Showing papers on "Switching time published in 2023"

Sub-Nanosecond Switching of Si:HfO2 Ferroelectric Field-Effect Transistor.

Abstract: The discovery of ferroelectric doped HfO2 enabled the emergence of scalable and CMOS-compatible ferroelectric field-effect transistor (FeFET) technology which has the potential to meet the growing need for fast, low-power, low-cost, and high-density nonvolatile memory, and neuromorphic devices. Although HfO2 FeFETs have been widely studied in the past few years, their fundamental switching speed is yet to be explored. Importantly, the shortest polarization time demonstrated to date in HfO2-based FeFET was ∼10 ns. Here, we report that a single subnanosecond pulse can fully switch HfO2-based FeFET. We also study the polarization switching kinetics across 11 orders of magnitude in time (300 ps to 8 s) and find a remarkably steep time-voltage relation, which is captured by the classical nucleation theory across this wide range of pulse widths. These results demonstrate the high-speed capabilities of FeFETs and help better understand their fundamental polarization switching speed limits and switching kinetics.

Reducing Threshold of Ferroelectric Domain Switching in Ultrathin Two-Dimensional CuInP2S6 Ferroelectrics via Electrical-Mechanical Coupling.

Abstract: Room-temperature out-of-plane two-dimensional ferroelectrics have promising applications in miniaturized non-volatile memory appliances. The feasible manipulation of polarization switching significantly influences the memory performance of ferroelectrics. However, conventional high-voltage-induced polarization switching inevitably generates charge injection or electric breakdown, and large-mechanical-loading-induced polarization switching may damage the structure of ferroelectrics. Hence, decreasing critical voltage/loading for ferroelectric polarization reversal is highly required. Herein, using atomic force microscopy experiments, the ferroelectric domain switching via both electric field and mechanical loading was demonstrated for an ultrathin (∼4.1 nm) CuInP2S6 nanoflake. The relevant threshold voltage/loading for polarization switching was ∼ -5 V/1095 nN, resulting from the electric field and flexoelectric effect, respectively. Finally, the electrical-mechanical coupling was adopted to reduce the threshold voltage/loading of CuInP2S6 significantly. It can be explained by the Landau-Ginzburg-Devonshire double-well model. This effective way for easily tuning the polarization states of CuInP2S6 opens up new prospects for mechanically written and electrically erased memory devices.

A Converter Based Switching Loss Measurement Method for WBG Device

Abstract: With the advent of WBG device like GaN and SiC, frequency has been pushed to very high in order to achieve the higher power density. Consequently, switching loss becomes a large part of device loss in high-frequency applications. Traditional double pulse test method is not suitable for measuring the switching loss of GaN or SiC device with very high turn-off speed. In this paper, a converter-based switching loss measurement method is proposed and demonstrated. By analyzing the total loss breakdown and measuring each component precisely, the switching loss can be calculated accurately. Using this method, the switching loss of the 600V GaN device is evaluated in soft switching up to MHz.

Field-free switching model of spin–orbit torque (SOT)-MTJ device with thermal effect based on voltage-controlled magnetic anisotropy (VCMA)

Abstract: Electrically driven magnetization switch has attracted much attention in the new spintronic memory, especially for spin–orbit torque (SOT)-based magnetic random access memory (MRAM). However, the published models are facing limitations with the continuous shrinkage of the feature size down to nanoscale. Also, the thermal effect caused by switching operation is non-negligible. Therefore, an effective model is needed to represent the switching dynamic of the device concerning the influences of the nanoscale and the thermal effect. In the paper, a compact model of three-terminal SOT-driven switching is established. The influence of the voltage-controlled magnetic anisotropy (VCMA) and spin transfer torque (STT) effect induced by bias voltage on the field-free SOT-driven switching is considered by numerically solving the LLG equations. Furthermore, a 3D model of the SOT-MTJ device is established by finite element method to trace the thermoelectric behavior inside the device. The thermoelectric behavior is integrated into the compact model to show the influence of the temperature on the switching behavior, highlighting the importance of the thermal effect for the realistic modelling of SOT-driven switching. Finally, a novel voltage pulse scheme is proposed, which can effectively shorten the switching time and improve the reliability of the device. The established model could provide strategies and guidelines for next-generation memory design and application.

