• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.437-443
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• 2001

In this paper the inverse problems for the Dirac Operator are studied. A set of values of eigenfunctions in some internal point and spectrum are taken as a data. Uniqueness theorems are obtained. The approach that was used in the investigation of inverse problems for interior spectral data of the Sturm-Liouville operator is employed.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.2
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• pp.117-122
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• 2016

Recently, the detection of pH with real-time and in vivo has been focal pointed in the environmental or medical fields. In this work, we developed the pH sensor using graphene sheet. Graphene has high biocompatibility. We fabricated flexible solution-gated field-effect transistors (SGFETs) on graphene sheet transferred on the polyethylene terephthalate (PET) substrate to detect pH in electrolyte solution. The gate length was $500{\mu}m$ and the gate width was 8 mm. We evaluated the current-voltage (I-V) transfer characteristics of graphene SGFETs in pH solution. The drain-source current ($I_{DS}$) and the gate-source voltage ($V_{GS}$) curves of graphene SGFETs were depended on pH value. The Dirac point of graphene SGFETs linearly shifted to the positive direction about 19.32 mV/pH depending on the pH value in electrolyte solution.

• Proceedings of the Korean Vacuum Society Conference
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• 2011.08a
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• pp.119-119
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• 2011

This study examined the synthesis of large area graphene and the change of its characteristics depending on the ratio of CH4/H2 by using the thermal CVD methods and performed the experiments to control the electron-hole conduction and Dirac-point of graphene by using chemical doping methods. Firstly, with regard to the characteristics of the large area graphene depending on the ratio of CH4/H2, hydrophobic characteristics of the graphene changed to hydrophilic characteristics as the ratio of CH4/H2 reduces. The angle of contact also increased to 78$^{\circ}$ from 58$^{\circ}$. According to the results of Raman spectroscopy showing the degree of defect, the ratio of I(D)/I(G) increases to 0.42% from 0.25% and the surface resistance also increased to 950 ${\Omega}$ from 750 ${\Omega}$/sq. As for the graphene synthesis at the high temperature of 1,000$^{\circ}$ by using CH4/H2 in a Cu-Foil, the possibility of graphene formation was determined as a function of the ratio of H2 included in the fixed quantity of CH4 as per specifications of every equipment. It was observed that the excessive amount of H2 prevented graphene from forming, as extra H-atoms and molecules activated the reaction to C-bond of graphene. Secondly, in the experiment for the electron-hole conduction and the Dirac-point of graphene using the chemical doping method, the shift of Dirac-point and the change in the electron-hole conduction were observed for both the N-type (PEI) and the P-type (Diazonium) dopings. The ID-VG results show that, for the N-type (PEI) doped graphene, Dirac-point shifted to the left (-voltage direction) by 90V at an hour and by 130 V at 2 hours respectively, compared to the pristine graphene. Carrier mobility was also reduced by 1,600 cm2/Vs (1 hour) and 1,100 cm2/Vs (2 hours), compared to the maximum hole mobility of the pristine graphene.

• Proceedings of the Korean Vacuum Society Conference
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• 2016.02a
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• pp.170.1-170.1
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• 2016

$Bi_2Te_3$ has long been studied for its excellent thermoelectric characteristics. Recently, this material has been known as a topological insulator (TI). The surface states within the bulk band gap of a TI, which are protected by the time reversal symmetry, contribute to the conduction at the surface, while the bulk is in insulating state. In contrast to the bulk defects tuning the chemical potential to the Dirac energy, the native defects near the surface are expected not to change the shape of the Fermi surface and the related spin structure. Using scanning tunneling microscopy (STM), we have systematically characterized surface or near surface defects in p- and n- doped $Bi_2Te_3$, and identified their structure by first principles calculations. In addition, bias-polarity dependences of STM images revealed the electron donor/acceptor nature of each defect. A detailed theoretical study of the surface states near the Dirac energy reveals the robustness of the Dirac point, which verifies the effectiveness of the disturbance on the backscattering from various kinds of defects.

