• Journal of the Korean Magnetics Society
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• v.18 no.1
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• pp.36-38
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• 2008

We calculate the electron scattering amplitude with reduced angular momentum expansion(RAME) and compare it with the plane wave approximation. By using WKB approximation it is shown that the curvature correction factor given by RAME is originated from the source wave centrifugal potential energy. The factor also can be understood as an effective wave number correction factor in plane wave approximation. Angular momentum and its relationship with scattering amplitude is explicitly shown.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.48 no.2
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• pp.141-146
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• 1999

The eigenvalue equations of multiple waveguides with step-index profile are derived by using the WKB theory. Phase changes unique to step-index discontinuity areintroduced when applying the WKB connection formula to turning points. The transfer matrix method is employed for the analysis of multiple structure and the derived eigenvalue equation are represented in the recursive form. The results by the WKB are compared with those by the FEM for a three-waveguide coupler.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.7
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• pp.1311-1316
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• 2016

This paper analyzes the influence of tunneling current on threshold voltage shift by channel length of short channel asymmetric double gate(DG) MOSFET. Tunneling current significantly increases by decrease of channel length in the region of 10 nm below, and the secondary effects such as threshold voltage shift occurs. Threshold voltage shift due to tunneling current is not negligible even in case of asymmetric DGMOSFET to develop for reduction of short channel effects. Off current consists of thermionic and tunneling current, and the ratio of tunneling current is increasing with reduction of channel length. The WKB(Wentzel-Kramers-Brillouin) approximation is used to obtain tunneling current, and potential distribution in channel is hermeneutically derived. As a result, threshold voltage shift due to tunneling current is greatly occurred for decreasing of channel length in short channel asymmetric DGMOSFET. Threshold voltage is changing according to bottom gate voltages, but threshold voltage shifts is nearly constant.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.5
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• pp.992-997
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• 2016

This paper analyzes the deviation of tunneling current for the ratio of top and bottom gate oxide thickness of short channel asymmetric double gate(DG) MOSFET. The ratio of tunneling current for off current significantly increases if channel length reduces to 5 nm. This short channel effect occurs for asymmetric DGMOSFET having different top and bottom gate oxide structure. The ratio of tunneling current in off current with parameters of channel length and thickness, doping concentration, and top/bottom gate voltages is calculated in this study, and the influence of tunneling current to occur in short channel is investigated. The analytical potential distribution is obtained using Poisson equation and tunneling current using WKB(Wentzel-Kramers-Brillouin). As a result, tunneling current is greatly changed for the ratio of top and bottom gate oxide thickness in short channel asymmetric DGMOSFET, specially according to channel length, channel thickness, doping concentration, and top/bottom gate voltages.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.7
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• pp.1617-1622
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• 2015

This paper analyzes the ratio of tunneling current for channel doping concentration of sub-10 nm asymmetric double gate(DG) MOSFET. The ratio of tunneling current for off current in subthreshold region increases in the region of channel length of 10 nm below. Even though asymmetric DGMOSFET is developed to reduce short channel effects, the increase of tunneling current in sub-10 nm is inevitable. As the ratio of tunneling current in off current according to channel doping concentration is calculated in this study, the influence of tunneling current to occur in short channel is investigated. To obtain off current to consist of thermionic emission and tunneling current, the analytical potential distribution is obtained using Poisson equation and tunneling current using WKB(Wentzel-Kramers-Brillouin). As a result, tunneling current is greatly changed for channel doping concentration in sub-10 nm asymmetric DGMOSFET, specially with parameters of channel length, channel thickness, and top/bottom gate oxide thickness and voltage.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.1
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• pp.163-168
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• 2015

This paper analyzed the deviation of tunneling current for bottom gate voltage of sub-10 nm asymmetric double gate MOSFET. The asymmetric double gate MOSFET among multi gate MOSFET developed to reduce the short channel effects has the advantage to increase the facts to be able to control the channel current, compared with symmetric double gate MOSFET. The increase of off current is, however, inescapable if aymmetric double gate MOSFET has the channel length of sub-10 nm. The influence of tunneling current was investigated in this study as the portion of tunneling current for off current was calculated. The tunneling current was obtained by the WKB(Wentzel-Kramers-Brillouin) approximation and analytical potential distribution derived from Poisson equation. As a results, the tunneling current was greatly influenced by bottom gate voltage in sub-10 nm asymmetric double gate MOSFET. Especially it showed the great deviation for channel length, top and bottom gate oxide thickness, and channel thickness.