Improvement of extinction in optically-controlled silicon thermo-optic switch based on micro-ring resonator with distinct probe signal

Abstract: Herein, an optically-controlled thermo-optic switch based on a micro-ring resonator is proposed and demonstrated. The latter converts pump light to heat using a metal layer close to the waveguides to generate a phase shift based on the thermo-optic effect, thereby realizing the switching operation. By using the probe and pump lights of the transverse electric and transverse magnetic modes, respectively, optical absorption is properly designed and an extinction ratio higher than that reported in the previous study is achieved. Further, 10%–90% switching times are measured to be 0.71 μs and 2.66 μs for the rising time and cooling time of temporal response, respectively. The burst-switching measurements reveal an on/off switching ratio of 7.3 dB at the through-port and 7.2 dB at the drop port, with a pump power of 16.8 mW.

Investigation of Field-Free Switching of 2-D Material-Based Spin–Orbit Torque Magnetic Tunnel Junction

Abstract: Spin Hall-assisted magnetization switching in a three-terminal magnetic tunnel junction (MTJ) has attracted much attention due to its high-speed magnetization switching, which enables low-power memory and logic applications. In this study, 2-D materials with high spin–orbit coupling (SOC) effects and high charge-to-spin conversion efficiency are used to assess the performance characteristics of spin–orbit torque MTJ (SOT-MTJ). External field-free switching in SOT-MTJ is accomplished by employing a standard MTJ structure with a bias magnetic layer on top of the structure that projects a dipolar magnetic field onto a free layer (FL). In addition, the Dzyaloshinskii–Moriya interaction (DMI), an asymmetric exchange interaction, is considered while evaluating the critical current density. We were able to demonstrate that the required critical current density decreases by 99.5%, while the switching speed increases by 86.67% in the proposed external field-free 2-D material-based SOT-MTJ. We have also shown the significance of DMI in the field-free switching of the magnetization without the requirement for additional mechanisms when the device shrank down to the subnanometer regime.

Low Inductive Characterization of Fast-Switching SiC MOSFETs and Active Gate Driver Units

Abstract: Accurate switching device characterization is necessary for effectively utilizing the technological ad-vantages of Silicon Carbide (SiC) Power Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) over their Silicon (Si) Insulated-Gate Bipolar Transistor (IGBT) counterparts. With switching times of few nanoseconds, the unprecedented switching speed of SiC semiconductor devices challenges today's converter and characterization setup designs in regard to parasitic layout inductances for optimal conversion and reliable characterization data. Fur-thermore, active gate driving is a key to unlock the potential of SiC MOSFETs, but requires performance assessment prior to integration. This paper presents a low-inductive test platform for flexible and high-accuracy characterization of fast-switching SiC MOSFETs and active gate drivers evalu-ation. The test circuit delivers high quality characterization data that is comparable with a commercial dynamic power device characterizer. In addition to the conventional hard-switching double-pulse tests with a two-level voltage source gate driver, the test circuit offers soft-switching and gate driver evaluation capability in addition. This test platform is a valuable tool for obtaining reliable characterization data to develop more accurate SiC MOSFET simulation models, and evaluate the combination of gate driver and MOSFET prior to the prototyping phase of a converter.

Investigation of 4H-SiC UMOSFET Architectures for High Voltage and High Speed Power Switching Applications

Abstract: A comparative TCAD (Technology Computer Aided Design) simulation study of various 4H-SiC trench gate MOSFET (Metal Oxide Semiconductor Field Effect Transistor) (or U-shaped trench gate MOSFET abbreviated for UMOSFET) architectures for high voltage and high-speed switching applications is reported. The DC (Direct Current) and AC (Alternating Current) characteristics of the different trench gate structures are investigated. Particularly, compared to conventional 4H-SiC UMOSFETs, the breakdown voltage of the UMOSFET having a p-type implanted bottom shield is increased by 44%. However, due to the extra JFET (Junction Field Effect Transistor) region, the specific on resistance also increases by 6%. Furthermore, under 1000 V drain bias, the peak electric field at the bottom oxide of the shielded trench gate is below 0.3 MV/cm. In contrast, the peak electric field of conventional UMOSFETs can be as high as 8 MV/cm, which might cause reliability issues. On the other hand, when the bottom oxide thickness of the trench gate is increased, the UMOSFET exhibits 22% less total gate charge, leading to 76% and 71% shorter switching delay time, compared to conventional UMOSFETs and bottom shield UMOSFETs, respectively. As revealed by the simulation results, the UMOSFETs with the p-type implanted bottom shield or thick bottom oxide are advantageous for high voltage and high-speed power switching applications.

