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### 基于分布式效应改进的SiGe HBTs CBE布局高频等效电路模型 #### 摘要与背景介绍本研究论文提出了一种针对具有CBE（Collector Base Emitter）布局的SiGe（硅锗）异质结双极型晶体管（HBTs）的改进高频等效电路模型。该模型考虑了基区内部的分布式效应，并将实际设备结构分为三个部分：链接基区、内在晶体管区域以及外在基区。通过分析这些区域的特性，作者构建了一个新的小信号等效电路模型。 #### 关键概念与技术 **SiGe HBTs（硅锗异质结双极型晶体管）** SiGe HBTs是一种高性能的双极型晶体管，它们利用硅锗材料的特殊性质来提高器件的速度、驱动能力和噪声性能。由于其优异的性能，SiGe HBTs被广泛应用于无线通信、模拟电路、快速数据采集和转换等领域。 **小信号等效电路模型** 小信号等效电路模型是用来表征晶体管在小信号工作状态下的行为的一种方法。它能够帮助设计者理解和优化器件的结构，并指导电路的设计。常见的小信号等效电路模型包括SGP、VBIC、HICUM和Mextram等。 **分布式效应** 分布式效应是指在高频工作条件下，晶体管内部结构中的电阻和电容不再可以简单地用集总参数来表示，而需要考虑分布在整个结构中的电阻和电容的影响。这在高频应用中尤为重要，因为高频信号会使得这些分布参数对器件性能产生显著影响。 #### 改进的高频等效电路模型在传统的紧凑模型中，晶体管的内在基区电阻通常被视为一个单一的集总参数。然而，在本研究中，作者提出了一种新的方法，即将内在基区电阻转移到一个新的内部基节点上。这种方法可以更好地解释传统紧凑模型中内在偏置依赖的集电极电阻出现异常变化的现象。具体来说，该模型将晶体管的实际结构分为三部分： 1. **链接基区**：位于空间氧化层下方，这部分基区主要受到空间氧化层的影响。 2. **内在晶体管区域**：位于发射窗口下方，这是晶体管的核心工作区域。 3. **外在基区**：这部分包含了除了核心工作区域之外的其他基区部分。每个区域都被视为一个二端口网络，并且由分布式的电阻和电容组成。通过求解传输线方程，可以得到各个区域的导纳参数，进而推导出小信号等效电路。 #### 结论本文提出的改进高频等效电路模型考虑了SiGe HBTs中基区的分布式效应，并通过引入一个新的内部基节点来改进内在基区电阻的处理方式。这种模型不仅能够更准确地反映晶体管的高频特性，还能够帮助解释传统模型中的一些异常现象。对于设计高性能的SiGe HBTs及其相关电路具有重要意义。 #### 参考文献 [1-3] 文章提到的关于SiGe HBTs在无线通信、模拟电路、快速数据采集和转换领域的应用和发展。 [4-6] 小信号等效电路模型如SGP、VBIC、HICUM和Mextram的相关文献。 #### PACS 编码 85.30.De - Bipolar transistors and related devices 85.30.Pq - Heterostructure devices (not otherwise provided for) 85.40.Bh - Circuit models and design techniques 通过以上分析，我们可以看出，该研究论文提出的模型是对现有SiGe HBTs高频等效电路模型的重要补充和完善，对于推进SiGe HBTs在高频领域的应用具有重要意义。

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Chin. Phys. B Vol. 26, No. 9 (2017) 098502

Improved high-frequency equivalent circuit model based on

distributed effects for SiGe HBTs with CBE layout

∗

Ya-Bin Sun(孙亚宾), Xiao-Jin Li(李小进)

†

, Jin-Zhong Zhang(张金中)

‡

, and Yan-Ling Shi(石艳玲)

Shanghai Key Laboratory of Multidimensional Information Processing, Department of Electrical Engineering,

