Static & Dynamic MEMS Device characterisation
It is widely recognised that Micro Electro Mechanical Systems (MEMS) will bring relevant technological breakthroughs and social benefits.
MEMS products reflect the technological trend of miniaturisation and multifunctional integration, which leads to the implementation of new product ideas and answers the market requirements of reduced material, low energy consumption, and advanced technology. In the near future, new potentials will be achievable, including improved sensing accuracy, higher performance communication, and faster diagnostic response.
Despite the exponential growth in research and development activities over the last decade, only a few different microproducts are commercially available, including accelerometers and sensors pressures.
The gap between research and the market is principally due to lack of confidence in realiability and robustness of the developed components [1]. Simple, accurate, and standard procedures to support MEMS design are therefore required, such as methodologies for functional analysis (e.g. static and dynamic Characterisation [2]), material properties testing (e.g. Young's Modulus, fracture strength and process residual stress [3], [4]), and estimation of the performance of packages. Specifically, in this article we address the application of two methods, respectively based on capacitance and optical measurement, suitable for studying the static and the dynamic response of MEMS structures.
Procedural steps
In this work, the static and the dynamic Characterisation of a MEMS system is intended as follows:
● defining the system displacement-voltage relationship while a DC voltage is applied;
● defining the system displacement–frequency relationship while a generic sinusoidal signal -VDC+ VACcos (ωt)- is applied.
The capacitance-based methodologies can be applied to achieve the first goal.
The general layout of a MEMS system consists of a proof mass suspended from the wafer while remaining anchored at discrete points through very compliant parts. Commonly, the actuation is obtained by means of electrostatic forces. Fixed parts are then arranged in the device area in such a way to form a capacitance bridge with the free system portion. Thus, the relative motion between the two masses modifies the geometrical configuration of the capacitors and the system displacement can be derived based on the change in capacitance.
The developed procedure involves three steps.
First, the mass position is related to the capacitor geometry through application of the theoretical definition of the capacitance. The required function assumes different expression with respect to the engine configuration.
Next, the operation of the device is studied through the system capacitance-voltage response. The structure is then excited by a DC signal sequence, and the output capacitance measured at each step. As shown in Fig. 1, a capacitance metre and a PC-unit are required for the test bed set-up. Specifically, the capacitance metre is also used as DC power supply, and the Low-High I/O are connected to the system rotor and stator mass, respectively. The instrument is controlled by software code which allows the user to define the desired DC signal (from a starting voltage value up to a final one by chosen increment) and to store the system capacitance output. The desired function is empirically obtained by way of properly fitting a curve through the experimental results.
Finally, both above obtained results are combined in an individual system displacement-DC voltage relationship in order to achieve the proposed objective.
The described procedure takes advantages from electrical measurements. Batch Characterisation can also be achieved for packaged devices. Additionally, design approaches based on on–chip test can be exploited providing the development of stable and inexpensive test system set-up.
In order to achieve the second proposed goal, the LDV (Laser Doppler Vibrometre) method is commonly used as particularly suitable for measuring the vibrational velocity and displacement of structures excited by a random frequency signal [5].
This methodology is based upon the physical principle of the Doppler phenomenon. Therefore, the velocity of the moving object, which reflects the reference beam focused on its surface, is calculated from the measured frequency shift, using the equation: (1).
where v and λ are, respectively, the velocity of the monitored structure and the wavelength of the reflected beam. This path length is then calculated based on optical interference. In this way, it is possible to measure the vibrational velocity as well as the mechanical displacement of the moving object by counting the typical number of interferometry bright-dark fringes generated on the beam detector.
Fig.2 shows a schematic view of the general system set-up. The following instruments are needed: a spectrum analyser, (typically also used as a power supply), the LDV systems, i.e., the laser generator and the processing unit, and a PC-unit provided with a software code specifically employed for storing the velocity/displacement data acquired by the analyser. Typically, a white noise signal is applied.
The method exploits all advantages of a non-contact measurement technique. It can be applied to a wide range of MEMS systems, including structures using non- capacitive excitation. However, the access to the object is enabled through a focused reference beam, which has to be positioned parallel to the vibration direction. Thus, only a single point of the device surface can be monitored at a time.
Case study description
The structure considered in this work is a reliability test device developed by STMicroelectronics with the specific objective of estimating the fatigue behaviour of the structural material involved in their commercial products.
The production technology is the surface micromachining ThELMA process (Thick Epipoly Layer for Microactuators and Accelerometers), which exploits several state-of-the-art integrated circuit technology steps, together with dedicated MEMS process steps such as high aspect ratio etching - i.e., trench - and sacrificial layer removal. It is characterised by the use of a thick epitaxial polysilicon layer as structural material.
The test device contains two springs (the samples) that are on one side connected to the substrate by a central anchor and on the other side to a suspended mass. The actuation is provided electrostatically by a rotating comb drive actuator, linked to the samples by the suspended mass (Fig.3). The nominal width of the samples varies between 1.8 μm and 4.4μm along their length axis. They are 34 μm in length, while the diameter of the actuator is about 1000μm.
