Abstract
Numerical solution of the time-dependent Schrödinger equation for open system structures has been impeded by the difficulty in handing open-system boundary conditions. This paper presents a new numerical method for time-dependent Schrödinger equation and a boundary condition method to simulate the interaction with ideal particle reservoirs at the structure boundaries.
Highlights
The time-dependent Schr6dinger equation is readily solved numerically for the case where,I, may be set to zero at the boundaries of the simulation [1], the open nature of the semiconductor device problem requires the formulation of nonzero boundary conditions to model the interaction of the device with particle reservoirs at the contacts, for both the time-dependent and the time-independent case [2]
Boundary conditions are imposed which model to second-order plane waves of constant amplitude incident at the contacts, and waves with modulated amplitude and phase exiting the contacts without reflection
Assuming that to a good approximation the variation of C(x) near the boundary may be regarded as a second-order term, the time-dependent Schr6dinger equation at the boundary becomes where t(x) li2k 0 C(x) "4
Summary
The time-dependent Schr6dinger equation is readily solved numerically for the case where ,I, may be set to zero at the boundaries of the simulation [1], the open nature of the semiconductor device problem requires the formulation of nonzero boundary conditions to model the interaction of the device with particle reservoirs at the contacts, for both the time-dependent and the time-independent case [2]. The implementation of this type of boundary condition for the timedependent problem proves to be a formidable task.
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