CN102680503A - Method for determining secondary electron emission characteristics of rough metal surfaces - Google Patents

Abstract

The invention relates to a method for determining the secondary electron emission characteristics of rough metal surfaces. The method is provided for judging whether electrons enter a material, and is utilizing for judging whether the electrons enter again after getting out of the material, consequently, the multiple interactions between the electrons and a rough metal surface are taken into full consideration, and by means of statistical analysis on a large quantity of electrons, the secondary electron emission characteristic of the metal material is obtained. According to the method, since the multiple interactions between the electrons getting away frsom the surface of the material and the rough surface are taken into full consideration, the obtained secondary electron emission characteristic is matched with an experimental result, and moreover, the method can be adopted to analyze the secondary electron emission characteristics of any surface morphologies, and can be used for researching the law between surface morphologies and secondary electron emission characteristics so as to provide theoretical direction for searching surface morphologies capable of inhibiting secondary electron emission.

Description

A kind of method of definite roughened metal surface secondary electron emission characteristic

Technical field

The invention discloses a kind of method of definite roughened metal surface secondary electron emission characteristic, belong to the Physical Electronics field.

Background technology

The interaction of electron beam and material is a very important field in the Physical Electronics research, and the secondary that is wherein excited by incident electron (being also referred to as secondary electron emissions) phenomenon has important use at modern electronic equipments such as scanning electron microscope, Auger electron spectrometer and electron multiplier and device.For example: in electron micrology and surface electron spectrum analysis, adopt the beam bombardment sample; The scattering of in material, passing through electronics produces the various characteristic signals of exosyndrome material character, thus various microscopic properties such as the crystal structure of acquisition material, constituent, electronic structure, surface topography, inherent vice.

Secondary not only relates to the scattering process of electronics at material internal, and electronics also can interact with material surface behind the outgoing material.The physical process of electronics after the material surface outgoing is remarkable to the influence of secondary electron emission characteristic, and this also is the experimental data of many secondary electron emission characteristics and the major reason that notional result can't be coincide.The method of confirming the secondary electron emission characteristic of material at present is divided into two big types: the one, go out analytic formula approximate description secondary electron emission characteristic through experimental fit; The 2nd, through the emission process of DSMC simulation secondary electron, obtain the secondary electron emission characteristic of material.The existing scheme overwhelming majority only is applicable to level and smooth material surface, has promptly only considered the physical process of electronics at material internal.And for real material, the surface is not desirable smooth flat, and it has certain roughness, and promptly the pattern on surface rises and falls.In individual other disposal route, adopt only as the secondary electron emission characteristic of probability method statistics electronics, ignored secondary electron when outgoing with the repeatedly interaction process on surface.

Summary of the invention

The objective of the invention is to overcome the above-mentioned deficiency of prior art; A kind of method of definite roughened metal surface secondary electron emission characteristic is provided; When this method has been considered electronics outgoing material surface and the repeatedly interaction of rough surface, the secondary electron emission characteristic and the experimental result of acquisition are more identical.

Above-mentioned purpose of the present invention mainly is achieved through following technical scheme:

A kind of method of definite roughened metal surface secondary electron emission characteristic comprises the steps:

(1) rough surface morphology to material characterizes, if material surface pattern rule is divided into rectangular node with surface topography, in the rectangular node arbitrarily the fluctuating of some height h adopt analytic expression to represent, and confirm the fluctuating height h that the surface is maximum _MaxIf material surface is the irregular surfaces pattern; Adopting microscope to carry out surface topography extracts; Adopt the method for rectangular node point to sample; And set up two Dimension Numerical and describe surface topography, obtain in the rectangular node point of surface topography maximal value h of all height h that rise and fall of the fluctuating of some height h and surface arbitrarily _Max

(2) with electronics from A _I-1Point moves to A _iThe length of the straight-line trajectory of point is designated as t _i, with electronics from A _iPoint moves to A _I+1The length of the straight-line trajectory of point is designated as t _I+1, t then _I+1Obtain by following recurrence relation, then:

