**2.2.1 Color purity consideration**

With the layer definition in Figure 11 and the Fabry-Perot interferometer concept, color designs in this section will help to decide how thick those layers should be and what kind of optical characteristics should they have for the three primary colors: red, green, and blue for full color applications. Previous report showed distinguishable yet poor colors especially for red. The root cause is the extra peak in blue region for red color, as a result a pink or purple color was shown. The author also implied a solution with new layer design which reduced the isolation layer's (Intermediate 5 in Figure 11) thickness from 370nm to 185nm. However, 185nm thickness was neither achieved nor disclosed. Besides the color purity issue, its transmittance for red, green, and blue was low and also not balanced. The unbalanced transmittance increased the design difficulty for backlight.

Within normally used metals, aluminum (Al) and copper (Cu) are widely used for their low cost and good conductivity while silver (Ag) and gold (Au) are also good but expensive. From the index of refraction (*n*) point of view, all Au, Al, and Cu show large difference under different wavelength. From the light wave phase (Φ) point of view,

$$\begin{aligned} \Phi &= a \times x \\ &= \frac{2\pi}{\lambda} \times x \\ &= \frac{2\pi f}{n \times v\_p} \times x \end{aligned} \tag{14}$$

where is the wavenumber, *x* is the propagation distance, *λ* is the wavelength, *n* is the index of refraction, *f* is the frequence and *vp* is the phase velocity. Thus the same input light with the same phase will generate two different phase output light owing to different index of refraction. According to this, a relatively uniform *n* value distribution for visible region (400-700nm) of a material is highly expected to solve the unbalanced intensity issue. Ag showed small *n* value difference across the visible region which suggests a structure change

Possibilities for Flexible MEMS:Take Display Systems as Examples 383

Without putting the output wavelength on a color chart it is very difficult to judge whether the output colors are vivid and pure or not; without quantifying the improvement it is very difficult to tell how good the new design is. Normally, the color purity is measured and illustrated on the CIE chromaticity diagram published in 1931 with (*x, y*) coordinate system or in 1976 with (*u', v'*) coordinate system. The translation between these two systems follows

4 '

9 '

*<sup>y</sup> <sup>v</sup>*

2 12 3

(15)

*x y*

Here, only the CIE 1931 chromaticity system is used. Figure 13 is the color purity comparison of previous work, this design, and a CRT display. One can easily find that this work greatly pushed the green color to a better purity place while keeping the red and blue colors' purity similar. In order to quantify how much the improvement is, a color purity deviation (*CPD*) is firstly defined as the shortest distance between two points on the

Here the subscript *T* means the target coordinate and the subscript *SE* means the simulated or experiment data coordinate. The best and the smallest *CPD* value are both 0 (zero). Based on the optical parameters analysis, the new design which inaugurated Ag as electrode material improved all the transmittance, balance between all colors, and the color purities. The incoming challenge thus lies on how to switch this Fabry-Perot interferometer system

*x*

2 12 3

2 2 *CPD x x y y* ( )( ) *T T SE SE* (16)

*x y*

*u*

**2.2.3 Color purity deviation** 

the following formulas:

diagram with the following equation:

between the two states illustrated in Figure 11.

Fig. 13. Color purity distribution and the improvement comparison.

solution: To replace Al by Ag for Intermediate 3 as electrodes in Figure 11. However, since the *n* value change and according to Equation 12, a suitable intermediate thickness (*d*) should also be evaluated.

#### **2.2.2 Transmittance consideration**

On the other hand, when trace the low transmittance with Al's optical parameters, a hint from its absorption coefficient (*k*) also emerges. Since *k* value means the decay behavior as well as how the light is absorbed in the intermediate, the higher *k* value is the lower the transmittance is. Al's *k* value ranges from 3.9 to 7 in visible region which is relatively higher when compared to Au, Ag, and Cu. We also understand that even Ag has higher *k* value in red and green region compared to Au and Cu, it is very suitable to replace Al to increase the transmittance for all red, green, and blue colors. Figure 12(a)-(c) and Figure 12(d)-(f) are the simulation results done by commercial software Optas-Film with structures of Figure 11(a) and Figure 11(b), respectively. The only variable in Figure 12(a)-(c) was the thickness of Intermediate 4 and the only variable in Figure 12(d)-(f) was the thickness of Intermediate 5 in Figure 11. The best condition for Intermediate 4's thickness was 600nm which shows a very distinguishable white color. With this setting, the best conditions of Intermediate 5's thickness are 160, 325, and 240nm for red, green, and blue, respectively. The transmittance in Figure 2-4 followed the optical design and thus proved higher transmittance with balanced output for all primary colors.

