Simulation method of collision diode space charge limiting current

Abstract

The invention discloses a method for simulating space charge limiting current of a collision diode, relates to a micro-nano device simulation technology, and provides a scheme for solving the problem of lack of collision background simulation in the prior art. Comprising the following steps: S1, determining simulation initial parameters; s2, judging that electron particles are injected into the cathode; s3, sequencing and numbering all the electronic particles; s4, calculating an electric field at each particle; s5, the motion state of the electron particles at the next moment is solved through the Runge-Kutta method iteration motion equation; s6, judging that the anode absorbs electron particles; s7, calculating new current density and electric field potential distribution; s8, if steady-state simulation is carried out, outputting a result of the step S7; and if transient simulation is carried out, the steps S2 to S8 are cycled, and the result of the step S5 is output. The method has the advantages that a meshless discrete electron model of the collision diode is provided by combining a plate capacitor model and a Poisson equation, and the method is suitable for the condition that electron particles are injected into any collision diode gap of background collision from a cathode at any initial velocity.

Description

Technical Field

[0001] The invention relates to micro-nano device simulation technology, and in particular to a simulation method for collision diode space charge limiting current. Background Art

[0002] Based on the collision diode structure with two electrodes separated by a certain distance in one dimension, the background collision caused by neutral background particles exists in the gap between the electrodes, so it is called a collision diode. Figure 1 As shown, the distance between the two electrodes of the collision diode is D, and the cathode potential is φ c =0, the anode potential is φ a =φ g ; There is a background medium with an equivalent electron mobility μ in the collision diode; The cathode always has a constant injection current density J in .

[0003] The space charge effect has been extensively studied in the past decades because it has a strong influence on the performance of many electronic devices, such as high-power microwave sources, ultrafast electron microscopes, and ion collision diodes for inertial fusion. In the case of one-dimensional non-relativistic zero initial velocity, the limiting current density in the vacuum gap of the collision diode is given by the classical CL law. Currently, the classical CL law has been extended to many fields such as two-dimensional and three-dimensional geometries, quantum and relativistic states, ultrafast time scales, field emission, and orthogonal magnetic fields.

[0004] Recently, many studies have begun to focus on the impact of collisions on space charge limited current. On the one hand, in non-vacuum environments, such as vacuum devices with slight leaks or microplasmas in combustion and medical applications, background collisions must be considered to determine the behavior of space charge limited current. On the other hand, characterizing the emission and transport of electrons in other background media (such as gases and liquids) is very important for understanding breakdown and plasma formation in micro-nanoelectronic devices.

[0005] Defects and shortcomings of the existing technology:

[0006] 1. The space charge limited current with a certain electron initial velocity only has a theoretical analytical expression in a vacuum background, while the space charge limited current in a collision background only has a theoretical analytical expression in the case of zero initial velocity. The theoretical research on the combined influence of the two factors of electron initial velocity and background collision relies on computer simulation algorithms for verification.

[0007] 2. Currently, the numerical algorithms suitable for simulating the motion of electron particles in collision diodes can only simulate the steady-state model behavior of collision diodes, and the transient simulation algorithms of collision diodes are still lacking.

[0008] 3. At the scale of micro-nano collision diodes, the spatial grids that traditional algorithms need to divide are too dense, and the excessively high grid accuracy greatly affects the efficiency of computational simulation. Summary of the invention

[0009] The purpose of the present invention is to provide a simulation method for the space charge limited current of a collision diode to solve the problems existing in the above-mentioned prior art. By introducing equivalent electron mobility to quantify the collision between electrons and background molecules and atoms, a discrete electron model of the collision diode is proposed based on the flat capacitor model and Poisson's equation to calculate the transient response of the space charge limited current and perform time-related behavior analysis. This method can solve the transient and steady-state changes of the space charge limited current in the collision diode, and is suitable for the case where electron particles are injected from the cathode into the gap of the collision diode with any background collision at any initial velocity, and adopts the idea of ​​the gridless method, which is more suitable for simulation calculations at the micro-nano scale.

[0010] The method for simulating the space charge limiting current of a collision diode described in the present invention comprises the following steps:

[0011] S1. Determine the initial simulation parameters;

[0012] S2. Determine the cathode injected electron particles;

[0013] S3. Sort and number all the electron particles;

[0014] S4. Calculate the electric field at each particle;

[0015] S5. Runge-Kutta method iterates the motion equation to find the motion state of the electron particle at the next moment;

[0016] S6. Determine the anode absorbs the electron particles;

[0017] S7. Calculate new current density and electric field potential distribution;

[0018] S8. If a steady-state simulation is performed, the result of step S7 is output; if a transient simulation is performed, steps S2 to S8 are looped and the result of step S5 is output.

