# Experimental and Numerical Simulation Study of a Semiconductor Opening Switch

Ejlal Shahriari, Anton Gusev, Antoine Silvestre de Ferron, Laurent

Pecastaing, Susan Parker, Simon Bland

► To cite this version:

Ejlal Shahriari, Anton Gusev, Antoine Silvestre de Ferron, Laurent Pecastaing, Susan Parker, et al. Experimental and Numerical Simulation Study of a Semiconductor Opening Switch. IEEE Transactions on Plasma Science, 2025, 53 (7), pp.1583-1591. 10.1109/TPS.2025.3573764. hal-05104736

HAL Id: hal-05104736

https://hal.science/hal-05104736v1

Submitted on 10 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et 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.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Experimental and Numerical Simulation Study of a Semiconductor Opening Switch

Ejlal Shahriari, Anton I. Gusev, Member, IEEE, Antoine Silvestre de Ferron, Laurent Pecastaing, Senior Member, IEEE, Susan Parker, Simon Bland, Member, IEEE

***Abstract***—This article examines the nanosecond interruption of high current in Semiconductor Opening Switch (SOS) diodes, with the goal of bridging the gap between experimental results and numerical simulations. The experimental results of SOS diodes (0.25 cm², 0.9 kV) operating as a nanosecond interrupter are presented in a wide range of cutoff current density from 300 A/cm² to 5 kA/cm² to analyze the two modes of operation, i.e., Drift Step Recovery Diode (DSRD) and SOS. In addition, the numerical simulations of the SOS diode are conducted to investigate the dynamics of the SOS diode in the DSRD and the SOS modes using the Synopsys TCAD. A mixed-mode device with a circuit simulator is utilized to simulate the SOS effect and the dynamic processes occurring during the current cutoff stage. Finally, the experimental and numerical simulation results of the SOS current and load voltage are compared indicating (i) the accuracy of the TCAD model in the commercially available software and (ii) the possibility of operating the SOS diode in a DSRD mode.

***Index Terms***—High-voltage opening switch, nanosecond pulse generator, numerical simulation, pulsed power systems, saturable pulse transformer, SOS diode, Synopsys TCAD.

## I. INTRODUCTION

NOWADAYS, nanosecond pulse generators that offer high power output, high pulse repetition frequency (PRF), adjustable pulse widths, and compact designs are gaining significant attention globally. In this context, fully controlled semiconductor switching pulse systems are highly regarded and are receiving considerable attention [1], [2], [3]. Pulse generators based on fully controlled switches are effective, but they have limitations in peak power. In order to produce nanosecond pulses with peak power in the range of megawatts to gigawatts, specific high-voltage opening switches are required.

A pulse generator circuit developed based on Inductive Energy Storage (IES) employs the high-voltage opening switch devices as the key components for rapid current interruption and energy transfer within nanosecond time scales. The

IES provides a high energy density suitable for designing a nanosecond pulse generator.

The two primary types of high-voltage opening switches include Semiconductor Opening Switch (SOS) diode [4], [5], [6], [7], [8], [9] and Drift Step Recovery Diode (DSRD) [10], [11], [12], [13], [14]. The main structural difference between SOS and DSRD diodes is a deeper diffusion of Aluminum (160-200 µm) in SOS diodes compared to DSRD switches, as stated in [4]. The formation of a deep p-n junction in these high-voltage devices facilitates reaching a higher current density in reverse pumping compared to DSRD diodes. This operational difference results in distinct parameters for cutoff current density and peak power: 10² A/cm² and 10⁸ W for DSRD diodes, and 10⁵ A/cm² and 10¹⁰ W for SOS diodes [15]. Therefore, a system based on IES and SOS diodes offers a promising solution for the development of high-power nanosecond pulse generators.

The typical pulse parameters of SOS- and DSRD-based generators, as reported in the literature, are as follows. A DSRD-based pulse generator tested with a 10 pF capacitive load (small area, 1 mm diameter, SAS diodes) provides a voltage rise rate of 5 kV/ns [16], whereas a SOS-based trigger generator tested with a 1 nF capacitive load (large area, 56 mm diameter, high-voltage thyristor) provides a voltage rise rate of 3 kV/ns [17].

The main drawback of these types of generators in general is the limited commercial availability of DSRDs and SOS diodes as the key elements of such pulse generators. This encourages research on off-the-shelf (OTS) opening switch replacement in [18], [19], [20]. Further research suggests the potential application of advanced technological methods, such as chemical vapor deposition (CVD), for the fabrication of SOS diodes [21].

The SOS diodes have traditionally been designed and studied using custom-developed models limited to the 1-D numerical simulation [6], [7], [22]. Moreover, the potential for SOS diodes to operate in DSRD mode, which may enhance their application in high-power pulse circuits, has not been thoroughly examined. The lack of numerical validation in the commercially-available TCAD software for these aspects hinders the broader understanding and practical adoption of SOS diodes.

In this study, an all-solid-state SOS-based pulse generator is developed employing a single compression stage method. To gain a deeper understanding of the inner dynamics of the SOS effect, a TCAD model of the SOS diode is proposed for

Manuscript received X 2025. This material is based upon work partially supported by the Air Force Office of Scientific Research under award number FA8655-24-1-7003 and the Investissements d'Avenir, a French Program managed by the Agence Nationale de la Recherche (ANR), under the framework of Energy and Environment Solutions (E2S) Université de Pau et des Pays de l'Adour (UPPA) (Solid-State Pulsed Power (S2P2) Chair) under Grant ANR-16-IDEX-0002.

Ejlal Shahriari, Anton Gusev, Antoine Silvestre de Ferron, and Laurent Pecastaing are with Université de Pau et des Pays de l'Adour, E2S UPPA, SIAME, Pau, France. (e-mail: ejlal.shahriari@univ-pau.fr).

