Harmonic Distortion Peculiarities of High-Frequency SiGe HBT Power Cells for Radar Front End and Wireless Communication

Abstract

High-frequency (h. f.) harmonic distortion (HD) of advanced SiGe heterojunction bipolar transistor (HBT)-based power cells (PwCs), featuring optimized metallization interconnections between individual HBTs, was investigated. Single tone input power (P_in) excitations at 1, 2, 5, and 10 GHz frequencies were employed. The output power (P_out) of the fundamental tone and its harmonics were analyzed in both the frequency and time domains. A rapid increase in the third harmonic of P_out was observed at input powers exceeding −8 dBm for a fundamental frequency of 10 GHz in two different PwC technologies. This increase in the third harmonic was analyzed in terms of nonlinear current waveforms, the nonlinearity of the HBT p-n junction diffusion capacitances, substrate current behavior versus P_in, and avalanche multiplication current. To assess the RF power performance of the PwCs, scalar and vectorial load-pull (LP) measurements were conducted and analyzed. Under matched conditions, the SiGe PwCs demonstrated good linearity, particularly at high frequencies. The key power performance of the PwCs was measured and simulated as follows: input power 1 dB compression point (P_{in_1dB}) of −3 dBm, transducer power gain (G_T) of 15 dB, and power added efficiency (PAE) of 50% at 30 GHz. All measured data were corroborated with simulations using the compact model HiCuM L2.

1. Introduction

Recent predictions and advancements in SiGe HBT performance [1,2,3,4] have enabled the realization of high-frequency (h. f.) power amplifiers (PAs), including stacked PAs, transceivers, and complete MIMO radar systems [5,6,7,8,9,10,11,12]. Among the critical components in an RF transceiver, the power amplifier plays a central role. It is typically composed of an array of so-called power cells (PwCs), which correspond to multifinger transistors or cells connected in parallel. The interconnections within the array significantly impact on the overall PA performance, including PAE%, P_out, and G_T [9]. The linearity and gain of the PAs at h. f. are limited by the parasitic effects, mutual self-heating, influence of the interconnection-induced parasitics, cell placement, and intrinsic nonlinearities of the HBT. Therefore, careful optimization of the PwC layout [9], based on electromagnetic (EM) simulations and nonlinear current behavior, is essential for each given process technology.

Maintaining high speed and power in a single device has consistently posed significant challenges. High-frequency SiGe HBT have highly doped collector region, which set a limit on the collector–emitter bias due to a low impact ionization voltage threshold in the base–collector region. Nevertheless, the collector emitter breakdown voltage (BV_CE0) can be improved by optimizing the base region to exhibit lower impedance [11,13,14]. An increase in the P_out of a high-speed SiGe HBT is typically achieved by combining multiple devices in parallel, particularly forming a power cell, as described earlier. This increases the total collector current and, conditionally, extends the P_out. However, this improvement is constrained by the 50 Ω load impedance at the PwC terminal and the substrate breakdown voltage, both defined by the process technology. These constraints impose limits on the number of parallel transistors in the stacking configuration. Moreover, parallel elements associated with interconnections and stacked transistor architectures impair high-frequency performance. Specifically, the gain of a PwC tends to degrade with increasing numbers of parallel cells, and this degradation is frequency dependent. In the frequency range up to the V-band, the power amplifiers can be effectively implemented using a “stacked configuration,” which leverages voltage scaling rather than current scaling. However, beyond the V-band, maintaining sufficient gain from individual power cells requires devices with intermediate emitter areas (A_E0) even for unit cells. This necessity arises because the maximum achievable output power from a single power cell diminishes at higher frequencies, necessitating power combination techniques. Therefore, depending on the application frequency, a power cell may consist of one or multiple high-speed devices and must be optimized accordingly. At these frequencies, the performance of the active device used in the power cell becomes highly dependent on its layout [15]. Parasitic elements—such as base, emitter, and collector resistances, substrate resistance, and coupling capacitances—ultimately determine the maximum achievable gain of the circuit. For a unit cell, the transit frequency (f_T) and maximum oscillation frequency (f_max) are defined by

$$f_{\mathrm{T}}={\displaystyle \frac{g_{\mathrm{m}}}{2\mathsf{\pi }{C}_{\mathrm{i}\mathrm{n}}}} , f_{\mathrm{m}\mathrm{a}\mathrm{x}}=\sqrt{{\displaystyle \frac{f_{\mathrm{T}}}{8\pi R_{\mathrm{B}}{C}_{\mathsf{\mu }\mathrm{t}\mathrm{o}\mathrm{t}}}}}$$

