• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.2
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• pp.27-38
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• 2002

A new self-consistent mathematical model for semiconductor quantum well device was developed. The model was based on the direct solution of the Boltzmann transport equation, coupled to the Schrodinger and Poisson equations. The solution yielded the distribution function for a two-dimensional electron gas(2DEG) in quantum well devices. To solve the Boltzmann equation, it was transformed into a tractable form using a Legendre polynomial expansion. The Legendre expansion facilitated analytical evaluation of the collision integral, and allowed for a reduction of the dimensionality of the problem. The transformed Boltzmann equation was then discretized and solved using sparce matrix algebra. The overall system was solved by iteration between Poisson, Schrodinger and Boltzmann equations until convergence was attained.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.2
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• pp.14-26
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• 2002

A new model for degenerate semiconductor quantum well devices was developed. In this model, the multi-subband Boltzmann transport equation was formulated by applying the Pauli exclusion principle and coupled to the Schrodinger and Poisson equations. For the solution of the resulted nonlinear system, the finite difference method and the Newton-Raphson method was used and carrier energy distribution function was obtained for each subband. The model was applied to a Si MOSFET inversion layer. The results of the simulation showed the changes of the distribution function from Boltzmann like to Fermi-Dirac like depending on the electron density in the quantum well, which presents the appropriateness of this modeling, the effectiveness of the solution method, and the importance of the Pauli -exclusion principle according to the reduced size of semiconductor devices.

• ETRI Journal
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• v.32 no.1
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• pp.68-72
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• 2010

The coupling between the transverse and longitudinal components of the channel electron motion in NMOS devices leads to a reduction in the barrier height. Therefore, this study theoretically investigates the effects of the in-plane velocity of channel electrons on the capacitance-voltage characteristics of nano NMOS devices under inversion bias. Numerical calculation via a self-consistent solution to the coupled Schrodinger equation and Poisson equation is used in the investigation. The results demonstrate that such a coupling largely affects capacitance-voltage characteristic when the in-plane velocity of channel electrons is high. The ballistic transport ensures a high in-plane momentum. It suggests that such a coupling should be considered in the quantum capacitance-voltage modeling in ballistic transport devices.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.7 s.337
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• pp.5-12
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• 2005

The device performance of nano-scale center-channel (CC) double-gate (DG) MOSFET structure was investigated by numerically solving coupled Schr$\"{o}$dinger-Poisson and current continuity equations in a self-consistent manner. The CC operation and corresponding enhancement of current drive and transconductance of CC-NMOS are confirmed by comparing with the results of DG-NMOS which are performed under the condition of 10-80 nm gate length. Device optimization was theoretically performed in order to minimize the short-channel effects in terms of subthreshold swing, threshold voltage roll-off, and drain-induced barrier lowering. The simulation results indicate that DG-MOSFET structure including CC-NMOS is a promising candidates and quantum-mechanical modeling and simulation calculating the coupled Schr$\"{o}$dinger-Poisson and current continuity equations self-consistently are necessary for the application to sub-40 nm MOSFET technology.