一种改进的InP HBT小信号模型的直接提取法

戚军军; 吕红亮; 张玉明; 张义门; 张金灿; QI Jun-Jun; LYU Hong-Liang; ZHANG Yu-Ming; ZHANG Yi-Men; ZHANG Jin-Can

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An improved direct extraction method for InP HBT small-signal model PDF

QI Jun-Jun ¹
LYU Hong-Liang ¹
ZHANG Yu-Ming ¹
ZHANG Yi-Men ¹
ZHANG Jin-Can ²

1. School of Microelectronics, Xidian University, Key Laboratory of Wide Band-Gap Semiconductor Materials and Devices, Xi’an 710071, China ； 2. Electrical Engineering College, Henan University of Science and Technology, Luoyang 471023, China

CLC： TN385

Updated：2020-06-15

DOI：10.11972/j.issn.1001-9014.2020.03.005

Abstract

In this paper, an improved direct extraction method to extract the model parameters in InP heterojunction bipolar transistor （HBT） small-signal equivalent circuit is presented and successfully applied to small-signal equivalent circuit of InP HBT. The distributed base-collector capacitance effect is taken into consideration in the adopted model. The extracting process of this method, which extracts parameters in turn from the peripheral parasitic elements to the intrinsic internal elements, is clearer than other direct extraction methods. Except for the parasitic parameters, all other parameters are calculated without any simplified approximation. This method relies on S parameters measurement. All of the equivalent circuit parameters are extracted directly from the S parameters without using approximations based on initial values. The direct extraction method is successfully validated on InP HBT in the frequency range of 0.1 ~ 40 GHz, and excellent agreement is achieved between the measured and calculated S parameters over the whole frequency range.

Keywords

direct extraction method; InP HBT; small-signal model; parameter extraction

Introduction

Owing to the characteristics of high-speed and high-frequency, InP HBT has been one of the most promising devices for future applications at microwave and millimeter-wave frequencies^[

1,2,3]. Small-signal model is the footstone of the entire transistor microwave model^{[参考文献 4
百度学术}4], and therefore accurate InP HBT device model is of great significance for the development of microwave and millimeter-wave integrated circuits.

With scaling down transistors’ size, in general, the structure of C-up HBT devices can ignore the extrinsic base-collector capacitance because the extrinsic area corresponding to the parasitic capacitance can be neglected^[

5]. Compact with the C-up devices, the E-up devices have a larger extrinsic area and need to consider the distributed base-collector capacitance effect. The effect is represented by extrinsic and intrinsic capacitances. By considering the effect, not only can this more clearly characterize the physical meaning of the base-collector capacitance, but it can further improve the model to make the model more accurate. In Ref.[6], although the authors have considered the effect in small-signal equivalent circuits, the calculation process is complicated and the calculation amount is too large. In Ref.[7,8], the approximations used in the extraction process leads to inaccurate parameter extraction.

In recent years, many methods that extract small signal model parameters have been reported, mainly including direct extraction method ^[

2,3,4,6,7,8] and numerical optimization method ^{[参考文献 9
百度学术}9,10]. The numerical optimization method uses numerical methods to locate the optimal parameter values, and finally obtains simulated results with good fitting characteristics to the measured results. Nevertheless, the method depends on parameters’ initial value and may not even converge. With the direct extraction method, each parameter of the equivalent circuit could be extracted using equations. However, the disorganized extraction process makes the direct extraction method very computationally intensive and complicated. In Ref.[4, 6-7], although the authors used some simplified approximations, they also obtained more complex parameter expressions.

In order to overcome these difficulties, an improved direct extraction method for InP HBT small-signal model is proposed. This method in turn extracts the parameters of small-signal equivalent circuit from the peripheral elements to the internal elements. Compact with the other direct extraction methods, the method has clear extraction process, simple calculation of parameters, and few approximations calculation.

1 Small-signal equivalent circuit model

The adopted hybrid-π equivalent circuit for HBT small-signal modeling is shown in Fig.1. This equivalent circuit includes two parts, i.e., the inner part contains intrinsic elements, and the outer part contains extrinsic elements ^[

11]. In this model, C_pbc、C_pbe and C_pce are pad parasitic capacitances, L_c、L_e and L_b are pad parasitic inductances, R_c,R_band R_e are extrinsic resistances of collector, base, and emitter, respectively. These extrinsic elements are considered to be bias independent.