(1)

where C_in is the total input capacitance (comprising both depletion and diffusion components), R_B is the base resistance, and C_μtot is the total base–collector capacitance. For optimal device performance, all these parameters should be minimized. However, their dependence on layout geometry varies, necessitating careful trade-off during design. For example, in multifinger HBT cell, the base resistance R_B decreases with the ratio of emitter width to total emitter length (w_E)/(l_E,tot). In such structures, wider emitter transistors exhibit lower base resistance, which results in an improved maximum oscillation frequency (f_max) and a lower noise figure (NF). Linearity is a critical characteristic of power amplifiers and is strongly influenced by the harmonic distortion (HD) behavior of the multifinger HBT cell. HD in HBTs and related circuits has been studied in a numerous works [16,17,18,19,20,21,22,23,24,25]. In this work we have taken the most advanced SiGe HBTs realized in IHP SiGe SG13G2 technology [26]. However, in most cases, the analysis is constrained to impractical low-power, linear operating regions and relies on Volterra series representations [27]. Volterra series applies to so-called NICE systems, which map periodic inputs to periodic outputs. Yet, SiGe HBTs are inherently strongly nonlinear devices that generate harmonics even under moderate excitation levels. Therefore, nonlinear measurements are essential—not only for accurate compact modeling, but also for gaining insights into PA behavior under realistic operating conditions, where linear approximations fall short. From another perspective, odd-order harmonics, particularly the third harmonic, are critical for improving the efficiency of any power amplifier operating beyond class AB. Among these, the third harmonic is typically the most accessible and effective to manipulate. Understanding the internal mechanisms of third-harmonic generation in the transistor is thus vital. Nonlinear Vector Network Analyzers (NVNAs) enable detailed investigation of hard nonlinear systems such as SiGe HBTs. NVNAs measure both the magnitudes and phases of incident and reflect power waves, as well as the phase relationships among generated harmonics [28]. This allows a comprehensive analysis of nonlinearities, fundamental signal components, and harmonics across varying input power levels, frequencies, and biasing conditions. In this study, nonlinear network analyzer, NVNA PNA-X 5247A was employed.

This work presents the current–voltage I(V) characteristics, RF performance, and high-frequency distortion behavior of a double-emitter high-speed PwC (with f_T = 300 GHz), under both 50 Ω and optimized output impedance conditions. The results are modeled and analyzed to gain insights into nonlinear behavior and design optimization of high-speed SiGe-based power cells.

2. DUT and Measurement Setup

The layout of the investigated PwC, embedded in Ground–Signal–Ground (G-S-G) pads, is shown in Figure 1. Although the emitter contact of the G-S-G configuration is grounded, it carries the highest current. Therefore, to ensure reliable operation under high current densities, the final emitter contact must be implemented using a thick and wide metal layer. The top view of the SiGe PwC layout 2xCBEBEBC in the Figure 1 illustrates the perpendicular layout of the investigated power cell, which consists of two interconnected CBEBEBC-type devices. Each device features a drawn emitter area of A_E0 = 0.13 µm × 10.16 µm × 2.

The IHP SG13G2 BiCMOS process provides seven metal layers for routing and interconnects [26]. In the layout depicted in Figure 1, two HBTs are connected and separated by a shallow isolation trench, forming a single composite power cell. The collectors and bases of the individual transistors are interconnected and terminated using Topmetal 2 of the process.

Two types of PwCs were implemented, as illustrated in Figure 2a,b. The emitter contacts are connected vertically and arranged in parallel (refer to Figure 1 and Figure 2). The emitter metallization forms a rooftop structure, which, being connected to ground, functions as an inverted microstrip line—see Figure 2a for reference.

