Simple Modeling and Analysis of Total Ionizing Dose Effects on Radio-Frequency Low-Noise Amplifiers

Abstract

In this study, the degradation characteristics of radio frequency (RF)-low-noise amplifiers (LNA) due to a total ionizing dose (TID) is investigated. As a device-under-test (DUT), sample LNAs were prepared using silicon–germanium (SiGe) heterojunction bipolar transistors (HBTs) as core elements. The LNA was based on a cascode stage with emitter degeneration for narrowband applications. By using a simplified small-signal model of a SiGe HBT, design equations such as gain, impedance matching, and noise figure (NF) were derived for analyzing TID-induced degradations in the circuit-level performance. To study radiation effects in circuits, the SiGe-RF-LNAs fabricated in a commercial 350 nm SiGe technology were exposed to 10-keV X-rays to a total ionizing dose of up to 3 Mrad(SiO₂). The TID-induced performance changes of the LNA were modeled by applying degradation to device parameters. In the modeling process, new parameter values after irradiation were estimated based on information in the literature, without direct measurements of SiGe HBTs used in the LNA chip. As a result, the relative contributions of parameters on the circuit metrics were compared, identifying dominant parameters for degradation modeling. For the TID effects on input matching (S₁₁) and NF, the base resistance (R_B) and the base-to-emitter capacitance (C_π) of the input transistor were mostly responsible, whereas the transconductances (g_m) played a key role in the output matching (S₂₂) and gain (S₂₁). To validate the proposed approach, it has been applied to a different LNA in the literature and the modeling results predicted the TID-induced degradations within reasonable ranges.

1. Introduction

Silicon–germanium heterojunction bipolar transistors (SiGe HBTs) have demonstrated promising suitability for a variety of wireless and communication applications. They exhibit good radio frequency (RF) performance parameters such as high unity-gain frequency (f_T) and maximum oscillation frequency (f_MAX) [1,2,3]. Moreover, in order to investigate their potential usage in extreme environment (e.g., space), radiation effects on SiGe-HBT devices and circuits have been studied in the literature [2,3,4,5,6]. It has been found that SiGe HBTs can often maintain performance up to an ionizing dose of hundreds of krad(SiO₂) or greater [3,4,5,6]. SiGe HBTs are not highly dependent on the quality of their oxide layers, unlike typical metal-oxide-semiconductor devices [2,3]. Still, SiGe HBTs undergo performance degradation due to total ionizing dose (TID), and they can show increases in leakage current and reductions in gain. The key mechanism associated with this degradation includes the generation of traps in the emitter-base (EB) spacer and oxide area of the shallow trench isolation (STI) [3,4,5,6,7,8].

One of the essential circuit blocks in RF applications is the low-noise amplifier (LNA) in a receiver. It is designed to provide impedance matching to the input port for good signal reception and sufficient gain for the subsequent stages, while minimizing noise contributions for better noise performance of the overall receiver system [9,10]. Regarding radiation effects, SiGe LNAs suffer from variations in input and output impedances, a reduction of signal gain, and an increase in noise figure (NF) [11], most of which are attributed to the degradation of active devices such as SiGe HBTs [12,13]. Previous workers have investigated TID effects on LNA performance [14,15,16], but few studies have addressed the relationships between device parameters and circuit performance. Moreover, in many cases full device-level characterization data are not available to circuit designers, imposing difficulties in analysis. Such an approach is helpful for predicting potential degradation and developing radiation-hardening design techniques that are well-trimmed to specific devices utilized in the circuit.

This paper is organized as follows. Section 2 explains the schematic and the analysis of the LNA, using simplified small-signal models of SiGe HBTs. Based on the equivalent circuit, TID-induced performance degradation is modeled. In Section 3, details of the experimental setup and performance variations of the sample SiGe LNA exposed to X-ray are presented. In Section 4, using device parameters of the equivalent circuit, we discuss modeling results and analyze the impact of SiGe-HBT parameters on LNA performance. For validating the proposed method, the modeling approach is applied to another example of an LNA in Section 5. Lastly, Section 6 summarizes the findings of this investigation.

2. LNA Schematic and Device Modeling

An RF LNA is the first gain stage in a receive chain and it plays a key role in (1) impedance matching between the antenna and the chip and (2) minimizing system noise performance. It must provide sufficient gain to the incoming signal for processing in the subsequent stages. In the aspect of small-signal operation, circuit performance is measured with scattering parameters (S-parameters); S₂₁, S₁₁, and S₂₂ represent power gain, input matching, and output matching, respectively [17]. In addition, noise performance is defined as the noise figure (NF) with units of dB [18]. Large-signal characteristics of an LNA are important as well, but this work primarily focuses on small-signal operation, where signal gain, impedance matching, and noise performance are more relevant.

