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This paper presents methods used to improve reflective dielectric film color pictures. These changes include improvements in color purity, increased brightness, and elimination of any light absorption within the film layers. The color picture is fabricated by varying the silicon dioxide film thicknesses across a silicon wafer and coating the entire wafer with a thin layer of silicon nitride. In addition to the demonstration of fabricated color pictures, we also present more detailed calculation of basis colors and provide details of the fabrication process.
©2004 Optical Society of America
1. Introduction
Permanent color displays are typically produced using ink or paint dyes. The dye appears a particular color because it absorbs a portion of the incident light. Since dyes absorb light they are susceptible to decay over time. The combination of decay in absorption and diffusion of the dye results in changes in the image colors. Ultraviolet light, such as solar exposure, accelerates the color change [1–3]. This paper describes a color picture created from a thin dielectric film on a reflective surface. The dielectric film does not absorb light but rather changes the amount of light that is transmitted into the absorbing substrate. The elimination of the light absorbing dyes makes this image resistant to color decay even in the presence of ultraviolet irradiation. In addition to the fabrication of permanent images, the proposed approach could also be applied to reflective displays similar to electrochromic displays [4, 5]. Furthermore, since the image is created through interference rather than typical light absorption it is very difficult to copy. This type of color image would therefore lend itself to security markers similar to the way holograms are used.
The basic concept of creating a color image using a dielectric layer has already been presented [6, 7]. However, this dielectric image had various deficiencies. First of all, the image appeared dim because the basis colors lacked color purity. The image also used improper basis colors and was not a true reflective image because the black was produced using a darkened photoresist that absorbed light. This paper presents improvements in these deficiencies and also provides a more detailed analysis.
2. Producing color through reflection
2.1 Basic Principle
In order to create color displays we have found that it is convenient to treat colors in terms of RGB parameters used for computer monitors. We have previously provided the basic process used to calculate the RGB parameters for an arbitrary film thickness. A description of this conversion process can be found in [8]. This process can be broken up into two steps. First, the reflected power as a function of wavelength is calculated. Second, the response of the eye is taken into account to calculate the RGB parameters.
Fig. 1 illustrates that the total reflection depends on the combination of multiple reflections off of the interfaces. In order to take into account the interference of these reflections we use a matrix optics approach [9] that is commonly used in the analysis of thin film coatings.
Once the correct reflected wavelength spectrum has been calculated, it can be converted into RGB parameters. The first step in calculating the RGB color parameters is to integrate the wavelength spectrum of the reflected light Pr(λ) times the color matching functions Xλ(λ), Yλ(λ), and Zλ(λ) [10]. The resulting color parameters known as XYZ parameters take into account the response of the eye to the wavelength spectrum. The device independent XYZ parameters are then converted into RGB parameters that are used by a computer monitor using a transformation matrix. [11, 12].
2.2 Improvements with silicon nitride
The matrix optics approach was used to calculate the reflectance for a single silicon dioxide film on silicon [7]. However, the purity (deepness) of the colors was limited because the reflectance never approached zero for any wavelength. This limited color purity is qualitatively caused by a difference in the power reflected off the top and bottom surfaces resulting in an incomplete interference. At normal incidence the fraction of the incident light that is reflected off of the top of the film Rsurf and off of the bottom of the film Rsub are given respectively by , and , where the magnitude of the refractive index of the cover (air), film (silicon dioxide), and substrate (silicon) are respectively nc=1.0, nf=1.46, and nsub=4.3. The resulting reflectances are Rsurf=0.19 and Rsub=0.49.
Because of the difference in reflectance, the constructive and destructive interference is incomplete resulting in ‘washed out’ colors being reflected off the film. In order to get more pure colors, the reflectivity of the top surface is increased by using a thin layer of silicon nitride. The refractive index of silicon nitride is n=2.04, resulting in a much greater reflection off the film’s surface (Rsurf=0.34,) and strengthening the interference effects considerably
The actual calculation of the film reflectance is accomplished using the matrix optics method. Figure 2 shows the calculated reflectance as a function of wavelength for a 360nm thick silicon dioxide film covered with different thicknesses of silicon nitride. The height and depth of the reflectance peaks and nulls are improved by increasing the thickness of the silicon nitride to greater than 40nm.
Fig. 2. Reflectance plot R(λ) for an oxide depth of 360 nm with 5 thicknesses of nitride coating ranging from no nitride up to 80nm of nitride..
Figure 3 shows the film colors as a function of oxide thickness with and without a 60nm thick layer of silicon nitride. These colors are shown as RGB representations calculated as outlined above. The improved resonance depth results in substantially purer colors.
Fig. 3. Colors produced by a thin layer of silicon dioxide as a function of thickness both (a) without and (b) with a 60nm thick layer of silicon nitride.
2.3 Silicon nitride anti-reflection coating
A major advantage to using reflective films rather than absorptive filters (dyes) to generate color is that the dielectric film does not absorb any of the incident light, and thus will not fade from prolonged exposure as an absorptive dye eventually will. The first-generation color picture, however, was not a completely reflective system, because it is impossible to generate black with only an oxide film on silicon [7]. Instead, carbonized photoresist was used to produce black. The color produced by the photoresist gave an acceptable black, but did so by light absorption, not reflection, making the first generation color picture an incompletely reflective system. A major improvement is made using a thin layer of silicon nitride to produce an anti-reflection (AR) coating over the bare silicon. The reduction in reflection results in an effective black.
At normal incidence, the first requirement for a single layer antireflection coating is that the refractive index be the geometrical mean between the two layers resulting in an ideal refractive index of , which is very close to the refractive index of a silicon nitride film (nSiN=2.04). The other requirement is that the layer thickness be d=λ/(4n)=62.5nm for an incident wavelength of 500nm.
