JPH11329224A - Orbit calculating method for charged particle and device thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To estimate on the orbits of electrons in a system where emitted electrons are reflected and scattered, and to quantify the quantity of the electrons getting to an accelerating electrode to which the electrons are emitted. SOLUTION: This orbit calculation method and its device calculate orbits of charged particles emitted from an electron emission element. In a system provided with the electron emitting element and an accelerating electrode accelerating the electrons emitted from the electron emitting element in the direct upper direction of the electron emitting element, the distribution f(x) of landing spots where the electrons emitted from the electron emitting element fall near the electron emitting element when the potential of the accelerating electrode is set at zero is calculated (S2). According to the calculated landing spot distribution f(x), a carry-over factor of the electrons from the electron emitting element to the accelerating electrode in the case where the effects from the voltage impressed on the accelerating electrode is considered is obtained from the integrated value of the landing spot distribution f(x) from a stagnation point xS multiplied by a constant.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for simulating the trajectory of electrons, and more particularly to a trajectory calculation method and apparatus for calculating the trajectory of charged particles emitted from an electron-emitting device. .

[0002]

2. Description of the Related Art There are many literatures on conventional electron orbit calculations in a vacuum. For example, the Principles of
Electron Optics PWHawkes and E. Kasper vol 1.2.
(Academic Press 1989). According to them, the trajectory of an electron can be calculated by calculating an electric field corresponding to the boundary condition and solving Newton's equation of motion with respect to the electric field. Various studies have been made on these calculation methods, and they have played an important role in the electro-optical design of electronic device elements using various electron sources (thermionic sources, Spindt type, etc.). In particular, it has greatly contributed to the development and design of monitors using conventional vacuum tubes.

[0003] As a physical system targeted by such a trajectory calculator, there is a trajectory calculation of electrons emitted from an electron-emitting device. Such an electron-emitting device will be described below.

Conventionally, two types of electron-emitting devices are known: a thermionic electron-emitting device and a cold cathode electron-emitting device. The cold cathode electron-emitting devices include a field emission type (hereinafter abbreviated as FE type), a metal / insulating layer / metal type (hereinafter abbreviated as MIM type), and a surface conduction type emission device (hereinafter abbreviated as SCE).

[0005] Examples of the FE type include WPDyke and WWD.
olan, "Field emission", Advance inElectron Physics,
8,89 (1956), or CASpindt, "Physical Propertie
s ofthin-film feld emission cathodes with molybden
ium cones ", J. Appl. Phys., 47, 5248 (1976), etc. An example of the MIM type is CA Mead," The tunnel emm.
Ission amplifier, J. Appl. Phys., 32, 646 (1961) and the like are known. Examples of SCE types include MIElinson, Radi
o Eng. Electron Phys., 10, (1965). Regarding the electron orbital calculation for the Spindt type electron source which is an example of the FE type, see, for example, WJ Orvis, CFMcConaghy, DR · Ciarl
o, JHYee and EWHee IEEE Trans.Electron Devices
36 (1989), 261-2658.

[0006] The SCE type utilizes a phenomenon in which electron emission occurs when a current flows in a small-area thin film formed on a substrate in parallel with the film surface. Examples of the surface conduction electron-emitting device include a device using an SnO2 thin film by Elinson et al. And a device using an Au thin film [G. Dittmer: "Thin So
lid Films ", 9,317 (192)], using In2O3 / SnO2 thin film [M. Hartwell and CGFonstad:" IEEE Trans.ED
Conf. ", 519 (1975)], using a carbon thin film [Hisashi Araki et al .: Vacuum, Vol. 26, No. 1, p. 22, p. 1983]
Etc. have been reported.

A typical device configuration of these surface conduction electron-emitting devices is described in the aforementioned M.A. Figure 1 shows the device configuration of Hartwell
It is shown in FIG. In the figure, reference numeral 2001 denotes an insulating substrate;
Reference numeral 02 denotes a thin film for forming an electron-emitting portion, which is formed of a metal oxide thin film or the like formed by sputtering in an H-shaped pattern. The electron emission portion 2 is formed by an energization process called forming, which will be described later.
003 is formed. Reference numeral 2004 denotes a thin film including the electron-emitting portion 2003. L1 in the figure is 0.5
１1 mm and W1 are set at 0.1 mm.

In these surface conduction type emission devices,
Before performing electron emission, the thin film 2002 for forming an electron emission portion is
Generally, the electron-emitting portion 2003 is generally formed in advance by an energization process called forming. Here, forming refers to applying a DC voltage or a very slowly increasing voltage, for example, about 1 V / min, to both ends of the thin film for forming an electron emission portion 2002 and energizing the thin film for forming an electron emission portion 2.
002 is locally broken, deformed or altered to form an electron emitting portion 2003 in an electrically high resistance state. Note that the electron-emitting portion 2003 has a crack in a part of the thin film 2002 for forming an electron-emitting portion, and the electron is emitted from the vicinity of the crack. Hereinafter, the thin film 2002 for forming the electron emitting portion including the electron emitting portion 2003 formed by the forming is referred to as the thin film 20 including the electron emitting portion 2003.
Call it 04. The surface-conduction emission type electron-emitting device subjected to the forming process is a thin film 200 including the above-mentioned electron emission portion 22003.
By applying a voltage to the element 4 and causing a current to flow through the element, electrons are emitted from the above-described electron emitting section 2003.

[0009]

However, the above S
Regarding the electron emission from the CE-type electron-emitting device, a phenomenon that cannot be explained only by the conventional electron orbital calculation, that is, an experimental fact cannot be reproduced without considering electron scattering. For example, in the above-mentioned surface conduction element (hereinafter, abbreviated as SCE element), the inventors of the present application have found that scattering of electrons on the anode surface of the SCE element is essential. The reflection of electrons on the anode surface of such an SCE element is a quantum mechanical phenomenon, and is known to be a phenomenon that does not follow the Newton equation conventionally used in electron orbit calculation.

