Frequency stability of InP HBT over 0.2 to 220 GHz

    Corresponding author: Kun Ren, hbrenkun@163.com
  • 1. The Key Laboratory for RF Circuits and Systems of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310037, China
  • 2. Science and Technology on Monolithic Integrated Circuit and Modules Laboratory, Nanjing Electronic Devices Institute, Nanjing 210016, China

Key words: double heterojunction bipolar transistor (DHBT)small-signal modelstability factor

Abstract: The frequency stabilities of InP DHBTs in a broadband over 1 to 220 GHz are investigated. A hybrid π-topology small-signal model is used to accurately capture the parasitics of devices. The model parameters are extracted from measurements analytically. The investigation results show that the excellent agreement between the measured and simulated data is obtained in the frequency range 200 MHz to 220 GHz. The dominant parameters of the π-topology model, bias conditions and emitter area have significant effects on the stability factor K. The HBT model can be unconditionally stable by reasonable selection of the proper bias condition and the physical layout of the device.

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1.   Introduction
  • Due to their superior high frequency performance, InP/InGaAs heterojunction bipolar transistors (HBT) have been demonstrated as being more powerful in the area of monolithic microwave integrated circuits (MMICs) design. An accurate and stable small signal HBT equivalent circuit model plays an important role in evaluating the process technology. As the technology fabrication matures and parasitics are minimized, it is necessary to analyze the limitations of high frequency performance of RF devices. A number of techniques of small-signal extraction have been proposed in the literature. Either~the $T$-topology~model[1, 2, 3]~or~the $\pi$-topology~small-signal~equivalent~circuit~model[4, 5, 6]~is~adopted; whichever, they just examine dozens of GHz. Due to on-wafer measurement and de-embedding uncertainties, an accurate extraction method is still a huge challenge at frequencies beyond 110 GHz. A model of SiGe HBT is validated in the frequency range of 100 to 300~GHz and has been reported[7]. There is still a lack of impressive work on the stability of the devices in these literatures[8]. Stability factor $K$ is important not only for linear, also for non-linear radio frequency circuit applications, especially in the microwave and mm-wave field, and is derived based on the HBT small-signal model mentioned above.

    In this paper, the small signal equivalent-circuit model has been analytically extracted from $S$-parameters measured based on the $\pi$-topology, followed by an analysis of the stability factor $K$. Therefore, the relationship between the model elements and the stability factor is discussed. With the ADS simulation tool, some conclusions are achieved directly from simulated results.

2.   Small signal model analysis
  • The InP common-emitter DHBT with an emitter area of 3 $\mu$m$^{2}$ was used in this procedure. The physical model and small-signal equivalent circuit are shown in Figures 1(a) and 1(b), including the extrinsic part denoted by the base, collector and emitter impedances ($Z_{\rm b}$, $Z_{\rm c}$ and $Z_{\rm e})$, and the base-collector and base-emitter extrinsic junction ($C_{\rm bcx}$, $R_{\rm bcx}$, $C_{\rm bex}$ and $R_{\rm bex})$. The intrinsic part is given by the base-collector and base-emitter intrinsic junction ($C_{\rm bci}$, $R_{\rm bci}$, $C_{\rm bei}$ and $R_{\rm bei})$, transconductance $g_{\rm m}$, output resistance $R_{\rm ce}$ and output capacitance $C_{\rm ce}$. For simplicity, the extrinsic parameters $C_{\rm bex}$ and $R_{\rm bex}$ are neglected in the extraction procedure. Due to the large junction resistance $R_{\rm bcx}$, $R_{\rm bci}$, and output resistance $R_{\rm ce}$, they are ignored in the extraction procedure. Figure 1(b) is usually characterized by the following $Z$-parameters[4]. $Y_{\rm int}$ is the intrinsic admittance.

    $Y_{\rm bi}$ $=$ 1 / $R_{\rm bi}+{\rm j} \omega C_{\rm bi}$, $Y_{\rm bei}$ $=$ 1 / $R_{\rm bei}+{\rm j} \omega C_{\rm bei}$, $Y_{\rm bcx}$ $=$ 1~/~$R_{\rm bcx}+{\rm j} \omega C_{\rm bcx}$, $Y_{\rm bci}$ $=$ j$\omega C_{\rm bci}$ / (1 $+$ j$\omega R_{\rm ci}C_{\rm bci})$ and $Y_{\rm ce}$ $=$ $R_{\rm ce}$ $+$ j$\omega C_{\rm ce}$, $Z_{\rm b}$ $=$ $R_{\rm b}$ $+$ j$\omega L_{\rm b}$, $Z_{\rm c}$ $=$ $R_{\rm c}$ $+$ j$\omega L_{\rm c}$, $Z_{\rm e}=R_{\rm e}$ $+$ j$\omega L_{\rm e}$, respectively.