Susan Parker and Simon Bland are with the Department of Physics, Faculty of Natural Sciences, Imperial College London, SW7 2BX London, U.K. (e-mail: sn.bland@imperial.ac.uk).
comprehensive numerical simulations. The developed model is extensively tested in both static and dynamic operation modes. Through experimental setups, the current density is varied over a wide range, from 0.3 kA/cm² to 5 kA/cm², enabling detailed analysis of the SOS diode's behavior in DSRD and SOS modes as a function of current density. Finally, by comparing experimental results with numerical simulations of the SOS-based pulse generator, the accuracy and reliability of the TCAD model are validated, enabling further investigations and optimization of SOS-based devices.

## II. EXPERIMENTAL SETUP

### A. Circuit Arrangement

A pulse generator based on IES employing SOS diodes is shown in Fig. 1. The different components of this circuit include: a primary switch ($S_1$), a Saturable Pulse Transformer (SPT), primary and secondary capacitors ($C_1$ and $C_2$), an assembly of SOS diodes, current measurement diagnostics ($R_{sh1}$ and $R_{sh2}$), and a demagnetizing circuit consisting of a current source ($I_b$), a choke, and a bias winding ($w_b$) on SPT.

The Primary switch ($S_1$) must withstand high voltage, high current, and a high current rise rate (dI/dt). In this study, $S_1$ is a solid-state switch developed at Imperial College London. This switch comprises 16 Solidtrons SP-205-01 (4 in series and 4 in parallel), each Solidtron features a rating of 1.5 kV blocking voltage, 3.5 kA peak current, and a dI/dt of up to 120 kA/µs [23]. To balance the voltage distribution, a 100 MΩ resistor is connected in parallel with each Solidtrons, as is standard for series-connected semiconductor devices. This solid-state switch features high voltage, high $dI/dt$, and low inductance, essential for the nanosecond SOS-based pulse generator's proper functioning [24], [25].

The SPT has a ferrite magnetic core (VAC W468) manufactured by Vacuumschmelze. The toroidal structure of the magnetic core is defined by an interior diameter of 70 mm, an exterior diameter of 108 mm, and a height of 30 mm. Moreover, the windings of the SPT are specified with a turn ratio of $w_1:w_2$ (1:7) where $w_1$ and $w_2$ represent the number of turns on the primary and secondary windings, respectively.

The primary capacitor ($C_1$) is a 100 nF film capacitor of 5 kV. The secondary capacitor ($C_2$) specifies as a ceramic high-voltage capacitor TDK UHV-9A of 40 kV chosen based on $C_2 = C_1/(w_2/w_1)^2 = 2$ nF.

The SOS assembly consists of five series-connected SOS diodes, each with a cross-sectional area of 0.25 cm² and a static breakdown voltage of 3.6 kV. Each diode comprises four soldered dies connected in series, with terminations made of copper and molybdenum disks. In this experiment, considering a single mode of operation, the five series SOS diodes can be stacked on top of each other.

A low inductance resistive load ($R$) of 24.1 Ω is installed in parallel with the SOS diode assembly.

In order to monitor the current waveforms of the SOS diode and the load, current shunts ($R_{sh1} = 0.5$ Ω and $R_{sh2} = 0.5$ Ω) are employed in series with the SOS diode assembly and the resistive load, respectively. These current monitoring shunts have a usable rise time of around 0.5 ns.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Schematic diagram of the SOS-based pulse generator.</figcaption></figure>

The circuit shown in Fig. 1 operates as follows. Upon triggering $S_1$, the stored energy in $C_1$ discharges through the primary winding ($w_1$) of the SPT, resulting in the resonant charging of $C_2$. The charging current flows through the SOS diode, supplying the forward pumping current. The transformer is designed to saturate at the peak voltage of $C_2$ when the forward current through the SOS diode reaches zero, indicating the end of the forward pumping phase.

Afterward, $C_2$ discharges through the SPT secondary winding ($w_2$) and the SOS diode, storing energy in inductive storage, which includes the saturated inductance of the secondary winding and the inductive energy storage ($L_2$). During this stage, the SOS diode undergoes reverse pumping. Ideally, the SOS diode cuts off the reverse current at its maximum, ensuring all energy has been transferred to the inductive storage.

A magnetic bias circuit is used to pre-magnetize the SPT core before each pulse, ensuring efficient energy transfer from the primary to the secondary capacitor. As shown in Fig. 1, this circuit consists of a current source ($I_s$), a choke, and a bias winding ($w_b = 3$). Ideally, the SOS diode cuts off the reverse current at its maximum, ensuring all energy has been transferred to the inductive storage. This results in the current being delivered to the load, producing a nanosecond high-voltage pulse with an amplitude ($V_R$) that depends on the load. The two signals were measured simultaneously by a 4-channel real-time digital oscilloscope (DPO70404C TEKTRONIX, 4 GHz, 25 GS/s), shown as Osc in Fig. 1.

### B. Experimental Results

This experimental work studies the performance of the SOS diode in the nanosecond high-voltage pulse generator, illustrated in Fig. 1. The SOS assembly is considered to operate in two modes with a focus on investigating (1) DSRD mode and (2) SOS-mode of operation of SOS diodes.

Firstly, in order to employ the SOS diodes in DSRD mode, the pulse generator provides a forward current density of 100-150 A/cm² in a very short time of 100-200 ns. Considering the forward pumping parameters, a reverse current density of 200-300 A/cm² is expected as the required characteristics of
the DSRD mode in [15]. In this experiment, a bias current of -1 A is applied to reset the SPT core before each pulse.

