Abstract:
A method of forming single and few layer graphene on a quartz substrate in one embodiment includes providing a quartz substrate, melting a portion of the quartz substrate, diffusing a form of carbon into the melted portion to form a carbon and quartz mixture, and precipitating at least one graphene layer out of the carbon and quartz mixture.

Description:
[0001]    This application claims the benefit of U.S. Provisional Application No. 61/655,540 filed Jun. 5, 2012, the entire contents of which are each herein incorporated by reference. 
     
    
       [0002]    This invention was made with government support under CMMI 1120577 awarded by the National Science Foundation and under N66001-08-1-2037 awarded by the Defense Advanced Research Projects Agency (DARPA). The government has certain rights in the invention. 
     
    
     TECHNICAL FIELD 
       [0003]    This invention relates generally to elemental carbon compositions and, more particularly, to products having graphene and methods of producing graphene. 
       BACKGROUND 
       [0004]    Graphene is a crystal of carbon atoms arranged in a honeycomb lattice. Single and few-layer graphene has emerged as a promising material for novel applications in electronics because the high carrier mobility and perfect charge carrier confinement of graphene result in outstanding electronic transport properties. Graphene thus holds promises for widespread applications including field-effect transistors, super-capacitors, and sensors. The semi-metallic nature of graphene when coupled with high carrier mobility and low opacity also makes graphene a good candidate for use as a transparent conductor for photovoltaic devices, touch panels, and displays. Graphene structures also have high chemical resistance and are relatively flexible when compared to some other transparent conductor materials such as indium tin oxide (ITO). Bilayer graphene (BLG) in particular holds further promise for use in post-silicon electronics applications because a bandgap up to 250 meV can be induced in the material using an electric field, which is not possible with single or monolayer graphene (SLG), and because exciton binding energies in BLG are tunable by electric field-induced bandgap. 
         [0005]    A monolayer or single layer graphene is a plane of carbon atoms bonded in a hexagonal array. Multiple layers of graphene are typically formed by first forming a single layer of graphene and them transporting the single layer onto another layer of graphene. The main approach in fabricating graphene has been mechanical exfoliation and chemical vapor deposition (CVD). Growth of large-scale single or few-layers graphene has been shown on Cu or Ni surfaces. For device fabrication, the graphene grown on Cu or Ni is subsequently transferred onto another insulating substrate. In addition to adding complexity, the transportation step increases the risk of contaminating the graphene sheet. 
         [0006]    Recently, it has been reported that a laser technique can be used for growing graphene on a nickel foil and also for epitaxially growing graphene on SiC. A method wherein few-layer graphene was grown on a silicon substrate using a laser-based technique without any metal catalysts has also been demonstrated. These methods produce graphene on a conductive substrate, however, and a transfer process is therefore needed for fabricating a graphene device on an insulating substrate. 
         [0007]    What is needed therefore is a method of producing single or few layer graphene on a non-conductive surface. A method of producing few-layer graphene without the need to transport a single layer graphene is also needed. 
       SUMMARY 
       [0008]    A method of forming single and few layer graphene on a quartz substrate in one embodiment includes providing a quartz substrate, melting a portion of the quartz substrate, diffusing a form of carbon into the melted portion to form a carbon and quartz mixture, and precipitating graphene layer out of the carbon and quartz mixture. 
