Characterization of the onset of carrier multiplication in power devices by a collimated radioactive alpha source

Characterization of the onset of carrier multiplication in power devices by a collimated radioactive alpha source

Microelectronics Reliability 100–101 (2019) 113343 Contents lists available at ScienceDirect Microelectronics Reliability journal homepage: www.else...

2MB Sizes 0 Downloads 11 Views

Microelectronics Reliability 100–101 (2019) 113343

Contents lists available at ScienceDirect

Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel

Characterization of the onset of carrier multiplication in power devices by a collimated radioactive alpha source

T

Mauro Ciappa⁎, Marco Pocaterra ETH Zurich, Integrated Systems Laboratory, Zurich, Switzerland

ARTICLE INFO

ABSTRACT

Keywords: Impact ionization Carrier multiplication Impact ionization coefficient extraction Collimated alpha source Detection circuitry

The quantitative characterization of charge multiplication in reverse biased junctions is mandatory to design robust power devices, as well as to define their safe operating area. This applies especially for failure mechanisms like single event burnout, where the charge generated by ionizing radiation is transported and eventually multiplied by the internal electric field of the reverse-biased device. Because of their limited sensitivity, DC techniques detect charge multiplication as an increase of the reverse current of the junction once the breakdown already occurred. Optical and particle beams with dedicated test structures have been exploited to improve the sensitivity at lower electric field. However, the latter solutions cannot be simply applied to real devices. Furthermore, they just deliver averaged values of the multiplication factor. In this paper, single alpha particles from a collimated radioactive source are used to generate controlled charge bursts in the close vicinity of the reverse-biased junction of a power diode. The fast reverse current pulse arising to the drift of the initial charge burst is collected by a dedicated spectrometry chain. The acquired data are processed to obtain the probability distribution of the multiplication factor under consideration of the stochastic nature of the impact ionization process. The results of the measurements are compared with the multiplication values obtained by analytical models and by Monte Carlo simulation. The technique is demonstrated based on a commercial 1.2 kV-70A power diode in the reverse bias range from 700 V to 1250 V. Finally, detailed information is provided about the proposed hardware solutions, which can easily be implemented under usual laboratory conditions.

1. Introduction The characterization of impact ionization in semiconductors is fundamental to the design and the robustness of power devices. As an example is the measurement of the onset of carrier multiplication that is often used to define the maximum reverse/blocking voltage for the survivability of high-voltage devices to single event burnout phenomena produced by cosmic rays [1]. In the case of power devices, the physics is quite clear. Electron-hole pairs generated in the close vicinity of a reverse-biased junction are separated by the local electric field. In the particular case of a PiN diode, electrons drift along the depleted region (punch-through diode) and are collected at the cathode. During the transport the carriers experience several inelastic scattering events, in particular with electrons and phonons. At high values of the local electric field, electrons (holes are neglected here) may acquire sufficient energy along their mean free path (inverse of the impact ionization coefficient) to ionize a semiconductor atom, resulting into an additional charge, i.e. in a charge



multiplication. Hence, impact ionization (and charge multiplication) can be seen as a non-homogeneous stochastic process, where the number of scattering events experienced by every single drifting carrier is a random variable, whose variance increases as the reverse bias applied to the diode approaches the breakdown voltage. Theoretical models are available to predict the impact ionization coefficients of electrons and holes as function of the local electric field and of the temperature. Such models, mainly provide an averaged value of the multiplication factor [2–6]. The probability distribution of the multiplication factor can only be obtained by Monte Carlo simulation [7], that nonetheless needs independent experimental data for calibration. In addition, Monte Carlo simulators are usually very demanding in terms of computation time and make use of quite complex and semi-empirical physical models. Experimentally, the multiplication factor is often inferred from the reverse current at a voltage quite close to the junction breakdown. However, this approach is not very accurate, because, in real devices, the breakdown first occurs at small isolated spots or lines (e.g. because

Corresponding author. E-mail address: [email protected] (M. Ciappa).

https://doi.org/10.1016/j.microrel.2019.06.035 Received 14 May 2019; Received in revised form 6 June 2019; Accepted 17 June 2019 Available online 23 September 2019 0026-2714/ © 2019 Elsevier Ltd. All rights reserved.

