Characterization and TCAD Modeling of Mixed-Mode Stress Induced by Impact Ionization in Scaled SiGe HBTs

We investigate the reliability of state-of-the-art SiGe heterojunction bipolar transistors (HBTs) in 55-nm technology under mixed-mode stress. We perform electrical characterization and implement a TCAD model calibrated on the measurement data to describe the increased base current degradation at different collector-base voltages. We introduce a simple and self-consistent simulation methodology that links the observed degradation trend to interface traps generation at the emitter/base spacer oxide ascribed to hot holes generated by impact ionization (II) in the collector/base depletion region. This effectively circumvents the limitations of commercial TCAD tools that do not allow II to be the driving force of the degradation. The approach accounts for self-heating and electric fields distribution allowing to reproduce measurement data including the deviation from the power-law behavior.

leads to degradation of the low-frequency gain β due to base current increase, which is conventionally attributed to surface states generation at the emitter-base (E-B) spacer oxide due to impinging hot carriers generated by impact ionization (II) [4]- [7]. In earlier technologies such as the 0.13-μm process from IHP [4] and the first generation of the 55-nm process from STM [8], the base current degradation was reported to empirically follow a power-law. However, deviations occurred at some point in time (typically after several hours), depending on the specific stress conditions, which is thought to be related to the combined effect of SH and II dynamics [4]. Nevertheless, in the literature, the physics of this mechanism was either only partially analyzed [5], [7], or explained by empirical [4] or approximated analysis [6] that are better suited for aging compact models to be used in circuit simulations than for TCAD aging models to be exploited for degradation-aware device optimization. This calls for more comprehensive modeling efforts, especially with further device scaling.
In this article, we perform electrical characterization of mixed-mode (MM) stress reliability of state-of-the-art scaled second-generation SiGe HBT technology from STM under different collector-base stress voltages. We implement a TCAD model of the HBT device and calibrate it to reproduce the behavior of fresh devices. A self-consistent simulation methodology that considers SH and the effect of 2-D electric field distribution is then introduced that allows correctly reproducing MM stress data by ascribing the degradation to hot holes generated by II at the collector/base junction that drift toward the E-B spacer oxide. The developed model gives a direct empirical connection between trap generation rate and II rate in contrast to earlier reports that either i) computed the generation rate from hot carriers models [5] or from the energy distribution function of carriers [7]; or ii) derived an approximated analytical solution for the generated trap density with generation rates used as fitting parameters [6].

II. DEVICES AND EXPERIMENTS
The devices analyzed in this study are state-of-the-art SiGe HBTs fabricated in 55-nm bipolar complementary-metaloxide-semiconductor technology (BiCMOS) by STM [9]. With respect to the first generation of the technology, device dimensions have been scaled in the vertical direction 0018-9383 © 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information. (e.g., base width W B ) and doping profiles were accordingly redefined, especially at base-collector junction. Each device is composed of two parallel HBT structures in the CBEBC configuration with three emitter fingers, with an emitter width and length of W E = 0.20 μm and L E = 5.56 μm (in the third dimension), respectively. The Gummel curves at V CE = 1.2 V and output curves at different V BE values (in the range 0.75-0.9 V) collected on fresh devices are shown in Fig. 2 Table I, benchmarked with IHP SG13S technology [10] (used for comparison also in the degradation analysis). To assess the reliability of the devices under study, we performed MM stress by forcing an emitter current density, J E,STR , of 1 mA/μm 2 , which corresponds to a V BE of ≈0.8 V. The base terminal is kept grounded while the voltage at the collector-base junction, V CB,STR , is set to different values ranging from 1.5 to 2.1 V. These values are chosen as a reasonable trade-off between keeping stress conditions close to the operating ones and getting a non-negligible degradation in a reasonable amount of time, with the total stress time set to 10 4 s. Indeed, in typical circuits for high-frequency applications such as power amplifiers, V CB ranges from 0 to 1.5 V [2], whereas J E (or equivalently J C ) varies in the range where the f T peaks-typically tenths to tens of mA/μm 2 [1], [4]. The stress sequence was interrupted every 100 s to measure Gummel curves at V CE = 1.2 V, as shown in Fig. 4(a), which allows extracting the relative increase (when compared to the fresh device) of I B at different V CB,STR as an indicator of the devices reliability. I B is evaluated at V BE = 0.7 V to directly compare the results reported here with the outcomes of MM stress experiments performed on a previous technology (0.13 μm) and reported in the literature [4]. All measurements are performed at room temperature.

