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Zhao Yan-Xiao, Zhang Wan-Rong, Xin Huang, Xie Hong-Yun, Jin Dong-Yue, Fu Qiang. Effect of lateral structure parameters of SiGe HBTs on synthesized active inductors. Chinese Physics B, 2016, 25(3): 038501  
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Effect of lateral structure parameters of SiGe HBTs on synthesized active inductors
Zhao Yan-Xiao, Zhang Wan-Rong†, , Xin Huang, Xie Hong-Yun, Jin Dong-Yue, Fu Qiang
School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China

 

† Corresponding author. E-mail: wrzhang@bjut.edu.cn

Project supported by the Natural Science Foundation of Beijing, China (Grant Nos. 4142007 and 4122014), the National Natural Science Foundation of China (Grant No. 61574010), and the Higher Educational Science and Technology Program of Shandong Province, China (Grant No. J13LN09).

Abstract
Abstract

The effect of lateral structure parameters of transistors including emitter width, emitter length, and emitter stripe number on the performance parameters of the active inductor (AI), such as the effective inductance Ls, quality factor Q, and self-resonant frequency ω0 is analyzed based on 0.35-μm SiGe BiCMOS process. The simulation results show that for AI operated under fixed current density JC, the HBT lateral structure parameters have significant effect on Ls but little influence on Q and ω0, and the larger Ls can be realized by the narrow, short emitter stripe and few emitter stripes of SiGe HBTs. On the other hand, for AI with fixed HBT size, smaller JC is beneficial for AI to obtain larger Ls, but with a cost of smaller Q and ω0. In addition, under the fixed collector current IC, the larger the size of HBT is, the larger Ls becomes, but the smaller Q and ω0 become. The obtained results provide a reference for selecting geometry of transistors and operational condition in the design of active inductors.

PACS: 85.30.−z;85.30.Pq;85.40.Qx;84.37.+q;
Keyword:SiGe HBT;lateral structure parameters;active inductor;
1. Introduction

Active inductors (AIs) synthesized by transistors have attracted increasing interest due to a number of unique advantages over its spiral counterpart including small chip area consumption, large inductance with wide tuning range, large and tunable quality factor, and high self-resonant frequency.[1–5] The popular synthesis method of AI is based on Gyrator-C principle. A gyrator consists of two back-to-back connected transistors as transconductors, and input capacitance Cπ of one transconductor acts as the load of the other transconductor,[1,6] then the gyrator-C behaves as a single-ended inductor. Therefore, the performance of transistors has a decisive effect on the performance of active inductor. Furthermore, the performance of transistors is almost determined by vertical and lateral structure parameters. For the transistors with the fixed vertical structure, their performance parameters are fundamentally determined by lateral structure.[7,8] Therefore, for an AI designer who relies on the library of foundry, it is important to know how to select transistors in the foundry library so as to meet the requirement of AI parameters, such as inductance Ls, quality factor Q, and self-resonant frequency ω0.

Up to now, there are many papers on synthesis of AI. It is shown that the AI parameters depend on the model parameters of transistors, such as capacitance, transconductance and resistance. Kia et al.[1,6,9] proposed novel AIs and derived that Ls can be expressed by transistor model parameters, so can Q and ω0. Kumari et al.[3] studied the dependence of Ls on the load capacitance C. Robert et al.[10] discussed the Q enhancement with the feedback resistance Rf. Chun et al.[11] discussed the effect of the input signal voltage on Ls and improved the AI linearity. However, there has been no report on the effect of lateral parameters of transistors on performance parameters of AI.

