**1. Introduction**

Micro Electro Mechanical Systems (MEMS) is developed based on the semi-conductor technology, however, relative material, design, fabrication, simulation, packaging and test are more complex than those in semi-conductor technology. In the primary stage, MEMS technology focused on the design and development, now on the commercialization and improving reliability and decreasing cost and price. So test is increasingly important to MEMS technology and testing cost is about 1/3 of the whole cost of MEMS. In order to improve the production and decrease the cost, producers and researchers pay more attention to MEMS test to solve all the testing problems from design to packaging process.

There are a number of methods to carry out these measurements, such as scanning electron microscopy (SEM), atomic force microscopy (AFM), stylus profiler, and optical profiler, etc. Every method has its advantages and disadvantages.


If MEMS devices need to fit the large-scale production, it is essential that these measurements must be cheaply and easily made at the wafer level, without the need for large space, expensive packaging or destructive test methods. Optical techniques can offer

MEMS Characterization Based on Optical Measuring Methods 91

Two sets of measurement systems were developed in our laboratory. The first one is for

As a foundation of our system, the nano-measuring machine (NMM) was used, which was developed in Ilmenau University of Technology of Germany for surface measurement within a measuring volume of 25mm×25mm×5mm. Three commercial interferometers inside the NMM read the stage position in real time so that the positioning control loop can assure a movement resolution of 0.1 nm. The sensor arrangement provides an Abbe errorfree measurement on all three NMM axes. Based on the NMM, various measuring systems

The layout of the first experimental system used in this context is illustrated in figure 2. To increase the optical system robustness, we chose a commercial interferometer system with halogen lamp fibre illumination from NIKON. A CCD camera recorded the interferogram at equidistant positions and transfered them into a computer for data processing. In the laboratory, the system was assembled inside a cover where a vibration isolation table was provided. Additionally, in order to further decrease the influence of vibrations, we placed

The second system is called micro motion analyzer (MMA). The structure of MMA is shown in figure 3. MMA was equipped with several long working distance optical objectives from Zeiss company, including 5×, 10×, 20× and 50×. There were two kinds of light sources: one was a high performance LED (Nichia NSPG 500S LED, central wavelength was 525nm, optical bandwidth was 40nm) to be used in the in-plane motion measurement; the other was a LD (Hitachi HL6501MG, the power was 50mW, the wavelength was 658nm) to be used in the out-of-plane motion measurement. A nano-positioner (PI P-721.CL, capacitor sensor feedback control in close loop) was used to shift the phase of the interferogram and adjust the optical path with sub-nanometer resolution. The bright field and interference field were switched by putting a stop plate in the reference optical path. Images were captured by a

static characterization, the other one is for dynamic characterization.

Fig. 2. Scheme of the static characterization system

the entire equipment on a special independent foundation.

could be integrated.

**2.2 Measurement system** 

solutions to many of these problems. This chapter uses computer micro-vision and microscopic interferometry to carry out MEMS measurements, including dimensional (static) and moving (dynamic) properties analysis. The moving properties can be classified into in-plane (lateral) movements and out-of-plane (vertical) movements. The techniques involved are simple, fast, non-destructive, requiring no sample preparation and may be carried out at wafer level - all important requirements for high volume production.

#### **2. System set-up**

#### **2.1 Microscopic interferometer**

The interferometer is the device which can generate the interferogram patterns. The typical microscopic interferometers used in MEMS measurement include Michelson-type, Mirautype and Linnik-type. The scheme of optical structures in these interferometers is shown in figure 1.

Fig. 1. Schematic layout of the three types of interferometers

Inside the interferometer the light is divided into two beams, one beam is guided on the sample surface as the test beam, and the other one goes to the reference mirror as the reference beam. When the OPD is within the coherence length, the reflected test beam and reference beam will interfere with each other and produce interference fringe patterns. Figure 1(a) presents the Michelson interferometer, where a beam splitter is placed in front of the objective. Hence, the working distance of the objective must be relatively large which makes the magnification of Michelson interferometer the lowest of the three types of interferometers shown in figure 1. Figure 1 (b) is the Mirau interferometer, which is widely equipped in lots of commercial optical profilers. Inside this interferometer, the light is split by a very thin and flat optical mirror. As result, the mechanical structure of this interferometer is more compact than that of Michelson type. Besides, the light path between the test beam and the reference beam is very similar, which can also minimize optical disturbance. Figure 1 (c) illustrates the layout of the Linnik interferometer, from where one can see the beam splitter is located behind the objective. Therefore, Linnik interferometer can use the objective with shorter working distance and higher magnification. However, the unconformity between the two objectives may cause measurement errors, and that is why in the application of Linnik interferometer the two objectives must be matched very well.