Fig. 12. Simulated transmittance with structures in Figure 11.

#### **2.2.3 Color purity deviation**

382 Microelectromechanical Systems and Devices

solution: To replace Al by Ag for Intermediate 3 as electrodes in Figure 11. However, since the *n* value change and according to Equation 12, a suitable intermediate thickness (*d*)

On the other hand, when trace the low transmittance with Al's optical parameters, a hint from its absorption coefficient (*k*) also emerges. Since *k* value means the decay behavior as well as how the light is absorbed in the intermediate, the higher *k* value is the lower the transmittance is. Al's *k* value ranges from 3.9 to 7 in visible region which is relatively higher when compared to Au, Ag, and Cu. We also understand that even Ag has higher *k* value in red and green region compared to Au and Cu, it is very suitable to replace Al to increase the transmittance for all red, green, and blue colors. Figure 12(a)-(c) and Figure 12(d)-(f) are the simulation results done by commercial software Optas-Film with structures of Figure 11(a) and Figure 11(b), respectively. The only variable in Figure 12(a)-(c) was the thickness of Intermediate 4 and the only variable in Figure 12(d)-(f) was the thickness of Intermediate 5 in Figure 11. The best condition for Intermediate 4's thickness was 600nm which shows a very distinguishable white color. With this setting, the best conditions of Intermediate 5's thickness are 160, 325, and 240nm for red, green, and blue, respectively. The transmittance in Figure 2-4 followed the optical design and thus proved higher transmittance with balanced

should also be evaluated.

output for all primary colors.

Fig. 12. Simulated transmittance with structures in Figure 11.

**2.2.2 Transmittance consideration** 

Without putting the output wavelength on a color chart it is very difficult to judge whether the output colors are vivid and pure or not; without quantifying the improvement it is very difficult to tell how good the new design is. Normally, the color purity is measured and illustrated on the CIE chromaticity diagram published in 1931 with (*x, y*) coordinate system or in 1976 with (*u', v'*) coordinate system. The translation between these two systems follows the following formulas:

$$\begin{aligned} u' &= \frac{4x}{-2x + 12y + 3} \\ v' &= \frac{9y}{-2x + 12y + 3} \end{aligned} \tag{15}$$

Here, only the CIE 1931 chromaticity system is used. Figure 13 is the color purity comparison of previous work, this design, and a CRT display. One can easily find that this work greatly pushed the green color to a better purity place while keeping the red and blue colors' purity similar. In order to quantify how much the improvement is, a color purity deviation (*CPD*) is firstly defined as the shortest distance between two points on the diagram with the following equation:

$$\text{CPD} = \sqrt{(\mathbf{x}\_T - \mathbf{x}\_{SE})^2 + (y\_T - y\_{SE})^2} \tag{16}$$

Here the subscript *T* means the target coordinate and the subscript *SE* means the simulated or experiment data coordinate. The best and the smallest *CPD* value are both 0 (zero). Based on the optical parameters analysis, the new design which inaugurated Ag as electrode material improved all the transmittance, balance between all colors, and the color purities. The incoming challenge thus lies on how to switch this Fabry-Perot interferometer system between the two states illustrated in Figure 11.

Fig. 13. Color purity distribution and the improvement comparison.

Possibilities for Flexible MEMS:Take Display Systems as Examples 385

Even though the main part of Figure 15 can be expressed by a parallel plate, the whole structure still contains fixed ends close to spacer structures. A complex model combines these two parts is then necessary. The complex model of a single pixel (one parallel plate set) was divided into two parts horizontally and was further divided into two parts of a singleend fixed cantilever and a parallel plate as shown in Figure 16. The left part of Figure 16 is a cantilever which is fixed at one end and bending at another. The right part of Figure 16 is a parallel plate system which moves up (OFF state) and down (ON state) when applied with electrostatic force. Since the cantilever part is connected to the parallel plate part, when the plate moves down the cantilever is pulled down. When ON, the parallel plate system suffers an electrostatic force and tends to stay in contact while the cantilever suffers a reaction force and tends to return to the original (upper) position. In this model, the displacement *x'* in

> 1 1 2 2 2 2 0 0 <sup>2</sup> <sup>2</sup> [( ) ] *W c W c F VV p r <sup>r</sup>*

*EWh F kg g <sup>c</sup> <sup>L</sup>*

<sup>3</sup> <sup>1</sup> <sup>2</sup> <sup>0</sup> <sup>2</sup> 2 3 [( ) ] 4( ) <sup>2</sup> *W c EWh V g <sup>r</sup> <sup>L</sup> gt g <sup>c</sup>*

By rearranging Equation 20, a relationship between the contact length (*c*) and the applied voltage (*V*) can be set up. With this relationship, one can estimate the contact area and its

'

An overall stable system will be formed when these two force are in equal:

*gt g t*

3

<sup>3</sup> 4( ) <sup>2</sup>

*c*

 

(19)

(18)

(20)

**2.3.1 Mathematical model** 

Figure 14 moved the entire gap *g*.