[0010] Furthermore, the electrons that collide with the anode surface of the SCE element do not scatter all the electrons on the anode surface of the SCE element, but some of the emitted electrons are absorbed by the anode of the SCE element. This is known from various experimental facts. In fact, it is known that when the potential of the accelerating electrode for accelerating emitted electrons toward the light emitting element arranged oppositely is low, about 90% or more of the emitted electrons are absorbed by the anode. I have. Therefore, when such an accelerating electrode does not exist, most of the electrons emitted from the electron emitting portion are absorbed by the anode of the SCE element. For this reason, it has been difficult to accurately calculate the trajectories of the electrons emitted from these SCE elements.

Therefore, the electron orbital calculation, which is a classical mechanics, and the surface reflection, which is a quantum mechanical effect, are fused in accordance with the actual system. There is a need for a method and apparatus for calculating a trajectory.

Such an electron orbital calculation can be performed by performing Monte Carlo calculation, but it requires a huge amount of calculation, increases the cost for calculation, and has been a problem when performing device design calculation.

The present invention has been made in view of the above conventional example, and estimates the trajectory of electrons in a system in which emitted electrons are reflected and scattered, and quantifies the amount of electrons reaching an acceleration electrode to be emitted. It is an object to provide a method and an apparatus for calculating the trajectory of charged particles.

Another object of the present invention is to provide a method and an apparatus for calculating the trajectory of a charged particle capable of obtaining the amount of electrons reaching the target accelerating electrode while reducing the amount of calculation.

[0015]

In order to achieve the above object, a charged particle trajectory calculation apparatus according to the present invention has the following arrangement. That is, a trajectory calculation device for calculating the trajectory of charged particles emitted from an electron-emitting device, comprising an electron-emitting device and an acceleration electrode for accelerating electrons emitted from the electron-emitting device in a direction directly above the electron-emitting device. A first calculating means for calculating a distribution of landing points at which electrons emitted from the electron-emitting device fall near the electron-emitting device without considering the influence of the accelerating electrode, in the system comprising: Based on the landing point distribution calculated by the means,
And a second calculating means for calculating a rate of arrival of electrons from the electron-emitting device to the acceleration electrode in consideration of an influence of a voltage applied to the acceleration electrode.

In order to achieve the above object, the method for calculating the trajectory of a charged particle according to the present invention comprises the following steps. That is,
A trajectory calculation method for calculating the trajectory of charged particles emitted from an electron-emitting device, which approximates the electric field distribution of a system including an electron-emitting device and an acceleration electrode provided substantially in parallel to the electron-emitting device, The direction of the positive electrode of the electron-emitting device is taken on the x-axis, the origin of the x-axis is taken as the point where the electrons are emitted, and the position xS on the x-axis at which the electric field generated on the positive electrode is substantially zero is obtained. The amount of electrons reaching the accelerating electrode is obtained based on the area of the landing point distribution on the x-axis using the position xS as a proportional coefficient.

[0017]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described below in detail with reference to the accompanying drawings.

FIG. 2 is a block diagram showing a schematic configuration of the electron trajectory calculation device of the present embodiment.

In FIG. 2, reference numeral 1 denotes an input unit for inputting various parameters used for calculation. Reference numeral 2 denotes an output unit such as a printer for outputting a calculation result. Reference numeral 3 denotes a control unit, which controls to execute a process shown in FIG. A storage unit 4 stores various data. Reference numeral 5 denotes a calculation unit which executes various calculations described later. Reference numeral 6 denotes a monitor for displaying calculation results and the like.
The input section 1 inputs parameters related to the electron orbit calculation and causes the calculation to be performed.

FIG. 1 is a flowchart showing a trajectory calculation process in the electron trajectory calculation device according to the embodiment of the present invention.

First, in step S1, necessary parameters are input, and then, in step S2, the calculation unit 5 causes the calculation unit 5 to execute electron trajectory calculation. Here, the potential of the accelerating electrode is set to zero (Va = 0), and the distribution of landing points of the electrons is calculated. Then, in step S3, the effect of the accelerating electrode is taken in from a stagnation point xS described later. calculate.
Then, the process proceeds to step S5, where the output unit 2 or the monitor 6
Output the result to

[Embodiment 1] First, the geometrical shape of an electron-emitting device which is an object of the electron trajectory calculation apparatus of the present embodiment will be described. This shape is a physical model that simulates a surface conduction electron-emitting device described later. The electron trajectory calculation in the present embodiment is performed on the physical model of this virtual electron-emitting device.

First, before describing the electron trajectory calculation apparatus of the present embodiment, a basic configuration of a surface conduction element which is a main object of the electron trajectory calculation of the present embodiment will be described with reference to FIG. .

FIG. 3 is a plan view (A) and a cross-sectional view (B) of the surface conduction electron-emitting device of this embodiment.

In FIG. 3, reference numeral 101 denotes a substrate;
03 is an element electrode (102 is a negative electrode, 103 is a positive electrode), and a thin film 104 is interposed between these element electrodes 102 and 103.
Is arranged. This thin film 104 has an electron emitting portion 10 having a crack formed by an energization forming process.
5 are provided.

Here, quartz glass,
Glass with reduced impurities such as Na, blue plate glass,
A glass substrate obtained by laminating SiO2 formed on a blue sheet glass by a sputtering method or the like, ceramics such as alumina, and the like can be given. The material of the device electrodes 102 and 103 may be any material as long as it has conductivity. For example, Ni, Cr. Au, Mo, W, Pt, T
metal or alloy such as i, Al, Cu, Pd and Pd, A
g, Au, RuO2, Pd-Ag or other metal or metal oxide and printed conductor made of glass, etc., In2O3-S
Examples include a transparent conductor such as nO2 and a semiconductor conductor material such as polysilicon.