Microelectronics Reliability 100–101 (2019) 113343

M. Ciappa and M. Pocaterra

of three-dimensional effects), where the local current density may achieve very high levels without reaching the current threshold, which can be detected by the usual instrumentation. To overcome this limitation, techniques have been proposed that exploit early generation of electron-hole pairs in the depletion layer of reverse-biased junctions by continuous or pulsed ionizing radiation beams (laser, particle beams), followed by the measurement of the resulting reverse current [5,6,8]. Unfortunately, such approaches also deliver just an average value of the impact ionization coefficients, without providing any direct information about the probability distribution of the multiplication factor. The proposed solution makes use of a single alpha particle emitted from an almost monoenergetic, collimated radioactive source to generate a very localized burst of electron-hole pairs in the close vicinity of the P+N−–junction of a power diode, biased at a given reverse voltage. A dedicated high-gain amplifying chain is used to collect the charge pulse (with duration in the nanosecond range) that arises at the terminals of the device as the initial charge burst drifted along the depleted layer. The probability distribution of the collected charge is built by cumulating typically 20,000 independent events. Finally, the probability distribution of the multiplication factor is obtained by statistical processing the acquired data. In addition to previous extraction procedure, averaged values of the multiplication factor are calculated based on two simplified extraction methods. Furthermore, the experimental values are compared with averaged multiplication factors extracted by the analytical Bologna model and by Monte Carlo simulation. The proposed technique is demonstrated using a 1.2 kV-75A commercial power diode with 1385 V breakdown voltage (measured at 1 μA). The onset of impact ionization and charge multiplication is characterized at a reverse bias from 700 V to 1250 V. The paper, also provides detailed information about the dedicated spectrometer.

Table 1 Model parameters of electron impact ionization coefficient after the Bologna model in Eq. (1) [9,11,12]. Following units apply: [αe(E)] = 1/cm; [E] = V/cm, [T] = K, [ai] = [bi] = V, [ci] = [di] = V/cm. Parameters a(T) = ∑ ak(T)k b(T) = ∑ bk(T)k c(T) = ∑ ck(T)k d(T) = ∑ dk(T)k 4.65403 a0 a1 –8.76031e−3 1.34037 e−5 a2 a3 –2.75108e−9 −0.128302 b0 b1 4.45552e−3 b2 −1.0866e−5 9.23119e−9 b3

2.1. Modeling the impact ionization, Bologna model, and Monte Carlo simulation

E a + b*exp

( ) d c+E

1 = M

W 0

e (E (x ))

exp

[1/ cm] (1)

x 0

(

e (E (x

))

h (E (x

c0 c1 c2 c3 d0 d1 d2

7.76221e3 25.18888 –1.37417e−3 1.59525e−4 7.10481e5 3.98594e3 −7.19956

The distribution of the final charge generated by the transport of a single charge burst is the result of the convolution of two distinct stochastic processes. The main random variable of the first stochastic process is the total charge that is generated by the alpha particle in the depletion region (probability function pCC0). pCC0can be easily measured at sufficiently low reverse bias, where all charges generated by the single alpha particle are collected but no multiplication occurs (in present measurement pCC0 is acquired at 700 V). The second stochastic process refers to the variability of the charge generation during the transport of the charge across the depletion region (probability function pMULT), which is correlated among others to the random number of scattering events experienced by the carriers during the transport. Summarizing, the combination of both relevant processes can be Table 2 Multiplication factors as calculated by the SMC Monte Carlo code [13] and by the New Bologna model [9,11,12] at 300 K (see Section 2.1).

where the model parameters are listed in Table 1. For single charge bursts, the multiplication factor M is defined [9] based on the impact ionization coefficients (αe and αh for electrons and holes, respectively), as

1

–1.82482e−12 –4.82689e−15 1.09402e−17 −1.24961e−20 7.55584e−24 −2.28615e−27 2.73344e−31

2.2. Extraction of the probability density function of the charge multiplication factor

Among the available models, the most accepted one is Chynoweth's law [4], whereby the impact-ionization rate is expressed as an exponential of the inverse electric field. Van Overstraeten and De Man [6] validated this model by measuring the multiplication factor in narrow PN-junctions in the electric-field range from 1.75 105 to 6 105 V/cm at room temperature. Additional investigations in the same electric-field range have been carried by BJT in common–base configuration, where the generation current can be easily extracted from the change of the base current. With the measurement of the gate current in more sensitive static-induction transistors [9,10] the multiplication factor could be characterized down to 5 × 104 V/cm. Based on latter data, an analytical model for the impact ionization coefficients of electron and holes (αe(E), αh(E)) has been validated over ten orders of magnitude [9] and then extended to the New Bologna Model [9,11,12]. The expression assumed by this model for αe(E) is

