JP3077755B2 - Sputter shape simulation method and computer readable recording medium recording the program - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for simulating the shape of a sputter in a contact hole. More particularly, the present invention relates to a method for simulating the data of the sputter rate and the sputter angle distribution corresponding to the incident angle and energy of sputtered particles. A sputter shape simulation method for calculating film growth after generating re-sputtered particles having a sputter rate and a sputter angle corresponding to the incident angle and energy of the sputtered particles by referring to the above table, and recorded a program thereof. The present invention relates to a computer-readable recording medium.

[0002]

2. Description of the Related Art In recent years, with the progress of miniaturization of semiconductor devices, it is necessary to optimally adjust the characteristics of a sputtering device used for manufacturing fine contact holes and the like in accordance with environmental conditions for each task. Therefore, it is indispensable to grasp the characteristics of the sputtering apparatus in advance.

[0003] However, it is not appropriate to develop and test an actual device each time due to cost and delivery time issues. Therefore, a technique for grasping a sputter shape using simulation has been developed. As a technique related to such a simulation, an example of a conventional sputter shape simulation system was disclosed in 1991, from page 7137 of the Journal: AppliedPhysics. 7140
It is disclosed in a paper by MM IslamRaja published on the page.

FIG. 7 is an explanatory diagram showing a calculation process of a conventional method of simulating a sputter shape. As shown in FIG. 7, this conventional method for simulating the shape of a sputter calculates a film growth by performing three-dimensional shadow determination from the trajectory of sputter particles calculated by the Monte Carlo method as follows.

[0005] 1. A mesh forming a contact shape on which an orbit generated by the Monte Carlo method or the like is incident is referred to as a shape mesh 1. 2. The sputtering rate SR is calculated from the incident angle and energy of the incident sputtered particles with respect to the mesh 1, SR re-sputtered particles are generated, and the movement amount of the mesh corresponding to the difference between the incident number and the sputtered number is calculated. 3. Determine where on the side the resputtered particles will adhere
For each mesh constituting the three-dimensional shape, a three-dimensional shadow determination as to whether or not it intersects the re-sputtered particles is performed. 4. The shape mesh in which shadow occurs (adheres) is defined as shape mesh 2, and the movement amount of one sputtered particle is added. 5. Perform steps 1 to 4 for all sputtered particles and all shape meshes, and calculate the shape at the next time step.

As a past representative patent application relating to this field, Japanese Patent Application Laid-Open No. 6-280010 discloses a magnetron having a complicated shape by calculating the orbits of a plurality of electrons by vector calculation. A technique for shortening a simulation analysis time of a target erosion distribution of a sputtering apparatus is disclosed.

Japanese Patent Application Laid-Open No. Hei 8-274084 discloses a simulation of a collision phenomenon between sputtered particles and surrounding gas in a step of filling a through hole in an insulating film on a semiconductor substrate. A technique is disclosed in which a trajectory of a sputtered particle from a predetermined position of a through hole on a substrate as a starting point to a target of a sputtering apparatus is inversely calculated, and an occurrence probability of the trajectory is obtained.

Furthermore, Japanese Patent Application Laid-Open No. 9-25572 discloses that when simulating an optimum parameter of a sputter apparatus for embedding a through hole, the trajectory of particles emitted from a target is calculated, and the shape of the embedding of the through hole or A technique is disclosed in which the film pressure is obtained as a function of a coefficient representing the occurrence probability of the trajectory, and the coefficient is obtained using a linear programming method based on the embedding shape or the optimization condition of the film pressure.

[0009]

However, the above prior art has the following problems. In other words, the calculation of the shape of the film growth taking into account re-sputtering requires a large amount of calculation time.

[0010] The reason is that shadow determination is performed on the trajectories of all sputtered particles including re-sputtered particles by determining whether or not the trajectories intersect with the three-dimensional shape.

Therefore, in devising the present invention, the data of the sputter rate and the sputter angle distribution corresponding to the incident angle and energy of the sputtered particles are measured in advance and stored in a table format. Resputtered particles are generated according to the angle and energy, and when calculating the film growth by the resputtered particles, it is assumed that the film growth by the resputtered particles is axially symmetric, and the film shape calculation is performed only on the shape cut surface. It has been studied to reduce the amount of calculation required for simulation calculation by performing data processing.

Also, utilizing the fact that the angle of the trajectory of the resputtered particles with the reattachment surface and the angle with the cross section of the shape is substantially equal, the direction is determined by mapping to the cross section of the shape, and the starting point of the resputtered particles is determined. It has been studied to further reduce the amount of calculation by calculating the amount of movement from the projection on the reattachment surface as the intersection of the plane and the shape including the intersection of the trajectory and the reattachment surface.