A target LNA employing SiGe HBTs was designed and optimized for achieving balanced gain, matching, and noise performance [18,19]. The schematic of the designed SiGe LNA is shown in Figure 1 [20,21,22]. This topology has been widely used for a variety of narrowband applications due to key advantages such as the ability to provide a real impedance with non-resistive components, low-noise characteristics, and good isolation between the input and the output terminals [20,21,22]. Specifically, the LNA was based on a cascode common-emitter (Q₁ and Q₂) stage as a main stage [5] and the second stage (Q₃ and Q₄) acted as a buffer for output-impedance matching. In the former, Q₁ was the input transistor that received the signal. Q₁, C_BE, L_E, and L_B were collectively optimized for the input-matching network and for noise impedance simultaneously. Q₂ was a cascode stage to improve gain performance and suppress Miller effects associated with the parasitic base-collector capacitance [23]. The emitter inductor L_E generated real impedance at the base terminal of Q₁ and provided negative feedback for stability. In addition, the base-to-emitter capacitance C_BE and C_π1 in Figure 2 were tuned for both input and noise matching. The second branch was configured as an emitter-follower stage, providing decoupling between the first stage and the load. Lc₂ resonated out the parasitic capacitance at the collector of Q₂, whereas Lc₁ was optimized for peak gain at the operation frequency. Lastly, C₁, C_2, and C₃ were tuned for DC blocking (or AC coupling) and R_BIAS supplied the desired current to the base terminal of Q₄.

For a theoretical analysis, a small-signal model of a SiGe HBT was constructed as shown in Figure 2 [24,25]. Whereas the complete small-signal-equivalent models were much more complex [26], only a few device parameters that were dominant in determining circuit performance were selected for simplicity. In this model, g_m, r_π, R_B, r_O, C_π, and C_μ represented the small-signal transconductance, the emitter-to-base resistance, the base parasitic resistance, the collector-to-emitter resistance, the base-to-emitter capacitance, and the base-to-collector capacitance, respectively. Regarding noise sources, $\overline{{\mathrm{V}}_{\mathrm{N}.\mathrm{B}}^2}$, $\overline{{\mathrm{I}}_{\mathrm{N}.\mathrm{B}}^2}$, and $\overline{{\mathrm{I}}_{\mathrm{N}.\mathrm{C}}^2}$ were the thermal noise of the R_B, the shot noise associated with I_B, and the shot noise associated with I_C, respectively.

The numerical value of each parameter in the equivalent model can be obtained if full characterization results or transistor models are available, following the extract methods presented in [27]. For instance, R_B was determined from the impedance parameters (Z-parameters), whereas intrinsic capacitances C_π and C_μ were determined from the admittance parameters (Y-parameters). The transconductance (g_m) was obtained by taking the derivative of I_C with respect to V_BE. In this work, Equations (1)–(6) were applied to the process-design-kit models of SiGe HBTs in order to extract parameter numbers. β and ω referred to the current gain and the angular frequency, respectively.

$${\mathrm{g}}_{\mathrm{m}}=\frac{\partial {\mathrm{I}}_{\mathrm{C}}}{\partial {\mathrm{V}}_{\mathrm{B}\mathrm{E}}}$$

(1)

$${\mathrm{R}}_{\mathrm{B}}=\mathrm{R}\mathrm{e}({\mathrm{Z}}_{11}-{\mathrm{Z}}_{12})$$

(2)

$${\mathrm{r}}_{\mathsf{\pi }}=\mathrm{R}\mathrm{e}\left({\mathrm{Z}}_{12}\right)=\frac{\mathsf{\beta }}{{\mathrm{g}}_{\mathrm{m}}}$$

(3)

$${\mathrm{r}}_{\mathrm{O}}=\frac{\partial {\mathrm{V}}_{\mathrm{C}\mathrm{E}}}{{\mathrm{I}}_{\mathrm{C}}}$$

(4)

$${\mathrm{C}}_{\mathsf{\pi }}=\frac{\mathrm{I}\mathrm{m}({\mathrm{Y}}_{11}+{\mathrm{Y}}_{12})}{\mathsf{\omega }}$$

(5)

$${\mathrm{C}}_{\mathsf{\mu }}=-\frac{\mathrm{I}\mathrm{m}\left({-\mathrm{Y}}_{12}\right)}{\mathsf{\omega }}$$

(6)

