Numerical aspects of noise simulation in MOSFETs by a Langevin–Boltzmann solver
Numerical aspects of noise simulation in MOSFETs by a Langevin–Boltzmann solver
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DOI：
10.1007/s10825-014-0642-4
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发表时间：
2015-03
影响因子：
2.1
通讯作者：
Dino Ruić;C. Jungemann
中科院分区：
文献类型：
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作者：
Dino Ruić;C. Jungemann
我们提出的方法来解决耦合组的玻尔兹曼，薛定谔和泊松方程的确定性，自洽和同时的牛顿方法的MOSFET。我们展示了如何小信号和噪声分析，可以实现一个封闭的二维电子气与薛定谔方程和泡利原理的充分列入非常高的工作精度和稳定性。我们展示了从动能到总能量的转换如何导致玻尔兹曼方程时间导数中的额外项，而平衡状态下器件的互惠性对数值实现产生了限制。薛定谔方程的加入导致了在用拉莫-肖克利定理推导终端电流时对守恒律的非平凡修正。此外，我们展示了我们的方法的有效性，并展示了如何非自洽的解决方案强烈不同意我们的自洽方法。
We present methods to solve the coupled set of Boltzmann, Schrödinger and Poisson equations deterministically, self-consistently and simultaneously by a Newton approach for a MOSFET. We show how small signal and noise analyses can be implemented for a confined 2D electron gas with the full inclusion of the Schrödinger equation and the Pauli principle with very high working precision and stability. We show how the transformation from the kinetic energy to the total energy leads to an additional term in the time derivative of the Boltzmann equation while reciprocity of the device in equilibrium puts constraints onto the numerical implementation. The inclusion of the Schrödinger equation results in non-trivial modifications to conservation laws when deriving the terminal currents with the Ramo–Shockley theorem. Furthermore, we show the validity of our methods and demonstrate how non-self-consistent solutions strongly disagree with our self-consistent approach.