The element electrode interval L is from several hundred angstroms to several hundred micrometers. This value is set based on the photolithography technology that is the basis of the method for manufacturing the device electrodes, that is, the performance of the exposure machine and the etching method, etc., and the voltage applied between the device electrodes and the electric field intensity capable of emitting electrons, etc., are preferably set. Is tens of micrometers rather than a few micrometers. Device electrode width W, device electrodes 102 and 10
3, the film thickness D is appropriately designed depending on the resistance value of the electrodes and the like. Normally, the length L between the device electrodes is several micrometers to several hundred micrometers, and the device electrodes 102, 1
The film thickness D of No. 03 is several hundred angstroms to several micrometers. The width W of the device electrode 102 is on the order of hundreds of nanometers to hundreds of microns, and is appropriately determined in relation to parameters such as device voltage, acceleration voltage, and distance to the acceleration electrode.

The thickness of the thin film 104 including the electron-emitting portion is preferably from several Angstroms to several thousand Angstroms, and particularly preferably from 10 Angstroms to 5 Angstroms.
00 angstrom and the device electrodes 102 and 103
Step coverage, the resistance value between the device electrodes 102 and 103, and the conductivity of the electron emission portion 105 are appropriately set according to the energization processing conditions described later and the like. The resistance value of the thin film 104 indicates a sheet resistance value of 10 3 to 10 7 [Ω / □]. Specific examples of the material forming the thin film 104 including the electron emitting portion include Pd, Ru, Ag, Au, T
i, In, Cu, Cr, Fe, Zn, Sn, Ta, W,
Metals such as Pb, PdO, SnO2, In2O3, Pb
Oxides such as O, Sb2O3, HfB2, ZrB2, La
Borides such as B6, CeB6, YB4, GdB4, TiC,
Carbides such as ZrC, HfC, TaC, SiC, WC, T
There are nitrides such as iN, ZrN and HfN, semiconductors such as Si and Ge, and carbon. Note that the fine particle film described here is a film in which a plurality of fine particles are aggregated, and has a fine structure not only in a state in which the fine particles are individually dispersed and arranged, but also in a state in which the fine particles are adjacent to each other or overlapped (island shape). Inclusive). The particle size may be from several Angstroms to several thousand Angstroms, preferably 1
It is 200 angstroms from 0 angstroms. The electron-emitting portion 105 is preferably a few Å to a few hundred Å, particularly preferably 10 Å.
It is made up of a number of conductive fine particles having a particle size of 500 angstrom to 500 angstrom. The thickness depends on the manufacturing method such as the thickness of the thin film 104 including the electron emitting portion 105 and the energization processing conditions described later, and is set as appropriate.

Various methods can be considered as a method for manufacturing the electron-emitting device having the electron-emitting portion 105.
An example is shown in FIG.

FIG. 4 is a cross-sectional view for explaining a manufacturing process of the surface conduction electron-emitting device of the present embodiment. In FIG. 4, portions common to FIG. 3 are denoted by the same reference numerals, and description thereof will be omitted.

(1) After sufficiently washing the substrate 101 with a detergent, pure water and an organic solvent, the materials of the device electrodes 102 and 103 are deposited by a vacuum evaporation method, a sputtering method, or the like, and then by photolithography. Device electrodes 102 and 103 are formed on the insulating substrate 101 (FIG. 4A).

(2) An organic metal thin film (conductive thin film) 104 is formed by applying an organic metal solution between the device electrode 102 and the device electrode 103 provided on the insulating substrate 101 and leaving it to stand. . In addition, this organometallic solution is
The aforementioned Pd, Ru, Ag, Au, Ti, In, Cu, C
This is a solution of an organic compound containing a metal such as r, Fe, Zn, Sn, Ta, W, and Pb as a main element. Thereafter, the organic metal thin film is heated and baked, and is patterned by lift-off, etching, or the like to form the electron-emitting-portion-forming thin film 104 (FIG. 4B). Although the present invention has been described with reference to the method of applying an organic metal solution, the present invention is not limited to this, and is formed by a vacuum evaporation method, a sputtering method, a chemical vapor deposition method, a dispersion coating method, a dipping method, a spinner method, or the like. You may.

(3) Subsequently, an energization process called energization forming is performed between the device electrodes 102 and 103.
This is an energization process in which a pulsed voltage or a rising voltage is applied by a power supply (not shown) to energize, and as a result, an electron emitting portion 105 having a structural change is formed at the portion of the electron emitting portion forming thin film 104. (FIG. 4 (c)). The electron emission portion forming thin film 104 is locally destroyed, deformed, or deteriorated by the energization process. The part where the structure has changed is referred to as an electron emitting part 105.

The evaluation of the electron-emitting device subjected to the energization forming process is performed by the evaluation device shown in FIG.
The evaluation device will be described below.

FIG. 5 is a block diagram showing the configuration of an evaluation device for measuring the characteristics of the surface conduction electron-emitting device of the present embodiment. Note that the same parts as those in the above-described configuration are denoted by the same reference numerals, and description thereof is omitted.

In FIG. 5, reference numeral 151 denotes an element electrode 102,
A power supply for applying the element voltage Vf during 103;
Reference numeral 0 denotes an ammeter, which is an element electrode 10 to which an element voltage Vf is applied.
The element current If flowing between 2 and 103 is measured.
153 is a power supply for applying an acceleration voltage (Va) to the anode electrode (acceleration electrode) 154. Reference numeral 152 denotes an ammeter, which is an emission current I emitted from the electron emission portion 105 of the device.
e is being measured. Further, if necessary, a mesh-shaped electrode or a fluorescent plate is attached to the anode electrode 154 so that the distribution of the arrival positions of the electrons can be measured.
The exhaust pump 156 is a pump for evacuating the inside of the container 155 to a vacuum, and includes a normal high vacuum device system such as a turbo pump and a rotary pump, and an ultrahigh vacuum device including an ion pump. Further, the entire vacuum apparatus and the electron-emitting device substrate 101 are heated for about 2
Can be heated up to 00 degrees. Note that the voltage of the anode electrode 154 is 1 kV to 10 kV, and the distance H between the anode electrode 154 and the electron-emitting portion 105 of the electron-emitting device is 2 mm.
It was measured in a range of ８8 mm.

