Abstract:
A film for writing may include: a rough layer, including a non-flat surface, configured to transmit a first light beam and a second light beam of different wavelength bands; and/or a photonic crystal layer, arranged on the rough layer, configured to transmit the first light beam and configured to reflect the second light beam. A film for writing, which transmits visible rays, may include: a non-flat layer. A difference between a maximum thickness and a minimum thickness of the non-flat layer may be from about 220 nanometers (nm) to about 2 microns (μm). A film for writing may include: a first layer; and/or a second layer on the first layer. The first layer may be configured to transmit first and second light beams of different frequency bands. The second layer may be configured to transmit the first light beam, but to reflect the second light beam.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
       [0001]    This application claims priority from Korean Patent Application No. 10-2014-0123702, filed on Sep. 17, 2014, in the Korean Intellectual Property Office (KIPO), the entire contents of which are incorporated herein by reference. 
       BACKGROUND 
       [0002]    1. Field 
         [0003]    Some example embodiments may generally relate to films for writing. Some example embodiments may generally relate to display apparatuses including the films for writing. 
         [0004]    2. Description of Related Art 
         [0005]    Along with rapid developments of information and communication technologies today, a video apparatus (e.g., a portable terminal), may include not only functions like phone call and text message, but also functions including digital multimedia broadcasting (DMB), Moving Picture Experts Group (MPEG)-1 or MPEG-2 Audio Layer III (MP3) players, games, facsimiles, e-mails, etc., thus being a complex portable computer. 
         [0006]    The portable computer may also be used as an electronic learning device for education. An electronic learning device may remotely maximize interactions between an educator and an educatee. If notes handwritten by an educatee and an educator are shared in real time, smooth interactions between the educator and the educatee may be maximized. 
         [0007]    However, many currently available mobile terminals may not support a handwriting function for writing thereon with a pen. Even mobile terminals supporting a handwriting function may include screen units for writing with little roughness. Therefore, users thereof may fail to get impressions like actual handwriting (e.g., the feel associated with actual handwriting). Therefore, there may be a limit for using handwriting function of a portable device. 
       SUMMARY 
       [0008]    Some example embodiments may provide films for writing with designated surface roughnesses. 
         [0009]    Some example embodiments may provide display apparatuses that include films for writing with designated surface roughnesses. 
         [0010]    Some example embodiments may provide films for writing that transmit light of visible ray wavelengths and reflect light of particular wavelengths. 
         [0011]    Some example embodiments may provide display apparatuses that include films for writing that transmit light of visible ray wavelengths and reflect light of particular wavelengths. 
         [0012]    In some example embodiments, a film for writing may comprise: a rough layer, comprising a non-flat surface, configured to transmit a first light beam and a second light beam of different wavelength bands; and/or a photonic crystal layer, arranged on the rough layer, configured to transmit the first light beam and configured to reflect the second light beam. 
         [0013]    In some example embodiments, a difference between a maximum thickness and a minimum thickness of the rough layer may be from about 220 nanometers (nm) to about 2 microns (μm). 
         [0014]    In some example embodiments, the rough layer may be transparent. The photonic crystal layer may be transparent. 
         [0015]    In some example embodiments, the non-flat surface of the rough layer may comprise: a first surface perpendicular to a direction in which the first light beam is configured to travel; and/or a second surface parallel to the direction in which the first light beam is configured to travel. 
         [0016]    In some example embodiments, the rough layer may have a mesh structure comprising a plurality of openings. 
         [0017]    In some example embodiments, at least one of the diameter of each of the plurality of openings and a distance between openings adjacent to each other may be less than or equal to a wavelength of the second light beam. 
         [0018]    In some example embodiments, the rough layer may further comprise: a plurality of lines spaced apart from one another. 
         [0019]    In some example embodiments, at least one of width of each of the plurality of lines and a distance between lines adjacent to each other may be less than or equal to a wavelength of the second light beam. 
         [0020]    In some example embodiments, the rough layer may further comprise: a plurality of protrusions spaced apart from one another. 
         [0021]    In some example embodiments, the first light beam may be incident via a bottom surface of the photonic crystal layer. The second light beam may be incident via the non-flat surface of the rough layer. 
         [0022]    In some example embodiments, the wavelength band of the first light beam may be a visible band. The wavelength band of the second light beam may be an infrared band. 
         [0023]    In some example embodiments, in the photonic crystal layer, a plurality of layers having different refractive indexes may be alternately stacked. 
         [0024]    In some example embodiments, the photonic crystal layer may comprise: a medium; and/or a plurality of nanoparticles distributed in the medium in a lattice structure. 
         [0025]    In some example embodiments, the film for writing may further comprise: a self-curing layer in contact with the rough layer. The self-curing layer may be configured to repair damage to the self-curing layer caused by external shock. 
         [0026]    In some example embodiments, the film for writing may be configured to attach to and detach from a display apparatus. 