III. TCAD MODEL AND CALIBRATION
The sketch of the SiGe HBT device cross section implemented in the simulator is shown in Fig. 1. The TCAD simulation tool is the commercial software SDevice by Synopsys, Inc. [11]. The device structure was derived by refining an existing model in SDevice for the HBT device, and the mesh was revised to optimize the trade-off among computation time, simulation accuracy, and reproducibility. Comparison of measurement data and calibrated TCAD simulations is shown in Fig. 2, in terms of Gummel plot, Fig. 2(a), and output characteristics, Fig. 2(b). Because the dc MM stress conditions represent an upper limit to HBT degradation under RF operating conditions, here we discuss only the calibration of the device dc characteristics. Analysis of dynamic characteristics (to estimate f T and f max , for instance) and comparison between measurements and simulations will be the subject of future work.
The Ge mole fraction (x) profile in the Si 1−x Ge x varies from 0 to 0.28 from the emitter to the collector junction. The base width was set to 26 nm (W B in Fig. 1). In agreement with results in the literature, the doping profile in the emitter is assumed flat, while a Gaussian doping profile is assumed in the base [1]. The doping profile in the collector/subcollector and, in general, the overall doping profile is in agreement with that suggested by a TCAD-based roadmap for SiGe HBT devices developed in the DOTSEVEN project [1]. Hydrodynamic simulations were carried out to correctly reproduce the currents in all regimes of operation [12]. The lattice, electron, and hole temperatures are self-consistently calculated in TCAD, which accounts for the effects of SH. Models for carriers' recombination (and doping-dependent Shockley-Read-Hall), II (Okuto model), and field-, material-, and doping-dependent mobility [12]- [14] were also included. Calibrating such models for SiGe required only a slight tuning of few parameters in agreement with earlier literature reports [8], [14]. To consolidate the soundness of the calibration procedure, default values for Si and polysilicon were used. Series resistances and thermal resistances were also included at all contacts, and their values were calibrated to capture the behavior of the output curves in the saturation region and in the active region, respectively, as confirmed by the good agreement between experimental and simulated output curves at different V CE [ Fig. 2(b)]. Specifically, the good agreement at high V CE -when SH effects start to be visible-was obtained by tuning the thermal resistance at the emitter, base, and collector contacts (which strongly depend on the structure of the overlying back-end of line). Conversely, to strengthen the dependability of the calibration procedure, the substrate thermal resistance was set in agreement with previous reports in the literature [14]- [16]. In addition, finite carriers' recombination velocity at the emitter was included [13]. Auger recombination and band-to-band tunneling were also included, as they are known to affect the excess base current at low bias. Finally, defects at the E-B spacer interface located at 0.5 ± 0.035 eV from the valence band with a peak density of 10 11 cm −2 eV −1 were included.
Note that although the simulated structure is a simplified version of the fabricated devices, a very good agreement between simulations and measurements could be achieved as shown in Fig. 2. The most relevant simulation parameters (electrical and thermal resistance at contacts, maximum doping levels) are collected in Table II.