         [0009]    In another embodiment, a method of forming at least one graphene layer includes providing a quartz substrate, forming a photoresist layer portion on an upper surface of the quartz substrate, the photoresist layer portion including the form of carbon, decomposing the photoresist layer portion to release the form of carbon, and coalescing the form of carbon into at least one graphene layer on the quartz substrate. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0010]      FIG. 1  depicts a basic process which can be followed to form a graphene film; 
           [0011]      FIG. 2  depicts a quartz substrate with a form of carbon provided by a photoresist layer formed on the upper surface of the quartz substrate in accordance with the process of  FIG. 1 ; 
           [0012]      FIG. 3  depicts a quartz wafer positioned on the upper layer of the photoresist layer of  FIG. 2  above the portion of the quartz substrate which is to be melted so as to trap the form of carbon above the upper surface of the quartz substrate when the form of carbon is released from the photoresist; 
           [0013]      FIG. 4  depicts a continuous wave laser heating the photoresist layer portion within a nitrogen gas atmosphere; 
           [0014]      FIG. 5  depicts the configuration of  FIG. 4  with the laser de-energized after the photoresist layer has been decomposed to release the form of carbon and the upper surface of the quartz substrate has been melted by heat transferred from the released form of carbon, some of which diffuses into the melted quartz to form a quartz/carbon mixture; 
           [0015]      FIG. 6  depicts the configuration of  FIG. 5  after the quartz wafer has been removed and the melted quartz has cooled resulting in precipitation and/or coalescence of one or more graphene layers on the formerly melted portion of the quartz substrate; 
           [0016]      FIG. 7  depicts an optical micrograph of a 4×4 graphene dot array with a spacing of 250 μm formed in accordance with the process of  FIG. 1 ; 
           [0017]      FIG. 8  depicts a magnified optical micrograph of a graphene dot of  FIG. 7 ; 
           [0018]      FIG. 9  depicts an AFM image of the graphene dot of  FIG. 8 ; 
           [0019]      FIG. 10  depicts a magnified AFM image of a central area of the graphene dot of  FIG. 9 ; 
           [0020]      FIG. 11  depicts Raman mapping of the ID/IG ratio of the graphene dot of  FIG. 8 ; 
           [0021]      FIG. 12  depicts Raman mapping of the I2D/IG ratio of the graphene dot of  FIG. 8 ; 
           [0022]      FIG. 13  depicts the Raman spectra from the marked points in  FIGS. 11 and 12 ; 
           [0023]      FIG. 14  depicts optical micrographs of the graphene dot of  FIG. 8  at different times during irradiation with a continuous wave laser; 
           [0024]      FIG. 15  depicts the corresponding Raman spectra recorded from the center of the laser-irradiated areas in  FIG. 14 ; 
           [0025]      FIG. 16  depicts the intensity of ratios ID/IG and I2D/IG of the graphene dots in  FIG. 14  as a function of growth time; 
           [0026]      FIG. 17  depicts a top plan view of a laser formed graphene film or dot interconnecting a plurality of contacts; and 
           [0027]      FIG. 18  depicts a chart of the sheet resistances between different contacts in the device of  FIG. 17 . 
       
    
    
     DETAILED DESCRIPTION 
       [0028]    For the purposes of promoting an understanding of the principles of the disclosure, reference will now be made to the embodiments illustrated in the drawings and described in the following written specification. It is understood that no limitation to the scope of the disclosure is thereby intended. It is further understood that the present disclosure includes any alterations and modifications to the illustrated embodiments and includes further applications of the principles of the disclosure as would normally occur to one skilled in the art to which this disclosure pertains. 
         [0029]    A graphene dot is formed generally in accordance with a process  130  shown in  FIG. 1 . At block  132 , a quartz substrate is provided. A form of carbon is then provided above an upper surface of the quartz substrate at block  134 . The form of carbon is heated and coalesced into a graphene spot of one or more layers at block  136 . 
         [0030]    Additional detail for one example of the process  130  is described with initial reference to  FIG. 2 . Initially, a quartz substrate  140  was provided. The quartz substrate in this example was a 1×2 cm quartz wafer which was cleaned by ultra-sonication in methanol, acetone, and DI water for 3 minutes. The quartz substrate  140  was then dried by high purity N 2  gas. 
         [0031]    A photoresist layer  142  in the form of a photoresist film was spin-coated on an upper surface  144  of the quartz substrate  140 . The photoresists layer  142  was a 1:6 diluted S-1805 photoresist solution spun at 10,000 rpm. The resulting thickness of the photoresists layer  142  was less than 100 nm. While the photoresist layer  142  is shown in  FIG. 2  as covering only a portion of the upper surface  144 , in some embodiments, the photoresist layer  142  covers the entire upper surface  144 . Once the desired photoresist layer  142  is formed, the quartz substrate  140  was baked for 5 minutes at 120° C. 
