A Novel Non-Invasive Cryostatic Spectrometry Technique to Characterize the Carriers’ Multiplication Factor in Silicon Carbide Power Devices

The design of robust power semiconductor devices and the assessment of their susceptibility to terrestrial cosmic rays induced failures requires the accurate characterization of the device-internal electric field. This work presents a non-invasive cryostatic spectrometry technique making use of a soft-gamma Am241 radioactive source, to sense the device-internal electric field of silicon carbide power devices, through the measurement of the carriers’ multiplication factor. TCAD and Monte Carlo simulations tools are coupled to predict the soft-gamma irradiation spectra and to localize the hotspots for charge multiplication in the device structure. An empirical relationship is derived to convert the carriers’ multiplication factor measured at cryogenic temperature to the multiplication factor at ambient temperature. Finally, by highlighting the correlation between the multiplication factor and the failure rate of power devices exposed to terrestrial cosmic radiation, the technique is proposed as a complimentary method for the on-field assessment of the Safe-Operating Area.


1-Introduction
Silicon Carbide (SiC) power devices have been observed to be susceptible to insidious failure mechanisms as single-event burnouts (SEB) when exposed by terrestrial cosmic radiation (TCR) [1]- [5]. This is the case for both SiC Schottky Diodes and MOSFETs rated over 1 kV, that have been observed to fail at similar rates when exposed to cosmic neutrons in the same biasing conditions, suggesting a fundamentally similar failure mechanism in both the device types [6]. The strength of the device-internal electric field, that is the driver of the carriers' multiplication, is a major factor in determining the failure rate of devices exposed to TCR [7], [8]. To ensure the robustness of SiC power devices against TCR induced failures, the electric field at the blocking junctions needs to be accurately characterized. Recently, the irradiation of power devices with radioactive sources has been proposed as a technique to characterize the internal electric field of SiC components through the measurement of carriers' multiplication [9]- [11]. Special focus has been devoted to a non-invasive technique that makes use of Am 241 as a soft-gamma radiation source [12], [13]. By exposing devices biased in the blocking state to the soft-gamma source, the technique has proven to be effective provided that the reverse current in the device under test (DUT) is much lower than the peak of the ionization current generated by a single absorbed photon. At ambient temperature (AT), this condition is fulfilled in such devices and in biasing conditions where the thermal generation of carriers is particularly low. However, in a variety of SiC devices the thermal noise dominates the useful signal, restricting the applicability of the technique to a limited number of DUTs. In this work, this limitation has been removed by carrying out measurements at liquid nitrogen temperature (LNT, 77 K) and converting the obtained carriers' multiplication factor to the operating temperature of the device. A novel spectroscopy setup has been developed, that makes use of a dedicated high-voltage capable cryostat, operating at 77 K. An empirical relationship is derived to convert the multiplication factor measured at LNT to the multiplication factor at the operating temperature. The experimental technique is demonstrated on the set of SiC commercial devices listed in Table 1. Additionally, an original simulation scheme, based on the coupling of TCAD and Monte Carlo tools, is used to accurately predict the measured irradiation spectra and to localize the multiplication hotspots within the device structure. In Section 2 and 3, the experimental setup and the original simulation scheme are presented, respectively. Section 4 discusses the experimental and simulation results, deriving the empirical relationship to convert the LNT multiplication factor to AT. Here, the correlation of the carriers' multiplication factor and the TCR induced failure rate assessed in literature [14] by neutron irradiation is discussed.

2-The experimental Setup.
The working principle. The working principle of the proposed technique can be summarized as follows. A SiC device (JBS diode or MOSFET) is biased in the blocking state while kept at LNT and irradiated with a collimated beam of soft-gamma particles from an Am 241 radioactive source to generate electron-hole pairs in the depletion region of the main blocking junction. The charge carriers are separated by the local electric field and eventually multiplied by impact ionization, generating a current pulse at the device terminals, that is collected by a dedicated spectrometer. Every single pulse is then processed offline to extract the related pulse charge and to build a pulse charge spectrum. For every DUT, spectra are collected for different biasing conditions, starting from a voltage for which no charge multiplication occurs, and the device is in full-depletion conditions (typically around 30% of the breakdown voltage of the DUT), up to close breakdown conditions (90% of the breakdown voltage). The carriers' multiplication factor is assessed based on the shift of the spectra referred to the spectrum acquired in no multiplication conditions, according to [9].