Fig. 16. The MEMS model from a half pixel of Figure 15(b).

 

 

The electrostatic force on the parallel plate system is:

The reaction force on the cantilever part is:

**2.3.2 Simulation prediction** 

#### **2.3 The MEMS model and simulation**

A MEMS controlled system to switch a multilayer structure (Figure 11) of Fabry-Perot interferometer for different colors has been decided in previous section. Since the color design in section 2.2 already showed a very promising two-state color system, this section will handle how to design and prepare the structure in Figure 11 as a MEMS. Within all MEMS driving methods, the electrostatic way is believed to be suitable for structure in Figure 11 owing to the straightforward vertical movement. The structure in Figure 11 is also designed for electrostatic driving since the two Intermediate 3 materials can serve as the two parallel electrodes and the Intermediate 5 material can serve as the isolation layer when the two parallel parts are in contact.

Fig.14. A parallel plate actuator system.

Suppose there are two particles in a space separated by distance *g*, a Coulomb (electrostatic) force *F* exists between these two charges:

$$F = k\_{\mathcal{C}} \frac{q\_1 q\_2}{g^2} \tag{17}$$

Here *kc* is the Coulomb force constant whose value is 8.99×109Nm2C-2, and *q1*, *q2* are the particle charges. A parallel plate system shown in Figure 14 consists two conductive layers and those layers are capable to stock charges. Charges can be supplied by outside source and the parallel plates start to attract with each other when the Coulomb force is strong enough. Thus, when two large plates are separated by spacer structure at the edges, its center part can be treated as a parallel plate system. A schematic plot is illustrated in Figure 15.

Fig. 15. The MEMS structure in (a) OFF state and (b) ON state.

#### **2.3.1 Mathematical model**

384 Microelectromechanical Systems and Devices

A MEMS controlled system to switch a multilayer structure (Figure 11) of Fabry-Perot interferometer for different colors has been decided in previous section. Since the color design in section 2.2 already showed a very promising two-state color system, this section will handle how to design and prepare the structure in Figure 11 as a MEMS. Within all MEMS driving methods, the electrostatic way is believed to be suitable for structure in Figure 11 owing to the straightforward vertical movement. The structure in Figure 11 is also designed for electrostatic driving since the two Intermediate 3 materials can serve as the two parallel electrodes and the Intermediate 5 material can serve as the isolation layer when the

Suppose there are two particles in a space separated by distance *g*, a Coulomb (electrostatic)

*q q F kc g*

Here *kc* is the Coulomb force constant whose value is 8.99×109Nm2C-2, and *q1*, *q2* are the particle charges. A parallel plate system shown in Figure 14 consists two conductive layers and those layers are capable to stock charges. Charges can be supplied by outside source and the parallel plates start to attract with each other when the Coulomb force is strong enough. Thus, when two large plates are separated by spacer structure at the edges, its center part can be treated as

a parallel plate system. A schematic plot is illustrated in Figure 15.

Fig. 15. The MEMS structure in (a) OFF state and (b) ON state.

1 2 2

(17)

**2.3 The MEMS model and simulation** 

two parallel parts are in contact.

Fig.14. A parallel plate actuator system.

force *F* exists between these two charges:

Even though the main part of Figure 15 can be expressed by a parallel plate, the whole structure still contains fixed ends close to spacer structures. A complex model combines these two parts is then necessary. The complex model of a single pixel (one parallel plate set) was divided into two parts horizontally and was further divided into two parts of a singleend fixed cantilever and a parallel plate as shown in Figure 16. The left part of Figure 16 is a cantilever which is fixed at one end and bending at another. The right part of Figure 16 is a parallel plate system which moves up (OFF state) and down (ON state) when applied with electrostatic force. Since the cantilever part is connected to the parallel plate part, when the plate moves down the cantilever is pulled down. When ON, the parallel plate system suffers an electrostatic force and tends to stay in contact while the cantilever suffers a reaction force and tends to return to the original (upper) position. In this model, the displacement *x'* in Figure 14 moved the entire gap *g*.

Fig. 16. The MEMS model from a half pixel of Figure 15(b).