         [0032]    Next, a quartz wafer  146  was positioned over the photoresist layer  142  (see  FIG. 3 ). The quartz wafer  146  was previously cleaned and dried in the same manner as the quartz substrate  140 . The quartz substrate  140  and quartz wafer  146  were then fixed on a high precision piezoelectric stage and a DC motorized stage by two clamps in a growth chamber (not shown). 
         [0033]    The growth chamber was pumped and purged with a high-purity N 2  gas, and maintained at a pressure below 0.1 Torr. A beam  148  from a continuous wave (CW) Nd:YAG laser (Coherent Verdi) with a wavelength of 532 nm and a beam width of about 45 microns was focused on the S-1805 photoresist layer  142  through the transparent quartz wafer  146  using a lens of 150 mm focal length as depicted in  FIG. 4 . In this embodiment, the photoresist layer  142  was exposed to the beam  148  at 2.8 Watt for five minutes. 
         [0034]    The focused beam  148  resulted in a high temperature of the portion  150  of the photoresist layer  142  that was in the beam  148 , with the remainder of the photoresist layer  142  remaining at or about room temperature. The beam  148  thus heated the photoresist layer  142  causing the portion  150  of the photoresist layer  142  within the footprint of the beam  148  to decompose resulting in a form of carbon  152  provided in the photoresist layer  142  to be disassociated with the photoresist layer  142  as depicted in  FIG. 5 . The quartz wafer  146  inhibited movement of the form of carbon  152  while allowing some gasses formed by the decomposition of the photoresist layer  142  to escape. The beam  148  was de-energized at the end of the five minutes and the form of carbon  152  was allowed to cool. As the form of carbon  152  cooled, it precipitated and/or coalesced into one or more graphene layers  154  (see  FIG. 6 ). 
         [0035]    For purpose of this example, the quartz substrate  140  and quartz wafer  146  were then moved by the high precision piezoelectric stage and a DC motorized stage to expose a different portion of the photoresist layer  142  to the beam  148 . The high precision piezoelectric stage and DC motorized stage allow for precise positioning of the quartz substrate  140  and quartz wafer  146  with respect to the beam  148 . Accordingly, a pattern (discussed below) of one or more graphene layers  154  was formed. 
         [0036]    To better understand the formation process of the one or more graphene layers  154  optical images were taken with an optical microscope (Olympus BX40) with reflected light illumination, and atomic force microscopy (AFM) images were taken using an AFM (Veeco Dimension 3100) with the tapping mode under ambient conditions. Raman spectroscopy and mapping was performed using a laser micro-Raman systems (XploRA, with laser excitation at 532 nm) equipped with a motorized sample stage. A 100× objective lens was used, and laser spot size was ˜0.6 μm. For Raman spectroscopy, the accumulation time was 20 seconds, and for Raman mapping, each spectrum was an average of 3 acquisitions (3s of accumulation time per acquisition). 
         [0037]      FIG. 7  shows an optical micrograph of a 4×4 laser processed area of the quartz substrate  140  with a pattern  160  of one or more graphene layers  154 , with a spacing of 250 μm (horizontally and vertically as depicted) between adjacent ones of the one or more graphene layers  154 . The one or more graphene layers  154  are shown as visible, round dots with bright rings  162  surrounding the one or more graphene layers  154  as shown more clearly in  FIG. 8 . 
         [0038]    The diameter of the graphene layers or dots  154  is about 50 μm. The higher magnification optical micrograph in  FIG. 8  shows that the one or more graphene layers  154  exhibit a uniform and smooth boundary which is clearly defined by the bright rings  162 . The rings  162  exhibit a uniform brightness immediately adjacent to the one or more graphene layers  154 , with the brightness of the photoresist layer  142  gradually decreasing radially away from the rings  162  and the one or more graphene layers  154 . A circle  164  having a diameter of about 43 μm is shown in  FIG. 8 . The circle  164  corresponds to the outer boundary of the one or more graphene layers  154 , and roughly correlates with the beam width of the laser beam  148 . A circle  166  having a diameter of about 53 μm is also shown in  FIG. 8 . The circle  166  corresponds to the outer boundary of the rings  162 . 