After triggering the solid-state switch ($S_1$), capacitor $C_1$, which is charged up to $V_{c1} = 0.5$ kV, discharges through SPT, providing simultaneous charging of capacitor $C_2$ and forward pumping of SOS-diode assembly. This forward pumping current is applied within 185 ns, providing a current density of 120 A/cm$^2$ through the SOS-diodes' cross-sectional area of 0.25 cm$^2$. When SPT saturates, capacitor $C_2$ discharges current through SOS-diodes in the reverse direction. This leads to a reverse current density of 300 A/cm$^2$. By nanosecond current cutoff, a voltage pulse appears across the resistive load of 24.1 Ω as recorded in Fig. 2. This voltage has a rise time ($T_r$) of 12.8 ns, and a voltage rise rate (dV/dt) of 71.2 V/ns, both considered from 20% to 90% of the maximum voltage. Moreover, the load voltage waveform indicates a prepulse both during forward and reverse pumping time up to the current cutoff moment at 273 ns. The purpose of this experiment is to observe the internal dynamics of the SOS-diode in the DSRD mode of operation by comparing experimental and numerical simulation results. The results are discussed in more detail in Section IV.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Experimental results of SOS current and voltage across the resistive load ($R = 24.1 \ \Omega$) in DSRD operation of SOS diodes, at $V_{c1} = 0.5$ kV. The load voltage has the $T_r$ of 12.8 ns, and the dV/dt of 71.2 V/ns</figcaption></figure>

Secondly, in order to obtain the full operation capacity of SOS diodes, the same experiment as the previous one, but on a higher primary capacitor voltage of $V_{c1} = 5$ kV and a bias current of 0.1 A is repeated. In this case, the forward pumping current is set within 185 ns, delivering a current density of 5 kA/cm$^2$ through the cross-sectional area of SOS diodes. Due to the high cutoff current density, the SOS effect is ensured, leading to a fast-high voltage pulse across the load. The $T_r$ and dV/dt of this pulse are calculated as 7.4 ns and 1.3 kV/ns, respectively. This voltage pulse reaches a maximum amplitude of 14 kV and a Full Width at Half Maximum (FWHM) of 18 ns, as recorded in Fig. 3. Considering the aforementioned characteristics of the voltage pulse, along with a nanosecond reverse current of 1.2 kA amplitude and a FWHM of 30 ns, one possible application of this pulse generator can be triggering thyristors in impact-ionization wave mode [26], [27].

<figure><img src="image_4.png" /><figcaption>Fig. 3. Experimental results of SOS current and voltage across the resistive load ($R = 24.1 \ \Omega$) in SOS mode of operation, at $V_{c1} = 5$ kV. The load voltage has the $T_r$ of 7.4 ns, and the dV/dt of 1.3 kV/ns</figcaption></figure>

### III. NUMERICAL SIMULATION MODEL

In order to analyze the physics behind the nanosecond current cutoff mechanism in SOS diodes, a TCAD model of an SOS diode's structure based on the well-known doping profile is created in the Synopsys TCAD. Then, the numerical simulation of this device has been performed in two modes. First, a static breakdown voltage test is performed to investigate the dc characteristics of the SOS model. Second, the SOS model is tested in a mix-mode operation to observe the dynamics of the cutoff current density.

This numerical simulation study employs the drift-diffusion model in which electrostatic potential within the semiconductor is determined by solving poisson's equations. The poisson's equations accounts for the distribution of charge from electrons, holes, and ionized dopants. The electric field is then calculated from this electrostatic potential. Afterward, the total current density is derived from the combination of drift and diffusion components for both electrons and holes. Subsequent calculations involve the continuity equations, which describe the conservation of charge carriers and their temporal changes. To solve the continuity equations, the activation of the generation-recombination process is required. The generation-recombination process employs impact-ionization generation models, as well as Shockley-Read-Hall and Auger recombination mechanisms. The iterative nature of the calculations allows for continuous updates of electron and hole concentrations, facilitating transient numerical simulations.

#### A. SOS Structure and Doping Profile

The first step to develop the TCAD model is to specify the doping profile (Fig. 4 (a)) of the SOS diode and a 2-D physical structure considering the length and depth of the SOS diode (Fig. 4 (b)). Then, an area factor is introduced to account for the width of the device as shown in Fig. 4 (c), as the cross-sectional area of the SOS diode is 0.25 cm$^2$.

Fig. 4 (a) illustrates an overview of the doping profile, which is adapted from the literature [7] for the SOS diode. The structure of the four-layer SOS diode ($p^+ - p - n - n^+$) is formed using an n-type silicon substrate doped with phosphorus at a
<figure><img src="image_5.png" /><figcaption>Fig. 4. The physical-based model of the SOS diode. (a) Doping profile, (b) the 2-D model of the SOS diode, and (c) the TCAD model derived from the 2-D model using an area factor.</figcaption></figure>

constant concentration of $10^{14} \text{ cm}^{-3}$ (50 Ω·cm). Subsequently, a deep p-n junction is created by diffusing aluminum (p) from the anode side to a depth of 180 µm. Two highly doped layers ($n^+$ and $p^+$) are then formed by diffusing phosphorus and boron at the surface concentrations of $2 \times 10^{19} \text{ cm}^{-3}$.

