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This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A Grating Light Modulator (GLM) based on Micro-Electro-Mechanical Systems (MEMS) is applied in projection display. The operating principle of the GLM is introduced in this paper. The electromechanical characteristic of the passive matrix addressing GLM is studied. It was found that if the spring constant is larger, both the response frequency and the driving voltage are larger. Theoretical analysis shows that the operating voltage and the pull-in voltage of the GLM are 8.16 and 8.74 V, respectively. When an all-selected pixel in a m×n array is actuated by a voltage V_{0}, the voltages of the half-selected pixel in row and column are V_{0}(m–1)/(m+n–1) and V_{0}(n–1)/(m+n–1), respectively, and the voltage of the non-selected pixel is V_{0}/(m+n–1). Finally, the experimental results indicate that the operating voltage and the pull-in voltage are 7.8 and 8.5V respectively, and the response frequency of the GLM is about 7 kHz. The crosstalk in a 16×16 GLM array is validated by the experiment. These studies provide a theoretical basis for improving the GLM driver.

Recently, with the development of MEMS technology, light modulators based on optical MEMS for projection displays have become a popular research focus [

A DMD has a three layer structure, so its fabrication process is very complicated. A typical GLV pixel consists of an even number of parallel, dual-supported ribbons formed of silicon nitride and coated with a reflective aluminum top-layer. Initially the phase difference of GLV is zero, and the diffraction intensity of GLV is mainly focused on zero order. When the GLV is controlled by a voltage, the phase difference becomes π, and GLV will diffract the light to the first diffraction order, so a GLV can switch the light from zero diffraction order to first diffraction order by controlling the phase difference electrically. The structure of a GLV is very simple, but it is a linear array, which needs a scanning device for displaying a 2D image. This scanning device increases the complexity and the assembly difficulties of the projection system. We propose herein a novel Grating Light Modulator (GLM) [

Currently the driving mode of the GLM array is a passive matrix addressing. This mode is very simple, and promotes the optimization of the device structure and parameters. The driver of the GLM array is a critical technology that affects the performance of the projection system. In order to improve the working performance of the GLM, the electromechanical characteristics of passive matrix addressing need to be analyzed. This paper introduces the operating principle and the fabrication process of the GLM, and analyzes its driving voltage and response frequency. Then, the crosstalk of passive matrix addressing for the GLM is analyzed. Finally, experiments are designed to measure the driving voltage and the response frequency, and validate the crosstalk in the GLM array.

Both the movable grating and the bottom reflector are made of aluminum, and they are separated by an insulating layer and an air gap. The movable grating and the bottom reflector form a phase grating, and the phase difference is determined by the space between the movable grating and the bottom reflector.

In ^{st} order. When a voltage is actuated between them, the electrostatic force pulls the movable grating downwards. The phase difference equals to 2n'π, and the diffraction light is mainly focused on the zero order. The switch between the dark state and the bright state can be realized by collecting the zero order or the ±1^{st} order diffraction light.

Passive matrix addressing for the GLM is composed of a horizontal electrode group and a vertical electrode group. Every GLM’s bottom reflector in a row connects to a horizontal electrode which produces a row pulse signal, and every GLM’s movable grating in a column connects to a vertical electrode which is taken as a data line. When all horizontal electrodes are scanned by the progressive mode, a frame image can be displayed by a GLM array.

The GLM fabrication process [

After the formation of SiO_{2} layer, 580 nm polyimide (PI) is spin-coated as a sacrificial layer, and four support post cavities are etched by plasma on the sacrificial layer. Then 200 nm aluminum is sputtered, and four support cavities are filled with aluminum. Then, the photoresist (PR) is spin-coated as a protection layer and exposed, and another 530 nm aluminum is sputtered. Two aluminum layers are lithographed to form the upper movable grating, and the aluminum under PR is formed to cantilever beam. Finally, both PI and PR are etched by plasma at the same time.

The motion of the movable grating is determined by the electrostatic force and the mechanical restoring force. The movable grating and the bottom reflector can be considered as a variable plane-parallel capacitor. The thickness of the cantilever beam using a buried-beam process is quite thin. The thickness of the movable grating is much thicker than the cantilever beam, as shown in _{1} and l_{2} are the two part lengths of the cantilever beam, t is the thickness of the cantilever beam, w is the width of the cantilever beam, d_{0} is the initial space between the movable grating and the dielectric layer, and d_{1} is the thickness of the dielectric layer. When the GLM is actuated by a voltage, the movable grating will pull down rigidly. The movable grating can be considered as a rigid body, so the spring constant of the movable grating can be ignored. A cantilever beam is taken as a spring, and the four cantilever beams are equivalent to the four shunt springs. Therefore, the GLM can be described as the capacitor-spring model.