=

b4 b5 b6 b7 b8 b9 b10

layer [8]. Since the impact ionization coefficient for the holes αh(E) in the considered range of the electric field is at least a factor of 10 lower than for electrons, it will be neglected for following considerations. Eq. (2) has been solved for M and the integral calculated by assuming the impact ionization coefficient of the electrons from Eq. (1) and a straight electron trajectory starting at the generation point of the electron-hole pairs and terminated at the N−–N+ junction. The local strength of the electric field has been calculated after Eqs. (5) and (6) in Section 2.5. The multiplication factors obtained for different values of the reverse bias across the diode have been summarized in Table 2. Similarly, the multiplication factors for the same reverse bias values have been calculated by the Simple Monte Carlo v1.0 (SMC, [13]) simulation tool originally developed to simulate single photon avalanche diodes and that uses a simplified band structure to reduce computational requirements. The parameters assumed by the simulator to solve the Poisson equation are specified in Section 2.5. The calculated multiplication factors are compared to those obtained by the Bologna Model in Table 2.

2. Experimental

e (E , T )

k = 0.3 k = 0.10 k = 0.3 k = 0.2

700 V 900 V 1000 V 1100 V 1200 V

))) dx dx (2)

where E is the instantaneous field and W is the width of the depletion 2

Monte Carlo SMC

New Bologna model

1.01 1.38 2.16 5.11 26.11

1.08 1.51 2.20 4.10 11.46

Microelectronics Reliability 100–101 (2019) 113343

M. Ciappa and M. Pocaterra

Fig. 1. (a) Simulation by SRIM 2013 [14] of the range of the alpha particles in the depletion region after crossing a 24.3 μm silicon-equivalent thick dead layer (impinging angle from −20° to +20°). (b) Probability function of the charge deposition in the depletion layer at 700 V (no multiplication). The calculation is based on the simulation by SRIM 2013 of the probability function of the residual energy of the alpha particles transmitted through the dead layer. The equivalent experimental curve at 700 V is shown in Fig. 7b.

represented analytically by the convolution integral

pCCM (Q ) = K1

C

pCC 0 (Q )*pMULT (Q

)d

C (pCC 0 , pMULT )

avoid the pile-up of two subsequent events. Measurements are repeated at increasing reverse-bias voltage, starting at a value, where no multiplication occurs (about 50% of the breakdown voltage) up to 90% of the rated breakdown voltage of the device. Under such conditions, single charge pulses with sub-nanosecond duration are generated, which range from 1fC to 1.2pC. These pulses are detected by a dedicated highgain charge amplifier and converted by a fast ADC to a digital waveform, which is stored for further processing. The acquired waveforms are processed off-line by a dedicated software to obtain the probability density functions pCC0and pCCM. Measurements are carried out first with a planar and then with collimated source.

(3)

where K1 is a normalization factor and pCCM is the probability density function of the charge pulses measured at a given reverse voltage. Therefore, as pCCMand pCC0are known, pMULT can be extracted numerically by following deconvolution integral

pMULT = K2 C

1 (p CCM , pCC 0 )

(4)

where K2 is again a normalization factor. It has to be noted that a third stochastic process related to the distribution of the generation site of the carriers (calculated by Monte Carlo simulation in Fig. 1a) can be neglected here, since the size of generation volume (< 3 μm) is much smaller than the width of the depletion region (77 μm).

2.5. The investigated sample: power diode The device tested in this work is a commercial power diode rated for 1.2 kV and 75A (PiN, [15]) in a DO-247 package, whose top view and cross-section are shown in Fig. 2a and b, respectively. In the following measurements, the device is decapsulated by fuming nitric acid, buffered, and reverse biased. The passivation layer, the metal layer, as well as the anode diffusion act as dead layer, i.e. they do not contribute to the generation of the collected charge. In spite of this, such a dead layer produces the attenuation of the energy, the increase the energy straggling, and the scattering angle of the impinging alpha particles. The thickness of the dead layer has been extracted from reverse Monte Carlo simulation by the code SRIM 2013 [14]. In the simulation, the thickness of the dead layer has been to fit the measured distribution of the collected charge at 700 V (no multiplication). As shown in Fig. 1a and b the resulting thickness is 55.8 μg/cm2 (or 24.3 μm silicon equivalent). The width Wd of the depletion region and the related dopant concentration NN− of the intrinsic region have been extracted from the capacitance to voltage curve, being 77 μm and 1.11014 cm−3, respectively. The electric field in the depletion region has a trapezoidal shape. The maximum electric field Emax and the minimum electric field Emin in the depletion region are reached at the PeN and at the N−-N+ junctions, respectively. The dependence of Emax and Emin on the reverse bias Vrev applied to the leads of the diode is