$t_{i+1}=\left\{\begin{array}{cc}{t}_i+\min (t_x,t_y)& n_x\≠0,n_y\≠0\\ t_i+t_x& n_x\≠0,n_y=0\\ t_i+t_y& n_x=0,n_y\≠0\\ |h_i-z_i|& n_x=0,n_y=0\end{array}\right.$

$t_x=\left\{\begin{array}{cc}(a-x_i)/n_x& n_x>0\\ -x_i/n_x& n_x<0\end{array}\right.$

$t_y=\left\{\begin{array}{cc}(b-y_i)/n_y& n_y>0\\ -y_i/n_y& n_y<0\end{array}\right.$

Wherein:

When electronics is in reference position or electronics free path starting point, make t ₁=0; I=1,2,3 ...;

(x _i, y _i) be A _iThe local coordinate of spot projection in the corresponding rectangle grid, z _iBe A _iSpot projection is perpendicular to the coordinate on the z axle of rectangular node;

(x _I+1, y _I+1) be A _I+1The local coordinate of spot projection in the corresponding rectangle grid, z _I+1Be A _I+1Spot projection is perpendicular to the coordinate on the z axle of rectangular node;

n _xAnd n _yBe respectively electron motion direction unit vector x and y to projection;

h _iBe local coordinate (x _i, y _i) corresponding surface undulation height;

(3) whether electronics with metal material surface interaction being taken place judges order

f＝(z _i-h _i)(z _i+1-h _i+1)

If f>=0 and z _I+1＞h _Max, showing that electronics can not interact with material, the energy and the direction of record electronics this moment get into step (8);

If f＞0 and z _I+1≤h _Max, show that electronics does not interact with metal material surface, makes t _i=t _I+1, return step (2);

If f≤0 shows that electronics is from A _iPoint moves to A _I+1Can pass material surface during point; If z _i-h _i＞0, show that electronics is from the outside material internal that gets into of material, gets into step (4); If z _i-h _i＜0, show electronics from the material internal outgoing, jump to step (6);

Wherein:

h _I+1Be local coordinate (x _I+1, y _I+1) corresponding surface undulation height;

(4) if electronics from the outside incident material internal of material, according to the incident direction of incident electron

Surface normal with the incidence point material

By energy conservation and the momentum conservation that electron motion satisfies, calculate the energy E of electron impact behind the material _iAnd direction of motion

E _i＝E _p+U ₀

$\stackrel{\&RightArrow;}{n_i}=\sqrt{\frac{E_p}{E_p+U_0}}\stackrel{\&RightArrow;}{n_p}+(\sqrt{\frac{E_p}{E_p+{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="HSA00000709748900031.png,HSA00000709748900032.png"\; state="\{\{state\}\}">U</figure-callout>}}_0}}\cos \mathrm{\&theta;}-\sqrt{\frac{{\mathrm{<figure-callout\; id="2"\; label="E\; p\; cos"\; filenames="HSA00000709748900031.png,HSA00000709748900041.png"\; state="\{\{state\}\}">E</figure-callout>}}_p{\cos }^{}{}^2\mathrm{\&theta;}+U_0}{E_p+U_0}})\stackrel{\&RightArrow;}{N_i}$

Wherein:

E _pBe the incident electron energy;

U ₀Be built-in potential, U ₀=E _F+ Φ, E _FBe the Fermi level of material, Φ is the work function of material;

is the incident direction of incident electron;

is the surface normal of incidence point material;

θ is the angle of surface normal of incident direction and the incidence point material of incident electron,

(5) according to the electron energy E that incides material internal _iAnd direction of motion

Adopt the scattering process of DSMC simulation electronic in material of conventional ideal surfaced, follow the trail of the track of incident electron and secondary electron, write down the electron energy E of each scattering _j, the electron motion direction Free path S with electronics _j, j=1 wherein, 2 ..., m, to electronics at every section free path S _jInterior rectilinear motion is handled according to step 2 and step 3;

(6) when electron motion arrived material surface, recorded electronic was from the position (x of material surface outgoing _m, y _m, z _m), according to the electronic motion direction Normal direction with the eye point material

Calculate electronics exit probability T:

Wherein:

Direction when

arrives material surface for electron motion;

is the normal direction of eye point material;

is the angle of electron motion direction and eye point material normal direction,

