TW201342102A - System and methods of reducing diffuse reflection of an optical stack - Google Patents

Abstract

The present disclosure relates to a method for improving optical qualities of transparent conductive films including a multilayer optical stack and conductive nanowires embedded therein.

Description

System and method for reducing diffuse reflection of optical stack [Cross-Reference to Related Applications]

This application is based on US Provisional Application No. 61/621,359, filed on Apr. 6, 2012, and U.S. Provisional Application No. 61/678,886, filed on August 2, 2012, filed on Apr. 6, 2012. The rights of U.S. Patent Application Serial No. 13/667,556, filed on Nov. 2, and U.S. Pat.

The transparent conductive film comprises a conductive material coated on a high transmittance surface or a substrate, and is widely used for a flat panel display (such as a liquid crystal display (LCD), a touch panel or an inductor), an electroluminescent device (for example, a light emitting device) In the polar body), the thin film photovoltaic cell is used as an antistatic layer and an electromagnetic wave shielding layer.

Currently, vacuum deposited metal oxides (such as indium tin oxide (ITO)) are used as industry standard materials for providing optical transparency and electrical conductivity to dielectric surfaces such as glass and polymeric films. However, metal oxide films are relatively brittle and susceptible to damage during bending or other physical stress. They also require high deposition temperatures and/or high annealing temperatures to achieve high conductivity levels. For some substrates that are easily absorbing moisture (for example, plastics and organic substrates (for example, polycarbonates), it is a problem to properly adhere the metal oxide film. Therefore, the application of the metal oxide film on the flexible substrate is severely restricted. In addition, vacuum deposition is an expensive method and requires special equipment.

In recent years, the replacement of current industry standard transparent conductive ITO films in flat panel displays by composites of metal nanowires (e.g., silver nanowires) has become a trend. Generally, a transparent conductive film is formed by first applying an ink composition including a silver nanowire and a binder on a substrate. The transparent UV or heat curable polymeric material can then be coated to form a protective layer. Nanowire-based coating technology is especially suitable for printed electronics. Using solution-based forms, printed electronics enables the fabrication of robust electronic devices on large-area flexible substrates.

The presence of nanowires in transparent conductive films can present some optical challenges that are not often encountered in continuous ITO films. For example, when the ITO touch sensor is turned off, the ITO touch sensor appears black in the surrounding light; and the touch sensor made from the silver nanowire-based transparent film can have a "whiter" or "blurred" The color. This opalescent appearance can affect image quality (when the LCD module is turned on), appearing with lower contrast or other image problems. Therefore, there is a need to address the unique optical challenges inherent in nanowire-based transparent conductors.

The present invention provides various embodiments of a method for addressing the opalescent appearance of a nanowire display by reducing or minimizing diffuse reflection in an optical stack comprising at least one nanowire-based conductive film.

An embodiment is a method comprising selecting an optical stacking parameter for an optical stack having a nanowire and calculating a plurality of diffuse reflection values based on the optical stacking parameters, each of which is a respective value of a plurality of optical stack configurations. The method additionally includes forming an optical stack layer based on at least one of the optical stack configurations selected based on comparing the diffuse reflectance values and in accordance with the selected optical stack configuration.

In one embodiment, the method includes calculating a plurality of specular reflection values, each of which is a respective value of the optical stack configurations.

In an embodiment, calculating the diffuse reflectance value comprises calculating a cross section of the nanowire.

In one embodiment, calculating the diffuse reflectance values for each optical stack configuration includes calculating an electromagnetic field of incident light from a position of a nanowire within the optical stack, respectively, and from the optical stack The light scattered by the intra-nanowire line calculates the transfer matrix.

In an embodiment, calculating the diffuse reflection comprises calculating a quantity of light scattered from the nanowire and a field of incident light from the nanowire position based on the scattering cross section.

In an embodiment, calculating the field from the incident light comprises calculating an electromagnetic field of diffusely scattered light from the position of the nanowire.

In an embodiment, the plurality of optical stacking parameters comprises a number of layers of the optical stack. In an embodiment, the plurality of optical stacking parameters comprises a thickness range of the optical stack layer. In an embodiment, the plurality of optical stacking parameters comprise a refractive index range of the optically stacked layer.

In one embodiment, forming the optical stack layer includes forming a first layer on the substrate and forming a second layer on the first layer, the nanowire being located in the first or second layer.

In one embodiment, the method includes calculating a plurality of specular reflection values based on the optical stacking parameters, each of which is a respective value of the plurality of optical stack configurations.

In an embodiment, calculating the plurality of specular reflection values comprises calculating a transfer matrix for the light incident on each of the optical stack configurations.

In an embodiment, one of the optical stack configurations is selected for comparison based on the specular reflection values.

In an embodiment, selecting one of the optical stack configurations includes selecting an optical stack configuration corresponding to a minimum diffuse reflectance value.

An embodiment is a method comprising inputting input optical stacking parameters for an optical stack having nanowires into a processor and storing the input optical stacking parameters in a memory circuit coupled to the processor. The method additionally includes calculating a plurality of diffuse reflection values for the plurality of optical stacks each having a respective configuration in the processor based on the optical stacking parameters. Calculating the diffuse reflection values for each configuration includes calculating an electromagnetic field value from a position of the incident light in the optical stack (corresponding to the position of the nanowire in the optical stack) and calculating a transfer matrix based on the electromagnetic field value, respectively. To provide a diffuse surface on the surface of the optical stack Shot value.

In an embodiment, the method includes comparing one of the diffuse reflection values to one another and selecting the diffuse reflection values.

In an embodiment, the method includes outputting, from the processor, a selected optical stack configuration corresponding to the selected diffuse reflection value.

In an embodiment, the input optical stacking parameters comprise a range of refractive indices of at least one layer of the optical stack. In an embodiment, the selected optical stack configuration includes a refractive index from the range of refractive indices. In an embodiment, the input optical stacking parameters comprise a thickness range of the optical stack layer.

In an embodiment, the selected optical stack configuration includes a thickness from a range of thicknesses of the optical stack.

In an embodiment, the method includes forming an optical stack in accordance with the selected optical stack configuration.

In an embodiment, calculating the diffuse reflection values comprises calculating a scattering cross section of the nanowires.

An embodiment is a system comprising a processor, a memory coupled to the processor, an input coupled to the processor and configured to receive a first parameter of the optical stack. The processor is configured to calculate a set of incident photoelectric field values for a position corresponding to a nanowire in the optical stack, calculate a light scattering distribution of the nanowire, calculate a set of diffuse reflection values at the optical stack surface, and A second set of parameters of the optical stack is estimated. The second parameters correspond to preferred values of the set of diffuse reflection values. An output is coupled to the processor and configured to receive a second parameter from the processor.

In an embodiment, the system includes a display coupled to the output, the display being configured to display the second parameter.

In one embodiment, the system includes a deposition device coupled to the output, the deposition device configured to receive the second parameter and to deposit the light based on the second parameter Learn the first optical layer of the stack.

An embodiment is a method comprising inputting optical stacking parameters into a processor, in the processor, estimating a set of electromagnetic field values from incident light at positions corresponding to the nanowires in the optical stack and in the processor The light scattering distribution of the nanowire is estimated. The method additionally includes estimating a set of diffuse reflectance values at the optical stack surface in the processor based on the electromagnetic field value and the cross section and outputting an optical stack configuration corresponding to the selected diffuse reflectance value from the processor.

In an embodiment, estimating the set of electromagnetic field values comprises calculating a first transfer matrix based on the optical stack parameters.

In an embodiment, estimating the set of diffuse reflectance values comprises calculating a second transfer matrix based on the optical stacking parameters.

30‧‧‧ Optical stacking

32‧‧‧Nami Line

34‧‧‧Low refractive index layer/transparent insulating layer

36‧‧‧Substrate

37‧‧‧ surface

38‧‧‧High refractive index layer

40, 42, 44‧ ‧ border

48, 50‧‧‧ graphical user interface

60‧‧‧ system

62‧‧‧Processor

64‧‧‧ memory

66‧‧‧Input module

68‧‧‧ display

70‧‧‧Manufacture equipment

120‧‧‧Table device

In the drawings, the same reference numerals indicate similar elements or acts. The dimensions and relative positions of the elements in the drawings are not necessarily to scale. For example, the shapes and angles of the various elements are not drawn to scale, and some of these elements are arbitrarily enlarged and positioned to improve the readability of the drawings. In addition, the particular shapes of the components are not intended to convey any information about the actual shapes of the particular elements and are only selected to facilitate the recognition in the drawings.

1 is a cross section of an optical stack including nanowires in accordance with an embodiment.

2A shows specular reflection from an optical stack, in accordance with an embodiment.

2B shows diffuse reflection from an optical stack in accordance with an embodiment.

Figure 3A is a diffuse reflection curve in an optical stack.

Figure 3B is a specular reflection curve in an optical stack.

Figures 4A-4C show diffuse reflection curves for several wavelengths in various media and at various thicknesses.

Figures 5A-5C show specular reflection curves for several wavelengths in various media and at various thicknesses.

Figure 6 is a cross section of an optical stack in accordance with an embodiment.

Figure 7 shows total internal reflection in an optical stack.

Figure 8 is a cross section of an optical stack comprising three layers, in accordance with an embodiment.