         [0039]      FIGS. 9 and 10  are atomic force microscopy (AFM) images of the one or more graphene layers  154 . For ease of comparison, the circle  164  of  FIG. 8  is replicated in  FIG. 9 . The circle  166  of  FIG. 8  is also replicated in  FIG. 9 .  FIG. 9  shows that the height of the at least one graphene layer drops continuously from an apex  168  at the center of the at least one graphene layer  154  to a nadir  170  in the ring  162 . The apex  168  is at about the same height as the remainder of the photoresist layer  142 , while the nadir  170  is up to 300 nm lower than the center of the one or more graphene layers  154 . 
         [0040]      FIG. 10  shows the apex area  168  of the one or more graphene layer  154 .  FIG. 10  shows that the apex area  168  is relatively flat. 
         [0041]    The nature and quality of graphene dots  154  formed by laser irradiation were evaluated using Raman spectroscopy. The main hallmarks of graphene are three Raman peaks, including D (˜1350 cm −1 ), G (˜1580 cm −1 ), and 2D (˜2700 cm −1 ) bands. The D band is the so-called “defect peak” of graphene, and the intensity ratio of D to G bands (I D /I G ) is a significant parameter to identify disorder of graphene. The 2D band is the most prominent feature in the Raman spectra of graphene, and its position, shape, I 2D /I G  intensity ratio, and full width at half-maximum (FWHM) are well-established characteristics of graphene layers. 
         [0042]    The scan Raman mapping with the ratio I D /I G  and I 2D /I G  of the graphene layer  154  is shown in  FIGS. 11 and 12 , respectively. A central circular area within the circle  164  shows low I D /I G  (0.1-0.2) and high I 2D /I G  (0.7-1.0), and its size is similar to the size of laser-processed area. 
         [0043]    Between the circle  164  and  166 , I D /I G  increases from 0.3 to 0.6 while the I 2D /I G  drops from 0.7 to 0.5. Outside of the circle  166 , the I D /I G  increases abruptly to 0.8-1.0 while the I 2D /I G  drops precipitously from 0.4 near the circle  166  to about 0.1 at point “C”. Hence, the growth of graphene occurs predominantly within the circle  164  with a transition to carbon between the circle  166  and the circle  164  and then to the photoresist layer  142  (no graphene) outside of the circle  166 . 
         [0044]    The Raman spectra chart  180  shown in  FIG. 13  includes lines  182 ,  184 , and  186  which correspond to the points marked by “A”, “B” and “C” in  FIGS. 11 and 12 . There is no signal of the 2D band outside the laser processed area (circle  166 ). Rather, the wide and strong D band  188  and G band  190  reveal sp 2 -rich amorphous carbon on the surface. 
         [0045]    Within the circle  164 , strong 2D bands  192 / 194  are evidenced at 2696 cm −1  with a FWHM (2D) of 58 cm −1  at the points A and B. Monolayer graphene results in a 2D band position at 2680 cm −1  with a FWHM (2D) of 30 cm −1 . The up-shifted and wider 2D bands  192 / 194  indicate that bi- or tri-layer graphene structures were produced. 
         [0046]    The I 2D /I G  ratio from 0.7 to 1.0 within the circle  164  also indicates that the graphene layer  154  has bi- or tri-layer structure. On the other hand, the I D /I G  ratio is an indication of the graphene crystallite sizes, L a (nm), which can be estimated as L a =(2.4×10 −10 )λ 1   4 (I D /I G ), where X is the Raman laser line wavelength in nanometers. From the experimental data, the I D /I G  ratio from 0.1 to 0.2 corresponds to the graphene domain size between 96 and 192 nm. Moreover, the correlation of the size of the area of graphene formation with the size of the beam width of the laser  148  indicates that the size, shape, and location of the formed graphene can be precisely controlled by controlling the area irradiated with the laser beam  148 . 