• Journal of the Korean Chemical Society
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• v.22 no.4
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• pp.202-220
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• 1978

Uniform semiclassical (WKB) solutions are obtained for nonseparable systems without using a close coupling formalism and are given explicitly in terms of well known analytic functions for various physically interesting and realistic cases. They do not become singular at turning points or surfaces and when taken in their asymptotic forms, they reduce to the usual WKB solutions that could be obtained if the Stokes phenomenon was properly taken care of for solutions. In obtaining such uniform solutions, the Schroedinger equations for nonseparable systems are suitably "renormalized" to solvable "normal" forms through certain transformations. Ehrenfest's adiabatic principle plays an important guiding role for obtaining such "renormalized" uniform solutions for nonseparable systems. The eigenvalues of the Hamiltonian can be calculated from the extended Bohr-Sommerfeld quantization rules when appropriate classical trajectories are obtained. An application is made to many-electron systems and for one of the simplest examples to show the utility of the method the approximate wavefunction is calculated of the ground state helium atom.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.10
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• pp.1815-1821
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• 2006

In this paper, the subthreshold swing has been analyzed for FinFET under channel length of 20nm. The analytical current model has been developed , including thermionic current and tunneling current models. The potential distribution by Poisson equation and carrier distribution by Maxwell-Boltzman statistics are used to calculate thermionic emission current and WKB(Wentzel-Kramers-Brillouin) approximation to tunneling current. The cutoff current is obtained by simple adding two currents since two current is independent. The subthreshold swings by this model are compared with those by two dimensional simulation and two values agree well. Since the tunneling current increases especially under channel length of 10nm, the characteristics of subthreshold swing is degraded. The channel and gate oxide thickness have to be fabricated as am as possible to decrease this short channel effects, and this process has to be developed. The subthreshold swings as a function of channel doping concentrations are obtained. Note that subthreshold swings are resultly constant at low doping concentration.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2006.05a
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• pp.865-868
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• 2006

In this paper, the subthreshold swing has been analyzed for double gate FinFET under channel length of 20nm. The analytical current model has been developed, including thermionic current and tunneling current models. The potential distribution by Poisson equation and carrier distribution by Maxwell-Boltzman statistics are used to calculate thermionic emission current, and WKB(Wentzel-Framers-Brillouin) approximation to tunneling current. The cutoff current is obtained by simple adding two currents since two current is independent. The subthreshold swings by this model are compared with those by two dimensional simulation and two values are good agreement. Since the tunneling current increases especially under channel length of 10nm, the characteristics of subthreshold swing is degraded. The channel and gate oxide thickness have to be fabricated as thin as possible to decrease this short channel effects and this process has to be developed. The subthreshold swings as a function of channel doping concentrations are obtained.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2006.05a
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• pp.869-872
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• 2006

In this paper, the threshold voltage roll-off been analyzed for nano structure double gate FinFET. The analytical current model has been developed , including thermionic current and tunneling current models. The potential distribution by Poisson equation and carrier distribution by Maxwell-Boltzman statistics are used to calculate thermionic emission current, and WKB(Wentzel- framers-Brillouin) approximation to tunneling current. The threshold voltage roll-offs are obtained by simple adding two currents since two current is independent. The threshold voltage roll-off by this model are compared with those by two dimensional simulation and two values are good agreement. Since the tunneling current increases especially under channel length of 10nm, the threshold voltage roll-off Is very large. The channel and gate oxide thickness have to be fabricated as thin as possible to decrease this short channel effects and this process has to be developed.