Here, in the energization forming process, the crest value of the voltage pulse applied between the device electrodes 102 and 103 is kept constant, and the crest value of the voltage pulse applied between the device electrodes 102 and 103 is increased. There are times when you do it. First, an example of a voltage waveform when the peak value of the voltage pulse is kept constant is shown in FIG.

In FIG. 6A, each of T1 and T2 indicates the pulse width and pulse interval of the voltage waveform, T1 is 1 microsecond to 10 milliseconds, and T2 is 10 microseconds to 1 microsecond.
00 ms. The peak value of the triangular wave (peak voltage at the time of forming) is appropriately selected, and 10 −5 [torr]
r] in a vacuum atmosphere.

FIG. 6B shows a voltage waveform when energization forming is performed while increasing the peak value of the voltage pulse.

In the drawing, each of T1 and T2 indicates the pulse width and pulse interval of the voltage waveform, T1 is 1 microsecond to 10 milliseconds, T2 is 10 microseconds to 100 milliseconds, and the peak value of the triangular wave (forming). The peak voltage at the time was increased by, for example, about 0.1 [V] step. The vacuum atmosphere during the forming was maintained at about 10 −5 [torr].

The energization forming process is completed by applying a voltage that does not cause local destruction or deformation of the electron emitting portion forming thin film 104 during the pulse interval T2, for example, a voltage of about 0.1 V. The element current was measured to obtain a resistance value. For example, when the resistance value showed a resistance of 1 M ohm or more, it was determined that the forming was completed. The voltage at the end of the forming is referred to as the energized forming voltage Vform.

As described above, the energization forming process is performed by applying a triangular wave pulse between the electrodes of the element, but the waveform to be applied is not limited to a triangular wave.
A waveform such as a rectangular wave may be used, and the peak value, pulse width, pulse interval, and the like are not limited to the values described above. A desired value may be selected according to the resistance value of the thin film or the like.

(4) Next, the element which has been subjected to the energization forming is subjected to a processing called energization activation processing. The energization activation process is a process of repeatedly applying a pulse having a constant peak value of a voltage pulse in a vacuum of about 10 −4 to 10 −5 [torr], similarly to the above-described energization forming processing. Means This is a process of remarkably changing the device current If and the emission current Ie by depositing carbon and a carbon compound from the organic substance existing in the vacuum on the electron emission portion 105. In this process, the activation process ends when the emission current Ie is saturated, for example, while measuring the element current If and the emission current Ie. The degree of progress of the activation process depends on the degree of vacuum, the pulse voltage applied to the element, and the like. This process changes the state of formation of the film near the thin film that has been deformed and altered by the energization forming process.

(5) The thus-produced electron-emitting device is driven in a vacuum atmosphere having a degree of vacuum higher than that of the activation processing. The vacuum atmosphere having a degree of vacuum higher than the degree of vacuum subjected to the activation treatment is a vacuum having a degree of vacuum of about 10 −6 [torr] or more, more preferably an ultra-high vacuum,
This is a degree of vacuum at which carbon and carbon compounds hardly newly accumulate near the electron-emitting portion even if current is applied between the device electrodes by display driving or the like thereafter. This makes it possible to suppress further deposition of carbon and carbon compounds, and the device can be used in a state where the device current If and the emission current Ie are constant and stable.

FIG. 7 is a graph showing the electron emission characteristics of the surface conduction electron-emitting device manufactured as described above.

As is apparent from FIG.
Exceeds the threshold voltage Vth, the element current If starts to flow,
It can be seen that the emission current Ie increases accordingly.

The potential distribution of a system including such a surface conduction electron-emitting device and an accelerating electrode is as shown in the schematic diagram of FIG. 8 when viewed on a plane substantially perpendicular to the electron emission portion 105 of the surface conduction electron-emitting device. , Can be approximately expressed by the following two-dimensional electric field.

[0048]

(Equation 1)

In the equation (1), d corresponds to the effective width of the electron emitting portion (crack) 105. FIG.
The horizontal axis along the anode 103 is the x-axis, and the direction toward the acceleration electrode perpendicular to the x-axis is the z-axis. FIG. 8 illustrates an equipotential surface obtained by integrating this electric field. As shown in FIG. 8, a point 700 at which the electric field stagnates (the x coordinate is xS), that is, a point where the electric field is zero is located at a position satisfying the following relational expression, measured from the center of the electron emission unit 105. .

[0050]

(Equation 2)

In this equation (2), the approximation equal to the second day is an equation that holds when Vf / d≫Va / H (sufficiently holds for a display panel using a surface conduction electron-emitting device). . The position represented by the x coordinate (xS) is called a stagnation point.

According to the electric field distribution and the electron trajectory calculation of the surface conduction electron-emitting device of the present embodiment, it has become clear that the following has occurred. (A) For some reason, electrons are emitted into the vacuum from the vicinity of the tip of the anode 103 near the electron emission portion (crack) of the surface conduction electron-emitting device. (B) The electrons thus emitted consist of the cathode 102 and the anode 1
The electron that moves in the electric field formed by the anode electrode 154 and the anode electrode 154 moves to the anode electrode 154 side due to the electric field of the anode electrode 154. (C) In a region where the electric field generated by the anode electrode 154 is not dominant, electrons fall again on the anode 103 (the thin film 104) due to the radial electric field generated by the cathode 102 and the anode 103, and a part is absorbed by the anode 103 ( Some of the other electrons are now scattered and redirected (because the electrons have a negative polarity) and are again released into the vacuum. As described above, the electrons in the region where the electric field from the anode electrode 154 is not dominant are absorbed when the electrons collide with the anode 103, or this scattering is repeated until the electrons can escape to the region where the electric field by the accelerating electrode 154 becomes dominant. . At this time, the anode 103
The electrons that have not been absorbed by the electrodes and have reached the region where the electric field of the anode electrode 154 is dominant are attracted to the anode electrode 154 and reach there.