A strategy for improving the SHEPWM commutation speed of CSI through hybrid switches

Abstract: High-power current source inverters (CSI) usually operate at a low switching frequency to reduce switching loss. To suppress low-order harmonics and simplify filter design, the selective harmonic elimination pulse width modulation (SHEPWM) technique is a feasible common modulation strategy in industrial applications. This paper proposes an operational strategy that uses an H7 current source inverter (H7-CSI) with hybrid switches to perform the SHEPWM technique. On the basis of retaining the conventional H6 inverter bridge, the commutation speed of the CSI is improved by an additional shunt-connected high-performance power switch. The proposed scheme solves the problem that the CSIs built with low-speed switches (such as GTOs) may have difficulty for implementing the setting pulse widths of null states, while further reducing the switching losses at an acceptable cost. In addition, mitigating the influence of overlap-time by optimizing the driving signal of the H6 converter bridge. Finally, simulation and experiments have verified the effectiveness of the proposed CSI scheme.

Enhanced Resistive Switching in Flexible Hybrid RRAM Devices With PVK:MoS₂/TiO₂ Bilayer

Abstract: High-performance flexible resistive random access memory (RRAM) devices were demonstrated by engineering the switching layer with PVK:MoS2 composite and TiO2 bilayer. These flexible RRAM devices exhibited excellent switching with low SET (1.2 V) and RESET (−1.5 V) voltages, a high repeatability of 1000 cycles, and an excellent retention time of 5000 s with an ON/OFF current ratio more than 102 at a read voltage of 0.2 V, significantly better than neat PVK/TiO2 devices. Moreover, devices with PVK:MoS2/TiO2 bilayer exhibited high stability upon bending with radii up to 7 mm for 100 cycles. Our results indicate that PVK:MoS2/TiO2 composite bilayer can be a promising switching layer candidate for high-performance flexible RRAM devices.

Novel four-port RF phase change switches based on GeTe thin film

Abstract: An indirect-heated phase-change switch (PCS) using germanium telluride (GeTe) has been fabricated using thermal actuation driven by thin film heater on the model. Switches require a low ON-state resistance and a high OFF-state resistance with OFF/ON resistance ratio of 105. The finite element analysis simulation is applied to simulate the temperature of individual node GeTe with different microwave heating pulses. Finally, in order to reduce the phase-change time and increase the switching speed of indirectly heated switching structures, a new four-port indirectly heated phase change switching structure is proposed. In this paper, the heat dissipation of the switch is increased by etching deep grooves on the back of the switch. This structure obviously reduces the phase change time compared to conventional indirectly heated phase change switches the time between ON-state and OFF-state is reduced by more than 19% and the total process is reduced by more than 47%. The GeTe PCSs with etched grooves not only significantly increases the switching speed, but also reduces the risk of recrystallization of the phase change material.

The Impact of the Dead-Time on the Reverse Recovery Behavior of SiC-MOSFET Body Diodes

Abstract: The impact of the dead-time on the body diode reverse recovery behavior for 1.2 kV silicon carbide MOSFETs has been studied in this paper. The plasma formation behavior of the body diode at different temperatures and load currents is investigated firstly. The time for the plasma stabilization can be estimated. Afterwards, the influence of the load current amplitude, the operating temperature, and the switching speed have been investigated with standard double-pulse tests. Different MOSFET cell designs of various manufacturers were compared. It has been found that selecting a suitable dead-time and switching speed is essential for the optimization of the overall losses, especially at higher operation temperatures.

Dynamics of an Electrically Driven Phase Transition in Ca2RuO4 Thin Films: Nonequilibrium High‐Speed Resistive Switching in the Absence of an Abrupt Thermal Transition

