of devices. Accurate fault models also enable pre- manufacture evaluation, thus allow for both manufacturing test and self test optimization.

Although most research work in MEMS focuses on design, technology and packaging problems, there has been some work in the MEMS testing field. In [4-61, the challenges associated with MEMS testing and the importance of MEMS models that are capable of capturing both defect and defect-free behavior have been addressed. Much effort has been placed in transferring mixed-signal test techniques to MEMS. In their work, an electrical schematic is used to represent both the electrical and mechanical components of MEMS. Faults are modeled by adding extra components or changing the parameters of existing components. Unfortunately, knowledge of real failures is not used to determine the components that should be added or modified from the schematic. Thus, there is no guarantee a correct mapping exists between the faults injected and the real failure mechanisms. In [7], the failure mechanisms of a CMOS-compatible MEMS process were classified based on their theoretical impact on key transducer parameters. Our past work combined process simulation and finite element analysis (FEA) [8] into a fault induction environment called CARAMEL [9] that mapped particle defects to mechanical misbehaviors. Here, we use CARAMEL to categorize all the possible defects that can be caused by particles. In addition, the impact of particle defects is extended to the electrical domain by considering an inertial-force measuring application.

' This research effort is sponsored by the National Science Foundation under grant MIP-9702678 and the Defense Research Projects Agency under Rome Laboratory. Air Force Materiel Command. USAF, under grant F30602-97-0323.

ITC INTERNATIONAL TEST CONFERENCE Paper132

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contributions and

Figure 1. Resonator structure and the corresponding sensing capacitance circuit formed from the resonator.

The vast amount of research performed on the resonator has made it a mat’ure surface-micromachined device [13- 161. It has wide use in many applications, such as accelerometers [3] 1 oscillators [ 171, high-Q IF filters [ 181, and micromirror optical beam steering [19]. Figure 1 shows the structure of d, resonator with examples of all the primitive elements identified. Also shown is the differential capacitive sensing brinciple used for inertial measurement. The shuttle mas$ is a block of material (typically polysilicon) which 1s suspended above the substrate by two anchored, folded-flexure spring beams. The spring is designed to be combliant in they direction but stiff in the x

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present conclusions.

direction. This design characteristic is used to ensure that the resonator is most sensitive to only one direction of acceleration. When an acceleration in the y direction is .applied to the resonator, the shuttle mass will move in the opposite direction but the flexure spring will provide a restoring force. At equilibrium, the shuttle mass will have a displacement d from its original position that is proportional to the voltage signal K. K is a differential capacitive signal generated by the two parallel-plate capacitors formed on either side of the resonator from beams called comb fingers. The beams attached to the shuttle are called movable fingers because they move along with the shuttle in response to an inertial force. The other beams are called fixed fingers, so-called because they are anchored to the substrate as shown in Figure 1.

Figure 2 shows the stages of our simulation environment. The first stage is process simulation: it is used to generate the full spectrum of defective structures induced by particulate contaminants. The next two stages, mechanical and electrical simulation, are used to evaluate the misbehaviors of the defective structures revealed in the process simulation stage. Mechanical simulation can, among other operations, determine the displacement of the shuttle mass under an applied inertial force, while electrical simulation can determine the pertinent characteristics of the output sensing voltage V , such as magnitude.

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3 PROCESS SIMULATION

In this study, we define a defect as any undesired geometrical deformation of the resonator that can either impede its movement or change its sensing capacitance. For simulation, we assume MUMPS (Multi-Users MEMs Processes [I]) is used to manufacture the resonator. (See Table 1 for a description of the manufacturing process steps used for the resonator.) Four thousand process simulations were conducted using CARAMEL [9], the MEMS procesdparticulate simulator developed from CODEF [20]. CARAMEL requires three inputs: a process recipe, characteristics about the, particulate contamination (i.e. its process step of introduction, its location in the layout, diameter, and conductivity), and the layout itself. CARAMEL was used in a Monte Carlo mode to distribute the 4000 particles randomly across all process steps and throughout the bounding-box area of the resonator. The diameter of the particles is chosen to range between 2pm and 4pm to maximize the occurrence rate of defects. This choice is based on the fact that particles with a diameter less than 2pm are not able to generate some defects, while particles with a large diameter are very rare ,in a real manufacturing environment. Most of the 4000 particles missed the active area of the structure or were removed along with temporary layers during the processing. A total of 492 defective structures were predicted by CARAMEL.

330

t layout

mesh with defect

ABAQUS E G 2

sensing signal K

Figure 2. Simulation environment for the development of generic fault models for MEMS: (a) The tool CARAMEL [9] accepts a process description, particulate information, and a layout: it generates a mesh that captures the impact of the defect on the microstructure. (b) Mechanical simulation is performed using the FEA tool ABAQUS to determine the effect of the resulting defect on the mechanical properties of the microstructure. (c) Finally, HSPICE is used to determine the impact of the particulate on the electrical characteristics of the microstructure.