#### **2.2 Measurement system**

90 Microelectromechanical Systems and Devices

solutions to many of these problems. This chapter uses computer micro-vision and microscopic interferometry to carry out MEMS measurements, including dimensional (static) and moving (dynamic) properties analysis. The moving properties can be classified into in-plane (lateral) movements and out-of-plane (vertical) movements. The techniques involved are simple, fast, non-destructive, requiring no sample preparation and may be carried out at wafer level - all important requirements for high volume

The interferometer is the device which can generate the interferogram patterns. The typical microscopic interferometers used in MEMS measurement include Michelson-type, Mirautype and Linnik-type. The scheme of optical structures in these interferometers is shown in

(a) Michelson interferometer (b) Mirau interferometer (c) Linnik interferometer

Inside the interferometer the light is divided into two beams, one beam is guided on the sample surface as the test beam, and the other one goes to the reference mirror as the reference beam. When the OPD is within the coherence length, the reflected test beam and reference beam will interfere with each other and produce interference fringe patterns. Figure 1(a) presents the Michelson interferometer, where a beam splitter is placed in front of the objective. Hence, the working distance of the objective must be relatively large which makes the magnification of Michelson interferometer the lowest of the three types of interferometers shown in figure 1. Figure 1 (b) is the Mirau interferometer, which is widely equipped in lots of commercial optical profilers. Inside this interferometer, the light is split by a very thin and flat optical mirror. As result, the mechanical structure of this interferometer is more compact than that of Michelson type. Besides, the light path between the test beam and the reference beam is very similar, which can also minimize optical disturbance. Figure 1 (c) illustrates the layout of the Linnik interferometer, from where one can see the beam splitter is located behind the objective. Therefore, Linnik interferometer can use the objective with shorter working distance and higher magnification. However, the unconformity between the two objectives may cause measurement errors, and that is why in the application of Linnik interferometer the two

production.

figure 1.

**2. System set-up** 

**2.1 Microscopic interferometer** 

objectives must be matched very well.

Fig. 1. Schematic layout of the three types of interferometers

Two sets of measurement systems were developed in our laboratory. The first one is for static characterization, the other one is for dynamic characterization.

Fig. 2. Scheme of the static characterization system

As a foundation of our system, the nano-measuring machine (NMM) was used, which was developed in Ilmenau University of Technology of Germany for surface measurement within a measuring volume of 25mm×25mm×5mm. Three commercial interferometers inside the NMM read the stage position in real time so that the positioning control loop can assure a movement resolution of 0.1 nm. The sensor arrangement provides an Abbe errorfree measurement on all three NMM axes. Based on the NMM, various measuring systems could be integrated.

The layout of the first experimental system used in this context is illustrated in figure 2. To increase the optical system robustness, we chose a commercial interferometer system with halogen lamp fibre illumination from NIKON. A CCD camera recorded the interferogram at equidistant positions and transfered them into a computer for data processing. In the laboratory, the system was assembled inside a cover where a vibration isolation table was provided. Additionally, in order to further decrease the influence of vibrations, we placed the entire equipment on a special independent foundation.

The second system is called micro motion analyzer (MMA). The structure of MMA is shown in figure 3. MMA was equipped with several long working distance optical objectives from Zeiss company, including 5×, 10×, 20× and 50×. There were two kinds of light sources: one was a high performance LED (Nichia NSPG 500S LED, central wavelength was 525nm, optical bandwidth was 40nm) to be used in the in-plane motion measurement; the other was a LD (Hitachi HL6501MG, the power was 50mW, the wavelength was 658nm) to be used in the out-of-plane motion measurement. A nano-positioner (PI P-721.CL, capacitor sensor feedback control in close loop) was used to shift the phase of the interferogram and adjust the optical path with sub-nanometer resolution. The bright field and interference field were switched by putting a stop plate in the reference optical path. Images were captured by a

MEMS Characterization Based on Optical Measuring Methods 93

Using a series of *I* measured at different phase *φ* value, Hariharan phase-shifting algorithm is used to extract height information on devices' surface in *I*. The intensities are *I1, I2, I3, I4*