In this paper, based on library of 0.35-μm SiGe BiCMOS process, the effect of lateral parameters of transistor such as emitter width, emitter length, and emitter stripe number on performance parameters of AI is investigated. The paper is arranged as follows. In Section 2, taking a typical active inductor topology for example, the dependence of the AI parameters including the Ls, Q, and ω0 on transistor model parameters input capacitance Cπ, transconductance gm, and input resistance rπ is given. Furthermore, in Section 3, by analyzing the dependence of the transistor model parameters on HBTs lateral parameters, we obtain the analytical expressions that reveal the effect of transistor lateral parameters on the AI parameters Ls, Q, and ω0. In Section 4, based on library of 0.35-μm SiGe BiCMOS process, the effect of lateral parameters of transistors such as emitter width, emitter length, and emitter stripe number on AI parameters is verified. Finally, the conclusion is given in Section 5.

2. A typical SiGe HBT active inductor

A typical SiGe HBT active inductor consists of common emitter configuration of transistor Q1 with a negative transconductance and common collector configuration of transistor Q2 with a positive transconductance, as shown in Fig. 1. The small signal equivalent circuit of the active inductor including SiGe HBT input capacitance Cπ, input resistance rπ, transconductance gm is shown in Fig. 2, and the input admittance of the active inductor Yin can be expressed as follows:

Fig. 1. A typical SiGe HBT active inductor.
Fig. 2. Small signal equivalent circuit.

The expression (1) can be represented by an RLC network as shown in Fig. 3 with its parameters given by

The self-resonant frequency ω0 of RLC network of the active inductor is derived from Eqs. (3) and (4) as

The input impedance Zin = 1/Yin has a zero at frequency

It is evident that the RLC network in Fig. 3 is inductive when ωz < ω < ω0.

The quality factor Q of the active inductor can be expressed as

where “//” represents Rp in parallel with RpL, and RpL ≈ Ls/(RsLCp).[12]

Fig. 3. RLC equivalent circuit.
3. Analytical expressions for AI parameters dependence on lateral structure parameters of SiGe HBTs

As shown in Section 2, the active inductor parameters Ls, Q, and ω0 depend on transistor model parameters Cπ, gm, and rπ. Obviously, they depend on the lateral structure parameters of the transistors. Therefore, the effect of the lateral structure parameters of SiGe HBTs on the AI is obtained by analyzing the dependence of Cπ, gm, and rπ on lateral structure parameters.

In general, the input resistance rπ of the transistor is expressed as

where β0 is the small-signal current gain of the transistor, and β0 can be calculated by

where WB is the width of the base, τn is the minority-carrier lifetime in the base, Dn is the diffusion coefficient for electrons, Dp is the diffusion coefficient for holes, Lp is the diffusion length for holes in the emitter, NA is doping density of the base, ND is doping density of the emitter. Equation (10) indicates that β0 is related mainly to the vertical structure parameters, and it is almost independent of the lateral structure parameters.

The transconductance gm of the transistor can be expressed as

where IC is the current of collector, JC is the current density of collector, q is the electron charge, k is the Boltzmann’s constant, T is the temperature, WE is the emitter width, LE is the emitter length, and NE is the emitter stripe number.

The input capacitance Cπ is composed of a bottom capacitance (CBottom) and a sidewall capacitance (CSW), and Cπ can be simply described as

where A and B are respectively capacitance per unit area for the bottom part and sidewall part, and DE is the junction depth of emitter. Because DE in the library of 0.35 μm SiGe BiCMOS technology is fixed, the capacitance is then proportional to WE, LE, and NE. Generally, LE is much greater than WE, and it can be considered that WE + LE ≈ LE, and equation (13) can be simplified as

For simplification, the transistors Q1 and Q2 in Fig. 1 is assumed to be identical. Therefore, they have the same rπ, Cπ, and gm. The inductance Ls can be derived by substituting Eqs. (11) and (13) into Eq. (4)

As shown in Eq. (14), the inductance is larger for smaller size of SiGe HBT at fixed JC, and inversely at fixed IC.

Quality factor Q is derived by substituting Eqs. (9), (11), and (13) into Eq. (8)

Because β0 ≫ 1, (2/β0 + 1) ≈1, equation (15) is simplified into

Equation (16) implies that Q is independence of LE and NE, and Q is larger with wider WE at fixed JC. On the other hand, Q is lower with larger size of SiGe HBT at fixed IC. In addition, Q is inversely proportional to the angular frequency ω and proportional to collector current density JC.