E _mEnergy during for electronics outgoing material surface;

(7) go up generation random number R ND in interval [0,1],

If T≤RND then makes electronics reflect on the surface, reflection back electronics is still with energy E _mContinuation is scattering in material, and direction of motion does

Jump to step (5) then;

If T＞RND then makes the electronics outgoing, the energy of electronics is E after the outgoing _s, direction of motion does

E _s＝E _m-U ₀

Return step (2)

(8) change the incident electron energy E _p, repeating step (2)～(7), the secondary electron direction of motion and the energy of record outgoing are added up the outgoing electron number under the different incident electron energy, obtain the secondary electron yield of said material; The direction and the energy of statistics outgoing electron, the secondary electron power spectrum and the exit direction that obtain said material distribute.

In the method for above-mentioned definite roughened metal surface secondary electron emission characteristic, in the step (1) if material surface is the irregular surfaces pattern, then in the rectangular node point of surface topography arbitrarily the fluctuating of some height h adopt the method acquisition of first-order linear interpolation, that is:

$h=h_{\mathrm{lu}}+\frac{h_{\mathrm{ru}}-h_{\mathrm{lu}}}{a}m+\frac{h_{\mathrm{ld}}-h_{\mathrm{lu}}}{b}n+\frac{h_{\mathrm{rd}}+h_{\mathrm{lu}}-h_{\mathrm{ru}}-h_{\mathrm{ld}}}{\mathrm{ab}}\mathrm{mn}$

Wherein:

(m n) is any point coordinate in the rectangular node under the local coordinate;

H is any fluctuating of some height in the rectangular node point;

h _LuFluctuating height for the rectangle upper left corner;

h _LdFluctuating height for the rectangle lower left corner;

h _RuFluctuating height for the rectangle upper right corner;

h _RdFluctuating height for the rectangle lower right corner;

A is the length of rectangular node point;

B is the wide of rectangular node point.

The present invention compared with prior art has following beneficial effect:

(1) the present invention has taken into full account the repeatedly interaction of the rough surface of electronics and metal reality, and the secondary electron emission characteristic and the experimental result of acquisition are more identical;

(2) novelty of the present invention provided judge electronics whether with the method for material surface interactions; Utilize this method can judge that electronics is after the material internal outgoing; Incident whether once more; Thereby considered behind the electronics outgoing material surface the repeatedly interaction with rough surface, the secondary electron emission characteristic of the metal material that obtains to coincide more with experimental result;

(3) the present invention has used the interaction of describing electronics and roughened metal surface near the method for electronics actual motion process, has disclosed the microscopic nature of electronics and Rough Metal Surface effect;

(4) the present invention can analyze the secondary electron emission characteristic of arbitrary surfaces pattern, can be used for studying the rule of surface topography and secondary electron emission characteristic, for exploring the surface topography that can suppress secondary theoretical direction is provided.

Description of drawings

Fig. 1 is the local coordinate system of irregular surfaces pattern rectangular node point of the present invention;

Fig. 2 is the synoptic diagram of cutting apart of trajectory of electron motion of the present invention;

Fig. 3 is the energy changing figure of electron impact of the present invention to material internal;

Fig. 4 is the energy changing figure of electronics of the present invention from the material internal outgoing;

Fig. 5 is the structural representation of rectangular channel in the embodiment of the invention;

Fig. 6 is the local coordinate system of the rectangular node point of rectangular channel in the embodiment of the invention;

Fig. 7 is electronic motion stepping in the embodiment of the invention;

Secondary electron yield that Fig. 8 obtains for the inventive method and experimental result, bibliographical information result's contrast synoptic diagram.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment the present invention is described in further detail:

The present invention confirms the flow process of the method for roughened metal surface secondary electron emission characteristic, mainly comprises following step:

Step 1,

The metal material surface pattern is characterized, if regular morphology is divided into rectangular node with surface topography, in the rectangular node arbitrarily the fluctuating of some height h adopt analytic expression to represent, and confirm the fluctuating height h that the surface is maximum _Max