The electrostatic force on the parallel plate system is:

$${}^{F}F\_{p} = \frac{1}{2} \varepsilon\_{0} \varepsilon\_{r} \frac{W \times c}{\left[ (g+t) - g \right]^{2}} V^{2} = \frac{1}{2} \varepsilon\_{0} \varepsilon\_{r} \frac{W \times c}{t^{2}} V^{2} \tag{18}$$

The reaction force on the cantilever part is:

$$F\_{\mathcal{C}} = k \times g = \frac{E \mathcal{W} \mathcal{W}^{\mathcal{G}}}{4(\frac{L}{2} - c)^{\mathcal{G}}} \times g \tag{19}$$

An overall stable system will be formed when these two force are in equal:

$$\frac{1}{2}\varepsilon\_{0}\varepsilon\_{r}\frac{W\times c}{\left[\left(g+t\right)-g\right]^{2}}V^{2}=\frac{E\mathcal{W}\hbar^{3}}{4\left(\frac{L}{2}-c\right)^{3}}\times g\tag{20}$$

#### **2.3.2 Simulation prediction**

By rearranging Equation 20, a relationship between the contact length (*c*) and the applied voltage (*V*) can be set up. With this relationship, one can estimate the contact area and its

Possibilities for Flexible MEMS:Take Display Systems as Examples 387

Until now, the device structure is designed and discussed vertically in detail thus its horizontal dimension and structure should also be considered. Previous report indicates high operation voltage with an enclosed Intermediate 4 in Figure 11 which is shown here in Figure 18(a) from its top. The author suggested some solutions to lower down the operation voltage such as to use thinner upper layer, to use thinner Intermediate 4, and to design a larger system. However, if the Intermediate 4 is trapped inside the system when ON, it will become a movement barrier or cause reliability issue unexpectedly. Since atmospheric air is designed for Intermediate 4, it is very possible to reduce the air pressure trapped inside the enclosed spacer area to alleviate the operation voltage. Figure 18(b) is the top view of a newly designed structure. Compared to Figure 18(a), the new design has some openings (air channel) on specific locations. These air channels serve as air evacuation paths when the device is ON. Figure 19 to Figure 21 are the simulations done with commercial software MEMSOne to explain how flexible can the air channel be designed and how the corresponding structure moves. Note that since there are design limitations on the structure by this software, the color legend means the areas in moving instead of its absolute displacement value. The value of opening ratio means the air evacuation efficiency while different designs imply different display shape because the air channel area can also be turned on if the opening ratio is large. Compared to the baseline design, we understand that increasing the opening ratio helps on enlarging the MEMS movement area. In the design of Figure 19, which represents the basic design in Figure 18 where the air channel was put in the center part of one spacer side, the displacement area increases when the opening ratio increases. The extreme model (Figure 19(c)) indicates that the displacement switched to the

Similar effects also appeared on the Figure 20 designs, in which the air channel was divided into two sub-channels and were put at the both ends of one spacer side. One can find that up to 40% opening ratio, the displacement area follows the Figure 19 designs but the opening ratio of 60% (not shown here) and 80% (Figure 20(c)) ones helped the displacement continued to expand inside the pixel area. With this design improvement, we can positively change the unexpected displacement area caused by air channel to a reasonable and expectable area within the pixel. Based on Figure 20, the sub-channels were moved to the two ends of one spacer side and the spacer corners were also removed. The opening ratio of

**2.4 The horizontal structure design 2.4.1 Air pressure consideration** 

air channel area rather than the pixel area.

Fig. 18. Renewed spacer layer design's top views.

percentage under certain applied voltage. Similarly, one can also expect the operation voltage for specific contact area. The following simulations were performed under the following parameter settings: *0* = 8.85×10-12 A2s4kg-1m-3, *<sup>r</sup>*= 3, *h* = 16m, *L* = 2000m, *t* = 0.3m, *E* = 6.1GPa, and *g* = 0.6m. Figure 17 is the simulation result with different pixel size (*L*). From these figures we understand that under the same applied voltage, a larger pixel will result in a larger contact area. From these figures we also understand that when one wants to achieve, for example, 90% contact area, a great operation voltage difference (55V for 1000m pixel and 15V for 2000m pixel) appears in Figure 17(a)-(b). Figure 17(c) is the simulation results with different spacer thickness (*g*). We understand that the operation voltage can be further reduced from 15V to 10V when change the spacer thickness from 600nm to 300nm. An examination in Figure 17(d) also indicated that when change the upper layer's thickness (*h*) from 16m to 8m, the operation voltage can be further reduced from 10V to 5V. Thus, a combination of these improvement designs, one can expect and design a low operation voltage device with this MEMS model. Other parameters concerning material characteristics such as *<sup>r</sup>* and *E*, can also help on the operation voltage lowering but will not be considered here.

Fig. 17. Simulation results with different parameters from the MEMS model.