The quality factor Q is also expressed as follows:

Therefore, ω0 can be given by

4. Verification and discussion
4.1. Effect of emitter width on performance parameters of the active inductor

Figure 4 shows the equivalent inductance Ls versus 1/WE at different frequency of 2 GHz, 6 GHz, and 7 GHz, respectively, for SiGe HBTs with LE = 10 μm and NE = 1 at a fixed JC = 0.05 mA/μm2. As WE increases from 0.3 μm to 0.9 μm, a decrease of 3.2 nH at f = 2 GHz and f = 6 GHz, and a 2.7 nH decrease at f = 7 GHz is observed. It indicates that Ls increases as WE decreases for a given frequency. Therefore, a large Ls can be obtained by small WE, which is consistent with Eq. (14).

Fig. 4. Ls versus 1/WE at JC = 0.05 mA/μm2.

Figure 5 gives Q and ω0 of the AI versus WE at a fixed JC = 0.05 mA/μm2. As WE increases from 0.3 μm to 0.9 μm, Q has an increase of 0.5 at f = 2 GHz and an increase of 0.3 at f = 6 GHz and f = 7 GHz, and ω0 has an increase of 1 GHz. It is shown that Q and ω0 increase slightly with increasing WE, which is consistent with Eqs. (16) and (18).

Fig. 5. Q and ω0 versus WE at JC = 0.05 mA/μm2.

Figure 6 shows Ls, Q, and ω0 of the AI versus WE for SiGe HBTs with LE = 15 μm and NE = 1 at IC = 0.2 mA and f = 1 GHz. As WE increases from 0.3 μm to 0.9 μm, Ls has an increase of 2.79 nH, Q has a decrease of 1.07 and ω0 has a decrease of 4.5 GHz. It indicates that Ls increases with WE because Ls is proportional to Cπ and inversely proportional to the square of gm. As we know, wider WE leads to larger Cπ, and gm is independence of WE at fixed collector current IC. Inversely, wider WE results in smaller Q because Q is inversely proportional to Cπ at fixed collector current IC. Similarly to Q, ω0 decreases with the increase of WE.

Fig. 6. Ls, Q, and ω0 versus WE at IC = 0.2 mA.
4.2. Effect of emitter length on performance of the active inductor

Figure 7 shows the equivalent inductance Ls versus 1/LE at different frequency of 2 GHz, 6 GHz, and 7 GHz, respectively, for SiGe HBTs with WE = 0.3 μm and NE = 1 at a fixed JC = 0.05 mA/μm2. As emitter length increases from 10 μm to 20 μm, Ls is reduced by 2.1 nH at f = 2 GHz, 1.8 nH at f = 6 GHz, and 1.4 nH at f = 7 GHz. Therefore, larger Ls can be obtained by narrowing down LE, which is consistent with Eq. (14).

Fig. 7. Ls versus 1/LE at JC = 0.05 mA/μm2.

Figure 8 gives Q and ω0 of the active inductor versus 1/LE at JC = 0.05 mA/μm2. As emitter length increases from 10 μm to 20 μm, Q is reduced by 0.19 at f = 2 GHz, 0.1 at f = 6 GHz, and 0.08 at f = 7 GHz, and ω0 is 10.5 GHz as emitter length is 10 μm, 15 μm, and 20 μm. It illustrates that LE has little effect on Q and ω0, which is consistent with Eqs. (16) and (18).

Fig. 8. Q and ω0 versus 1/LE at JC = 0.05 mA/μm2.

Figure 9 shows Ls, Q, and ω0 of the active inductor versus LE for SiGe HBTs with WE = 0.3 μm and NE = 1 at IC = 0.2 mA and f = 1 GHz. As LE increases from 10 μm to 20 μm, Ls has an increase of 1.61 nH, but Q is reduced by 2.66 and ω0 is lowered from 13.5 GHz to 7 GHz. It indicates that under fixed collect current IC, larger Ls can be obtained by longer emitter length, but this can lower Q and ω0.

