用Gram Schmidt方法快速估算无结双栅MOSFET阈值电压的代数方法
An Algebraic Approach to Fast Estimation of the Threshold Voltage of Junctionless Double Gate MOSFETs Using the Gram Schmidt Method
摘要：
降低漏致势垒降低（DIBL）的效应是MOSFET家族中不期望的短沟道效应之一，其导致晶体管的阈值电压通过增加漏极的电压而降低。这种效应使得电路设计者不可能将VT视为恒定值，因此，必须将VT计算为漏极电压的函数。因此，为了在集成电路的设计中考虑DIBL的影响，对系统施加了很大的计算负担，这减慢了电路级仿真器中的仿真过程，特别是当要仿真大量晶体管时。因此，本文提出了一种使用Gram-Schmidt正交化方法的多输入单输出（MISO）非线性自回归（N-AR）模型，该模型计算新一代MOSFET的阈值电压，即，无结双栅MOSFET（JL-DG-MOSFET），具有高精度和显着的速度在计算过程中的模型。结果表明，平均而言，所提出的数值方法比最先进的分析模型快313倍。所提出的模型和解析模型之间的归一化均方误差的计算百分比平均为0.435%，表明所提出的方法可以快速，准确地替代解析建模。
英文摘要：
The effect of decreasing Drain-Induced Barrier Lowering (DIBL) is one of the non-desirable short-channel effects in the MOSFETs family, which causes the threshold voltage of the transistor to be reduced by increasing the voltage of the drain. This effect makes it impossible for circuit designers to consider VT as a constant value, and hence, it is necessary to calculate VT as a function of the drain voltage. Therefore, to consider the effect of DIBL in the design of integrated circuits, a large computational burden is imposed on the system, which slows down the simulation process in circuit-level simulators, particularly when a large number of transistors are to be simulated. Accordingly, in this paper, a multiple input single output (MISO) Nonlinear Autoregressive (N-AR) model using the Gram-Schmidt orthogonalization approach is proposed, that calculates the threshold voltage of the new generation of MOSFETs, i.e., Junctionless Double-Gate MOSFETs (JL-DG-MOSFETs), with a high precision and a significant speed-up in the computational procedure of the model. It is shown that, on average, the proposed numerical method is 313 times faster than the state-of-the-art analytical model. The calculated percentage of normalized mean square error between the proposed model and analytical one is 0.435% on average, showing that the proposed approach can be a fast and accurate candidate for replacing the analytical modeling.
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