Zhiguo Zeng
email: zhiguo.zeng@centralesupelec.fr

Enrico Zio
email: enrico.zio@centralesupelec.fr

Joint optimization of business continuity by designing safety barriers for accident prevention, mitigation and emergency responses

Keywords: Safety barrier, business continuity, optimization, condition-based maintenance, redundancy allocation, event tree, nuclear power plant, steam generator tube rupture EBCV Expected Business Continuity Value. NPP Nuclear Power Plant. PWR Pressurized Water Reactor

In this paper, an optimization model is developed for optimal design of the safety barriers in a nuclear power plant. By applying the developed model, safety barriers of different natures, i.e., the prevention, mitigation, emergency and recovery measures, can be optimized jointly for business continuity. A hierarchical numerical optimization method based on golden search and genetic algorithm is developed to obtain the optimal solutions. A numerical case study regarding the allocation of resources among the safety barriers prevention, mitigation and emergency in a nuclear power plant is worked out to maximize business continuity against the threat of steam generator tube ruptures.

I. INTRODUCTION

Business continuity, defined by the International Organization of Standards (ISO) as the capability of an organization to continue delivery of products or services at acceptable levels following disruptive events [START_REF] Standardization | Societal Security-business Continuity Management Systems-requirements[END_REF], provides an integrated way to design and manage safety barriers in a plant. In a recent work of the authors, an integrated model is developed for quantitative business continuity analysis [START_REF] Zeng | An integrated modeling framework for quantitative business continuity assessment[END_REF], which allows calculating the business continuity metrics considering the performances of different safety barriers for accident prevention, mitigation, emergency and recovery [START_REF] Zeng | An integrated modeling framework for quantitative business continuity assessment[END_REF].

In this paper, we use the integrated business continuity metrics defined in [START_REF] Zeng | An integrated modeling framework for quantitative business continuity assessment[END_REF] to drive a joint optimization of the prevention, mitigation and emergency safety barriers in a Nuclear Power Plant (NPP), focusing on the Steam Generator Tube Rupture (SGTR) accident. The Steam Generator (SG) is an important system in Nuclear Power Plants, which absorbs the heat generated in the reactor core and generates steam to drive turbines and produce electricity [START_REF] Sui | Investigation on response of hpr1000 under different mitigation strategies after sgtr accident[END_REF]. SGTR occurs when one or more tubes in the SG breaks [START_REF] Sui | Investigation on response of hpr1000 under different mitigation strategies after sgtr accident[END_REF]. As SGTR can lead to accidents with severe consequences like core meltdown, a number of safety barriers are needed to protect the NPP. How to design these safety barriers, so that the normal operation of the NPP can be ensured using a limited budget, is, therefore, an important but challenging problem. Currently, this problem is mainly solved by optimizing each safety barrier individually, in terms of minimizing their failure probabilities. Depending on the different natures of the safety barriers, different optimization models might be used (c.f., conditionbased maintenance optimization [START_REF] Grall | A conditionbased maintenance policy for stochastically deteriorating systems[END_REF], redundancy optimization [START_REF] Coit | Reliability optimization of series-parallel systems using a genetic algorithm[END_REF], etc.). These individual optimization models, however, can only guarantee the local optimal performance on the individual safety barrier. To ensure a collectively optimal performances considering all the safety barriers, a joint optimization model needs to be developed based on the business continuity metrics that integrates the effects of all the safety barriers.

II. SYSTEM DESCRIPTION

In this paper, we consider the optimal design of the safety barriers in a NPP against the threat of SGTR. The goal is to minimize the impact of SGTR on the business continuity of the NPP. For simplicity of illustration, let us consider an assumed NPP which contains only one SG. The SG is assumed to be the same type as the one in the Zion Pressurized Water Reactor (PWR) NPP, which contains 3592 inverted U-shaped tubes used for absorbing the heat produced by the reactor core and generating steam that drives the turbines to produce electricity [START_REF] Di Maio | Condition-based probabilistic safety assessment of a spontaneous steam generator tube rupture accident scenario[END_REF].