9A is a cross section showing an optical stack of top and bottom modes propagating in an optical stack, in accordance with an embodiment.

Figure 9B is a cross section of an optical stack of top and bottom modes showing diffuse scattered light propagating in an optical stack, in accordance with an embodiment.

FIG. 10A shows a GUI in accordance with an embodiment.

FIG. 10B shows a GUI in accordance with another embodiment.

Figure 10C is a graph of optimal specular and diffuse reflections in accordance with an embodiment.

FIG. 10D shows a GUI in accordance with an embodiment.

FIG. 10E shows a GUI in accordance with another embodiment.

Figure 11 is a block diagram of a system in accordance with an embodiment.

Figure 12 is a diagram of a method of reducing diffuse reflection from an optical stack in accordance with an embodiment.

Figure 13 is a diagram of a method of reducing diffuse reflection from an optical stack in accordance with another embodiment.

Figure 14 shows a tablet device including an optical stack, in accordance with an embodiment.

The present invention includes the cause of the "milky" appearance of the nanowire display, its solution, and an optical stack with a lower or no milky white appearance. As used herein, "optical stack" refers to a multilayer film stack in which light from an external or internal source travels, one or more of which affect the optical behavior of the light. The film in the optical stack is typically a functional film (eg, a transparent conductive film, a polarizer, a color filter, an anti-glare film, or an anti-reflective film) with a protective coating and a clear adhesive. The films may be flexible (eg, polymeric substrates) or rigid (eg, glass substrates). The optical stack is typically coupled to another functional unit, such as a display. In addition to the films, the interstices between the films or between the thin ether and the display also have an effect on the optical behavior of the light and are considered to be part of the optical stack.

Moreover, in film oriented content, the film "overlying" another film is configured to be closer to the external source (or observer) than the other film. For example, a coating overlying the nanowire layer is always disposed between the external light source (or observer) and the nanowire layer. The film "underlying" another film is configured to be further from the external source (or observer) than the other film. For example, in an optical stack employing a coating underlying the nanowire layer, the nanowire layer is always disposed between the external light source (or observer) and the undercoat layer.

Figure 1 shows an optical stack 30 that conducts a transparent film. In the base optical stack (30) (as in a more complex one (eg, a full touch panel)), many or all of the layers or structural elements may constitute diffuse reflection to some extent. Various embodiments of the present invention relate to methods for reducing diffuse reflection by controlling and modifying individual layers or structural elements. However, it should be appreciated that any one or more of the individual embodiments can be combined to provide additional benefits in further reducing diffuse reflection. Accordingly, embodiments are directed to an optical stack comprising at least one nanowire layer and at least one substrate adjacent to the nanowire layer, wherein the nanowire layer comprises a plurality of conductive nanowires, and wherein the incident light is Diffuse reflection (as observed from the optical stack on the same side as the incident light) is a percentage of the incident light. As used herein, "adjacent" refers to the relative position of the substrate to the layer of nanowires. They may be in direct contact or close to each other in such a manner as to have one or more intermediate layers therebetween.

The optical stack 30 includes conductive nanowires 32 embedded in a transparent insulating layer 34. The transparent insulating layer 34 and the nanowires 32 are located on the substrate 36.

The optical stack 30 is a type that can be used in flat panel displays. Therefore, it is desirable to have the optical stack 30 have the property of maximizing the visual characteristics of the optical stack. As previously described, the optical stack 30 comprising the nanowires 32 can result in a milky white or hazy quality. This opalescent quality can detract from the visual characteristics of the optical stack 30. In particular, when it is desired to display a dark color (e.g., black), the optical stack 30 may instead display a milky white that compromises the quality of the displayed image.

These undesired features are derived from the diffuse reflection of the nanowires 32. Typically, when light encounters a surface or object, the angle of reflection is equal to the angle of incidence. This is called specular reflection. The specular reflection system is shown in Figure 2A. In Figure 2A, light is incident on surface 37 of optical stack 30 at an angle of incidence Φ _i . The light is reflected from the surface 37 of the optical stack 30 at an angle Φ _r (which is equal to Φ _i ).

However, as shown in FIG. 2B, a portion of the light that strikes the surface 37 of the optical stack 30 or virtually any surface is also diffusely reflected at a plurality of angles θ _r . This diffuse reflection refers to the expected reflection angle scattering of light in many directions rather than specular reflection. Although only one corner is labeled θ _r in FIG. 2B, the diffuse reflection light is reflected at a plurality of angles θ _r . In Figure 2B, light incident on the surface 37 is scattered in a number of directions. While a very small portion of the light is typically diffusely reflected from any surface, the optical stack 30 of Figure 2B results in further diffuse reflection due to the presence of the nanowires 32.

When light is incident on an object or structure having a size smaller than the wavelength of light, light is diffusely scattered from the object. The nanowires 32 and the optical stack 30 typically have a radius of less than 100 nm (e.g., a radius between 5 and 100 nm). 100 nm is much smaller than the minimum wavelength of visible light. Thus, when any visible light encounters the nanowire 32, it diffuses from the nanowire 32. In a transparent film, a substantial portion of the light incident on surface 37 is transmitted through surface 37 and into layer 34 of embedded nanowires 32. Only a small percentage of the light is reflected on the surface. However, part of the light that interacts with the nanowire 32 is diffusely reflected. This diffuse reflection is the primary cause of the milky white quality, which can sometimes be decremented including the appearance of the optical stack 30 of the nanowires 32. It has been shown that when there is a nanowire 32 in the optical stack 30, the calculation of diffuse reflection from the nanowire 32 can be reduced in several ways.

One such method reduces the refractive index of layer 34 of embedded nanowires 32. FIG. 3A shows a plot of diffuse reflection versus the wavelength of light incident on the nanowire 32. Three curves have been shown, each corresponding to a layer having refractive indices of 1.43, 1.33, and 1.23. The peak of the curve with a refractive index of 1.43 is significantly higher than the curve with n equal to 1.33 and n equal to 1.23. For a layer having a refractive index equal to 1.43, a diffuse reflection peak occurs when the wavelength of light is about 400 nm. The 400 nm line is at the edge of the visible spectrum and corresponds to violet light. Humans usually cannot see wavelengths less than 380 nm, which corresponds to In the ultraviolet light.

When the refractive index is lowered to n = 1.33, not only the peak diffuse reflection is reduced, but also shifted to a smaller wavelength. For materials having a refractive index n = 1.33, the peak is reduced to about 6 x 10 ^-4 and the peak wavelength is about 370 nm. Thus, not only is the light diffusely reflected off the surface 37 of the optical stack 30 reduced, but most of the reflected light is shifted out of the visible spectrum and into the ultraviolet spectrum. It should be noted here that in this graph, the diffuse reflectance values are in arbitrary units, but it is still advantageous to understand that changing the parameters of the optical stack 30 has a considerable influence on the diffuse reflection.

The diffuse reflection of the material having a refractive index n = 1.23 is the smallest of the three curves. The peak diffuse reflection of n = 1.23 is about 4.5 x 10 ^-4 , and it is equally important that the peak wavelength is even further shifted into the ultraviolet region that is invisible to the human eye. Thus, placing the nanowires 32 in the layer 34 having a lower refractive index reduces diffuse reflection and shifts the peak diffuse reflection out of the visible spectrum.

It is also desirable to reduce specular reflection as much as possible. Figure 3B shows three curves of the specular reflection versus the wavelengths of the three refractive indices n of Figure 3A. As can be seen from Fig. 3B, the layer 34 of the refractive index n = 1.43 has the highest specular reflection. For n = 1.43, the peak specular reflection is about 0.04. However, this peak is outside the visible range, around 300 nm. For layer 34 having a refractive index n = 1.33, the amount of reduction in peak specular reflection is small. However, for most of the visible spectrum (equivalent to a wavelength of about 400 nm to 700 nm), the specular reflection of n = 1.33 is much lower than the specular reflection of n = 1.43. Thus, while the primary focus of the present invention is to reduce diffuse reflection, specular reflection should not be overlooked. Reducing specular and diffuse reflections maximizes the visual characteristics of the optical stack 30.

For the layer 34 having a refractive index n = 1.23, the specular reflection system is the lowest among all. Not only is the peak specular reflection reduced, but the specular reflection of most of the visible spectrum is also very close to zero, with the low point at about 500 nm. Therefore, reducing the refractive index of the layer of embedded nanowires 32 is very beneficial for both diffuse and specular reflections.

Another parameter of the optical stack 30 that can affect specular and diffuse reflection is the thickness of layer 34 of embedded nanowires 32. Figure 4A shows diffuse reflection with respect to several wavelengths and refractive index n = 1.23 The relationship between the thicknesses of the layers 34 of the buried nanowires 32 is shown. As can be seen, the diffuse reflection of light at a wavelength of 400 nm is slightly higher than the diffuse reflection of light at a wavelength of 450, 500 or 650 nm. Perhaps most notably, the diffuse reflection of any given wavelength remains substantially constant over the entire thickness range of layer 34 having a thickness of between about 20 and 400 nm. In FIG. 4A, the diffuse reflection of 400 nm light is larger and more variable than the diffuse reflection values of other wavelengths. In other optical stacks, this is not the case. In fact, this layer thickness may be important in some configurations.