         [0027]    In some example embodiments, a film for writing, which transmits visible rays, may comprise: a non-flat layer. A difference between a maximum thickness and a minimum thickness of the non-flat layer may be from about 220 nanometers (nm) to about 2 microns (μm). 
         [0028]    In some example embodiments, the film for writing may further comprise: a self-curing layer in contact with the non-flat layer. The self-curing layer may be configured to repair damage to the self-curing layer caused by external shock. 
         [0029]    In some example embodiments, a display apparatus, may comprise: a display panel; and/or a film for writing on the display panel. The film for writing may comprise a rough layer, comprising a non-flat surface, configured to transmit a first light beam and a second light beam of different wavelength bands; and/or a photonic crystal layer, arranged on the rough layer, configured to transmit the first light beam and configured to reflect the second light beam. 
         [0030]    In some example embodiments, the non-flat surface of the rough layer of the film for writing may be exposed to outside of the display apparatus. 
         [0031]    In some example embodiments, the display apparatus may further comprise: a touch panel between the film for writing and the display panel. The film for writing may contact the touch panel. 
         [0032]    In some example embodiments, a film for writing may comprise: a first layer; and/or a second layer on the first layer. The first layer may be configured to transmit first and second light beams of different frequency bands. The second layer may be configured to transmit the first light beam, but to reflect the second light beam. 
         [0033]    In some example embodiments, the first layer may be a non-flat layer. 
         [0034]    In some example embodiments, a difference between a maximum thickness and a minimum thickness of the first layer may be greater than or equal to about 220 nanometers (nm) and less than or equal to about 2 microns (μm). 
         [0035]    In some example embodiments, the first layer may be transparent. 
         [0036]    In some example embodiments, the second layer may be transparent. 
         [0037]    In some example embodiments, the second layer may comprise a plurality of nanoparticles. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0038]    The above and/or other aspects and advantages will become more apparent and more readily appreciated from the following detailed description of example embodiments, taken in conjunction with the accompanying drawings, in which: 
           [0039]      FIG. 1A  is a sectional view of a film for writing according to some example embodiments; 
           [0040]      FIG. 1B  is a plan view of the film for writing of  FIG. 1 ; 
           [0041]      FIG. 2  is a sectional view of a photonic crystal layer having a multi-layer structure; 
           [0042]      FIG. 3  is a diagram showing a photonic crystal layer including nanoparticles; 
           [0043]      FIGS. 4A through 4C  are diagrams showing films for writing including various types of rough layers; 
           [0044]      FIGS. 5 through 7  are diagrams showing films for writing according to some example embodiments; 
           [0045]      FIG. 8  is a diagram showing that a film for writing according to some example embodiments is attached to a display screen of a display apparatus; 
           [0046]      FIG. 9  is a diagram showing a display apparatus including a film for writing; 
           [0047]      FIG. 10  is a diagram showing a portion of a display apparatus including a touch panel, according to some example embodiments; 
           [0048]      FIG. 11  is a diagram schematically showing a display apparatus including a separate pen detecting module according to some example embodiments; 
           [0049]      FIG. 12  is a diagram showing an optical pen for detecting reflected lights, according to some example embodiments; and 
           [0050]      FIG. 13  is a diagram showing a display apparatus in which a detecting area and a display area are separately arranged. 
       
    
    
     DETAILED DESCRIPTION 
       [0051]    Example embodiments will now be described more fully with reference to the accompanying drawings. Embodiments, however, may be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. Rather, these example embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope to those skilled in the art. In the drawings, the thicknesses of layers and regions may be exaggerated for clarity. 
         [0052]    It will be understood that when an element is referred to as being “on,” “connected to,” “electrically connected to,” or “coupled to” to another component, it may be directly on, connected to, electrically connected to, or coupled to the other component or intervening components may be present. In contrast, when a component is referred to as being “directly on,” “directly connected to,” “directly electrically connected to,” or “directly coupled to” another component, there are no intervening components present. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. 
         [0053]    It will be understood that although the terms first, second, third, etc., may be used herein to describe various elements, components, regions, layers, and/or sections, these elements, components, regions, layers, and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer, and/or section from another element, component, region, layer, and/or section. For example, a first element, component, region, layer, and/or section could be termed a second element, component, region, layer, and/or section without departing from the teachings of example embodiments. 
         [0054]    Spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “upper,” and the like may be used herein for ease of description to describe the relationship of one component and/or feature to another component and/or feature, or other component(s) and/or feature(s), as illustrated in the drawings. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. 
         [0055]    The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting of example embodiments. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes,” and/or “including,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
         [0056]    Example embodiments may be described herein with reference to cross-sectional illustrations that are schematic illustrations of idealized example embodiments (and intermediate structures). As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, example embodiments should not be construed as limited to the particular shapes of regions illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. For example, an implanted region illustrated as a rectangle will typically have rounded or curved features and/or a gradient of implant concentration at its edges rather than a binary change from implanted to non-implanted region. Likewise, a buried region formed by implantation may result in some implantation in the region between the buried region and the surface through which the implantation takes place. Thus, the regions illustrated in the figures are schematic in nature, their shapes are not intended to illustrate the actual shape of a region of a device, and their shapes are not intended to limit the scope of the example embodiments. 