图1 HBT小信号等效电路

Fig.1 HBT small-signal equivalent circuit

Intrinsic elements are supposed to be bias dependent, mainly including the dynamic base resistance R_bi, the dynamic base-emitter resistance R_be, the base-emitter capacitance C_be, the base-collector capacitance C_bc, the dynamic base-collector resistance R_bc, DC transconductance g_m0 and delay time τ. Besides, C_bcx is extrinsic base-collector capacitance, and it is considered to be bias independent.

2 Parameter extraction procedure

2.1　Extraction of parasitic parameters and the extrinsic resistances

Pad parasitic parameters consist of parasitic capacitances and inductances which are extracted by the Open Test Structure and the Short Test Structure^[

12], respectively. The extrinsic resistances are extracted by the open-collector method ^{[参考文献 13
百度学术}13], and the equivalent circuit diagram is illustrated in Fig.2.

图2 集电极开路等效电路

Fig.2 open-collector equivalent circuit

The Z-parameters of the open-collector equivalent circuit in Fig. 2 is written as

$Z_{11} = R_{b} + R_{b i} + \frac{R_{b e}}{1 + g m \cdot R_{b e}}$ ,

（1）

$Z_{12} = R_{e} + \frac{R_{b e}}{1 + g m \cdot R_{b e}}$ ,

（2）

$Z_{21} = R_{e} + (1 - g m \cdot R_{b e}) \cdot \frac{R_{b e}}{1 + g m \cdot R_{b e}}$ ,

（3）

$Z_{22} = R_{c} + R_{e} + (1 + \frac{R_{b c}}{R_{b e}}) \cdot \frac{R_{b e}}{1 + g m \cdot R_{b e}}$ ,

（4）

$R_{b e} = \frac{η b e K T}{q I b e}$ ,

（5）

$R_{b c} = \frac{η b c K T}{q I b c}$ .

（6）

When I_b approaches ∞, R_beand R_bc become very small at approximately 0 because the junction resistance and the junction current are inversely proportional. Moreover, with the increasing of the base current I_b, the total resistance of the base gradually approaches the base contact resistance^[

13], i.e., R_b+ R_bi ≈ R_b. Therefore, the intrinsic resistances R_b、R_eand R_c can be obtained （taking the real part of the Z parameter to indicate the resistance value which makes the extraction result more accurate）:

$R_{b} = r e a l (Z_{11} - Z_{12})$ ,

（7）

$R_{e} = r e a l (Z_{12})$ ,

（8）

$R_{c} = r e a l (Z_{22} - Z_{12})$ .

（9）

The relationship between real（Z₁₁-Z₁₂）, real（Z₂₂-Z₁₂） and real（Z₁₂） and 1/I_b is linearly extrapolated to the ordinate to obtain the values of R_b, R_c and R_e, as shown Fig.3^[

14]. The extraction values of the bias-independent elements are tabulated in Table 1.

图3 Z11-Z12, Z22-Z12 和 Z12的实部与1/Ib的关系图

Fig.3 Plots of the real part of Z₁₁-Z₁₂, Z₂₂-Z₁₂ and Z₁₂ versus 1/I_b

Table 1 Extraction of extrinsic parameters values

表1 非本征参数的提取结果

parasitic parameters	V_ce=2.5 V, I_c=12.5 mA
C_pb_c/fF	2.62
C_pb_e/fF	15.60
C_pce/fF	16.20
L_b/pH	52.25
L_c/pH	57.75
L_e/pH	8.88
R_e/Ω	4.27
R_b/Ω	1.77
R_c/Ω	7.31

2.2　Extraction of the extrinsic base-collector capacitance

Once all the parasitic elements are de-embedded, only the extrinsic base-collector capacitance C_bcx and the intrinsic elements （inside the dashed line） are remained in the equivalent circuit, as shown in Fig.4. To overcome the problem of unclear parameter extraction process, we need to extract sequentially from the external circuit to the internal circuit, that is, we need to extract C_bcx first. However, the intrinsic equivalent circuit of the small signal equivalent circuit needs to be analyzed first before extracting the extrinsic base-collector capacitance.