The measurement setup. A block representation of the measurement setup employed in this work is given in Fig. 1(a). The different components are discussed in the following section.
The high-voltage cryostat. At the front-end of the measurement setup, the DUT is biased in the blocking state using a high-voltage power supply operated at ambient temperature and insulated from the net by a power-line transformer. The DUT is enclosed in a dedicated cryostat, whose structure is shown in Fig. 1(b), alongside with the Am 241 compact source. The cryostat consists of a 25 liters Dewar, partially filled with liquid nitrogen, in which an aluminum bracket acts as an efficient heat conductor between the liquid and the DUT. The bias voltage is carried to the DUT by a shielded coaxial cable traversing a 1 cm large hole machined in the polystyrene lid of the Dewar. The aluminum bracket and the Dewar's metallic enclosure are grounded to ensure safety and to generate an efficient Faraday cage that shields to DUT from EM noise. The DUT temperature, acquired over 800 hours of operation, is stable within 1 K.  The Am 241 radioactive source. The experimental setup employs a collimated (exempt-quantity) compact Am 241 radioactive source, with an activity lower than 37 kBq. Am 241 exhibits an almost monoenergetic gamma emission at 59.5 keV. In the present application, the soft-gamma transition is used to form the collimated ionizing beam that induces the generation of charge pairs at the DUT blocking junction. Fig. 2 shows the gamma emission spectrum of the Am 241 source, as measured by a 250 μm thick silicon photodiode, alongside the attenuation of gamma radiation in SiC. The 59.5 keV photons from the Am 241 source interact with SiC by photoelectric effect and by incoherent scattering with comparable probability. In the present case, the relevant interaction mechanism is the photoelectric effect, which results in the almost uniform generation of 59.5 keV secondary photoelectrons across the full depth of the irradiated DUT. Incoherent scattering results in the generation of secondary electrons whose energy is at least six times smaller than the one of the photoelectrons [12] and can be neglected as the amount of equivalent deposited charge is below the detection limit of the spectrometer. Fig. 3(a) reports the Monte Carlo simulation of the interaction of 59.5 keV photoelectrons with SiC, showing that their range does not exceed 18 μm and that 90% of their kinetic energy is released almost isotopically within 12 μm from the interaction point of the softgamma particle. This allows for a quite local generation of electron-hole pairs, localized in the depleted region of the DUTs. The use of the Am 241 soft-gamma source for the measurement of charge multiplication has been preferred to other irradiation techniques as it allows for many different advantages.  Compared to alpha irradiation techniques, using the soft-gamma approach allows to operate with packaged DUTs, whose pristine state is not altered by decapsulation procedures. Furthermore, alpha particles exhibit a limited range that in some cases cannot produce carriers generation over the full width of the depletion layer [15]. This is not the case for the secondary photoelectrons generated by Am 241 soft-gamma radiation, whose low charge deposition does not alter the steady-state deviceinternal electric field. Compared to emitters that provide gamma particles of higher energy (e.g., Co 60 , Cs 137 ), Am 241 allows to limit the interaction volume of the particles to around 18 μm, preventing unwanted long-range effects. Furthermore, it ensures ease of collimation by a compact lead collimator. Co 60 and Cs 137 would require lead collimators whose thickness is in the order of centimeters. This is not the case for the soft-gamma emission of Am 241 . Fig. 3(b) shows the lead collimator employed in this application. As shown in Fig. 3(c), the 1 mm thick lead collimator allows to attenuate 99% of the intensity of the gamma radiation and to achieve a 1.8 mm beam spot at the surface of the DUT, when the source is placed on top of the package of the DUT. This allows to irradiate selectively the active area of the device, avoiding spurious signal originating from the irradiation of the termination region. The Am 241 source has also been preferred to an x-ray generator, as its compactness is essential to fit in the high-voltage cryostat and its emission does not exhibit an unwanted bremsstrahlung component. The advantages exhibited by the soft-gamma emission of Am 241 come at the price that the charge generated by every single ionization interaction is small (about 1.2 fC in SiC) and so the use of the cryostat is essential to achieve good SNR in the charge pulse acquisitions.