Once the device parameters of the SiGe HBT in the LNA were extracted, the modeling was conducted for the pre- and post-irradiation conditions [25,27]. For parameters that changed after irradiation, their values were modeled based on the information in the literature [3,4]. In this stage, circuit performance metrics such as matching, gain, and noise figure were derived as closed-form equations. For simplicity, parameters that had little or negligible contributions were omitted. For example, in the equation of the input impedance, it was mainly derived with L_B, L_E, C_BE, C_π1, and g_m1. Other parameters such as r_o and C₁ were assumed to be open and short, respectively. In addition, C_μ was selectively eliminated from the analysis, depending on the metrics of interest. The value of C_μ was negligible in the input impedance, but it affected the overall gain performance of the LNA. The input impedance of the LNA that incorporated the changes after irradiation is shown in Equation (7), where the real and the imaginary terms should be matched close to 50 Ω and 0 Ω for minimized reflection at the input interface. Since the dominant parameters that affected the input impedance in the post-irradiation results were the base-to-emitter capacitance (C_π1) and the base resistance (R_B) of the input transistor, their values were decomposed as the pre-irradiation values with “0” subscripts and delta symbols.

$$\begin{gathered} {\mathrm{Z}}_{\mathrm{I}\mathrm{N}}={\mathrm{Z}}_{\mathrm{I}\mathrm{N},0}+∆{\mathrm{Z}}_{\mathrm{I}\mathrm{N}} \\ =\left[\frac{1}{\mathrm{s}{\mathrm{C}}_{\mathrm{B}\mathrm{E}}}||\left({\mathrm{R}}_{\mathrm{B}\mathrm{1,0}}+∆{\mathrm{R}}_{\mathrm{B}1}+\frac{1}{\mathrm{s}\left({\mathrm{C}}_{\mathsf{\pi }\mathrm{1,0}}+∆{\mathrm{C}}_{\mathsf{\pi }1}\right)}\right)\right]+\mathrm{s}\left({\mathrm{L}}_{\mathrm{E}}+{\mathrm{L}}_{\mathrm{B}}\right) \\ +\frac{{(\mathrm{g}}_{\mathrm{m}\mathrm{1,0}}+∆{\mathrm{g}}_{\mathrm{m}1}){\mathrm{L}}_{\mathrm{E}}}{\left({\mathrm{C}}_{\mathsf{\pi }\mathrm{1,0}}+∆{\mathrm{C}}_{\mathsf{\pi }1}\right)+{\mathrm{C}}_{\mathrm{B}\mathrm{E}}+\mathrm{s}\left({\mathrm{C}}_{\mathsf{\pi }\mathrm{1,0}}+∆{\mathrm{C}}_{\mathsf{\pi }1}\right){\mathrm{C}}_{\mathrm{B}\mathrm{E}}({\mathrm{R}}_{\mathrm{B}\mathrm{1,0}}+∆{\mathrm{R}}_{\mathrm{B}1})} \end{gathered}$$

(7)

To analyze the output impedance of the LNA, the circuit was simplified as illustrated in Figure 3a. The impedance looking into the output terminal of the first branch (Z_CAS) that included the cascode stage was assumed to be very high (or simply an open circuit). Then, the total output impedance of the circuit (Z_OUT) was derived as Equation (8). In addition, r_o and C₂ were assumed to be an open and a short, respectively.

$$\begin{array}{l}{\mathrm{Z}}_{\mathrm{O}\mathrm{U}\mathrm{T}}={\mathrm{Z}}_{\mathrm{O}\mathrm{U}\mathrm{T},0}+{∆\mathrm{Z}}_{\mathrm{O}\mathrm{U}\mathrm{T}}\\ =\frac{1}{r_{\mathsf{\pi }}\left({\mathrm{g}}_{\mathrm{m}\mathrm{4,0}}+∆{\mathrm{g}}_{\mathrm{m}4}\right)}[\{({\mathrm{R}}_{\mathrm{B}\mathrm{4,0}}+∆{\mathrm{R}}_{\mathrm{B}4})+\mathrm{s}{\mathrm{L}}_{\mathrm{C}1}\}||\frac{1}{s\left(C_{\mathsf{\mu }\mathrm{2,0}}+∆{\mathrm{C}}_{\mathsf{\mu }2}\right)}+r_{\mathsf{\pi }}]\end{array}$$

(8)

Then, since the remaining circuitry expressed real and imaginary impedances, it was further reduced to a parallel topology as shown in Figure 3b. The expressions of the components in the equivalent model were given below:

$$\begin{array}{l}{\mathrm{R}}_{\mathrm{P}}={\mathrm{R}}_{\mathrm{P},0}+{∆\mathrm{R}}_{\mathrm{P}}\\ =\frac{{\left({\mathsf{\omega }}_{\mathrm{o}}{\mathrm{L}}_{\mathrm{C}1}\right)}^2}{\left\{r_{\mathsf{\pi }}\left({\mathrm{g}}_{\mathrm{m}\mathrm{4,0}}+∆{\mathrm{g}}_{\mathrm{m}4}\right)\right\}\left\{{\mathsf{\omega }}_o^2{r}_{\mathsf{\pi }}\right(C_{\mathsf{\mu }\mathrm{2,0}}+∆{\mathrm{C}}_{\mathsf{\mu }2}){\mathrm{L}}_{\mathrm{C}1}+({\mathrm{R}}_{\mathrm{B}\mathrm{4,0}}+∆{\mathrm{R}}_{\mathrm{B}4}\left)\right\}}\end{array}$$

