CN115128423A - Heavy ion irradiation influence beta-Ga 2 O 3 Method for simulating electrical performance of MOSFET device - Google Patents

Abstract

The invention provides a method for influencing beta-Ga by heavy ion irradiation ₂ O ₃ A method of electrochemical performance of a MOSFET device, comprising: doping the epitaxial layer with beta-Ga of the donor Si element ₂ O ₃ Carrying out heavy ion irradiation with different fluence at room temperature; detecting beta-Ga before and after heavy ion irradiation ₂ O ₃ Monoclinic structure, flexural vibration, tensile mode optical properties and chemical bonding state of the epitaxial wafer; summarizing the experimental data obtained in the step S2 to obtain the heavy ion irradiation beta-Ga ₂ O ₃ Point defects generated after the wafer is epitaxial; introducing the point defect generated in step S3 into beta-Ga ₂ O ₃ In the MOSFET model, the output simulates an electrical performance curve. The invention is prepared by mixing beta-Ga ₂ O ₃ Irradiation study of epitaxial wafers and beta-Ga ₂ O ₃ Simulation studies of MOSFET devices were combined,for beta-Ga ₂ O ₃ The radiation-resistant mechanism research of the MOSFET device produces remarkable effects.

Description

Simulation of the Effect of Heavy Ion Irradiation on the Electrical Properties of β-Ga2O3 MOSFET Devices method

technical field

The invention relates to the field of electronic technology, in particular to a method for influencing the electrochemical performance of a β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation.

Background technique

Gallium oxide (Ga ₂ O ₃ ) has a wide band gap of about 4.4-5.3 eV, and is one of the representative wide band gap semiconductor materials. Ga ₂ O ₃ has many different polymorphs, and different polymorphs have different structural symmetry and anisotropy, among which the β phase has a monoclinic crystal structure and is the most stable phase in thermodynamics. In recent years, most of the studies have focused on β-Ga ₂ O ₃ . When β-Ga ₂ O ₃ materials and devices are applied in space environment, they are usually exposed to various types of particles and radiation. When β-Ga ₂ O ₃ materials are irradiated by low-energy heavy ions, the particles It will be deposited inside the material, form Bragg peaks, and generate displacement defects such as single vacancies and interstitial atoms, and these defects will significantly affect the physical and chemical properties of the material.

Recently, β _{- Ga2O3} has attracted great attention as an ultra-wide bandgap oxide semiconductor for future power and photodetector devices, and β _{- Ga2O3} MOSFET (Metal-Oxide-Semiconductor Field-EffectTransistor , Metal-Oxide Semiconductor Field Effect Transistor) is one of the commonly used β-Ga ₂ O ₃ devices. In order to achieve high performance and reliability of semiconductor devices, it is critical to control crystal defects, as these defects can have negative and destructive effects on device performance, and in some cases, even cause leakage current and higher low breakdown voltage. Therefore, it is crucial to characterize defects in crystals and understand their formation mechanism, but there is little research on this, and it is impossible to determine which specific defects are the main source of transistor instability.

SUMMARY OF THE INVENTION

The problem solved by the present invention is how to provide a method for influencing the electrochemical performance of β-Ga ₂ O ₃ MOSFET devices by heavy ion irradiation, and to study which specific defect is the main source of transistor instability.

In order to solve at least one aspect of the above problems, the present invention provides a method for affecting the electrochemical performance of a β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation, comprising the following steps:

Step S1, washing the epitaxial wafer of β-Ga ₂ O ₃ doped with the donor Si element in the epitaxial layer, and then performing heavy ion irradiation with different fluences at room temperature;

Step S2, detecting the monoclinic structure, bending vibration, tensile mode optical properties and chemical bonding state of the β-Ga ₂ O ₃ epitaxial wafer before and after heavy ion irradiation;

In step S3, the experimental data obtained in step S2 are summarized, and the point defects and their derivatization processes generated after the β-Ga ₂ O ₃ epitaxial wafer is irradiated by heavy ions are obtained;

Step S4 , introducing the point defects generated in step S3 into the β-Ga ₂ O ₃ MOSFET model, outputting a simulated electrical performance curve, and performing analysis.