2( ) ( , ) arctan <sup>2</sup>

*x y III*

This algorithm need change π/2 between two successive image capturing. This algorithm is repressive to the calibration error of the phase-shifter and the nonlinear errors of the

Measurements using single-wavelength interferometry have an inherent 2π phase ambiguity, which means phase maps must be unwrapped by removing artificial 2π jumps before they can be properly interpreted in terms of surface height. This process is called phase unwrapping. Now there are many kinds of phase unwrapping algorithms. In the experiments, considering about the testing speed and the real quality of the interferogram, quality-guided path following algorithm is used to retrieve the actual phase map. The

> 4 *h*

Figure 4 shows the wrapped phase map and the unwrapped map in the process of dealing

 (a) Wrapped phase map (b) Unwrapped phase map

PSI is widely used to test smooth surfaces and is very accurate, resulting in vertical measurements with sub-nanometer resolution. However, PSI cannot obtain a correct profile for objects that have large step changes because it becomes ineffective as height discontinuities of adjacent pixels exceed one quarter of the used wavelength (λ/4), which is

 

2 4 315

*I I*

is as follows.

(3)

(2)

and *I5* respectively. The formula of calculating wrapped phase

detector, so it improves the measurement accuracy.

surface height can be calculated by the following formula.

with the captured images. The tested sample is a membrane.

Here, λ is the wavelength of the light source.

Fig. 4. Pictures of processed results

also called "phase ambiguity".

**3.1.2 White light scanning interferometry (WLI)** 

digital CCD camera (Microvision, 1280×1024 pixels, 9μm pixel distance, 100% filling factor, 10 bits grayscale resolution), then transferred to the server to be post-processed. The user can transfer and receive instructions and data through TCP/IP protocol on a client PC. The system was also equipped with a signal generating unit and a high voltage amplifying unit to output high voltage signal and stimulate the tested MEMS device. The system was placed on a vibration isolation table (TMC Lab Table) to decrease the effect of outside vibration. The system was also equipped with a probe station (Karl Suss, Germany) to test the unpackaged MEMS devices. Here digital phase lock loop (PLL) made the stimulating signal, illuminating signal and the image capturing synchronized. The frequency range of Arbitrary Waveform Generator (AWG) was from 1 Hz to 10 MHz, and the sampling frequency was 40 MHz.

Fig. 3. Structure diagram of the MMA

#### **3. Measurement principles**

#### **3.1 Static characterization**

Static characterization is a very important aspect in MEMS technology, especially for the design and manufacture of micro- or nano-sensors and actuators. In general case, the goal of static characterization is to derive the geometrical parameters, such as surface topography, profile, waviness, roughness and depth-width ratio, etc.

#### **3.1.1 Phase-shifting interferometry (PSI)**

If we denote the coordinates in the plane of the CCD array as (x, y), we can write the intensity of the interference pattern I(x, y) as:

$$I(\mathbf{x}, y) = A(\mathbf{x}, y) + B(\mathbf{x}, y)\cos[\phi(\mathbf{x}, y) + \phi] \tag{1}$$

Where *A(x, y)* is the function representing the mean background intensity of the interferogram; *B(x, y)* is the function determining the modulation of the interferogram;  *(x, y)* is the function dependent on the unwrapped phase *θ(x, y)* which represents the height change on the sample; phase *φ* is a constant, which can be adjusted by changing the position in the axial direction between the objective and the sample.

digital CCD camera (Microvision, 1280×1024 pixels, 9μm pixel distance, 100% filling factor, 10 bits grayscale resolution), then transferred to the server to be post-processed. The user can transfer and receive instructions and data through TCP/IP protocol on a client PC. The system was also equipped with a signal generating unit and a high voltage amplifying unit to output high voltage signal and stimulate the tested MEMS device. The system was placed on a vibration isolation table (TMC Lab Table) to decrease the effect of outside vibration. The system was also equipped with a probe station (Karl Suss, Germany) to test the unpackaged MEMS devices. Here digital phase lock loop (PLL) made the stimulating signal, illuminating signal and the image capturing synchronized. The frequency range of Arbitrary Waveform Generator (AWG) was from 1 Hz to 10 MHz, and the sampling frequency was 40 MHz.