(9)

$${\mathrm{L}}_{\mathrm{P}}={\mathrm{L}}_{\mathrm{P},0}+{∆\mathrm{L}}_{\mathrm{P}}=\frac{{\mathrm{L}}_{\mathrm{C}1}}{{\mathrm{r}}_{\mathsf{\pi }}\left({\mathrm{g}}_{\mathrm{m}\mathrm{4,0}}+∆{\mathrm{g}}_{\mathrm{m}4}\right)}$$

(10)

$${\mathrm{C}}_{\mathrm{P}}={\mathrm{C}}_{\mathrm{P},0}+{∆\mathrm{C}}_{\mathrm{P}}=\frac{1}{{\mathrm{r}}_{\mathsf{\pi }}\left({\mathrm{g}}_{\mathrm{m}\mathrm{4,0}}+∆{\mathrm{g}}_{\mathrm{m}4}\right)(C_{\mathsf{\mu }\mathrm{2,0}}+∆{\mathrm{C}}_{\mathsf{\mu }2})}$$

(11)

$${\mathrm{Z}}_{\mathrm{O}\mathrm{U}\mathrm{T}}={\mathrm{Z}}_{\mathrm{O}\mathrm{U}\mathrm{T},0}+{∆\mathrm{Z}}_{\mathrm{O}\mathrm{U}\mathrm{T}}={\mathrm{R}}_{\mathrm{P}}|\left|\mathrm{s}{\mathrm{L}}_{\mathrm{P}}\right||\frac{1}{s{\mathrm{C}}_{\mathrm{P}}}$$

(12)

where ω₀ = 2πf₀ and f₀ is the operation frequency. Performance-dominant parameters in the output-impedance characteristics after TID irradiation were R_B4 and g_m4 of Q₄. This will be confirmed in detail by the degradation modeling in Section 4.

The voltage gain of the SiGe LNA was derived in Equation (13), which included dominant components of the small-signal equivalent circuit. The gain equation was composed of multiple circuit-level components (L_C1, L_E, and L_B) and also included transistor parameters such as g_m1, g_m4, C_π1, and C_π2. Similar to the input and the output-impedance equations, the parameters that most affected post-irradiation degradations were expressed with the delta terms.

$$\begin{array}{l}{\mathrm{A}}_{\mathrm{V},\mathrm{L}\mathrm{N}\mathrm{A}}={\mathrm{A}}_{\mathrm{V},\mathrm{L}\mathrm{N}\mathrm{A},0}+{∆\mathrm{A}}_{\mathrm{V},\mathrm{L}\mathrm{N}\mathrm{A}}\\ =\frac{s{\mathrm{L}}_{\mathrm{C}1}\left[1+{\mathrm{s}}^2{\mathrm{L}}_{\mathrm{E}}\left({\mathrm{C}}_{\mathsf{\pi }\mathrm{1,0}}+∆{\mathrm{C}}_{\mathsf{\pi }1}\right)\right]\left[1+s{\mathrm{L}}_{\mathrm{E}}\left({\mathrm{g}}_{\mathrm{m}\mathrm{1,0}}+∆{\mathrm{g}}_{\mathrm{m}1}\right)\right]}{\left[1+{\mathrm{s}}^2\left({\mathrm{L}}_{\mathrm{E}}+{\mathrm{L}}_{\mathrm{B}}\right)\left({\mathrm{C}}_{\mathrm{B}\mathrm{E}}+{\mathrm{C}}_{\mathsf{\pi }\mathrm{1,0}}+∆{\mathrm{C}}_{\mathsf{\pi }1}\right)\right]\left(1+\mathrm{s}\frac{{\mathrm{C}}_{\mathsf{\pi }\mathrm{2,0}}}{{\mathrm{g}}_{\mathrm{m}\mathrm{2,0}}}\right)}(1+\frac{∆{\mathrm{g}}_{\mathrm{m}4}}{{\mathrm{g}}_{\mathrm{m}\mathrm{4,0}}})\end{array}$$

(13)

Achieving low noise contributions from an LNA is important requirement for maintaining a high signal-to-noise ratio. In Figure 2, the thermal noise of the base resistor (R_B) and the shot noise of the base and collector currents were modeled as shown in Equations (14)–(16), which were the main sources of noise in the SiGe HBTs. In the derivation of the NF of the LNA, however, not all noise sources of the constituent transistors were included. Thus, noise contributions from the cascode- and the second-stage transistors were much smaller than those from the input transistor and were omitted. The portions of noise voltages generated from neglected parameters were estimated using the full small-signal equivalent circuits. Again, dominant parameters in the post-irradiation results were identified and corresponding delta terms were added.