Preferably, the heavy ion irradiation is N ion irradiation.

Preferably, in the step S1, the energy of the N ion irradiation is 400keV, the particle flux is 1×10 ¹³ atomcm-2·s ^-1 , and the particle fluence is 5×10 ¹⁵ ions/cm ² , 5×10 ¹⁶ ions/cm ² and 5×10 ¹⁷ ions/cm ² .

Preferably, in the step S2, when detecting the monoclinic structure, bending vibration and tensile mode of the β-Ga ₂ O ₃ epitaxial wafer before and after heavy ion irradiation, the excitation wavelength is set to 532 nm, and the test range is 100-800 cm ^-1 , the resolution is set to 0.5cm ^-1 .

Preferably, in the step S2, a 325 nm He-Cd laser with an optical power of 35 mW is used to study the optical properties of the β-Ga ₂ O ₃ epitaxial wafer before and after heavy ion irradiation.

Preferably, the PL light from the β _{- Ga2O3} epitaxial wafer is directed onto a Jobin Yvon Triax320 monochromator, then recorded by a Hamamatsu Si photomultiplier and using a lock-in amplifier synchronized with a 20Hz photo-chopper Improve the signal-to-noise ratio.

Preferably, in the step S2, the chemical bonding state of the β-Ga ₂ O ₃ epitaxial wafer before and after heavy ion irradiation is detected by X-ray photoelectron spectroscopy, using a monochromatic aluminum target X-ray source and a standard calibrated at 284.8 eV The carbon binding energy is used as a reference.

Preferably, in the step S3, point defects generated in the β-Ga ₂ O ₃ material after heavy ion irradiation are analyzed by comparing the test results of X-ray photoelectron spectroscopy.

Preferably, in the step S4, the β-Ga ₂ O ₃ MOSFET model is found in the simulation example of the silvaco TCAD semiconductor simulation software, the point defects obtained by the analysis in the step S3 are introduced, the simulated electrical performance curve is output, and the analyze.

Preferably, the simulation is performed using Atlas and Athena modules in silvaco TCAD semiconductor simulation software.

The invention can generate different point defects on the β-Ga ₂ O ₃ material by irradiating the β-Ga ₂ O ₃ epitaxial wafer doped with the donor Si element under different ion fluence conditions, and then analyze Changes in properties of β-Ga ₂ O ₃ materials before and after N ion irradiation, and point defects are obtained. The point defects obtained by analysis are introduced into the β-Ga ₂ O ₃ MOSFET model, and β-Ga ₂ before and after the introduction of different point defects is analyzed. The electrochemical properties of the O ₃ MOSFET model were obtained to obtain the effect of different point defects on the electrochemical performance of the β-Ga ₂ O ₃ MOSFET model. Since different point defects correspond to N ion radiation with different ion fluences, Therefore, the effect of N ion irradiation with different ion ions on the β-Ga ₂ O ₃ MOSFET model can be obtained; the present invention combines the irradiation research of β-Ga ₂ O ₃ epitaxial wafer with the β-Ga ₂ O ₃ MOSFET device. Combined with the simulation research of β-Ga 2 O 3 MOSFET, the relationship between N ion irradiation and the performance of β-Ga ₂ O ₃ MOSFET devices is provided, which has a significant effect on the study of radiation resistance mechanism of β-Ga ₂ O ₃ MOSFET devices.

Description of drawings

Fig. 1 is the flow chart of the method for the electrochemical performance of β-Ga ₂ O ₃ MOSFET device affected by heavy ion irradiation in the embodiment of the present invention;

Fig. 2 is the PL broad spectrum diagram of the β-Ga ₂ O ₃ epitaxial wafer before and after N particle irradiation in the embodiment of the present invention and its fitting result diagram;

FIG. 3 is an XPS fitting result diagram of a β-Ga ₂ O ₃ epitaxial wafer before and after N particle irradiation in an embodiment of the present invention;

FIG. 4 is an analysis diagram of electrochemical performance before and after introducing point defects in a β-Ga ₂ O ₃ MOSFET in an embodiment of the present invention.

Detailed ways

In order to make the above objects, features and advantages of the present invention more clearly understood, specific embodiments of the present invention will be described in detail below.