         [0057]    Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which example embodiments belong. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and should not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
         [0058]    Although corresponding plan views and/or perspective views of some cross-sectional view(s) may not be shown, the cross-sectional view(s) of device structures illustrated herein provide support for a plurality of device structures that extend along two different directions as would be illustrated in a plan view, and/or in three different directions as would be illustrated in a perspective view. The two different directions may or may not be orthogonal to each other. The three different directions may include a third direction that may be orthogonal to the two different directions. The plurality of device structures may be integrated in a same electronic device. For example, when a device structure (e.g., a memory cell structure or a transistor structure) is illustrated in a cross-sectional view, an electronic device may include a plurality of the device structures (e.g., memory cell structures or transistor structures), as would be illustrated by a plan view of the electronic device. The plurality of device structures may be arranged in an array and/or in a two-dimensional pattern. 
         [0059]    Reference will now be made to example embodiments, which are illustrated in the accompanying drawings, wherein like reference numerals may refer to like components throughout. 
         [0060]      FIG. 1A  is a sectional view of a film for writing  100  according to some example embodiments, and  FIG. 1B  is a plan view of the film for writing  100  of  FIG. 1A . The film for writing  100  includes a rough layer  110 , which has a non-flat surface and transmits both a first light beam and a second light beam of different wavelength bands, and a photonic crystal layer  120 , which transmits the first light beam but reflects the second light beam due to a photonic band gap characteristic. The film for writing  100  may be arranged at the outermost location of a display apparatus. Therefore, a user may write on the film for writing  100 . Here, the first light beam may be light emitted by a display apparatus via the photonic crystal layer  120  and the rough layer  110 , whereas the second light beam may be light that is incident from outside via a surface of the rough layer  110 , reflected by the photonic crystal layer  120 , and is emitted back to outside via the rough layer  110 . 
         [0061]    The rough layer  110  includes a non-flat surface, where the surface may have a surface roughness. Therefore, when a user writes on the surface of the rough layer  110  by contacting a writing tool (e.g., a pen), the user may get impressions like actual handwriting due to the surface roughness of rough layer  110 . 
         [0062]    For the rough layer  110  to have a surface roughness, the rough layer  110  may have an embossed surface as shown in  FIG. 1A . In other words, thickness ‘t’ of the rough layer  110  may not be uniform. The thickness T may include a first thickness t 1  and a second thickness t 2  alternately. For example, the rough layer  110  may include a plurality of protrusions  112  in a direction in which light travels. The protrusions  112  may have a polygonal shape, such as a triangular shape or a rectangular shape, a circular shape, an elliptical shape, and any of various other shapes. 
         [0063]    The plurality of protrusions  112  may be 2-dimensionally (2D) arranged. Therefore, the rough layer  110  may include a first surface S 1  corresponding to the first thickness t 1 , a second surface S 2  corresponding to the second thickness t 2 , and a third surface S 3  interconnecting the first surface S 1  and the second surface S 2 . The first surface S 1  and the second surface S 2  may be arranged next to each other at different heights, where the third surface S 3  may be arranged in perpendicular to the first surface S 1  and the second surface S 2 . The first through third surfaces S 1 , S 2 , and S 3  may have equal areas and, thus, surface roughness of the rough layer  110  may be uniform. Although  FIG. 1A  shows that the thickness ‘t’ of the rough layer  110  includes the first thickness t 1  and the second thickness t 2 , it is merely for convenience of explanation, and thickness ‘t’ of the rough layer  110  is not limited thereto. The rough layer  110  may include three or more thicknesses different from one another. 
         [0064]    A first light beam and a second light beam of different wavelength bands may be transmitted through the rough layer  110  according to some example embodiments. The rough layer  110  may exhibit a transmittance of about 91% or higher with respect to lights of a wavelength band from about 400 nm to about 800 nm. A wavelength band of the first light beam may be narrower than that of the second light beam. The wavelength band of the first light beam may cover shorter wavelengths than the wavelength band of the second light beam. For example, the wavelength band of the first light beam may be a visible band (e.g., wavelength from about 400 nm to about 700 nm), whereas the wavelength band of the second light beam may be an infrared band (e.g., wavelengths from about 700 nm to about 1 millimeter (mm)). However, the inventive concepts are not limited thereto. 
         [0065]    The second light beam may be, for example, in a wavelength band from about 700 nm to about 1,050 nm (although in the infrared band, these wavelengths may be visible to a user). However, the inventive concepts are not limited thereto. 