If non-regular morphology adopts atomic force microscope or laser microscope to carry out surface topography and characterizes, adopt the method for rectangular node point to sample, and set up two Dimension Numerical and describe surface topography.Each element of array is corresponding to a point on the surface topography, the height h of its value to putting.The method acquisition of the height h of some employing first-order linear interpolation arbitrarily in the rectangular node, as shown in the formula:

$h=h_{\mathrm{lu}}+\frac{h_{\mathrm{ru}}-h_{\mathrm{lu}}}{a}m+\frac{h_{\mathrm{ld}}-h_{\mathrm{lu}}}{b}n+\frac{h_{\mathrm{rd}}+h_{\mathrm{lu}}-h_{\mathrm{ru}}-h_{\mathrm{ld}}}{\mathrm{ab}}\mathrm{mn}---\left(1\right)$

h _max＝max(h) (2)

h _MaxThe maximal value of all height h that rise and fall for the surface;

Be illustrated in figure 1 as the local coordinate system of irregular surfaces pattern rectangular node point of the present invention, true origin is positioned at the rectangle upper left corner; (m n) is any point coordinate in the rectangular node under the local coordinate; H is any fluctuating of some height in the rectangular node point; h _LuFluctuating height for the rectangle upper left corner; h _LdFluctuating height for the rectangle lower left corner; h _RuFluctuating height for the rectangle upper right corner; h _RdFluctuating height for the rectangle lower right corner; A is the length of rectangular node point; B is the wide of rectangular node point.

Step 2,

If electronics outside material, is divided into some segments with its straight-line trajectory; If electronics at material internal, is divided into some segments with the straight path between the double scattering of electronics, with electronics from A _I-1Point moves to A _iThe length of the straight-line trajectory of point is designated as t _i, with electronics from A _iPoint moves to A _I+1The length of the straight-line trajectory of point is designated as t _I+1, t then _I+1Obtain by following recurrence relation:

$t_{i+1}=\left\{\begin{array}{cc}{t}_i+\min (t_x,t_y)& n_x\&NotEqual;0,n_y\&NotEqual;0\\ t_i+t_x& n_x\&NotEqual;0,n_y=0\\ t_i+t_y& n_x=0,n_y\&NotEqual;0\\ |h_i-z_i|& n_x=0,n_y=0\end{array}\right.$

$t_x=\left\{\begin{array}{cc}(a-x_i)/n_x& n_x>0\\ -x_i/n_x& n_x<0\end{array}\right.---\left(3\right)$

$t_y=\left\{\begin{array}{cc}(b-y_i)/n_y& n_y>0\\ -y_i/n_y& n_y<0\end{array}\right.$

Wherein:

When electronics is in reference position or electronics free path starting point, make t ₁=0, i=1,2,3 ...;

(x _i, y _i) be A _iThe local coordinate of spot projection in the corresponding rectangle grid, z _iBe A _iSpot projection is perpendicular to the coordinate on the z axle of rectangular node; (x _I+1, y _I+1) be A _I+1The local coordinate of spot projection in the corresponding rectangle grid, z _I+1Be A _I+1Spot projection is perpendicular to the coordinate on the z axle of rectangular node; n _xAnd n _yBe respectively electron motion direction unit vector x and y to projection; h _iBe local coordinate A _i(x _i, y _i), the surface undulation height that adopts step 1 to calculate.

Be illustrated in figure 2 as the synoptic diagram of cutting apart of trajectory of electron motion of the present invention.

Step 3,

Whether electronics with metal material surface interaction is taken place judge order

f＝(z _i-h _i)(z _i+1-h _i+1) (4)

If f>=0 and z _I+1＞h _Max, showing that electronics can not interact with material, the energy and the direction of record electronics this moment get into step 8;

If f＞0 and z _I+1≤h _Max, show that electronics does not interact with metal material surface, makes t _i=t _I+1, return step 2;

If f≤0 shows that electronics is from A _iPoint moves to A _I+1Can pass material surface during point; If z _i-h _i＞0, show that electronics is from the outside material internal that gets into of material, gets into step 4; If z _i-h _i＜0, show that electronics from the material internal outgoing, jumps to step 6.

Wherein:

h _I+1Be local coordinate A _I+1(x _I+1, y _I+1), the surface undulation height that adopts step (1) to calculate.