Since the tubes have thin walls and are operated under high pressures, they are susceptible to spontaneous rupture during operation. If tube rupture occurs in the SG, the reactor core might lose the necessary coolant for cooling it down. If not contained promptly, the SGTR event could evolve and lead to very severe consequences, such as core meltdown [START_REF] Kim | Prognostics for integrity of steam generator tubes using the general path model[END_REF]. Therefore, safety barriers are needed to protect the NPP from the potential impact of the SGTR. Based on their purposes, these safety barriers can be divided into barriers for prevention, mitigation, emergency and recovery (Sect. II-A-II-C).

A. Prevention barriers

Prevention barriers aim at preventing the SGTR from occuring. As 60% -80% SGTRs in practice are caused by Stress Corrosion Cracking (SCC) [START_REF] Di Maio | Condition-based probabilistic safety assessment of a spontaneous steam generator tube rupture accident scenario[END_REF], the main prevention barrier against SGTR is to inspect crack lengths periodically and conduct condition-based maintenance based on the results of the inspections. An illustration of a typical SCC growth process is given in Figure 1. Normally, the periodical inspections and condition-based maintenances are conducted during the planned shutdowns of the NPP (i.e., every x months), where x is usually 18 -24 months: Eddy current testing is used to measure the crack lengths and once the crack reaches a given threshold (denoted by y th ), the associated tube is plugged to prevent the tube rupture from happening [START_REF] Di Maio | Condition-based probabilistic safety assessment of a spontaneous steam generator tube rupture accident scenario[END_REF].

B. Mitigation and emergency barriers

Mitigation and emergency barriers serve the purpose of containing the damages caused by an undesirable initiating event (in this case, the tube rupture). In this paper, without loss of generality, let us consider the following mitigation and emergency barriers, which are widely used to protect NPPs in practice:

• Reactor Trip System (RTS), which detects the pressure losses in the primary loop due to the tube rupture and shuts down the reactor within a required time [START_REF] Kim | Prognostics for integrity of steam generator tubes using the general path model[END_REF];

• Reactor Depressurization System (RDS), which releases the increased pressure inside the reactor core due to the loss of coolant caused by the tube rupture [START_REF] Di Maio | Condition-based probabilistic safety assessment of a spontaneous steam generator tube rupture accident scenario[END_REF]; • Refueling Water Storage Tank (RWST), which provides water to the reactor coolant system for emergency cooling of the reactor core [START_REF] Di Maio | Condition-based probabilistic safety assessment of a spontaneous steam generator tube rupture accident scenario[END_REF]; • Reator Cooling System (RCS), which pumps water into the reactor core for emergency cooling [START_REF] Di Maio | Condition-based probabilistic safety assessment of a spontaneous steam generator tube rupture accident scenario[END_REF].

C. Recovery barriers

After the SGTR is successfully contained by the safety barriers, recovery needs to be undertaken to restore normal operation of the NPP. The recovery barrier associated to the SGTR is to replace the affected SG and clear the influence of the leaked nuclear-active materials on the environment. Normally, the recovery process is modelled by a random variable T rec , which represents the time needed for the NPP to get back to normal operations after the accident [START_REF] Zeng | An integrated modeling framework for quantitative business continuity assessment[END_REF].

III. BUSINESS CONTINUITY MODELING

As defined in Sect. I, business continuity is the capability of an organization to continue delivery of products or services at acceptable levels, following disruptive events [START_REF] Standardization | Societal Security-business Continuity Management Systems-requirements[END_REF]. It measures the system's performance under the threat of disruptive events, considering prevention, mitigation, emergency and recovery barriers. A numerical metric, called Expected Business Continuity Value (EBCV), is defined in [START_REF] Zeng | An integrated modeling framework for quantitative business continuity assessment[END_REF] to quantify the business continuity in a given interval [0, T ]:

EBCV = 1 - E [L([0, T ])] L tol , (1)
where E [L([0, T ])] is the expected value of the financial losses an organization suffers due to the impact of disruptive events; L tol is the maximal tolerable losses that an organization can suffer before it goes into financial problems (e.g., bankruptcy). The financial loss L([0, T ]) comprises of the direct loss L D ([0, T ]), which is directly caused by the disruptive event (e.g., damages of the NPP), and the indirect loss L I ([0, T ]), which refers to the revenue losses due to the unexpected shutdown of the business caused by the disruptive event. Due to the inherent stochastic nature of disruptive events, L([0, T ]) is uncertain and is treated as a random variable. As can be seen in Eq. ( 1), the physical meaning of EBCV is the expected safety margin of an organization to a financially critical state, considering the potential financial losses caused by the disruptive events that could impair its business continuity.

