非线性晶体管模型参数提取技术详解

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"该资源详细介绍了非线性晶体管模型参数提取技术，涵盖了有源器件建模的关键领域，包括寄生效应、内在提取、统计、提取不确定性、非线性与直流参数、自热和陷阱、噪声以及封装影响。通过行业专家和学术界人士的深入洞察，读者将了解到如何将相似的参数提取方法应用于不同技术，并通过实际工业例子和测量结果理解理论在实践中的应用。这本书由马蒂亚斯·鲁道夫撰写，他是德国勃兰登堡工业大学射频和微波技术的乌尔里希-路德维希-罗德教授，他在电路设计模型方法和新旧设备类型的模型开发方面有着丰富的经验。" 在电子工程中，非线性晶体管模型参数提取是模拟集成电路设计的关键步骤，它关系到器件性能的精确预测和电路仿真效果。此资源详细探讨了这个主题，旨在帮助工程师和研究人员准确可靠地提取模型参数。首先，"寄生效应"是指在理想情况下不考虑但在实际中对器件性能有显著影响的附加元件，如电阻、电容和电感。了解和处理这些寄生参数对于构建实际应用中的准确模型至关重要。 "内在提取"涉及到晶体管的基本特性，如增益、阈值电压、互导等。这部分内容会指导如何从测量数据中准确地提取这些参数，以便在电路设计中正确反映器件的内在行为。 "统计"和"提取不确定性"部分讨论了参数提取过程中可能出现的随机性和系统性误差，以及如何评估和控制这些不确定性，这对于批量生产和可靠性分析尤其重要。 "非线性与直流参数"的提取是建模的核心，因为晶体管的行为在不同偏置条件下可能会显著变化。这部分内容将介绍如何捕捉这些非线性行为并将其纳入模型。 "自热"和"陷阱"现象在高速和高功率操作中尤为显著，它们可能导致温度上升和载流子捕获，影响器件性能。学习如何考虑这些因素对于高精度建模是必不可少的。 "噪声"是电子系统中不可避免的一部分，理解和量化晶体管噪声特性对于低噪声设计至关重要。最后，"封装影响"部分提醒我们，晶体管不仅受其内部特性影响，封装材料和工艺也会对其性能产生影响，这部分内容将阐述如何将这些外部因素纳入模型。这本书是从事有源器件建模、电路设计或设备开发的专业人士的宝贵参考资料，它提供了一个全面的指南，涵盖了从基本理论到实际应用的所有关键环节。通过学习，读者可以提升自己的技能，更好地应对各种技术和设备类型的建模挑战。

xiv Preface

of a transistor process, and an overview of measurement techniques for extraction and

validation.

The editors would like to thank all the authors for their contributions. We enjoyed

the workshop presentations very much and felt that publishing this knowledge in an

appropriate way would constitute a valuable contribution to the ﬁeld. The estimate of

the workload to transform a talk into a book chapter turned out to be initially a little

optimistic, so we especially appreciate the authors’ extra efforts.

We would also like to thank Cambridge University Press, especially Dr. Julie Lan-

cashire and Ms. Sarah Matthews, for their support of the project. It was always a pleasure

to work with the staff at Cambridge.

Cottbus, Germany; G

oteborg, Sweden; and Santa Rosa, CA, USA

M.R., C.F., D.E.R.

1 Introduction

Matthias Rudolph

Brandenburg University of Technology

If one is about to design a circuit, one certainly relies on a circuit simulation tool that

provides us with the capability to determine circuit performance with high accuracy

without even fabricating a prototype. We expect the simulation to provide us with the

numerical algorithm that is capable of accurately calculating the relevant variables,

such as currents, voltages, noise, distortion products, etc. At least as important is the

description of the components that will be used, since ultimately the simulation can

never be more accurate than the models of the components used. Component models

commonly are provided as drag-and-drop components in modern circuit simulators. At

least for established technologies, accurate models are available for passive and active

components. All problems solved?

Unfortunately not. The models, especially compact transistor models, are

parametrized. It is a big step from the general-purpose model that is capable of describ-

ing, say, SiGe heterojunction bipolar transistors (HBTs) in general to the speciﬁc model

for a speciﬁc transistor of a speciﬁc size, from a speciﬁc foundry, that one plans to use

in the actual design.

But why bother? One would expect the foundry selling the transistor also to provide

us with a valid model.

In reality the situation is more like the following:

1. Some vendors simply do not provide their customers with appropriate models.

Either one gets just plain data sheets providing some ﬁgures of merit and printed

S-parameters. Or quite often, even for the most advanced transistors, only very basic

SPICE-type model parameters are provided. While these models are available in lit-

erally all circuit simulators, their accuracy is often quite limited, since these models

only describe the very basic transistor behavior.

2. If one deals with the most advanced generation of devices, the model might not yet

be determined. This happens frequently in research.

3. Often, it turns out that the model provided by the device manufacturer is generally

of good accuracy, but unfortunately not for the special application one is aiming at.

Therefore, a model parameter reﬁnement is required.

This book presents an overview of the different aspects and methods of model param-

eter extraction. In this context, we assume and take for granted that the model chosen is,

in general, accurate. This means that the underlying mathematical formulation is able

to account for all effects that are observed. The method behind how a parameter for

2 Introduction

a speciﬁc model is extracted depends on which physical effect it describes rather than

what speciﬁc model is used. This holds even for different types of device. Hence, the

chapters in this book address the relevant issues in parameter extraction topic by topic.

Speciﬁc device technologies are only addressed in order to provide examples, while the

methods in general can be applied also to other transistor technologies.