Step 4,

If electronics is from the outside incident material internal of material, according to the incident direction of incident electron

Surface normal with the incidence point material

By energy conservation and the momentum conservation that electron motion satisfies, calculate the energy E of electron impact behind the material _iAnd direction of motion

E _i＝E _p+U ₀ (5)

$\stackrel{\&RightArrow;}{n_i}=\sqrt{\frac{E_p}{E_p+U_0}}\stackrel{\&RightArrow;}{n_p}+(\sqrt{\frac{E_p}{E_p+{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="HSA00000709748900031.png,HSA00000709748900032.png"\; state="\{\{state\}\}">U</figure-callout>}}_0}}\cos \mathrm{\&theta;}-\sqrt{\frac{{\mathrm{<figure-callout\; id="2"\; label="E\; p\; cos"\; filenames="HSA00000709748900031.png,HSA00000709748900041.png"\; state="\{\{state\}\}">E</figure-callout>}}_p{\cos }^{}{}^2\mathrm{\&theta;}+U_0}{E_p+U_0}})\stackrel{\&RightArrow;}{N_i}---\left(6\right)$

Wherein:

E _pBe incident electron energy (with respect to vacuum level);

U ₀Be built-in potential, U ₀=E _F+ Φ, E _FBe the Fermi level of material, Φ is the work function of material;

E _iBe the energy (with respect to conduction band bottom) of electron impact to material internal;

is the incident direction of incident electron;

is the surface normal of incidence point material;

θ is the angle of surface normal of incident direction and the incidence point material of incident electron,

Be illustrated in figure 3 as the energy changing figure of electron impact of the present invention to material internal.

Step 5,

According to the electron energy E that incides material internal _iAnd direction Adopt the scattering process of DSMC simulation electronic in material of conventional ideal surfaced, follow the trail of the track of incident electron and secondary electron, write down the electron energy E of each scattering _j, the electron motion direction

Free path S with electronics _j(j=1,2 ..., m), to electronics at every section free path S _jInterior rectilinear motion is handled according to step 2 and step 3; E wherein _m,

S _mEnergy, direction of motion and free path when being respectively electronics from the material surface outgoing.

Step 6,

When electron motion arrived material surface, recorded electronic was from material surface eye point A _mPosition (x _m, y _m, z _m), according to the electronic motion direction

Normal direction with the eye point material

Calculate exit probability T:

Wherein:

Direction when

arrives material surface for electron motion;

is the normal direction of eye point material;

is the angle of electronics exit direction and eye point material normal direction,

E _mEnergy during for electronics outgoing material surface.

Step 7,

Go up generation random number R ND in interval [0,1], if T≤RND then makes electronics reflect on the surface, reflection back electronics is still with energy E _mContinuation is scattering in material.And direction of motion is

Jump to step 5 then.

If T＞RND then makes the electronics outgoing, the energy of electronics is E after the outgoing _s, direction of motion does

E _s＝E _m-U ₀ (9)

Jump to step 2 then.

Wherein:

E _sBe the energy (with respect to vacuum level) behind the electronics outgoing material;

is the direction of motion behind the electronics outgoing material.

Be illustrated in figure 4 as the energy changing figure of electronics of the present invention from the material internal outgoing.

Step 8,

Change the incident electron energy E _pRepeating step two～step 7; Record can outgoing secondary electron direction of motion and energy; Add up the secondary electron yield that outgoing electron number under the different projectile energies can obtain this metal material, the direction of statistics outgoing electron and secondary electron power spectrum that energy can obtain this metal material and exit direction distribution.

Embodiment

Impinge perpendicularly on the Au material surface with electronics, the Au material surface is the rectangular channel structure, and the parameter of rectangular channel is degree of depth 500nm, the wide 180nm of bottom land, the wide 25.4nm of cell wall, cycle 205.4nm.Fig. 5 has provided the structural representation of rectangular channel.