The response frequency which affects the grayscale of the passive matrix GLM is a key parameter. The faster the response frequency is, the larger the grayscale is. The driving voltage is also a key parameter for the passive matrix GLM, and the lower driving voltage can decrease the complexity and power in system control circuits. The fabricated GLM should have high response frequency and low driving voltage characteristics. Furthermore, the passive matrix addressing for the GLM results to the crosstalk which will reduce the contrast and the light utilization of the GLM.

The resonant frequency w_{0} equals to
_{1} is the relative dielectric constant of the dielectric layer, and ε which is the relative dielectric constant of the air equals to 1.

The initial phase difference of the designed GLM is (2n'+1)π. When a voltage is applied on the GLM, the electrostatic force pulls the movable grating down. If y is λ/4(λ is the wavelength of incident light), the phase difference becomes 2n'π, and this driving voltage is called the operating voltage of the GLM. If y is

The spring constant k’ of a cantilever beam which is determined by the structure parameter and the material characteristic of the cantilever beam is composed of two spring constants. k’ is the sum of k_{1} and k_{2}. Where k_{1} results from the stiffness of the cantilever beam, and k_{2} is caused by the residual stress. First, the spring constant k_{1} can be written as [_{2} can be obtained as [

Finally, because of four shunt cantilever beams, the spring constant of the GLM is the sum of the four cantilever beams’ spring constants, and it can be expressed as follows:

According to _{on} is 8.16 V; when y is 217.3 nm (
_{PI} is 8.74 V.

The GLM can be equivalent to a capacitor C_{g} which can be expressed as follows [_{0} is the thickness of the movable grating as shown in _{0}+d_{1}/ε_{1}−y).

A passive matrix addressing for the GLM causes the matrix capacitance’s coupling effect which is also called crosstalk. In a m×n GLM array, a voltage V_{0} is applied on the cross pixel of the i row and the j column, and this cross pixel is called all-selected pixel, as shown in

It’s supposed that the initial voltages of all pixels are zero. By using Kirchhoff’s current law(KCL)and Kirchhoff’s voltage law(KVL)[_{AB} is the voltage of the half-selected pixel in the all-selected pixel row, V_{CD} is the voltage of the half-selected pixel in the all-selected pixel column, and V_{BC} is the voltage of the non-selected pixel. According to

Every GLM is the same in the GLM array, so the capacitance value of every GLM is the same:

Taking

From

A single GLM is actuated by a voltage, which results in the crosstalk in the GLM array. When the GLM array is scanned by the progressive mode, there may be lots of pixels which are actuated by the different voltages at the same time. It can be analyzed by the same method as before. The voltages of the half-selected pixel and the non-selected pixel may be different, but the crosstalk is more obvious. So the GLM array addressed by passive matrix can be applied in projection display with a low resolution and a low definition.

^{st} order diffraction light is passed by the aperture. Then, the ±1^{st} order diffraction light passes the projection lens and displays an image of the GLM array. Only a single GLM pixel enters the photoelectric diode. The light intensity of the ±1^{st} order diffraction can be converted to a photocurrent by the photoelectric diode. This photocurrent is amplified and converted to a voltage signal by the current amplifier, and this voltage signal is displayed on the oscilloscope.

In ^{st} order intensity response of the GLM. ^{st} order initial phase difference of the fabricated GLM is (2n'+1)π. According to the operating principle of the GLM, when no voltage is applied, the intensity of the ±1^{st} order diffraction light is the bright state, and a high voltage signal is read out on the oscilloscope. When the ramp-wave voltage increases slowly, the movable grating moves down slowly, the intensity of the ±1^{st} order diffraction light will decrease, and the voltage signal of the ±1^{st} order diffraction light on the oscilloscope reduces. When the movable grating moves down a λ/4 distance, the phase difference become 2n'π, and the light intensity is in a minimum which is the dark state. As a result of the phase’s period, the ramp-wave voltage continues to increase, the light intensity increases, but as the movable grating pulls in, the light intensity jumps to a maximum. _{on} of the GLM is 7.8 V and the pull-in voltage V_{PI} of the GLM is 8.5 V, which are very close to the theoretical values. The difference between the theoretical value and the experimental value results from the slight difference between the designed structure and the fabricated structure.