Fig. 9. Ls, Q, and ω0 versus LE at IC = 0.2 mA.
4.3. Effect of emitter stripe number on performance of the active inductor

Figure 10 shows the equivalent inductance Ls versus 1/NE at different frequency of f = 2 GHz, 6 GHz, and 7 GHz, respectively, for SiGe HBTs with WE = 0.3 μm and LE = 10 μm at a fixed JC = 0.05 mA/μm2. As emitter stripe number increases from 1 to 5, Ls is reduced by 3.25 nH at f = 2 GHz, 2.89 nH at f = 6 GHz, and 2.43 nH at f = 7 GHz. Therefore, larger Ls can be obtained by smaller NE, which is consistent with Eq. (14).

Figure 11 gives Q and ω0 of the active inductor versus 1/NE at JC = 0.05 mA/μm2. As emitter stripe number increases from 1 to 5, Q is reduced by 0.1 at f = 2 GHz, 6 GHz, and 7 GHz, and ω0 is 10.5 GHz as emitter stripe number is 1, 3, and 5. It illustrates that NE has little effect on Q and ω0, which is consistent with Eqs. (16) and (18).

Fig. 10. Ls versus 1/LE at JC = 0.05 mA/μm2.
Fig. 11. Q and ω0 versus 1/NE at JC = 0.05 mA/μm2.

Figure 12 shows Ls, Q, and ω0 of the active inductor versus NE for SiGe HBTs with WE = 0.3 μm and LE = 10μm at a fixed IC = 0.2 mA and f = 1 GHz. As NE increases from 1 to 5, Ls increases from 2.48 nH to 8.89 nH, Q decreases from 8.21 to 2.06, ω0 reduces from 13.5 GHz to 2.5 GHz. It can be seen that Ls becomes larger, but Q and ω0 become lower with more emitter stripes in parallel.

Fig. 12. Ls, Q, and ω0 versus WE at IC = 0.2 mA.
4.4. Effect of collect current density on performance of the active inductor

The above results are obtained at the fixed collect current density and the fixed collect current, respectively. Figure 13 shows the active inductor parameters Ls, Q, and ω0 versus the collect current density JC for SiGe HBTs with WE = 0.3 μm, LE = 10 μm, and NE = 1 at f = 2.5 GHz. As collect current density increases from 0.02 to 0.20 mA/μm2, Ls reduces from 16.1 nH to 0.44 nH, Q increases from 0.95 to 19.10, and ω0 increases from 4 GHz to 33.5 GHz. It indicates that smaller JC is beneficial for active inductor to obtain larger Ls, but higher Q and ω0 need active inductor operates at larger JC.

Fig. 13. Ls, Q, and ω0 versus the collect current density JC at a fixed size of HBTs.
5. Conclusion

In the paper, we analyze the effect of lateral structure parameters including emitter width, length and emitter stripe number of HBT on the performance parameters of the active inductor (AI), such as inductance Ls, quality factor Q, and self-resonant frequency ω0 based on library of 0.35-μm SiGe BiCMOS process. The simulation results show that for a given collector current density JC, the large Ls of the AI can be obtained by the narrow, short emitter stripe and few emitter stripes, but Q and ω0 have little dependence on the geometry sizes of SiGe HBTs. For a fixed HBT size, smaller JC is beneficial for AI to obtain larger Ls, but with a cost of smaller Q and ω0. In addition, for the fixed collector current IC, the large HBT size results in large Ls, but small Q and ω0. Therefore, in the design of an AI, a tradeoff exists among the AI parameters, the lateral structure parameters of HBT, and operational current density or operational current. The obtained results provide a basis for selecting the transistors lateral geometry from the library of foundry and operational condition in the design of active inductors.

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