East China Normal University, Shanghai 200241, China

(Received 23 March 2017; revised manuscript received 2 June 2017; published online 31 July 2017)

In this paper, we present an improved high-frequency equivalent circuit for SiGe heterojunction bipolar transistors

(HBTs) with a CBE layout, where we consider the distributed effects along the base region. The actual device structure is

divided into three parts: a link base region under a spacer oxide, an intrinsic transistor region under the emitter window,

and an extrinsic base region. Each region is considered as a two-port network, and is composed of a distributed resistance

and capacitance. We solve the admittance parameters by solving the transmission-line equation. Then, we obtain the small-

signal equivalent circuit depending on the reasonable approximations. Unlike previous compact models, in our proposed

model, we introduce an additional internal base node, and the intrinsic base resistance is shifted into this internal base node,

which can theoretically explain the anomalous change in the intrinsic bias-dependent collector resistance in the conventional

compact model.

Keywords: SiGe heterojunction bipolar transistors (HBT), small-signal equivalent circuit, distributed effects,

CBE layout

PACS: 85.30.De, 85.30.Pq, 85.40.Bh DOI: 10.1088/1674-1056/26/9/098502

1. Introduction

In recent years, SiGe heterojunction bipolar transistors

(HBTs) have undergone rapid growth because of their high

speed, high driving power, and low noise, and they have been

applied to ﬁelds such as wireless communication, analog cir-

cuit, fast data acquisition, and conversion.

[1–3]

Small-signal

equivalent circuit models, such as the lumped SGP, VBIC,

HICUM, and Mextram, are often used to characterize tran-

sistor performance, optimize the device structure, and guide

circuit design.

[4–6]

However, bipolar transistors are actually

large distributed networks that are composed of a basic re-

sistance and capacitance, and their design is not always as

easy as described in the above lumped models. Although most

transistor electrical performances can be effectively character-

ized by lumped models, there remain fundamental limitations

with respect to actual device structures.

[7]

When extracting the

small-signal model parameters in conventional Mextram, we

ﬁnd that the bias-dependent collector epilayer resistance R

C1C2

monotonously decreases as the base voltage V

increases,

which clearly deviates from basic device physics theory, and

the underlying physical mechanism should therefore be inves-

tigated.

Owing to its special base structure, SiGe HBTs show

a built-in multi-Mrad total dose hardness with no inten-

tional hardening.

[8–10]

However, single-event effects (SEE) re-

main a serious problem, with recent results demonstrating a

low linear energy-transfer threshold and high saturated cross-

sections.

[11–14]

A reduction in the sensitive area enclosed by

deep trench isolation is considered an effective method of im-

proving the net upset cross section. Therefore, a transistor with

minimum feature size, i.e., using only a single collector, base,

and emitter (CBE) contacts, possesses a high SEE immunity,

compared with standard devices with double collector and

base contacts (CBEBC).

[11,12]

Furthermore, when the transis-

tors are exposed to the space-energetic particle environment,

the distributed effect is more signiﬁcant because the irradia-

tion damages are generally not uniformly distributed through-

out the whole transistor structure.

[8]

Therefore, it is necessary

to investigate the small-signal equivalent circuit based on the

distributed effects for SiGe HBTs with a CBE layout.

In the present work, in order to determine the phys-

ical mechanisms by which the extracted R

decreases as

increases, we propose an improved small-signal equiv-

alent circuit that is based on the distributed effects for SiGe

HBTs with a CBE layout. The whole transistor is divided

into three parts along the base region. Then, we obtain the

high-frequency equivalent circuit under the cut-off mode by

solving transmission line equations, and taking into account

the distributed effects. The intrinsic base resistance R

pushed into the internal base node, and the added component

of R

)/3C

is found to contribute to the declined

∗

Project supported by the National Natural Science Funds of China (Grant Nos. 61574056 and 61504156), the Natural Science Foundation of Shanghai,

China (Grant No. 14ZR1412000), Shanghai Sailing Program, China (Grant No. 17YF1404700), and the Science and Technology Commission of Shanghai

Municipality, China (Grant No. 14DZ2260800).