Static characterization is a very important aspect in MEMS technology, especially for the design and manufacture of micro- or nano-sensors and actuators. In general case, the goal of static characterization is to derive the geometrical parameters, such as surface topography,

If we denote the coordinates in the plane of the CCD array as (x, y), we can write the

*Ixy Axy Bxy xy* ( , ) ( , ) ( , )cos[ ( , ) ]

Where *A(x, y)* is the function representing the mean background intensity of the interferogram; *B(x, y)* is the function determining the modulation of the interferogram;

*y)* is the function dependent on the unwrapped phase *θ(x, y)* which represents the height change on the sample; phase *φ* is a constant, which can be adjusted by changing the position

(1)

 *(x,* 

Fig. 3. Structure diagram of the MMA

profile, waviness, roughness and depth-width ratio, etc.

in the axial direction between the objective and the sample.

**3.1.1 Phase-shifting interferometry (PSI)** 

intensity of the interference pattern I(x, y) as:

**3. Measurement principles 3.1 Static characterization** 

Using a series of *I* measured at different phase *φ* value, Hariharan phase-shifting algorithm is used to extract height information on devices' surface in *I*. The intensities are *I1, I2, I3, I4* and *I5* respectively. The formula of calculating wrapped phase is as follows.

$$\phi(x, y) = \arctan\left[\frac{2(I\_2 - I\_4)}{2I\_3 - I\_1 - I\_5}\right] \tag{2}$$

This algorithm need change π/2 between two successive image capturing. This algorithm is repressive to the calibration error of the phase-shifter and the nonlinear errors of the detector, so it improves the measurement accuracy.

Measurements using single-wavelength interferometry have an inherent 2π phase ambiguity, which means phase maps must be unwrapped by removing artificial 2π jumps before they can be properly interpreted in terms of surface height. This process is called phase unwrapping. Now there are many kinds of phase unwrapping algorithms. In the experiments, considering about the testing speed and the real quality of the interferogram, quality-guided path following algorithm is used to retrieve the actual phase map. The surface height can be calculated by the following formula.

$$
\hbar \mathbf{h} = \frac{\partial}{4\pi} \mathcal{A} \tag{3}
$$

Here, λ is the wavelength of the light source.

Figure 4 shows the wrapped phase map and the unwrapped map in the process of dealing with the captured images. The tested sample is a membrane.

(a) Wrapped phase map (b) Unwrapped phase map

Fig. 4. Pictures of processed results

**3.1.2 White light scanning interferometry (WLI)**  PSI is widely used to test smooth surfaces and is very accurate, resulting in vertical measurements with sub-nanometer resolution. However, PSI cannot obtain a correct profile for objects that have large step changes because it becomes ineffective as height discontinuities of adjacent pixels exceed one quarter of the used wavelength (λ/4), which is also called "phase ambiguity".

MEMS Characterization Based on Optical Measuring Methods 95

Carré proposed a new phase shifting interferometry in 1966. Unlike the conventional PSI, Carré's method does not require several fixed phase steps (for example, /8), but only equal ones, which makes it much easier for most PZTs to fulfill. Suppose the phase step is set to be

> 1 0 *I xy I* ( , ) {1 cos[ ( , ) 3 ]}

2 0 *I xy I* ( , ) {1 cos[ ( , ) ]} 

3 0 *I xy I* ( , ) {1 cos[ ( , ) ]} 

4 0 *I xy I* ( , ) {1 cos[ ( , ) 3 ]} 

Where *I1* to *I4* are the recorded intensities, *I0* is the background irradiance,

*tg II II*

falls within (-, +] and the surface information can be written as:

is the phase term needed to be extracted.

1 14 23 23 14 23 14 [( ) ( )][3( ) ( )] [( ) ( )] *II II II II*

> 4 *h*

wavelength used. The relative heights on every point together can then give a surface 3D

However, in the white light correlogram, the existence of *g(z)* will make *g* be a function of the spatial position along the scanning direction, which means error occurs when we employ the Carré method to carry out the phase computation from a white light interferogram. In the next, we will use computer simulation to study how much this kind of

2

is set to be 500 nm(

(11)

*=lc/ 2*

*/500*. Assumed the wavelength is 600 nm, this error

2 [(n-20) ] 4 ( ) 200 200exp{- } cos[ ( 20) ] <sup>7</sup>

of the light source), the additional phase term due to different reflections is set to be /7. Figure 6 is the phase computation simulation, which indicates that: phase extraction error owing to the visibility variety is minimum at the position of the coherence peak; on the other hand, the phase error has a trend of becoming bigger while the phase position travels away from the centre. The minimum phase error is less than 0.02 rad and the equivalent