Figure 4B plots the diffuse reflection of the nanowires 32 in layer 34 from a refractive index n = 1.33. A slight increase in the refractive index results in an increase in the amount of diffuse reflection. In particular, the diffuse reflection of light at 400 nm increases more than the diffuse reflection of light at 450, 500 or 650 nm. Thus, Figures 3A and 3B and Figures 4A through 4C illustrate that diffuse reflection is most severely fluctuating near the violet end of the visible spectrum.

In Fig. 4C, the refractive index is n = 1.43. As the refractive index increases, the diffuse reflection of 400 nm light has increased significantly. The diffuse reflection of light at wavelengths of 450 nm, 500 nm, and 650 nm has also increased slightly, but to a much smaller extent.

However, the change in the thickness of layer 34 of embedded nanowire 32 causes the specular reflection to fluctuate greatly. This specular reflection follows the sine wave pattern of each of the four wavelengths of light drawn in Figure 5A. As the thickness of layer 34 increases, the magnitude of the specular reflection of all wavelengths of light experiences peaks and valleys. When the layer thickness is close to zero, the specular reflection of each of the four wavelengths of light approaches a peak of about 4%.

When the thickness is increased to about 100 nm, the four wavelengths depicted in Figure 5A experience minimal specular reflection. When the thickness of the layer 34 increases toward 200 nm, the four wavelengths of light again approach the peak. Depending on the thickness of the layer in the stack, light will experience constructive interference at the entire optical stacking position involving destructive interference. Additionally, light reflected from surface 37 may be 180 degrees out of phase with light reflected from below. Thus, depending on the thickness and material of the layers (34, 38), light reflected from below can destructively interfere with light reflected from surface 37 and thereby reduce specular reflection.

In Fig. 5B, specular reflection of four wavelengths of light is illustrated when layer 34 has a refractive index of 1.33. The peaks and valleys appear at substantially the same position as when the refractive index is 1.23. However, the minimum value at this time is higher than n=1.23. In particular, these minimums only drop to approx. 1% specular reflection, while for n = 1.23, the minimum value drops to about zero.

In Figure 5C, the layer 34 of embedded nanowire 32 has a refractive index n = 1.43. The peak here is kept at about 4% (as in Figures 5B and 5A). However, the minimum value of the specular reflection percentage has increased to about 2.5%, while n = 1.33 is 1% and n = 1.23 is 0%. Therefore, to reduce specular reflection, it is desirable to have a lower refractive index in certain optical stacks.

FIG. 6 shows an optical stack 30 in accordance with an embodiment. According to an embodiment, the optical stack 30 includes a nanowire 32 in the insulating layer 34. Layer 34 is placed on layer 38, which is a high refractive index layer. Layer 38 is also optically transparent. Layer 38 enhances the forward scatter of the diffused light from nanowire 32. When the nanowires 32 are placed in the layer 34 having a relatively lower refractive index than the layer 38, then more forward scatter of the diffused light is promoted. In other words, as the light diffuses from the nanowire 32, more of the light will be forward scatter toward layer 38. Therefore, the light that diffusely reflects back to the surface 37 of the optical stack 30 will decrease. This is due in part to the fact that forward scatter has a high density of states relative to backscatter when the high refractive index layer is adjacent to the low refractive index layer. This high density of states promotes forward scatter as previously described.

Another advantage of having a high refractive index layer 38 beneath the nanowire 32 is that total internal reflection of diffusely reflected light can occur within the high refractive index layer 38 (as shown in Figure 7). The critical angle θ _c is the angle of incidence above which total internal reflection can occur. The angle of incidence is measured from the normal at the refraction boundary. When light passes from the high refractive index layer 38 to the low refractive index layer 34, the light that illuminates the interface between the layer 34 and the layer 38 is deflected toward the high refractive index layer 38. When the incident angle is sufficiently large, the transmission angle in the low refractive index layer 34 reaches 90° with respect to the normal. At this time, light is no longer transmitted into the low refractive index layer 34. This interaction follows the Snell's law, which is expressed as: n ₁ sin(θ) ₁ = n ₂ sin(θ) ₂ .

According to simple mathematics, the critical angle θ _{c at} which total internal reflection occurs can be calculated as follows: θ _c = arcsin(n ₂ /n ₁ ) .

Therefore, the larger the difference between the low refractive index layer 34 and the high refractive index layer 38, the smaller the critical angle will be. When the critical angle becomes smaller, once the high refractive index layer 38 and the low refractive index layer are reached At the boundary of 34, more light will experience total internal reflection. Thus, selecting a layer 38 having a sufficiently high refractive index can further reduce the amount of diffusely reflected light that reaches the surface 37 of the optical stack 30. Thus, promoting total internal reflection is associated with enhanced forward scatter as described in FIG. In particular, the more light that is scattered forward from the nanowire 32 into the high refractive index layer 38, the more light will be totally internally reflected within the high refractive index layer 38 and will not reach the surface and thus result in a milky white increase.

6 illustrates an optical stack 30, as previously described, wherein the high refractive index layer 38 is placed below the low refractive index layer 34 and above the substrate 36, in accordance with an embodiment described above. An optical stack 30 having a nanowire 32 including a low refractive index layer 34 embedded in the low refractive index layer 34 and adjacent to the high refractive index layer below the low refractive index layer is provided as described in Figures 6 and 7. Enhanced. The already existing substrate 36, which typically has a refractive index between the low refractive index layer 34 and the high refractive index layer 38, provides additional structural support and allows for attachment to a flat panel device.

While the foregoing embodiments of optical stack 30 provide various benefits, it is still very difficult to optimize the optical stack to minimize diffuse and specular reflection. In order to provide an optical stack with minimal diffuse reflection, an efficient method of calculating the diffuse reflection of the optical stack 30 of the layer and the nanowires of a given configuration is useful. The diffuse reflection of the optical stack 30 can be calculated by solving the optical stack 30 for Maxwell's equations. The differential form of Maxwell's equation describing the properties of electric field E and magnetic field B is as follows: Where ρ is due to the charge density of free charge and polarized charge; J-type current density; ε ₀ is the permittivity of free space and the permeability of μ ₀ free space. It is quite difficult to utilize Maxwell's equations in the method of calculating diffuse reflection, and when it is desired to calculate diffuse reflection for many optical stacks 30, a large amount of time and processor resources may be required. The complexity of Maxwell's equations makes it difficult to solve and calculate the preferred parameters of the optical stack 30.

Additionally, each time a new different layer is added to the optical stack 30, it is not easy to control the Maxwell equation to provide a further optimization of the optical stack 30 including other parameters. In some cases, multiple layers can be added below and above the nanowire 32. Certain optical stacks may be subject to specific limitations. Each time the parameters or limits of the optical stack 30 are changed, Maxwell's equations are re-solved, thereby consuming more time and processor resources.

9A and 9B will describe a low resource intensive method of calculating specular and diffuse reflections of an optical stack via a transfer matrix. Since Maxwell's equations are second-order partial differential equations, a set of total solutions of these equations utilizes a set of at least two linear independent families (patterns) of the solution. One embodiment defines these two families as "top" and "bottom" modes. The first set of solutions (top mode) corresponds to a field distribution that can be induced by light incident on the system from the top (as in the case of specular reflection). This second set of solutions (bottom mode) describes the field distribution throughout the system that can be induced by the light source on the substrate side of the structure (below the layer 36 in Figure 9A). These solutions also exist in the process of diffuse reflection.

The specular reflection process is now considered in more detail in accordance with the arrow on the right side of Figure 9A. During this process, a portion of the incident light is transmitted. FIG. 9A shows an optical stack 30 in accordance with an embodiment. The nanowire 32 is not shown in Figure 9A because the nanowire 32 does not appear to exist when performing the calculations for the optical stack of Figure 9A. The position y = 0 in the optical stack corresponds to the position occupied by the nanowire 32 in the optical stack. The optical stack 30 includes a low refractive index layer 34 as previously described. The low refractive index layer 34 is on the high refractive index layer 38 and the high refractive index layer 38 is on the substrate 36. The optical stack 30 is illuminated with a light source. Light is incident on the surface 37 of the low refractive index layer 34.

It is assumed that no nanowires exist to calculate the EM field distribution throughout the multilayer structure. Perform these calculations using the transfer matrix method, where the fields in each layer are made up of a series throughout the system The plane waves (reflected/transmitted waves) moving up and down represent and establish the relationship of the amplitudes of the waves in the adjacent layers via the transfer matrix.

Light from the source is incident on surface 37 of optical stack 30. The right side of the optical stack corresponds to the top mode because it carries energy from the top of the system. A portion of the incident light from the source above the optical stack is transmitted through surface 37 into low refractive index layer 34, as indicated by the arrows in the optical stack on the right side down into layer 34 in FIG. 9A. A portion of the light incident on the optical stack 30 is reflected from the surface 37 as indicated by the arrow exiting at an angle from the arrow entering the layer 34. This angle of the arrow is not intended to represent the angle at which light is reflected from the surface, only indicating that part of the light is returning upwards and partially passing. This is true for all the arrows in Figure 9A. It seems that the arrows at an angle are only angled to distinguish them from the arrows that pass through the boundary. In fact, the direction of light propagation depends on the illumination source and is described by the solution of Maxwell's equation.