2.3. Monte Carlo simulation of the range and deposited charge in the depletion region Both range and charge deposition in the depletion region of alpha particles emitted by the 210Po source have been calculated by the Monte Carlo simulation code SRIM 2013 [14]. The simulated monoenergetic source emits alpha particles with 5308 keV energy with an emission angle ranging from −20° to 20° (collimation). In the simulation, the target is considered as a pure silicon target. The thickness of the dead layer (see sect. 2.5) has been varied to fit the peak of the charge distribution as measured at 700 V reverse bias (pCC0, no multiplication). The simulated distribution of the deposited charge is derived from the energy distribution of the alpha particles that have been transmitted through the dead layer divided by 3.62 eV, i.e. the energy required to the generation of a single electron-hole pair, and finally multiplied by the elementary charge. The calculated range of the alpha particles in the depletion region and the simulated distribution of the collected charge pulses at 700 V are shown in Fig. 1a and b, respectively. The tail at the low end of the curve in Fig. 1b is due to alpha particle impinging at high angles, which results in a shorter range and therefore in smaller charge pulses. In the measurement, this tail is suppressed below 10fC because of the energy cut-off of the spectroscopy chain.

EMax = 142.85*Vrev + 5.41 10 4 [V /cm] EMin = EMax

2.4. The measuring principle

1.08 105 [V / cm]

(5) (6)

The electric field is assumed to decrease linearly within the depletion region, which is completely depleted starting from Vrev = 380V. As

For this experiment, a source with a very low activity is used to 3

Microelectronics Reliability 100–101 (2019) 113343

M. Ciappa and M. Pocaterra

Fig. 2. (a) Basic cross-section of the irradiated power diode showing the dead layer (24,3 μm silicon equivalent), the depleted layer (77 μm), and the carrier generation process. The energy of the alpha particle is calibrated in such a way that a burst of electrons and holes are generated in the depletion region, close to P+N− junction. The carriers are separated by the local electric field. In particular, electrons are accelerated towards the cathode and are forced to move through the depleted drift layer, where they experience impact ionization and eventually cause charge multiplication. This mainly happens in the top portion of the drift layer, where the electric field reaches the peak. (b) Top view of the power diode after decapsulation. The red dot indicates the location where the collimated source is pointed at. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

shown in Fig. 2b, the device is provided with guard ring terminations. 2.6. The alpha source The alpha source used for present setup is the isotope Polonium-210 (210Po). 210Po is an almost pure alpha emitter, with a main decay channel resulting in alpha particles at 5.305 MeV. Exempt quantity sources have been used to avoid safety issues and to prevent the occurrence of the pile up of two subsequent ionization events. In the planar source, with an activity of 0.1 μCi, a thin layer of the radioactive isotope is deposited on the top of an aluminum slab mounted within a 2.5 mm deep recess in epoxy, with a total active surface of 12mm2. Before reaching the depletion region the alpha particles have to cross a 2.5 mm air layer (stopping power of 92 keV/ mm [16]), and a 24.3 μm thick dead layer (silicon equivalent, stopping power of 144 keV/μm [16]). This reduces the maximum alpha particle energy down to about 0.5 MeV. In the rod source, a thin layer of 210Po is deposited at the top of a thin steel rod (0.7 mm diameter), resulting in a source activity of about 0.01 μCi (after collimation). In order to reduce the size of the beam spot at the surface of the target and to avoid excessive straggling of the beam energy, a collimator in conjunction with a rod source have been used. As published in a previous work [17], the collimator consists of a quartz capillary with 0.7 mm inner and 1.0 mm outer diameter. The rod source can slide along the axis of the capillary, such that the distance from the bottom of the capillary can be finely adjusted to achieve the optimum trade-off between beam spot and the luminosity of the source. This results in a 700 μm beam spot radius with imping angle ranging from 0° to 20°. Since, the bottom of the collimator is in direct contact with the diode surface, no energy loss occurs in air. The location, where the collimator has been placed on the diode surface is shown in Fig. 2b. A picture of the collimated source and the related energy spectrum are shown in Fig. 3a and b, respectively.

Fig. 3.