1.1 Model extraction challenges

Before parameter extraction is discussed in detail, some basic issues shall be addressed:

ﬁrst, what it means that a model is accurate. To state that a model possibly predicts device

performance very well is, however, not sufﬁcient. It needs to do so under realistic working

conditions. Simulation of realistic cases is usually numerically much more challenging

than the standard test cases commonly used to judge model accuracy. Whether or not

a simulation converges depends not only on the numerical solver the simulator uses,

but also model description and model parameter values extracted. These aspects, which

parameters to determine, and which ranges of values are advisable therefore also need to

be discussed in this introduction. The ﬁnal section will address how to choose a suitable

type of transistor for the modeling procedure.

1.1.1 Accuracy

If one asks for the model of a speciﬁc transistor, this is what one usually gets: a set of

parameters, and, hopefully, some comparison between the simulation results with mea-

surement. Typically, output IV-curves, and S-parameters at a few bias points are shown.

Is it safe to trust the model, provided that the agreement of simulated and measured

data we have seen is perfect? The obvious answer: not necessarily. Whether the model

parameter set is valid depends on a number of questions that will be discussed in the

following in more detail: what is the application one wants to simulate? How accurate is

the measurement? How about performance variations of nominally identical transistors?

1.1.1.1 Circuit application

So far, we spoke of an accurate model, but, as with everything on earth, a model cannot

be just completely accurate. All we will get is a model that is accurate within certain

limits. Model validity can only be guaranteed within a certain range of, e.g., bias points,

frequencies, temperatures, or output power levels. These limits need to match the targeted

circuit type. Some examples:

1. True small-signal operation requires only the bias point to be predicted well, together

with the S-parameters in the respective frequency range. Of course, this model is

restricted to one bias point. If another bias point is to be simulated (e.g., in order to

minimize power consumption or to improve noise performance), accuracy cannot be

assumed a priori without proving ﬁrst how well the model will match.

2. Weakly nonlinear operation can be assumed in the case of a low-noise ampliﬁer. The

transistor will only be subject to low-power signals, but the small-signal condition

1.1 Model extraction challenges 3

out

TOI

t (ns)

80 90 100 110 120

−4

−2

out

(V)

weakly nonlinear

two-tone

measurement

(V)

(A)

switch-mode PA

6543210

0.1

0.2

0.3

0.4

0.5

out

(dBm)

−60

−40

−20

−15 −10 −5 0 5 10 15 20

(dBm)

Figure 1.1 Depending on the circuit application, a model is required to be accurate in different

operation areas, while others can be neglected. Shown here are two extreme cases: slightly

nonlinear class-A operation, and switching operation.

might be violated which calls for a nonlinear model. The common two-tone mea-

surement for the determination of the third-order intercept points characterizes this

operation condition. Besides the bias point, S-parameters also need to be predicted

well within a limited operating area around the quiescent bias point. This area is

showningrayinFigure1.1. While high accuracy is required here, no speciﬁc accu-

racy requirements apply outside. Again: if the bias point is shifted, the model needs

to be re-examined and possibly the parameters need to be adjusted.

3. Power compression results from output voltages reaching the minimum, or currents

approaching the maximum. Starting from the weakly nonlinear operation, the voltage

and current swings increase with increasing transistor output power. The range of

currents and voltages, where the model needs to be accurate, therefore increases.

However, things change signiﬁcantly once the voltage dynamically drops below the

knee voltage, and the current swings into the saturation (bipolar transistors) or linear

(ﬁeld-effect transistors) region. In this region, the transistor is working in a different

mode than in class A, and a different subset of parameters is used to describe it in the

model. Therefore, a model that is very accurate in class-A operation can completely

fail to predict the compression behavior.

4. In order to extend the last statement: if any additional nonideal effect comes into play,

for example breakdown or self-heating, the respective model parameters need to be

determined and the model is to be veriﬁed by appropriate measurements. No compact

4 Introduction

reverse operation

knee region

self-heating

breakdown

(mA)

(V)

−5 0 5 10 15 20 25 30

100

−20

−40

−60

−80

Figure 1.2 Schematic output-IV curves of a FET. Some critical areas are highlighted where the

electrical behavior is dominated by physical effects that are not signiﬁcant elsewhere.

model can be expected to predict all physical effects. All need to be characterized

ﬁrst and the respective model parameters need to be determined.

5. A special case are switch-mode power ampliﬁers, such as class-E power ampliﬁers.

For this application, the transistor model needs to be highly accurate in on and off

states. The common class-A operation area is in the switch-mode case only shortly

touched during the switching event. A gray area in Figure 1.1 shows the area where

high model accuracy is required for this operation condition.

6. Another special case is the resistive mixer. The ﬁeld effect transistor (FET) is biased

at a drain-source voltage of zero. The model therefore needs to describe the transistor

performance in forward and in reverse mode. It needs to be accurate not only for a

certain voltage swing at the gate, but also for a certain voltage swing at the drain

around zero volts. At negative drain voltages, drain and source terminals exchange

their functionality, with drain becoming the effective source and vice versa. This

reverse operation condition is commonly ignored completely during model parameter

extraction.

At this point, it is pretty obvious that a semiconductor manufacturer who provides

us with a model parameter set cannot be expected to anticipate all possible modes of

operation. Commonly, the parameter sets are determined for the generic case of class-A

types of operation at the optimum bias point of the respective device. Therefore, without

careful assessment of model accuracy, no more than an estimate of circuit performance

can be expected from using the model. If the mode of operation is too far from class A,

such as in the cases of resistive mixer or switch-mode ampliﬁer, the model might even

fail to provide a rough estimate.

Figure 1.2 illustrates possible sources of error. Depending on the mode of operation,

different physical effects come into play such as breakdown or self-heating. These

might not be present during parameter extraction, but the model cannot extrapolate

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