Part of the light from the air passing through the boundary 37 continues to propagate in the layer 34 until it reaches the boundary 44 between the layers 34 and 38. At boundary 44, a portion of the light passes through and is partially reflected, as indicated by the arrow pointing downward through the boundary 44 and returning to the arrow in layer 34 (which represents the reflection at boundary 44). This reflected light will return further to boundary 37, with portions forming a first specular reflection (upward arrow) and a portion forming a primary transmission (downward arrow). In the context of Figure 9A, these subsequent re-reflections and re-transmissions are combined and represented by a single combination of transmissive (downward) and reflective (upward) arrows. According to an embodiment, the description is consistent with a transfer matrix technique that can be used to automatically calculate the overall reflection/transmission coefficients.

Likewise, at boundary 42, a portion of the light passing through layer 38 to boundary 42 passes through boundary 42 to layer 36. Similarly, a portion of the light incident on boundary 42 is reflected back into layer 38. A portion of the light passes through any of the layers 40 to below layer 36.

The imaginary light source is shown below layer 36 of optical stack 30. The dashed arrow on the left side of the optical stack originates from this source and corresponds to the "bottom mode" because it carries energy from the bottom of the system upwards. A portion of the light propagates through the boundary 40 into the layer 36 of the optical stack It faces the boundary 42 and part of this light will be reflected. At boundary 42, a portion of the light from layer 36 passes through boundary 42 to layer 38. At the same time, part of the light is reflected back to boundary 40 at boundary 42. Likewise, at boundary 44, a portion of the light passes into layer 34 and a portion is reflected back into layer 38 at boundary 44.

Finally, at surface 37 of optical stack 30, a portion of the light passes through layer 34 to the air surrounding optical stack 30.

By using a transfer matrix, the amplitude of the field propagating up and down in each layer can be calculated. In particular, for the top mode, the calculation of the amplitude of the light reflected upward from interface 37 can be used to calculate the full specular reflection very accurately. Additionally, the amplitudes of the other waves that make up the top mode can be used to calculate the electromagnetic field at any given vertical position within the stack 30. In this way, the field at the 32 position of the nanowire can be calculated.

In an embodiment, the size of the optical stack in the z-direction (ie, facing the direction within the page) is assumed to be infinite. Thus, the total field in the optical stack 30 can be represented by a linear combination of two fields having different polarizations. The first set of fields (referred to as TE waves) have an electric field component along the z-axis, so their magnetic fields have only x and y components. Likewise, the second set of waves (TM waves) have a magnetic field aligned with the z-axis and their electric field is in the xy plane.

At the interface of two arbitrarily selected adjacent layers ( j and j +1) within the optical stack 30, the incident light system wave vector is assumed to have a component { Plane wave of }. The relationship between the amplitudes of the plane waves in adjacent layers can be determined by considering the boundary conditions of the electric field and the magnetic field. Specifically, for the interface between layers j and j+1 (eg, corresponding to layers 34 and 38), this relationship is expressed as follows: Wherein α ^- and α ⁺ are the amplitudes of the waves propagating in the negative and positive y directions respectively; the polarization dependent constant K _{j of the} TE polarized waves is Representing and the polarization dependent constant K _{j of the} TM polarized wave is Said. The matrix that relates the amplitude of the field in the adjacent layer is called the transfer matrix. The transfer matrix is merely one type of transfer matrix that can be used to calculate the amplitude of specular, diffuse, or optical waves to the optical stack 30. Many other types of transfer matrices are available. Additionally, in accordance with the principles of the present invention, diffuse reflection can be calculated using methods other than transfer matrices.

Figure 9B shows the optical stack 30 of Figure 9A. In Figure 9A, the nanowires 32 have scattered incident light incident on the optical stack 30 of Figure 9A. The light source present in Figure 9A is not present in Figure 9B, and the focus now emphasized is diffuse reflection rather than specular reflection. Thus, the nanowire 32 scatters light in a plurality of directions.

The diffuse reflection corresponds to the amount of light passing through the surface 37 scattered from the nanowires 32 present in the optical stack 30. Thus, a method of calculating diffuse reflection according to an embodiment includes calculating the amount of light scattered from the nanowire 32 in all directions. As previously described, when calculating the transfer matrix to determine specular reflection, the field at any location in the optical stack can also be calculated. One step in calculating the light scattered by the nanowire 32 is to calculate the field at the position of the nanowire 32.

When the field of the nanowire position has been calculated or estimated, the amount of light scattered by the nanowire can be obtained by calculating or estimating the scattering cross section of the nanowire 32. The scattering cross section of the nanowire can be obtained by solving Maxwell's equation for a long cylindrical line of a given shape. In the case of a line having a cylindrical cross section, the scattering cross section can be calculated without causing a significant load on the processor resources. The scattering cross section can also be calculated for lines of other shapes, such as lines having a polygonal or other cross section. In one example of such calculations, the solution of Maxwell's equation is represented by a set of cylindrical waves, and the boundary conditions along the circumference of the line are used to establish a relationship with the amplitude of the waves. In the paper (Viktor A. Podolskiy, Evgenii Narimanov, Wei Fang, and Hui Cao, Chaotic microlasers based on dynamical localizatioo, Proc. Nat. Acad. Sci. v. 101 (29) pp. 10498-10500 (2004) and This form has been described using light emitted from, for example, a dielectric resonator, in the reference. This paper is incorporated herein by reference in its entirety. Once the relationship is found, the relationship between the energy flux of the line scattering and the energy flux incident on the line is established directly, and the relationship is used to calculate the scattering cross section of the line. The scattering cross section depicts the light incident on the nanowire 32 by the nanowires 32. proportion.

The amount of light scattered by the nanowires 32 can be calculated by multiplying the field from the light incident on the nanowire 32 by the scattering cross section of the nanowire. The full diffuse reflection from the optical stack 30 can be calculated or estimated by recalculating the transfer matrix of light scattered by the nanowires 32 in the optical stack 30. The diffuse reflection is the amount of light that is scattered from the surface 37 from the optical stack 30 by the nanowires 32. In one embodiment, the nanowires are treated such that the light appears to be equally scattered in all directions. Mathematically, the spectrum A(k _x ) of diffusely scattered light does not depend on the x component of the wave vector k _x .

Similar to the specularly reflected light in Figure 9A, the diffusely reflected light from the nanowires in Figure 9B is also transmitted through and reflected from boundaries within the optical stack. The transfer matrix used to calculate the diffuse reflection is calculated for the top and bottom modes previously described.

Light that is forward scattered from the nanowire 32 as previously described will be incident on the boundary 44 between the layers 34 and 38. Some of this light will be reflected back to surface 37. Part of the forward scattered light from the nanowire 32 will pass through the boundary 44 into the layer 38. The light will again propagate to the boundary 44 between layers 38 and 36 where a portion of the light will transmit and a portion will reflect upward back to boundary 44. Part of the light transmitted through boundary 36 will be reflected at boundary 40 and partially will pass through boundary 40. All of the light passing through the boundary 40 will represent diffuse transmitted light. The light reflected by each interface (44, 42, 40) will constitute a diffuse reflection. However, the main contribution of diffuse reflection comes from the light that is emitted into the bottom mode of the system (shown above the nanowire in Figure 9B). The amount of light transmitted through the interface 37 (which will represent all of the light scattered by the line into the bottom mode and the portion of the light that was originally emitted into the top mode and then reflected by the interface (44, 42, 40)) represents the overall in the system Diffuse reflection.

Diffuse reflection can be calculated in a manner similar to specular reflection as described in Figure 9A. That is, a scattering cross section is obtained and a transfer matrix calculation is performed on the diffuse scattered light transmitted and reflected at all boundaries within the stack 30. In this way, the overall diffuse reflection can be approximated while using relatively little processor resources.

In an embodiment, the field at which the nanowire is located may include a field from incident light and a field from previously scattered light. In other words, part of the light scattered by the nanowire 32 will be in the optics The stack 30 is internally reflected and is again scattered by the nanowires 32. The accuracy of the diffuse reflection calculation can be improved by considering the field of diffuse scattered light from the position where the nanowire is located.

The calculation of light scattering usually takes into account the phase of the scattered light. To achieve this, it is assumed that the radius of the nanowire is very small, so the scattering is controlled by the lowest possible column harmonic function (empirical calculation indicates that TE scattering is controlled by m=0 [polar angle independent] cylindrical mode, and TM scattering is m=1 [like dipole] cylindrical mode control. Therefore, the spectral spectrum of these scattered waves is proportional to the following: Where n is the refractive index of the material surrounding the line; k is the wave vector and ω is the angular frequency. Note that when the line radius is small enough, both cases are reduced to the aforementioned unrelated k _x spectrum.

The scattered light is expressed as the sum of the "emission" waves (the bottom mode is y > 0, the top mode is y < 0) plus the sum of the reflection components of the top and bottom modes. The amplitudes of the top and bottom modes emitted by the source are the same as the TE polarization and opposite to the "dipole" TM polarization. When considering the interference of the top and bottom modes, the effective amplitude of the emitted light becomes: for the TE wave:

And for the TM wave:

Where a ( k _x ) is the amplitude of the emitted light and r _t , r _b is the reflection coefficient of the components of the top and bottom modes.