IV. DEGRADATION DURING MM STRESS
Typically, the base current degradation resulting from MM stress in SiGe HBT devices is attributed to the generation of interface states at the E-B spacer interface [1], [4], [8], [14], [17]. The latter is supposed to stem from the carriers generated by II in the collector-base depletion region that travel toward the E-B spacer interface under the action of the vertical field and depassivate Si-H bonds at the Si/SiGe interface. Results reported in the literature for the 0.13-μm IHP technology [4] are consistent with this hypothesis and show that the resulting I B degradation approximately follows a power-law (∼at b ) with a slope b ≈ 0.5, although showing deviations starting from ∼10 h of stress [18]. Actually, the photograph is more complex, and b is found to be less than 0.5 even at low-stress times (i.e., few minutes) for higher stress current densities [18]. In Fig. 3, we report a comparison of the relative trends of I B degradation (normalized to I B at t STR = 100 s) for the IHP technology investigated in [4] and [18] and the STM technology used in this work. We compare I B for the same J E,STR ≈ 1 mA/μm 2 . Note that we have used a slightly lower exponent than 0.5 (in light of the considerations in [18]), b = 0.42 that better fits the IHP data. Interestingly, we find that STM I B data deviate from the power-law behavior at t * 1 (≈2 × 10 3 s), prior than IHP data (t * 2 ≈ 1.5 × 10 4 s), indicating an earlier onset of traps passivation mechanism. . The black dashed line follows a power-law and serves as a guide to the eye to show the deviation of data from it, which occurs at t * 1 ≈ 2 × 10 3 s and t * 2 ≈ 1.5 × 10 4 s for the STM and IHP technology, respectively. This deviation calls for a more precise modeling strategy of degradation phenomena.
In the following, we exploit TCAD simulations to refine our understanding of I B degradation (and its deviation from the single power-law behavior) by linking it to the effects of device geometry and II rate, and to check whether additional mechanisms must be considered in the description of the degradation. To this extent, the calibrated simulation deck is used to reproduce measured degradation data. Analogous conditions to those used during the stress tests (described in Section II) were adopted in the simulations. The constant emitter current density (J E,STR = 1 mA/μm 2 ) was set by applying a negative voltage to the emitter contact with the base grounded. This was done for numerical reasons as this solution guaranteed convergence for all stress conditions with different V CB,STR . Stress was simulated for t STR = 10 2 , 10 3 , 10 4 s, after which the I B -V BE curves were recorded. The device aging in terms of interface traps generation (at the emitter/base access region-the SiGe/SiO 2 interface, see Fig. 1) was reproduced by adapting the reaction-diffusion (R-D) model available in SDevice [11]. The evolution of interface trap concentration (N IT ) reads where ν(γ ) is the depassivation (passivation) rate. γ = γ 0 N H /N 0 H where γ 0 is obtained by imposing the equilibrium condition at t = 0, that is, is the concentration of defects at t = 0, ν 0 , and γ 0 are the depassivation/passivation constants, respectively). N H (N 0 H ) is the (equilibrium) hydrogen concentration at the interface (in the oxide). In this work, we assume degradation to be mostly limited by reaction, thus N H /N 0 H = 1. The approach followed in [19], that considered similar depassivation rates but passivation rates depending on hydrogen concentration (and thus on the diffusion rate), reached similar conclusions regarding the deviation from the single "power-law" behavior (due to partial annealing of defects). The dependence of ν on the activation energy (E 0 A ) and on the electric field is written  as [11], [20] where E A = −E(E ⊥ )+(1+β)E T ln(N IT /N 0 IT ) is the change in E 0 A due to stretching of Si-H bonds by the perpendicular electric field and by chemical potential variation (first and second term, respectively). E T = kT + E(E ) is energy of hydrogen in Si-H bonds (T is the lattice temperature) that depends on the electric field parallel to the interface. However, this model as is cannot be successfully used to verify the role of II in the degradation dynamics since the depassivation rate does not depend directly on the hot carrier current, see (2). This comes from the fact that ν does not depend on the excess carrier generation due to II. Thus, for reproducing the measurements in Fig. 4, we varied E 0 A (see Table III) to equivalently take into account the effect of increased V CB,STR in the R-D model. This allowed to self-consistently consider the effect of lattice temperature and both parallel and vertical electric field on the degradation process. It is important to observe that E 0 A is varied only to mimic the ν variation with V CB,STR in the simulator without altering the model implementation itself (as done for example in [5]). The actual physical mechanism that causes ν variation is in fact II, and not a change in E 0 A . The set of parameters that allows reproducing the measured data is reported in Table III. Specifically, the lattice temperature at different stress conditions was directly extracted from the TCAD by averaging the temperature profile along the E-B spacer interface. The resulting N IT versus t STR profile under the four different stress conditions obtained from these simulations are reported as symbols in Fig. 5(a).