$$\begin{array}{l}\overline{{\mathrm{I}}_{\mathrm{N}.I_B}^2}=\overline{{\mathrm{I}}_{\mathrm{N}.I_{B,0}}^2}+∆\overline{{\mathrm{I}}_{\mathrm{N}.I_B}^2}\\ =2\mathrm{q}({\mathrm{I}}_{\mathrm{B},0}+∆{\mathrm{I}}_{\mathrm{B}})\frac{1+s{\mathrm{g}}_{\mathrm{m}}{L}_{\mathrm{E}}}{s\left(L_{C1}+L_{C2}\right)}(R_{\mathrm{B},0}+∆R_{\mathrm{B}}+s{L}_E)||(s{L}_{\mathrm{E}}+\frac{1}{s({\mathrm{C}}_{\mathrm{B}\mathrm{E}}+{\mathrm{C}}_{\mathsf{\pi },0}+∆{\mathrm{C}}_{\mathsf{\pi }})})\end{array}$$

(14)

$$\overline{{\mathrm{V}}_{\mathrm{N}.I_C}^2}=\overline{{\mathrm{V}}_{\mathrm{N}.I_{C,0}}^2}=2\mathrm{q}{\mathrm{I}}_{\mathrm{C}}s\left(L_{C1}+L_{C2}\right)(1-\frac{s{\mathrm{g}}_{\mathrm{m}}{L}_{\mathrm{E}}}{1+s{\mathrm{g}}_{\mathrm{m}}{L}_{\mathrm{E}}})$$

(15)

$$\begin{array}{l}\overline{{\mathrm{V}}_{\mathrm{N}.{\mathrm{R}}_B}^2}=\overline{{\mathrm{V}}_{\mathrm{N}.{\mathrm{R}}_{B,0}}^2}+∆\overline{{\mathrm{V}}_{\mathrm{N}.{\mathrm{R}}_B}^2}\\ =4\mathrm{k}\mathrm{T}\frac{1+s{\mathrm{g}}_{\mathrm{m}}{L}_{\mathrm{E}}}{s(L_{C1}+L_{C2})(R_{\mathrm{B},0}+∆R_{\mathrm{B}})}\left(R_{\mathrm{B},0}+∆R_{\mathrm{B}}+s{L}_{\mathrm{E}}\right)||(s{L}_{\mathrm{E}}+\frac{1}{s({\mathrm{C}}_{\mathrm{B}\mathrm{E}}+{\mathrm{C}}_{\mathsf{\pi },0}+∆{\mathrm{C}}_{\mathsf{\pi }})})\end{array}$$

(16)

$$\overline{{\mathrm{V}}_{\mathrm{N}.\mathrm{o}\mathrm{u}\mathrm{t}}^2}=\overline{{\mathrm{V}}_{\mathrm{N}.\mathrm{o}\mathrm{u}\mathrm{t},0}^2}+∆\overline{{\mathrm{V}}_{\mathrm{N}.\mathrm{o}\mathrm{u}\mathrm{t}}^2}=\overline{{\mathrm{V}}_{\mathrm{N}.{\mathrm{R}}_B}^2}+\overline{{\mathrm{V}}_{\mathrm{N}.I_B}^2}+\overline{{\mathrm{V}}_{\mathrm{N}.I_C}^2}+4kT{R}_{\mathrm{S}}{\mathrm{A}}_{\mathrm{V},\mathrm{L}\mathrm{N}\mathrm{A}}^2$$

(17)

$$\mathrm{N}\mathrm{F}={\mathrm{N}\mathrm{F}}_0+∆\mathrm{N}\mathrm{F}=1+\frac{\overline{{\mathrm{V}}_{\mathrm{N}.\mathrm{o}\mathrm{u}\mathrm{t}}^2}}{4kT{R}_{\mathrm{S}}{\mathrm{A}}_{\mathrm{V},\mathrm{L}\mathrm{N}\mathrm{A}}^2}$$

(18)

Using the above equations, the performance degradation of the SiGe LNA due to TID was modeled. Results are analyzed in the next section.