To quantitatively evaluate the EBCV of the NPP, an event tree model is developed first, as shown in Figure 2. It can be seen from the Figure that depending on the performance of the protection, mitigation and emergency measures, three types of consequences might be resulted. Detailed explanations to the consequences are summarized in Table I.

From the event tree model in Figure 2, the occurrence probabilities of the consequences, denoted by p Ci , i = 1, 2, 3, can be easily calculated as a function of the event probabilities along the sequences:

p Ci = f ET (p SGT R , p 1 , p 2 , p 3 , p 4 ),
where p SGT R is the probability of rupture of a single tube; p i , i = 1, 2, 3, 4 represent the failure probability of the RTS, RDS, RWST and RCS, respectively. When consequences C 2 and C 3 occur, the NPP becomes temporarily unavailable for producing electricity, until the recovery barriers successfully restore the normal operation of the NPP. The indirect losses suffered in the recovery process can, therefore, be modelled by:

L I,Ci = Q • C • T rec,Ci ,
where L I,Ci denotes the indirect losses in the recovery process of the ith consequence; Q is the unit price for electricity; C is the generation capacity of the NPP; T rec,Ci is a random variable that represents the recovery time for the ith consequence.

Then, the E [L([0, T ])] in Eq. ( 1) becomes

E [L([0, T ])] = 3 i=1 E[L Ci ([0, T ])] • p Ci = 3 i=1 E[L D,Ci + L I,Ci ] • p Ci = p C2 • (L D,C2 + Q • C • E[T rec,C2 ])+ p C3 • (L D,C3 + Q • C • E[T rec,C3 ]). (2)
Then, EBCV can be easily calculated based on Eq. (1).

IV. BUSINESS CONTINUITY GUIDED OPTIMIZATION

A. Model formulation

In this paper, we consider the joint optimization of prevention, mitigation and emergency barriers with the objective of business continuity. The purpose of the prevention measure is to reduce the probability of SGTR. As shown in Figure 1, p SGT R depends on the inspection interval x and the plugging threshold y th . Therefore, x and y th are considered as decision variables that influence the performance of the prevention barriers. The physics-based SCC growth model developed in [START_REF] Di Maio | Condition-based probabilistic safety assessment of a spontaneous steam generator tube rupture accident scenario[END_REF] and [START_REF] Lewandowski | Incorporation of Corrosion Mechanisms into a State-dependent Probabilistic Risk Assessment[END_REF] is used to relate p SGT R to x and y th . We do not present this model in details due to space limitations. Interested readers can refer to [START_REF] Di Maio | Condition-based probabilistic safety assessment of a spontaneous steam generator tube rupture accident scenario[END_REF] and [START_REF] Lewandowski | Incorporation of Corrosion Mechanisms into a State-dependent Probabilistic Risk Assessment[END_REF].

The performances of the mitigation and emergency barriers, i.e., the RTS, RDS, RWST and RCS in Figure 2, can be represented by their failure probabilities. Adding redundancies is a common approach used for reducing failure probabilities of mitigation and emergency barriers. In this paper, we assume that parallel redundancy using the same type of system is considered for the four mitigation and emergency safety barriers. It is easy to show that the failure probability of the ith barrier becomes:

p i = (p i,b ) ni+1 , (3)
where p i,b is the failure probability of the ith safety barrier system and n i is the number of redundant systems added to the original system. A joint optimization model is set up in Eq. ( 4) to maximize the business continuity of the NPP against the threat of SGTR, where x is the inspection interval for the tube crack growth process: Eddy current testing is performed every x months to measure the crack lengths for all the tubes; y th is a threshold value for the crack lengths (measured in mm), above which the corresponding tube will be plugged; n 1 , n 2 , • • • , n 4 are the number of redundant systems for the RTS, RDS, RWST, RCS, respectively.

max EBCV = g(x, y th , n 1 , n 2 , n 3 , n 4 ) (4) s.t. p plug ≤ p th , (5)
C ≤ C th , (6) x, n i ∈ N, i = 1, 2, 3, 4, y th ≥ 0. (7)
The first constraint in the optimization model is the constraint on the maximal allowable number of plugged tubes in a SG. As the number of plugged tubes increases, the heat exchange efficiency of the SG decreases. According to the nuclear regulations, an SG of the type employed in Zion PWR NPP can tolerate up to 30% plugged tubes before a significant reduction in efficiency occurs [START_REF] Di Maio | Condition-based probabilistic safety assessment of a spontaneous steam generator tube rupture accident scenario[END_REF]. Therefore, we set p th = 0.3.