         [0047]    From the topographical data of  FIG. 9 , it is evident that topographical remodeling occurred in the quartz substrate  140  itself. For example, the photoresist layer  142  has a thickness of less than 100 nm, yet the height excursion across the at least one graphene layer  154  approaches 300 nm. Consequently, in addition to decomposing the photoresist layer  142 , the laser beam  148  caused the quartz substrate  140  immediately below the portion  150  (see  FIG. 4 ) to melt. Since the quartz substrate  140  does not exhibit increased temperatures when directly exposed to the laser beam  148 , the heat necessary for melting the quartz substrate  140  is necessarily transmitted to the quartz substrate  140  by another mechanism. 
         [0048]    In order to investigate further the remodeling of the quartz substrate  140 , a series of microscope images and Raman spectra were obtained after varying exposure times of the quartz substrate  140 , photoresist layer  142 , and quartz wafer  146  to the laser beam  148 . The images are depicted in  FIG. 14  wherein the scale bars are each 20 μm, and the Raman spectra are depicted in  FIG. 15 . 
         [0049]    Image  200  of  FIG. 14  was taken after a five second exposure with the laser beam  148 . A careful examination of the image  200  reveals a circle beginning to form slightly inside of the circle  202 . The Raman spectra associated with the image  200  is depicted as line  204  of  FIG. 15 . The Raman spectra  204  shows a slight modification from a Raman spectra  206  which was obtained prior to exposing the quartz substrate  140 , photoresist layer  142 , and quartz wafer  146  to the laser beam  148 . The Raman spectra  202  thus indicates some disordered Raman signals which might result from fragments from decomposition of S-1805 photoresist. The Raman spectra  202  does not, however, include any indicia of graphene formation. Thus, while decomposition of the photoresist layer  142  has begun, no graphene has formed. Additionally, the lack of any ring structure indicates that the quartz substrate  140  has not begun to melt. 
         [0050]    Image  206  of  FIG. 14  was obtained after 20 seconds of exposure to the laser beam  148 . A ring  208  has started to appear and a center portion  210  is markedly darker than the surrounding photoresist layer  142 . The ring  208  is formed farther inwardly of the circle  202  than the circle identified as starting to form in image  202 . Additionally, the photoresist layer  142  outwardly of the circle  202  has lightened. This indicates that the photoresist layer  142  outwardly of the circle  202  is decomposing. 
         [0051]    The Raman spectra  212  of  FIG. 15  is associated with the image  206 . The Raman spectra  212  includes a broad D band  214  and a broad G band  216 . There is, however, no 2D band. Accordingly, the Raman spectra  212  indicates that carbon has been released from the photoresist layer  142  but has not formed graphene. Additionally, the carbon appears to be consolidating toward the center of the image  206 , hence the darkened center portion  210 . 
         [0052]    Image  220  was taken after a 40 second exposure. Noticeable changes are evident in comparing image  220  to image  206 . The diameter of the ring  208  has expanded to substantially the same size as the circle identified as starting to form in image  202 . The ring  208  is also more clearly defined. Additionally, the center portion  210  has expanded, while maintaining substantially the same shading as the smaller version of the center portion  210  in image  206 . 
         [0053]    The Raman spectra  222  of  FIG. 15  is associated with the image  220 . The Raman spectra  222  includes a better defined D band  224  and a better defined G band  226 . A slight 2D band  228  is also beginning to be evidenced. Accordingly, the Raman spectra  222  indicates that graphene has begun to form within the center portion  210 . 
         [0054]    Image  230  was taken after a one minute exposure. Further changes are evident in comparing image  230  to image  220 . The diameter of the ring  208  has expanded to substantially the same size as the circle identified as starting to form in image  202 . The ring  208  is also brighter, but the inner edge of the ring  208  is rougher than in the image  220 . Additionally, the center portion  210  has expanded, and a darker central portion  232  is evident. 