210

Po rod source and quartz collimator (diameter 700 μm).

than the observed event frequency. The block diagram of detection chain is represented in Fig. 4. The first stage, shown in Fig. 5, employs a high-bandwidth trans-impedance amplifier (250 MHz, preamplifier) to convert the current pulse collected from the power diode and is followed by a second high-bandwidth amplifier with gain 6. A Sallen-Key second order active low-pass filter with pole-zero cancellation (pulse shaper) in Fig. 6 is added as the second stage to adapt the pulse bandwidth to the sampling rate of the fast 14bit analog to digital converter (ADC). The acquired waveform is then saved in mass-storage unit for offline processing. The solution based on offline processing is preferred to the use of a standard online multichannel pulse height analyzer, since the first is much more reliable when dealing with single event processes. Therefore, a dedicated software is used to filter out spurious waveform and to accurately extract the value of the collected charge under consideration of the instantaneous signal noise. Finally, a histogram of frequency against the pulse amplitude is built. This detection chain is linear over the full operating range and has been designed to deal with high-voltage devices rated up to 3.5 kV DC. The linearity check and the calibration procedure are completed before data acquisition and the sensitivity range is adjusted to the specific experimental task.

2.7. The spectroscopy chain Since the measurement is aimed to characterize the onset of the charge multiplication, a dedicated spectroscopy chain that saturates at a multiplication factor of 50 is used. The pulse pile-up is suppressed (occurrence probability lower than 10−5) both by a very low flux of the alpha particles reaching the depletion layer of the diode (2 per s), as well as by the use of a detection chain that is at least ten times faster 4

Microelectronics Reliability 100–101 (2019) 113343

M. Ciappa and M. Pocaterra

Fig. 4. Block scheme of the spectroscopy chain used to measure the signal in the low multiplication range (M = 1–35) with 1fC resolution. The hardware consists of a pre-amplifier, a pulse shaper, and a fast 14bit analog to digital converter. The acquired waveforms are processed offline by a dedicated software. The spectrometer is designed to operate up to 3.5 kV input voltage.

in Fig. 2b, irradiating selectively the P+–N−-junction of the power diode. Measurements have been carried out at 700 V, 900 V, 1000 V, 1200 V and 1250 V for a duration of 5 h each. The latter measurement is not considered for the evaluation of the multiplication factor, since the resulting pulse charge produced the saturation of the preamplifier. Fig. 7b shows the probability distributions of the charge pulses as measured at different reverse bias conditions. Pulses are acquired up to 1.2pC and down to 10fC (cut-off by of the spectroscopy chain). As confirmed by the calculations in Section 2.1, at 700 V reverse bias no multiplication occurs. Therefore, this curve is assumed as the reference pCC0. The distribution is relatively tight but asymmetrical, since it exhibits a tail at the rising edge, due to charge deposition by alpha particles impinging at high angles. This is confirmed by the curve obtained by Monte Carlo simulation in Fig. 1b, which reproduces both the shape and the height of the measured distribution. The distributions acquired at higher reverse bias clearly show an evident smearing effect due to the multiplication of the charge. Up to 1100 V the distributions are almost box-shaped. Starting from 1200 V, the charge pulses cover a broad interval of values, indicating a large variance in the number of scattering events of the electrons.

3. Results and discussion 3.1. Planar source The electrically-insulated planar source is placed on the top of the opened package. Fig. 7a shows the spectra of the collected charge when the power diode is irradiated at different reverse bias conditions. The qualitative dependency of the distributions on the reverse bias seems to be evident. However, the presence of peaks, which do not shift, or shift with a different voltage rate, makes these spectra non-useful for the quantitative extraction of the multiplication factor. In fact, the planar source irradiates, besides the active area, also the terminations, which are at the very top surface of the diode (where the stopping power is still relatively low). Therefore, the terminations generate parasitic charge pulses in the low-charge region of the spectrum with a dependence on the bias, which depends on the local electric field and not on the electric field at the P+–N−-junction. As shown in the following, such parasitic components can be eliminated by the use of a collimated alpha source pointing selectively at the active area of the diode. 3.2. Collimated source

3.2.1. Multiplication factor 3.2.1.1. Normalizing to the reference charge. A first raw estimate of the

The collimated source has been first pointed at the location shown

Fig. 5. Detailed scheme of the dedicated two-stages transimpedance amplifier (TIA) used as pre-amplifier in the spectroscopy chain. The reverse-biased device is connected at the input in box 1 and capacitively coupled to a high-gain charge sensitive amplifier (box 3) where the feedback resistor and capacitor are 100 MΩ and 1.4 pF, respectively. The amplitude of the 140 μs output pulses is proportional to the detected charge. The second stage (box 4) is a low-gain voltage amplifier used to calibrate the spectroscopy chain in conjunction with the 1 pF injection capacitor (box 2) and the voltage amplifier in the pulse shaper. 5