We calculated the actual reflectance using the matrix optics approach in order to take into account factors such as: the change in refractive index with wavelength, the complex refractive index of the silicon substrate, the non-normal incident angle, etc. Figure 4(a) shows the calculated percent reflection for a fluorescent light source as a function of silicon nitride thickness and Fig. 4(b) shows the corresponding color calculated using the method described above. We used a nitride thickness of 60nm to represent black.
Fig. 4. (a) The fraction of the power reflected, and (b) the color as a function of film thickness for a silicon nitride film on silicon at a viewing angle of 18°.
3. Pixel layout
A colored image requires a method to produce a set of basis colors and a means of mixing these colors to produce an arbitrary color. The basis colors are produced by creating four different thicknesses of oxide and then coating the entire image with nitride. The thicknesses are chosen to produce red, green, blue, and yellow basis colors. Yellow is added as a basis color because the current process produces a purer yellow than green or red. The mixed colors are then varied pixel by pixel to produce a colored image. The basis colors are mixed by varying their respective areas [7]. Since the light power cannot be varied, the brightness is achieved by adding a black area to the pixel.
To produce a picture using this approach, the initial jpeg image is adjusted to have a resolution of 260×260 pixels. On the fabricated image, each pixel will be 240x240 microns, making it possible to fit the picture onto a 100mm silicon wafer. The width of the black portion of the pixel is chosen to produce the proper pixel brightness as given by
,
where R, G, and B are the jpeg color components of the particular pixel. The remaining area of the pixel is then divided between the basis colors to produce the pixel hue. Since we can produce a purer yellow than red or green, the yellow basis color is substituted for common R and G components.
Table 1 shows the calculated widths of the various colors for the example colors shown in Fig. 5. The first column shows the original RGB values from the jpeg image. The maximum RGB value is used to calculate the black area of each pixel as shown in column 2. The RGB values are then scaled to 255 to show only the color hue. Column 4 shows how the common red (R) and green (G) components are replaced with yellow (Y). We tried various replacement algorithms and found that this straight substitution provides the best result.
Table 1. Example of area calculations to produce the colors shown in Fig. 5(a).
The 240µm wide pixel is then divided up into the various colors as shown in columns 5–8. The width increment in the pixel areas is limited to 10µm for fabrication reasons [7]. Figure 5 shows the four representative colors specified in Table 1 with their respective areas.
4. Selecting basis colors
Colors are produced by growing a silicon dioxide layer on silicon and depositing a 60nm thick film of silicon nitride. The basis colors are produced by choosing four different oxide thicknesses. In order to choose the best thicknesses we calculated the RBG parameters as a function of oxide thickness.
Fig. 6. (a) The RGB parameters as a function of oxide thickness without a silicon nitride layer and (b) with a 60nm thick layer of silicon nitride, where the actual basis colors are shown.
Figure 6(b) shows the RGB parameters as a function of silicon dioxide thickness, where vertical lines indicate the actual thicknesses used. These color calculations were performed assume that the light is incident at an angle of θ=15°. Variation in the incident angle causes a shift in the perceived color especially for thicker films like the red.
This figure shows that the blue is a fairly pure color because the red and green components are low. On the other hand, the red and green basis colors are not as pure because they have significant undesired color components. However, Fig. 6(b) shows that the yellow which is a combination of red and green is a fairly pure color. For this reason yellow is used as an optimum basis color in place of red and green where possible. For comparison, Fig. 6(a) shows the RGB parameters for the silicon dioxide film without the silicon nitride over layer. This comparison illustrates the dramatic improvement attained by using the silicon nitride over coating. The sRGB parameters that were used as our basis colors are red (218,156,167), green (125,218,124), yellow (222,226,72), and blue (66,76,255).
5. Fabrication
Figure 7 illustrates an individual pixel throughout the basic fabrication steps followed to produce a dielectric color picture. The silicon dioxide is thermally grown on a silicon wafer to a thickness of 760nm (see Fig. 7(a)), which will correspond to the red layer. However, as illustrated in Fig. 7(a), the color does not appear red until after the silicon nitride layer is deposited on the entire image. The red portion is then masked with photoresist and the oxide is etched using a buffered oxide etch (BOE) to a thickness of 460nm (see Fig. 7(b)). The red and green areas are then covered and the oxide is etched down to 310 nm corresponding to the yellow color (see Fig. 7(c)). The red, green and yellow areas are then covered and the oxide is etched down to the blue thickness (see Fig. 7(d)). The entire colored portion of each pixel is then covered and the oxide over the black portion is completely removed. A 60nm thick layer of silicon nitride is then deposited over the entire wafer (see Fig. 7(f) and Fig. 7(g)). Over the colored portion, the nitride results in an enhancement in color purity and over the bare silicon it acts as an AR coating resulting in a black color.
6. Results
Figure 8 shows pictures of both the original and the improved dielectric images, which were taken with a digital camera. The improvements on the new system are evidenced in the brighter, more vibrant colors under the same lighting conditions. The colors in the new dielectric color image was attained by (1) using a thin silicon nitride coating, (2) refining the choice of basis colors, and (3) using yellow to replace portions of the red and green color components. We can also see that the silicon nitride coating used in the new image, in addition to making the image completely non-absorptive, produces a much darker ‘black’ than carbonized photoresist. Even though the colors are brighter, it is still not possible to produce a pure white. The best white is an equal mix of the basis colors resulting in only approximately one third of the light being reflected.
Fig. 8. Dielectric color pictures fabricated with (a) just silicon dioxide on silicon and (b) silicon dioxide and silicon nitride on silicon.
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