3.1 Defect Classification

Based on the resulting geometrical properties, defects are classified into three categories: surface, anchor and broken structure.

Surface defects. Surface defects are caused by particles introduced onto the surface of the suspended structure. There are several subtypes associated with this category.

Surface non-finger protrusion defects are caused by particles adhering to the surface of the structural layer. The only impact of these defects is a small increase in resonator mass. This defect is always caused by particles introduced after the strip of the structural layer photoresist (step 20 of Table 1) or the final release (step 21). See Figure 3a for a three-dimensional rendering of CARAMEL'S output for this type of defect.

Surface finger protrusion defects are caused by particles located on the surface of two adjacent comb fingers, introduced after the strip of the structural layer photoresist or the final release. These defects weld the two fingers together. Figure 3b shows an example of this type of defect.

Lateral finger protrusion defects reduce the gap between comb fingers. They are caused by particles occurring after the photoresist spin-on for the structural layer (step 16) and before the structural layer etching (step 19). A particle introduced between these steps either prevents the exposure of the underlying structural layer photoresist or directly protects the structural layer between adjacent comb fingers: either case leads to a lateral protrusion between the fingers.

This defect type can be' further sub-divided, based on the location and amount of gap reduction:

1. Overlap. sticking: protrusion is located in the overlap region of two fingers, and is large enough to weld the fingers together.

2. Overlap. non-sticking: protrusion is located in the overlap region of two fingers but is large enough to only reduce the gap. (See Figure 3c.)

3. Non-overlap, stickincr: protrusion is outside the overlap region of two fingers but may cause sticking during shuttle movement. (See Figure 3d.)

4 . Non-overlap, non-sticking: protrusion is outside the overlap region of two adjacent fingers but may reduce gap during shuttle movement,

Anchor defects. Anchor defects are caused by particles located between the substrate and suspended structure. They fix the two surfaces together and hence impede resonator movement under an applied inertial force. Anchor defects stem from particles occurring before the structural layer deposition (excluding the sacrificial layer and photoresist related steps) and the final release step, thus steps 1-3, 8 and 21. Particles introduced only after these process steps can survive the subsequent processing. There are two subtypes associated with this category of defects.

0 Mass and finger defects cause an anchor under the shuttle mass or a comb-finger.

Spring beam defects cause an anchor under a spring beam.

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Figure 3. Reptesentative examples of the defect categories caused by particles: (a) Surface protrusion located on the shuttle, (b) surface finger protrusion that welds two adjacent fingers, (c) lateral finger protrusion that reduces finger gap in the overlap region, (d) surface finger protrusion that lies outside the overlap region of two adjacent fingers, and (e) broken spring beam.

Table 11 All manufacturing process steps involved in fabricating the resonator and their classification as either vulnerable (V) or resistant (R).

I Broken structurks. Broken structure defects are caused by particles introduded before the photoresist spin-on for the structural layer. ilntroduction of the particle after this step creates a vulnerable location in the structural material at the location of the particle. The over-etching that takes place at this location creates a broken structure. There are three sub- defect types based on which element of the resonator is affected. Hence, there can be broken shuttle, finger, and beam defects. An example of a broken spring beam is shown in Figure 3e.

3.2 Process Step Classification

Process simulation results indicate that some process steps are more desistant to particles than others. This information is quite useful for failure analysis since defect characteristics cm, be used as pointers to culprit processing steps. A common feature of the resistant steps is the use of some temporary materials, i.e., the phosphosilicate glass (PSG) sacrificial dyer and photoresist for the non-structural layer polyo. Processing steps related to these materials are resistant to particles because they are eventually removed along with the strip of these temporary materials, and thus do not affect the structural layer. All other steps can have defects induced frqm particles and are therefore vulnerable. Table 1 lists all the MUMPs process steps involved in manufacturing the resonator and their classification as either resistant or vhnerable.

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3.3 Relative Probability of Occurrence (WO) For each defect type or category, we can assign a

relative probability of occurrence (RPO). RPO for a defect type is defined as the ratio of the number of defects of this type to the total number of defects. Assigning an RPO to a defect type is useful for many reasons. Grading a MEMS test methodology against an RPO gives a more realistic measure of defect “coverage”. In the context of limited resources, an RPO can be used to identify which defects to focus upon. For example, it may be cost effective to focus resources (BIST, manufacturing test, etc.) on defects that are likely to occur than on those that are very rare.