The second constraint in the optimization model regards the budget. As discussed in Sect. II, the total cost C covers the cost of improving the prevention barriers, denoted by C P , and the cost from improving the mitigation and emergency barriers, denoted by C M :

C = C P + C M . ( 8
)
The cost of the prevention barrier is determined by x and y th :

C P = n insp • C insp + n tube • p plug • C plug (9) = T x • C insp + n tube • p plug • C plug , (10)
where [0, T ] is the interval considered for the business continuity analysis; C insp is the price for one inspection; n tube is the number of tubes in the SG; C plug is the unit price for plugging one tube; and p plug is the plugging rate, which further depends on x and y th and needs to be calculated through simulations.

The cost for improving the mitigation and emergency barriers can, then, be calculated by

C M = 4 i=1 C i • n i , ( 11
)
where C i is the price of adding one ith safety barrier for redundancy.

B. Model solution

The business continuity optimization model in Eq. ( 4) is a mixed integral programming model, which is computationally hard to solve directly. In this paper, we propose to use a hierarchical optimization framework for this problem, as shown in Algorithm 1. c = c 0 ; while current EBCV is not optimal do Update c; Solve the sub-optimization model in Eq. ( 12) for p * rup,SG and C * P ; Solve the sub-optimization model in Eq. (13) for EBCV; end return c; Algorithm 1: Hierarchial optimization for business continuity

min p rup,SG = f (x, y th ) s.t. p plug ≤ p th , C P ≤ c. ( 12
) max EBCV = h(n 1 , n 2 , n 3 , n 4 ; p * rup,SG ) s.t. 4 i=1 C i • n i ≤ C th -C * P (13)
By introducing a an auxiliary variable c, which represents the budget limit assigned for improving the prevention measure, the original optimization model can be divided into two sub-optimization models. The sub-optimization model in Eq. ( 12) corresponds to optimizing the prevention barriers under the current value of c; the sub-optimization model in Eq. ( 13) optimizes the mitigation (and emergency) barrier using the remaining budget. Algorithm 1 is repeated until an optimal value of c is found that maximizes the EBCV. It can be shown that solving the optimization model using Algorithm 1 is equivalent to solving the original optimization model directly.

Different methods can be used in Algorithm 1 for updating the value of c and solving the two sub-optimization models. In this paper, we use the golden search algorithm to search for the optimal value of c, while using the genetic algorithm for solving the two sub-optimization models. It should be noted that the p rup,SG in Eq. ( 12) is the probability that there is at least one tube rupture in the SG, and can be calculated from p SGT R :

p SGT R = 1 -(1 -p SGT R ) n tube .

V. RESULTS AND DISCUSSIONS

In this section, we conduct a numerical case study using the NPP described in Sect. II. The event tree model in Figure 2 is used to analyze the consequences following the SGTR and EBCV is calculated using Eq. ( 1) and ( 2). Algorithm 1 is used to solve the optimization model in Eq. ( 4). The parameter values used in this numerical case study are summarized in Table II.

The result of the optimization is given in Table III. It can be seen from the Table that the optimal design solution requires to do a periodical inspection of the SG every 11 months and plug the tube whose crack length exceeds 18.11 (mm). At the same time, three redundant systems are added to the RDS and RCS, respectively. It can also be seen that in the optimal design plan, most of the budget is spent on the prevention barriers. This can be explained by the fact that the prevention barriers have the highest structural importance (see the event tree in Figure 2). Besides, improving the performance of the prevention barriers requires more investment than the mitigation and emergency barriers (see the comparison between C insp and C i , i = 1, 2, 3, 4 in Table III.)