In this work, the metal stack of the PwC, along with the RF pads, was (EM) simulated using Keysight Momentum. The simulation results were combined (incorporated) with a compact model (CM) within the power simulation environment of Keysight Advanced Design System (ADS). On-wafer measurements of DC, RF (0.1–67 GHz), and nonlinear characteristics were conducted using NVNA PNA-X N5247A, SMU N6705C, and HP4142, cf. Figure 3. NVNA calibration—including the phase reference module—was performed in accordance with the procedure detailed in the Keysight application note: 5989-8575: Nonlinear Vector Network Analyzer (NVNA). All losses introduced by cables and probes were carefully characterized and compensated for during the system calibration. Transferred and reflected voltage and current waves were measured across various frequencies and RF power levels using both input and output excitation of the device under test (DUT). The performance data for both PwC variants were evaluated. Version (a) was selected for detailed analysis due to its superior power performance. Load-pull data at 30 GHz showed the following:

• Version (a) P_in/P_out/G_T = −25 dBm/−9.9 dBm/15 dB.
• Version (b) P_in/P_out/G_T = −25 dBm/−11 dBm/13 dB.

A comprehensive set of I(V) characteristics and S-parameters was measured at various temperatures to enable the extraction and verification of compact model (CM) parameters. The comparison between simulated and measured data is provided to validate the model and to support an analysis of the power-related characteristics. Circuit-level simulations were carried out using the HiCuM/L2 compact model, implemented in Verilog-A. This modeling approach ensures accurate representation of device behavior across a wide range of operating conditions, including nonlinear and temperature-dependent effects.

High-frequency scalar load-pull measurements were performed with the Maury Microwave Automated Tuner System, while vectorial load-pull (LP) measurements were performed using the Focus Microwaves Delta Tuner System [29]. Both setups were integrated with an MPI TS3500 SE probe station from MPI corporation (Hsinchu, Taiwan), equipped with a thermal chuck, enabling precise on-wafer measurements. The chuck provided stable temperature control across a wide range, from −60 °C to +300 °C, allowing for accurate thermal characterization of the devices under test.

Delta impedance tuners offer several advantages, including ultra-low vibration during motor actuation, which helps maintain reliable contact on aluminum (Al) pads, and low insertion loss due to the direct connection of RF probes to the tuner input. Integrated directional couplers allow seamless integration of Delta tuners into any four-port Vector Network Analyzer (VNA) equipped with direct access to both receivers and sources. Accurate and efficient load-pull (LP) calibration and measurements were achieved through in situ fast calibration using Focus Microwaves FDCS software, which also manages tuner characterization. A circulator was included in the input circuitry to suppress back-reflected RF power from the device under test (DUT). A well-matched 50-ohm power sensor was employed for system calibration and simultaneously served as a load at the bias Tee (BT), as illustrated in Figure 4. To enable time-domain measurements with phase synchronization, the Mesuro PR67 phase reference module was integrated into the system [29]. The vectorial load-pull system was controlled via FDCS 3.8 software from Focus Microwaves (Saint-Laurent, QC, Canada). The vectorial load-pull system was controlled with FDCS 3.8 software from Focus Microwaves. All measurements were conducted at the laboratories of TUD CEDIC and Automatisierungs Technik Voigt.

3. Results and Discussion

3.1. DC and RF Characteristics

The current–voltage output characteristics, J_C (V_CE) driven by V_BE and I_B, for the power cell are shown in Figure 5 and Figure 6, respectively. Avalanche carrier multiplication is observed, leading to a negative base current with a threshold voltage at V_BE = 0.74 V, corresponding to a breakdown voltage BV_CE0 = 1.7 V (see Figure 5). Additionally, the load circles at incident RF power levels P_in = −9.4 and +5 dBm at a fundamental frequency of 10 GHz are presented in both figures. It is important to note that the quiescent J_C (V_CE) and J_B (V_CE) characteristics shown in both plots do not include dynamic currents associated with incident RF power. The superimposed load circles indicate the range of the current swing under RF excitation.