Further, in the surface conduction electron-emitting device of the present embodiment, when the electron is emitted, the energy of the electron is 1 unit.
The electron-emitting device has a very small kinetic energy of 0 [eV]. Therefore, the quantum mechanical wavelength of the electron becomes as large as 0.4 [nm], and it is considered that the electron is governed by the (one) quantum mechanical effect.
Therefore, all the electrons are not absorbed by the surface of the anode 102, and some of the electrons are scattered (backward) and re-emitted into the vacuum (diffuse reflection). The electron wavelength is 0.4
Since it is about [nm], it is considered that electrons are scattered without distinguishing the atomic structure on the surface of the anode 103. That is, it can be considered that the surface of the anode 103 looks sufficiently smooth for electrons. Therefore, the electrons can be considered to be elastically scattered due to (one) quantum mechanical effect. Furthermore, when transmitted through a vacuum, there is no interaction with others, so it seems that there is no problem even if it is regarded as a classical charged particle. The potential of the anode electrode 154 is 1 [K
V], the electron velocity is as small as about 2% of the speed of light, and the relativistic effect can be ignored.

Also, of the electrons that collided on the anode 103,
(Backward) The electrons that have not been elastically scattered interact with electrons, phonons, etc. in the vicinity of the surface of the anode 103 and lose energy, a part of which is absorbed, and the rest is converted into inelastic scattered electrons again in vacuum. To be released again. However, this inelastic scattered electron is considered to be negligible from the property of (classical) electron orbit calculation described below. In other words, as described below, the trajectory of an electron changes its scaling constant exponentially with respect to the kinetic energy of the electron, so if the energy is lost, the number of scattering of the electron will increase sharply according to the energy. The majority of the electrons are the anode 103
It can be ignored because it seems to be absorbed by

On the other hand, electrons that have collided with the anode electrode 154 have energy of about 1000 [eV], so that most of them are absorbed as they are, and those that are reflected and scattered can be ignored. In fact, when such a physical system is applied to an image forming apparatus, a phosphor is arranged on the anode electrode 154 to emit light. Therefore, the anode electrode 15
At the boundary of No. 4, the simulated electron of the electron orbit calculation device is a non-scattering boundary where scattering is not performed.

The electron trajectory calculation device of the present embodiment is applied to a system having such physical characteristics.

The electron trajectory calculation device of the present embodiment will be described again. A virtual electron emission system is assumed for the surface conduction type emission device as described above.

FIG. 9 is a diagram schematically showing a system in which electron emission is performed in this computer.

In the figure, reference numerals 11, 12, and 13 denote a virtual cathode 11, a virtual anode 12, and an electron emitting portion 13, respectively, of the virtual electron emitting device. 14 is virtual acceleration (anode)
Electrodes. In this virtual electron emission device, an electron emission (crack) portion 13 exists between the cathode portion 11 and the anode portion 12. Here, the potential of the accelerating electrode 14 is Va [V],
Is 0 [V], and the potential of the anode 13 is Vf [V]. The distance between the virtual electron-emitting device and the virtual acceleration electrode 14 is H. Since these correspond to the respective physical quantities described above, the same symbols are used. Further, it is assumed that the electrodes 11, 12 and the electron emitting portion 13 are on a two-dimensional plane, and that there is no influence from the boundary between the electrodes. Further, since the electron emitting portion 13 has a linear shape, the physical dimension of this physical model is basically two-dimensional in terms of symmetry. In addition, the width of the crack in the electron-emitting portion 13 is assumed to be as close as possible to "0", and its size is ignored electrostatically below. Further, it is assumed that the distance between the virtual acceleration electrode 14 and the virtual electron emission unit 13 is sufficiently long as compared with the current distance of interest. These assumptions are justified by the actual arrangement, shape, and the like of an electron-emitting device using a surface conduction electron-emitting device described later.

The electric field distribution of the virtual electron-emitting device having such a shape is such that an axis perpendicular to the x-plane is defined as an x-plane on the anode 12 of the virtual electron-emitting device in a plane perpendicular to the electron-emitting section 13. z. Then, when the origin of these coordinates is taken to the electron emission unit 13,

[0061]

(Equation 3)

(See FIG. 10). This is obtained by ignoring d in the above equation (1) (d = 0). In this electric field distribution, the above-mentioned electric field stagnation point 700, that is, x of the stagnation point where the electric field becomes zero,
The coordinates (xS) are exactly

[0063]

(Equation 4)

Is obtained. This value is an amount having a dimension of only one length in a virtual electron emission element of a physical model electrostatically.

Accordingly, Va = 0 at which the coordinate value xS diverges.
In this regard, there is no characteristic length in the system electrostatically. That is, the system has a similar symmetry or a conformal symmetry.

In such an idealized virtual electron-emitting device, the electron trajectory when Va> 0, as shown in FIG. 10, repeats multiple scattering to reach the accelerating electrode 14, or The light is absorbed by the anode 12 of the electron-emitting device. Such calculations can be made by incorporating the effects of isotropic scattering and absorption by Monte Carlo.

However, the purpose of this embodiment is to further simplify the calculation, to reduce the calculation time and the calculation cost.

First, the behavior of the electrons at Va = 0 is considered, and the distribution of the falling (landing) points of the electrons at that time is derived.
As a physical model of the surface conduction electron-emitting device, it is assumed that the electron emission position is isotropically emitted from the vicinity of the tip of the anode 12 of the virtual electron-emitting device, that is, from a point d / 2 away from the electron emission portion 13 having no thickness. I do. This is a thick electron emission part 1
(Va)
The electron trajectory assuming multiple scattering at = 0 is shown in FIG. 11). This assumption is evaluated under analysis with experimental values.