The spectrometry chain. The DUT is connected to a dedicated spectrometry chain, that is operated at ambient temperature. The spectrometer employed in the experimental setup is described in very detail in [16]. Its functioning can be summarized as follows. The DUT's high-voltage terminal is AC-coupled to the first stage of the spectrometry chain. This is a charge sensitive preamplifier that converts the current pulses collected at the DUT terminals to voltage signals, employing a highbandwidth (250 MHz) trans-impedance amplifier followed by a high-bandwidth voltage amplifier. The preamplifier is followed by a shaping amplifier with an 8 μs shaping time, consisting in a Sallen-Key second-order active band-pass filter with pole-zero cancellation, that adapts the bandwidth of the pulse signal to the sampling rate of the following ADC, while providing noise and pile-up rejection. The output signal of the shaping amplifier is acquired by a 14-bit ADC and stored in a solid-state memory for offline post-processing. Details of the post-processing procedures are given in [16]. The main source of noise affecting the measurement setup originates from the fluctuations of the leakage current in the DUT [16], so from the thermal generation of carriers in its depletion region. Employing the high-voltage cryostat reduces by at least two orders of magnitude the thermal current of the tested DUTs, compared to the ambient temperature case, strongly reducing the intensity of the 6 Technologies and Application of Engineering Materials leakage current fluctuations, and improving the accuracy of the spectrometer. Under these conditions, the resolution of the spectrometer is mainly limited by the capacitance of the DUT and allows to acquire charge pulses down to 0.5 fC with a 4% resolution.

3-TCAD and Monte Carlo Simulations.
A dedicated simulation scheme that couples TCAD and Monte Carlo tools has been developed for the simulation of single-event soft-gamma interaction with the SiC devices investigated in this work. Here, the discussion is limited to the case of a SiC JBS diode, as the results for a SiC MOSFET of the same voltage class do not differ significantly. A simulation model, given in Fig. 4(a), has been implemented in the TCAD simulation environment of Sentaurus Device [17]. This model is representative for the SiC JBS diode (JBS1) investigated experimentally. Fig. 4(b) and (c) present the principles of the simulation procedure. At first, the dependency of the multiplication factor on the position within the DUT of the charge deposition and on the applied reverse voltage has been calculated by the sequential TCAD simulation of the transport of a probe charge deposited in the vertices of a regular grid defined across the active region. The simulation occurs as follows. The single JBS cell model is brought to a reverse bias condition via quasi-static voltage steps. Once reached a selected bias condition, a probe charge is injected in the position of interest and the transport of the excess charge is simulated by a transient analysis. Charge multiplication is assessed by integrating the current pulse originating at the device terminals following the charge injection, normalized to the initial charge injected. The probe charge is calibrated to allow for minimal distortion of the steady-state electric field, while ensuring reasonable simulation times. The probe charge injection is achieved by a dedicated C++ code implemented in the Sentaurus Physical Model Interface [17]. The following simulation step consists in a Monte Carlo process that accounts for the charge generated along the ionization track of a photoelectron in the SiC JBS cell, as shown schematically in Fig. 4(c). The simulation starts with a random process generating the interaction site of every single gamma photon according to a uniform distribution, reasonable due to the low attenuation of photons in the target material. A second random process defines the angle of the emission direction of the secondary photoelectron, starting from the interaction location of the primary photon. The emission direction is assumed uniform (-180°, 180°). The third phase of the Monte Carlo process deals with the density of carriers generated by the photoelectron along its ionization track. For the sake of simplicity, the generated carriers' density is assumed as uniform along the whole length of the ionization track, while the initial energy is generated based on the experimental spectra of the gamma emission of Am 241 (Fig. 2(a)). The length of the ionization track is assumed to be 18 μm, based on the Monte Carlo simulation of the interaction of photoelectrons with SiC, shown in Fig. 3(a). The multiplication factor referred to a given interaction event is obtained by integrating along the ionization track produced by every single photoelectron the interpolated 3Dfunction calculated by the TCAD simulation in the first phase of the procedure. A spectrum, for a given biasing condition, is finally obtained by iterating this procedure to calculate the distribution of the charge generated by several thousand of soft-gamma interaction events.

4-Results.