         [0066]    The wavelength band of the first light beam may be, for example, an ultraviolet band (e.g., wavelength from about 10 nm to about 400 nm), whereas the wavelength band of the second light beam may be the visible band (e.g., wavelengths from about 400 nm to about 700 nm). However, the inventive concepts are not limited thereto. 
         [0067]    The first light beam may be, for example, in a wavelength band from about 310 nm to about 400 nm (although in the ultraviolet band, these wavelengths may be visible to a user). However, the inventive concepts are not limited thereto. 
         [0068]    The wavelength band of the first light beam may be, for example, a portion of the visible band (e.g., wavelength from about 400 nm to about 500 nm), whereas the wavelength band of the second light beam also may be a portion of the visible band (e.g., wavelengths from about 600 nm to about 700 nm). However, the inventive concepts are not limited thereto. 
         [0069]    The first light beam may be, for example, in a wavelength band from about 310 nm to about 700 nm. However, the inventive concepts are not limited thereto. Having the wavelength band of the first beam outside of or overlapping the visible band may impact the color perception of a user. 
         [0070]    The second light beam may be, for example, in a wavelength band from about 400 nm to about 1,050 nm. However, the inventive concepts are not limited thereto. Having the wavelength band of the second beam in or overlapping the visible band may impact the color perception of a user. 
         [0071]    The rough layer  110  may have a regular pattern. The regular pattern may extend in on, two, or three dimensions of the rough layer  110 . The rough layer  110  may not have a regular pattern, as long as the rough layer  110  provides a desired surface roughness or provides the feel associated with actual handwriting. 
         [0072]    The first light beam may be incident via the photonic crystal layer  120  and may be transmitted through the rough layer  110 . Furthermore, the second light beam may be incident via a surface of the rough layer  110 , reflected by the photonic crystal layer  120 , and may be emitted back to outside via the rough layer  110 . The first surface S 1  and the second surface S 2  of the rough layer  110  may be perpendicular to a direction in which the first light beam travels, whereas the third surface S 3  may be parallel to the direction in which the first light beam travels. Therefore, reflection of the first light beam due to the rough layer  110  may be reduced. 
         [0073]    A distance ‘d’ between two different thicknesses of the rough layer  110  adjacent to each other may be smaller than wavelength of the second light beam. Therefore, even if the second light beam is incident to the rough layer  110  at a tilted angle, diffuse reflection of the second light beam may be reduced. For example, a distance between the first and second thicknesses t 1 -t 2  of the rough layer  110  adjacent to each other may be from about 200 nm to about 20 μm. 
         [0074]    Furthermore, to reduce diffuse reflection of the second light beam even in case where the second light beam is incident to the rough layer  110  at a tilted angle, width ‘w’ of the protrusions  112  inside the rough layer  110  may be smaller than wavelength of the second light beam. For the same reason, a distance ‘d’ between the protrusions  112  of the rough layer  110  adjacent to each other may be smaller than wavelength of the second light beam. For example, at least one of the width ‘w’ of the protrusions  112  and the distance ‘d’ between the protrusions  112  adjacent to each other may be from about 200 nm to about 20 μm. 
         [0075]    The rough layer  110  may be formed of a transparent material. For example, the rough layer  110  may be formed of glass. 
         [0076]    The rough layer  110  shown in  FIGS. 1A and 1B  is merely an example, and the rough layer  110  may have any of various other structures with non-flat surfaces. Some of the various other structures that may be applied to the rough layer  110  will be described below. 
         [0077]    Due to photonic band gap characteristic of the photonic crystal layer  120 , the first light beam may be transmitted through the photonic crystal layer  120 , whereas the second light beam may be reflected by the photonic crystal layer  120 . 
         [0078]    The photonic crystal layer  120  may include photonic crystals that form a photonic band gap for reflecting the second light beam. The term “photonic crystal” refers to an artificial crystal that is formed by periodically arranging materials with different dielectric constants to form a photonic band gap (PBG) in the energy spectrum of electromagnetic waves. When lights are incident to a photonic crystal, lights of most wavelengths are transmitted through the photonic crystals without diffusion. However, a reflective area through which light of particular wavelengths (or frequencies) may not be transmitted is formed, where the reflective area is referred to as a photonic band gap. When light having a wavelength (or frequency) within the photonic band gap is incident to a photonic crystal, the light is unable to propagate into the photonic crystal and is reflected. As described above, a photonic crystal has both selective light transmitting characteristics and selective light reflecting characteristics. A photonic crystal is formed by periodically arranging dielectric materials, where size or location of a photonic band gap may vary based on refraction indexes of dielectric materials and periodic structures. 