^{st} order light intensity responses of the GLM actuated by the square-wave voltages of 7.8 V and different frequencies. For a half period, no voltage is actuated on the GLM, and the light intensity is in the maximum. For the other half period, a 7.8 V voltage is actuated on the GLM, and the light intensity is in the minimum.

In ^{st} order diffraction light intensity of the different pixels. As the fabrication processes of all pixels in array are the same, the pixels with the same peak-to-peak value of the diffraction light intensity have the same actuated voltage in the same scope of the phase difference. By comparing

The ±1^{st} order diffraction intensities of the different pixels when an all-selected pixel is actuated by 1 V to 6 V square-wave voltages are shown in

The operating theory of passive matrix addressing for GLM is introduced in this paper. The response frequency and the driving voltage of the GLM are analyzed, and the crosstalk which influences the performance of the GLM array is also studied in detail. It is concluded that: (1) both the response frequency and the driving voltage are related to the spring constant of the GLM. The theoretical operating voltage and the pull-in voltage are 8.16 V and 8.74 V respectively; (2) in a GLM array, the half-selected pixel voltage is half of the all-selected pixel in an array, and the voltage of the half-selected pixel is much larger than that of the non-selected pixel. With the increase of the GLM array, the crosstalk becomes more serious; (3) the experimental results indicate that the operating voltage and the pull-in voltage are 7.8 V and 8.5 V, respectively, very close to their theoretical values. When the GLM is actuated by a square-wave voltage of 7.8 V and 1 kHz frequency, the rise and the fall times of the intensity response are about 43.64 μs and 43.24 μs, respectively. The response frequency of the GLM is about 7 kHz. Another experiment confirms the crosstalk in the GLM array. A GLM array addressed by passive matrix can be applied in low resolution and low definition projection displays. These studies can provide a theoretical basis for improving the driving characteristic of the GLM. In future, in order to eliminate the crosstalk of passive matrix addressing for GLM, we are planning to use an active matrix method in driving the GLM array, which can be applied in projection display with high resolution and high definition.

The authors thank the anonymous reviewers for their suggestions, which greatly improve the paper. This work was supported by National Natural Science Foundation of China (No. 60708017) and Academician Foundation of Chongqing in China (CSTC, 2008BC3002).

The structure of a single GLM.

The operating principle of the GLM.

The diffraction intensity distribution of the GLM.

A SEM photograph of passive matrix addressing for the 16×16 GLM array.

The fabrication process of GLM.

The photograph of the fabricated GLM array.

The structure and the parameters of the GLM.

The simulation of the displacement and the driving voltage.

The matrix capacitance model of a m×n GLM array. (a) The initial model. (b) The simplified model.

The experimental system. (a) The sketch diagram of the experimental system. (b) The actual experimental system.

The testing results of the ±1^{st} order diffraction light. (a) The intensity response of the GLM actuated by a ramp-wave. (b) The intensity response of the GLM actuated by a square-wave of 7.8 V and 1 kHz frequency. (c) The intensity response of the GLM actuated by a square-wave of 7.8 V and 7 kHz frequency. (d) The intensity response of the GLM actuated by a square-wave of 7.8 V and 10 kHz frequency.

The ±1^{st} order diffraction light intensities of the different pixels when an all-selected pixel is actuated by different square-waves. (a) all-selected pixel when actuated by a 1V square-wave. (b) half-selected pixel when an all-selected pixel is actuated by a 1V square-wave. (c) non-selected pixel when an all-selected pixel is actuated by a 1V square-wave. (d) all-selected pixel when actuated by a 2 V square-wave. (e) half-selected pixel when an all-selected pixel is actuated by a 2V square-wave. (f) non-selected pixel when an all-selected pixel is actuated by a 2V square-wave.

The ±1^{st} order diffraction light intensity of different pixels when an all-selected pixel is actuated by 1V to 6V square-waves voltages.

The correlative parameters of the designed GLM [

_{1} (μm) |
_{1} |
_{0} (F/m) |
_{0} (μm) |
^{2}) |
_{1} (μm) |
_{2} (μm) |
||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

0.28 | 3.9 | 8.854 × 10^{−12} |
0.58 | 1.28 | 1533 | 0.2 | 4.0 | 10.5 | 3.5 | 77 | 0.3 | 100 |