To calculate the feedback field (i.e., the diffuse scattered light incident on the nanowire 32 again), we multiply the emission fields by their respective reflection coefficients and add the two. Therefore, the total amplitude of the field at the line position becomes: And for the TM wave: Factor dk _x represents a step in order wave vector spectrum using numerical calculation. The self-consistent calculation of the field at the nanowire position may include incident light and diffuse reflected light from an external source. In a self-consistent solution, the field can be described as: a ( k _x )= A ( k _x ) a _tot , which results in a matrix relationship describing the emission spectra:

Where A ( k _x , Descriptive self-wave vector The plane wave is scattered into a plane wave having a wave vector k _x , and the (diagonal) matrix There is a component corresponding to the coefficient of a _tot previously described.

As described above, such calculations can be simplified in the case where the percentage of diffusely reflected light returning to the position of the nanowire is small. In this case, the energy flux of the spectral component of the diffusely reflected light is enhanced.

In some applications, it may be advantageous to calculate or estimate partial diffuse scattered light rather than full diffuse reflection. For example, it may be important to estimate the amount of light diffusely scattered toward the viewer or the amount of light that is only scattered away from the viewer rather than diffusely scattered in all directions. In these cases, the form developed above can be used to calculate the energy flux because the diffuse reflection system acts as the angle of incidence. And a function of the reflection angle θ _γ . The transfer matrix form described above for calculating/estimating full diffuse reflection can be used to calculate or estimate the angular distribution of the diffuse reflection. In such cases, the incident angle and the reflection angle may be the longitudinal component of the wave vector k _x via parameterization and then represents the angle of the energy flux distribution of the diffuse reflection spectrum calculation in accordance with the amplitude a (k _x) of the angle.

To improve the accuracy of estimating angle-dependent diffuse reflection, different scattering probabilities A ( k _x , The model is incorporated into these calculations. Certain words, using k _x - independent spectrum, dipole directional spectrum, combinations thereof, or other directional spectrum. In one embodiment, the scattering probability A is dependent on the polarization of the TE polarized wave (which produces a direction-independent performance flux) and the dipole-type radiation pattern of the TM polarized wave [having a flux of energy) Cos ² ( + θ _γ )]. In another embodiment, the energy flux of the TE polarized wave is Proportional, and TM polarized wave energy flux .

There may be many different scattering probability A models, which are within the scope of the disclosure. When developing these models, it is useful to remember that the transfer matrix model represents an estimate of the diffuse scattering method. Therefore, the coefficients can be fine-tuned by comparing the predicted values of the transfer matrix encoding with the strict (but more time-consuming) solutions of Maxwell's equations using finite element methods, time domain finite difference methods, rigorous coupled wave approximations, or other methods. .

Using conventional methods to calculate or estimate the diffuse reflection of the optical stack described above, an optimization program can be utilized to calculate the diffuse reflection of a plurality of optical stacks 30 having different parameters to seek for an optical stack 30 that provides the lowest diffuse reflection. Diffuse reflection optimization of a plurality of optical stack configurations can be performed in accordance with the principles of the present invention using commercially available optimization programs (e.g., those available from Matlab). In conjunction with the above methods for calculating diffuse reflection, such optimization programs can assist in the search for optical stacks with relatively low diffuse reflection.

The specific optimization goals of the method depend on the end application. For example, full diffuse reflection of the system can be optimized for a given wavelength. The optimization targets may also be a weighted average of diffuse reflections corresponding to a particular direction or a combination of weighted full diffuse reflections with a constraint that the diffuse reflection of a particular direction remains below a certain value. It is also possible to estimate the diffuse reflection of light of different wavelengths and sum up these estimates in a certain way (average, weighted average, etc.) to achieve the final target figure of merit that will be optimized. Those skilled in the art can implement all such combinations in light of the present disclosure.

Although diffuse and specular reflections have been described using transfer matrices, other methods other than transfer matrices can be used in accordance with the principles of the present invention to obtain diffuse reflectance values. These other methods are also included in the scope of the invention.

An example of such methods includes extending the method of the present invention to optically from a set of fixed thick layers (which may include a thick underlayer (eg, optical adhesive) or a thick upper layer (eg, a protective glass layer)) The diffuse and specular reflections of the stack are optimized. "Optics here" "Thick" means that the layer thickness is greater than or equal to the coherence length present in the stack.

The propagation of light through the optically thick layer is somewhat similar to the method of creating the top and bottom modes described above. See, for example, the specular reflection of the top mode shown in Figure 9A. As described above, light entering the optical stack through interface 37 will be partially reflected and partially transmitted through this interface. The transmissive portion will enter layer 34 and reach interface 44 where a portion of the light will be transmitted into layer 38 and a portion of the light will be reflected back into layer 34. This reflected light will reach interface 37 where portions will be transmitted out of the optical stack (constituting specular reflection) and partially reflected back into the optical stack. When layer 34 is optically thick, the second (and subsequent) contribution to specular reflection will not interfere with the light originally reflected by interface 37. Conversely, the corresponding energy fluxes will be added together. The specular reflection of the stack of several optical thick layers can be calculated directly from the (fluid-based) reflectance (R) and transmittance (T) of the inner interface.

For example, the following recursive techniques can be used. It is assumed that the layer in Fig. 9A is optically thick. The reflectance of interface 40 can then be calculated using the square of the absolute value of the corresponding Fresnel coefficients. The reflectance of the light entering interface 42 can then be calculated as:

among them The (total) reflectivity of light entering the system from 42 from layer 38; a single interface reflectivity of the interface 42 as the light travels from the layer 38; The reflectivity of the same interface that travels into layer 38 (usually = );and The overall reflectivity of the light that reaches the interface 40. The same equation can then be used to calculate the overall reflectivity of light entering interface 44 (and finally entering interface 37).

If the system contains a mixture of optical thick layers and optical thin layers, the optical properties (reflectance and transmittance) of the optical thin layer can be calculated using the transfer matrix form, which can then be approximated as a single interface in an optical thick stack (with Reflectance/transmittance is known).

Similar techniques can be used to calculate the diffuse reflection in the presence of an optically thick layer.

Figure 10A shows a graphical user interface (GUI) 48 of an optical stack optimization software program stored in a computer readable medium. The GUI can be displayed on a display coupled to the processor to enable the technician to implement the optimization program for optical stacks 30 having parameters that produce better diffuse reflectance values. The processor reads software instructions from a memory circuit coupled to the processor. Thus, the software instructions for running the optimization program to seek the preferred parameters of the optical stack 30 are stored in memory coupled to the processor. Thus, the processor causes the display to display the GUI and the technician can enter the parameter range of the optical stack via a mouse and keyboard or any other suitable input device. The parameters may include the number of layers in the stack, the refractive index of the substrate 36, and the environment in which the optical stack 30 will be placed.

Thus, in the exemplary GUI 48 of Figure 10A, the topsheet has a refractive index of 1 because it is air. The substrate refractive index is listed as 1.5 and corresponds to the substrate 36 of the optical stack 30. The user can enter any substrate or topsheet refractive index desired. The radius of the nanowire 32 is also input to calculate the scattering cross section. The line radius entered in the GUI 48 according to an embodiment is 50 nm. However, depending on the particular nanowire 32 or other nanostructure used in the optical stack 30, the line radius can be any other suitable radius. The user can likewise select which layer in the optical stack 30 to position the nanowires 32. In the exemplary GUI 48 of FIG. 10A, the line layer has been selected as the second layer, which corresponds to layer 34 of optical stack 30. In the area marking the active layer parameters, the user can enter the minimum and maximum thicknesses corresponding to the layers 34 and 36 of the first and second layers in the GUI 48. In the example of Figure 10A, both layer 34 and layer 36 have a thickness of 50 nm to 200 nm. The refractive indices of layers 34 and 36 are each within 1.2 to 2.2. These ranges are limitations in which the optimization program will select parameters for the optical stack 30 to calculate the parameters that produce the best diffuse reflection. When the program is executed, diffuse and specular reflections are calculated for several optical stacks whose layer thickness, refractive index, and wavelength parameters of light are within the input range. The optimization program calculates diffuse and specular reflections using other suitable methods in accordance with the foregoing methods or in accordance with the principles of the present invention.

In one embodiment, in contrast to calculating the diffuse reflection for each possible iteration within the input range, the optimization program is for the first set of optical stacking meters having various parameters within a given range. Calculate diffuse reflection. Next, the optimization program selects a second set of optical stacks that have parameters that are somewhat different than those that produced the lowest diffuse reflections in the first set. The optimization program continues to calculate the diffuse reflection of the optical stack in this manner until better diffuse reflection has been achieved. This optimization program effectively finds the parameters that produce better diffuse reflections without having to calculate every possible iteration. In this manner, a particular configuration of the optical stack 30 that produces relatively low diffuse reflection can be selected. This is possible because of the aforementioned simpler method of calculating or estimating the diffuse reflection of the optical stack 30.