图4 剥离寄生参数后的等效电路图

Fig.4 equivalent circuit after de-embedding off parasitic elements

The Z-parameters of the equivalent circuit after de-embedding in Fig. 4, is written as

$[Z] = (\begin{matrix} Z_{11} & Z_{12} \\ Z_{21} & Z_{22} \end{matrix}) = (\begin{matrix} \frac{g m Z_{b e} R_{b i} + Z_{b e} + R_{b i} + D Y_{b c x}}{A} & \frac{Z_{b e} + D Y_{b c x}}{A} \\ \frac{Z_{b e} + D Y b c x - Z_{b c} Z_{b e} g m}{A} & \frac{Z_{b e} + Z_{b c} + D Y_{b c x}}{A} \end{matrix})$ ,

（10）

where $D = Z_{b c} \cdot Z_{b e} + R_{b i} \cdot Z_{b c} + Z_{b e} \cdot R_{b i}$ , $A = (1 + g m Z_{b e}) [1 + Y_{b c x} (R_{b i} + Z_{b c})]$ , $Z_{b e} = \frac{R_{b e}}{1 + j ω R_{b e} C_{b e}}$ , $Z_{b c} = \frac{R_{b c}}{1 + j ω R_{b c} C_{b c}}$ , $Y_{b c x} = j ω C_{b c x}$ , and $g_{m} = g_{m 0} e^{- j ω τ}$

From （10）, the dynamic base resistance R_bi can be expressed as

$R_{b i} = \frac{(Z_{Δ})}{1 - Y_{b c x} (Σ Z)}$ ,

（11）

where $Σ Z = Z_{11} + Z_{22} - Z_{12} - Z_{21} = \frac{Z_{b c} + R_{b i}}{1 + Y_{b c x} (Z_{b c} + R_{b i})}$ , and $Z △ = Z_{11} - Z_{12} = \frac{R_{b i}}{1 + Y_{b c x} (Z_{b c} + R_{b i})}$

The extrinsic base-collector capacitance can be expressed by taking the imaginary part of equation （11） equal to 0 as

$C_{b c x} = \frac{1}{ω} \frac{- i m a g (Z_{Δ})}{i m a g (Z_{Δ}) i m a g (Σ Z) + r e a l (Z_{Δ}) r e a l (Σ Z)}$ ,

（12）

Fig.5 shows the extracted result as a function of frequency for ωC_bcx at V_ce=2.5V, I_c=12.5mA.

图5 ωCbcx随频率变化的关系图

Fig.5 ωC_bcx versus frequency

2.3　Extraction of the intrinsic elements

Once the parasitic elements and extrinsic base-collector capacitance is de-embedded, the remaining intrinsic elements of the small signal equivalent circuit model can be directly determined. The Z-parameter corresponding to the intrinsic circuit can be written as

$[Z_{i n}] = (\begin{matrix} Z_{i n, 11} & Z_{i n, 12} \\ Z_{i n, 21} & Z_{i n, 22} \end{matrix}) = (\begin{matrix} R_{b i} + \frac{Z_{b e}}{1 + g_{m} Z_{b e}} & \frac{Z_{b e}}{1 + g_{m} Z_{b e}} \\ \frac{Z_{b e} - g_{m} Z_{b e} Z_{b c}}{1 + g_{m} Z_{b e}} & \frac{Z_{b e} + Z_{b c}}{1 + g_{m} Z_{b e}} \end{matrix})$ .

（13）

From （13）, the intrinsic base resistance R_bi can be expressed as

$R_{b i} = r e a l (Z_{i n, 11} - Z_{i n, 12})$ .

（14）

Fig.6 shows the extracted result as a function of frequency for R_bi at V_ce=2.5V, I_c=12.5mA. Then de-embed off R_bi and get a new small signal equivalent circuit, as shown in Fig.7.

图6 Rbi随频率变化的关系图

Fig.6 R_biversus frequency

图7 剥离Rbi后的等效电路图

Fig.7 the equivalent circuit of de-embedding R_bi

The Y parameter of the corresponding equivalent circuit （Fig.7） could be expressed as

$[Y_{i n t}] = (\begin{matrix} Y_{i n t, 11} & Y_{i n t, 12} \\ Y_{i n t, 21} & Y_{i n t, 22} \end{matrix}) = (\begin{matrix} \frac{1}{Z_{b e}} + \frac{1}{Z_{b c}} & - \frac{1}{Z_{b c}} \\ - \frac{1}{Z_{b c}} + g_{m} & \frac{1}{Z_{b c}} \end{matrix})$ .