## B. Static Breakdown Voltage

The first numerical simulation is based on the dc characterization of the SOS diode model. A simple numerical simulation test is used to examine the static breakdown voltage of a single-die SOS diode. In this simulation, we only simulate one die and assume an equal voltage distribution among 20 dies in the SOS diode assembly in the experiment, voltages were scaled by a factor of 20. The total diode capacitance was not taken into account in the simulation. Initially, the reverse-biased SOS diode allows only a slight leakage current to flow from the cathode to the anode, indicating that the diode is operating in blocking mode. As the cathode-to-anode voltage is increased to a critical level, the p-n junction undergoes avalanche breakdown indicating the static breakdown voltage ($V_0 \approx 1.27$ kV). In this state, there exists significant carrier movement, resulting in a substantial current that is constrained by an external resistance of $R = 1$ MΩ. It is notable to mention this breakdown voltage is consistent with the literature [21], [28]. However, the value of static breakdown voltage in the experiment indicates 0.9 kV. We assume that the lower value of the static breakdown voltage in the experiment is imposed by non-ideal edge termination, leading to possible surface breakdown, since the SOS diodes are not developed for dc operation and the dynamic operation of these diodes is prioritized while manufacturing them.

As in dynamic operations, high voltage is only applied to the device momentarily during current interruption—typically lasting just a few dozen nanoseconds—leaving insufficient time for surface breakdown to occur. Consequently, there is no requirement for voltage dividers or specialized edge profile designs. While this significantly simplifies both the manufacturing and assembly processes, it also increases the risk of surface breakdown in the static breakdown experiment.

<figure><img src="image_6.png" /><figcaption>Fig. 5. A simplified electric circuit of the SOS-based generator is used to conduct numerical simulations.</figcaption></figure>

## IV. EXPERIMENT VERSUS NUMERICAL SIMULATION

To investigate the accuracy of the SOS-diode TCAD model, the experimental results obtained in Section II (B) are compared with numerical simulation as follows. Basically, the numerical simulation in dynamic mode employs a mixed-mode model combining the physical-based model of the SOS diode within an electric circuit. A simplified electric circuit (Fig. 5) is employed to replicate the operation principle of the SOS circuit shown in Fig. 1. The impedance $Z_1 = 1$ Ω, along with the voltage pulse source, is employed to provide a proper current pulse over the SOS diode assembly. The impedance $Z_2 = 0.4$ Ω is the wire connection impedance between the SOS diode and the load. In addition, the parasitic impedances of $Z_{p1} = Z_{p2} = 0.5$ Ω + $j\omega \times 2$ nH include the resistive shunts (shown in Fig. 1) with their low parasitic inductances as well as the impedances of wire branches. These parasitic components, seen in Fig. 5, are considered for a more accurate comparison between the experimental and the numerical simulation results. In this numerical analysis, assuming an equal voltage distribution among the SOS diodes, a single SOS diode is tested. The load voltage or the voltage across an SOS diode is then extrapolated for 20 SOS dies in the experiment. Two operational modes of the SOS diode are investigated by comparing experiments and numerical simulations.

The first mode corresponds to the DSRD mode, where the SOS diode indicates a cutoff current density of approximately 300 A/cm$^2$. This cutoff current density is notably low to observe the SOS effect whereas it is a suitable value for
the DSRD mode. Fig. 6 shows the experimental results in comparison with the numerical simulation for both the SOS diode’s current and the voltage of the resistive load. The numerical simulation in Fig. 6 (a) illustrates that the SOS diode cuts off the current at 300 A/cm² in the reverse pumping stage, which is in acceptable agreement with the experiment (the cutoff current ($I_{cutoff}$) of -75 A, and the cutoff time ($T_{cutoff}$) of 17 ns for the experiment; and $I_{cutoff}$ of -75.66 A, and $T_{cutoff}$ of 26 ns for the simulation). In Fig. 6 (b), both experiment and numerical simulation indicate a pre-pulse on load voltage during the forward and reverse pumping stage until the moment of current cutoff. This pre-pulse on load voltage is caused by the SOS diode’s substrate resistivity and parasitic inductance of the SOS-diode branch. In addition, Fig. 6 (b) shows the $T_r$ and dV/dt for the experiment and numerical simulation are 12.8 ns and 71.2 V/ns, and 26 ms and 39 V/ns, respectively.

<figure><img src="image_7.png" /><figcaption>Fig. 6. The experimental and numerical simulation results of SOS diodes in the DSRD mode (a) the SOS current (measured: $I_{cutoff}$ = -75 A, $T_{cutoff}$ = 17 ns; and simulated $I_{cutoff}$ = -75.6 A, $T_{cutoff}$ = 26 ns), and (b) the load voltage (measured: $T_r$ = 12.8 ns, dV/dt = 71.2 V/ns; and simulated $T_r$ = 23.9 ns and dV/dt = 39 V/ns).</figcaption></figure>

In the second mode, the full capacity of the SOS diodes in the pulse generator circuit is tested to observe the SOS effect in the numerical simulation model. In this case, the cutoff current density of more than 5 kA/cm² happens after a few dozen nanoseconds in the reverse pumping condition, displaying a precise agreement between the experiment and numerical simulation result ($I_{cutoff}$ of -1.25 kA, $T_{cutoff}$ of 29 ns for the experiment and $I_{cutoff}$ of -1.26 kA, $T_{cutoff}$ of

28 ns for the simulation), as seen in Fig. 7 (a). As the SOS diode switches to the opening state, the numerical simulation in Fig. 7 (b) depicts a nanosecond overvoltage pulse across the resistive load with a clear agreement with the experiment (The $T_r$ and dV/dt for the experiment and numerical simulation are 7.4 ns and 1.3 kV/ns, and 7.6 ns and 1.33 kV/ns, respectively).

The agreement between numerical simulations and experiments is critical for analyzing the inner dynamics of both operation modes; further analysis and discussion are presented in Section V.