[0013]

SUMMARY OF THE INVENTION The present invention has been made in view of the above-described problems in the conventional method of simulating a sputter shape, and has a sputter shape capable of reducing the calculation time required for the simulation calculation as compared with the conventional method. It is an object of the present invention to provide a simulation method and a computer-readable recording medium on which the program is recorded.

[0014]

In order to solve the above-mentioned problems, a method of simulating a sputter shape according to the present invention is directed to a method of simulating a sputter shape of a sputter device used in a contact hole forming step of a semiconductor device manufacturing process. In the method, a sputter rate preparing step of storing data of a sputter rate corresponding to an incident angle and an incident energy of sputter particles in a storage area in advance, a sputter particle incident step of incident the sputter particles, and a sputter particle incident step With the implementation of the above, the sputtering rate corresponding to the incident angle and the incident energy of the incident sputtered particles is searched from the storage area, and the re-sputtering to generate the number of re-sputtered particles corresponding to the searched sputter rate. In the particle generation step and the shape calculation of film growth, The orbit determination step of the re-sputtered particles that determines the orbit of the re-sputtered particles corresponding to the incident angle and the incident energy of the sputtered particles using a random number or a pseudo-random number, and that the film growth by the re-sputtered particles is axially symmetric. It is assumed that the method has a film shape calculation step of performing data processing for film shape calculation only on the shape cut plane (XZ plane) of the contact hole (claim 1). The above object can be achieved.

Further, in the above-mentioned method for simulating a shape of a sputter, the step of preparing a sputter rate includes extracting a trajectory of sputter particles in a semiconductor device calculated at least using a simulation method including the Monte Carlo method in the center of the wafer, The method further includes a step of storing, in a table format, measured data of a sputtering rate corresponding to an incident angle and an incident energy of the incident sputtered particles to the contact hole at the center of the wafer (claim 2).

In the step of projecting the sputtered particles, one point is selected from string points constituting a cross-sectional shape of the contact hole corresponding to the XZ plane of the contact hole, and the selected point is defined as an incident point of the incident sputtered particle. (Claim 3).

In the re-sputtering particle generation step, an incident angle of the incident sputter particle is calculated from a normal to a tangent plane of the incident point and a trajectory direction of the incident sputter particle, and a sputter rate SR is obtained from the incident angle. Generating a re-sputtered particle of an event corresponding to the SR (claim 4).

Calculating the incident angle by θin of the following equation (1):

(Equation 3) When the integer part of SR is SRn, the sputtering rate SR
Is compared with the following inequality (2) (claim 5). e3> (SR-SRn) (2)

The step of determining the trajectory of the re-sputtered particles includes a step of determining the trajectory direction of the re-sputtered particles passing through the incident point from the incident angle and incident energy of the incident sputter particles by a rejection method using the table. (Claim 6).

In calculating the trajectory direction of the re-sputtered particles passing through the incident point by the rejection method, a temporary re-sputtering angle θrsp_r is calculated using a uniform random number or a uniform pseudo-random number e4.
jc is determined by the following equation (4) as θrjc = π / 2 · e4 (4), and a uniform random number or a uniform pseudorandom number e5 and a repetition rate corresponding to the incident energy and the incident angle retrieved from the table are obtained. Maximum value Fmax of frequency measurement data of sputter angle
The frequency Frjc is calculated from the following equation (5) as Frjc = Fmax · e5 (5), and the trajectory of the re-sputtered particles after re-sputtering is calculated using the following equation (6). There is a step of obtaining by a straight line formula (claim 7). Z-Zin = Pxz · (X-Xin), Z-Zin = Pyz · Y (6)

In the film shape calculation step, the trajectory of the re-sputtered particles is once determined for a movement vector in a simulation calculation composed of a projection vector of the flux onto the cross-section of the shape corresponding to the re-sputtered particles.
Calculating the direction and the absolute value of the movement vector after projecting it on the reattachment surface; and calculating the rotation angle between the reattachment surface and the shape section, and then moving the movement vector around a symmetry axis. And the step of rotating on the XZ plane (claim 8).

The flux of the resputtered particles was changed to Fresp Z
From the axis component Fresp_z and the projection component Fresp_r on the reattachment surface, the absolute value | M | of the movement amount vector M is calculated from the following equation (8), and | M | = √ ｛Fresp_z ² + Fresp_r ² · sin ² θ_redepo｝ (8) In the formula (8), sinθredepo is a sine calculated from the following formula (9), which is the angle between the reattachment surface and the shape section, and sinθ_redepo = Ycross ² / ｛2 Rcross · (Rcross · Xcross)｝ (9) Assuming that the angle of rotation about the axis of symmetry of the movement vector M is Θ, the angle 求 め is obtained by the following equation (10).