（15）

From （15）, the intrinsic elements can be expressed as

$R_{b c} = - \frac{1}{r e a l (Y_{i n t, 12})}$ ,

（16）

$C_{b c} = - \frac{i m a g (Y_{i n t, 12})}{ω}$ ,

（17）

$R_{b e} = \frac{1}{r e a l (Y_{i n t, 11} + Y_{i n t, 12})}$ ,

（18）

$C_{b e} = \frac{i m a g (Y_{i n t, 11} + Y_{i n t, 12})}{ω}$ ,

（19）

$g_{m 0} = m a g (Y_{i n t, 21} - Y_{i n t, 12})$ ,

（20）

$τ = \frac{- 1}{ω} t a n^{- 1} (\frac{i m a g (Y_{i n t, 21} - Y_{i n t, 12})}{r e a l (Y_{i n t, 21} - Y_{i n t, 12})})$ .

（21）

3 Results and discussion

A hybrid-π small-signal equivalent circuit with distributed base-collector capacitance effect was adopted to study the microwave and millimeter-wave behavior of the InP HBT. An improved direct extraction method has been established to accurately extract the small-signal parameters. The improved method extracts parameters from the peripheral circuit to the internal circuit and gives a clearer solution process. Extraction results of small signal equivalent circuit are depicted in table 2, for bias points.

Table 2 Extraction of Intrinsic Parameters at V_ce=2.5V

表2 本征参数在Vce=2.5V时的提取结果

Intrinsic parameters	I_c=2.5mA	I_c=12.5mA	I_c=22.5mA
C_bcx/fF	49.21	35.60	58.31
R_bi/Ω	36.22	8.32	2.45
R_be/Ω	2497.68	121.02	113.50
R_bc/Ω	1.90×10⁴	2.66×10⁴	1.04×10⁴
C_bc/fF	32.03	18.26	16.59
C_be/fF	145.30	718.85	915.30
g_m0/S	0.08	0.60	1.19

Fig. 8 shows the calculated S-parameters of the small-signal equivalent circuit of the HBT including the distributed base-collector capacitance with the measured data. The comparison shown in Fig. 8 demonstrates a good agreement from 0.1 ~ 40.0 GHz, which also verifies the validity of the model and extraction techniques.

图8 在100 MHz~40 GHz之间测量和计算的1×15μm2InP HBT 的S参数

Fig.8 Measured and calculated S-parameters of 1×15 μm² InP HBT between 100 MHz~40 GHz

However, the Smith plots of S parameters do not clearly reflect agreement of fit between measured and calculated data. The residual error between the measured results and the calculated results are quantified using the following equation ^[16]

$E = \frac{1}{4 N} \overset{2}{\sum_{i, j = 1}} \overset{N}{\sum_{k = 1}} \frac{|S_{i j}^{m} (f_{k}) - S_{i j}^{c} (f_{k})|}{m a x i j (|S_{i j}^{m} (f_{k})|)}$ ,

（22）

where N is the number of frequency points, S_i_j^m （f_k） and S_i_j^c （f_k） are the measured and calculated S-parameters at frequency f_k, respectively. The residual errors between the measured and modeled S-parameters are around 3.3~3.8%.

4 Conclusion

An improved direct extraction method for the hybrid-π small-signal equivalent circuit with the base-collector capacitance effect has been proposed. The extracting process of this method, which extracts parameters in turn from the peripheral parasitic elements to the intrinsic internal elements, is clearer than other direct extraction methods. Furthermore, this method can extract all intrinsic parameters directly by the equation without approximation and numerical optimization. Good agreement is obtained between calculated and measured results for an InP HBT with 1×15 μm²emitter area over a wide range of bias points up to 40GHz.