<figure><img src="image_8.png" /><figcaption>Fig. 7. The experimental and numerical simulation results of SOS diodes in the SOS mode (a) the SOS current (measured: $I_{cutoff}$ = -1.25 kA, $T_{cutoff}$ = 29 ns; and simulated $I_{cutoff}$ = -1.26 kA, $T_{cutoff}$ = 28 ns), and (b) the load voltage (measured: $T_r$ = 7.4 ns, dV/dt = 1.3 kV/ns; and simulated $T_r$ = 7.6 ns and dV/dt = 1.33 kV/ns).</figcaption></figure>

## V. DYNAMICS OF THE SOS DIODE

This section explores the inner dynamics of the nanosecond current cutoff to provide further insight into this phenomenon. In this context, the electric field and the electron-hole densities at the critical moments are investigated for two modes of operation of SOS diodes i.e., (1) DSRD mode, and (2) SOS mode.

In the first scenario, i.e., the DSRD operation of SOS diodes, the four simulation points (square marks in Fig. 8) are considered for inner dynamic analysis. The first simulation point (1) is at the end of the forward pumping time (212 ns). Fig. 9 (a) and (b) (curve number (1)) illustrate the accumulation of electron-hole plasma inside the SOS-diode’s structure, specifically near the p-n junction. This plasma is
<figure><img src="image_9.png" /><figcaption>Fig. 8. The numerical simulation results of SOS diodes operating under DSRD mode (a) SOS current, and (b) load voltage. The square marks indicate simulation points for inner dynamic analysis considered at 212 ns (1), 265 ns (2), 285 ns (3), and 292 ns (4).</figcaption></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. The simulation result of the SOS-diode inner dynamics under the DSRD mode (a) electron density, and (b) hole density. The simulation time is considered at 212 ns (1), 265 ns (2), 285 ns (3), and 292 ns (4), (shown as square marks in Fig. 8).</figcaption></figure>

mainly created by minority carriers, i.e., electrons in the p region and holes in the n region which are injected from the highly doped regions of n⁺ and p⁺, respectively. This residual plasma is essential to delay the reverse current cutoff moment leading to a rise of reverse current as the minority carriers (which are injected during the forward pumping) need time to leave the surrounding region near the p-n junction.

At the moment of current cutoff (point (2), 265 ns in Fig. 8),

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 10. The 2D simulation result of electric field development inside the SOS diode operating under DSRD mode. The simulation time is considered at (a) 265 ns, (b) 285 ns and (c) 292 ns, (shown as square marks numbered with (2), (3) and (4) in Fig. 8).</figcaption></figure>

the minority carriers i.e., electrons in the p region and holes in the n region, initiate departing these regions leading to the formation of two fronts as can be seen Fig. 9 (a) and (b) (curve number (2)). This movement of carriers leads to an increase in the electric field in the absence of plasma behind these two fronts as shown in Fig. 10 (a) and Fig. 10 (d) (curve number (2)).

After the current is cut off, the SOS diode opens, which yields an overvoltage pulse across the load. This event is majorly initiated by a further decrease in minority carriers
in the p and n regions, as seen in Fig. 9 (a) and (b) (curve number (3)). The formation of two electric field waves in the p and n regions concurs with the abovementioned event, as depicted in Fig. 10 (b) and Fig. 10 (d) (curve number (3)).

<figure><img src="image_16.png" /><figcaption>Fig. 11. The numerical simulation results of SOS diodes operating under SOS mode (a) SOS current, and (b) load voltage. The square marks indicate simulation points for inner dynamic analysis considered at 205 ns (1), 255 ns (2), 271 ns (3), and 281 ns (4).</figcaption></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 12. The simulation result of the SOS-diode inner dynamics under the SOS mode (a) electron density, and (b) hole density. The simulation time is considered at 205 ns (1), 255 ns (2), 271 ns (3), and 281 ns (4), (shown as square marks in Fig. 12).</figcaption></figure>

Finally, at the moment of maximum overvoltage pulse across the load and SOS diode (point (4), 292 ns in Fig. 8), further decrease in minority carriers in the p and n region

is quite symmetrical on both sides of the p-n junction, as shown in Fig. 9 (a) and (b) (curve number (4)). This is verified by the appearance of a high electric field across the p-n junction (Fig. 10 (c) and Fig. 10 (d) (curve number (4)). This phenomenon, i.e., the formation of a high electric field at the p-n junction—a typical characteristic of the DSRD mode of operation—suggests that an SOS diode may operate in a DSRD mode.

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>Fig. 13. The 2D simulation result of electric field development inside the SOS diode operating under SOS mode. The simulation time is considered at (a) 255 ns, (b) 271 ns and (c) 281 ns, (shown as square marks numbered with (2), (3) and (4) in Fig. 12).</figcaption></figure>

In the second scenario, the dynamics of the nanosecond current cutoff are highlighted in the SOS mode. Similar to
the previous scenario, four simulation points (square marks in Fig. 11) are considered for inner dynamic analysis. As depicted in Fig. 12 (a) and (b) (curve number (1)), at the end of the forward pumping time (205 ns), the higher accumulation of electron-hole plasma is noticeable in SOS mode compared to the DSRD operation. In this study, the electron-hole plasma accumulation in SOS mode is approximately 13 times greater than in the DSRD mode. This is due to a higher forward pumping current, facilitating further delay in the current cutoff leading to higher current density applied to the SOS diodes in the reverse pumping. By reaching the high current density of 5 kA/cm², electron and hole plasma fronts are formed as illustrated in Fig. 12 (a) and (b) (curve number (2)) meanwhile the electric field starts to increase behind the plasma fronts, shown in Fig. 13 (a) and Fig. 13 (d) (curve number (2)).