It should be noted that the features in the embodiments of the present invention may be combined with each other without conflict. The meanings of the terms "comprising", "including", "containing", "having" are non-limiting, that is, other steps and other ingredients may be added that do not affect the result. The above terms cover the terms "consisting of" and "consisting essentially of". Unless otherwise specified, materials, equipment and reagents are all commercially available.

An embodiment of the present invention provides a method for affecting the electrochemical performance of a β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation, as shown in FIG. 1 , including the following steps:

Step S1, washing the epitaxial wafer of β-Ga ₂ O ₃ doped with the donor Si element in the epitaxial layer, and then performing heavy ion irradiation with different fluences at room temperature;

Step S2, detecting the monoclinic structure, bending vibration, tensile mode optical properties and chemical bonding state of the β-Ga ₂ O ₃ epitaxial wafer before and after heavy ion irradiation;

In step S3, the experimental data obtained in step S2 are summarized, and the point defects and their derivatization processes generated after the β-Ga ₂ O ₃ epitaxial wafer is irradiated by heavy ions are obtained;

Step S4 , introducing the point defects generated in step S3 into the β-Ga ₂ O ₃ MOSFET model, outputting a simulated electrical performance curve, and performing analysis.

Wherein, in step S1, the epitaxial wafer of β-Ga ₂ O ₃ doped with the donor Si element in the epitaxial layer is cut into blocks of the same size, which are used for research under different heavy ion irradiation conditions. _The epitaxial wafer of _-Ga2O3 was sonicated with acetone and then washed with distilled water to remove impurities from its surface. The cleaned epitaxial wafers of β-Ga ₂ O ₃ were irradiated with different fluences of N ions at room temperature in a tandem van der Graaff accelerator (Peking University) with an energy of 400 eV. Among them, the particle flux is 1×10 ¹³ atom cm-2·s ^-1 , and the particle fluence is 5×10 ¹⁵ ions/cm ² , 5×10 ¹⁶ ions/cm ² and 5×10 ¹⁷ ions/cm ² , respectively .

Pure semiconductor materials are non _- conductive at room temperature, but to make the semiconductor conductive requires _doping with donor elements. -The epitaxial wafer of Ga ₂ O ₃ is conductive, which is convenient for subsequent detection of its indicators. Using N ion irradiation with different particle fluence can make β-Ga ₂ O ₃ material produce different point defects, and can study the correspondence between particle fluence and point defects.

In step S2, the monoclinic structure, bending vibration, tensile mode optical properties and chemical bonding state of the β-Ga ₂ O ₃ epitaxial wafer before and after N ion irradiation are detected.

The monoclinic structure, bending vibration and tensile modes of epitaxial wafers of β-Ga ₂ O ₃ before and after N ion irradiation were monitored in an InVia-Reflex tip-enhanced laser confocal Raman spectroscopy system, where the excitation wavelength was set to 532 nm, and the test The range is 100-800cm ^-1 and the resolution is set to 0.5cm ^-1 .

The optical properties _of β _- Ga ₂ O ₃ epitaxial wafers before and after N ion irradiation were investigated using a 325 nm He-Cd laser with an optical power of 35 mW. ) were directed onto a Jobin Yvon Triax 320 monochromator, and then recorded by a Hamamatsu Si photomultiplier, and a lock-in amplifier synchronized with a 20Hz photo-chopper was used to improve the signal-to-noise ratio.

The chemical bonding state of β-Ga ₂ O ₃ epitaxial wafers before and after N ion irradiation was detected by X-ray photoelectron spectroscopy (XPS), and the monochromatic aluminum target X-ray source and the standard carbon element binding energy calibrated at 284.8 eV were used as the refer to.

In step S3, the result detected in step S2 is analyzed to analyze which point defects are generated in the β-Ga ₂ O ₃ epitaxial wafer after being irradiated by N ions with different particle fluences. By comparing and analyzing the test results before and after N particle irradiation, it is possible to analyze which point defects are generated in the β-Ga ₂ O ₃ epitaxial wafer, so as to obtain the corresponding relationship between the particle fluence of N particle irradiation and the point defects generated.