         [0079]      FIG. 2  is a sectional view of a photonic crystal layer  120   a  having a multi-layer structure. As shown in  FIG. 2 , the photonic crystal layer  120   a  may have a structure in which a plurality of layers  121  and  122  having different refractive indexes n 1  and n 2  are alternately stacked. Wavelengths of light to reflect may depend on thicknesses of the respective layers, a difference between refractive indexes of the respective layers, etc. The greater the difference between refractive indexes is, the narrower the wavelength band of light to reflect may become. In the photonic crystal layer  120   a  according to some example embodiments, a plurality of different layers may be alternately stacked to reflect the second light beam. 
         [0080]    The plurality of layers  121  and  122  of the photonic crystal layer  120   a  may be replaced using optical filters to achieve the selective light transmitting characteristics and selective light reflecting characteristics. For example, dichroic filters may be used to control light transmitting and reflecting characteristics in wavelength bands including infrared, visible, and ultraviolet light. Such dichroic filters may include a series of optical coatings. A suitable bandpass filter, for example, may include selected longpass and shortpass filters. 
         [0081]    The plurality of layers  121  and  122  of the photonic crystal layer  120   a  may be replaced using optical filters to achieve the selective light transmitting and reflecting characteristics. For example, guided-mode resonance filters may be used to control light transmitting and reflecting characteristics in wavelength bands including infrared, visible, and ultraviolet light. Such guided-mode resonance filters may include a series of optical coatings. The number of layers required for a guided-mode resonance filter may be fewer than required for an equivalent dichroic filter. 
         [0082]      FIG. 3  is a diagram showing a photonic crystal layer  120   b  including nanoparticles. As shown in  FIG. 3 , the photonic crystal layer  120   b  may include a medium  123  and nanoparticles  124  dispersed in the medium  123 . The nanoparticles  124  may be charged and be dispersed in the medium  123  in a lattice-like structure. In the photonic crystal layer  120   b,  the nanoparticles  124  are regularly dispersed based on electrokinetic phenomena and form a photonic crystal structure. Photonic band gap depends on a distance ‘d’ between nanoparticles or size of nanoparticles. Therefore, due to the size of nanoparticles in the photonic crystal layer  120   b  or a distance ‘d’ between the same, the photonic crystal layer  120   b  may reflect the second light beam. 
         [0083]    The photonic crystal layer  120   b  may be replaced using thin-film optics to achieve the selective light transmitting characteristics and selective light reflecting characteristics. For example, photonic crystals more generally may be used to control light transmitting and reflecting characteristics in wavelength bands including infrared, visible, and ultraviolet light. 
         [0084]    Although  FIG. 1A  shows an embossed pattern of the surface of the rough layer  110  that is not flat, the inventive concepts are not limited thereto. The rough layer  110  may include any of various other patterns having surface roughness.  FIGS. 4A through 4C  are diagrams showing films for writing including various types of rough layers. As shown in  FIG. 4A , a rough layer  110   a  may be formed to have a mesh-like structure including a plurality of openings  114 . 
         [0085]    The plurality of openings  114  may be 2-dimensionally (2D) and periodically arranged. The openings  114  may have a polygonal shape, such as a triangular shape or a rectangular shape, a circular shape, elliptical shape, and any of various other shapes. Size of the openings  114 , a distance ‘d’ between the openings  114 , and thickness ‘t’ of the openings  114  may be constant. Since size of the openings  114 , a distance ‘d’ between the openings  114 , and thickness T of the openings  114  are constant, the rough layer  110   a  may have a uniform surface roughness. At least one from among size of the openings  114 , a distance ‘d’ between the openings  114 , and thickness T of the openings  114  may be smaller than or equal to wavelength of the second light beam. For example, at least one from among size of the openings  114 , a distance ‘d’ between the openings  114 , and thickness T of the openings  114  may from about 200 nm to about 20 μm. Particularly, if the openings  114  smaller than wavelength of the second light beam are periodically arranged, transmittance of the second light beam may be improved due to surface plasmon resonance. 
         [0086]    Alternatively, as shown in  FIG. 4B , a rough layer  110   b  may include a plurality of lines  116  arranged apart from one another. A material constituting the lines  116  may be transparent. For example, the lines  116  may include glass. In  FIG. 4B , the lines  116  are arranged in the y-axis direction. However, the inventive concepts are not limited thereto. The lines  116  may also be arranged in the x-axis direction. Widths of the lines  116  and a distance ‘d’ between the lines  116  may be from about 200 nm to about 20 μm. 
         [0087]    Alternatively, as shown in  FIG. 4C , a rough layer  110   c  may include a plurality of protrusions  118  arranged apart from one another. The plurality of protrusions  118  may be 2-dimensionally (2D) and periodically arranged. The protrusions  118  may have a polygonal shape, such as a triangular shape or a rectangular shape, a circular shape, elliptical shape, and any of various other shapes. Size of the protrusions  118 , a distance ‘d’ between the protrusions  118 , and thickness ‘t’ of the protrusions  118  may be smaller than or equal to wavelength of the second light beam. For example, at least one from among size of the protrusions  118 , a distance ‘d’ between the protrusions  118 , and thickness ‘t’ of the protrusions  118  may from about 200 nm to about 20 μm. 