The high reverse current density of more than 1 kA/cm² contributes to the SOS effect, indicating the departing process of electrons as minority carriers from the p region. A high electric field in the p region is what distinguishes the SOS mode from the DSRD mode. This electric field occurs at the moment of maximum voltage across the SOS diodes (point (3) in Fig. 11) as electrons move from the p region towards the n base. The detail of this process is shown in (Fig. 12 (a) and (b), curve number (3)) and (Fig. 13 (b), and (d) curve number (3)). The difference between the SOS and DSRD modes arises from the distinct current cutoff mechanisms in the two modes: in the SOS, the current cutoff occurs within the p region, whereas in the DSRD, the current cutoff is observed at the p-n junction.

The final simulation point (4) at 281 ns, as shown in Fig. 11, indicates further retrieval of minority carriers, i.e., electrons from the p region and holes from the n region, as illustrated in Fig. 12(a) and (b), curve (4). Since the overvoltage pulse across the load and the SOS diode is reduced compared to simulation time (3) at 271 ns, the electric field at 281 ns (4) is evidently lower as depicted in Fig. 13 (c), and (d) curve number (4).

Based on the experimental and numerical simulation results presented in this paper, it can be concluded that (i) the SOS diode can operate in both DSRD and SOS modes, as demonstrated experimentally and through numerical simulations using the TCAD model. This means the SOS diode exhibits a similar cutoff mechanism at the p-n junction when it operates with a cutoff current density comparable to that of the DSRD diode. (ii) The cutoff current density is the critical factor determining the operational mode of the SOS diode (around 300 A/cm² for DSRD mode and more than 1 kA/cm² for SOS mode).

In this numerical simulation, a 2-D rectangle, accounting for length and depth, is simulated using a 2-D mesh, and then the area factor is applied as the width of SOS diode. Thus, for more accurate results in the edges, it is necessary to simulate a 3-D structure with a 3-D mesh. However, since the processes in bulk rather than at the edge define the physics of operation, results obtained in this 2-D simulation can be trusted. Considering the good agreement of the simulation results, such as the cutoff current and switching time, with the experimental data, we believe the proposed model adequate for this study.

## VI. CONCLUSION

This study presents a comprehensive investigation into the experimental and numerical simulation of the SOS diode. Two modes of SOS-diode operation i.e., (i) DSRD and (ii) SOS have been investigated both experimentally and based on numerical simulation model. The experimental results and the numerical simulation model show strong agreement in both DSRD and SOS modes. The results confirm that the cutoff current density is a critical parameter in defining the operation mode of the SOS diodes, with lower current densities corresponding to DSRD behavior and higher current densities leading to the SOS effect.

Future research could focus on optimizing the doping profile and structural parameters of SOS diodes to achieve even faster switching times and higher peak powers. Additionally, integrating alternative wide band gap semiconductor materials such as SiC or GaN may unlock new performance capabilities for the next-generation semiconductor opening switches.

## REFERENCES

[1] X. Wang, Q. Huang, L. Xiong, L. Xu, Q. Chen, and Q. Xiong, "A compact all-solid-state repetitive pulsed power modulator based on Marx generator and pulse transformer," *IEEE Transactions on Plasma Science*, vol. 46, no. 6, pp. 2072-2078, 2018.

[2] C. Yao, X. Zhang, F. Guo, S. Dong, Y. Mi, and C. Sun, "FPGA-controlled all-solid-state nanosecond pulse generator for biological applications," *IEEE Trans. Plasma Sci.*, vol. 40, no. 10, pp. 2366-2372, Oct. 2012.

[3] K. Liu, J. Qiu, Y. Wu, X. Liu, and H. Xiao, "An all solid-state pulsed power generator based on Marx generator," in *Proc. IEEE Int. Pulsed Power Conf.*, Jun. 2007, pp. 720-723.

[4] S. Rukin, "Pulsed power technology based on semiconductor opening switches: A review," *Review of scientific instruments*, vol. 91, no. 1, 2020.

[5] A. B. J. M. Driessen, F. J. C. M. Beckers, T. Huiskamp, and A. J. M. Pemen, "Design and implementation of a compact 20-kHz nanosecond magnetic pulse compression generator," *IEEE Transactions on Plasma Science*, vol. 45, no. 12, pp. 3288-3299, 2017.

[6] A. Engelko and H. Bluhm, "Optimal design of semiconductor opening switches for use in the inductive stage of high power pulse generators," *J. Appl. Phys.*, vol. 95, no. 10, pp. 5828-5836, 2004.

[7] S. N. Rukin and S. N. Tsyranov, "The effect of a space charge on the operation of a high-power semiconductor current interrupter," *Tech. Phys. Lett.*, vol. 30, no. 1, pp. 19-22, 2004.

[8] A. Bushlyakov, S. Lyubutin, A. Ponomarev, S. Rukin, B. Slovikovsky, S. Timoshenkov, and S. Tsyranov, "Solid-state SOS-based generator providing a peak power of 4 GW," *IEEE Transactions on Plasma Science*, vol. 34, no. 5, pp. 1873-1878, 2006.

[9] T. Sugai, W. Jiang, and A. Tokuchi, "Influence of forward pumping current on current interruption by semiconductor opening switch," *IEEE Transactions on Dielectrics and Electrical Insulation*, vol. 22, no. 4, pp. 1971-1975, 2015.

[10] I. Grekhov and G. Mesyats, "Physical basis for high-power semiconductor nanosecond opening switches," *IEEE Transactions on Plasma Science*, vol. 28, no. 5, pp. 1540-1544, 2000.

[11] A. G. Lyublinsky, S. V. Korotkov, Y. V. Aristov, and D. A. Korotkov, "Pulse power nanosecond-range DSRD-based generators for electric discharge technologies," *IEEE Transactions on Plasma Science*, vol. 41, no. 10, pp. 2625-2629, 2013.