    The initial values are extracted using proper equations described by $Y$-parameters and $Z$-parameters transformed by the measured $S$-parameters.

    $S$-parameters are measured using an Agilent N5247A network analyzer (up to 70 GHz), a millimeter wave controller N5262A, a VNA (vector network analyzer), frequency extenders from Farran Technology of series FEV-10-TR (75-110~GHz), a FEV-05-TR (140-220 GHz) and a probe station from Cascade Microtech (Summit 12000 m). An impedance standard substrate (ISS) calkit and surface wave absorber have been used. An LRRM[7] (line-reflect-reflect-match) calibration is performed on the commercial ISS. The LRRM calibration procedure is used to have the test reference plane at the tip of the probe (WinCal software from Cascade Microtech). At the "over-driven $I_{\rm b}$" bias condition, according to Lee[5], the expressions of resistances and inductances are shown below.

    Usually, $R_{\rm bi}$ are relatively smaller than $R_{\rm bei}$ and $R_{\rm bci}$ and the intrinsic part is independent of frequency, after $R$ in Equation (2) is obtained, $C_{\rm bc}$, $C_{\rm ce}$, $R_{\rm bei}$, $C_{\rm be}$ and $g_{\rm m}$ are extracted by the $Y$-parameters proposed by Hafedh[4].

    $C_{\rm bci}$ and $C_{\rm bcx}$ can be derived by using the ratio of the emitter contact area to the base area[9].

    The LRRM calibration on the ISS is followed by open-short de-embedding in the frequency range of 0.2-67 GHz and 75-110 GHz. The elements of the intrinsic part are extracted from $S$-parameters measured in 0.2-67 GHz and 75-110 GHz after de-embedding. With an open structure modeled in the frequency range of 0.2-220 GHz precisely, the $S$-parameter of the DUT measured in G-band is de-embedded by the $S$-parameter of the open structure modeled in G-band. The extrinsic resistances and inductances can be extracted from $S$-parameters measured in 0.2-67 GHz, 75-110 GHz and 140-220 GHz. Only the parameters of the small signal model are taken into the optimization algorithm; the parameters are presented in Table 1. With the PAD structure, the excellent agreement between the measured $S$-parameters and the simulated ones is shown in Figure 2, containing the real and imaginary part of $S_{11}$, $S_{22}$ and $S_{21}$. The parameters of the small signal model extracted above are used for the following stability analysis combined with the hybrid $\pi $-topology small-signal equivalent circuit presented in Figure 1(b).

3.   Stability analysis
  • For microwave transistors, LNA and PA design, the $K$-factor is one of the factors to evaluate their performance. As $K$ is above unity, it means an RF circuit, device or system is absolutely, or unconditionally stable. Stability factor $K$ decreases while decreasing frequency, and becomes less than 1 in the lower frequency regime[8, 10]. The widely accepted conditions necessary and sufficient for devices and circuits to be unconditionally stable are shown below[8]:

    According to Equations (18) and (19), the $K$ factor can be easily derived from the measured $S$-parameters, and often conveniently characterized in terms of $S$-parameters. It is widely used to evaluate the stability of circuits and devices.

    An intrinsic two-port impedance matrix ($Y$-parameters) can be used to achieve more superior insights of device stability factor $K$[10].

    For efficiency, only the $Y$-parameters of the intrinsic part discussed in Section 2 are taken into account, so we get the following equation.

    The relationship between the stability factor and $f_{\rm T}$, $f_{\rm MAX}$ is linked by intrinsic parameters. The expressions of $f_{\rm T}$ and $f_{\rm MAX}$ are shown below[11]. $C_{\rm je}$ is the base-emitter junction capacitance. $C_{\rm bc}$ is the base-collector capacitance. $R_{\rm b}$ is the base resistance. $K$ is Boltzmann's constant. Devices would become potentially unstable while increasing $f_{\rm T}$ and $f_{\rm MAX}$. This is examined by the following part of the paper.