(Equation 4) When a vector formed by moving the movement vector M on the XZ plane is M ′, the X, Y, and Z components M′x, M′y, and M′z of the vector M ′ are respectively X, Y, Z
Using the components Mx, My, and Mz, calculation is performed according to the following formula (11) (claim 9). M′x = √ (Mx ² + My ² ), M′y = 0, M′z = Mz (11)

In the film shape calculation step, the trajectory of the re-sputtered particle is set to be different from the re-attached surface with respect to the movement vector in the simulation calculation composed of the projection vector of the flux onto the shape cross section corresponding to the re-sputtered particle. Using the fact that the angle made and the angle made with the shape section are substantially equal, the direction of the movement vector is obtained by projecting the shape vector on the shape section, and the starting point of the movement vector is re-established with the trajectory of the re-sputtered particles. A step of calculating an absolute value of the movement amount vector from a projection on the reattachment surface as an intersection between the plane and the shape including the intersection with the attachment surface (claim 1).
0).

The sine sin θeq of the equiangular angle θeq is defined by the coordinates (Xcr) of the intersection when the re-sputtered particles cross the side wall.
oss, Ycross) and the contact radius R on the horizontal plane including the intersection point is calculated by the following equation (12), and sinθ_ep = Ycross ² / {2 · Rcross · (Rcross · Xcross)} (12) The projection vector of the flux onto the shape section of the re-sputtered particles is Fresp, and the shape point located at the intersection of the shape section and the horizontal plane including the intersection of the re-sputtered particles with the shape section in the opposite direction to the above-described Fresp is defined as the starting point. When the vector to be moved is the movement amount vector M due to the re-sputtered particles, the X and Z components Fresp of Fresp of the flux of the re-sputtered particles
_X and Fresp_z, the absolute value | M |
Is calculated by the following equation (13) (claim 11). | M | = {Fresp_z ² + Fresp_x ² · sin ² θ_ep} (13)

In order to solve the above-mentioned problems, a computer-readable recording medium storing a program for causing a computer to execute the sputtering shape simulation method according to the present invention is provided. .

The operation of the present invention will be described. The data of the sputter rate and the sputter angle distribution corresponding to the incident angle and energy of the sputtered particles are measured in advance and recorded in a table format, and the incident angle and energy of the sputtered particles are measured. The re-sputtered particles are generated in accordance with, and when calculating the film growth by the re-sputtered particles, it is assumed that it is axially symmetric, and from this assumption, the data processing of the film shape calculation is performed.
By performing the calculation only on the shape cut surface, the amount of calculation required for the simulation calculation is saved.

[0027]

Embodiments of the present invention will be described below with reference to the drawings. (First Embodiment) FIGS. 1 to 3 are flow charts for explaining the operation of a method for simulating a sputter shape according to a first embodiment of the present invention. Less than,
The operation of the method for simulating a sputter shape according to the present embodiment will be described with reference to FIGS.

In step S101, the trajectory of sputter particles in the apparatus calculated by the Monte Carlo method or the like is extracted at the center of the wafer, and data of the angular distribution and velocity distribution of the sputter particles incident on the contact hole at the center of the wafer is created. , Stored in a storage device.

In step S102, one of the string points constituting one of the incident sputtered particles (incident point)
Turn to.

In step S103, the incident angle is calculated from the normal of the tangent plane to the incident point and the direction of the trajectory of the incident sputtered particle, and the sputter rate SR corresponding to the incident angle and the velocity of the incident sputtered particle is stored in the storage device. The re-sputtered particles of the event corresponding to the SR are obtained by searching.

In step S104, the incident point is moved in the direction of the incident sputtered particles by an amount corresponding to the projection of the vector of the size F (1-SR) onto the shape cut surface. Here, F is a flux representative of incident sputtered particles.

In step S105, the trajectory direction of the re-sputtered particles emitted from the incident point is determined by the rejection method using the incident angle and the incident energy as parameters, and the trajectory is represented by a linear equation. At 106, an intersection Pcross between the horizontal plane passing through the comparison reference point and the trajectory of the re-sputtered particle is determined using the point adjacent to the incident point as the comparison reference point.