[12] A. S. Kesar, M. Wolf, A. Raizman, D. Cohen-Elias, and S. Zoran, "A 1-kV, 0.84-kV/ns epi-Si drift-step-recovery diode," *IEEE Transactions on Plasma Science*, vol. 51, no. 4, pp. 1133-1137, 2023.

[13] S. Korotkov, Y. Aristov, A. Zhmodikov, and D. Korotkov, "High-voltage closing switches with nanosecond switching time based on shock ionization dynistors connected in series," *IEEE Transactions on Plasma Science*, vol. 51, no. 5, pp. 1320-1324, 2023.

[14] A. S. Kesar, Y. Sharabani, I. Shafir, S. Zoran, and A. Sher, "Characterization of a drift-step-recovery diode based on all epi-Si growth," *IEEE Transactions on Plasma Science*, vol. 44, no. 10, pp. 2424-2428, 2016.
[15] I. V. Grekhov and G. A. Mesyats, "Nanosecond semiconductor diodes for pulsed power switching," *Physics-Uspekhi*, vol. 48, no. 7, pp. 703-712, 2005.

[16] M. Ivanov, V. Brylevskiy, I. Smirnova, and P. Rodin, "Picosecond-range switching of high-voltage Si diode due to the delayed impact-ionization breakdown: experiments vs simulations," *Journal of Applied Physics*, vol. 131, p. 014502, 01 2022.

[17] A. I. Gusev, S. K. Lyubutin, S. N. Rukin, B. G. Slovikovsky, and S. N. Tsyranov, "High-current pulse switching by thyristors triggered in the impact-ionization wave mode," *Instruments and Experimental Techniques*, vol. 60, no. 4, pp. 545-550, July 2017.

[18] A. S. Kesar, "A compact, 10-kV, 2-ns risetime pulsed-power circuit based on off-the-shelf components," *IEEE Transactions on Plasma Science*, vol. 46, no. 3, pp. 594-597, 2018.

[19] M. R. Degnon, A. I. Gusev, A. S. de Ferron, L. Pecastaing, A. Baranov, C. Mielot, S. Boisne, M. J. Barnes, V. Senaj, T. Kramer, and B. M. Novac, "A saturable pulse transformer based on nanocrystalline magnetic cores for an adjustable nanosecond high-voltage generator," *IEEE Transactions on Plasma Science*, vol. 51, no. 10, pp. 2849-2857, 2023.

[20] M. R. Degnon, A. I. Gusev, A. S. de Ferron, L. Pecastaing, A. Piaser, F. Bayol, S. Boisne, and B. M. Novac, "A 500-kV nanosecond pulse generator based on an off-the-shelf solid-state opening switch," *IEEE Transactions on Plasma Science*, pp. 1-9, 2024.

[21] A. S. Kesar, A. Raizman, O. Trachtenberg, D. Cohen-Elias, M. Wolf, O. Belozerov, Y. E. Krasik, and M. Katz, "Development of a semiconductor opening switch at Soreq NRC," *IEEE Transactions on Plasma Science*, vol. 52, no. 11, pp. 5385-5391, 2024.

[22] S. A. Darznek, S. N. Rukin, and S. N. Tsiranov, "Effect of structure doping profile on the current switching-off process in power semiconductor opening switches," *Technical Physics*, vol. 45, no. 4, pp. 436-442, 2000.

[23] Excelitas. Solidtron. Accessed: Apr. 08, 2025. [Online]. Available: https://www.excelitas.com/file-download/download/public/76696?filename=Solidtron_SP205-01_SP205-01T_Fpak_Datasheet.pdf

[24] J. Yan, S. Parker, and S. Bland, "An investigation into high-voltage spiral generators utilizing thyristor input switches," *IEEE Transactions on Power Electronics*, vol. 36, no. 9, pp. 10005-10019, 2021.

[25] A. I. Gusev, I. Lavrinovich, S. Bland, A. S. de Ferron, L. Pecastaing, S. Parker, J. Yan, and B. M. Novac, "New SOS diode pumping circuit based on an all-solid-state spiral generator for high-voltage nanosecond applications," *IEEE Transactions on Plasma Science*, vol. 51, no. 10, pp. 2858-2865, 2023.

[26] E. Shahriari, T. Maysonnave, A. I. Gusev, A. S. de Ferron, and L. Pecastaing, "Series-parallel connection of thyristors triggered in impact-ionization wave mode," *IEEE Transactions on Plasma Science*, vol. 52, no. 9, pp. 4286-4293, 2024.

[27] E. Shahriari, A. I. Gusev, T. Maysonnave, A. Silvestre de Ferron, and L. Pecastaing, "Experimental and simulation study of parallel-connected thyristors in impact-ionization switching mode," *IEEE Transactions on Plasma Science*, vol. 52, no. 9, pp. 4332-4340, 2024.

[28] G. Shafir, M. Kreif, J. Z. Gleizer, S. Gleizer, Y. E. Krasik, A. V. Gunin, O. P. Kutenkov, I. V. Pegel, and V. V. Rostov, "Experimental research of different plasma cathodes for generation of high-current electron beams," *Journal of Applied Physics*, vol. 118, no. 19, p. 193302, November 2015.

<figure><img src="image_23.png" /></figure>

**Ejjal Shahriari** (Member, IEEE) was born in Nowdesheh, Kurdistan, Iran. He received the M.Sc. degree in power system engineering from the K.N. Toosi University of Technology, Tehran, Iran, in 2014, and the master's degree in electrical engineering for sustainable development (E2SD) from University of Lille, Lille, France, in 2019, and the Ph.D. degree in electrical engineering from university of Pau, Pau France in 2024.

From 2020 to 2021, he worked on modular multilevel converter (MMC)-based HVDC control systems at EnergyVille Genk, Belgium. His research interests include TCAD simulation of semiconductor devices, high voltage nanosecond pulsed generators, picosecond impact-ionization switching of high voltage thyristors, and HVDC power systems control.