         [0088]      FIGS. 5 through 7  are diagrams showing films for writing according to some example embodiments. Compared to the film for writing  100  of  FIG. 1 , a film for writing  200  of  FIG. 5  may further include a self-curing layer  130  for curing a scratch. Since the rough layer  110  and the photonic crystal layer  120  of  FIG. 5  are identical to those described above, detailed descriptions thereof will be omitted. 
         [0089]    The self-curing layer  130  may be arranged on a surface of the rough layer  110 . When self-curing layer  130  is damaged by a scratch, the scratch is repaired by the self-curing layer  130  as time passes, so that the scratch may become hardly visible. 
         [0090]    The self-curing layer  130  may be based on an acrylic resin and may contain surface-treated silica and an acrylate that hardens when exposed to light. The self-curing layer  130  may further include a fluorine-based compound. Furthermore, the self-curing layer  130  may be formed of a material formed by adding a resin composition including acryl-modified polyester polyol and melamine hardener to siloxane-modified epoxy resin, or may be formed of a resin composition containing an acrylic resin, an aliphatic polyester resin, a silicon-modified polyacrylate resin, a polydimethyl siloxane, an alkoxy silane compound, an aliphatic isocyanate hardner, etc. Furthermore, in the self-curing layer  130 , nano-sized or micro-sized capsules may be distributed in an acrylic resin. Therefore, when an external shock is applied to the self-curing layer  130 , capsules displaced due to the external shock may return to original locations, thereby repairing any damage caused by the external shock. 
         [0091]    The self-curing layer  130  may prevent the film for writing  200  from being damaged by usage of a pen. Furthermore, although the surface roughness of the rough layer  110  is insufficient, the restoration of the self-curing layer  130  to its original form after being deformed by pressure applied using a pen increases the surface roughness of the film for writing  200 . Furthermore, hardness of the self-curing layer  130  may be less than that of the rough layer  110 , thereby reducing awkwardness of handwriting experience on a mobile terminal or a portable device. 
         [0092]    A film for writing  300  of  FIG. 6  may further include a base layer  140  which is arranged on the photonic crystal layer  120 . Since the rough layer  110  and the photonic crystal layer  120  of  FIG. 5  are identical to those described above, detailed descriptions thereof will be omitted. 
         [0093]    The base layer  140  may be highly adhesive with respect to other layers. Therefore, for example, the base layer  140  may contain at least one from among polyethylene terephthalate (PET), polyethylene terephthalate co-polymer (co-PET), polymethyl metacrylate (PMMA), and polymethyl metacrylate co-polymer (co-PMMA). Hardness of the base layer  140  may be greater than that of a layer arranged on the base layer  140 . Therefore, the base layer  140  may protect a display apparatus. 
         [0094]    A film for writing  400  of  FIG. 7  may include the base layer  140  on the rough layer  110 , instead of the photonic crystal layer  120 . In some cases, the photonic crystal layer  120  may be omitted. The photonic crystal layer  120  may be selectively arranged based on type of a pen paired with the film for writing  400 . Furthermore, although not shown, the film for writing  400  may include the base layer  140 , the rough layer  110 , and the self-curing layer  130 . 
         [0095]    The films for writing  100 ,  200 ,  300 , and  400  may be arranged on a display screen of a display apparatus. Here, the display apparatus may refer to any of various display apparatuses, such as organic light emitting display (OLED) apparatus, a plasma display panel (PDP), a flat cathode ray tube (FCRT), a vacuum fluorescent display (VFD) panel, a light emitting diode (LED) panel, and a liquid crystal display (LCD) panel, and may be either a portable display apparatus or a stationary display apparatus. 
         [0096]      FIG. 8  is a diagram showing that a film for writing  500  according to some example embodiments is attached to a display screen of a display apparatus  550 . As shown in  FIG. 8 , an adhesive layer  150  may be further arranged on the bottom surface of the film for writing  500 . Therefore, the film for writing  500  may be detachably attached to a front surface  560  of the display apparatus  550  via the adhesive layer  150 . The films for writing  100 ,  200 ,  300 , and  400  may be applied to the film for writing  500  of  FIG. 8 . However, since the film for writing  500  is arranged on a display screen of the display apparatus  550 , the film for writing  500  may be formed of a material that transmits lights emitted by the display apparatus  550 . 
         [0097]    Although the film for writing  500  of  FIG. 8  may be attached to and detached from a display apparatus, the inventive concepts are not limited thereto. The film for writing  500  may also be integrated with a display apparatus. 
         [0098]      FIG. 9  is a diagram showing a display apparatus including the film for writing  600 . As shown in  FIG. 9 , the display apparatus includes a display panel  620 , a light polarizing plate  630 , and the film for writing  600 . Although the display apparatus further includes other components (e.g., a driving circuit, a backlight unit, etc.), those components are omitted for convenience of explanation. 