In step S107, the distance Rcross between the point Pcross and the axis of symmetry is obtained and compared with the distance R between the comparison reference point and the axis of symmetry. If Rcross <R, the opposite side of the incidence point of the comparison reference point is used. Is set as a new comparison reference point, and R
The process is performed until cross ≧ R or all the shape points are compared.

In step S108, step S107
When Rcross ≧ R, the intersection of a straight line from the symmetry axis to the point Pcross and a circle having a radius of Rcross is defined as Pred
The trajectory of the re-sputtered particles is projected on a vertical plane passing through the symmetry axis with Predepo, and the movement amount due to the re-sputtered particles is calculated.

In step S109, the Prede
An angle Θ between the vertical plane passing through po and the axis of symmetry and the shape calculation section is obtained from the inner product of the direction vector of Rcross and the direction vector of R.

In step S110, the movement vector due to the re-sputtered particles is rotated by を about the symmetry axis, and the comparison reference point is moved by the movement vector.

In step S111, step S102
By the operation of Step S110, the movement of the shape point due to re-sputtering is calculated for the trajectories of all incident sputter particles.

In step S112, step S102
By the operation of Step S111, the movement of the shape point due to the re-sputtering is calculated at the coordinate points constituting all the shapes.

FIG. 4 is an explanatory diagram for explaining a process of calculating the film growth of the re-sputtered particles in the sputtering shape simulation method according to the first embodiment of the present invention.

FIG. 5 is an explanatory diagram showing the angle from the shape cross section of the attachment point of the re-sputtered particles in the method for simulating the shape of a sputter according to the first embodiment of the present invention.

Hereinafter, the calculation process in the sputtering shape simulation method according to the embodiment of the present invention will be described.
This will be described with reference to FIGS. 4 and 5 while referring to the flowcharts of FIGS.

First, the velocity of sputtered particles incident on the contact hole at the center of the wafer is calculated by the Monte Carlo method or the like. As described in step S101, the trajectory of the sputtered particles is calculated by the Monte Carlo method or the like in consideration of the position and velocity of the sputtered particles in the sputtering apparatus, and the pressure and temperature of the background gas, and these trajectories are set at the center of the wafer. Are extracted in a specific region located at the center of the wafer, and this is used as a data group of the angular distribution and energy distribution of the trajectory of the incident sputtered particle in the contact hole at the center of the wafer.

Next, as shown in FIG. 4A, the incident sputtered particles are directed to one of the string points (incident point) constituting the shape on the XZ plane. As described in step S102, the trajectory of one sputtered particle of the data group of the trajectory of the incident sputtered particle generated earlier is changed to one of the string points constituting the contact hole cross-sectional shape on the XZ plane. This point is defined as the incident point of the incident sputtered particles.

Further, the incident angle is calculated from the normal to the tangent plane of the incident point and the orbital direction of the incident sputtered particles, the sputter rate SR is obtained from the incident angle, and the resputtered particles of the event corresponding to SR are generated. As described in step S103, the tangent plane at the incident point is determined as a plane tangent to a circle including points before and after the incident point, and the normal vector Us of the tangent plane is determined.
And the inner product of the vector Vsp of the incident trajectory of the sputtered particle and the incident angle θin is calculated by the following equation (1).

(Equation 5)

Next, the incident angle θin and the sputtering rate corresponding to the energy of the incident sputtered particles are read from a table obtained by actual measurement. That is, the sputter rate at each incident angle and incident energy is stored in the storage device in advance in a table format, and the sputter rate SR corresponding to the incident angle θin and the incident energy is searched from the table. Furthermore, the integer part of SR is
As n, a uniform random number or a uniform pseudo random number e3 is compared and determined by the following inequality (2). e3> (SR-SRn) (2)

Here, if the inequality shown in Expression 2 holds,
SN = SRn + 1, and if not satisfied, SN = SRn
To generate SN particles.

Next, the incident point is moved in the direction of the incident sputter particles by an amount corresponding to the projection of the vector of the size F (1-SN) onto the shape cut surface. As described in step S104, the magnitude of the direction vector of the incident sputtered particle is
The size of the flux of the incident sputtered particles is calculated using F,
X, Z components nx, nz when the unit vector n in the incident sputtering direction is projected onto the shape cut surface, where F (1-SN)
Is used, the amount of movement in the X and Z directions within the shape cutting plane, d
x and dy are calculated by the following equation (3), and move according to the calculated movement amount. dx = F (1−SN) · nx / | n |, dy = F (1−SN) · ny / | n | (3)

Next, the trajectory direction of the re-sputtered particles passing through the incident point is determined from the incident angle and the incident energy by the rejection method, and the determined trajectory direction is represented by a linear equation.