As a comparison, an individual optimization of the prevention barrier is conducted by investing all the budget C th on the it. The result is also represented in Table III. It can be seen from the comparison that although the individual optimization model can achieve lower SGTR occurrence probability for (0.0049 compared to 0.0089), its EBCV value is lower than the joint optimization model. This is because in the individual optimization model, all the resources are invested on prevention barriers. The mitigation and emergency barriers, however, are neglected and become bottlenecks to the business continuity of the NPP. Using the joint optimization model, on the other hand, can achieve a global optimal solution with higher business continuity by optimal allocation of resources across all the safety barriers.

VI. CONCLUSIONS

In this paper, a joint optimization model is developed for allocating resources among prevention, mitigation and emergency barriers to achieve optimal business continuity. A hierarchical optimization method based on golden search and genetic algorithm is developed for finding the optimal solution. The developed method was applied to design the safety barriers in a NPP against the threat of SGTR. The results of the optimization were compared to those from conventional methods that optimize the different safety barriers individually. The results show that using the joint optimization model leads to globally optimal business continuity. The conventional methods, on the other hand, often end up with local optimums of each individual safety barrier, but the global performance of business continuity is not optimal. The proposed optimization model can be further improved from two aspects. First, how to treat the uncertainty in the optimization model deserves further investigation. Secondly, to achieve better accuracy in the optimization results, large numbers of samples are needed in the Monte Carlo simulation, which creates a challenge to the computational costs of the optimization method. Hence, more advanced methods can be developed to improve computational efficiency.

Fig. 1 .

 1 Fig. 1. An illustration of the tube crack growth process

Fig. 2 .

 2 Fig. 2. Event tree model for the SGTR accident (adapted from [6])

TABLE I

 I

		CONSEQUENCES FOR THE SGTR
	Consequence	Meaning
	C

[START_REF] Standardization | Societal Security-business Continuity Management Systems-requirements[END_REF]

No SGTR occurs: the NPP is operating normally. C 2 SGTR occurs, but the consequence is successfully contained by mitigation and emergency barriers: no core damage occurs, but some nuclear active materials leak to the environment. C 3

Core damage is caused by the SGTR.


Besar Asllani

Pascal Bevilacqua

A Zaoui

G Grosset

Dominique Planson

Hervé Morel

High-Voltage SiC-JFET Fabrication and Full Characterization

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ID: 1099

High-Voltage SiC-JFET Fabrication and Full Characterization B. Asllani 1 , P. Bevilacqua 1 , A. Zaoui 1 , G. Grosset 2 , D. Planson 1 and H. Morel 1 1) Univ Lyon, INSA Lyon, CNRS, AMPERE, F-69621 Villeurbanne, France 2) ION BEAM SERVICES, F-13790 PEYNIER , France herve.morel@insa-lyon.fr Silicon Carbide (SiC) enables to develop high-voltage devices. The present study focuses on JFETs. The targeted rating was 3300 V, 20 A.

To reach these characteristics a vertical structure with vertical and lateral channels was designed as shown in Fig. 1. The lateral channel enables an easy design with a low absolute value of the gate-source threshold voltage. It is easier to manufacture but yields a higher on-state resistance (R ON ) in comparison with a pure vertical channel.

Devices are fabricated on a n-type epitaxial layer (supplied by Showa Denko) with a thickness of 32.7 µm and a doping concentration of 9.7x10 14 cm -3 . 13 photolithography mask levels were used. A double gate structure one buried gate fabricated by ion implantation and a surface gate obtained by epitaxy regrowth. The edge termination of the JFETs includes a MESA structure and junction termination extension (JTE). The front side and back side metalizations are in Ag. The second passivation uses polyimide.

Electrical characteristics

Die dimensions (mm)

Source pad dimensions (mm)

Gate pad dimensions (mm)

3300V/20A 5,8 x 5,8 3,91x2,21 0,96x0,96

Best dies were diced and packaged to enable high current measurements. The packaging was an optimization of Iso4 standard package made by DeepConcept Company as shown in Fig. 2. The size is the same but the internal design is optimized for SiC and for 3300 V voltage. The package can operate up to 200°C. In this case, the support is a metal one: (Cu, Al + termination Ni, Au, Ag).

The electrical characterization includes: standard static characteristics as the output characteristic (Fig. 3), the transfer characteristic, dynamic characteristics like Crss, Ciss. For such standard characterization a Keysight B1506A curve tracer was used. An IWATSU CS-5400 curve tracer was used for measuring the on-resistance versus the temperature. A specific test-bench for high voltage double pulsed test was used for the switching characterization (Fig. 4) and the associated turn-on and turn-off switching energy.