In step S4, find the β-Ga ₂ O ₃ MOSFET model in the simulation example of the silvaco TCAD semiconductor simulation software, use the Atlas and Athena modules in the software for analysis, and use the trap parameter to introduce the point defect analyzed in step S3, and use e .level sets the discrete trap level, degen.fac defines the degeneration factor for the trap level and is used to calculate the density, and sign and sigp define the trap trapping cross section for electrons or holes. Through simulation, the electrical performance curves of the β-Ga ₂ O ₃ MOSFET model before and after the introduction of different defect points are output, the influence of defect points on the electrical performance is analyzed, and the defect points that can be generated under the condition of N ion irradiation with different particle fluences are analyzed. , to analyze the influence of N particle irradiation conditions on the electrical properties of β-Ga ₂ O ₃ MOSFET devices with different particle fluence conditions.

By irradiating the β-Ga ₂ O ₃ epitaxial wafer doped with donor Si element with N ions under different ion fluence conditions, different point defects can be generated on the β-Ga ₂ O ₃ material, and then by analyzing the N ions Changes in the properties of β-Ga ₂ O ₃ materials before and after irradiation to obtain point defects, and introduce the point defects obtained by analysis into the β-Ga ₂ O ₃ MOSFET model, and analyze the β-Ga ₂ O ₃ before and after introducing different point defects The electrochemical performance of the MOSFET model can be obtained to obtain the effect of different point defects on the electrochemical performance of the β-Ga ₂ O ₃ MOSFET model. The effects of N ion irradiation with different ion ions on the model _of β _- Ga ₂ O ₃ MOSFET _were obtained _; Combined, the relationship between N ion irradiation and the performance of β-Ga ₂ O ₃ MOSFET devices is provided, which has a significant effect on the study of radiation resistance mechanism of β-Ga ₂ O ₃ MOSFET devices.

The following describes the simulation method that heavy ion irradiation affects the electrical properties of β-Ga ₂ O ₃ MOSFET devices in conjunction with specific embodiments:

Example

1.1. The epitaxial wafer of β-Ga ₂ O ₃ doped with donor Si element in the epitaxial layer was cut into small pieces of uniform size, which were re-sonicated in acetone, and then washed with distilled water. The β-Ga ₂ O ₃ epitaxial wafer was irradiated by N particles. In the experiment, the particle flux of N ions was 1×10 ¹³ atom cm-2·s ^-1 , and the particle fluence was set to 5×10 ¹⁵ ions respectively. /cm ² , 5×10 ¹⁶ ions/cm ² and 5×10 ¹⁷ ions/cm ² ;

1.2. The InVia-Reflex tip-enhanced laser confocal Raman spectroscopy system was used to monitor the monoclinic structure, bending vibration and tensile mode of the epitaxial wafer of β-Ga ₂ O ₃ before and after N ion irradiation. The detection conditions were: excitation The wavelength was set to 532nm, the test range was 100-800cm ^-1 , and the resolution was set to 0.5cm ^-1 ; the optical properties of β-Ga ₂ O ₃ epitaxial wafers before and after N ion irradiation were studied using a 325nm He-Cd laser with an optical power of 35mW , the PL light from the β _{- Ga2O3} epitaxial wafer was directed onto a Jobin Yvon Triax 320 monochromator during detection, which was then recorded by a Hamamatsu Si photomultiplier using a lock-in amplifier synchronized with a 20Hz optical chopper to Improve the signal-to-noise ratio; detect the chemical bonding state of β-Ga ₂ O ₃ epitaxial wafers before and after N ion irradiation by XPS, and use a monochromatic aluminum target X-ray source and a standard carbon element binding energy calibrated at 284.8 eV as a reference.