3. Experimental Results

3.1. Test Setup for Performance Measurement

The designed RF SiGe LNAs in the previous section were fabricated using GlobalFoundries 350 nm SiGe BiCMOS technology, which featured a peak f_T and f_MAX of 23 GHz and 110 GHz, respectively [28,29,30]. Figure 4 shows the chip micrograph of an LNA sample. For S-parameter measurement, a network analyzer (Agilent PNA E8364B), custom-designed printed circuit boards (PCBs), and a probe station were used. Two port (input and output) measurements were calibrated using a short-open-load-through substrate (SOLT) for on-chip probing, and dc pads were wire-bonded to the board. Noise performance was characterized with a noise source (N4002A) and a PXA signal analyzer (N9030A). The supply voltage of the LNA was set to 2.5 V and the bias current of I_BIAS1 and I_BIAS2 were 830 μA and 600 μA, respectively. In addition, for the radiation experiment an Aracor X-ray source was used with the total dose up to 3 Mrad (SiO₂) [31,32,33]. An LNA sample was irradiated under unbiased conditions by disconnecting all cables from the circuit board, which could exist under deep-power-down mode or power-gating control in low-power transceiver applications [34,35]. For the case with a total of 1 Mrad(SiO₂), the dose rate was set to about 30 krad (SiO₂)/min. The time between the irradiation and the measurement was about 24 h. The pre-irradiation condition showed that the peak gain of the LNA was 12.8 dB at 6 GHz, and the spot noise figure (NF) was 3.4 dB. The input- and the output-matched frequencies were observed at 5 GHz and 5.8 GHz, respectively.

3.2. Performance Degradation and Small-Signal Modeling

After the radiation experiment, branch currents did not show significant changes, implying that the collector currents of the SiGe HBTs were about the same. But the base current gradually increased (from about 8 μA to about 13 μA) as the total dose accumulated, resulting in a decrease in current gain [34]. In general, the performance of SiGe HBT LNAs was influenced by several factors, including by changes in the internal resistances and capacitances, transconductance, and/or current gain [4,35]. In this work, passive devices such as capacitors and inductors as external components were assumed to have little effect on the performance degradation [36]. The modeling of circuit performance was conducted for the pre-irradiation and the 1 Mrad cases.

Figure 5 shows the input matching (S₁₁) and the output matching (S₂₂) of the SiGe LNA for pre-irradiation and 1 Mrad cases. Comparing S₁₁ and S₂₂ responses, the S-parameter values increased at the matched frequencies, showing degradation in signal transfer characteristics. Regarding the locations of resonant frequencies, there were no noticeable frequency shifts between the pre- and the 1 Mrad-irradiation cases. Figure 6 shows the performance changes for power gain (S₂₁) and NF. Similar to the S₁₁ and S₂₂ cases, unfavorable shifts (e.g., a reduction of gain and an increase in NF) in a vertical direction were observed, but there were no noticeable horizontal shifts.

From Equations (7), (12), (13) and (18), the key LNA characteristics were modeled by assigning relevant degradation factors into device parameters, including capacitances (C_π and C_μ), g_m, and R_B. In this process, it was possible to relate them to circuit metrics, which, in turn, provided expected performance changes of similar LNAs to designers. SiGe HBTs can degrade due to irradiation traps generated in the EB spacer region, leading to an increase in the junction capacitance [4,37,38]. X-ray irradiation does not necessarily lower transconductance (g_m) [3], but slight deviations from the initial biasing point may lead to smaller g_m, degrading the gain and noise performance of a SiGe LNA [4,11,35,36]. Next, after irradiation R_B will increase due to the reduction of charge carriers, as generated traps capture a greater proportion of electrons. Moreover, dopants tend to be deactivated under the increased fluence, further raising the base resistance [18]. Therefore, it is reasonable to assume that the combined changes in device capacitances g_m and R_B will collectively affect circuit response in terms of S-parameters and NF after X-ray irradiation.

To capture and represent the TID-induced degradation characteristics, modeling based on the small-signal equivalent circuit and the design equations was performed. For example, as shown in Equation (13), the gain of the LNA was dependent on multiple parameters. With the assumption of constant values of passive components after irradiation, the changes in the gain should be modeled by assigning degradations to device-internal parameters such as the transconductances (g_m) and the base-to-emitter capacitance (C_π) of the SiGe HBTs. Similar processes were applied to the input and the output impedances and the noise of the LNA. As shown in Figure 5 and Figure 6, the modeled results were matched around the resonant (or operation) frequencies in terms of S-parameters and NF. As frequencies move away from the center, however, some discrepancies such as magnitude and slope differences were observed, exhibiting the limitations of using simplified device models and ignored circuit parameters.

Figure 7a,b show the degradations in the input and the output-impedance matching under different total doses with reference to the pre-irradiation results, respectively. The ionizing dose caused poorer matching at the operation frequency, implying the presence of potential unwanted ripples or system instability. In addition, the gain (S₂₁) and NF characteristics exhibited overall degradations as plotted in Figure 8a,b, respectively. One thing to note was that when the TID reached the total dose of 3 Mrad(SiO₂), a slight performance recovery was observed. This was attributed to the annealing effect in the device. as the X-ray irradiation time increased, which compensated for some performance loss, and the degree of recovery over a period may vary depending on the temperature and the irradiation time [39,40,41,42,43].

Table 1. Degradation of LNA performance due to TID.

