Simulation Method of Nonlocal Quantum Tunneling Between Energy Bands with Current Conservation Property

Abstract

The invention discloses an energy interband non-local quantum tunneling simulation method with a current conservation characteristic. The method comprises the steps of generating a linear equation system which adopts a nodal value increment of a solved physical variable as a variable in a dispersing semiconductor device physical region; processing non-local quantum tunneling, determining a public energy zone for defining a first side and a second side; carrying out weight distribution on point-to-point tunneling current density and energy integral volume produced by interpolation; dividing a coefficient matrix of the linear equation system into a principal matrix caused by general differential equation dispersing and an additional coefficient matrix caused by non-local quantum tunneling with the current conservation characteristic, and storing; adopting a Gaussian origin eliminating method to solve the coefficient matrix. According to the energy interband non-local quantum tunneling simulation method with the current conservation characteristic provided by the invention, the non-local quantum tunneling current conservativeness is ensured, and the simulation error and the uncertainty brought by non-conservation are eliminated; by utilizing a method combining the principal matrix and an auxiliary incidence matrix, the coefficient linear equation system obtained through linearizing a non-linear equation system can be quickly solved, and the solving efficiency is improved.

Description

technical field [0001] The invention relates to a semiconductor device simulation method, in particular to a non-local quantum tunneling simulation method between energy bands with the characteristic of current conservation. Background technique [0002] Nonlocal quantum tunneling between different energy bands is a very common physical effect in compound semiconductor devices, which is common in many semiconductor devices, such as multi-junction solar cells and tunneling field effect transistors. How to accurately simulate this physical phenomenon is always concerned with semiconductor device physics and numerical mathematics. The usual method is to convert the point-to-point tunneling current density into a composite term of various continuity equations. The more commonly used is the Kane local model (E.O.Kane, "Zener tunneling in semiconductors", J.Phys.Chem.Solids, vol.12, pp.181-188, 1959), in this model, the energy band Non-local quantum tunneling is treated as a quan...

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Problems solved by technology

[0003] However, the above-mentioned non-local model still treats the point-to-point tunneling current as a compound item in the carrier continuity equation, and does not consider the conservation of the overall tunneling current on both sides, that is, the quantum tunneling current from one side The current density across the other side should be equal

For example, in practice, it is found that the current density on both sides of the above-mentioned non-local model will be twice as large, which will bring certain errors to the numerical analysis of the device structure.

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