• Proceedings of the Korean Vacuum Society Conference
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• 2014.02a
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• pp.114.1-114.1
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• 2014

Copper is considered to be the most promising substrate for the growth of high-quality and large area graphene by chemical vapor deposition (CVD), in particular, on the (111) facet. Because the interactions between graphene and Cu substrates influence the orientation, quality, and properties of the synthesized graphene, we studied the interactions using angle-resolved photoemission spectroscopy. The evolution of both the Shockley surface state of the Cu(111) and the p band of the graphene was measured from the initial stage of CVD growth to the formation of a monolayer. Graphene growth was initiated along the Cu(111) lattice, where the Dirac band crossed the Fermi energy ($E_F$) at the K point without hybridization with the d-band of Cu. Then two rotated domains were additionally grown as the area covered with graphene became wider. The Dirac energy was about 0.4 eV and the energy of the Shockley surface state of Cu(111) shifted toward the $E_F$) by 0.15 eV upon graphene formation. These results indicate weak interactions between graphene and Cu, and that the electron transfer is limited to that between the Shockley surface state of Cu(111) and the p band of graphene. This weak interaction and slight lattice mismatch between graphene and Cu resulted in the growth of rotated graphene domains ($9.6^{\circ}$ and $8.4^{\circ}$), which showed no significant differences in the Dirac band with respect to different orientations. These rotated graphene domains resulted in grain boundaries which would hinder a large-sized single monolayer growth on Cu substrates.

• Proceedings of the Korean Vacuum Society Conference
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• 2013.08a
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• pp.146.2-146.2
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• 2013

Copper is considered to be the most promising substrate for the growth of high-quality and large area graphene by chemical vapor deposition (CVD), in particular, on the (111) facet. Because the interactions between graphene and Cu substrates influence the orientation, quality, and properties of the synthesized graphene, we studied the interactions using angle-resolved photoemission spectroscopy. The evolution of both the Shockley surface state of the Cu(111) and the ${\pi}$ band of the graphene was measured from the initial stage of CVD growth to the formation of a monolayer. Graphene growth was initiated along the Cu(111) lattice, where the Dirac band crossed the Fermi energy (EF) at the K point without hybridization with the d-band of Cu. Then two rotated domains were additionally grown as the area covered with graphene became wider. The Dirac energy was about -0.4 eV and the energy of the Shockley surface state of Cu(111) shifted toward the EF by ~0.15 eV upon graphene formation. These results indicate weak interactions between graphene and Cu, and the electron transfer is limited to that between the Shockley surface state of Cu(111) and the ${\pi}$ band of graphene. This weak interaction and slight lattice mismatch between graphene and Cu resulted in the growth of rotated graphene domains ($9.6^{\circ}$ and $8.4^{\circ}$), which showed no significant differences in the Dirac band with respect to different orientations. These rotated graphene domains resulted in grain boundaries which would hinder a large-sized single monolayer growth on Cu substrates.

• Proceedings of the Materials Research Society of Korea Conference
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• 2012.05a
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• pp.67.1-67.1
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• 2012

Graphene has attracted much attention for future nanoelectronics due to its superior electrical properties. Owing to its extremely high carrier mobility and controllable carrier density, graphene is a promising material for practical applications, particularly as a channel layer of high-speed FET. Furthermore, the planar form of graphene is compatible with the conventional top-down CMOS fabrication processes and large-scale synthesis by chemical vapor deposition (CVD) process is also feasible. Despite these promising characteristics of graphene, much work must still be done in order to successfully develop graphene FET. One of the key issues is the process technique for gate dielectric formation because the channel mobility of graphene FET is drastically affected by the gate dielectric interface quality. Formation of high quality gate dielectric on graphene is still a challenging. Dirac voltage, the charge neutral point of the device, also strongly depends on gate dielectrics. Another performance killer in graphene FET is source/drain contact resistance, as the contact resistant between metal and graphene S/D is usually one order of magnitude higher than that between metal and silicon S/D. In this presentation, the key issues on graphene-based FET, including organic-inorganic hybrid gate dielectric formation, controlling of Dirac voltage, reduction of source/drain contact resistance, device structure optimization, graphene gate electrode for improvement of gate dielectric reliability, and CVD graphene transfer process issues are addressed.