As described in step S105, the magnitude of the re-sputtering angle θrsp corresponding to the incident angle θin and the incident energy is generated by a rejection method using a table obtained in advance by actual measurement. For this reason, as shown in the graph of FIG. 4B, actual measurement data of the frequency of the resputtering angle at each incident energy and incident angle is divided in advance into 10 by dividing the resputtering angle from 0 to π / 2. ,
The maximum value Fmax of the frequency in each range and the linear interpolation data of the frequency are tabulated.

At the time of shape calculation, a tentative re-sputtering angle θrsp_rjc is obtained by the following equation (4) using a uniform random number or a uniform pseudo-random number e4 as follows: θrjc = π / 2 · e4 (4) Using the uniform random number or uniform pseudo-random number e5 and Fmax, the frequency Frjc is calculated from the following equation (5) as Frjc = Fmax · e5 (5), and the data including θrsp is obtained by the bisection method. A pair is obtained, and it is determined whether or not Frjc is greater than the frequency of linear interpolation. If it is larger, it is rejected, and if smaller, it is adopted. This operation is performed until Frjc is adopted, and θrsp_rjc at the time when Frjc is adopted is used as the re-sputtering angle θrsp.

Further, from the components Vrsp_x, Vrsp_y, and Vrsp_z of the vector Vrsp obtained by rotating the normal vector Us of the tangent plane at the incident point by θrsp in the incident plane, the inclination of the projection of Vrsp on the XZ plane and the YZ plane, Pxz = Vrsp_x
/ Vrsp_z, Pyz = Vrsp_y / Vrsp_z is obtained, and the equation of a straight line on the XZ and YZ planes is obtained by the following equation (6) from the condition passing through the incident point (Xin, 0, Zin). Z-Zin = Pxz · (X-Xin), Z-Zin = Pyz · Y (6)

Next, a point adjacent to the incident point is set as a comparison reference point,
An intersection Pcross between the horizontal plane passing through the comparison reference point and the trajectory of the re-sputtered particles is determined. As described in step 106, a point adjacent to the incident point is selected, and a comparison reference point (Xcmp, Xcmp,
0, Zcmp), and a horizontal plane Z = Zcmp passing through the comparison reference point
Pcross (Xcross, 0,
Zcross) each coordinate Xcross = (Z−Zin) / Pxz + Xin,
Ycross = (Z−Zin) / Pyz, Zcross = Zcmp.

Further, the distance Rc between the point Pcross and the axis of symmetry is
ross is obtained and compared with the distance R between the reference point and the axis of symmetry,
If Rcross <R, the next point on the side opposite to the incident point of the comparison reference point is set as a new comparison reference point, and the processing is performed until Rcross ≧ R or all the shape points are compared. Step S1
As described in 07, the square Xcross ² + Ycross ² of the distance Rcross between the point Pcross and the axis of symmetry is calculated, and the square Xcmp ² of the distance R between the comparison reference point and the symmetry axis is calculated. The magnitude is determined by the following inequality (7). Xcross ² + Ycross ² <Xcmp ² (7)

In the inequality shown in the above equation 7, Rcross ² is R
If it is smaller than ^{2, the} point adjacent to the comparison reference point is set as a new comparison reference point, and the calculation is repeated from the calculation of the intersection with the horizontal plane.

Next, when Rcross ² is larger than R ² , the intersection of a straight line from the symmetry axis to the point Pcross and a circle having a radius of Rcross is Predepo, and a vertical plane passing through Predepo and the symmetry axis is given by The trajectory of the re-sputtered particles is projected, and the amount of movement by the re-sputtered particles is calculated. Step S10
As described in 8, when Rcross2 is larger than R2, the intersection of the straight line from the symmetry axis to Pcross and the circle having the radius of Rcross is calculated, and this is defined as Predepo and Predepo.
The vertical plane passing through the axis of symmetry with the depo is defined as the reattachment surface, and the projection vector of the flux of the resputtered particles on the reattachment surface is Fre.
In the opposite direction, a vector starting from the intersection of the horizontal surface including the intersection of the reattachment surface and the trajectory of the resputtered particles is defined as a movement vector M by the resputtered particles. At this time, the flux of the re-sputtered particles is represented by a Z-axis component Fresp_z of Fresp and a projection component Fresp_r
Thus, the moving amount of the re-sputtered particles, that is, the absolute value | M | of the moving amount vector M is calculated from the following equation (8). | M | = {Fresp_z ² + Fresp_r ² · sin ² θ_redepo} (8)