Abstract: In Mott‐type resistive switching phenomena, which are based on the metal–insulator transition in strongly correlated materials, the presence of an abrupt temperature‐driven transition in the material is considered essential for achieving high‐speed and large‐resistance‐ratio switching. However, this means that the freedom of material/device design in applications is significantly reduced for this type of switching by the strict requirement of transition abruptness. Here, high‐speed, abrupt resistive switching with a switching time of 140 ns is demonstrated in epitaxial films of Ca2RuO4/LaAlO3 (001), which is a material with a nonthermal metal–insulator transition driven by current, despite the complete absence of an abrupt thermal transition in the resistivity–temperature characteristics. Highly smooth negative‐differential‐resistance behavior, very high cycling stability, and an endurance over 106 cycles are also demonstrated in the current–voltage and current–time characteristics, which confirm the nonstochastic nature of the abrupt switching. These results suggest that strict control of the resistivity–temperature characteristics is not necessarily required in a material with a nonthermal‐type metal–insulator transition to obtain high‐speed resistive switching because of the independence of the dynamics from those of the thermal transition, and this phenomenon potentially has important advantages in resistive switching applications.

A Novel Super-junction MOSFET with Enhanced Switching Performance and Ruggedness

Abstract: Abstract In this paper, a novel super-junction (SJ) MOSFET with enhanced switching performance and ruggedness is proposed and investigated by the method of TCAD simulations. An N + /P - polysilicon junction gate electrode and separation layer between P-base and P-pillar are introduced to the trench SJ-MOSFET. For the N + /P - junction trench gate, the P - polysilicon located in the bottom of the trench plays the role of insulating layer, which efficiently reduces the gate charge (Q G ), thus increasing the switching speed and reducing the switching loss. The P-pillar does not contact with P-base so a depletion region is formed and the gate to drain charge (Q GD ) is reduced. Besides, the specific separation layer also inhibits the activation of the parasitic bipolar transistor (BJT) to improve the unclamped inductive switching (UIS) capability. The results of the simulation reveal that the proposed SJ-MOSFET is better in switching performance and ruggedness.

Ferroelectric behavior of sputter deposited Al0.72Sc0.28N approaching 5 nm thickness

Abstract: Ferroelectric Al1−xScxN has raised much interest in recent years due to its unique ferroelectric properties and complementary metal oxide semiconductor back-end-of-line compatible processing temperatures. Potential applications in embedded nonvolatile memory, however, require ferroelectric materials to switch at relatively low voltages. One approach to achieving a lower switching voltage is to significantly reduce the Al1−xScxN thickness. In this work, ferroelectric behavior in 5–27 nm films of sputter deposited Al0.72Sc0.28N has been studied. We find that the 10 kHz normalized coercive field increases from 4.4 to 7.3 MV/cm when reducing the film thickness from 27.1 to 5.4 nm, while over the same thickness range, the characteristic breakdown field of a 12.5 μm radius capacitor increases from 8.3 to 12.1 MV/cm. The 5.4 nm film demonstrates ferroelectric switching at 5.5 V when excited with a 500 ns pulse and a switching speed of 60 ns.

Real-Time FPGA Simulation of High-Voltage Silicon Carbide MOSFETs

Abstract: This article presents a real-time field-programmable gate array (FPGA)-based dynamic model of high-voltage and high-current silicon carbide (SiC) metal-oxide-semiconductor field-effect transistor ( mosfet ) half-bridge power modules. The dynamic switching model utilizes the Shichman and Hodges equations using voltage-dependent nonlinear device capacitances and module electrical parameters to obtain an accurate dynamic model of the device switching transients. The key device states gate-source voltage, drain current, and drain-source voltage are modeled and discretized using forward Euler discrete integration method. Analysis of synthesizing the discrete-time model into real-time FPGA-based system with real-time data output from the on-board digital-to-analog converter is presented in detail. The model is utilized in modeling a 320-kW, medium-voltage dc/dc dual-active bridge converter and verified using dynamic experimental results from a 3.3-kV SiC mosfet half-bridge power module. It has been shown that the presented discrete-time dynamic switching model accurately describes the turn- on and turn- off switching transients of the SiC power module at various voltage and current levels. Such models are useful for rapid and cost effective design and prototyping of SiC-based power electronic systems by defining key design and operating parameters, such as deadtime, switching frequency, and switching losses.

Robust (Q,S,R)-γ-Dissipative and H2 Performances for Switched Systems with Mixed Time Delays

Abstract: This paper investigates the switching on switching rule and sampling input to guarantee (Q,S,R)-γ-dissipative and H2 performances for switched systems with mixed time delays. Synchronous switching can be used to overcome the difficulty in implementation of real-time switching for signals and sampling. The design of sampling input under arbitrary switching for a switched system is also considered in this paper. A new proposal for a full matrix formulation approach and inequality are applied to achieve the main results. Finally, some numerical examples are illustrated to show the efficiency of the main contribution.