Microelectronics Reliability 100–101 (2019) 113343

M. Ciappa and M. Pocaterra

Fig. 6. Detailed scheme of the dedicated pulse shaper aimed to format the output pulse into a double-exponential for optimum conversion in the 14bit analog to digital converter. A second order Sallen-Key filter is implemented by four stages based on operational amplifiers. The first stage is a differentiator, which includes a pole-zero cancellation function to cancel possible undershoots in output pulses. The second stage is an integrator, followed by low-pass filter with programmable gain the third stage. The final stage acts at the same time as filter and as buffer.

Fig. 7. (a) Spectrum of the charge pulses, as obtained by irradiating the power diode with the planar 210Po source under reverse bias conditions: the higher the reverse-bias, the broader the distribution. The spurious pulses and background at low charge values are due to the unwanted irradiation of the diode terminations. (b) Spectrum of the charge pulses, as obtained by the collimated 210Po source. The total number of collected charge pulses is the same for the different reverse bias values. The highest peak has been measured at 700 V and is in excellent agreement with the Monte Carlo simulation in Fig. 1b. Since it does not exhibit charge multiplication, it is used as reference spectrum for the charge generation (pCC0) to estimate the multiplication factors in Figs. 8a, b, and 10b. Because of the strong multiplication, the curve at 1250 V saturates the detection circuit, such that it cannot be used for quantitative calculation.

Fig. 8. (a) In the first approach, the charge multiplication (dots) has been estimated by dividing the total charge collected at a given reverse voltage (over the same time interval) to the total charge collected at 700 V (no multiplication). The data have been fitted by a double exponential (M = a * exp (b * V) + c * exp (d * V); a = 0.5565, b = 0.0008211, c = 7.546e-08, d = 0.01453). The dashed lines indicated the minimum and the maximum value of the electric field in the depletion region at the different reverse Voltages V. (b) In the second approach, the distribution of the charge multiplication has been estimated normalizing the charge axis to the peak of the curve acquired at 700 V (no multiplication). The cumulated distributions of the multiplication factors at the different reverse voltages have been calculated by integration. The extracted mean, median, and maximum values are summarized in Table 3. 6

Microelectronics Reliability 100–101 (2019) 113343

M. Ciappa and M. Pocaterra

3.2.1.3. Extraction by deconvolution. A more accurate extraction of the multiplication factor is obtained by the deconvolution procedure presented in Section 2.2. In Fig. 9, the probability distributions are shown separately. For sake of simplicity, following considerations are limited to the 1200 V case. In this case, the (smearing) distribution pMULT is searched that transforms by convolution the 700 V distribution (pCC0, no multiplication) into the 1200 V distribution (pCCM). pMULT as calculated by numerical deconvolution is shown in Fig. 10a, as the frequency of the occurring multiplication factors at 1200 V. After renormalization, pMULT is represented in Fig. 10b, as the probability distribution of the multiplication factor. The latter results clearly demonstrate that characterization techniques, which just deliver a single value for the multiplication factor can be too optimistic in defining such safe operating conditions of a device, where avalanching is not allowed. In fact, present measurements clearly show that a relevant charge multiplication can be achieved due to “lucky electrons” even at low reverse bias values in the range of 70 − 80% of the breakdown voltage. As an example, the presented method is a simple and accurate characterization technique that can be used to define the maximum allowed reverse bias (derating factor) of power devices to avoid single event burnout failures induced by terrestrial cosmic rays. Finally, since pMULT is directly related to the stochastic process describing the impact ionization process (number of scattering events per electron), this result can also be used as a valid tool to calibrate and validate simulation codes for the impact ionization based on stochastic models.

Table 3 Multiplication factors as extracted from the charge normalization in Fig. 8a and from the cumulated distributions in Fig. 8b. (* = no multiplication).