Compact model simulations (shown as lines) exhibit good agreement with experimental data. At an RF input power of +5 dBm, the load circles become significantly distorted, reflecting nonlinear behavior and dynamic load modulation effects. The nonlinear dynamic collector–emitter voltage V_CEd swing exceeds the breakdown voltage BV_CE0, indicating that nonlinearities associated with impact ionization (I.I.) currents may contribute to harmonic distortion (HD). Nevertheless, the choice of a relatively high V_CE0 = 1.8 V remains advantageous for power circuit applications [5,30,31], provided that the input power is not excessively high. Although the compact model shows better agreement with measured data at lower frequencies (e.g., 2 and 5 GHz), a higher RF frequency of 10 GHz was deliberately selected to enable analysis of the peculiar behavior of the third harmonic in high-frequency SiGe HBT power cells (PwCs).

The Gummel plot at V_CE = 1.5 and 1.8 V is shown in Figure 7. The observed dips in the absolute values of base current density J_B values at V_CE = 1.8 V are attributed to avalanche multiplication currents occurring in the base–collector junction. The dynamic base–emitter voltage waveforms V_BEd, induced by the incident RF input power, extend into the nonlinear region of the static J_C (V_BE) and J_B (V_BE) characteristics, thereby triggering nonlinearity in the transconductance. This nonlinear behavior is frequency-dependent and may also be influenced by the nonlinear behavior of the input capacitance C_in. It is important to note that J_C shown in Figure 7 does not account for the superposition of the dynamic RF currents. The dynamic V_BEd waveforms in the time domain at 2 and 10 GHz serve to illustrate the extent of bias swing within the static quiescent bias scale under high input power excitation. The collector’s current cut-off frequency f_T and maximum oscillation frequency f_max as a function of J_C are presented in Figure 8. At 2 GHz and an input power P_in = 0 dBm, the dynamic current density wave becomes distorted (flattened) and reaches the J_C level corresponding to the peak f_T. The ripples in the current waves stem from a too-low harmonic number (5), while Fourier transformation is applied for the signal conversion from the frequency to the time domain. High input RF power waves, especially at lower frequencies, face limitations because of nonlinearity in the transconductance.

Measured total collector (J_C), and base current (J_B) densities (including both static and dynamic components) as a function of incident RF power are presented in Figure 9 and Figure 10. For P_in = −15 dBm at V_CE = 1 V, the frequency-dependent J_C and J_B increase with P_in. At lower frequencies, the increases in J_C (P_in) and J_B (P_in) are more pronounced, suggesting a capacitive origin of the nonlinear dynamic current. At V_CE = 1.8 V, impact ionization (I.I.) additionally occurs and contributes positively to the total collector current density (J_C + J_Cd), as shown in Figure 9 (red curve, Delta J_C). This term represents the current component arising from I.I. and includes a minor contribution from self-heating effects (cf. the pink line in Figure 5, which shows only a slight increase with V_CE).

The complete (quiescent and dynamic) frequency-dependent base current densities J_B (P_in) at V_CE = 1 V and 1.8 V are depicted in Figure 10. The frequency dependence of both J_C and J_B at both V_CE values is attributed to the junction diffusion and substrate capacitances. At higher incident powers and elevated electric fields (i.e., V_CE = 1.8 V) hot electrons in the base–collector (BC) region undergoes impact ionization, leading to a negative contribution to the base current, as seen in the J_B (P_in) behavior in Figure 10. The impact-ionization-induced current and the nonlinear dynamic current act in opposition: while the I.I.-related current reduces J_B, potentially turning it negative, the nonlinear dynamic current increases with P_in, driving J_B toward positive values. At lower frequencies (f = 2 and 5 GHz), the nonlinear component of the base current contribution is more pronounced and counteracts the impact ionization (I.I.) component in J_B (P_in), as shown in Figure 10. At V_CE = 1.8 V, the initially negative base current density J_B becomes positive once the incident power P_in exceeds the frequency-dependent threshold. This transition indicates the emergence of a nonlinear dynamic current that competes with the impact ionization (I.I.) contribution and includes a component due to self-heating effects (cf. Figure 10). The dynamic collector current component remains positive across all conditions, as does the I.I. contribution to the collector current.

The frequency-dependent nonlinear current is also influenced by the base–emitter bias: increasing V_BE enhances the I.I. current. Accordingly, the base current density, resulting from impact ionization, becomes more pronounced at higher V_BE values, as shown in Figure 11.