The final paper will present with further details, the main device characteristics for a datasheet like construction, the measurement protocols, and the associated test benches. Moreover turn-on and turn-off switching losses will be included in the range 500 V -2000 V.

Fig. 1 :Fig

 1 Fig. 1: Schematic of the designed JFET structure

Acknowledgments: the authors would like to thank FilSiC project in the framework of the French research program, Investments for the Future, for fnancial support (FilSiC: Convention n°O13953-410188).


Besar Asllani

A Castellazzi

Dominique Planson

Hervé Morel

Hervé Morel Subthreshold Drain

Subthreshold Drain current hysteresis of planar SiC MOSFETs

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ID: 1178 (ID number can be found at the top right corner of submission page.) Subthreshold drain current hysteresis of planar SiC MOSFETs B. Asllani 1,2) , A. Castellazzi 1) , D. Planson 2) , H. Morel 2) 1) PEMC Group, University of Nottingham, Nottingham NG7 2RD, UK 2) Univ Lyon, INSA Lyon, CNRS, Ampère, F-69621 Villeurbanne, France E-mail: besar.asllani@gmail.com 4H-SiC MOSFETs are available in the market as discrete devices or power modules. These devices present many advantages for power conversion compared to Si IGBTs but still suffer from some (reliability) drawbacks [1][START_REF] Unger | Proc. Int. Symp. Power Semicond. Devices ICs[END_REF][START_REF] Jesd | Procedure for Wafer-Level DC Characterization of Bias Temperature Instabilities[END_REF]. The Vth instability of SiC MOSFETs is topic that mainly focuses on permanent drift of the Vth. Recoverable enhancement of the drain current in the subthreshold domain has been pointed out formerly for SiC MOSFETs [START_REF] Rescher | [END_REF] and is becoming a trending topic since it may affect the device stability. This phenomenon is not completely unknown since it affects Si devices as ell [5], but the Wide Band Gap of SiC enhances this effect and can produce a shift of the Vth up to several volts. As a matter of fact, hysteresis can make the devices switch faster, which could be an advantage to normal operation, but it can also make the devices switch on at lower gate bias, thus making them prone to undesired switching and leading to short circuit failure. Another problem can arise in the case of short-circuit, since the drain current will attain higher values and thus putting the device to higher thermal stress. 4H-SiC MOSFETs drain current subthreshold hysteresis can range from several tens of millivolts to several volts depending on the structure of the device. They are usually attributed to slow interface states that capture holes when the gate is negatively biased [START_REF] Rescher | [END_REF]6]. In this paper we will focus only on the Vth subthreshold Hysteresis of planar MOSFETs through measurements and TCAD simulation. This will give a better understanding of the role of the interface states in this phenomenon.

The subthreshold drain current depends strongly on the prior state of the device. In the subthreshlod domain, for same value of drain current we need higher gate bias when going from on-state to off-state than vice versa. Once the gate is biased above the Vth voltage, the drain current doesn't depend on the previous state anymore. This behaviour is illustrated in figure 1, where depending on the off-state starting voltage the subthreshold drain current can be almost 2 decades higher. The measurements in figure 1 were performed at room temperature, whereas figure 2 shows the hysteresis as a function of off-state starting gate bias voltage for several temperatures. The hysteresis decreases for higher temperature and is probably due to an acceleration of capture-emission mechanisms near the interface. To validate this hypothesis, the dependence of the surface potential on the gate bias voltage was extracted from C(V) measurements. C(V) measurement at different temperatures are shown in figure 3, where one can see that the Vfb is slightly shifted whereas the Vth stays the same. The extracted surface potential indicates a very low Vfb voltage which is certainly due to the difference of the workfunctions and probably the positive fixed charge in the oxide. The surface potential shows the band bending near the interface and can be related to the Fermi level near the interface. Since the occupancy of traps depends on the position of the Fermi level, one can predict the nature of the traps, donors or acceptors, and the capture/emission mechanisms happening at the interface. For a better assessment of the role of the interface states in the hysteresis phenomenon TCAD simulations have been performed. The simulated structure is shown in figure 5, whereas the simulated C(V) curves for different types of traps are shown in figure 6. The final paper will contain other measurements and will explain the dynamics of the phenomenon. All of these data may help manufacturers fine tune their device processing in order to avoid this undesired phenomenon.