[0019] The simulation method of the space charge limited current of the collision diode described in the present invention has the advantage that a gridless discrete electron model of the collision diode is proposed by combining the flat plate capacitor model and the Poisson equation, which is applicable to the case where electron particles are injected from the cathode into the gap of the collision diode with any background collision at any initial velocity under the premise of non-relativism. The numerical algorithm adopts the gridless simulation technology, avoids the overly dense spatial grid at the micro-nano scale, and improves the computational simulation efficiency. It realizes the solution of the transient and steady-state changes of many physical quantities of the collision diode during the movement of the electron particles, and solves the applicability limitations of the theoretical analytical formulas currently proposed. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the structure of the collision diode described in the present invention.

[0021] Figure 2 It is a schematic diagram of the flow of the simulation method described in the present invention.

[0022] Figure 3 It is a graph showing the relationship between space charge limited current density and collision conditions during steady-state simulation of the simulation method described in the present invention.

[0023] Figure 4 It is a graph showing the relationship between the transmission current density and the injection current density during steady-state simulation of the simulation method described in the present invention.

[0024] Figure 5 It is the time evolution behavior of space charge limited current and the phase diagram of electron particles under constant initial velocity during transient simulation of the simulation method described in the present invention.

[0025] Figure 6 It is the time evolution behavior of space charge limited current and the phase diagram of electron particles under Maxwell distribution during transient simulation of the simulation method described in the present invention.

[0026] Figure 7 It is the spectrum analysis of space charge limited current and the frequency response diagram of each factor during transient simulation of the simulation method described in the present invention. DETAILED DESCRIPTION

[0027] like Figure 2 As shown, the simulation method of the space charge limiting current of the collision diode described in the present invention numbers each electron particle between the collision diodes from small to large in the direction from the anode to the cathode, and the number corresponds to the position of the electron particle. Then, according to the flat capacitor model, Poisson's equation and Gauss's theorem, the corresponding electric field strength of each electron particle is solved as follows:

[0028]

[0029] Among them, q is the charge carried by the electron particle, N is the total number of electron particles, i is the number of the electron particle, ε0 is the vacuum dielectric constant, D is the distance between the two electrodes in the collision diode, and A is the cathode electron emission area.

[0030] For the electron particles in the collision diode space, the equation of motion is:

[0031]

[0032] in represents the second-order derivative of the electron particle displacement x, represents the first-order derivative of the displacement x of the electron particle, e is the elementary charge, m e is the electron mass, μ is the equivalent electron mobility, and the more intense the background collision, the smaller μ. Set the simulation time step to Δt, and iterate the motion state of the electron particles at the next moment through the fourth-order Runge-Kutta method, and iterate the simulation in a loop, so as to realize the transient simulation of various physical quantities in the collision diode. At each moment, that is, at each simulation step, the potential electric field distribution and space charge limited current density in the collision diode can be determined according to the state of the electron particles. By comparing with the previous moment, it is possible to detect and judge whether the collision diode can finally stabilize and output the steady-state simulation results.

[0033] To perform a steady-state simulation:

[0034] The simulations show the variation of the saturated transmission current of the collision diode with the change of the equivalent electron mobility under two initial velocity distributions, and the variation of the transmission current of the collision diode with the injection current under different background collision conditions. The initial velocity of the electron particles obeys the Maxwell distribution with temperature T or the constant initial velocity distribution corresponding to the thermal average velocity.

[0035] Considering the initial velocity of the electron particle as v0, the maximum transmission current density of the flat plate collision diode under vacuum conditions has a theoretical analytical formula that is consistent with the experiment:

[0036]

[0037] in is the Child-Langmuir law, which describes the maximum transmission current density of a classical plate collision diode with zero initial velocity under vacuum conditions. is the initial velocity factor.

[0038] In this embodiment, the relevant parameters of the collision diode are:

[0039] D=100nm,A=D 2 ,φ g =2V,T=1500K.

[0040] Figure 3The relationship between the saturation transmission current density and the equivalent electron mobility μ under the constant initial velocity distribution and Maxwell distribution at T=1500K is shown. For smaller μ, no matter what the initial velocity of the electron is, the initial velocity of the electron will quickly decay to a relatively small amount due to frequent collisions. The influence of the friction term introduced by the collision in the equation of motion is quite significant, far greater than the influence of the difference in initial velocity distribution. For larger μ, the time-averaged transmission current density under constant initial velocity is significantly different from the Maxwell distribution. As the space charge accumulates, a gradually increasing potential barrier appears between the collision diodes until electron reflection occurs. Since all electron particles have the same velocity under constant initial velocity, all electron particles are reflected when reflection occurs. This destroys the original space charge distribution and enters a stage of re-establishment. As a result, an unstable state of virtual cathode oscillation occurs in the collision diode, causing the saturation transmission current to be lower than For the Maxwell distribution, as the space charge accumulates and the potential barrier increases, more and more electrons are reflected, but some high-energy electrons can still reach the anode. In this case, it is not necessary to reflect all electrons to prevent further accumulation of space charge, so the collision diode does not show obvious oscillation behavior, and the time-averaged transmission current will be close to or even slightly higher than prediction.