The dynamic base–emitter voltage (V_BEd) at V_CE = 1 V (I.I. free) exhibits a dependence on the input power, as shown in Figure 12. At higher V_BE and at frequency of 10 GHz, the V_BEd contribution is less pronounced.

The dependence of dynamic base–emitter voltage V_BEd at the fundamental frequency of 10 GHz on P_in, measured at V_CE = 1.8 V (including I.I.), is shown on a logarithmic scale. The dynamic V_BEd (V_in in Figure 13) exhibits highly linear behavior with respect to P_in, with no significant increase in the third-harmonic component of V_BEd beyond the input power of interest (−8 dBm). This suggests that the observed rise in the third-harmonic power is not attributed to the input capacitance.

Rapid increase in the third harmonic of the total output voltage V_out (V_CEd) is observed in the V_out (P_in) dependence, as shown in Figure 14. This effect is frequency-dependent and appears for the fundamental incident frequencies between 10 GHz and 12 GHz. A similar drop-out of the third-harmonic power was also seen in B11HFC process technology of SiGe HBT power cells [32] (cf. Figure 15). This indicates that the effect is systematic and cannot be attributed to specific technological process variations. The same measurement setup was used to characterize other standard SiGe power transistors as well as InP HBTs, and no such drop-out was observed in those devices. We therefore hypothesize that the effect originates from reactive components in the transistor’s output structure, particularly in the base–collector p-n junction capacitance C_BC and/or substrate–collector capacitance C_SC, and nonlinearity of diffusion capacitances.

Although standard compact model (CM) simulations, including EM-simulated parasitic capacitances of the transistor’s metal interconnects, show good agreement with the measured results, they do not capture the observed third-harmonic behavior. Specifically, the resonance is not due to parasitic capacitances of the metallic routing. Data analysis shows that the drop-out of the third-harmonic power is not related to I.I. current since it occurs for both V_CE = 1 V and 1.8 V.

In the next section, an analysis of the capacitance behavior under RF power at different frequencies is given.

3.2. Dynamic Behavior of the Diffusion Capacitances

At a lower RF input power (P_in = −9.4 dBm), simulated collector current density shows agreement with the measured data, as evidenced by the load lines in Figure 5 and Figure 6. However, at higher input powers (P_in > −8.4 dBm), the dynamic current behavior is influenced by multiple nonlinear mechanisms: nonlinear transconductance, the nonlinearity due to diffusion capacitances, impact ionization currents, and the self-heating effect. It is known that avalanche current creates traps in the emitter–base region, particularly within the shallow trench isolation of the HBT. In the shallow trench of the HBT, an increase in the substrate capacitance C_SC was observed [30].

To investigate the impact of incident RF power on the SiGe HBTs, capacitance measurements and extractions were performed at different incident RF power levels, as shown in Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20. The base–collector and base–emitter junction capacitances were extracted from measured S-parameters. Such extraction is valid unless there is no gain in the DUT. As shown in Figure 16, the base–emitter junction capacitance C_BE increases with V_BE, as expected. However, under certain conditions (P_in = −5 dBm), C_SC becomes significantly negative (−150 fF). A negative substrate capacitance can be interpreted as an inductive behavior, which may give rise to dynamic current resonance, at the corresponding frequency—a phenomenon observed in Figure 14, where a third harmonic emerges for P_in > −8 dBm. The physical interpretation and implications of negative capacitance are discussed in detail in Section 3.3.

As shown in Figure 17, deviations of C_BC from a uniform (homogeneous) increase begin to appear at P_in > −8 dBm. The non-uniform dependence of C_BC (V_BE) behavior indicates the presence of a harmonic distortion source.

The diffusion-related components of the junction capacitances—C_BE, C_BC, and particularly C_SC—exhibit sensitivity to the incident RF power. During nonlinear harmonic measurements, incident power waves can reach levels as high as +5 dBm. At higher RF power levels, starting from approximately −8.4 dBm, the base–collector junction capacitance C_BC displays non-uniform behavior with respect to input power, as illustrated in Figure 17.