         [0055]    The Raman spectra  234  of  FIG. 15  is associated with the image  230 . The Raman spectra  234  includes a D band  236  and a G band  238  which are more clearly divided. Additionally, the D band  236  has decreased in intensity from the level of the D band  224 . A 2D band  240  is also better defined. Accordingly, the Raman spectra  234  indicates that graphene has continued to form within the center portion  210 . 
         [0056]    Image  250  was taken after a two minute exposure. The main difference when comparing image  250  to image  230  is that the darker central portion  232  has enlarged significantly. The ring  208  is also slightly brighter, and better defined than in the image  230 . 
         [0057]    The Raman spectra  252  of  FIG. 15  is associated with the image  250 . The Raman spectra  252  includes a D band  254  and a G band  256 . The D band  254  is now less intense than the G band  256 . A 2D band  258  is larger and narrower than the 2D band  240 . Accordingly, the Raman spectra  252  indicates that graphene has continued to form within the center portion  210 . 
         [0058]    Image  260  was taken after a three minute exposure. The main difference when comparing image  260  to image  250  is that the darker central portion  232  appears to extend completely to the edge of the ring  208  and the ring  208  is brighter in image  260 . The ring  208  in image  260  has also expanded in diameter, although it is still smaller in diameter than the circle  202 . 
         [0059]    The Raman spectra  262  of  FIG. 15  is associated with the image  260 . The Raman spectra  262  includes a D band  264  and a G band  266 . The D band  264  is now rather small while the size of the G band  266  is comparable to the G band  256 . The 2D band  268  intensity is greater than the 2D band  258 , and roughly equivalent to the G band  266 . Accordingly, the Raman spectra  262  indicates that graphene has continued to form within the center portion  210 . 
         [0060]    Image  270  was taken after a five minutes exposure. The main difference when comparing image  270  to image  260  is that another dark portion  272  has appeared within the darker central portion  232 . Additionally, the ring  208  has expanded to be substantially the same diameter as the circle  202 . 
         [0061]    The Raman spectra  274  of  FIG. 15  is associated with the image  270 . The Raman spectra  274  includes a D band  276  and a G band  278 . The D band  276  has become even smaller while the G band  276  is comparable to the G band  266 . The 2D band  280  remains roughly equivalent to the G band  278 . Accordingly, the Raman spectra  274  indicates that graphene has continued to form within the center portion  210 . 
         [0062]    Several conclusions are possible based upon the foregoing data. For example,  FIG. 16  shows a chart  282  of the ID/I G  ratio  284  and the I 2D /I G  ratio  286  as a function of laser processed time.  FIG. 16  indicates the graphene domain size was increasing gradually with laser illumination time, indicating the graphene crystallization process. 
         [0063]      FIGS. 14 and 15  confirm that graphene domain size was increasing gradually with laser illumination time, indicating the graphene crystallization process. After three minutes, two or three layers of graphene was been formed.  FIGS. 14 and 15  further implicate a growth mechanism wherein the focused laser beam  148  raises the temperature in the S1805 film, driving the decomposition of S-1805 to form amorphous carbon and carbon vapor. 
         [0064]    More specifically,  FIG. 9  indicated that the upper surface  144  of the quartz substrate  140  has been remodeled by melting and the ring  162 , in particular, is the result of such remodeling. Since quartz substrate  140  is not directly heated by the laser beam  148 , an intermediary is necessary.  FIG. 14  indicates that decomposition of the photoresists layer  144  precedes the remodeling of the upper surface  144 . Accordingly, one or more of the amorphous carbon and carbon vapor are the most likely candidates for transferring heat to the quartz substrate  140 . 
         [0065]    In the absence of remodeling of the quartz wafer  146  which is exposed to the carbon vapor but not the amorphous carbon, the main or sole heat transfer mechanism is the amorphous carbon in contact with the quartz substrate  140 . Consequently, the appearance of the ring  208  in image  206  indicates that amorphous carbon was formed slightly prior to the twenty second image  206 . 