• Proceedings of the Korean Vacuum Society Conference
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• 2016.02a
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• pp.291.1-291.1
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• 2016

Graphene by one of the two-dimensional (2D) materials has been focused on electronic applications due to its ultrahigh carrier mobility, outstanding thermal conductivity and superior optical properties. Although graphene has many remarkable properties, graphene devices have low on/off current ratio due to its zero bandgap. Despite considerable efforts to open its bandgap, it's hard to obtain appropriate improvements. To solve this problem, heterojunction barristor was proposed based on graphene. Mostly, this heterojunction barristor is made by transition metal dichalcogenides (TMDs), such as molybdenum disulfide ($MoS_2$) and tungsten diselenide ($WSe_2$), which have extremely thickness scalability of TMDs. The heterojunction barristor has the advantage of controlling graphene's Fermi level by applying gate bias, resulting in barrier height modulation between graphene interface and semiconductor. However, charged impurities between graphene and $SiO_2$ cause unexpected p-type doping of graphene. The graphene's Fermi level modulation is expected to be reduced due to this p-doping effect. Charged impurities make carrier mobility in graphene reduced and modulation of graphene's Fermi level limited. In this paper, we investigated theoretically and experimentally a relevance between graphene's Fermi level and p-type doping. Theoretically, when Fermi level is placed at the Dirac point, larger graphene's Fermi level modulation was calculated between -20 V and +20 V of $V_{GS}$. On the contrary, graphene's Fermi level modulation was 0.11 eV when Fermi level is far away from the Dirac point in the same range. Then, we produced two types heterojunction barristors which made by p-type doped graphene and graphene treated 2.4% APTES, respectively. On/off current ratio (32-fold) of graphene treated 2.4% APTES was improved in comparison with p-type doped graphene.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1071-1084
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• 2000

We show that a weak solution of the Cauchy problem for he nonlinear Schrodinger equation, {i∂(sub)t u + ∂$^2$(sub)x u = f(u,u), t∈(-T,T), x∈R, u(0,x) = ø(x).} in the negative solbolev space H(sup)s has a smoothing effect up to real analyticity if the initial data only have a single point singularity such as the Dirac delta measure. It is shown that for H(sup)s (R)(s>-3/4) data satisfying the condition (※Equations, See Full-text) the solution is analytic in both space and time variable. The argument is based on the recent progress on the well-posedness result by Bourgain [2] and Kenig-Ponce-Vega [18] and previous work by Kato-Ogawa [12]. We give an improved new argument in the regularity argument.

• Proceedings of the Korean Vacuum Society Conference
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• 2016.02a
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• pp.280.2-280.2
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• 2016

The graphene, a single atomic sheet of graphite, has attracted tremendous interest owing to its novel properties including high intrinsic mobility, optical transparency and flexibility. However, for more diverse application of graphene devices, it is essential to tune its transport behavior by shifting Dirac Point (DP) of graphene. So, in the following context, we suggest a method to tune structural and electronic properties of graphene using atomic layer deposition. By atomic layer deposition of zinc oxide (ZnO) on graphene using 4-mercaptophenol as linker, we can fabricate n-doped graphene. Through ${\pi}-{\pi}$ stacking between chemically inert graphene and 4-mercaptophenol, conformal deposition of ZnO on graphene was enabled. The electron mobility of graphene TFT increased more than 3 times without considerably decreasing the hole mobility, compared to the pristine graphene. Also, it has high air stability. This ZnO doping method by atomic layer deposition can be applicable to large scale array of CVD graphene TFT.