         [0099]    The display panel  620  receives light from a backlight unit (not shown) and displays an image in response to a driving signal from a driving circuit (not shown). 
         [0100]    The display panel  620  includes an array substrate  10 , a color filter substrate  20 , a liquid crystal layer  40  interposed between the array substrate  10  and the color filter substrate  20 , and a sealant  30 . 
         [0101]    The array substrate  10  is formed by forming a pixel array layer  12 , in which a plurality of pixels are arranged in a matrix shape, on a first base substrate  11 . Although not shown, each of the pixel is defined by gate lines and data lines, which are formed to cross each other and be insulated from each other, and includes a thin-film transistor (TFT) and a pixel electrode electrically connected to the TFT. The TFT switches a voltage applied to the pixel electrode. A data line applies a pixel voltage to a corresponding TFT, whereas a gate line applies a gate voltage to a correspond TFT. Therefore, each pixel applies a pixel voltage to a pixel electrode in response to a gate voltage. 
         [0102]    The array substrate  10  and the color filter substrate  20  are combined with each other to face each other. The color filter substrate  20  is formed by forming a color array layer  22  on a second base substrate  21 . The color array layer  22  includes a color filter layer, a black matrix, and a common electrode. The color filter layer includes a plurality of color pixels respectively corresponding to the plurality of pixels, and the black matrix is formed at a location corresponding to the gate lines and the data lines. The common electrode is formed on the plurality of color pixels and the black matrix and faces the pixel electrodes. A common reference voltage is applied to the common electrode. Therefore, as transmittance of the liquid crystal layer  40  is controlled based on a potential difference between a pixel voltage and the common voltage, an image is displayed on the display panel  620 . 
         [0103]    The liquid crystal layer  40  is injected into the space between the array substrate  10  and the color filter substrate  20  via drop filling method or vacuum injection method. Alignment direction of liquid crystals constituting the liquid crystal layer  40  is changed based on a potential difference between a pixel voltage and the common voltage, and transmittance of light provided by a backlight unit varies based on the alignment direction. 
         [0104]    The sealant  30  is interposed between the array substrate  10  and the color filter substrate  20 , and combines the array substrate  10  and the color filter substrate  20  to each other. Furthermore, the sealant  30  seals the space between the array substrate  10  and the color filter substrate  20  to prevent the liquid crystal layer  40  from leaking out. 
         [0105]    The light polarizing plate  630  is attached onto the display panel  620  and polarizes light provided to the display panel  620 . The light polarizing plate  630  may be formed to have a multilayer structure that includes not only a layer including a polarizer, but also a supporting layer for maintaining durability, mechanical strength, and heat resistance of the light polarizing plate  630 , an anti-static (AS) layer for preventing a static electricity generated by the light polarizing plate  630  from flowing into a display panel, etc. 
         [0106]    The film for writing  600  may be attached on the top surface of the light polarizing plate  630 . The films for writing  100 ,  200 ,  300 , and  400  as described above may be applied as the film for writing  600 . If the film for writing  600  is integrated with the display apparatus, it may be necessary for the film for writing  600  to include a base layer to prevent the display apparatus from being damaged. 
         [0107]    Although a LCD display apparatus is shown as an example of display apparatuses, it is merely for convenience of explanation, and the inventive concepts are not limited thereto. The display apparatus may also include an organic light emitting display apparatus (OLED), a plasma display panel (PDP), a flat cathode ray tube (FCRT), a vacuum fluorescent display panel (VFD), a light emitting diode (LED) panel, etc. 
         [0108]    Furthermore, a display apparatus may further include a touch panel.  FIG. 10  is a diagram showing a portion of a display apparatus including a touch panel, according to some example embodiments. The touch panel may be a resistive-film type or an electrostatic-capacitance type, where the latter is exemplified in  FIG. 10 . As shown in  FIG. 10 , a display apparatus  700  may include a display panel  710  and a touch panel  720 , which is arranged on the display panel  710  to receive touch inputs. Here, the display panel  710  may not only be the display panel  620  as shown in  FIG. 9 , but also be any of various other display panels including an organic light emitting display panel. 
         [0109]    Referring to  FIG. 10 , the touch panel  720  includes a base layer  721 , a plurality of conductive detecting cells  722  formed below the base layer  721 , and location detecting lines  723  for connecting the conductive detecting cells  722  to an external driving circuit. 
         [0110]    The conductive detecting cells  722  are formed at a touch activating area on a surface of the base layer  721  by using a transparent electrode material, such as indium-tin-oxide (ITO) and includes first detecting cells  722   a  connected in a first direction and second detecting cells  722   b  connected in a second direction, where the second direction is different from the first direction. The first detecting cells  722   a  and the second detecting cells  722   b  may be arranged on a same layer, and may be connected in the first direction and the second direction by first connecting patterns (not shown) and second connecting patterns (not shown) that are insulated from each other by interposing an insulation layer therebetween or may be arranged on different layers by interposing an insulation layer therebetween. 
