**2.1 The Fabry-Perot interferometer**

**2.1.1 Mono layer model**  The model in Figure 10 shows the basic composition of a Fabry-Perot interferometer. In the figure there are two intermediates which form two interfaces. When a light goes through the Intermediate 1 and reaches the Interface 1, a reflective light and a transmissive light will be generated at Interface 1. The transmissive part will again be divided into a reflective light and a transmissive light at Interface 2 when it goes through the Intermediate 2 and reaches the Interface 2. Likewise, a reflective light and a transmissive light will be generated at any

raised from the plate surface, the transferred ink amount depends only on the substrate's surface condition and ink's characteristic. However, flexography is suitable for thin layer (<2m) deposition for good uniformity. There's also no ink rheology requirement generated from gravure printing's ink merge process. For pattern isolation, both hot embossing and laser ablation introduce fast and simple solutions but also bring some uniformity concerns. For layer deposition, even though gravure is used for thick layer and flexography is used for thin layer, how precise the thicknesses are seriously influence the optical design in a display device. But apparently, to perform integration process on a flexible substrate, the printing techniques described in this section are compulsory. Other printing techniques such as screen, inkjet, and offset are not suitable for this study but are widely discussed for flexible

Section 1.1 already detail described why flexible display is necessary in the future and how those promising technologies are being realized and commercialized nowadays. The technologies introduced in section 1.1 have different target applications and markets and thus are with different concepts. It is obvious that no single technology can satisfy all requirements with all advantages such as low power consumption, high brightness, and fast response time. As a result, this chapter wants to cover and target at the large scale flexible display area for signage, advertisement, and decoration purpose. This means that this chapter is not necessarily pursuing a fine resolution, vivid true color, and fast response which are fundamental factors for TVs and monitors. Nevertheless, this study still looks for and tries to realize these good characteristics as reasonable as possible under some natural limitation such as availabilities of materials and configuration of apparatus. One of the most interesting examples of its applications for this study is to replace the mosaic windows which are usually decorated in churches as a motive. When the above targets are realized, the large scale flexible display sheet will be very distinguishable from previously mentioned flexible display systems and also those MEMS devices listed in section 1.2. Finally, this device will not only support uneven surfaces but will also be programmable to change the

**2. System design, material evaluation, mechanism, and simulation** 

Some flexible display ideas and control mechanism have been introduced. Within them, the Fabry-Perot was evaluated as the most promising system to be controlled by MEMS. This chapter then chose the MEMS as the flexible display's control system with Fabry-Perot color

The model in Figure 10 shows the basic composition of a Fabry-Perot interferometer. In the figure there are two intermediates which form two interfaces. When a light goes through the Intermediate 1 and reaches the Interface 1, a reflective light and a transmissive light will be generated at Interface 1. The transmissive part will again be divided into a reflective light and a transmissive light at Interface 2 when it goes through the Intermediate 2 and reaches the Interface 2. Likewise, a reflective light and a transmissive light will be generated at any

electronic devices' applications.

mosaic patterns without artificial backlight.

**2.1 The Fabry-Perot interferometer** 

interference concept.

**2.1.1 Mono layer model** 

**1.4 Target application** 

interface even though both the reflective light and the transmissive light decay in the intermediates.

Fig. 10. A basic Fabry-Perot interferometer.

Color interference takes place when there is optical path length difference (Γ) between two or more light components traveling together. In this figure, the reflective Light 1 and the reflective Light 2 have optical path length difference Γ:

$$
\Gamma = n\_2(\overline{\rm AB} + \overline{\rm BC}) - n\_1 \overline{\rm AD} \tag{3}
$$

Here, *n1* and *n2* is the index of refraction of Intermediate 1 and Intermediate 2, respectively. Since the angle of incidence equals to the angle of reflectance, which is *θ2* in Figure 10, thus,

$$\overline{\mathbf{AB}} = \overline{\mathbf{BC}} = \frac{d}{\cos \theta\_2} \tag{4}$$

$$\begin{aligned} \overline{\mathbf{AD}} &= \overline{\mathbf{AC}} \sin \theta\_1 \\ &= 2 \overline{\mathbf{EB}} \sin \theta\_1 \\ &= 2 (\overline{\mathbf{AE}} \tan \theta\_2) \sin \theta\_1 \\ &= 2d \tan \theta\_2 \sin \theta\_1 \end{aligned} \tag{5}$$

According to Snell's law:

$$n\_1 \sin \theta\_1 = n\_2 \sin \theta\_2 \tag{6}$$

The distance AD becomes

$$\overline{AD} = 2d \tan \theta\_2 (\frac{n\_2}{n\_1} \times \sin \theta\_2) \tag{7}$$

Replace AB , BC , and AD by Equation 4 and Equation 5 into Equation 3,

Possibilities for Flexible MEMS:Take Display Systems as Examples 381

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

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

*x*

*x*

(14)

*<sup>f</sup> <sup>x</sup> n vp*

is the wavenumber, *x* is the propagation distance, *λ* is the wavelength, *n* is the

2

2

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

Fig. 11. The system design for two colors.

transmittance increased the design difficulty for backlight.

under different wavelength. From the light wave phase (Φ) point of view,

**2.2 Color design and simulation 2.2.1 Color purity consideration** 

where

$$\Gamma = 2n\_2 d \frac{1 - \frac{1}{n\_1} \times \sin^2 \theta\_2}{\cos \theta\_2} \tag{8}$$

With trigonometric function:

$$
\cos\theta\_2 \tan\theta\_2 = \sin\theta\_2\tag{9}
$$

$$
\cos^2 \theta\_2 + \sin^2 \theta\_2 = 1 \tag{10}
$$

and take atmospheric air as Intermediate 1 with *n1*=1, the optical path length difference becomes

$$
\Gamma = 2n\_2 d \cos \theta\_2 \tag{11}
$$

A constructive interference takes place when the two reflective lights are in-phase and a destructive interference takes place when the two reflective lights are out-of-phase. A maximum constructive interference happens when the two lights are with 0° phase difference or zero (or 2π) phase change:

$$2n\_2 d \cos \theta\_2 = m\lambda \tag{12}$$

Similarly, a minimum destructive interference happens when the two light are with 180° phase difference or π phase change:

$$2n\_2d\cos\theta\_2 = (m - \frac{1}{2})\lambda\tag{13}$$

Here *m* is an integer and λ is the wavelength for both cases. The interference from the transmissive side can be also evaluated from the Interface 2.

#### **2.1.2 Multiple layer model**

Since the system is designed for information display, a maximum constructive interference is expected. According to Equation 12, one can easily design specific output light (wavelength) with specific intermediate (*n2, d*) under fixed angle of incidence *θ2*. It is also possible to calculate a multilayer system according to Equation 8 when the intermediate material is not air. Based on Figure 10, a multilayer structure shown in Figure 11 was chosen for color filtering. A premise is also made here: The color (color 1) filtered by the structure in Figure 11(a) is different from the color (color 2) filtered by the structure in Figure 11(b). The change of the multilayer structure hence lies on the mechanical control by MEMS. Here a special note should be put that a color of either color 1 or color 2 is not necessary to be both destructive interferences, rather, a color will be good enough to distinguish from another even though it is not formed by interference. The multilayer system in Figure 11 is switching between six layers and five layers (excluding ambient air layers: Intermediate 1). Thus, when talking about a multilayer system with more than three intermediates (four interfaces), the optical path length difference becomes relatively complicated which will be discussed and simulated by commercial software later.

Fig. 11. The system design for two colors.