Applying a sinusoidal input voltage, the suspended mass oscillates in the plane around a certain equilibrium point. Therefore, the samples are alternatively bent and cyclically stressed. Varying the signal components, a wide range of induced stress levels can be achieved. Thus, once the induced stress is known, the Woehler diagram can be obtained by counting the life-cycle numbers before the sample breaks.
The system design has been supported by using the Finite Element Method (FEM). A FEM model of the rotor mass including the central anchor was created in the virtual environment of Ansys 7.0. Specifically, the nominal geometrical values have been reduced by a factor of 0.45 μm, which corresponds to the over etch, i.e., the dimensional loss of the samples during release, measured by SEM. As a boundary condition, the electrostatic force generated by the engine for a given DC voltage was applied to the rotor arm edges as a constant pressure, while zero displacement was applied to the nodes of the central anchor.
The simulated static electromechanical behaviour of the structure was finally expressed as follows:
Equation (4)
where the term C indicates the system capacitance.
Referring to Fig.4, eq.4 assumes the following expression [6]:
where ε0 indicates the dielectric constant of the vacuum, ri the radial distance between the ith comb finger and the central anchor, w the thickness of the epitaxial layer, R the relative sum, d the gap between two adjacent fingers, and N and n, respectively the comb drive rotor arms and cell number. Thus, the engine moment is proportional to the square of the DC voltage as well as the system angular displacement, as indicated in eq. 2. Specifically, the proportional constant cθ equals the induced angular displacement while a DC voltage of 1V is applied.
Device static Characterisation
The capacitive procedure described in Sec.2 has been used in order to verify the static electromechanical behaviour of the structure predicted by FEM.
As indicated in eq.5, the system capacitance is a function of the angular displacement. It is given by:
In order to study the operation of the device through the system capacitance-voltage response, the structures were excited by a DC signal sequence starting from 1ν up to 40 ν with a unitary increment while the stator-rotor capacitance outputs were measured at each step based on the test bed setup showed in Fig.1.
A total amount of 25 structures from two different wafers has been tested. In Fig. 6, the measured responses are shown. Unfortunately, some devices located at the wafer edges, exhibited poor behaviour and therefore can not be considered for the fatigue Characterisation.
After removing the constant term due to the initial overlap, the measured C-V curves were built into the quadratic function:
as suggested by the system displacement–voltage relationship. The achieved mean value of A is 0.405 ± 0.012 fF/V2.
3.2. Device dynamic Characterisation
Further investigation of the dynamic electromechanical behaviour of the system was needed. In fact, under working conditions, i.e., applying a differential voltage with bias to the rotor stator arms, the oscillation amplitude, and thus the induced stress, are amplified by the frequency modulation [7].
In order to extract the FRF (Frequency Response Function) of the structure, the LDV (Laser Doppler Vibrometre) method has been used, following the system set-up procedure described above (Fig.2). In particular, the velocity monitoring option has been chosen. In fact, displacements can be directly obtained by way of dividing the measured velocities by the frequencies. A total amount of 20 devices has been excited. Specifically, the applied DC voltage equals 1V while the AC amplitude is 500mV; the frequency is random. In Fig.8, the obtained experimental results are plotted.
This data was then built in the resonator curve:
which allows the expression of the dynamic system displacement (X) with respect to the DC gain (X0), i.e., the achieved displacement at null frequency, as a function of the resonance frequency (fn), of the Quality factor (Q) and of the random frequency (f). Specifically, the following mean values have been obtained through data fitting: fn = 4033 ± 54 Hz; Q =16.3 ± 1.3 as reported in Fig.8. In this contest, it is also important to realise that, while the natural frequency of a system could be obtained theoretically or using simulations, the determination of the quality factor requires the exact knowledge of the medium damping constant and, therefore, in any case, the application of experimental measurements.
The angular displacement-voltage and the induced stressvoltage relationships of the fatigue test device under working conditions can be then expressed as follows:
and where σf indicates the system displacement ratio of eq.8 calculated at the 1st and 2nd harmonic of the signal.
4. Conclusion
This article proposes the application of two empirical methods suitable for the static and dynamic Characterisation of micrometersized devices, responding to the microtechnology field requirements of developing simple and standard procedures enabling the improvement of the MEMS product design flow. The methodologies are based on capacitance measurement and laser interferometry, respectively. In the first case, the method exploits the general layout of electrostatic actuated devices for characterising the system static response based on the capacitive variation.
The method takes advantage of electrical measurements. The batch Characterisation of packaged devices is also achievable, as the development of inexpensive on-chip testing procedures is feasible. In the second case, the frequency response of a system is detected based on the combination of the physical principle of the Doppler phenomenon and optical measurements. The procedure can be applied to a wide range of structures, including non-capacitive MEMS. In this work, the methodologies have been successfully applied for studying the electromechanical model of a reliability test device. The case study highlights how the techniques may be coupled to the usual design approaches for completing and verifying the information given by theory and simulations.