Now, let us consider an electron isotropically emitted at a certain position x0 on the surface of the anode 12 of the virtual electronic element.
The orbit of each electron is

[0070]

(Equation 5)

According to the Newton equation given by
In the equation (5), me represents the mass of an electron, and e represents the charge of the electron.

At this time, assuming isotropic emission, the distribution f (x) of the landing point distribution of the virtual electrons integrated in the y direction is shown in FIG.
2 and as shown in FIG.

[0073]

(Equation 6)

This is again called a landing point distribution. Here, N is a normalized constant, and f (x) integrated over the entire area is "1".
It is made to become. g (x) is shown in FIG. FIG.
Is linear for position x and distribution, and FIG. 13 is logarithmic for both position x and distribution. As is clear from FIG. 12 or the aforementioned equation (6), when Cx0>x> x0, a significant feature is that the distribution function is substantially proportional to 1 / x. C changes depending on the initial energy of virtual electrons. The value of C will be described later.

Since there is no characteristic length dimension in the system, the distribution of landing points of electrons depends only on the scale of several times the emission position. In order to take this product structure into account, taking into account the distribution measure dx,

[0076]

(Equation 7)

When the coordinate transformation is performed, the above distribution function f
(X, x0) is

[0078]

(Equation 8)

Is converted to

[0080]

(Equation 9)

Is obtained. This distribution function is scale invariant where ξ is greater than ξ0.

Therefore, for simplicity, in the present embodiment, F (Ｆ) and f (x) are

[0083]

(Equation 10)

[0084]

[Equation 11]

As a function, only (ξ> ξ0 (x> x0)) is treated as a function, and the effect of G (ξ) is taken only by the normalized constant. However, θ (x) is a Heaviside function (also called a step function),

[0086]

(Equation 12)

Is a function defined as

Since such a landing point distribution has no characteristic length in the system when Va = 0, when the position of the emission point x0 is determined, it depends on the distance from the center of the electron emission portion 13. It is similar. Therefore, consider the effect of multiple scattering. That is, it is assumed that when the virtual electrons fall on the anode 12 of the virtual electron-emitting device, they are stochastically elastically reflected and the scattering distribution is isotropic and elastically scattered. Here, assuming that the scattering probability is β, the distribution ftotal (x) of the electrons to be finally absorbed by the anode 12 is

[0089]

(Equation 13)

Here, f0 (x) represents the first virtual electron emission distribution,

[0091]

[Equation 14]

[0092] In the expression (14), δ represents a delta function. This equation (14) is referred to as a total landing point distribution.

The effect obtained when Va ≠ 0 is taken into the final distribution of all landing points obtained in this manner by the following algorithm. That is, the distance d / 2 from the tip of the anode 12
The ratio の of the number of electrons reaching the accelerating electrode 14 with respect to all the electrons ejected from the position of corresponds to the number of electrons that have fallen from the electron emitting portion 13 to a place that is a constant multiple of the stagnation point (xS). Assume.

[0094]

(Equation 15)

Assume that Here, α is a function of a parameter space characterizing the system described below, and takes a real value. In the present embodiment, α = 1.0.

This value is called an electron arrival rate, and calculating the electron arrival rate under the various approximations described above is the measurement algorithm of the electron trajectory calculator of the present embodiment.

Now, when the scattering rate β is small, the equation (1)
3) performs a sufficiently fast convergence of β, so that equation (1)
The infinite series of 3) can be approximated by a polynomial regarding β. Therefore, in the present embodiment, is to calculate an approximate expression of Expression (13).

Here, the maximum arrival position Cx0 (formula (6)) when electrons are emitted from the point x0 on the anode 12 of the electron-emitting device with a certain kinetic energy will be described. C is a scaling parameter determined by the kinetic energy of the electrons at the time of emission, as described above. Here, the kinetic energy at z = 0 is given by (eVf-Wf), and thus becomes a function of the device voltages Vf and Wf. . Here, Wf is a work function on the anode 12 of the virtual electron-emitting device. According to a detailed calculation, this constant C can be expressed by the following equation.

[0099]

(Equation 16)

Here, eVf (Wf + eVf) = ｛2+
Noting that (eVf−Wf) / eVf｝ is the −1 power, this function C is a function of the magnitude (eVf−Wf) of the electron kinetic energy at z = 0 and the potential Vf between the electrodes. Can be considered. That is, assuming that the kinetic energy of the electron at z = 0 is K, C = C (K, Vf). Here, considering that K / (eVf) becomes small with respect to a small K and the characteristic of the exponential function, C becomes K
It can be seen that the smaller the is, the sharper it becomes. Therefore, when C in Expression (6) becomes smaller, the arrival distance of electrons also becomes shorter in proportion thereto, and multiple scattering must be repeated in order to reach the integration region of Expression (15). However, each time such scattering is repeated, the aforementioned scattering rate β is multiplied by a factor.
When x of the landing distribution of electrons having
The distribution will decrease sharply. That is, even if there is an electron having a small kinetic energy, it is considered that the contribution of such an electron to Expression (15) is extremely small.
Accordingly, the influence of scattering (inelastic scattering) accompanied by a decrease in energy is due to the electron arrival rate ζ in equation (15).
Is negligible in the calculation of. That is, only the elastic scattering that conserves the energy of the electrons needs to be considered.

Therefore, the parameters input from the input unit 1 include the work function W of the anode 12 of the virtual electron-emitting device.
f, the potential Va of the accelerating electrode 14, the distance H between the element and the accelerating electrode 14, the potential Vf between the electrodes 11 and 12 of the element, the scattering efficiency β, the electron emission position at the tip of the anode 12, and the actual element If the distance d between the electron emitting portions (cracks) is d, there is a crack length d and a distribution f0 (x) of the first electron emitting points.

A description will be given with reference to a flowchart 1 showing a calculation method of the electron trajectory calculation apparatus according to the present embodiment.