         [0066]    Once the quartz substrate  140  begins to melt, at least some of the amorphous carbon is infused into the melted quartz. The carbon vapor which is trapped by the quartz wafer  146  provides another source for infusion of carbon into the melted quartz, and increases the amount of graphene which is ultimately formed. The quartz wafer  146  also acts as a thermal insulator, keeping the portion of the quartz substrate  140  within the laser beam  148  from losing heat. 
         [0067]    Once the laser beam  148  is terminated, the melted quartz begins to cool. During cooling of the melted quartz/carbon mixture, the dissolved carbon atoms are separated and nucleated. These precipitated carbon atoms form graphene segments because sp 2 -bonded graphene is energetically more favorable than sp a -rich amorphous carbon. 
         [0068]      FIG. 17  depicts a portion of a device  300  which includes a quartz substrate  302  with a plurality of contacts  304 ,  306 ,  308 ,  310 ,  312 ,  314 ,  316 , and  318  formed thereon. The contacts  304 ,  306 ,  308 ,  310 ,  312 ,  314 ,  316 , and  318  were fabricated of Ti/Au, 20 nm/80 nm, using e-beam lithography. The contacts  304 ,  306 ,  308 ,  310 ,  312 ,  314 ,  316 , and  318  are electrically connected by a graphene connector  320  which was formed in accordance with the process  130  of  FIG. 1 . The graphene connector  320  is surrounded by a ring of carbon  322 . 
         [0069]    The conducting quality of a graphene layer formed in accordance with the above described laser-induced process was evaluated using the device  300 . In the device  300 , each of the contacts  304 ,  306 ,  308 ,  310 ,  312 ,  314 ,  316 , and  318  is positioned 20 μm away from the oppositely positioned contact. Sheet resistance between oppositely position contacts was obtained by 2-point current-voltage (I-V) measurement and 4-point Van der Pauw method at the room temperature. Results of a current-voltage (I-V) measurement obtained between the oppositely positioned contacts are depicted in graph  330  of  FIG. 18 . 
         [0070]    The results depicted in  FIG. 18  reveal sheet resistance values in the range of 780-805 Ω/sq. This value is comparable with values measured for wet-transferred graphene layers (650-900 Ω/sq) and chemically reduced graphene oxide layers (700-1300 Ω/sq). The above described laser-induced process resulted in values that were lower than values of Cu-catalyzed graphene layers (50-75 Ω/sq) but much better than Ni-catalyzed graphene layers (6 k-11 kΩ/sq) and catalyst-free nanographene layers (7 k-11 kΩ/sq). Therefore, the laser-induced graphene formation process has potential applications in transparent electrode, cathode ray tube, and touch screens. 
         [0071]    The laser-induced graphene formation process described herein provides a laser-induced graphene growth method for growing graphene directly on an insulating substrate, quartz. This simple, rapid, single-step, and controllable method for synthesizing graphene has significant promise for graphene-device fabrication and applications. The laser-induced graphene formation process is in general an attractive alternative technique for materials synthesis, with the intrinsic benefits of localized, fast, and single-step synthesis. In contrast to the conventional thermal chemical vapor deposition (CVD) process, laser-induced graphene formation can produce a much higher temperature in a confined area, while the rest of the material (substrate) still maintains at the room temperature. 
         [0072]    The data presented above further indicates that as is true with the commonly used CVD approach for growing graphene on metals, the growth temperature, pressure, concentration of carbon sources, and solubility of carbon are basic factors, which contribute to the formation and quality of graphene film in the laser-induced graphene formation process. Deformation of the laser-processed area, however, suggests that the surface experienced melting in the formation of graphene. Therefore, the growth mechanism of graphene on quartz is not the same as the surface-catalyzed process or carbon dissolution and precipitation in solid metal when graphene is grown in metal. 
         [0073]    While the invention has been illustrated and described in detail in the drawings and foregoing description, the same should be considered as illustrative and not restrictive in character. Only the preferred embodiments have been presented and all changes, modifications and further applications that come within the spirit of the invention are desired to be protected.