The connection between ν and hot carriers (generated by II) is then estimated by rewriting the depassivation rate change at each V CB,STR in terms of an empirical factor k HC as follows: where k HC in (3) can be assumed to be a power-law function of hot carrier current [11] or II rate α n as follows: where δ HC and ρ HC are fitting parameters (α 0 = 1 cm −1 is a normalization factor). To verify the validity of the proposed model and to determine the fitting parameters δ HC and ρ HC we evaluated the relation between ν/ν 0 and the II coefficient α n as obtained from simulations. This is shown in Fig. 5(b), where the power-law trend is evidenced. The resulting fitting parameters are also shown in Fig. 5(b). Moreover, we compared the N IT versus t STR profiles obtained by using (1) and (2) by varying E 0 A [symbols in Fig. 5(a)] with the ones obtained by using (1), (3), and (4) [black solid lines in Fig. 5(a)] obtaining an excellent agreement. Note that, while α n accounts for the likelihood of hot holes generation, the parameter α 0 could be used to account for the probability of the generated hot holes to recombine or scatter while drifting toward the E-B spacer interface, which determines the generation rate of interface states. Therefore, in principle, α 0 could be taken to be dependent on J E,STR , which regulates the scattering chance. Still, analyzing this dependence is out of the scope of this article and will be addressed in future works.
As shown in Fig. 4, the model allows reproducing the base current degradation at different stress times and conditions. The experimental and simulated I B -V BE curves at V CB,STR = 1.5 V for different t STR in Fig. 4(a) show excellent agreement. Fig. 4(b) shows the experimental and simulated relative I B variation (I B = (I t str B − I 0 B )/I 0 B ) at a fixed V BE = 0.7 V (conventionally used to estimate the device lifetime [17]) for the four V CB,STR [see legend in Fig. 4(b)] under investigation in this work. Notably, also the curvature of the degradation trend in Fig. 4(b) is well captured (i.e., the deviation from the power-law approximation). The sudden base current increase occurring for V CB,STR = 2.1 V at t STR ≈ 2000 s is likely due to collector-base junction breakdown (as confirmed by the concurrent collector current increase, not shown for brevity). This behavior could not be captured with simulations possibly due to the simplified simulated structure (see Fig. 1) that could lead to an underestimation of electric field peaks possibly present in the real device. However, since the goal in this work was to capture the base current degradation due to E-B spacer interface trap generation (that does not cause breakdown) the validity of the present analysis is not affected by this discrepancy.
The overall good agreement between measurements and simulations confirms the validity of the proposed approach and highlights the following.
1) Even in scaled devices, the main source of MM stress degradation is the generation of hot holes due to II drifting toward the E-B spacer interface where depassivation of Si-H bond may happen. 2) In scaled devices, the power-law approximation of the base current degradation leads to strong deviations from the actual trend even at fairly short stress times (≈2000 s).

V. CONCLUSION
We investigated the reliability of state-of-the-art SiGe HBTs in 55-nm technology under MM stress. Experimental results were successfully reproduced by using a TCAD model calibrated on fresh devices. We developed a self-consistent simulation methodology that connects the observed degradation trend to interface traps generation (ascribed to II-generated hot holes) at the E-B spacer oxide. This approach circumvents the limitations of commercial TCAD tools that do not allow II to be the driving force of the degradation. In addition, it i) accounts for SH and electric fields distribution; ii) directly links the II coefficient (α n ) to the generation of traps; and iii) allows reproducing measurement data including the deviation from the power-law behavior observed at relatively short stress times.