Fig. 8a Fig. 8b

Ratio Mean Median Maximum

700 V⁎

1000 V

1100 V

1200 V

1.00 0.92 0.94 1.75

1.17 1.37 1.37 2.91

1.45 1.93 1.87 5.54

4.30 6.61 4.43 34.09

multiplication factor is obtained by normalizing the total collected charge for a given reverse bias to the total charge collected at 700 V, i.e. at no multiplication. The results are shown in Fig. 8a, in conjunction with the maximum and minimum electric field values in the depletion region. It can be noticed from Table 3 that the measured multiplication factors are lower than the values predicted by Monte Carlo simulation and by the New Bologna model in Table 2. The value at 1250 V has been censored, because of the saturation of the detection chain. 3.2.1.2. Normalizing to the reference peak. A second estimate of the multiplication factor is carried out by normalizing the charge axis to the peak of the 700 V distribution. The cumulated distributions at 1000 V, 1100 V and 1200 V after normalization are shown in Fig. 8b. The related mean, median, and maximum values are summarized in Table 3. It is interesting to note that at 1200 V, about 10% of the alpha particles results in a multiplication factor that ranges from 20 to 34, whereas at 1000 V and 1100 V, the multiplication factor does not exceed 5.54.

Fig. 9. Disaggregated and semilogarithmic representation of the spectra in Fig. 7b. The curves at 700 V (pCC0) and at 1200 V (pCCM) have been assumed for the deconvolution procedure in Eq. (4). 7

Microelectronics Reliability 100–101 (2019) 113343

M. Ciappa and M. Pocaterra

Fig. 10. (a) Result of the numerical deconvolution of the spectrum at 700 V from the spectrum at 1200 V after Eq. (4) (pMULT). Every electron burst generated by a single alpha particle is subjected to multiplication according to the factor M = i Mi , where the addends of the sum are the multiplication values in pMULT. (b) Probability distribution of the multiplication factor, as extracted from Fig. 10a and its cumulated distribution. The mean value of the multiplication is 9.63, the minimum 1, and the maximum 35, respectively.

3.3. Comparison of the different methods

proper spectrometry chain, whose circuitry has been presented in very detail. The aimed probability distribution of the multiplication factor is obtained by numerical deconvolution of the measured curve with a measured reference curve. The transport of alpha particle through the semiconductor material, as well as the local charge generation by ionization have been validated by Monte Carlo simulation. The experimental data have been compared with the multiplication values obtained by an analytical model for impact ionization and a simple Monte Carlo code. This has demonstrated that the multiplication factors calculated up to about 90% of the breakdown voltage underestimate by about 30% the extreme values of the experimental distribution. In converse, multiplication factors calculated on the base of the mean and median values of the experimental distributions have been shown to be too optimistic in predicting such extreme values. The probability distribution of the multiplication factor as obtained by deconvolution of the experimental data has been presented in such a form that the total averaged multiplication factor is disaggregated in the single multiplication components with the related probabilities. This quantitative information can be easily used either to calibrate or validate simulation tools for impact ionization. Finally, the extreme values of the distribution have been used to propose a way to define the safe operating area of a power diode to survive single event burnout produced by cosmic rays.

Up to 1100 V, the multiplication factors obtained in Table 2 by the SMC Monte Carlo simulator and by the analytical Bologna model are quite close to each other and to the values obtained experimentally. At 1200 V, the SMC code delivers a multiplication factor that is five up to six times higher than the averaged experimental values and that is quite close to the maximum observed experimental value. In converse, the Bologna model predicts that at 1200 V the device already reached the breakdown. The results of the simplified extraction procedures listed in Table 3, clearly show that the ratio, mean, and median parameters strongly underestimate the maximum multiplication value achieved at each reverse bias. This issue is quite evident at 1200 V, where the maximum multiplication is six up to seven times higher than the averaged values. However, it is interesting to note that the Bologna model and in particular the SMC Monte Carlo code, estimate the extreme values of the experimental distributions in Fig. 9 within 30%. Finally, the probability distribution of the multiplication factor in Fig. 10b, obtained by deconvolution of the data acquired at 1200 V shows at the same time the maximum value of the distribution (35) and the occurrence probability of all other multiplication factors down to 1. The plot evidences that the most probable values of Mrange from 1 to 18. However, in about 15% of the cases the multiplication factor exceeds 20. This quantitative information is relevant, both for the calibration of simulation tools, as well as to define the safe operating area of power devices. In fact, the maximum reverse DC operating voltage of a device to survive SEB events can be defined on the base of the maximum acceptable multiplication factor. As an example, if the maximum acceptable multiplication factor of the diode under investigation is assumed as two (three), the corresponding maximum reverse DC operating voltage is close to 800 V (1000 V), i.e. 67% (83%) of the rated voltage and 58% (72%) of the actual breakdown voltage, respectively.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] S. Kuboyama, S. Matsuda, T. Kanno, T. Ishii, Mechanism for single-event burnout of power MOSFETs and its characterization technique, IEEE Trans. Nucl. Sci. 39 (1992) 1698–1703, https://doi.org/10.1109/23.211356. [2] T. Lackner, Avalanche multiplication in semiconductors: a modification of Chynoweth’s law, Solid. State. Electron. 34 (1991) 33–42, https://doi.org/10.1016/ 0038-1101(91)90197-7. [3] W. Maes, K. De Meyer, R. Van Overstraeten, Impact ionization in silicon: a review and update, Solid. State. Electron. 33 (1990) 705–718, https://doi.org/10.1016/ 0038-1101(90)90183-F. [4] A.G. Chynoweth, Ionization rates for electrons and holes in silicon, Phys. Rev. 109 (1958) 1537–1540. [5] K.G. McKay, K.B. McAfee, Electron multiplication in silicon and germanium, Phys. Rev. 91 (1953) 1079–1084, https://doi.org/10.1103/PhysRev.91.1079. [6] R. Van Overstraeten, H. De Man, Measurement of the ionization rates in diffused