It has the potential for low diffuse reflection and at the same time an unacceptably high specular reflection. Therefore, the area under the active layer parameter area is marked as the area of maximum reflection. In this area, the technician can specify the maximum allowable specular reflection. In this case, the maximum specular reflection has been chosen to be 1.5%. This means that when transferring the matrices for specular and diffuse reflections, a better stacking configuration will be chosen for the lowest diffuse reflection results in which the specular reflection is no more than 1.5%.

In the right area, an optical stack is displayed. The optical stack 30 includes a low refractive index layer 34 that includes a nanowire 32 on a high refractive index layer 38. Layer 38 is on substrate 36 having a refractive index of 1.5. The refractive index of the air above the optical stack is one. In layers 34 and 38, on the left side of each layer, a range of thicknesses and a range of refractive indices are provided. This is indicated on the left side of layer 34 by w ₂ = 50 nm to 200 nm and n ₂ = 1.2 to 2.2. The thicknesses and ranges of refractive indices of the tie layers 34 will be iterated over the calculated transfer matrix to obtain specular and diffuse reflections. The range w ₁ =50 nm to 200 nm and n ₁ =1.2 to 2.2 are also specified on the left side of layer 38. On the right side of layer 34, a preferred thickness and a preferred index of refraction are listed. In particular, the preferred thickness of layer 34 is specified to be 118.2 nm. The preferred refractive index of layer 34 is 1.2. The preferred thickness of the high refractive index layer 38 is 50 nm and the preferred refractive index is 1.7779. Below the optical stack, the specular reflection is listed as R ₀ =0.0144 or about 1.4%. The diffuse reflection R _{diffuse is} listed as 5.469 × 10 ^-5 .

Thus, the GUI 48 that allows the method of optimizing the optical stack 30 allows the user to input the first parameter or input parameter of the optical stack and the program operates, performs calculations, and lists preferred specular and diffuse reflections and produces The layer thickness and refractive index of the preferred result. Those skilled in the art will be aware of the methods and specific GUIs that may be described in accordance with the present invention and The input and output provided are subject to numerous modifications.

FIG. 10B shows a GUI 50 in accordance with an embodiment. The GUI 50 is directed to a method whereby a detailed process of calculating specular and diffuse reflections for various wavelengths can be output based on the preferred parameters from the GUI 48 of Figure 10A. Specifically, the user can output the number of layers according to the preferred output (in this example, 2, the substrate refractive index of the substrate layer 36 is 1.5 and the top index of refraction is 1). Then, the active layer can be selected, in this case, the second active layer is emphasized, which means that the parameters of layer 34 can be entered in the fixed parameter region. The preferred feature layer 34 measured from the GUI 48 of Figure 10A has a thickness of 118.2 nm and a refractive index of 1.2. The active layer can then be emphasized and the preferred features calculated for layer 38 in accordance with GUI 48 of FIG. 10A can be entered. In this case, the preferred features are a 50 nm thickness and a refractive index of 1.7779. A range of wavelengths of light can be input in the region labeled wavelength (nm) below the fixed layer parameters, which will generate a graph. In this example, the minimum wavelength is 300 nm and the maximum wavelength is 800 nm, and the iteration step is 10 nm.

Figure 10C shows a graph generated by the GUI 50 of Figure 10B. In particular, Figure 10C is a plot of specular and diffuse reflection for the wavelength range specified in Figure 10B. The specular and diffuse reflections experience a brief 400 nm peak in the UV range. The specular reflection drops and reaches a minimum of about 1% at 500 nm and then gradually increases to about 2.5% at 800 nm. The diffuse reflection drops and also reaches a low point around 500 nm, but remains fairly flat until 800 nm, but gradually slopes upwards. In this case, the diffuse reflection has been maintained to about 5 x 10 ^{-5 for} most of the visible spectrum. For most of the visible spectrum, the specular reflection has been maintained between 1% and 2%.

In software instructions stored in memory, certain wavelengths of light may have a higher weight than other wavelengths of light. When calculating the transfer matrix, each transfer matrix is subjected to a wavelength range in addition to the layer thickness and the layer refractive index range. When calculating a preferred diffuse reflection, in one embodiment, the reflection of certain wavelengths may have a higher weight than the reflection of other wavelengths. The human eye is more sensitive to certain wavelengths than other wavelengths. Thus, for some optical stacks, the diffuse reflection of the less prominent wavelength is somewhat higher, while the more prominent wavelength is near minimum. In this case Next, although some wavelengths are not close to the minimum diffuse reflection, the diffuse reflection may be a better diffuse reflection. Therefore, it may be desirable to provide higher weight for diffuse reflection of certain wavelengths. In one example, the visible spectrum between 400 and 700 nm is segmented in 50 nm increments. The software that stores the program used to calculate the diffuse reflection can be modified to provide higher or lower relative weights for various wavelengths. For example, in one example, wavelengths between 450 nm and 600 nm have higher weights than other wavelengths. Of course, the technician can change the code stored in the memory to select the weight. This weight can also be implemented to calculate specular reflection.

Figure 10D shows a GUI configured to seek a software program of an optical stack with relatively low diffuse reflection, in accordance with an embodiment. The GUI of Figure 10D allows the user to select the number of layers of the optical stack 30 and locate the 32 layers of nanowires. The number of layers in the example of Fig. 10D is 3 and the nanowire is the second layer. After the nanowire layer has been selected, the user can enter the thickness and refractive index range of the other layers in the optical stack 30. However, in the embodiment of Fig. 10D, the thickness and refractive index of the nanowire layer cannot be changed by using the GUI; these parameters are fixed in the embodiment of Fig. 10D. The first layer parameter can be input by selecting the first layer as the active layer, and then the thickness and refractive index range are input in the marked area. Layer 3 parameters can be entered in the same way. In Fig. 10D, the user has selected the thickness of the first layer and the third layer to be in the range of 30-300 nm. The refractive indices of the first layer and the third layer have been selected to be in the range of 1.2 to 2.2. These ranges are those in which the optimization program will select thickness and refractive index values for each layer during the optimization routine.

The topsheet and substrate refractive index can also be selected by inputting values in the marked regions. These have been selected to be 1 and 1.5, respectively, in the example of Figure 10D. Once these parameters have been selected, the basic pattern of the layers of the optical stack 30 will be displayed on the right side of the GUI, indicating the position of each layer, the position of the nanowire layer, the range of refractive index and thickness, and the refractive index of the top liner and substrate.

The user can also choose whether the optimization routine optimizes diffuse or specular reflection by appropriate selection of the kernel pair in the optimized region. If you choose to optimize diffuse reflection, you can then choose the maximum specular reflection by entering a value in the maximum specular reflection area. The program An optical stack with low diffuse reflection and specular reflection equal to or lower than the selected maximum value will be selected. Alternatively, if the user chooses to optimize specular reflection, then the user can enter the maximum diffuse value for the optical stack.

Finally, the user can click on the start button to proceed with the optimization program. The optimization program will then calculate diffuse and specular reflections for a number of possible optical stacks and select an optical stack with relatively low diffuse reflection and specular reflection below the selected maximum. The parameters of the selected optical stack will then be output. The user can also store the optimal optical stack or load the previously stored optical stack by clicking on the appropriate button.

FIG. 10E shows a GUI for computing and rendering diffuse and specular reflections in accordance with another embodiment. The GUI of Figure 10E allows the user to select the number of layers of the optical stack 30 and locate the 32 layers of nanowires. The number of layers in the example of Fig. 10E is 3 and the nanowire is the second layer. The thickness and refractive index cannot be changed by using the GUI; these parameters are fixed in the embodiment of Fig. 10E. After the nanowire layer has been selected, the user can input the thickness and refractive index of the other layers in the optical stack 30. The third layer parameter is input by selecting the third layer as a fixed layer, and then the thickness and refractive index are input in the lower mark region. The first layer parameters can be entered in the same way. The top liner and the refractive index of the substrate can also be selected; they have been selected to be 1 and 1.5, respectively. Once these parameters have been selected, the basic pattern of layers of optical stack 30 is shown to the right of the GUI. In the example of Figure 10E, the nanowire layer is the second layer.

You can also enter the wavelength range and the step size for calculation and plotting. In the example of Figure 10E, the selected wavelength range is 300 to 800 nm in steps of 10 nm. After all the fields have been filled in, the user can click the start button to start the calculation routine. Specular and diffuse reflections are calculated for all wavelengths. A graph showing the specular and diffuse reflections of each wavelength can be output. A table of values of diffuse reflection and specular reflection for each wavelength step in the display wavelength range can also be output. Many other GUI configurations are possible in accordance with the present invention. All such other configurations are within the scope of the invention.

Diffuse reflections may be selected for selected surfaces relative to optical stack 30, as previously described The angular or diffuse angle range is used to calculate the diffuse reflection. In some applications, it is useful to know the amount of light that is diffusely reflected at a particular angle relative to the surface of the optical stack 30. Thus, in an embodiment, the user of the optimized software may select a plurality of angles (the diffuse reflection of each optical stack configuration will be estimated for the equal angle).

In one embodiment, a set of diffuse values are calculated or estimated for each iteration of the optical stacking parameters. Each set of diffuse values includes a plurality of diffuse values for a selected angle relative to the optical stack 30. The optimization routine can be configured to select an optical stack configuration based on the set of diffuse reflection values. In particular, the sets of diffuse reflection values can be compared to each other and the optimization routine can select an optical stack configuration based on the comparison. The optimization routine can also be configured to compare the diffuse values and thresholds of the individual corners. The optimization routine can then select one of the sets of diffuse reflection values based in part on the comparison with the thresholds.