Here, sinθredepo is the sine of the angle formed between the reattachment surface and the cross section of the shape, and is calculated from the following equation (9). sinθ_redepo = Ycross ² / {2 · Rcross · (Rcross · Xcross)} (9)

Further, the angle Θ between the vertical plane passing through the Predepo and the symmetry axis from the symmetry axis and the shape calculation cross section is defined by Rcros
It is determined from the inner product of the direction vector of s and the direction vector of R. As described in step S109, P
As shown in FIG. 5, the angle な between the vertical plane passing through the redepo and the axis of symmetry and the shape calculation section is calculated from the inner product of the direction vector Rcross of Rcros and the direction vector R of R as shown in the following equation (10). Ask for.

(Equation 6)

Next, the movement vector due to the re-sputtered particles is rotated by Θ around the axis of symmetry, placed on the XZ plane, and the comparison reference point is moved in the direction of the movement vector.
As described in step S110, the movement vector M due to the re-sputtered particles is rotated by Θ about the axis of symmetry,
Calculate M ′ on the XZ plane. At this time, X, Y,
M'x, M'y, and M'z, which are the Z components, are calculated by the following formula (11) using the X, Y, and Z components Mx, My, and Mz of the vector M, respectively. M′x = √ (Mx ² + My ² ), M′y = 0, M′z = Mz (11)

The comparison reference point is moved in the direction of the rotated movement vector M 'according to the result of the calculation by the above formula. That is, it is moved by M'x and M'z in the X and Z directions, respectively, and the movement of the shape due to the re-sputtered particles is calculated.

From the operation of directing the incident sputtered particles to one of the string points forming the shape, the movement of the shape point by re-sputtering is calculated for the trajectories of all the incident sputtered particles by the operations up to this point.

As described in step S111, the trajectories of all the incident sputtered particles are changed from the operation of directing the incident sputtered particles to one of the string points constituting the shape to the calculation of the shape movement by the re-sputtered particles. Calculate the move for

Further, from the operation of directing the incident sputtered particles to one of the string points constituting the shape, the movement of the shape point by re-sputtering is calculated at the coordinate points constituting all the shapes by the operations up to this point. .

As described in step S112, the operation of turning the incident sputtered particles to one of the string points constituting the shape starts with the operation of all the incident sputtered particles.
By the operation up to this point, the movement of the shape point due to re-sputtering is calculated at the trajectories of all the incident sputter particles and the coordinate points constituting all the shapes.

The effect of the method for simulating the shape of a sputter according to the present embodiment is as follows. For example, when a calculation incorporating the effect of re-sputtering is performed in all three dimensions, it takes three times as long in shadow judgment, and the particle Since the calculation of the movement of the attachment point is made one-dimensionally extra, it becomes 1.5 times. Furthermore, the shadow judgment and the calculation of the deposition growth of the re-sputtered particles are improved to the same extent. Since the ratios to the whole are about 0.2 and 0.1, respectively, the total calculation time is 1 / (0.2 × 3 + 0.1 ×
1.5) / 2 = 2/3.

The reason for this is that data of the sputtering rate depending on the incident angle and energy obtained by the actual measurement is taken in, and the data processing for calculating the shape change only on the shape cut surface is processed.

(Second Embodiment) FIG. 6 is an explanatory diagram for explaining a method of simulating a sputter shape according to a second embodiment of the present invention.

In the present embodiment, the calculation formula used when calculating the growth process of the film shape is different from the calculation formula used in the first embodiment. That is, in the present embodiment, when calculating the film deposition direction after re-sputtering, the orbit of the re-sputtered particles and the triangle formed by Rcross and R are substantially equilateral triangles when viewed from above the via. First, a sine sin θeq of the equiangular θeq of the isometric triangle is obtained. To calculate the sine sin θeq, the coordinates (Xcross, Ycross) of the intersection when the re-sputtered particle intersects the side wall
Using the following calculation formula (12) using the contact radius R on the horizontal plane including the intersection, sin θ_ep = Ycross ² / {2 · Rcross · (Rcross · Xcross)} (12)

The projection vector of the flux onto the cross section of the shape of the re-sputtered particles is assumed to be Fresp.
A vector starting from a shape point located in the opposite direction to resp and located at the intersection of the shape cross section, the attached cross section, and the horizontal plane including the intersection of the re-sputtered particles is defined as a movement amount vector M by the re-sputtered particles. At this time, the moving amount of the resputtered particles, that is, the absolute value | M of the moving amount vector, is obtained from the X and Z components Fresp_x and Fresp_z of the resputtered particle's flux Fresp.
Is calculated from the following formula (13), and | M | = {Fresp_z ² + Fresp_x ² · sin ² θ_ep} (13) The film growth is calculated by moving the shape point by M.