1.3. Summarize the experimental data obtained in step 1.2, analyze the changes of the β-Ga ₂ O ₃ epitaxial wafer before and after N ion irradiation, and determine the point defects generated by the β-Ga ₂ O ₃ epitaxial wafer. The PL spectra of β-Ga ₂ O ₃ epitaxial wafers before and after N ion irradiation, and the fitting results under different particle fluence conditions, a) in Figure 2 is the PL broad spectrum before and after irradiation, as can be seen from the figure The β-Ga ₂ O ₃ epitaxial wafer showed luminescence peaks spanning 300-600 nm, and the luminescence peaks of β-Ga ₂ O ₃ epitaxial wafers were fitted with a UV PL band at 365 nm (3.39 eV) and a UV PL band at 410 nm (3.02 eV). Blue PL band. Combined with the results of optical transition energy levels calculated by Quoc et al. using first-principles, the UV band peak is attributed to self-trapped excitons, which consist of GaO _tetrahedral complexes and self-trapped holes; the blue emission peak is derived from Donor-acceptor pair (DAP) composite emission band of electrons in donor impurities and holes in acceptor impurities, where the donor band consists of V _o and the acceptor band consists of V _Ga2 ^1- . b) in Fig. 2 and c) in Fig. 2 are the PL fitting results under the conditions of particle fluence of 5×10 ¹⁵ ions/cm ² and 5×10 ¹⁷ ions/cm ² , respectively. It can be seen from the figure that PL The intensity varies with the fluence of irradiated particles. Under the condition of low particle fluence, the PL peak increases significantly when irradiated by N particles, but with the increase of particle fluence, the luminescence intensity of the PL peak decreases. This is mainly due to that, under low particle fluence conditions, the concentration of single-vacancy defects such as _Vo and V _Ga2 ^1- that cause blue emission increases significantly, resulting in an increase in the intensity of the PL peak, however, with the particle fluence With the increase of , a large number of N ions will enter the material and participate in the bonding. At this time, the unstable _Vo defects may be replaced by N ions to form No ^1- defects, and the derivatization process of _Vo defects will cause a quenching effect, resulting in PL peaks strength has decreased. Fig. 3 shows the XPS fitting results of N1s in β-Ga ₂ O ₃ epitaxial wafers before and after N ion irradiation, in which a) in Fig. 3 is the unirradiated condition and the ion fluence of 5×10 ¹⁵ ions/cm ² Figure 3 b) is the result under the condition that the fluence is 5×10 ¹⁷ ions/cm ² , it can be seen from Figure 3 that there are 3 sub-peaks in both a) in Figure 3 and b) in Figure 3 , in which the peak near 398.4 nm is the peak of N atoms, and the other two peaks correspond to Ga-N and No ^1- defects, respectively. With the increase of particle flux, a part of N ions replace _Vo defects. This result is the same as that in Fig. 2. The PL results shown are consistent, further demonstrating the effect of particle fluence on defects in β _{- Ga2O3} epitaxial wafers.

1.4. Find the β-Ga ₂ O ₃ MOSFET model from the simulation example of silvaco TCAD semiconductor simulation software, and use trap parameters to introduce V _o , V _Ga2 ¹ and No ^1- defects, where e.level in the statement is used to set discrete traps Energy level, degen.fac is used to define the degradation factor of the trap energy level, and can also be used to calculate the density, sign and sigp are used to define the trap trapping cross section for electrons or holes, and output β-Ga ₂ O before and after the introduction of defects ₃ The electrochemical performance curve of the MOSFET model is shown in Figure 4, where a) in Figure 4 is the transfer characteristic curve, and b) in Figure 4 is the output characteristic curve. It can be seen from the figure that the transfer characteristic curve has an obvious negative drift after the introduction of point defects, and the drift of No ^1- is significantly larger than that of V _Ga ¹ and V _o ; in addition, after the defect occurs, β-Ga ₂ O ₃ MOSFET The output characteristics of β-Ga 2 O 3 are significantly improved, so that the β-Ga ₂ O ₃ MOSFET device can be turned on at a lower gate voltage V _GS .

Through simulation, it can be found that the introduction of point defects has a great negative impact on the electrical properties of β-Ga ₂ O ₃ MOSFET devices. For example, reducing the threshold voltage will increase the static power _consumption of the device. It should be in the off state, but can be turned on after a defect occurs, causing related logic errors, increasing the risk of leakage, and even causing the entire system to fail.