The rectangular channel structure is a regular morphology, can adopt analytic expression to represent.Divide the rectangular node point according to rectangular node local coordinate shown in Figure 6, the long limit a of rectangular node point is 205.4nm, and broadside b is an endless.The surface undulation of arbitrfary point is in the rectangular node:

$h=\left\{\begin{array}{cc}0& 0\&le;x<180\mathrm{nm}\\ 500& 180\mathrm{nm}\&le;x<205.4\mathrm{nm}\end{array}\right.$

Suppose that electronics initially is positioned at rectangular channel central authorities and vertical incidence surface, A ₁Position coordinates be (90, y ₁, 500) and (because rectangular channel does not have limit for width, y ₁Can be arbitrary value), it is at (the x that is projected as of rectangular node point ₁, y ₁)=(90, y ₁), A ₁Spot projection is perpendicular to the coordinate z on the rectangular node z axle ₁=500, A ₁The fluctuating height h of point ₁=0.According to step 2, t ₁=0, n _xAnd n _yBe respectively electron motion direction unit vector x and y to projection because vertical incidence, n _x=0 and n _y=0, next movement length t of electronics then ₂=| h ₁-z ₁|=500, next movement position A of electronics ₂For (90, y ₁, 0), A ₂Spot projection is perpendicular to the coordinate z on the rectangular node z axle ₂=0, A ₂The fluctuating height h of point ₂=0.Be illustrated in figure 7 as electronic motion stepping in the embodiment of the invention.

According to step 3, f=0, z ₁-h ₁＞0, show that electronics enters into material internal from the material outside.

According to step 4, the Fermi level E of gold copper-base alloy _F=5.1eV, work function Φ=5.1eV, built-in potential U ₀=10.2eV.The electronics vertical incidence; Angle theta=0 of the surface normal

of incident direction

and incidence point material; With incident electron energy 1000eV is example, energy E i and the direction of motion

of electron impact behind the material

E _i＝E _p+U ₀＝1010.2(eV)

$\stackrel{\&RightArrow;}{n_i}=\sqrt{\frac{E_p}{E_p+U_0}}\stackrel{\&RightArrow;}{n_p}+(\sqrt{\frac{E_p}{E_p+{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="HSA00000709748900031.png,HSA00000709748900032.png"\; state="\{\{state\}\}">U</figure-callout>}}_0}}\cos \mathrm{\&theta;}-\sqrt{\frac{{\mathrm{<figure-callout\; id="2"\; label="E\; p\; cos"\; filenames="HSA00000709748900031.png,HSA00000709748900041.png"\; state="\{\{state\}\}">E</figure-callout>}}_p{\cos }^{}{}^2\mathrm{\&theta;}+U_0}{E_p+U_0}})\stackrel{\&RightArrow;}{N_i}$

$=(2\sqrt{\frac{E_p}{E_p+U_0}}-1)\stackrel{\&RightArrow;}{n_p}$

Step 5 adopts the scattering process of DSMC simulation electronic in material of conventional ideal surfaced, writes down the electron energy E of each scattering _j, the electron motion direction

J=1 wherein; 2; ...; M, " the Monte Carlo Modeling for Electron Microscopy and Microanalysis " that concrete grammar can be shown referring to Chinese University of Science and Technology's doctorate paper " scanning electron microscopy learn in the Monte Carlo simulation that produces of secondary electron " and Divid C.Joy.

Suppose through step 5 the energy E of electronics _mBe 400eV, the electronic motion direction does

Surface normal with the eye point material

Angle be 80 °,

X axle and y axle be projected as 0.5 and 0.848, the local coordinate of eye point position be (200, y _m, 500) because z _m=h _m, judge f=0 according to step 3, and electronics has z when material internal moves _M-1＜h _M-1, jump to step 6.

According to step 6, because the probability T of

electronics outgoing:

According to step 7, go up generation random number R ND=0.6 in interval [0,1], since T＞RND, then electronics outgoing, and the energy of electronics is E after the outgoing _s, direction of motion does

E _s＝E _m-U ₀＝389.8(eV)

The exit direction of electronics and eye point normal direction angle are 68.6 °.

Return step 2, A _mThe point coordinate be (200, y _m, 500), the exit direction unit vector at x and y to being projected as 0.473 and 0.802.t _x=(205.4-200)/and 0.473=11.42, because b is infinitely great, obvious t _xMinimum, then t _M+1=t _m+ t _x=11.42, A _M+1Position coordinates be (205.4, y _m+ 9.16,504.16), A _M+1Spot projection is perpendicular to the coordinate z on the rectangular node z axle _M+1=504.16, A _M+1The fluctuating height h of point _M+1=500.