*I n n*

 

 

 

> 

(9)

*x y* (5)

*x y* (6)

*x y* (7)

*x y* (8)

(10)

is the unwrapped phase term,

, *lc* is the coherence length

is a constant

is the

**3.1.3 White light phase-shifting interferometry (WLPSI)** 

can be computed as:

Where *h* is the relative height of the surface,

The generated discrete white light signal *I(n)* is as follows:

**3.1.3.1 Phase extraction** 

indicated the visibility and

map of the tested sample.

error affects the measuring accuracy.

measurement error is smaller than

is the scanning step 60 nm,

Then the phase term

Here 

Where 

2, Carré's method can be expressed as:

White light scanning interferometry (WLI) provides a good solution to overcome "phase ambiguity". Here we track point P and Q in figure 5 to illustrate the scan process of WLI. When Q stays outside the coherence length of the light source, the intensity detected is nearly the same with the background irradiance, corresponding to t1 to t2. Afterwards, from time t2 when Q starts to move into the coherence length zone, the signals extracted of point Q will be kept modulating by the interferogram until it travels out at t5. During the scan, the maximum visibility will occur at t4 where the testing beam matches the reference beam. The above process is roughly similarity for point P. Once retrieved the correlogram, the peak position of the intensities can then be used as an indicator of the surface relative height.

Fig. 5. Schematic diagram of white light vertical scanning interferometry

The white light correlogram recorded by the CCD camera in the white light interferometry can be expressed as:

$$I = I\_0 \left[ 1 + \gamma g(z) \cos(\phi + a) \right] \tag{4}$$

Where *I* is the measured intensity, *I0* is the background irradiance value, *γ* is a constant, *g(z)* is the fringe visibility in the form of Gaussian function, is the phase value depended on the optical path difference and the is the additional phase term due to different reflections. Generally, the maximum location of *g(z)* is usually extracted for the height evaluation. This process can be done either in spatial space or in frequency domain.

So far, the white light signal demodulation techniques can be basically categorized into two main groups: spatial domain algorithms and frequency domain algorithms. The first group consists of polynomial interpolation, centroid method and Hilbert transform, whereas the latter has Fourier transform, wavelet transform and spatial frequency domain analysis, etc. In general case, algorithms from the second group can perform the surface characterization with a higher resolution. Nevertheless, because of the transform procedures from the spatial domain to frequency domain (various types of convolutions), the second group algorithms are usually time consuming; on the contrary, the first group is efficient but with lower resolution. The other methods are generally based upon the above algorithms and will not be mentioned here.

#### **3.1.3 White light phase-shifting interferometry (WLPSI)**

#### **3.1.3.1 Phase extraction**

94 Microelectromechanical Systems and Devices

White light scanning interferometry (WLI) provides a good solution to overcome "phase ambiguity". Here we track point P and Q in figure 5 to illustrate the scan process of WLI. When Q stays outside the coherence length of the light source, the intensity detected is nearly the same with the background irradiance, corresponding to t1 to t2. Afterwards, from time t2 when Q starts to move into the coherence length zone, the signals extracted of point Q will be kept modulating by the interferogram until it travels out at t5. During the scan, the maximum visibility will occur at t4 where the testing beam matches the reference beam. The above process is roughly similarity for point P. Once retrieved the correlogram, the peak position of the intensities can then be used as an indicator of the

Fig. 5. Schematic diagram of white light vertical scanning interferometry

is the fringe visibility in the form of Gaussian function,

process can be done either in spatial space or in frequency domain.

The white light correlogram recorded by the CCD camera in the white light interferometry

*I I gz* <sup>0</sup> 1 ( )cos( ) 

Where *I* is the measured intensity, *I0* is the background irradiance value, *γ* is a constant, *g(z)*

Generally, the maximum location of *g(z)* is usually extracted for the height evaluation. This

So far, the white light signal demodulation techniques can be basically categorized into two main groups: spatial domain algorithms and frequency domain algorithms. The first group consists of polynomial interpolation, centroid method and Hilbert transform, whereas the latter has Fourier transform, wavelet transform and spatial frequency domain analysis, etc. In general case, algorithms from the second group can perform the surface characterization with a higher resolution. Nevertheless, because of the transform procedures from the spatial domain to frequency domain (various types of convolutions), the second group algorithms are usually time consuming; on the contrary, the first group is efficient but with lower resolution. The other methods are generally based upon the above algorithms and will not

 

is the additional phase term due to different reflections.