Therefore, according to the simulation method for the influence of heavy ion irradiation on the electrical performance of β-Ga ₂ O ₃ MOSFET device provided in the embodiment of the present invention, it can be concluded that the point defects caused by heavy ion irradiation will lead to the β-Ga ₂ O ₃ MOSFET device. The threshold value is negatively shifted, and the influence of the external defect No ^1- is the most serious. The simulation method has obvious effects on the electrochemical performance of β-Ga ₂ O ₃ MOSFET devices and its application in space environment.

Although the present disclosure is disclosed above, the scope of protection of the present disclosure is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present disclosure, and these changes and modifications will fall within the protection scope of the present invention.

Claims (10)

1. a heavy ion irradiation affects the method for β-Ga ₂ O ₃ MOSFET device electrochemical performance, is characterized in that, comprises the following steps: Step S1, washing the epitaxial wafer of β-Ga ₂ O ₃ doped with the donor Si element in the epitaxial layer, and then performing heavy ion irradiation with different fluences at room temperature; Step S2, detecting the monoclinic structure, bending vibration, tensile mode optical properties and chemical bonding state of the β-Ga ₂ O ₃ epitaxial wafer before and after heavy ion irradiation; In step S3, the experimental data obtained in step S2 are summarized, and the point defects and their derivatization processes generated after the β-Ga ₂ O ₃ epitaxial wafer is irradiated by heavy ions are obtained; Step S4 , introducing the point defects generated in step S3 into the β-Ga ₂ O ₃ MOSFET model, outputting a simulated electrical performance curve, and performing analysis. 2 . The method for influencing the electrochemical performance of a β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation according to claim 1 , wherein the heavy ion irradiation is N ion irradiation. 3 . 3. The method for affecting the electrochemical performance of β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation according to claim 2, wherein in the step S1, the energy of N ion irradiation is 400keV, and the particle flux is 1×10 ¹³ atom cm-2·s ^-1 , and the particle fluences are 5×10 ¹⁵ ions/cm ² , 5×10 ¹⁶ ions/cm ² and 5×10 ¹⁷ ions/cm ² , respectively. 4. The method for impacting the electrochemical performance of β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation according to claim 1, wherein in the step S2, detecting the β-Ga ₂ O ₃ before and after heavy ion irradiation In the monoclinic structure, bending vibration and tensile modes of the epitaxial wafer, the excitation wavelength is set to 532 nm, the test range is 100-800 cm ^-1 , and the resolution is set to 0.5 cm ^-1 . 5. The method for impacting the electrochemical performance of β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation according to claim 1, wherein in the step S2, using a 325nmHe-Cd laser with an optical power of 35mW to study heavy ions Optical properties of β-Ga ₂ O ₃ epitaxial wafers before and after ion irradiation. 6 . The method for influencing the electrochemical performance of a β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation according to claim 5 , wherein the PL light emitted by the β-Ga ₂ O ₃ epitaxial wafer is guided to the Jobin. 7 . A Yvon Triax 320 monochromator was then recorded by a Hamamatsu Si photomultiplier and a lock-in amplifier synchronized with a 20Hz optical chopper was used to improve the signal-to-noise ratio. 7. The method for affecting the electrochemical performance of β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation according to claim 1, wherein in the step S2, heavy ion irradiation is detected by X-ray photoelectron spectroscopy analysis technology The chemical bonding state of β-Ga ₂ O ₃ epitaxial wafers before and after irradiation was observed, using a monochromatic aluminum target X-ray source and a standard carbon binding energy calibrated at 284.8 eV as a reference. 8. The method for affecting the electrochemical performance of β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation according to claim 7, wherein in the step S3, by comparing the X-ray photoelectron spectroscopy analysis test results, analyze Point defects generated in β _{- Ga2O3} materials after heavy ion irradiation. 9. The method for impacting the electrochemical performance of β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation according to claim 1, wherein in the step S4, β is found in the simulation example of silvaco TCAD semiconductor simulation software -Ga ₂ O ₃ MOSFET model, introducing the point defects analyzed in the step S3, outputting the simulated electrical performance curve, and performing analysis. 10 . The method for influencing the electrochemical performance of a β-Ga ₂ O ₃ MOSFET device by heavy ion irradiation according to claim 9 , wherein the simulation is performed using Atlas and Athena modules in silvaco TCAD semiconductor simulation software. 11 .

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