C_BE (V_BE) behavior remains homogeneous over a wide range of input powers, as shown in Figure 18. Similarly, the harmonic component of the input voltage V_in (P_in) also exhibits a homogeneous response, as shown in Figure 13. Compact-model-based simulations performed at P_in = −30 dBm show excellent agreement with the measured data.

The dependence of the total (depletion and diffusion) base–collector junction capacitance on RF power and bias across the base–collector p–n junction V_BC dependence for the PwC and single h. s. SiGe HBT are presented in Figure 19. The CM simulation at P_in = −30 dBm matches the measured data. The homogeneous C_BC (V_BC) increase with P_in does not imply any anomalies that could be associated with a rapid rise in third-harmonic power or dynamic resonance effects. The typical biasing range of the transistor V_BC is between −0.5 to 0 V, cf. Figure 19. In this area, C_BC is less RF-power-dependent. The substrate capacitance is quite sensitive to input RF power at positive V_BC only, cf. Figure 20.

The usual biasing of the transistor is between V_BC of [−1 to 0] V, where C_SC(V_BC) exhibits nearly linear behavior with minimal dependence on RF power. Simulated data partially captures C_SC(V_BC) reduction for positive V_BC, but only at lower incident RF power levels, as shown in Figure 20.

The absence of a resonance at 30 GHz in single high-frequency SiGe HBTs is attributed to the substrate–collector capacitance C_SC being significant smaller, compared to that of the PwC HBTs, in a single h. f. SiGe HBT (Figure 20) and negligible in A_IIIB_V HBTs. The expected resonance for a single SiGe HBT with more than 4 times smaller C_SC capacitance may be shifted to a higher frequency. The resonance of the third harmonic power at 30 GHz was also found in a different technology [32] SiGe HBT PwC, cf. Figure 15.

The third-harmonic drop-out in an IFX device occurs at a lower P_in = −14 dBm, compared to the IHP technology, where the drop-out begins at P_in = −8.4 dBm.

The third harmonic drop-out in is not evident at this frequency for a PDK h. f. SiGe HBT (Figure 21) probably due to a smaller C_SC value. The shape of the harmonic power P₃ (P_in) dependence on a single h. f. SiGe HBT is similar to that of the PwC but with a less expressed increase beyond −10 dBm of P_in.

The measured P_out (P_in) at 10 GHz and the corresponding third harmonic at various ambient temperatures (T_a) are presented in Figure 22. It is clearly observed that the peculiar behavior of the third harmonic is not temperature dependent. This indicates that the nonlinearity of transconductance, which is very sensitive to T_a, is not the main reason for the peculiar behavior of the third harmonic. However, the threshold input power at which the nonlinear effect begins shifts to a higher P_in with a decrease in temperature.

What happens when high RF input power is applied? P_in with 2 and 10 GHz frequencies is applied to the SiGe PwC input. Using Fourier transformation, P_out was converted to the corresponding RF power waveforms. The extracted V_BC waves were superimposed on the C_SC (V_BC), cf. Figure 23. It is seen that incident RF power-related dynamic V_BC output waves can exceed quiescent V_BC = 1 V, cf. Figure 23, and cause C_SC (V_BC) reduction down to negative values, consistent with observations in Figure 16.

Negative capacitance can introduce effective inductive behavior, potentially leading to resonance at specific frequencies within the circuit.

3.3. Understanding Negative Capacitance in the HBT

The frequency-dependent complex dielectric permittivity, ε_eff (ω) = ε′(ω) − i ε″(ω), or the corresponding complex capacitance, C (ω) = C′(ω) − i C″(ω), define the response of dielectric polarization to an alternating electric field or the stored charge to alternating voltage on a capacitor [33]. Usually ε′, ε″, C′, and C″ are positive, indicating that the polarization/charge is in phase with the driving field/voltage and energy losses are present due to dielectric relaxation. Negative values of ε″ and C″ are incompatible with a passive system; otherwise, that would create an energy gain from the polarization change, which violates the principles of energy conservation. The case of a negative real part, ε′ or C′, corresponds to a system in which the oscillations of polarization/charge are in antiphase with the driving field/voltage, and this is the case in resonant systems above the resonant frequency [33]. One possible situation raising negative charge in the system is the presence of two charge carrier species of opposite sign in a semi-insulating medium. If one charge, e.g., electrons, is injected as homo charge at the negative electrode, the current is limited by the resulting space charge, but this may be relieved by the arrival of the hetero charge of opposite polarity from the other electrode. The time delay to the onset of a rising current under these circumstances is determined by the transit time of the hetero charges across the sample [33]. Investigated SiGe power cells exhibited negative C_SC versus V_BE in the operating V_BE range: 0.8 V to 0.92 V, cf. Figure 15.