In one example, the technician can select 11 different reflection angles for calculating the diffuse reflection. The 11 corners may include (relative to the normal) 75°, 60°, 45°, 30°, 15°, 0° (ie normal), -15°, -30°, -45°, -60° And -75°. Each set of diffuse values will include diffuse values for each selected angle. In this example, each set of diffuse values will include 11 diffuse values. Of course, you can choose more or fewer corners. The specific angles and angular numbers above are provided by way of example only.

In an example, a larger reflection angle relative to the normal has a higher threshold than an angle closer to the normal. In other words, higher diffuse reflections can be tolerated at larger angles relative to the normal. This is because in some embodiments, the optical stack 30 can be included in a display screen, where it is more important to have a high quality system at an angle very close to the normal. A larger angle relative to the normal corresponds to the peripheral viewing angle of the display screen including the optical stack 30 and maintaining high optical quality at such angles may be less important. Thus, the diffuse reflection threshold at an angle near the normal can be much smaller than the threshold for an angle away from the normal. This is because it is more common to view the display system from an angle relative to the normal to the display screen.

In an embodiment, if any of the diffuse reflection values in a particular group exceeds the respective diffuse reflections For thresholds, the optical stack configuration associated with that particular group is not selected.

Alternatively, each set of diffuse reflectance values can be compared to a single diffuse reflectance threshold. If any of the diffuse values in a particular group exceeds the diffuse threshold, the optical stack configuration associated with that particular group is not selected.

In an embodiment, the total diffuse reflection value of each set of diffuse reflection values can be calculated. This optimization routine selects an optical stack configuration that corresponds to the lowest total diffuse reflectance value. Calculating the total diffuse reflectance value can include summing the equal diffuse reflectance values. Alternatively, calculating the total diffuse reflectance value can include assigning a relative weighting factor to each of the reflection angles.

In an embodiment, the average diffuse reflectance of each group can be calculated. The average diffuse reflectance of each group corresponds to the average of the calculated values of the diffuse reflections of the set. This optimization routine selects the optical stack configuration based on the average diffuse reflection of each group.

This optimization routine can be configured to provide greater weight for diffuse values at certain angles and lower weight values for diffuse values at other angles. This optimization routine can also provide greater weight for specific wavelengths of light at various angles. This optimization routine can select an optical stack configuration by considering diffuse reflection of a large number of wavelengths at various reflection angles.

Many other optimization routines, software programs, and methods for calculating or estimating diffuse reflection at various angles can be implemented. All such other routines, programs, and methods are included within the scope of the invention.

Figure 11 shows a system 60 in accordance with an embodiment. The system 60 includes a processor 62 that is configured to execute software instructions stored in the memory circuit 64. The memory circuit 64 stores information that can be read by the processor to perform the aforementioned optimization methods. Input module 66 is also coupled to processor 62. A technician operating the system 60 can input input parameters to the optical stack 30 at the input module 66, and the processor 62 will then optimize the parameters and output parameters reflecting the optimization. Display 68 is coupled to processor 62. Processor 62 can cause GUI 48 or 50 to be displayed on display 60. A technician operating the input module 66 can then enter the appropriate area by visually viewing the GUI 48 or 50 on the display 68. These optimization parameters can also be displayed on the display On the 68.

In an embodiment, the system 60 includes a manufacturing device 70 coupled to the processor 62. In this embodiment, processor 62 outputs the output parameters directly to the fabrication facility, which then deposits the appropriate layers and thicknesses as described in Optimizing the Output. For example, optical stacking includes a low refractive index layer 34 (which embeds nanowires 32) and a high refractive index layer 38 (which is located below the low refractive index layer 34) and a substrate 36 (which is located below the high refractive index layer 38). 30. The optimized outputs can be provided to manufacturing apparatus 70, which can then deposit layer 38 on substrate 36 and layer 34 on layer 38. The foregoing system 60 is provided by way of example. Many other components and software instructions not described herein may be included. When the user operates the input module 66 to input the input parameters, the input parameters can be stored in the memory 64 coupled to the processor 62.

In one embodiment, the memory 64 can include EEPROM, ROM, SRAM, DRAM, or any other suitable memory. The software instructions for performing the optimization method can be stored in the memory 64. The input instructions can be temporarily stored in memory 64 or in a separate buffer memory coupled to the processor. Any suitable components for input parameters and software instructions can be stored in a manner readable by processor 62. Alternatively, an output from a method for selecting optical parameters can be used to fabricate the optical stack without the need to physically couple to the fabrication equipment of the circuitry for selecting optical stacking parameters.

FIG. 12 is a flow chart showing a method of optimizing parameters of optical stack 30. At 80, the technician inputs layer parameters to the processor. The input parameters are then stored in a memory coupled to the processor. The input parameters may include the number of layers of the optical stack 30, the thickness range of the layers in the optical stack 30, the refractive index range of the layers in the optical stack 30, the wavelength range to be used for calculating the diffuse and specular reflections, and the various wavelengths in the desired wavelength range. The relative weight value provided. At 82, the processor calculates the field at the position of the nanowire 32 in the optical stack 30. The field calculation of the nanowire position can be performed by using a transfer matrix or any other suitable calculation that can provide a field at the nanowire 32 position. In another embodiment, as previously described, the field calculation of the nanowire position may include a field from previously scattered light.

At 84, the scattering cross section of the nanowire 32 is calculated. The scattering cross section of the nanowire 32 indicates the direction and magnitude of scattering of the diffusely reflected light from the nanowire 32. The nanowire 32 allows the light to be diffusely reflected in any direction. At 86, the processor calculates diffuse reflection based on the field and scattering cross sections calculated at the nanowire position. In one embodiment, the diffuse reflection is estimated by calculating the boundary of the layers of diffusely reflected light in the optical stack 30 and the transfer matrix through the transmission and reflection of the layers.

At 88, the field at the 32-bit position of the nanowire, the scattering cross section of the nanowire 32, and the diffuse reflected light reaching the surface are repeatedly calculated for a plurality of optical stacks 30 covering a series of input parameters. In an embodiment, a diffuse reflection calculation is performed on the first set of optical stacks. The first set of optical stacks can have a layer thickness, a layer index of refraction, etc., the values of which are selected to provide a broad first sample of the optical stack covering the range of possible inputs. For example, the first set of optical stacks can include an optical stack in which the first layers each have a minimum thickness, a maximum thickness, and some thickness distributed therebetween. Diffuse reflections are calculated for this first set and compared to each other.

The diffuse reflection is then calculated for the second set of optical stacks. In an embodiment, the parameters of the second set of optical stacks are selected based in part on the diffuse reflection of the first set. For example, the second set of optical stacks includes an optical stack having one or more parameters that are close to one or more parameters in the first set of optical stacks that produce the lowest diffuse reflectance values. This allows the processor to seek better diffuse reflection values without having to calculate every possible optical stack within the ranges. Conversely, the processor can analyze the optical stack that is most likely to have low diffuse reflection parameters. As long as time and computing power allow, the process can continue as needed to achieve a comprehensive optimization process. Finally, the processor can select an optical stack with parameters that produce the best diffuse reflectance values. At 92, the optical stack 30 is formed by depositing a layer having features corresponding to optimal output parameters.

Materials that can be used in layers of optical stacks made in accordance with the present invention are known in the art. Examples of such materials include, for example, TiO ₂ (R _D = 1.8), polyimine (R _D = 1.7), and transparent polymers containing high refractive index particles such as ZnO, ZrO _{2 ,} and TiO ₂ .

Table 1 shows a number of relatively low folds of layers that can be used in optical stacks made in accordance with the present invention. Emissivity optical material.

Table 2 shows a number of relatively high refractive index optical materials that can be used in layers of optical stacks made in accordance with the present invention.

Methods of depositing optical layers having the desired thickness using coating, printing, sputtering or other techniques are known in the art. Especially in terms of coating technology, Edward Cohen and Edgar Gutoff's "Modern coating and Drying Technology" (John Wiley & Sons, 1992, see pages 11 and 25-28) (which is incorporated herein by reference) A coating with the desired wet film thickness. The dry film thickness formed from a given wet film thickness depends on the composition of the coating solution used and is known to those of ordinary skill. A method of coating and printing a nanowire conductive layer is disclosed in, for example, U.S. Patent No. 8,094,247, and U.S. Patent Application Serial No. 12/380,293, the entire disclosure of each of In this article.

FIG. 13 shows a method of parameter optimization of an optical stack 30 in accordance with an embodiment. At 94, the optical stack input parameters are input to a processor, which stores the input parameters in a memory circuit. The processor executes software instructions stored in the memory to begin a method of optimizing the optical stacking parameters. At 96, the processor calculates a transfer matrix for the light incident on the optical stack, the optical stack having a value within a range of parameters input to the processor at step 94. The table from the optical stack 30 can be obtained by calculating the transfer matrices Specular reflection of face 37. After calculating the transfer matrices, the field of the position of the nanowire 32 within the stack 30 can be calculated (at 98).