Hereinafter, performing this operation for all the orbits of the sputtered particles and all the shape points is the same as in the first embodiment.

The effect of the method for simulating the shape of a sputter according to this embodiment is, for example, that the trajectory of the re-sputtered particles is projected onto the re-adhesion surface once in the first embodiment, Since the amount of calculation for rotating the movement amount vector by calculating the rotation angle with the above is about 10%, the whole calculation time can be reduced by 10%.

The reason is that the direction is determined by mapping to the cross section of the shape by utilizing the fact that the angle of the trajectory of the resputtered particle with the reattachment surface is substantially equal to the angle with the cross section of the shape, and the starting point is resputtered. The intersection between the plane and the shape, including the intersection of the particle trajectory and the reattachment surface, is used.
This is because they are calculating.

A program for causing the processing device to perform the above processing, such as the programs shown in the flowcharts of FIGS. 1 to 3, is stored and distributed on a computer-readable recording medium such as a CD-ROM. Is also good. A computer including at least a microcomputer, a personal computer, and a general-purpose computer may read the program from the recording medium and execute the program.

[0073]

As described above, according to the simulation method of the sputter shape according to the present invention, the data of the sputter rate depending on the incident angle and the energy obtained by the actual measurement is taken in advance, and the data on the shape cut surface is obtained. By calculating the shape change only by using the conventional method, the calculation of the simulation for shape prediction incorporating the effect of re-sputtering can be reduced to 2 /
It can be reduced to about three. Also, utilizing the fact that the angle of the trajectory of the re-sputtered particles with the reattachment surface and the angle of the cross-section of the shape are substantially equal, the direction is determined by mapping to the cross-section of the shape, and the starting point is determined as the trajectory of the re-sputtered particles By calculating the amount of movement from the projection on the reattachment surface, the amount of movement is calculated as the intersection of the plane including the intersection with the attachment surface and the shape.

[Brief description of the drawings]

FIG. 1 is a flowchart for explaining an operation of a sputtering shape simulation method according to a first embodiment of the present invention.

FIG. 2 is a flowchart illustrating an operation of a method for simulating a sputter shape according to the first embodiment of the present invention.

FIG. 3 is a flowchart for explaining the operation of the method for simulating a sputter shape according to the first embodiment of the present invention.

FIG. 4 is an explanatory diagram for explaining a process of calculating the film growth of re-sputtered particles in the sputtering shape simulation method according to the first embodiment of the present invention, and FIG.
Is a schematic diagram showing a sputter shape, and FIG. 4B is a graph showing actual measurement data of a sputter angle and its frequency.

FIG. 5 is an explanatory diagram showing angles of reattachment points of re-sputtered particles from a shape cross section in the method for simulating a sputter shape according to the first embodiment of the present invention.

FIG. 6 is an explanatory diagram for explaining a sputtering shape simulation method according to a second embodiment of the present invention.

FIG. 7 is an explanatory diagram showing a calculation process of a conventional method of simulating a sputter shape.

[Explanation of symbols]

 P1 Incident point of incident sputtered particles P2 Incident point of resputtered particles P3 Point near the incident point of resputtered particles.

Claims (12)