Total Dose	S11 *	S22 *	S21 +	NF *
Pre-irradiation	−15.62 dB	−23.66 dB	12.89 dB	3.45 dB
500 krad	−11.52 dB	−17.11 dB	7.34 dB	5.6 dB
1 Mrad	−11.27 dB	−11.19 dB	7.14 dB	5.66 dB
3 Mrad	−11.79 dB	−17.36 dB	7.55 dB	5.78 dB

* Numbers were negative peaks. ⁺ Numbers were positive peaks.

summaries the TID-induced changes in performance metrics under different total doses.

4. Degradation Modeling and Analysis

The degradation characteristics of SiGe HBTs due to ionizing radiation showed an increase in device resistance and capacitance, whereas g_m was reduced due to changes in the operation points, especially under the fixed current bias scheme. Based on these trends, simulations were conducted using the small-signal model of a SiGe HBT. Due to TID effects, the input and the output matching were affected by R_B, C_π, and g_m as shown in Equations (7) and (8). Changes of S₁₁ (ΔS₁₁) were influenced by ΔC_π1 with a contribution of 40% and ΔR_B1 with a contribution of 35%, as illustrated in Figure 9a. For output matching, ΔS₂₂ has the largest dependency on g_m4 at 45%, followed by C_μ2 (10%) (see Figure 9b). In Figure 9, other parameters contributed to ΔS₁₁ and ΔS₂₂, but their portions were only about 7% and 23%, respectively.

Gain changes (ΔS₂₁) were mostly affected by the decreases in transconductance (see Figure 10a). ΔS₂₁ was dominated by Δg_m4 (about 30%) and Δg_m1 (about 20%), whereas the contributions of other capacitances such as C_π1 and C _μ2 were much lower. Regarding noise modeling, since large portions of NF was proportional to the base resistance, it was predicted that would NF degrade as R_B1 increased (see Figure 10b). In addition, the contribution of C_π1 was ranked in the second place. Simulations using the small-signal circuit revealed that Δg_m1 and ΔC_π1 had the most influence on NF degradation. Like the input matching and the output matching, minor parameters in gain (S₂₁) and NF (Figure 10) were responsible for only 26% and 18%, respectively. In the case of NF, the derived equation assumes perfect impedance-matching conditions. Due to TID irradiation, however, this condition might not be valid as inferred from the degradation in S₁₁. Therefore, in order to improve the modeling accuracy of NF, more parameters would be required to be included in the analysis stage.

Table 2. Relative contributions of device parameters on the LNA degradation by TID.

Performance Metric	Contribution Rank #1	Contribution Rank #2	Contribution Rank #3	Portion in the Total Degradation
ΔS11	Cπ1 (40%)	RB1 (35%)	gm1 (15%)	90%
ΔS22	gm4 (45%)	RB4 (22%)	Cμ2 (10%)	77%
ΔS21	gm4 (30%)	gm1 (20%)	Cπ1 (14%)	64%
ΔNF	RB1 (35%)	Cπ1 (20%)	RB2 (15%)	70%

summarizes the dominant parameters in the degradation of LNA performance by rank. Among many device parameters, the key contributors included C_π1, R_B1, g_m4, R_B4, and g_m1. More than 90% of the change in S₁₁ was attributed to degradation in the top two parameters of C_π1 and R_B1. Regarding the change in gain (S₂₁), however, the top three parameters were responsible only for 64% of degradation. This was because the gain equation relied on multiple parameters in the equivalent circuit; a similar result was observed in the NF case. Therefore, depending on a performance metric of interest, the accuracy of the proposed approach may be different if the number of dominant parameters is limited in the modeling.

Table 3. Modeled device parameters for pre- and post-irradiation conditions.

Parameter	Unit	Pre-Irradiation	Post-Irradiation (1 Mrad)
Cπ1, Cπ2	fF	250	475
Cπ4	fF	240	430
Cμ1, Cμ2	fF	15	28
Cμ3, Cμ4	fF	13	25
gm1, gm2	mS	45	38
gm4	mS	17	13
RB1, RB2	Ω	100	120
RB4	Ω	90	110

shows the variations in device parameters of SiGe HBTs before and after X-ray irradiation. In the table, it is assumed that parameters of the same-sized transistors undergo the same degree of changes, but slightly different degradation factors are allowed between transistors of different dimensions to improve modeling accuracy. The above discussion implies that proper modeling of key device parameters can predict the overall degradation characteristics due to TID effects in RF SiGe LNAs. With prior knowledge of parameter values after irradiation, the model will better estimate the performance degradation. In reality, many factors other than device parameters may affect the modeling accuracy. Dependent on the type of radiation source, the annealing effects, test configurations, and/or the materials of passive devices or PCBs, the actual modeling process should take the relevant contributions into account.

5. Application to Another LNA Example

In order to further validate the proposed method of TID modeling in RF LNAs, the same approach was applied to an example circuit in the literature [4]. The DUT was a narrowband LNA employing a single SiGe-HBT stage with emitter degeneration as shown in Figure 11. The input-matching network was composed of two inductors (L_B and L_E) and the output matching was performed by L_C, C_C, and C_out.