The experimental spectra. Fig. 5 reports the experimental spectra resulting from the irradiation with Am 241 soft-gamma particles at LNT of some selected devices of Table 1. As the reverse bias applied to the blocking junction increases, the spectra shift towards higher charges due to carriers' multiplication. To avoid the saturation of the spectrometer due to an excessive count-rate, a cut-off is applied to low-intensity pulses that results in the low-side truncation of the experimental spectra acquired at increased voltage bias. The SiC DUTs exhibit a spectrum that is significantly different from the ones acquired in the same irradiation conditions in the case of silicon-based devices of comparable rating. This is mainly due to the difference in the thickness of the depletion region. While the range of 59.5 keV photoelectrons in silicon and SiC is comparable, the thickness of the depletion region of SiC devices is eight to ten times smaller compared to the silicon counterparts of comparable rating. In the case of silicon devices rated 1.2 kV or more, the energy released by the secondary photoelectrons is frequently completely absorbed in the depletion region. This is not the case for the SiC devices investigated here, as the thickness of their fully depleted depletion region (10-15 μm) is comparable to the range of the secondary photoelectrons and only a part of their energy is effectively collected. This fundamental difference is further empathized by the simulation results in the following section.
The TCAD-Monte Carlo simulation. Fig. 6(a) reports the soft-gamma spectra resulting from the simulation scheme described previously, applied to the SiC JBS diode model of Fig. 4(a). Fig. 6(b) reports the results of the same kind of simulation carried out for a Si PiN diode model of the same voltage rating, for comparison purposes. As shown in the experimental spectra of the previous section, at high blocking voltage values, the spectra show tails in the high charge section generated by interaction events resulting in large multiplication values. In the case of the silicon device, due to the thickness of the depletion region, the multiplication factor only slowly depends on the interaction site of the soft-gamma photon. In its spectrum this results in a photopeak which maintain its shape while shifting towards higher charges as the reverse bias increases.

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The simulation scheme allows to locate the origin of such events. Fig. 6(c) shows a map of the simulated multiplication factor as a function of the soft-gamma interaction site and photoelectron emission angle, for the SiC JBS model. In the case of the SiC JBS diode, the incomplete collection of the charge generated by the soft-gamma interaction results in a greater statistical spread and pulses of lower intensity. Furthermore, a multiplication is observed that depends more strongly than in the silicon case on the interaction site of the gamma photon, as highlighted in the map of Fig. 6(c). Therefore, the formation of a complete photopeak is not observed in the SiC device case. Intense peaks of multiplication are observed in the case of soft-gamma interactions in the close vicinity of the N -N + junction. This effect is in consequence of the fact that in SiC the impact ionization coefficient of holes is larger than for electrons, and holes generated at this location can be accelerated across the whole thickness of the depleted region, undergoing massive multiplication. This observation is dual in the case of the siliconbased device, for which peaks of multiplication are observed in proximity of the P + Njunction.
The multiplication factor at operating temperature. Some DUTs (e.g., JBS1, MOS1 and MOS2) already exhibit a sufficiently low level of thermal generated reverse current at ambient temperature that allows for the measurement of the charge multiplication by soft-gamma irradiation. This fact allows for a comparison of the multiplication factor measured at LNT to the one measured at AT, shown in Fig. 7(a) for JBS1, MOS1 and MOS2. Here, the applied reverse bias voltage has been normalized with respect to the breakdown voltage of the DUT, measured at the respective temperature. By such normalization, it is observed that the multiplication curves are almost superimposed, within the limit of experimental accuracy. This suggests that the charge multiplication factor is essentially a function of the normalized bias VBIAS / VBD. This observation is corroborated by Miller's empirical formula, expressing the multiplication factor (M) in step junctions [18]: Where V is the reverse bias voltage and n is a fitting exponent. Furthermore, VBD is an expression for the breakdown voltage, which includes implicitly its dependency on the temperature. The dependency of the carriers' multiplication factor on the normalized bias VBIAS / VBD has also been investigated by TCAD simulation. For this scope, the transport and multiplication of carriers in the SiC JBS of Fig. 4(a) has been simulated according to the procedure described in the Section 3 for different temperature values (300-580 K), within the validity range of the Hatakeyama [19] (hydrodynamic) model for the avalanche generation of carriers by impact ionization. The simulations show that, in the investigated temperature range, the multiplication of carriers decreases with increasing temperature following the reduction of the mean free path for carriers. Nevertheless, as shown in Fig. 7(b), the multiplication factor shows almost no dependence on temperature once represented as a function of the normalized bias voltage VBIAS / VBD, with peak variations in the 3.5% range. Following the previous considerations, an empirical relationship is derived for the conversion of the multiplication factor measured at LNT to the multiplication factor at operating temperature: Where VBD-LT and VBD-HT are the breakdown voltages of the device at LNT and operating temperature, respectively.