According to step 3, f=0 and z _M+1＞h _M+1, electronics can not interact with material, the energy E of record electronics this moment _sAnd direction

Get into step 8;

The step that provides is to specifications calculated, and makes projectile energy E _p=100eV, 200eV, 300eV; ..., 1900eV, 2000eV; 2500eV, 3000eV, repeating step two～step 7; Add up the outgoing electron number under the different projectile energies, can obtain the secondary electron yield of this metal material, the ratio of the secondary electron yield of this secondary electron yield and ideal plane is relative secondary electron yield; Its result is as shown in Figure 8, and Fig. 8 has provided secondary electron yield that the inventive method obtains and experiment, bibliographical information result's contrast synoptic diagram, but by Fig. 8 knowledge capital inventive method because when having considered electronics outgoing material surface and the repeatedly interaction of rough surface; The secondary electron emission characteristic and the experimental result that obtain are more identical, and the inventive method can be confirmed the secondary electron emission characteristic of metal material real surface.

The above; Be merely the best embodiment of the present invention, but protection scope of the present invention is not limited thereto, any technician who is familiar with the present technique field is in the technical scope that the present invention discloses; The variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.

The content of not doing to describe in detail in the instructions of the present invention belongs to this area professional and technical personnel's known technology.

Claims (2)

1. the method for a definite roughened metal surface secondary electron emission characteristic is characterized in that comprising the steps:

(1) rough surface morphology to material characterizes, if material surface pattern rule is divided into rectangular node with surface topography, in the rectangular node arbitrarily the fluctuating of some height h adopt analytic expression to represent, and confirm the fluctuating height h that the surface is maximum _MaxIf material surface is the irregular surfaces pattern; Adopting microscope to carry out surface topography extracts; Adopt the method for rectangular node point to sample; And set up two Dimension Numerical and describe surface topography, obtain in the rectangular node point of surface topography maximal value h of all height h that rise and fall of the fluctuating of some height h and surface arbitrarily _Max

(2) with electronics from A _I-1Point moves to A _iThe length of the straight-line trajectory of point is designated as t _i, with electronics from A _iPoint moves to A _I+1The length of the straight-line trajectory of point is designated as t _I+1, t then _I+1Obtain by following recurrence relation, then:

$t_{i+1}=\left\{\begin{array}{cc}{t}_i+\min (t_x,t_y)& n_x\&NotEqual;0,n_y\&NotEqual;0\\ t_i+t_x& n_x\&NotEqual;0,n_y=0\\ t_i+t_y& n_x=0,n_y\&NotEqual;0\\ |h_i-z_i|& n_x=0,n_y=0\end{array}\right.$

$t_x=\left\{\begin{array}{cc}(a-x_i)/n_x& n_x>0\\ -x_i/n_x& n_x<0\end{array}\right.$

$t_y=\left\{\begin{array}{cc}(b-y_i)/n_y& n_y>0\\ -y_i/n_y& n_y<0\end{array}\right.$

Wherein:

When electronics is in reference position or electronics free path starting point, make t ₁=0; I=1,2,3 ...; (x _i, y _i) be A _iThe local coordinate of spot projection in the corresponding rectangle grid, z _iBe A _iSpot projection is perpendicular to the coordinate on the z axle of rectangular node;

(x _I+1, y _I+1) be A _I+1The local coordinate of spot projection in the corresponding rectangle grid, z _I+1Be A _I+1Spot projection is perpendicular to the coordinate on the z axle of rectangular node;

n _xAnd n _yBe respectively electron motion direction unit vector x and y to projection;

h _iBe local coordinate (x _i, y _i) corresponding surface undulation height;

(3) whether electronics with metal material surface interaction being taken place judges order

f＝(z _i-h _i)(z _i+1-h _i+1)

If f>=0 and z _I+1＞h _Max, showing that electronics can not interact with material, the energy and the direction of record electronics this moment get into step (8);

If f＞0 and z _I+1≤h _Max, show that electronics does not interact with metal material surface, makes t _i=t _I+1, return step (2);