Each ionizing dose led to performance degradation due to changes in the device parameters such as resistance, capacitance, and transconductance of the SiGe HBT in the LNA circuits. Among various performance metrics, input matching (S₁₁) and gain (S₂₁) characteristics are modeled in this section. As the first step, the small-signal equivalent circuit was constructed with a simplified device model of the SiGe HBT. After modeling the pre-irradiation performance metrics with design equations, the range of overall degradation in each parameter was set. With the degraded parameters, the post-irradiation results were matched. The performance changes of the LNA were attributed to the changes in the base resistance, the internal parasitic capacitances, and transconductance. Their values were modeled for the fluence of 1 × 10⁻¹⁵ p/cm².

Figure 12a shows the measured and the modeled results of S₁₁, and Figure 12b shows the measured and the modeled gain (S₂₁). At the resonant frequency of 1.6 GHz, the input matching was changed from −11.6 dB to −15.8 dB, which implied that the input impedance in the pre-irradiation condition was not set at 50 Ω. After irradiation, the input matching improved. The power gain decreased by 1 dB from 18.5 dB to 17.5 dB at 1.45 GHz. Following a similar method, the post-irradiation performance was reproduced by the modeling process. Figure 13 shows the relative contributions of device parameters to the performance variations of the SiGe LNA. The top contributors in ΔS₁₁ were R_B and C_π, which are the same as in the previous section; their portions were 46% and 28%, respectively. Due to the differences in the matching network and the core structure, the specific contributions of these parameters were not the same as the results in Figure 9a. Regarding the changes in S₂₁, values of g_m, R_B, and C_π were responsible for most of the degradation. The contribution of R_B to ΔS₂₁ was ranked in third place. Thus, the proposed method was able to model the TID-induced degradation in RF LNAs. Depending on the topology and the technology, the impact of device parameters can be different among circuits, requiring detailed analysis based on equivalent models and design equations.

Based on the analysis of SiGe LNAs, it is worth discussing the following points about circuit design. First, the use of a buffer stage in the LNA is likely to introduce additional noticeable performance degradation. In general, a buffer provides wider matching bandwidth at the output port and less interaction between an amplifier and a load stage. In terms of S₂₁, however, changes in the transconductance of a transistor in a buffer stage led to a significant gain reduction. As shown in Figure 10a, the largest contribution to ΔS₂₁ was associated with g_m4 in the two-stage SiGe cascode LNA (Figure 1). Thus, it is recommended to minimize the use of a buffer unless there is a specific requirement. Second, inclusion of a cascode transistor lowers the impact of the changes of the base-to-collector capacitance (C_μ) in the LNA gain metric. As C_μ was not present in the gain expression Equation (13), its variations had also negligible effect on the post-irradiation results. In contrast, ΔC_μ was the fourth dominant parameter in the total gain degradation of the single-stage LNA. By comparing Figure 10a and Figure 13b, it was shown that the contribution of C_μ of the input transistor was much lower in the cascode LNA than in the single-ended counterpart.

In Figure 12a, it was shown that the input matching was improved by the radiation’s influence, which was in the opposite direction of change in the case of the cascode LNA (Figure 5a). To allow comparison of the results, S₁₁ parameters of both circuits were plotted on the Smith chart in Figure 14, showing that the changes in the real impedance were more dominant than those in the imaginary impedance. This could be attributed to the increases in R_B and C_π due to ionizing radiation, which moved the traces toward the right side as shown in Figure 14. Therefore, in terms of long-term reliability against radiation effects, the initial design of the input impedance can be targeted to slightly lower resistance than 50 Ω in order to extend the functional lifetime of the LNA under TID irradiation. From the experiments, the shifts in the center frequencies are expected to be less severe than magnitude changes. In addition, the use of a cascode stage and the elimination of a buffer will effectively minimize performance variations in LNAs.

6. Summary

Degradation characteristics of an RF SiGe LNA under TID effects are investigated using a small-signal equivalent model of a SiGe HBT. Based on the design equations of the LNA, the performance changes due to 1 Mrad(SiO₂) X-ray irradiation are modeled for input matching and output matching, gain, and noise figure characteristics. It is observed that for each circuit metric, the relative contributions of the device parameters were different. Among many parameters, transconductances, base resistances, and base-to-emitter capacitances were mostly responsible for the degradation of the LNA performance. The proposed approach not only provides the relationship between device parameters and circuit metrics but also identifies the dominant parameters that are critical in modeling TID responses. In addition, the proposed method is applied to a different example LNA circuit, exhibiting the ability to reproduce radiation effects with reasonable accuracy. Therefore, the findings of this work can be utilized to effectively predict potential degradations in RF SiGe LNAs due to TID, which will be useful in the early-stage evaluation of radiation sensitivity or hardness.