4. Summary and conclusions A collimated radioactive alpha source has been used to measure the probability distribution of the multiplication factor in a commercial reverse biased power diode. The proposed measurement technique does not require any special infrastructure and can be easily implemented under industrial conditions. An exempt quantity 210Po rod source is used in conjunction with a 8

Microelectronics Reliability 100–101 (2019) 113343

M. Ciappa and M. Pocaterra

[7] [8] [9]

[10] [11]

silicon p-n junctions, Solid. State. Electron. 13 (1970) 583–608, https://doi.org/10. 1016/0038-1101(70)90139-5. N. Sano, T. Aoki, M. Tomizawa, A. Yoshii, Electron transport and impact ionization in Si, Phys. Rev. B 41 (1990) 12122–12128, https://doi.org/10.1103/PhysRevB.41. 12122. S.L. Miller, Avalanche breakdown in germanium, Phys. Rev. 99 (1955) 1234–1241, https://doi.org/10.1103/PhysRev.99.1234. S. Reggiani, E. Gnani, M. Rudan, G. Baccarani, C. Corvasce, D. Barlini, M. Ciappa, W. Fichtner, M. Denison, N. Jensen, G. Groos, M. Stecher, Measurement and modeling of the electron impact-ionization coefficient in silicon up to very high temperatures, IEEE Trans. Electron Devices. 52 (2005) 2290–2299, https://doi.org/ 10.1109/TED.2005.856807. I. Takayanagi, K. Matsumoto, J. Nakamura, Measurement of electron impact ionization coefficient in bulk silicon under a low-electric field, J. Appl. Phys. 72 (1992) 1989–1992, https://doi.org/10.1063/1.351625. E. Gnani, S. Reggiani, M. Rudan, G. Baccarani, Extraction method for the impactionization multiplication factor in silicon at large operating temperatures, 32nd Eur. Solid-State Device Res. Conf, 2002, pp. 227–230, , https://doi.org/10.1109/ ESSDERC.2002.194911.

[12] S. Reggiani, E. Gnani, M. Rudan, G. Baccarani, C. Corvasce, D. Barlini, M. Ciappa, W. Fichtner, M. Denison, N. Jensen, G. Groos, M. Stecher, Experimental extraction of the electron impact-ionization coefficient at large operating temperatures, IEDM Tech. Dig. IEEE Int. Electron Devices Meet. 2004, 2004, pp. 407–410, , https://doi. org/10.1109/IEDM.2004.1419171. [13] J.S. Petticrew, J.D. Dimler, S.J. Ng, No title simple Monte Carlo simulator for modelling linear mode and Geiger mode avalanche photodiodes in C++, J. Open Res. Softw 6 (2018) 17. [14] J.F. Ziegler, M.D. Ziegler, J.P. Biersack, SRIM – the stopping and range of ions in matter (2010), Nucl. Instruments Methods Phys. Res. Sect. B Beam Interact. with Mater. Atoms. 268 (2010) 1818–1823 https://doi.org/10.1016/j.nimb.2010.02. 091. [15] Datasheet STTH75S12, (n.d.). https://www.st.com/resource/en/datasheet/ stth75s12.pdf. [16] NIST, Stopping Power and Range Tables for Helium Ions, https://physics.nist.gov/ PhysRefData/Star/Text/ASTAR.html, (2018). [17] M. Ciappa, Y. Pang, C. Sun, Experimental characterization of critical high-electric field spots in power semiconductors by planar and scanning collimated alpha sources, Microelectron. Reliab. 88–90 (2018) 476–481.

9