Negative capacitance was also observed in the bipolar transistor, but without a proper physical explanation [34]. Indeed, in the SiGe HBT, the charge of the base/collector junction and the charge in the collector substrate corresponds to two charge species with opposite signs. This explains the negative charge in the SiGe HBT. Alternating high-frequency power inserted from the RF (the source of the Vector Network Analyzer) source stays in phase with Q_BE dynamic charge but is in antiphase to the other, Q_SC, charge, thus releasing it. This implies a rise in the substrate dynamic frequency-dependent current and results in a significant increase in harmonic distortion.

The case of a negative real part, ε′ or C′, corresponds to a system in which the oscillations of polarization/charge are in antiphase with the driving field/voltage, and this is the case in resonant systems above the resonant frequency. The electrical lumped component representation involves an inductance L that necessarily implies the existence of magnetic energy storage in the system, which may not always be physically plausible. A series electrical circuit consisting of resistance R and inductance L may be represented, in the limit of high frequencies, ω >> R/L, by an effective capacitance C_eff = −l/ω²L that has the required negative sign but also has the specific inverse quadratic frequency dependence. Genuine inductive behavior requires, therefore, that the observed ‘negative capacitance’ should be seen at ‘high’ frequencies, that it should have a physical explanation, involving magnetic storage of energy, and that its frequency dependence should be l/ω²L [35].

3.4. Power Characteristics of CE Power Cell, Discussion

The investigated devices yield high f_T/f_max (250/220 GHz), cf. Figure 8, and acceptable power linearity up to moderate input powers of P_in = −5 dBm (Figure 24 and Figure 25). The compact model accounts for most of the nonlinearity sources in SiGe HBT PwCs, except for the odd behavior of the third harmonic. In general, there are six known main sources of distortion in SiGe HBTs, related to I_B (V_BE), I_CE (V_BE,V_BC), I_CB (V_BE,V_CB), C_BC (V_BC), C_BE (V_BE), and C_SC (V_SC) [16,17,18,36]. Following nonlinear measurement data analysis, the dominant power transfer through the HBT nonlinearity source up to −5 dBm of input power in the investigated SiGe PwCs is related to transconductance nonlinearity.

The power of the third harmonic shows a sharp increase beyond P_in > −13 dBm for Infineon technology [32] PwCs and −8.4 dBm for IHP technology [26] PwCs at a 30 GHz frequency, cf. Figure 15 and Figure 24. Data analysis shows that the drop-out of the third harmonic is related to the peculiarities of the substrate capacitance. This behavior is frequency-dependent and is observable only for SiGe power cells at fundamental frequency of around 10 GHz (not present at 2 GHz, cf. Figure 25). Large signal measurements at cryogenic and elevated temperatures (T_a = 4.2 K–400 K) show that the peak of rapid increase in the third harmonic does not depend on T_a and on V_CE in a reasonable range.