Influence of driving and parasitic parameters on the switching behaviors of the SiC MOSFET

Abstract: The SiC MOSFET has lower conduction loss and switching loss than the Si IGBT, which helps to improve the efficiency and power density of the converter, especially for those having strict requirements for volume and weight, for example, electrical vehicles (EVs), on-board chargers (OBCs), and traction drive systems (TDS). However, the faster switching speed will cause overshoot and oscillation problems, which will affect the efficiency and security of the SiC devices and power electronic systems. For the SiC MOSFET to be better used, combining a theoretical analysis, the double-pulse test platform is built. The controllable principles of SiC MOSFETs are validated. The turn-on and turn-off delay, switching delay, switching di/dt, switching du/dt, switching overshoot, and switching loss of SiC MOSFETs under different driving and parasitic parameters are explored. Finally, some valuable suggestions for designing are proposed for a better application of the SiC MOSFET.

An Accurate Analytical Model of SiC MOSFETs for Switching Speed and Switching Loss Calculation in High-Voltage Pulsed Power Supplies

Abstract: Nanosecond output pulse and high efficiency are achieved in high-voltage pulsed power supplies (HVPPSs) by applying silicon carbide (SiC) metal-oxide-semiconductor field-effect transistors ( mosfet s), whose switching speed and switching loss are two vital characteristic parameters. However, the existing research on switching characteristics of SiC mosfet s is mainly based on the double pulse test circuits with inductive loads, which is not suitable for assessing the devices in HVPPSs with resistive loads. Besides, some simplified analytical methods in HVPPSs lead to poor precision. To accurately predict the switching behavior of SiC mosfet s in HVPPSs for guiding the design of gate driving circuits and power loops, this article proposes an accurate analytical model considering parasitic inductances, nonlinear parasitic capacitances, transfer characteristic, and output characteristics of SiC mosfet s. High-precision fitting of transfer characteristic is realized by using the Gaussian function. Besides, the dynamic parasitic gate-drain capacitance is measured by experiment, and three-dimensional curve fitting is performed on the output characteristics to exactly represent on -resistance. Furthermore, switching speed and switching loss can be directly calculated according to the solved state variables. Finally, the analytical model is verified by experiment, and the effects of gate driving circuits and power loops on switching characteristics are researched in detail.

Strategies for Ultra-Fast Bit Generation of Two-Terminal Threshold Switch-Based True Random Number Generator using Drift-Free Ge-doped SiO2 Threshold Switch Device

Abstract: To achieve fast random bit generation under 50 ns per bit by employing the threshold voltage (Vth) variation of a simple two-terminal threshold switch (TS) device, we have confirmed that Vth drift-free switching characteristics, along with large Vth variation and fast switching speed, are key factors for implementing true random number generator (TRNG) devices. We analyzed the drift-switching characteristics of various TS devices together with our innovative oxide TS device for TRNG applications. Our findings show that stochastic switching is degraded by the Vth drift characteristics of a conventional ovonic threshold switch (OTS) for fast random bit generation. Conversely, the drift-free insulating-to-metal transition (IMT)-based TS device has very tight Vth variation, which is not suitable as a dynamic entropy source for TRNG. However, the Ge-doped SiO2-based TS device operates with drift-free and large Vth variation switching characteristics. Finally, we successfully demonstrated the potential of a Ge:SiO2-based TS device for TRNG application pertaining to fast random bit generation under 50 ns per bit without a complex circuit system.

A New Multi-stage SiC MOSFET Gate Drive Circuit for Improving Device Switching Characteristics

Abstract: SiC MOSFETs are particularly suitable for high power density high frequency applications due to their fast switching speed, low power loss, and high thermal conductivity. However, the high switching frequency also leads to voltage spikes and high switching oscillations. This paper proposes a new multi-level SiC MOSFET drive circuit and control method, which can adjust the gate resistance of the main control chip to optimize the switching characteristics of SiC MOSFETs, effectively solving the shortcomings of traditional gate drive circuits in dealing with voltage spikes and switching oscillations.