†

Corresponding author. E-mail: xjli@ee.ecnu.edu.cn

‡

Corresponding author. E-mail: jzzhang@ee.ecnu.edu.cn

098502-1

Chin. Phys. B Vol. 26, No. 9 (2017) 098502

as V

increases. Finally, we obtain the equivalent circuit

in the forward-active mode by adding four additional modules

into the equivalent circuit in the cut-off states.

2. Background

The conventional hybrid-.π small-signal equivalent cir-

cuit for SiGe HBTs under forward- active mode is depicted

in Fig. 1, as adopted in HICUM or Mextram. The collector

series resistance and base series resistance are separately di-

vided into two parts: a constant external part R

and intrinsic

bias-dependent epilayer resistance R

C1C2

, a constant external

resistance R

, and a variable intrinsic resistance R

BCX

C1C2

E(S)

exp(-jωτ)

Fig. 1. Conventional small-signal equivalent circuit for SiGe HBTs.

-1.2 -0.8 -0.4 0

400

600

800

1000

1200

1400

1600

1.2T30 mm

SiGe HBT

Fig. 2. Extracted collector epitaxy layer resistance R

C1C2

as a function

of V

As demonstrated in our previous study, the small-signal

model parameters can be precisely extracted based on the non-

linear rational function ﬁtting.

[15]

However, we observed an

abnormal variation of the collector epilayer resistance R

C1C2

and it decreases as the base voltage V

increases, as shown in

Fig. 2. It appears that this variation deviates from basic device

physics theory, and R

C1C2

is actually expected to increase as

decreases. According to the cross-sectional view of the in-

trinsic transistor under the emitter window, as shown in Fig. 3,

the depletion width W

narrows as V

increases, and this is

because of the decreased reverse bias voltage. Consequently,

the width of the neutral collector region W

increases, caus-

ing an increase in R

C1C2

emitter

base

collector

c1/W

Fig. 3. (color online) A simpliﬁed cross-sectional view of the intrinsic

transistor.

Therefore, in the conventional compact model, the ob-

tained R

C1C2

contradicts basic device physics theory. In or-

der to ﬁnd the underlying physical mechanism, starting with

the actual device structure, we propose an improved high-

frequency small-signal equivalent circuit for SiGe HBTs based

on the distribution effects. The intrinsic base resistance R

pushed into the introduced internal base node, and contributes

to the collector resistance with certain proportion, and this can

fundamentally explain the above abnormal variation of R

C1C2

versus the base voltage V

3. Device-under-test and method for the pro-

posed model

The device evaluated in this work features a single-stripe

CBE conﬁguration, i.e., with only one CBE, as opposed to the

larger CBEBC stripe conﬁguration. The typical cross-section

is shown in Fig. 4. The key process includes an n

−

collector

epitaxy, a graded SiGe base epitaxy, an in-situ doped polysil-

icon emitter, LOCOS isolation, an n

collector sinker, and

an ion-implanted extrinsic base. Along the base region, the

whole transistor structure is divided into three parts: I) a link

base region including the spacer oxide, II) an intrinsic transis-

tor region, and III) an extrinsic BC junction containing metal

silicide.

In the present work, we separately determine the small-

signal equivalent circuit under the cut-off and forward-active

mode. Each region is considered as a two-port network

composed of several basic resistors and capacitors. We ob-

tained the admittance parameters by solving the transmission-

line equation, and we then determine the small-signal equiv-

alent circuit in the cut-off mode depending on some rea-

sonable approximations, using the well-known π network

characteristics,

[16]

as shown in Fig. 5. Finally, we directly ob-

tained the equivalent circuit in forward-active mode by adding

four additional modules.

098502-2

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