         [0111]    When an object, such as a man&#39;s hand or a stylus pen, contacts the touch panel  720 , changes of electrostatic capacitance based on contacted locations are transmitted from the conductive detecting cells  722  to a driving circuit (not shown) via the location detecting lines  723 . 
         [0112]    Furthermore, the film for writing  100  as shown in  FIG. 1  may be arranged on the base layer  721 . Alternatively, the photonic crystal layer  120  of the film for writing  100  may function as the base layer  721  of the touch panel  720 . Although the film for writing  100  of  FIG. 1  is shown in  FIG. 10 , the inventive concepts are not limited thereto, and any of various types of films as described above may be applied. 
         [0113]    Pens that may be paired with the film for writing according to some example embodiments may include an optical pen using light and a digital pen using electromagnetic signals. A stylus pen employed for a touch panel is a digital pen. Furthermore, the film for writing may include a reflective type, for which movement of a pen is detected by the pen, and a transmissive type, for which movement of a pen is detected by another device (e.g., a display apparatus). Generally, movement of a digital pen is detected by a display apparatus, for example. Therefore, the transmissive film for writing may be employed. The transmissive film for writing does not necessarily include the photonic crystal layer  120  as described above. 
         [0114]    A device employing a transmissive film for writing may further include a separate pen detecting module other than a touch panel.  FIG. 11  is a diagram schematically showing a display apparatus including a separate pen detecting module according to some example embodiments. As shown in  FIG. 11 , a display apparatus  800  may include a film  810  to be contacted by a pen  900 , a touch panel  820  for detecting a user&#39;s touch, a display panel  830  for outputting images, and a pen detecting module  840  for detecting movement of the pen  900 . Although the pen detecting module  840  is arranged below the display panel  830  in  FIG. 11 , the inventive concepts are not limited thereto. The pen detecting module  840  may also be arranged above the display panel  830 . A detecting mechanism of the pen detecting module  840  may be integrated with a tip of the pen  900 . For example, if a source of the pen  900  emits light, the pen detecting module  840  may include an optical sensor. If a source of the pen  900  emits a magnetic field, the pen detecting module  840  may include a magnetic sensor. Since it is optional for a transmissive film to reflect particular light, the photonic crystal layer  120  as described above may be omitted. 
         [0115]    Meanwhile, light emitted by a pen may be detected after being reflected by the film for writing  100 . For example, a pen may detect movement of the pen by detecting reflected lights.  FIG. 12  is a diagram showing an optical pen for detecting reflected lights, according to some example embodiments. As shown in  FIG. 12 , an optical pen  1000  includes a housing  1010 , a light source  1020 , which is arranged in the housing  1010  and emits light to a film for writing  100 , a sensor  1030  for detecting lights reflected by the film for writing  100 , a control unit  1040  for obtaining information regarding movement of the optical pen  1000  by using the detected lights, and a communication unit  1050  for transmitting information regarding movement of the optical pen  1000  to an external device (e.g., a display apparatus). Information regarding movement of the optical pen  1000  may include images and/or texts. The film for writing  100  of  FIG. 12  may not only be the film for writing  100  of  FIG. 1 , but also be the films for writing  100 ,  200 , and  300  of  FIGS. 2 through 6 . The modified rough layers  110   a  through  110   c  may also be applied. 
         [0116]    The film for writing  100  may be arranged on a display screen of a display apparatus. However, the inventive concepts are not limited thereto. The film for writing  100  may be applied not only to a display apparatus, but also an electronic device with pen writing function. Furthermore, the film for writing  100  may also be arranged at an area of a display apparatus other than a display screen.  FIG. 13  is a diagram showing a display apparatus in which a detecting area and a display area are separately arranged. As shown in  FIG. 13 , a display apparatus  1300  may be divided into a writing area  1310 , to which information is input based on movement of a pen, and a display area  1320 , which displays information. The outermost layer of the writing area  1310 , that is, a layer contacting outside may be the film for writing  100  as described above. Since no image is displayed at the writing area  1310 , it is not necessary for the film for writing  100  to be transparent. In other words, at least one layer of the film for writing  100  may be formed of a non-transparent material. 
         [0117]    As described above, according to one or more of the above example embodiments, since a film for writing has a designated surface roughness, the film for writing may provide a handwriting experience on a mobile terminal or portable device similar to that when using a pen to write on paper. Furthermore, pen usage on a mobile terminal or portable device may increase. 
         [0118]    It should be understood that the example embodiments described herein should be considered in a descriptive sense only and not for purposes of limitation. Descriptions of features or aspects within each embodiment should typically be considered as available for other similar features or aspects in other embodiments. 
         [0119]    Although example embodiments have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these example embodiments without departing from the principles and spirit of the disclosure, the scope of which is defined by the claims and their equivalents.