(4)

is the phase value depended on the

surface relative height.

can be expressed as:

be mentioned here.

optical path difference and the

Carré proposed a new phase shifting interferometry in 1966. Unlike the conventional PSI, Carré's method does not require several fixed phase steps (for example, /8), but only equal ones, which makes it much easier for most PZTs to fulfill. Suppose the phase step is set to be 2, Carré's method can be expressed as:

$$I\_1(\mathbf{x}, y) = I\_0 \{ 1 + \chi \cos[\phi(\mathbf{x}, y) - \mathbf{3}\mathcal{S}] \}\tag{5}$$

$$I\_2(\mathbf{x}, y) = I\_0 \{ 1 + \chi \cos[\phi(\mathbf{x}, y) - \delta] \}\tag{6}$$

$$I\_3(\mathbf{x}, y) = I\_0 \{ 1 + \chi \cos[\phi(\mathbf{x}, y) + \delta] \}\tag{7}$$

$$I\_4(\mathbf{x}, y) = I\_0 \{ 1 + \chi \cos[\phi(\mathbf{x}, y) + \mathbf{3}\mathcal{S}] \} \tag{8}$$

Where *I1* to *I4* are the recorded intensities, *I0* is the background irradiance, is a constant indicated the visibility and is the phase term needed to be extracted. Then the phase term can be computed as:

$$\phi = \text{tg}^{-1} \frac{\sqrt{\left[ (I\_1 - I\_4) + (I\_2 - I\_3) \right] \left[ \Im(I\_2 - I\_3) - (I\_1 - I\_4) \right]}}{\left[ (I\_2 + I\_3) - (I\_1 + I\_4) \right]} \tag{9}$$

Here falls within (-, +] and the surface information can be written as:

$$
\hbar \mathbf{h} = \frac{\overline{\overline{\phi}}}{4\pi} \mathcal{A} \tag{10}
$$

Where *h* is the relative height of the surface, is the unwrapped phase term, is the wavelength used. The relative heights on every point together can then give a surface 3D map of the tested sample.

However, in the white light correlogram, the existence of *g(z)* will make *g* be a function of the spatial position along the scanning direction, which means error occurs when we employ the Carré method to carry out the phase computation from a white light interferogram. In the next, we will use computer simulation to study how much this kind of error affects the measuring accuracy.

The generated discrete white light signal *I(n)* is as follows:

$$I(n) = 200 + 200 \exp\{-\frac{\left[\left(n \cdot 20\right) \times \Lambda\right]^2}{\sigma^2}\} \cos\left[\frac{4\pi}{\lambda}(n - 20) \times \Lambda + \frac{\pi}{7}\right] \tag{11}$$

Where is the scanning step 60 nm, is set to be 500 nm(*=lc/ 2*, *lc* is the coherence length of the light source), the additional phase term due to different reflections is set to be /7. Figure 6 is the phase computation simulation, which indicates that: phase extraction error owing to the visibility variety is minimum at the position of the coherence peak; on the other hand, the phase error has a trend of becoming bigger while the phase position travels away from the centre. The minimum phase error is less than 0.02 rad and the equivalent measurement error is smaller than */500*. Assumed the wavelength is 600 nm, this error

MEMS Characterization Based on Optical Measuring Methods 97

the target. The MMA needs two things: a target that can be moved in a periodic manner,

The MMA calculates the motion of a selected region in a sequence of images using machine vision algorithms. The MMA algorithms are hybrids constructed from a broad class of algorithms (gradient based) that exploit changes in brightness (grayscale values) between

Fast moving targets appear blurry. One way of looking at fast moving targets is to slow down their apparent motion using a strobed light source. The scheme shown in figure 7 outlines how carefully timed pulses of light can capture snapshots (samples) of an object motion. These snapshots or images can then be used to reconstruct the displacement trajectory of the target. This is the case for displacements in the focal plane of the microscope or for displacements along the optical axis. It turns out that sometimes different types of images are better for measuring different types of displacements. The MMA optics module provides illumination

By shining a monochromatic incoherent beam of light through the objective lens and uniformily illuminating the target, a bright field image is produced. This is the familiar view through the microscope eyepiece. A bright field image of a MEMS device is shown in figure

Optical flow is used to describe the measured motion of brightness patterns between images. The algorithms used by the MMA are optical flow algorithms and are based on two important assumptions or constraints: 1) The brightness of a target region is constant over

Motion of the target modulates brightness in the image. The image of a MEMS target moves across an array of pixels. The position of the image is shown at two consecutive timesteps and the registers at the bottom of each image represent the nominal brightness of the corresponding pixel in row 6 (in figure 9). Even sub-pixel motion has measureably changed

images and are capable of measuring motions smaller than the individual pixel size.

and a target whose video image has contrast or structure when illuminated.