We assume that the likelihood of a particle occurring during any given process step is equal. Also, we assume that every location of the particle within the bounding box of the resonator is also equally likely. The critical area for a given defect category is defined to be the portion of the layout that produces the defects within the category, normalized by the percentage of process steps for which this category of defects can occur. For example, the critical area for shuttle anchor defects is the area of the bounding box that includes the shuttle, increased on all sides by one- half the particle diameter d (see Figure 4), multiplied by 5/21=0.24, since these defects are only possible in five of the 21 MUMPs steps used. The RPO for the shuttle anchor defect is then computed as the ratio of its normalized critical area to the total sum of normalized critical area of all defect categories.

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7 8 9 10

I 11 I Broken spring beam I 15 I 0.01 I 21 I 0.004

(non-overlap, non-sticking) Mass and finger anchor 1-3.8, 21 0.37 2287 0.41 Spring beam anchor 1-3,8, 21 0.07 458 0.08 Broken shuttle 15 0.04 378 0.07 Broken finger 15 0.01 40 0.01

Table 2. Process steps that create each of the defect categories along with simulation-based and theoretical values for relative probability of occurrence.

Figure 4. Critical area of shuttle anchor defects corresponding to particles of diameter d.

45 40 35

n 30

25 20 15 10 5 0

1 2 3 4 5 6 7 8 9 1 0 1 1 Defect type no.

Figure 5. Simulation RPO (light bars) and theoretical RPO (dark bars) comparisons for all defect types.

A simulation-based RPO can also be computed based on our process simulation results. It can be simply defined as the number of defects of a given type divided by the total defects generated. The simulation-based and theoretical RPO values are listed in Table 2 and plotted in the histogram of Figure 5. The theoretical RPO values are computed using a particle diameter of 3 y m The simulation-based and theoretical RPO values match very well. The small deviation is attributed to the fact that the

simulations utilized a particle diameter that has a probability density function that ranges between 2ym and 4ym.

4 MECHANCIAL SIMULATION

The defective structure generated by CARAMEL is represented as a mesh using three-dimensional brick elements. The generated mesh is completely compatible with the FEA tool ABAQUS [8]. FEA is used to determine the impact of defects on the mechanical frequency response of the resonator. It is used to study all categories of defective structures. Frequency response is analyzed because many key mechanical parameters, such as spring constant K, quality factor Q, and resonant frequency fo , can be obtained from the spectrum. The displacement d of the resonator along the sensing axis y can also be determined from the spectrum. Displacement is later used as a critical parameter in the electric model.

The mechanical frequency response is obtained by applying a sinusoidal acceleration signal with a magnitude of lOOg in the y direction that has a frequency range between 1Hz and 10 MHz. The spectrums obtained from our defect categories fall into four different classes:

Class I: Spectrums in this class essentially match the defect-free case. Defects that include surface protrusions, lateral protrusions that do not cause sticking, and broken shuttles and fingers have little impact since they either slightly increase or decrease the mass of the resonator.

Class 2 Spectrums in this class exhibit about an order of magnitude of reduction in displacement. Resonator movement has been seriously impeded (Figure 6) due to welded comb fingers or anchors under the shuttle mass or fingers.

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defect-free

closest e * - e - - -

10-4 I . . , . ..., , I , , . ..., . , . , ..., , , , ..., . , . , ,., . . 100 101 1 1 0 2 103 IO' 105

I n p u t a c c e l e r a t i o n f r e q u e n c y ( H z ) I Figure 6. Comparison of a defect-free frequency

spectrum with tlie spectrum of a resonator affected by welded fingers ok anchors under the shuttle or fingers.

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to shuttle mass P b _ _ _ _ _ _ _ _ _ _ - - - - - - - - - +--o-a 1

10.

4 Y

a CI

10-

: 2 10- 0

a -4 n

IO'

~ defect-free 1

Figure 8. SpectruA plots for resonators with broken spring beam defedts.

Class 3: Spectruis in this class are caused by unwanted anchor defects alohg the spring beam. An additional spring beam anchor changes the spring constant: the amount of the

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change is obviously dependent upon its location. As the anchor location moves closer to the shuttle, the stiffer the spring beam becomes. In Figure 7, we show three representative cases from this class of defects.

Class 4 Spectrums in this class are the result of floppier spring beams caused by particles that break the spring beam. Figure 8 shows that resonators with a floppier spring have a displacement larger than the nominal case.

=.