    Firstly, four different HBTs: 2.8, 3.5, 4.2 and 7 $\mu $m$^{2}$, are used to analyze the $K$-factor. Results are shown in Figure 3, the stability factor $K$ can be increased while using a larger emitter area. Due to the larger emitter area enhancing the base-emitter junction capacitor, according to Equations (21) and (22), the $K$ factor is increased while $f_{\rm T}$ is decreased.

    The effect of biases on the $K$-factor is illustrated in Figure 4. The $K$ factor is increased as the bias $i_{\rm b}$ is increased. $C_{\rm bei}$ also keeps increasing. More energy of the RF signal is coupled to the ground by increasing $C_{\rm bei}$. This is in accordance with Figure 3.

    In order to enhance $f_{\rm T}$ and $f_{\rm MAX}$, we should keep the denominator lower. A high base doping allows a transistor to have a low base sheet resistance $R_{\rm b}$, a low emitter doping reduces the base-emitter junction capacitance $C_{\rm je}$ and reducing the emitter area can keep $C_{\rm je}$ lower, so the high frequency performance is improved. But these methods will make the stability factor $K$ worse.

    Secondly, the effect of the main parameters of the HBT model on the $K$-factor is analyzed at 80 GHz by using an ADS tool. The low emitter doping reduces the base-emitter junction capacitance, and the same with the $K$-factor. This is examined in Figure 5. While increasing the base-emitter and base-collector junction capacitors, more high frequency energy is coupled to the ground. This is in agreement with Equation (21).

    Figure 6 gives the effect of extrinsic and intrinsic resistors $R_{\rm bx}$, $R_{\rm cx}$ and $R_{\rm e}$, $R_{\rm bi}$ and $R_{\rm ci}$ on the $K$-factor. Except for $R_{\rm e}$ and $R_{\rm ci}$, increasing $R_{\rm bx}$, $R_{\rm cx}$ and $R_{\rm bi}$ can improve the $K$-factor. The input and output reflection coefficients are given in Equations (24) and (25)[8]. Increasing $R_{\rm bx}$, $R_{\rm cx}$ and $R_{\rm bi}$ is equal to making the real part of the input and output reflection coefficients positive, and obtaining a stable network. Opposite to them, device stability will become worse while keeping Re increasing. This is in agreement with the analysis in Chen[12].

    At a given bias, when $R_{\rm e}$ is increased, the voltage $V_{\rm bei}$ is decreased, and bias dependent capacitance $C_{\rm bei}$ is also reduced. From the analysis in Figure 6, the stability gets worse while increasing $R_{\rm e}$. So in order to improve both the $K$-factor and $f_{\rm T}$, a lower $R_{\rm e}$ transistor is used. A high base doping (lower $R_{\rm b})$ is used to enhance $f_{\rm T}$, but make the stability factor $K$ lower.

    The effect curve of transconductance parameter $g_{\rm m}$ is presented in Figure 7. The result does not agree with Chen[12]. According to Equation (26), increasing $g_{\rm m}$ is equivalent to increasing $I_{\rm c}$. Stability factor $K$ of the HBT declines while $I_{\rm c}$ increased[12]. Here $q$ is the charge on an electron, $T$ is the junction temperature, and $K$ is Boltzmann's constant. We can get the same conclusion from Equation (21). This will guide a circuit designer to make a trade-off between stability and power gain.

4.   Conclusion
  • An accurate method for extracting the HBT small-signal model parameters up to 220 GHz has been presented, indicating good accuracy and robustness of this extraction technique, followed by a comprehensive study of the $K$ factor based on the small signal equivalent circuit model aforementioned. The effects of biasing, emitter area and the main parameters of the HBT equivalent circuit model on stability were analyzed. The results indicate that increasing capacitance, emitter area, base currents, and base and collector extrinsic resistances can reduce the potentially unstable bandwidth, and increase stability factor $K$. It is proposed that an active circuit can be unconditionally stable while excellently selecting model parameters and bias conditions without any other stability related matching network, which consumes more chip area and increases cost. This conclusion can guide the designer who is making a trade-off between the different conditions that impact stability while keeping the device stable.

Figure (7)  Table (1) Reference (12) Relative (20)

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