**3.2.1 In-plane motion measurement using video microscopy** 

for two types of images, both of which are acquired in a similar manner.

Fig. 7. Freezing rapid movement by stroboscopic illumination

time, 2) The target region moves as a rigid body.

**3.2.1.1 Bright field image** 

the brightness in the pixels.

8(a).

could be about 1nm and is negligible in comparison with the environment disturbance. This can be explained as the weak modulation effect of the Gaussian function around the zero order fringe of the white light signal, where the value of the Gaussian function can be treated as 1(for normalized Gaussian function).

Fig. 6. Phase extraction simulation

#### **3.1.3.2 Height evaluation**

Based on the phase computation simulation, the relative height of the tested profile *h* can then be determined as:

$$h = \text{(stepnumber} - \text{peakstep)} \times \Delta - t \times \left[\frac{\phi + 2k\pi}{4\pi}\lambda\right] \tag{12}$$

Where *stepnumber* is the scanning numbers, *peakstep* corresponds to the phase term which comes out of Carré method, is the scanning step and *t* is the NA parameter. Concerning the NA parameter, both Katherine Creath and C.J.R.Sheppard have given lots of detailed research on the relationship between the objective NA and the fringe width. Here we take this relationship into account and use the results from Ingelstam's equation to calculate this parameter.

$$t = 1 + \frac{\left(NA\_{eff}\right)^2}{4} \tag{13}$$

Where *NAeff* is the effective numerical aperture.

#### **3.2 Dynamic characterization**

The MMA is a highly integrated video microscope, using stroboscopic techniques to capture images of small, fast moving targets. The MMA uses both bright field and interference field based illumination modes combined with sophisticated machine vision algorithms to quantify micro motions. The MMA server and optics head combine the video microscopy with interferometry. However, successful measurements demand several characteristics in

could be about 1nm and is negligible in comparison with the environment disturbance. This can be explained as the weak modulation effect of the Gaussian function around the zero order fringe of the white light signal, where the value of the Gaussian function can be

Based on the phase computation simulation, the relative height of the tested profile *h* can

( 2) ( )[ ] <sup>4</sup> *<sup>k</sup> h stepnumber peakstep t*

Where *stepnumber* is the scanning numbers, *peakstep* corresponds to the phase term which

the NA parameter, both Katherine Creath and C.J.R.Sheppard have given lots of detailed research on the relationship between the objective NA and the fringe width. Here we take this relationship into account and use the results from Ingelstam's equation to calculate this

> <sup>2</sup> ( ) <sup>1</sup> 4

The MMA is a highly integrated video microscope, using stroboscopic techniques to capture images of small, fast moving targets. The MMA uses both bright field and interference field based illumination modes combined with sophisticated machine vision algorithms to quantify micro motions. The MMA server and optics head combine the video microscopy with interferometry. However, successful measurements demand several characteristics in

(12)

 

*NAeff <sup>t</sup>* (13)

is the scanning step and *t* is the NA parameter. Concerning

treated as 1(for normalized Gaussian function).

Fig. 6. Phase extraction simulation

**3.1.3.2 Height evaluation** 

then be determined as:

comes out of Carré method,

**3.2 Dynamic characterization** 

parameter.

Where *NAeff* is the effective numerical aperture.

the target. The MMA needs two things: a target that can be moved in a periodic manner, and a target whose video image has contrast or structure when illuminated.

### **3.2.1 In-plane motion measurement using video microscopy**

The MMA calculates the motion of a selected region in a sequence of images using machine vision algorithms. The MMA algorithms are hybrids constructed from a broad class of algorithms (gradient based) that exploit changes in brightness (grayscale values) between images and are capable of measuring motions smaller than the individual pixel size.