Figure 9. Schematic used for electrical simulation for determining the sensing voltage V,

5 ELECTRICAL SIMULATION

Figure 9 is the differential sensing circuitry widely used in accelerometers [3]. The mechanical analysis of the displacement value d is used to compute the change of capacitance for the variable capacitors Cl and Cz formed from the inter-digited comb fingers. V+ and V- are high- frequency modulation signals that are 180" out of phase. Cfl and Cn are fixed-valued capacitors introduced to the electrical model to represent the additional sensing capacitance caused by lateral protrusion defects. The single particle assumption means that either Cfl or Cn will always be zero, depending on which side of the resonator is affected by the particle. The capacitance of Cl, Cz, Cfl , and C, are modeled using the following formulas:

(2N- l)€,t(L+d) Eot(L+d- b@ C1= +

g g 2 N ~ o t ( L - d)

g c, =

where €0 is the dielectric constant of air, N is the number of the fingers on each side of the shuttle, t is the thickness of the structural layer, L and g are the overlap and gap of adjacent fingers, respectively, and d is the displacement of the resonator for a lOOg, low-frequency input. The parameter Weis introduced to model the geometry of the lateral protrusion on the finger sidewall. For simplicity, we assume the lateral protrusion is cuboid in shape with a length and width equal to We and a thickness 1. A parallel-

Defect type

Surface non-finger protrusion Defect-free resonator

Surface finger protrusion Surface Lateral finger protrusion defects (overlap, sticking)

Lateral finger protrusion (overlap,

Sensing voltage K Percentage change (mV) from nominal 4.07 not applicable 4.07 0%

0.00-0.06 98%-100% Electric short not applicable

4.07-several hundred 0 - >1000%

Table 3. Sensing voltage V , and its level of deviation from nominal due to the various types of defects.

Anchor Defects

Broken Structures

:he capacitance of C1 and Cz-in opposite directions, thus leading to a non-zero sensing output voltage signal V,. For ihe defect-free situation, V , is proportional to the applied inertial force. Defective resonators can change V , in one of several ways. If displacement is somehow affected by a defect, then the amount of capacitance change is modified which in turn affects V,. A lateral protrusion, on other hand, changes the topology of the circuit model to include either Cfl or &, while a broken finger affects the total capacitance of either Cl or Cz.

Table 3 provides the electrical simulation results. The first and second column lists the defect categories and sub- categories, respectively. The third column lists the output voltage V , generated by simulation for each defect category, while the fourth column lists the percentage change from the defect-free value of V,. Some defect categories have a range of misbehaviors. For example, lateral finger protrusions have an output voltage that range from the nominal value of 4 mV to several hundred mV depending on the amount of gap reduction due to the protrusion. In these cases, we provide the range of possible output values from these defects.

The most interesting electrical simulation results correspond to the broken finger defects and lateral finger protrusions. These defects lead to a very small increase or decrease in the shuttle mass. The mass change is so small that the mechanical frequency response of the resonator is

Lateral finger protrusion Not determined not applicable (non-overlap, sticking) Lateral finger protrusion Not determined not applicable (non-overlap, non-sticking) Mass and finger anchor 0.00-0.06 98%-100% Spring beam anchor-1 4.01 2% (closest to shuttle) Spring beam anchor-2 0.01 99% (farthest from shuttle) Broken shuttle 4.07 0% Broken finger 4.07-80.6 0 - >1000% Broken spring beam-1 4.94 21% (connects to shuttle) Broken spring beam-2 5.08 25%

date capacitor model is then used to compute the lateral retrusion capacitance Cf

The electrical schematic of Figure 9 is simulated using HSPICE to determine the impact of the various categories Df defects on the output-sensing signal V,. The displacement +

Df the shuttle mass under an applied inertial force changes

80%

Table 4. Impact of lateral finger protrusion defects (overlap, non-sticking) on sensing voltage V, and its percentage deviation from nominal.

19.2 372

% of finger Sensing voltage YO change remaining K (mv) from nominal

Intact 99% 95% 7.83 94

50% 42.0 932

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Broken shuttle 1 Broken finger 1 Broken spring beam

Tables 4 and 5 further illustrate the wide range of misbehaviors asspciated with these two defect types. I

J J J J 4

J J

6 FAULT CLASSES

harmless.

Many defect types can have an impact ranging from

17 CONCLUSIONS I The failure mechanisms of a surface-micromachined

comb-drive microresonator due to particulate contaminations were studied within a simulation environment. A Monte Carlo analysis of particulates allowed the comblete categorization of defective structures based on theit geometrical properties. Theoretical probabilities of occurrence for each defect type were computed and found to closely match the defect probabilities observed through simulation. In addition, manufacturing dteps are classified as either resistant or vulnerable to phiculate contaminations based on their susceptibility to particles.

FEA and I$PlCE simulations were performed to evaluate misbehaviors associated with the categories of defective structures. Simulations results indicate that FEA

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alone cannot reveal all the misbehaviors caused by particles. In particular, defects that cause broken comb fingers or lateral protrusions on the sidewalls of comb fingers are only exposed by electrical simulation.

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