Dr. Shahriari received the IEEE Nuclear and Plasma Sciences Society (NPSS) Outstanding Student Paper Award at the IEEE Pulsed Power and Plasma Science Conference, held in San Antonio, TX, USA, in 2023. In 2024, he was honored with the Outstanding Young Researcher Award at the Euro-Asian Pulsed Power Conference (EAPPC) in Amsterdam, Netherlands.

<figure><img src="image_24.png" /></figure>

**Anton I. Gusev** (Member, IEEE) was born in Miass, Russia, in 1988. He received the M.S. degree in electrophysics from Ural Federal University (UrFU), Yekaterinburg, Russia, in 2012, and the Ph.D. degree in engineering sciences from the Institute of Electrophysics, Ural Branch of the Russian Academy of Sciences (IEP), Yekaterinburg, in 2019.

From 2008 to 2019, he was with IEP as an Intern, a Ph.D. Student, and a Junior Researcher with the Pulsed Power Laboratory. At the same time, from 2014 to 2019, he was with UrFU as a Senior Teacher. In 2019, he became a Post-Doctoral Researcher with the Université de Pau et des Pays de l'Adour (UPPA), Pau, France, where he has been an Assistant Professor with the Laboratoire des Sciences de l'Ingénieur Appliquées à la Mécanique et au Génie Électrique (SIAME Laboratory) since 2020. His research interests include semiconductor physics, high-power semiconductor switches, and high-voltage solid-state generators, which provide nano- and subnanosecond pulses.

Dr. Gusev is a member of the International Society on Pulsed Power Applications (ISP) and the Association for the Advancement of Pulsed Power (A2P2). He has been awarded the Young Researcher at major international pulsed power conferences (the Energy Fluxes and Radiation Effects (EFRE) 2016, the Euro-Asian Pulsed Power Conference (EAPPC) 2018, and the Gas Discharge Plasmas and Their Applications (GDP) 2021), including two supported by IEEE Pulsed Power Conference (PPC) 2017 and the IEEE International Power Modulator and High Voltage Conference (IPMHVC) 2018.

<figure><img src="image_25.png" /></figure>

**Antoine Silvestre de Ferron** was born in Tarbes, France, in 1977. He received the master degree in electrical and electronic engineering from the University of Toulouse, Toulouse, France, and the Ph.D. degree in electrical engineering from the University of Pau, Pau, France, in 2002 and 2006, respectively.

From 2006 to 2008, he was a Researcher with the Atomic Energy Commission (CEA), a French government-fund technological research organization in Le Barp, France. He is currently an engineer at the head of the High Voltage Processes Teams in the SIAME laboratory of the University of Pau, France. His research interests include high-pulsed power generation, with military and civil applications. He is specialized in Marx generator and pulse forming lines in high voltage generation, in high voltage transient probes associated and in high current discharges in liquids.
<figure><img src="image_26.png" /></figure>

**Laurent Pecastaing** (Senior Member, IEEE) received the Ph.D. and Research Directorship Habilitation degrees in electrical engineering from the Université de Pau et des Pays de l'Adour (UPPA), Pau, France, in 2001 and 2010, respectively. He is currently a Full Professor in pulsed power with University of Pau. He is the director of the SIAME laboratory and he is also the Director of a Common Laboratory between UPPA and CEA, France.

His current research interests include high-power microwave sources, compact pulsed power systems, and ultrafast transient probes. Dr. Pecastaing was the chairperson of the Euro-Asian Pulsed Power Conference/High-Power Particle Beams/Megagauss Magnetic Field Generation and Related Topics (EAPPC/BEAMS/MEGAGAUSS) Conference, France, in 2021. He is also a member of the International Steering Committees for both the BEAMS Conferences and the Euro-Asian Pulsed Power Conferences.

<figure><img src="image_27.png" /></figure>

**Susan Parker** (Member, IEEE) received the B.A. degree in textile science technology and design from the University of Bradford, Bradford, U.K., in 1979. From 1970 to 1975, during vacations, she was a part-time Electronics Apprentice with Chelsea Instruments Ltd., Molesey, U.K., including working on BRV continuum light sources. From 1980 to 1985, she was an Electronics Design Engineer with Chelsea Instruments Ltd., working in instrumentation control and data acquisition for fluorimeters and monochromators. From 1985 to 2008, she was self-

employed as an Electronics Design Consultant for instrumentation hardware, microcontroller programming, and printed circuit board design. She is currently a Group Technician with the Department of Physics, Imperial College London, London, U.K. Her research interests include signal acquisition systems, motor controllers, pulse power high-voltage triggers and generators, and promoting open-source design. Mrs. Parker is also a member of the Institution of Engineering and Technology (IET) and the Audio Engineering Society (AES)..

<figure><img src="image_28.png" /></figure>

**Simon Bland** (Member, IEEE) received an M.Sc. degree in physics from the Imperial College London in 1997, and the Ph.D. degree from the Plasma Physics Group at Imperial College in 2001. Since 2001, he has remained at Imperial, first as a Research Associate and then as a Research Fellow, before helping to establish the Institute of Shock Physics in 2009. In 2023, he became a Professor in the Plasma Physics Group. Simon has authored/coauthored over 130 journal articles and is a Liveryman of the Worshipful Company of Scientific Instrument Makers.

His research activities revolve around using pulsed power to generate high-energy-density conditions and applications from ICF to Laboratory Astrophysics. Simon has helped to organize a number of international conferences and workshops and is an elected member of the Pulsed Power Science and Technologies committee of the IEEE Nuclear and Plasma Sciences Society.