• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.243-256
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• 2022

In 1914, Bohr proved that there is an r₀ ∈ (0, 1) such that if a power series ∑^∞_m=0 c_mz^m is convergent in the open unit disc and |∑^∞_m=0 c_mz^m| < 1 then, ∑^∞_m=0 |c_mz^m| < 1 for |z| < r₀. The largest value of such r₀ is called the Bohr radius. In this article, we find Bohr radius for some univalent harmonic mappings having different dilatations. We also compute the Bohr radius for functions that are convex in one direction.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.321-337
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• 2000

• Transactions on Electrical and Electronic Materials
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• v.4 no.1
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• pp.29-33
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• 2003

Europium doped yttrium oxide submicron-sized particles were prepared by ultrasonic aerosol pyrolysis. To examine the size effect of submicron-sized-particle, the photoluminescence of the particles was investigated. The particle size was controlled by pH, reaction temperature, molar concentration of yttrium in precursor solution. The PL intensity of submicron-sized particles was decreased with particles size. When the particle size is above about 150 times of Bohr radius of Y$_2$O$_3$, the optical property of the particles shows the bulk characteristics.

• Proceedings of the Korean Society Of Semiconductor Equipment Technology
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• 2003.12a
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• pp.109-116
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• 2003

Amorphous GaN Quantum dots(a-GaN QDs) with particle diameters less than bohr radius(~11nm) were successfully fabricated at room temperature by a laser ablation of high densified GaN target. Transmission electron microscopy, SAED diffraction pattern and X-ray photoelectron spectroscopy confirmed the presence of a-GaN QDs with particle size of 7.9, 6.9, 4.4nm under the Ar gas pressures of 50, 100 and 200 Pa, respectively. The room temperature PL and absorbance spectra showed a strong band emission centered at 3.9 eV in a-GaN QDs made under the gas pressures of 100 and 200 Pa, which is nearly 0.5eV blueshifted with respect to the bulk crystal band gap.

• Proceedings of the Korean Vacuum Society Conference
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• 2012.08a
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• pp.189-189
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• 2012

Lead sulfide (PbS) nanocrystal quantum dots (NQDs) are promising materials for various optoelectronic devices, especially solar cells, because of their tunability of the optical band-gap controlled by adjusting the diameter of NQDs. PbS is a IV-VI semiconductor enabling infrared-absorption and it can be synthesized using solution process methods. A wide choice of the diameter of PbS NQDs is also a benefit to achieve the quantum confinement regime due to its large Bohr exciton radius (20 nm). To exploit these desirable properties, many research groups have intensively studied to apply for the photovoltaic devices. There are several essential requirements to fabricate the efficient NQDs-based solar cell. First of all, highly confined PbS QDs should be synthesized resulting in a narrow peak with a small full width-half maximum value at the first exciton transition observed in UV-Vis absorbance and photoluminescence spectra. In other words, the size-uniformity of NQDs ought to secure under 5%. Second, PbS NQDs should be assembled carefully in order to enhance the electronic coupling between adjacent NQDs by controlling the inter-QDs distance. Finally, appropriate structure for the photovoltaic device is the key issue to extract the photo-generated carriers from light-absorbing layer in solar cell. In this step, workfunction and Fermi energy difference could be precisely considered for Schottky and hetero junction device, respectively. In this presentation, we introduce the strategy to obtain high performance solar cell fabricated using PbS NQDs below the size of the Bohr radius. The PbS NQDs with various diameters were synthesized using methods established by Hines with a few modifications. PbS NQDs solids were assembled using layer-by-layer spin-coating method. Subsequent ligand-exchange was carried out using 1,2-ethanedithiol (EDT) to reduce inter-NQDs distance. Finally, Schottky junction solar cells were fabricated on ITO-coated glass and 150 nm-thick Al was deposited on the top of PbS NQDs solids as a top electrode using thermal evaporation technique. To evaluate the solar cell performance, current-voltage (I-V) measurement were performed under AM 1.5G solar spectrum at 1 sun intensity. As a result, we could achieve the power conversion efficiency of 3.33% at Schottky junction solar cell. This result indicates that high performance solar cell is successfully fabricated by optimizing the all steps as mentioned above in this work.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2009.04b
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• pp.7-7
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• 2009

Lead telluride (PbTe) is a very promising thermoelectric material due to its narrow band gap (0.31 eV at 300 K), face-centered cubic structure and large average excitonic Bohr radius (46 nm) allowing for strong quantum confinement within a large range of size. In this work, we present the thermoelectric properties of individual single-crystalline PbTe nanowires grown by a vapor transport method. A combination of electron beam lithography and a lift-off process was utilized to fabricate inner micron-scaled Cr (5 nm)/Au (130 nm) electrodes of Rn (resistance of a near electrode), Rf (resistance of a far electrode) and a microheater connecting a PbTe nanowire on the grid of points. A plasma etching system was used to remove an oxide layer from the outer surface of the nanowires before the deposition of inner electrodes. The carrier concentration of the nanowire was estimated to be as high as $3.5{\times}10^{19}\;cm^{-3}$. The Seebeck coefficient of an individual PbTe nanowire with a radius of 68 nm was measured to be $S=-72{\mu}V/K$ at room temperature, which is about three times that of bulk PbTe at the same carrier concentration. Our results suggest that PbTe nanowires can be used for high-efficiency thermoelectric devices.

• Proceedings of the Korean Vacuum Society Conference
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• 2012.08a
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• pp.413-413
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• 2012

Lead sulfide (PbS) Colloidal quantum dots (CQDs) are promising material for the photovoltaic device due to its various outstanding properties such as tunable band-gap, solution processability, and infrared absorption. More importantly, PbS CQDs have large exciton Bohr radius of 20 nm due to the uniquely large dielectric constants that result in the strong quantum confinement. To exploit desirable properties in photovoltaic device, it is essential to fabricate a device exhibiting stable performance. Unfortunately, the performance of PbS NQDs based Schottky solar cell is considerably degraded according to the exposure in the air. The air-exposed degradation originates on the oxidation of interface between PbS NQDS layer and metal electrode. Therefore, it is necessary to enhance the stability of Schottky junction device by inserting a passivation layer. We investigate the effect of insertion of passivation layer on the performance of Schottky junction solar cells using PbS NQDs with band-gap of 1.3 eV. Schottky solar cell is the simple photovoltaic device with junction between semiconducting layer and metal electrode which a significant built-in-potential is established due to the workfunction difference between two materials. Although the device without passivation layer significantly degraded in several hours, considerable enhancement of stability can be obtained by inserting the very thin LiF layer (<1 nm) as a passivation layer. In this study, LiF layer is inserted between PbS NQDs layer and metal as an interface passivation layer. From the results, we can conclude that employment of very thin LiF layer is effective to enhance the stability of Schottky junction solar cells. We believe that this passivation layer is applicable not only to the PbS NQDs based solar cell, but also the various NQDs materials in order to enhance the stability of the device.