Controllable tuning of ferroelectric switching via the lattice in crystallographically engineered molecular ferroelectrics

Abstract: Reducing the switching energy and improving the switching speed of ferroelectrics remain an important goal in the pursuit of electronic devices with ultralow energy consumption and ultrafast response. Molecular ferroelectrics with concise dipole switching mechanism and facile structural tunability are a good platform for manipulating the ferroelectric domains. A methodology is demonstrated to manipulation of ferroelectric domain switching by tailor-made lattice parameters of molecular ferroelectrics, by following which, we succeeded in lowering the threshold electric field and improving the dynamics of ferroelectric switching. Our findings advance the fundamental understanding of microscopic mechanism and provide important insights in controllable tuning of ferroelectric domain switching.

Design and Analysis of Two Ultra-Fast All-Optical Plasmonic Dual- Band OFF-ON and Bi-Directional Switches Based on Nonlinear Kerr Materials

Abstract: Abstract In this study, two ultra-fast all-optical plasmonic switches based on metal–insulator–metal (MIM) plasmonic waveguides side-coupled to cavity by stubs are proposed. The cavities are filled with a nonlinear Kerr material and the switching occurs due to the self-phase-modulation (SPM) effect. In the first structure, an OFF-ON switching functionality is achieved either by varying the incident light intensity or using the optical bistability effect at the two telecommunication windows of 1550 nm and 850 nm. In the second structure, by adding another nonlinear cavity a bi-directional switch is designed. The finite-deference time-domain (FDTD) method is used to obtain the simulation results. The proposed ultra-fast switches have significant switching mechanisms and picosecond response time (0.25ps for the OffON switch and 1.5ps for the bi-directional switch). The proposed all-optical switches have potential of significant applications in photonic integrated circuits (PICs).

Micromagnetics of Microwave-Assisted Switching in Co-Pt-Based Nanostructures: Switching Time Minimization

Abstract: Microwave-assisted switching (MAS) is simulated for different CoPt and CoPt/Co3Pt nanosrtuctures as a function of applied DC field and microwave frequency. In all the cases, the existence of microwave excitation can lower the switching field by more than 50%. However, this coercivity reduction comes at a cost in the required switching time. The optimal frequencies follow the trends of the ferromagnetic resonances predicted by the Kittel relations. This implies that: (a) when the DC field is applied along the easy axis, the coercivity reduction is proportional to the microwave frequency, whereas (b) when the coercivity is lowered by applying the DC field at an angle of 45° to the easy axis, extra MAS reduction requires the use of high frequencies.

Research on the Switching Characteristics Based on the SiC MOSFET Model

Abstract: With the continuous development of power electronics technology, the third-generation semiconductor materials represented by SiC and GaN have significant advantages in the band gap width, breakdown electric field, thermal conductivity, electron saturation rate and other key parameters, which meet the needs of modern industry for high power, high voltage and high frequency. When the SiC MOSFET plays its high frequency advantage, with the increase of switching frequency, the voltage change rate and current change rate of the device will be larger in the process of turning on and off. This paper mainly analyzes the characteristics of SiC MOSFET devices, and modifies the model based on the model provided by the manufacturer. By establishing static and dynamic test circuits, the static characteristic curves of the model were observed, and the drain voltage and current waveforms of the original model and the optimized model were compared during the switching process. The results show that the switching time of the optimized model is improved, and the oscillation waveform is greatly improved. Then, the accuracy of the optimized model is verified by the double-pulse circuit, and the drain source voltage and the drain source current are studied and observed under different temperature and drive resistance conditions. This paper provides data support for improving the switching characteristics of SiC MOSFET in practical applications.

An alternative method for the optimal switching problem of linear quadratic switched system

Abstract: Optimal switching is a special class of optimal control problems for hybrid dynamic systems. In this paper, we consider the optimal switching problem of linear-quadratic switched systems. The aim is to design a suitable switching strategy with the constraint on the number of switchings so that the quadratical performance achieves the minimum value. This problem is difficult to be solved because of the tight coupling between the continuous switching time and the discrete switching sequence. In our method, we first divide this hybrid optimization problem into two subproblems. In each of them, only one type of variable is considered. Then, we develop a gradient-based method with the time-scaling transformation to process the optimal switching time problem and a branch and bound method based on a series of exact lower bounds to handle the optimal switching sequence problem, respectively. By solving these two subproblems alternatively, the optimal switching strategy satisfying the constraint on the number of switchings can be obtained. Numerical examples are given to demonstrate the efficiency of the proposed method.