Correlation of the multiplication factor to the failure rate of devices exposed to TCR. In [14], Lichtenwalner et al. carried out accelerated tests of SiC power devices by neutron irradiation, revealing that the TCR induced SEB failure rate of SiC MOSFETs and diodes exhibits a universal  Fig. 4(a). Under normalization of the reverse bias V BIAS /V BD , the multiplication just slightly depends on the temperature over the whole validity range of the Hatakeyama Model [19] for impact ionization.

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scaling behavior as a function of the normalized reverse bias voltage VBIAS / VBD. Recent works [12], [13], have demonstrated the correlation between the TCR failure rate of power devices assessed by neutron irradiation and the multiplication factor measured by soft-gamma irradiation at ambient temperature. Although the latter technique has proven to be very promising, its application at room temperature was limited to those devices with a low level of reverse current. Fig. 8(a) shows the multiplication factor as measured by soft-gamma irradiation at LNT for all the DUTs listed in Table  1. Here, the multiplication factor is given also for DUTs (e.g., MOS3) that exhibit excessive levels of reverse current at ambient temperature for the accurate measurement of multiplication, demonstrating the improved versatility of the technique granted by the cryostatic operation of the spectrometer. For all the investigated samples, the multiplication factor scales with the normalized bias VBIAS / VBD. Fig. 8(b) reports about the correlation of the multiplication factor as measured by soft-gamma irradiation at LNT to the failure rate assessed according to the universal scaling function introduced by Lichtenwalner et al. in [14]. The failure rate is shown to increase as the multiplication factor increases, in a similar fashion for all the investigated samples. Furthermore, the failure rate rapidly increases in the multiplication range from 1 to 1.5-2, where the value of about 100 FIT/cm 2 is reached. Starting from this multiplication level, the failure rate (λ) seems to slow down, converging to a similar trend line, expressed by: Where A= 177.5 FIT/cm 2 and B = 0.917. The observed scaling behavior suggests the possibility of describing the failure rate as a function of the multiplication factor according to a universal law, similarly to what has been proposed in the literature for the normalized bias VBIAS/VBD [14]. In this case, the characterization of the multiplication factor by the Am 241 soft-gamma source could become a complementary technique to the traditional assessment methods based on neutrons or heavy ions irradiations [5], [14], [20], [21], as well as an efficient tool for the definition of the Safe operating area of semiconductor power devices.

5-Summary and Conclusions.
The soft-gamma emission of an Am 241 radioactive source has been used in conjunction with a dedicated cryostatic spectrometry setup to sense the device-internal electric field of SiC power devices, by the measurement of the carriers' multiplication factor. Thanks to the novel setup, measurements of the multiplication factor have been extended to devices that could not be characterized at ambient temperature.  Table 1, as measured at liquid nitrogen temperature. (b) Correlation of the measured multiplication to the TCR failure rate, from [14]. Continuous line: measured failure rate. Dashed line: failure rate estimated from the universal scaling function for SiC power devices [14].
An empirical relationship has been proposed to convert the multiplication factor measured at cryogenic temperatures to the one at operating temperature. A dedicated simulation scheme, which couples TCAD and Monte Carlo simulations has been developed and used to simulate efficiently the observed spectra and to locate the multiplication hotspots occurring in power devices. Finally, the multiplication factor of a set of sample DUTs as measured by soft-gamma irradiation has been correlated to the TCR induced SEB failure rate as measured by neutron irradiation, showing the possibility of describing the failure rate as a function of the multiplication factor according to a universal law, opening some new perspective for the use of the proposed technique for the definition of the Safe Operating Area of power devices operated under the influence of terrestrial cosmic rays.