If f≤0 shows that electronics is from A _iPoint moves to A _I+1Can pass material surface during point; If z _i-h _i＞0, show that electronics is from the outside material internal that gets into of material, gets into step (4); If z _i-h _i＜0, show electronics from the material internal outgoing, jump to step (6);

Wherein:

h _I+1Be local coordinate (x _I+1, y _I+1) corresponding surface undulation height;

(4) if electronics from the outside incident material internal of material, according to the incident direction of incident electron

Surface normal with the incidence point material

By energy conservation and the momentum conservation that electron motion satisfies, calculate the energy E of electron impact behind the material _iAnd direction of motion

E _i＝E _p+U ₀

$\stackrel{\&RightArrow;}{n_i}=\sqrt{\frac{E_p}{E_p+U_0}}\stackrel{\&RightArrow;}{n_p}+(\sqrt{\frac{E_p}{E_p+U_0}}\cos \mathrm{\&theta;}-\sqrt{\frac{E_p{\cos }^2\mathrm{\&theta;}+U_0}{E_p+U_0}})\stackrel{\&RightArrow;}{N_i}$

Wherein:

E _pBe the incident electron energy;

U ₀Be built-in potential, U ₀=E _F+ Φ, E _FBe the Fermi level of material, Φ is the work function of material;

is the incident direction of incident electron;

is the surface normal of incidence point material;

θ is the angle of surface normal of incident direction and the incidence point material of incident electron,

(5) according to the electron energy E that incides material internal _iAnd direction of motion

Adopt the scattering process of DSMC simulation electronic in material of conventional ideal surfaced, follow the trail of the track of incident electron and secondary electron, write down the electron energy E of each scattering _j, the electron motion direction

Free path S with electronics _j, j=1 wherein, 2 ..., m, to electronics at every section free path S _jInterior rectilinear motion is handled according to step 2 and step 3;

(6) when electron motion arrived material surface, recorded electronic was from the position (x of material surface outgoing _m, y _m, z _m), according to the electronic motion direction

Normal direction with the eye point material Calculate electronics exit probability T:

Wherein:

Direction when

arrives material surface for electron motion;

is the normal direction of eye point material;

is the angle of electron motion direction and eye point material normal direction,

E _mEnergy during for electronics outgoing material surface;

(7) go up generation random number R ND in interval [0,1],

If T≤RND then makes electronics reflect on the surface, reflection back electronics is still with energy E _mContinuation is scattering in material, and direction of motion does

Jump to step (5) then;

If T＞RND then makes the electronics outgoing, the energy of electronics is E after the outgoing _s, direction of motion does

E _s＝E _m-U ₀

Return step (2)

(8) change the incident electron energy E _p, repeating step (2)～(7), the secondary electron direction of motion and the energy of record outgoing are added up the outgoing electron number under the different incident electron energy, obtain the secondary electron yield of said material; The direction and the energy of statistics outgoing electron, the secondary electron power spectrum and the exit direction that obtain said material distribute.

2. the method for a kind of definite roughened metal surface secondary electron emission characteristic according to claim 1; It is characterized in that: in the said step (1) if material surface be the irregular surfaces pattern; The then method acquisition of the fluctuating of some height h employing first-order linear interpolation arbitrarily in the rectangular node point of surface topography, that is:

$h=h_{\mathrm{lu}}+\frac{h_{\mathrm{ru}}-h_{\mathrm{lu}}}{a}m+\frac{h_{\mathrm{ld}}-h_{\mathrm{lu}}}{b}n+\frac{h_{\mathrm{rd}}+h_{\mathrm{lu}}-h_{\mathrm{ru}}-h_{\mathrm{ld}}}{\mathrm{ab}}\mathrm{mn}$

Wherein:

(m n) is any point coordinate in the rectangular node under the local coordinate;

H is any fluctuating of some height in the rectangular node point;

h _LuFluctuating height for the rectangle upper left corner;

h _LdFluctuating height for the rectangle lower left corner;

h _RuFluctuating height for the rectangle upper right corner;

h _RdFluctuating height for the rectangle lower right corner;

A is the length of rectangular node point;

B is the wide of rectangular node point.

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