标题: 双闸极暨绝缘层上矽场效应电晶体有效位势量子修正模式的线性回归
Application of Linear Regression to Effective Potential of Double-Gate and Silicon-on Insular Metal-Oxide-Semiconductor Field-Effect Transistors
作者: 张景岚
Ching-Lan Chang
周幼珍
李义明
Yow-Jen Jou
Yiming Li
统计学研究所
关键字: 有效位势;线性回归;双闸极;effective potential;linear regression;double gate
公开日期: 2005
摘要: 现今在系统晶片积体电路中的半导体元件尺寸已经缩小到奈米刻度的尺寸,随着尺寸的缩小,因应各种特殊设计,半导体元件中氧化层的厚度也随之变薄。因为氧化层厚度变薄的因素,在氧化层及通道的界面便产生了能量井,量子效应也就产生。在模拟上我们该如何考虑所谓的量子效应,是一个重要的议题。
传统上,为了模拟量子效应会加入水丁格(Schrödinger equation)方程式在半导体方程式中。然而,水丁格方程式在数值计算上相当耗时及会有数值收敛上的麻烦,在二维度或三维度空间中边界条件的设定也不容易。为了避免此方程式在模拟上的困难,许多替代的量子修正模型也陆续被提出,在这许多的模型中,大都还是存在着偏微分方程式。近年来被提出的有效位势(effective potential)理论,是一个简单的积分方程式。除此之外,在演算法中也大大的改善了耗时的缺点。不过在有效位势模型中,存在着一个具有不确定性的变数(波包的标准差,standard deviation of wave packet)。随着标准差的变化,所模拟得到的结果也会有所差异。为了得到正确的值,吾人利用波松-水丁格方程式的结果为基准,调整波包的标准差以达到两者的结果最为接近。而另外一个问题随之出现,随着元件外加不同的条件(偏压、氧化层厚度…等等),标准差的值也会随之变化。
在此论文中,所探讨的元件结构为双闸极以及绝缘层上矽金属氧化物半导体场效电晶体为主,探讨不同的条件对波包的标准差的影响为何。吾人在各种不同的外加条件下,以波松-水丁格方程式的结果为基准,求出各个不同的波包标准差值。接着利用统计的方法,建立出波包标准差以及各外加条件的模型。首先,我们以散布图观察各外加条件对波包的标准差的关系图,发现之间并没有复杂的关系,所以我们建立一个二阶的线性模型。经过变数转换得到不错的结果。
在此提出的模型在结构,外加条件上有所限制,可以将此模型的适用性扩展到更多结构、或是特性相似的半导体元件上。文章中所提出的统计方法可以广为应用在其他的半导体元件特性分析上。
Within the next decade or so, it is expected that gate lengths will shrink to 45 nm or less in devices found in integrated circuits. Quantum effects are known to occur in the channel region of MOSFET devices, in which the carriers are confined in a triangular potential well at the semiconductor-oxide interface. How might we expect quantum mechanics to arise in the transport through these small devices?
Typically, these effects are quantified by a simultaneous solution of the Schrödinger and Poisson equations, which can be a very time consuming procedure if it needs to be incorporated in realistic device simulations. Besides, different methods are proposed to include quantization effects in simulation of carrier transport in nanoscale devices. For instance, Hansch, MlDA, Van Dort, Density Gradient model … etc. Among these approaches, Density Gradient method are used generally. However, the quantum potential is defined in terms of the second derivative of the square root of local density. Such and approach is highly sensitive to noise in the determination of the local carrier density. Recently, Ferry propose an efficient method, effective potential, to include quantum effects. This approach avoids complex computation. Later, an more complicated effective potential is develop, but it is not included in our discussion.
Effective potential method is quite convenient to calculate. However, one variable, standard deviation of wave packet, in the model influence the results quite significantly. Unfortunately, value of this parameter is not known exactly. How to determine the value is an interesting problem.
In this thesis, we do some simulations with various conditions to calibrate value of the variable by Schrödinger equation. And try to establish a model of standard deviation of wave packet by using statistical methods. First, we draw the scattering plots and find that correlations between outer conditions and value of standard deviation of wave packet are simple. So we just establish a second order multiple linear model. We get results which are satisfied through power transformation. The model is established corresponding to double-gate and silicon-on-insulator (SOI) MOSFET structures. Though the model is not suitable for any structure, conditions of devices. This method can be expanded to establish other models more generally.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT009226522
http://hdl.handle.net/11536/76893
显示于类别:Thesis


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