First, in step S1, the above-mentioned various parameters are input from the input unit 1. Next, in step S2,
When the potential Va of the virtual accelerating electrode 14 is 0, the maximum arrival position Cx0 is obtained by the above-described equation (16), the landing point distribution f (x, x0) is obtained by the equation (6), and the equation (13) is obtained. The electron distribution ftotal finally absorbed by the anode 12 is determined according to the following equation. Here, when calculating the integral series of Expression (13), the series is truncated at a point where β is sufficiently small. For example, in the present embodiment, the cutoff is performed at the fifth power of β.
In addition, the integration is a normal numerical integration (eg, Simpson's rule,
Numerical integration using a method such as Gaussian formula).

In step S3, the ratio の of the number of electrons reaching the accelerating electrode is calculated in step S3 for the landing point distribution thus obtained. These steps S
The processes 2 and 3 are numerically calculated by the arithmetic unit 5.

The process then proceeds to step S4, where the electron arrival rate 得 obtained in this way is output to the output unit 2 or the monitor 6
Output to

FIG. 14 shows experimental data and calculated values when the electron arrival rate ζ (emission current value Ie) thus obtained is plotted on the vertical axis and the voltage Va applied to the accelerating electrode is plotted on the horizontal axis. It is a graph which shows the relationship of. In FIG. 14, the distance between the element and the accelerating electrode is 5 mm, and the element voltage Vf is 14 mm.
[V], scattering probability β = 0.15, device electrode thickness D =
It is 3 nm.

In FIG. 14, “○” indicates the current value due to the electrons emitted from the surface conduction electron-emitting device at the accelerating electrode, and the curve indicates the electron arrival rate which is the result of calculation by the electron trajectory calculator of this embodiment. Is shown.

As described above, the electron trajectory calculation apparatus of the present embodiment can easily calculate the arrival rate of electrons, and obtained a calculation result that substantially matches the actual measured value.

Further, in the above-mentioned equation (13), the distribution of all landing points is calculated and defined only for the function f.
Similarly, the function F may be used. In that case, the calculation may be easier.

[Second Embodiment] In the second embodiment,
The measurement is performed on the same virtual electron-emitting device by the same apparatus as in the first embodiment and the processing shown in FIG. 1. In the second embodiment, the distribution of all the landing points of the electrons on the virtual electrode is expressed by the following equation. This is performed without using (6) and (13). That is, according to the electron emission distribution set as the initial condition, the electrons are calculated in the state of Va = 0 according to the equation of motion (Equation (5)) as shown in FIG. At this time, the distribution of multiple scattering and absorption and scattering of electrons on the anode 12 of the virtual electron emission element is dealt with by performing Monte Carlo calculation. If necessary, this device can also deal with inelastic scattering such as secondary electron scattering by Monte Carlo calculation. This makes it possible to calculate the landing point distribution f (x) of the electrons under the boundary condition of a more arbitrary shape.

Using this method, the electron arrival rate can be calculated by using the equation (15) in the same manner as in the flowchart 1 of the first embodiment.

These calculation methods are of the Spindt type or the so-called model Field Emitter (for example, J. Itoh).
In Technical Digest of IVMC 91 ed by S. Namba, YN
An electron emission device using an annichi, and T. Utsumi) is also effective. That is, in the electron emission device using the Spindt-type or the horizontal-type Field Emitter in the device capable of calculating the electron trajectory under arbitrary boundary conditions according to the second embodiment, the potential at the acceleration electrode potential (Va = 0) is used. By calculating the drop point distribution of the electrons, the electron arrival rate at the accelerating electrode when the potential of the accelerating electrode is not zero is calculated by the above-mentioned equation (1).
It can be obtained by substituting 5) into the modified equation and calculating.

The present invention can be applied to a system including a plurality of devices (for example, a host computer, an interface device, a reader, a printer, etc.), but can be applied to a single device (for example, a copying machine, a facsimile). Device).

An object of the present invention is to provide a storage medium storing a program code of software for realizing the functions of the above-described embodiments to a system or an apparatus, and to provide a computer (or CPU) of the system or apparatus.
Or MPU) reads and executes the program code stored in the storage medium.

In this case, the program code itself read from the storage medium realizes the functions of the above-described embodiment, and the storage medium storing the program code constitutes the present invention.

Examples of a storage medium for supplying the program code include a floppy disk, hard disk, optical disk, magneto-optical disk, CD-ROM, and CD.
-R, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.

When the computer executes the readout program code, not only the functions of the above-described embodiment are realized, but also the OS (Operating System) running on the computer based on the instruction of the program code. ) Performs part or all of the actual processing, and the processing realizes the functions of the above-described embodiments.

Further, after the program code read from the storage medium is written into a memory provided in a function expansion board inserted into the computer or a function expansion unit connected to the computer, based on the instruction of the program code, The case where the CPU of the function expansion board or the function expansion unit performs part or all of the actual processing, and the function of the above-described embodiment is realized by the processing.

As described above, according to the present embodiment, when electrons emitted from the electron-emitting device are scattered, the electron arrival rate is reduced by the characteristic of the electron orbital of the electron-emitting device. It can calculate efficiently and accurately in a short time.

As a result, the design and development of an electron-emitting device, particularly, a surface conduction electron-emitting device can be efficiently performed.

[0121]

As described above, according to the present invention, it is possible to estimate the trajectory of electrons in a system in which emitted electrons are reflected and scattered, and to quantify the amount of electrons reaching the accelerating electrode to be emitted. This has the effect.

Further, according to the present invention, there is an effect that the amount of electrons reaching the target acceleration electrode can be obtained with a reduced amount of calculation.

[0123]

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating an algorithm for orbit calculation in an electron orbit calculation device according to an embodiment of the present invention.

FIG. 2 is a block diagram illustrating a schematic configuration of an electron trajectory calculation device according to the present embodiment.

3A and 3B are diagrams illustrating a basic configuration of a surface conduction electron-emitting device according to the present embodiment, wherein FIG. 3A is a plan view and FIG. 3B is a cross-sectional view.