Fig. 1 -

 1 Fig. 1 -Drain current subthreshold hysteresis of commercial 900 V planar SiC MOSFET.

Fig. 2 -

 2 Fig. 2 -Temperature dependence of the drain current subthreshold hysteresis of 900 V SiC MOSFET extracted at 100 nA.

Fig. 3 -

 3 Fig. 3 -4H-SiC planar MOSFET capacitance for different temperatures.

Fig. 4 -

 4 Fig. 4 -4H-SiC planar MOSFET Vth Hysteresis and the corresponding surface potential as a function of the gate bias voltage.

Fig. 5 -

 5 Fig. 5 -Simulation of the charge captured in the interface traps of a 4H-SiC planar MOSFET Fig. 6 -C(V) simulation of the effect of the interface traps in a planar 4H-SiC MOSFET.


ID: 2757801

Near breakdown voltage optical beam induced current (OBIC) on 4H-SiC bipolar diode D. Planson 1) , B. Asllani 1) , H. Hamad 1) , M.-L. Locatelli 2) 3) , L. Wei 2) 3) , C. Raynaud 1) , P. Bevilacqua 1) , L.V. Phung 1) 1) Université de Lyon, INSA Lyon, CNRS UMR 5005, Ampère, Lyon, France Silicon Carbide (SiC) is an attractive semiconductor material for high power and high temperature applications. In order to reach the expected breakdown voltage, an effective junction termination is required to spread the peripheral electrical field lines. Among different techniques used for periphery protection, Junction Termination Extension (JTE) is often chosen. The key parameters are the accurate dose of the electrically activated implanted dopants and the control of the semiconductor surface charge passivation. SIMS is a destructive way to measure the concentration profile of implanted species in the JTE but it does not allow to distinguish between electrically active dopants and inactive ones. In this paper, OBIC technique is applied to high voltage bipolar diodes to observe the behavior of the periphery protection with respect to the applied reverse voltage. The measured OBIC signal (i.e the current flowing towards the reverse biased junction) is related to the electric field in the bipolar junction space charge.

For voltages near the breakdown voltage, the electric field becomes high; the electron-hole paires (EHPs) which are generated by the UV beam into the space charge region are accelerated by this high electric field, gained enough kinetic energy to generate new EHPS during a collision with the atoms of the crystalline structure. This is the pre-avalanche regim, which lead to an increase in the OBIC signal [1].

The measurements are realized on a square bipolar diode protected with a single JTE. The anode contact area radius curvature is set at 200 µm, and its total side length is 700 µm. The distance between the metal periphery and the JTE extremity is 250 µm. A cross section of the device is shown in Fig. 1.

The surface of the diode is scanned by the laser beam focused by several lens in a spot of ~10µm diameter. A schematic description of the experimental bench is shown in Fig. 2. The measurement is performed in a vacuum chamber able to sustain high voltages up to 3500V. Tests have been carried out at 0 V, but also at higher voltages: 1000 V in Fig. 3 and 2350 V in Fig. 4. Near the breakdown voltage, an increase in the OBIC signal could be observed at the edge of the JTE by the side of the tip. This phenomenon is correlated with the observed luminescence due to the radiative recombination of EHPs generated by avalanche multiplication [2][3], as shown in Fig. 5.

More experimental results (including TCAD simulations) showing the variation of the OBIC signals with the applied reverse voltages will be published in the final paper. Also theoretical simulations will be used to try to estimate the concentration of active dopants. x (µm) y (µm)

Fig. 1 .

 1 Fig. 1. Cross section of the protected bipolar PiN diode.

Fig. 2 .

 2 Fig. 2. Schematic of OBIC experimental bench.

Fig. 3 .

 3 Fig. 3. Top view of OBIC measurement at 1000 V. Position of the tip is deduced from the lower signal level.

Fig. 4 .

 4 Fig. 4. 2D-cartography of OBIC signal vs. beam position at 2350 V (current is expressed in nA).

Fig. 5 :

 5 Fig. 5: Luminescence observed at 2351 V.

Acknowledgments: the authors would like to thank FilSiC research program for financial support and also gratefully acknowledge Dr. Gregory GROSSET and Lionel DUPUY for the realization of test structures.