At 99, the scattering cross section of the nanowire 32 is calculated. The scattering cross section of the nanowire 32 indicates the amount of diffusely reflected light scattered in each direction within the optical stack 30. At 100, a transfer matrix is calculated for the diffusely reflected light scattered from the nanowires 32 within the optical stack 30 in all directions. The transfer matrices provide a portion of the diffusely reflected light that reaches surface 37 of optical stack 30.

At 102, the processor collates to determine if the input parameters require more iterations. In an embodiment, the processor will perform a diffuse reflection calculation on the first set of optical stacks. For example, if the first layer has a possible thickness range of 50 nm to 200 nm, the processor can calculate the diffuse reflection values for the minimum and maximum thicknesses and some thickness therebetween, while maintaining other parameters. The diffuse values are compared and the processor follows an iteration based on comparing the diffuse reflection selection values of the first set of optical stacks. The processor selects parameters for the next iteration (at 104) and the processor performs specular reflection on a new set of parameters, field of nanowire position, and calculation of diffuse reflection. At 106, the processor selects a preferred diffuse reflection from the set of diffuse reflections that have been calculated for the input parameter range and outputs a particularly good parameter for the optical stack 30 that produces better diffuse reflection.

FIG. 14 shows a tablet device 120 including an optical stack 30 in a touch screen display in accordance with an embodiment. The optical stack 30 that has been fabricated has layer parameters obtained from the optimization method as previously described. The display of the tablet device 120 does not experience milky white or turbidity as previously described.

While specific layers, thicknesses, and properties of optical stack 30 have been described herein, many other suitable optical stack configurations are possible, including more or fewer layers, multiple layers of nanostructures, or any other suitable feature. All such stacks are included within the scope of the invention.

As such, although the present invention has disclosed a particular method of optimizing the optical characteristics of optical stack 30, many other suitable variations are possible in the method. For example, field, specular, and diffuse reflections may be approximated in other ways while still being included within the scope of the invention. can Enter more, fewer, or different parameters into the processor to optimize the stack. Similarly, parameters other than specular and diffuse reflections can be optimized. The word best should not be understood to mean the most feasible configuration, but refers to values or configurations that are superior to other values or configurations. Similarly, optimal reflection does not necessarily mean the lowest reflection, but rather the desired reflection in such feasible reflections.

Other embodiments may be provided in conjunction with the various embodiments described above. U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patent cases, foreign patent applications, and non-patent publications cited in the Application Data Sheet cited in this specification and/or application data sheet All of them are incorporated herein by reference in their entirety. If it is necessary to adopt the concepts of various patents, applications, and disclosures, the embodiments may be modified to provide other embodiments.

These and other changes can be made to the embodiments in light of the above detailed description. In general, the following items are not to be construed as limiting the scope of the patent application to the specific embodiments disclosed in the specification and the scope of the claims. And the full scope of equivalents of such patent applications. Therefore, the scope of such patent applications is not limited by the disclosure.

60‧‧‧ system

62‧‧‧Processor

64‧‧‧ memory

66‧‧‧Input module

68‧‧‧ display

70‧‧‧Manufacture equipment

Claims (31)

A method comprising: selecting an optical stacking parameter for an optical stack having a nanowire; calculating a complex array of diffuse reflection values for each of the plurality of optical stacking configurations according to the optical stacking parameters, each set of diffuse reflection values including a plurality of diffuse reflection values from respective reflection angles of the optical stack reflection; selecting one of the optical stack configurations based at least in part on comparing the sets of diffuse reflection values for the plurality of angles; and according to the selected optical stack The configuration forms an optical stack. A method of claim 1, comprising calculating a plurality of specular reflection values for a plurality of reflection angles for each optical stack configuration. The method of claim 1, comprising: calculating a plurality of specular reflection values for respective optical stack configurations; comparing the specular reflection values to predetermined specular reflection values; and selecting a comparison with the predetermined specular reflection values One of these optical stack configurations. The method of claim 2, wherein selecting one of the optical stack configurations comprises selecting an optical stack configuration having a specular value below the predetermined specular value. The method of claim 1, comprising: comparing each set of diffuse reflectance values to at least one predetermined diffuse reflectance value; and selecting one of the optical stack configurations based at least in part on a comparison with the at least one predetermined diffuse reflectance value By. The method of claim 5, wherein selecting one of the optical stack configurations comprises selecting an optical stack configuration in which a diffuse reflectance value of each of the reflected angles is below the at least one predetermined diffuse reflectance threshold. The method of claim 1, wherein selecting one of the optical stack configurations comprises selecting an optical stack configuration corresponding to a minimum diffuse reflectance value. The method of claim 1, comprising: calculating a respective total diffuse reflection value for each group; and selecting an optical stack configuration corresponding to the minimum total diffuse reflection value. The method of claim 8, wherein calculating the respective total diffuse reflectance values for each of the groups comprises summing the set of diffuse reflectance values. The method of claim 8, wherein calculating the respective total diffuse reflection values comprises assigning respective weighting factors to the diffuse reflections according to respective reflection angles. The method of claim 1, comprising: calculating a plurality of respective diffuse reflection average values, each diffuse reflection average value corresponding to an average of respective sets of diffuse reflection values; and selecting the optical stack based at least in part on the plurality of diffuse reflection average values configuration. The method of claim 1, wherein calculating the diffuse reflectance values comprises calculating a cross section of the nanowire. The method of claim 1, wherein calculating the diffuse reflectance values for each optical stack configuration comprises: calculating an electromagnetic field of incident light from a position of a nanowire within the optical stack; and correcting a nanowire from the optical stack The scattered light calculates the transfer matrix. The method of claim 13, wherein calculating the diffuse reflectance values comprises calculating an amount of light scattered from the nanowire and a field of incident light from the nanowire position based on the scattering cross section. The method of claim 14, wherein calculating the field from the incident light comprises calculating an electromagnetic field from the diffuse scattered light at the location of the nanowire. The method of claim 1, wherein the plurality of optical stacking parameters comprises a number of layers of the optical stack. The method of claim 1, wherein forming the optical stack layer comprises: forming a first layer on the substrate; and forming a second layer on the first layer, the nanowire being located in the first or second layer in. A method comprising: storing the input optical stack parameters in a memory circuit coupled to the processor; calculating, in the processor, a plurality of optical stacks having respective configurations in the processor according to the optical stacking parameters The set of diffuse reflection values, each set of diffuse reflection values includes a plurality of diffuse reflection values for respective reflection angles reflected from the surface of the optical stack, and calculating the set of diffuse reflection values for each configuration includes: calculating corresponding from the optical stack An electromagnetic field value of incident light at a position of a nanowire position in the optical stack; and a portion of calculating a transfer matrix based on the electromagnetic field value to provide a plurality of diffuse reflection values of the plurality of reflection angles reflected from the optical stack surface; An optical stack configuration is selected based on the diffuse reflectance values. The method of claim 18, wherein selecting the optical stacking configuration comprises selecting an optical stacking configuration corresponding to a minimum diffuse reflection value. The method of claim 18, comprising: calculating a respective total diffuse reflectance value for each group; and selecting an optical stack configuration corresponding to the minimum total diffuse reflectance value. The method of claim 18, wherein the input optical stacking parameters comprise a refractive index range of at least one layer of the optical stack. The method of claim 21, wherein the selected optical stack configuration comprises a refractive index from the range of refractive indices. The method of claim 18, wherein the input optical stacking parameters comprise optical stacking The thickness range of the layer. The method of claim 23, wherein the selected optical stack configuration comprises a thickness from a range of thicknesses of the optical stack. The method of claim 17, wherein calculating the set of diffuse reflectance values comprises calculating a cross section of the nanowire. A system comprising: a processor; a memory coupled to the processor; an input coupled to the processor and configured to receive a first parameter of the optical stack, the processor configured to correspond to Calculating a set of incident photoelectric field values in the optical stack, calculating a light scattering distribution of the nanowire, calculating a diffuse reflection value of the complex array on the optical stack surface, and estimating a second parameter of the optical stack The second parameter corresponds to a preferred set of diffuse reflection values, each set of diffuse reflection values comprising a plurality of diffuse reflection values for respective reflection angles reflected from the optical stack surface; and coupled to the processor and grouped State to receive the output of the second parameter from the processor. A system as claimed in claim 26, comprising a display coupled to the output, the display being configured to display the second parameters. The system of claim 26, comprising a deposition device coupled to the output, the deposition device configured to receive the second parameter and to deposit a first optical layer of the optical stack based on the second parameter. A method comprising: inputting an optical stacking parameter into a processor; estimating, in the processor, a set of electromagnetic field values from incident light corresponding to a position of a nanowire in the optical stack; Estimating a light scattering distribution of the nanowire in the processor; estimating, according to the electromagnetic field value and the scattering cross section, a diffuse reflection value of the complex array on the optical stack surface in the processor, each set of diffuse reflection values including a plurality of diffuse reflection values of respective reflection angles of the optical stack surface reflection; and an optical stack configuration output from the processor corresponding to the selected set of diffuse reflection values. The method of claim 29, wherein estimating the set of electromagnetic field values comprises calculating a first transfer matrix based on the optical stack parameters. The method of claim 30, wherein estimating the set of diffuse reflectance values comprises calculating a second transfer matrix based on the optical stacking parameters.