FIG. 4 is a diagram illustrating a manufacturing process of the surface conduction electron-emitting device of the present embodiment.

FIG. 5 is a block diagram illustrating a configuration of a measurement and evaluation device for a surface conduction electron-emitting device according to the present embodiment.

FIG. 6 is an explanatory diagram of a pulse waveform applied between device electrodes in a manufacturing process of the surface conduction electron-emitting device of the present embodiment.

FIG. 7 is a graph illustrating electron emission characteristics of the surface conduction electron-emitting device of the present embodiment.

FIG. 8 is a diagram illustrating an electric field distribution and emission of electrons when electrons are emitted from the surface conduction electron-emitting device of the present embodiment.

FIG. 9 is a model diagram showing the arrangement of virtual electron-emitting devices and acceleration electrodes for explaining electron trajectory calculation according to the present embodiment.

FIG. 10 is a diagram showing a reaching path of emitted electrons in the virtual model of the present embodiment.

FIG. 11 is a diagram showing a reaching path of emitted electrons in the virtual model of the present embodiment.

FIG. 12 is a diagram illustrating a distribution of landing points of emitted electrons in the virtual model according to the present embodiment.

FIG. 13 is a diagram illustrating the distribution of landing points of emitted electrons in the virtual model of the present embodiment in a logarithmic manner with respect to the position x and the distribution.

FIG. 14 is a diagram illustrating a relationship between a calculation result obtained by the electron trajectory calculation apparatus according to the present embodiment and an emission current value obtained by an experiment.

FIG. 15 is a diagram showing a basic configuration of a conventional surface conduction electron-emitting device.

Claims (15)

[Claims] 1. A trajectory calculation device for calculating a trajectory of a charged particle emitted from an electron-emitting device, wherein the electron-emitting device and an electron emitted from the electron-emitting device are accelerated directly above the electron-emitting device. And a first calculating unit that calculates a distribution of landing points at which electrons emitted from the electron-emitting device fall near the electron-emitting device without considering the influence of the acceleration electrode, A second calculating means for calculating an arrival rate of electrons from the electron-emitting device to the accelerating electrode based on the landing point distribution calculated by the first calculating means, in consideration of an influence of a voltage applied to the accelerating electrode; A trajectory calculation device comprising: 2. The trajectory calculation apparatus according to claim 1, wherein the first calculation means calculates a stagnation point at which the electric field in the system becomes substantially zero. 3. The coordinate value of the stagnation point is given by: x = Vf · H / πVa, where x-coordinate position where electrons are emitted is zero.
The orbit according to claim 2, wherein (Vf is a voltage applied to the electron-emitting device, H is a distance between the electron-emitting device and the acceleration electrode, and Va is a voltage applied to the acceleration electrode). Computing device. 4. The apparatus according to claim 1, wherein the first calculating means calculates the landing point distribution using an approximate polynomial relating to a probability that the emitted electrons are multiple-scattered on the electron-emitting device. Orbit calculator as described. 5. The method according to claim 2, wherein the second calculating means calculates the arrival rate of the electrons by integrating the landing point distribution in a direction away from a position that is a predetermined multiple of the stagnation point. Orbit calculator as described. 6. The trajectory calculation apparatus according to claim 1, wherein said electron-emitting device is a surface conduction electron-emitting device. 7. The trajectory calculation device according to claim 6, wherein the electrons are emitted from an electron emission portion of the surface conduction electron-emitting device and land on an anode of the surface conduction electron-emitting device. 8. A trajectory calculation method for calculating a trajectory of charged particles emitted from an electron-emitting device, comprising: accelerating an electron-emitting device and electrons emitted from the electron-emitting device in a direction directly above the electron-emitting device. A first calculating step of calculating a distribution of landing points at which electrons emitted from the electron-emitting device fall near the electron-emitting device without considering the influence of the acceleration electrode, A second calculation step of calculating an arrival rate of electrons from the electron-emitting device to the acceleration electrode when considering an influence of a voltage applied to the acceleration electrode based on the landing point distribution calculated in the first calculation step; A trajectory calculation method comprising: 9. The trajectory calculation method according to claim 8, wherein in the first calculation step, a stagnation point at which the electric field in the system becomes substantially zero is calculated. 10. The coordinate value of the stagnation point is x = Vf · H / πVa, where x-coordinate position where electrons are emitted is set to zero.
The trajectory according to claim 9, wherein (Vf is a voltage applied to the electron-emitting device, H is a distance between the electron-emitting device and the acceleration electrode, and Va is a voltage applied to the acceleration electrode). Method of calculation. 11. The method according to claim 8, wherein in the first calculation step, the landing point distribution is calculated using an approximate polynomial relating to a probability that the emitted electrons are multiple-scattered on the electron-emitting device. Orbit calculation method described. 12. The method according to claim 9, wherein in the second calculating step, the arrival rate of the electrons is obtained by integrating the landing point distribution in a direction away from a position that is a predetermined multiple of the stagnation point.
Or the trajectory calculation method according to 10. 13. The trajectory calculation method according to claim 8, wherein said electron-emitting device is a surface conduction electron-emitting device. 14. The trajectory calculation method according to claim 13, wherein the electrons are emitted from an electron emission portion of the surface conduction electron-emitting device and land on an anode of the surface conduction electron-emitting device. 15. A trajectory calculation method for calculating the trajectory of charged particles emitted from an electron-emitting device, comprising: an electric field of a system including an electron-emitting device and an accelerating electrode provided substantially parallel to the electron-emitting device. Approximating the distribution, taking the direction of the positive electrode of the electron-emitting device on the x-axis,
The origin of the axis is the point from which the electrons are emitted, the position xS on the x-axis at which the electric field generated on the positive electrode is substantially zero, and the landing point on the x-axis with the position xS as a proportional coefficient A trajectory calculation method, wherein an amount of electrons reaching the acceleration electrode is obtained based on an area of the distribution.