Let us consider avalanche-current-related nonlinearity. At V_CE = 1.5 V, avalanche current in J_B (Figure 7: stars and blue line) is not present, but an increase in the third-harmonic power is evident, cf. Figure 24. The avalanche multiplication factor (M-1) decreases with J_C, resulting in a decrease in related nonlinearity with the collector current density [18]. At the input powers, beyond P_in = −8.4 dBm, where the third harmonic drops out (Figure 24), the current density is approximately J_C = 2.8 mA/µm² for V_CE = 1.8 V, 10 GHz. This point fits the J_C value at the peak f_T. At such high saturation of the DC current density, the thermal heating is set on with an ambient temperature (simulated value: T_a = 393 K), which reduces impact ionization itself [37]. The dynamic current gives rise to additional heating, especially for parallel power cell devices, where the heat interaction between them is significant. Therefore, at such high J_C values, avalanche-multiplication-current-related nonlinearity cannot dominate. Avalanche multiplication current’s contribution to nonlinearity itself is not responsible for the sharp increase in the third-harmonic power. On the other hand, avalanche multiplication current causes the device to degrade. Generated hot carriers in the base–collector space charge region (SCR) travel to the emitter–base and base–collector dielectric and damage the emitter–base and collector–base dielectric, creating traps in the shallow trench [30]. As a result, the base current degrades [35,38,39]. It was found that large voltage swings, even at low V_CE, where avalanche is not present, degrade the base current. The observed effect is frequency-dependent: for 1, 2, and 5 GHz, the third harmonic does not show such a sharp increase and perfectly fits the model, cf. Figure 25, indicating that the observed effect is related to the charge, is not dependent on V_CE, and finally, is not due to the systematic error. The observed dips in the harmonic powers are due to the cancellation effect, which was well explained with the transfer function and third-order derivative of input voltage swing [40]. An increase in the third harmonic power has the threshold origin: it moves toward lower P_in with an increase in quiescent bias V_BE, cf. Figure 26. The input power generated by dynamic V_BEd compensates quiescent V_BE to maintain the threshold power.

An evaluation of the summarized threshold bias V_BEΣ = V_BE + V_BEd from the measured power characteristics at 10 GHz of fundamental excitation yields an average threshold bias value of V_BEΣ = 0.88 V (from 0.86 V to 0.9 V). To reveal the possible contribution of C_BC (V_BC), C_BE (V_BE), and C_SC (V_SC) nonlinearities, the bias dependencies of C_BC and C_BE are presented in Figure 23 and Figure 27. In the measured devices, the V_BC swings with incident powers of −8.4 dBm and −5 dBm did not reach the strong nonlinear region of the C_BC (V_BC), cf. Figure 23. The selected bias point at V_CE = 1.8 V pushes incident wave away from the C_BC strong nonlinearity bias area (V_BC > 0.25 V), thus disabling the harmonic distortion source from the base–collector C_BC and substrate capacitance C_SC nonlinearities in favor of the transfer current nonlinearity, which was shown to be a significant one at higher V_CE values and at moderate current densities [16,18,36,41]. Analysis of the input voltage wave of incident power beyond P_in > −9.4 dBm reveals that the voltage swing hits the nonlinear region of C_BE bias dependency, cf. Figure 27, thus invoking the contribution of C_BE nonlinearity to the total distortion.

Nevertheless, the nonlinearity contribution from C_BE is negligible (cf. Figure 13) [24,36] compared to g_m and transfer current nonlinearity stemming from the self-heating and accumulated charge in the collector at a high V_BE.

To show the power capabilities of the investigated SiGe HBT PwC, scalar and vectorial load-pull measurements at 10, 30, and 50 GHz were performed. The high-speed power cell exhibited a transducer power gain of G_T = 22/11 dB at 10/50 GHz, respectively. The load-matched output power compression depends on the frequency and is correlated with the base current, cf. Figure 28.

4. Conclusions

The harmonic distortion and load-pull behavior of high-frequency SiGe power cells were investigated. A frequency-dependent increase in the third harmonic of 10 GHz fundamental incident power was observed. This increase in P₃ (P_in) exhibits a threshold-like origin and is not attributed to avalanche multiplication or to nonlinearities in base–collector junction capacitance C_BC (V_BC) behavior. The frequency-dependent drop-out of the third harmonic in the output power is linked to resonance effects, associated with negative-charge-behavior-related resonance behavior in the substrate capacitance C_sc (P_in). This phenomenon was observed in SiGe HBTs fabricated with two different technologies, indicating that it is not technology specific. A detailed analysis confirms that impact ionization (I.I.) is not responsible for the unusual behavior of P₃ (P_in). Furthermore, the effect persists in the SiGe HBT PwCs across a wide temperature range (T_a = 4.2 K–400 K), suggesting its robustness. The SiGe HBT h. f. power cell in matched load conditions exhibits good linearity beyond 30 GHz frequency and is suitable for power applications in the V- and W-bands.