[0041] Figure 4 The relationship between the time-averaged transport current density and the injected current density under the constant initial velocity distribution and the Maxwell distribution is shown, where each row of pictures corresponds to a different background collision condition: The first row μ = 0.001 m 2 / Vs, second row μ=0.01m 2 / Vs, third row μ=1m 2 / Vs. Figure 4 The black diagonal lines in (a)-(c) represent the expected transmission current in the absence of reflection, and the grey dashed lines correspond to the space charge limited current limit. Figure 4 (d)-(f) are the transmission characteristics of the constant initial velocity space charge limited current under large injection saturation state. As μ decreases, the transmission current behavior between the two velocity distribution modes gradually approaches, which is consistent with Figure 3 For larger μ, when the injection current is lower than the space charge limited current limit, there is almost no reflected current in the collision diode. When the injection current is slightly higher than the SCL limit, the transmission current under the constant initial velocity distribution drops sharply, causing the collision diode transmission current to enter the saturation state. Under vacuum conditions, the transmission current J in the saturation state trans With the injection current J in The relationship is:

[0042]

[0043] Where a, b, c are constants, a=α GCL =(1+β 2 ) 3 / 2 For larger μ, the impact of the collision is very weak, so it can be approximated as a vacuum, and a≈α should be GCL In this embodiment, according to the initial parameters, α GCL =1.0771, and Figure 4 The best fit of (f) is a=1.078, b=0.5156, c=-0.3194, which is consistent with the theoretical prediction. For medium-sized μ, when the initial velocity is constant, when the injection current just starts to exceed the space charge limited current limit, the transmission current will slowly decrease like in a vacuum, but as the injection current increases, the transmission current will quickly stabilize at J after a sharp drop. trans / J CL = 0.582. For small μ, it is almost impossible to distinguish the constant initial velocity distribution from the Maxwell distribution by the time-averaged transport current.

[0044] To perform a transient simulation:

[0045] When the injected current is greater than the space charge limited current limit, the collision diode enters the virtual cathode oscillation state. These periodic oscillation characteristics make the study of space charge limitation effects very important for applications such as high-power microwave sources and terahertz oscillations. The steady-state simulation case shows that the collision has a great influence on the transmission characteristics of the space charge limited current, so this case will further study the time evolution behavior (transient behavior) of the space charge limited current.

[0046] Figure 5 and Figure 6 The time evolution behavior of space charge limited current and the phase diagram of electron particles under three background collision conditions are shown respectively, where red and blue are used to distinguish between electron particles reflected back to the cathode and electron particles that can reach the anode. and the transfer time under the classical CL law After normalization, the relevant parameters of the collision diode are consistent with those in case 1.

[0047] The time evolution behavior of the space charge limited current under different initial velocity distributions is very different, especially when the collision diode enters the saturation state of dynamic equilibrium. In order to show the difference more clearly, the Fourier transform analysis of the space charge limited current signal under three background collision conditions is performed, such as Figure 7 As shown in (a)-(c), μ increases successively. Although the Maxwell distribution eliminates the virtual cathode oscillation, it also introduces low-frequency noise, which is particularly obvious in the case of smaller μ. Figure 7 (d)-(f) show the combined effects of collision, anode potential, collision diode spacing, and temperature (initial velocity) on the virtual cathode oscillation frequency. In general, the virtual cathode oscillation frequency decreases as μ increases. For strong background collision conditions, collisions slow down the amplitude of space charge changes and shorten the time of space charge periodic changes, so the frequency of virtual cathode oscillations increases while the amplitude is suppressed. When μ is small enough, the low-frequency amplitude is very small, making the harmonic frequency the new main frequency, resulting in a step-by-step increase in the oscillation frequency. From Figure 7 (d)-(f) also show that when the electric field is large or the initial velocity is low, the frequency can get out of the step-down state faster with the increase of μ, and these two cases correspond to higher vacuum oscillation frequencies. The phenomenon that the oscillation frequency decreases with the decrease of electric field strength has been confirmed by many studies. In addition, when the background collision is quite strong, the too small electric field between the collision diodes will make the virtual cathode oscillation disappear.

[0048] For those skilled in the art, various other corresponding changes and deformations can be made according to the technical solutions and concepts described above, and all of these changes and deformations should fall within the protection scope of the claims of the present invention.

Claims

1. A method for simulating the space charge limiting current of a collision diode, characterized in that: The following steps are involved: S1. Determine the initial simulation parameters; S2. Determine the cathode injected electron particles; S3. Sort and number all the electron particles; S4. Calculate the electric field at each particle; S5. Runge-Kutta method iterates the motion equation to find the motion state of the electron particle at the next moment; S6. Determine the anode absorbs the electron particles; S7. Calculate new current density and electric field potential distribution; S8. If a steady-state simulation is performed, the result of step S7 is output; if a transient simulation is performed, steps S2 to S8 are looped and the result of step S5 is output.

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