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2 TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2 Papadopoulos George J.

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Tunnelling effects of a Gaussian wave packet impinging on a barrier

Papadopoulos George J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2020

Vol. 24, No 1

83--91

A general procedure based on momentum-like quantity provides the reflection and transmission amplitudes for a given barrier sandwiched by semiconductor reservoirs is presented. Furthermore, the evolution of the wave function stemming from an initial Gaussian wave packet located on the left hand side of the barrier with ignorable barrier overlap is obtained. The evolving wave function enables obtaining the associated probability and current densities space and time-wise. As application, the case of smooth double barrier is considered. The numerical results exhibit similar picture as obtained via propagator in the limited case of square barrier, e.g. repeated current density reversal at the barrier entrance, while being unidirectional at the exit. Presently, the treatment takes account of any barrier, inclusive of applied voltage. The basic quantity required is the value of the momentum-like quantity at the barrier entrance, which is obtained solving a Riccati equation governing the quantity, in question, whose value is known at the barrier exit in terms of the carrier energy and applied bias.

Tunneling throught a barrier under transverse magnetic field and I-V characteristic

Papadopoulos George J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2018

Vol. 22. No 2

125--133

The case whereby the transmission coefficient through a barrier, sandwiched by semiconductor reservoirs, under bias is provided by a general formula involving the logarith micwave function derivative at the barrier entrance is now extended to include the influence of magnetic field perpendicular to the longitudinal barrier direction. Under the circumstances, theequation governing the logarithmic wave function derivative is appropriately modified via aneffective potential energy which takes account of the magnetic field. Subsequently, the procedurefor obtaining the transmission coefficient is applied to the case involving a smooth double, as wellas quadruple, barrier for which theI-V characteristic is obtained. The results show reduction incurrent with increase in the magnetic field, up to a certain value of bias. Furthermore, increasein temperature exhibits increase in current as well as movement of the current peaks in the I-V curves towards lower bias.