Fast moving targets appear blurry. One way of looking at fast moving targets is to slow down their apparent motion using a strobed light source. The scheme shown in figure 7 outlines how carefully timed pulses of light can capture snapshots (samples) of an object motion. These snapshots or images can then be used to reconstruct the displacement trajectory of the target. This is the case for displacements in the focal plane of the microscope or for displacements along the optical axis. It turns out that sometimes different types of images are better for measuring different types of displacements. The MMA optics module provides illumination for two types of images, both of which are acquired in a similar manner.

Fig. 7. Freezing rapid movement by stroboscopic illumination

#### **3.2.1.1 Bright field image**

By shining a monochromatic incoherent beam of light through the objective lens and uniformily illuminating the target, a bright field image is produced. This is the familiar view through the microscope eyepiece. A bright field image of a MEMS device is shown in figure 8(a).

Optical flow is used to describe the measured motion of brightness patterns between images. The algorithms used by the MMA are optical flow algorithms and are based on two important assumptions or constraints: 1) The brightness of a target region is constant over time, 2) The target region moves as a rigid body.

Motion of the target modulates brightness in the image. The image of a MEMS target moves across an array of pixels. The position of the image is shown at two consecutive timesteps and the registers at the bottom of each image represent the nominal brightness of the corresponding pixel in row 6 (in figure 9). Even sub-pixel motion has measureably changed the brightness in the pixels.

MEMS Characterization Based on Optical Measuring Methods 99

(larger than a pixel) can be measured by using the modulation of the brightness of relevant pixels. It is also clear from figure 9 that changes in the measured brightness can be produced by factors other than motion of the target such as noise in the CCD camera's electronics or

In order to quantify in-plane or out-of-plane displacements, the algorithms need a length

For bright field images (in-plane measurements and optical sectioning), an in-plane length standard such as a grating (a target with a ruling of known spacing) is used to calibrate the length per pixel for a given magnification. The algorithms then convert the calculated

Interference images have a more convenient length scale available. In this case, measurements are quantified using the known wavelength of the illumination source. This

After the data acquisition process is finished, the stimulating system is turned off and the measurement is done again. These two kinds of data are analyzed using the same processing method. Then repeating it five times, the noise floor is described by the RMS

A 10 μm standard step height fabricated by VLSI (9.976 μm+0.028 μm) was measured, as shown in figure 10, the mean height is 9.984 μm, while the standard deviation is 0.010 μm. The result comparison was presented in figure 11. We can clearly see the step height derived from WLPSI stays in the middle of all the results. Since the algorithms from the second group can achieve higher measurement resolution, the WLPSI can improve the

(a) 3D structure (b) Profile

Fig. 10. Measurement of the 10 μm standard step height

measurement resolution compared with that of the algorithms from the first group.

scale. It means that different measurements need corresponding length scale.

fluctuations in the illumination intensity.

displacements from pixels to micrometers.

length standard is independent of magnification.

**4.1.1 10 μm standard step height measurement** 

**3.2.3 Qualifying displacements** 

**3.2.4 Noise floor analysis** 

**4. Experimental results** 

**4.1 Step structure measurement** 

value.

(a) Bright field image (b) Interferometric field image

Fig. 9. In-plane motion measurement using optical flow algorithm

The optical flow algorithms used by the MMA work for in-plane or out-of-plane measurements. For out-of-plane measurements, image sequences can be collected at different planes of focus (optical sectioning). In this way, brightness gradients can be sampled along the optical axis and then used in a manner identical to in-plane sequences.

#### **3.2.1.2 Interference field image**

Figure 8(b) is the interference field image, which is formed by the reflected light from the tested sample and the reference mirror in the optics module. The interferogram in the picture is sensitive to the optical path change of the sample, which can be used to calculate the height of the sample and the out-of-plane motion between images.

#### **3.2.2 Sub-pixel displacements measurement**

The final result of the computation is an extremely powerful tool capable of measuring motions of magnified targets well below the resolution of human vision. Although, the resolution of a single static image is limited in a theoretical sense by the wavelength of the light used to generate the image, the resolution of a motion measurement is limited by the sensitivity of the CCD camera as shown in figure 9. Sub-pixel motion of an object or region (larger than a pixel) can be measured by using the modulation of the brightness of relevant pixels. It is also clear from figure 9 that changes in the measured brightness can be produced by factors other than motion of the target such as noise in the CCD camera's electronics or fluctuations in the illumination intensity.