References

Hossain M, Nosaeva K, Janke B, et al. A G-Band High Power Frequency Doubler in Transferred-Substrate InP HBT Technology[J]. IEEE Microwave and Wireless Components Letters, 2016, 26（1）:49-51. [百度学术]

Yun J, Yoon D, Kim H, et al. 300-GHz InP HBT oscillators based on common-base cross-coupled topology[J]. IEEE Transactions on Microwave Theory and Techniques, 2014, 62（12）:3053-3064. [百度学术]

Ao Z, Yi-Xin Z, Bo-Ran W, et al. An approach to determine small-signal model parameters for InP HBT up to 110 GHz[J]. Journal of Infrared and Millimeter Waves, 2018. [百度学术]

Sun Y, Liu Z, Li X, et al. Distributed Small-signal Equivalent Circuit Model and Parameter Extraction for SiGe HBT[J]. IEEE Access, 2019:1-1. [百度学术]

Yamahata S, Kurishima K, Kobayashi T, et al. InP/InGaAs collector-up heterojunction bipolar transistors fabricated using Fe-ion-implantation[C] International Conference on Indium Phosphide & Related Materials. IEEE, 1995. [百度学术]

Horng T S, Wu J M, Huang H H. An extrinsic-inductance independent approach for direct extraction of HBT intrinsic circuit parameters[J]. IEEE Transactions on Microwave Theory and Techniques, 2001, 49（12）:2300-2305. [百度学术]

Oudir A, Mahdouani M, Mansouri S, et al. Small-signal modeling of Emitter-up HBT using an improved analytical approach. Application to InGaAlAs/GaAsSb/InP DHBT with strained base[J]. Solid-State Electronics, 2010, 54（1）:67-78. [百度学术]

Johansen T K, Krozer V, Nodjiadjim V, et al. Improved External Base Resistance Extraction for Submicrometer InP/InGaAs DHBT Models[J]. IEEE Transactions on Electron Devices, 2011, 58（9）:3004-3011. [百度学术]

Degachi L, Ghannouchi F M. An Augmented Small-Signal HBT Model With Its Analytical Based Parameter Extraction Technique[J]. IEEE Transactions on Electron Devices, 2008, 55（4）:968-972. [百度学术]

Samelis A, Pavlidis D. DC to high-frequency HBT-model parameter evaluation using impedance block conditioned optimization[J]. IEEE Transactions on Microwave Theory and Techniques, 1997, 45（6）:886-897. [百度学术]

Gao J, Li X, Wang H, et al. An approach to determine small-signal model parameters for InP-based heterojunction bipolar transistors[J]. IEEE Transactions on Semiconductor Manufacturing, 2006, 19（1）:138-145. [百度学术]

Gao J. Heterojunction Bipolar Transistors for Circuit Design: Microwave Modeling and Parameter Extraction[M]. Singapore: Wiley, 2015. [百度学术]

Bousnina S, Mandeville P, Kouki A B, et al. Direct parameter-extraction method for HBT small-signal model[J]. IEEE Transactions on Microwave Theory and Techniques, 2002, 50（2）:529-536. [百度学术]

Zhang Jincan, Liu Bo, et al. A rigorous peeling algorithm for direct parameter extraction procedure of HBT small-signal equivalent circuit. Analog Integr Circ Sig Process （2015） 85:405-411. [百度学术]

Johansen, Tom K, Leblanc, Remy, Poulain, Julien, et.al. Direct Extraction of InP/GaAsSb/InP DHBT Equivalent-Circuit Elements from S-Parameters Measured at Cut-Off and Normal Bias Conditions[J]. IEEE Transactions on Microwave Theory & Techniques, 64（1）:115-124. [百度学术]

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English Version

An improved direct extraction method for InP HBT small-signal model PDF

Abstract

Keywords

Introduction

1 Small-signal equivalent circuit model

2 Parameter extraction procedure

2.1　Extraction of parasitic parameters and the extrinsic resistances

2.2　Extraction of the extrinsic base-collector capacitance

2.3　Extraction of the intrinsic elements

3 Results and discussion

4 Conclusion

References

An improved direct extraction method for InP HBT small-signal model PDF

Abstract

Keywords

Introduction

1 Small-signal equivalent circuit model

2 Parameter extraction procedure

2.1 Extraction of parasitic parameters and the extrinsic resistances

2.2 Extraction of the extrinsic base-collector capacitance

2.3 Extraction of the intrinsic elements

3 Results and discussion

4 Conclusion

References

2.1　Extraction of parasitic parameters and the extrinsic resistances

2.2　Extraction of the extrinsic base-collector capacitance

2.3　Extraction of the intrinsic elements