(57) [Claims] In a method for simulating a sputtering shape of a sputtering device used in a contact hole forming step of a semiconductor device manufacturing process, data of a sputtering rate corresponding to an incident angle and an incident energy of sputtered particles is stored in a storage area in advance. A sputtering rate preparation step to be performed, a sputter particle incident step of injecting the sputter particles, and a sputter rate corresponding to an incident angle and an incident energy of the incident sputter particles with the execution of the sputter particle incident step. A re-sputtering particle generating step of retrieving from the storage area and generating a number of re-sputtering particles corresponding to the retrieved sputter rate; and calculating the shape of the film growth, in accordance with the incident angle and incident energy of the sputter particles. The random number or pseudo-random number Determining the trajectory of the re-sputtered particles determined by using the method described above, and assuming that the film growth by the re-sputtered particles is axially symmetric, and calculating the film shape only on the shape cut surface (XZ plane) of the contact hole. A film shape calculation step for performing data processing for the simulation. 2. The method according to claim 1, wherein the trajectory of the sputtered particles in the semiconductor device calculated by using a simulation method including at least the Monte Carlo method is extracted at the center of the wafer. 2. The method for simulating a sputter shape according to claim 1, further comprising the step of storing, in a table format, measured data of a sputter rate corresponding to the incident angle and incident energy of the incident sputter particles. 3. The step of projecting the sputtered particles comprises selecting one of string points constituting a cross-sectional shape of the contact hole corresponding to the XZ plane of the contact hole, and assigning the selected point to the incident sputtered particles. The method for simulating a sputter shape according to claim 1, further comprising a step of setting an incident point. 4. The re-sputtering particle generation step calculates an incident angle of the incident sputter particle from a normal to a tangent plane of the incident point and a trajectory direction of the incident sputter particle, and obtains a sputter rate SR from the incident angle. The method according to claim 3, further comprising the step of generating re-sputtered particles of an event corresponding to the SR. 5. The angle of incidence is defined as θin in the following equation (1).
And calculating: When the integer part of SR is SRn, the sputtering rate SR
5. The method for simulating the shape of a sputter according to claim 4, further comprising: e3> (SR-SRn) (2). 6. The trajectory determining step of the re-sputtered particles is a step of determining the trajectory direction of the re-sputtered particles passing through the incident point from the incident angle and incident energy of the incident sputter particles by a rejection method using the table. The method for simulating a sputtered shape according to claim 4, wherein: 7. When calculating the trajectory direction of the re-sputtered particles passing through the incident point by the rejection method, a temporary re-sputtering angle θrsp is calculated using a uniform random number or a uniform pseudo-random number e4.
_Rjc is determined by the following equation (4) as θrjc = π / 2 · e4 (4), and a uniform random number or a uniform pseudorandom number e5 and a re-corresponding to the incident energy and the incident angle searched from the table are obtained. Maximum value Fmax of frequency measurement data of sputter angle
The frequency Frjc is calculated from the following equation (5) as Frjc = Fmax · e5 (5), and the trajectory of the re-sputtered particles after re-sputtering is calculated using the following equation (6). 7. The method for simulating a sputter shape according to claim 6, further comprising a step of obtaining a straight line equation, Z-Zin = Pxz. (X-Xin), Z-Zin = Pyz.Y. 8. The film shape calculation step includes, for a movement amount vector in a simulation calculation composed of a projection vector of a flux onto the shape cut surface corresponding to the re-sputtered particle, temporarily changing the re-sputtered particle trajectory. Calculating the direction and absolute value of the movement amount vector after projecting it on the reattachment surface, and calculating the rotation angle between the reattachment surface and the shape cutting surface, and then setting the movement amount vector to the axis of symmetry. A step of rotating the object around the center and placing the object on the XZ plane.
The method for simulating a sputter shape according to any one of 4, 5, 6, and 7. 9. The flux of re-sputtered particles is represented by a Z-axis component Fresp_z of Fresp and a projection component Fresp_r on the reattachment surface.
Then, the absolute value | M | of the movement amount vector M is calculated from the following calculation formula (8), and | M | = {Fresp_z ² + Fresp_r ² · sin ² θ_redepo} (8) where the calculation formula (8) Where sin θ_redepo is a sine calculated from the following calculation formula (9) of the angle between the reattachment surface and the shape cross section, and sin θ_redepo = Ycross ² / {2 · Rcross · (Rcross · Xcross)} (9) Assuming that the angle of rotation about the axis of symmetry of the movement vector M is Θ, the angle Θ is obtained by the following equation (10). When a vector formed by moving the movement vector M on the XZ plane is M ′, the X, Y, and Z components M′x, M′y, and M′z of the vector M ′ are respectively X, Y, Z
Using the components Mx, My, and Mz, the following formula (11) is used to calculate: M′x = √ (Mx ² + My ² ), M′y = 0, M′z = Mz (11) The method for simulating a sputter shape according to claim 8, wherein 10. The trajectory of the re-sputtered particles is re-attached with respect to a movement vector in a simulation calculation composed of a projection vector of a flux onto the cross section of the shape corresponding to the re-sputtered particles. Using the fact that the angle formed by the plane and the angle formed by the shape cutting plane are substantially equal, the direction of the movement vector is obtained by projecting the shape on the shape cutting plane, and the starting point of the movement vector is re-sputtered particles. And a step of calculating an absolute value of the movement amount vector from a projection on the reattachment surface as an intersection between a plane and a shape including an intersection of the trajectory and the reattachment surface. 2, 3, 4, 5, 6 or 7
A simulation method of the described sputter shape. 11. A sine sin θeq of the equiangular θeq is calculated using the coordinates (Xcross, Ycross) of the intersection and the contact radius R on a horizontal plane including the intersection when the re-sputtered particle intersects the side wall. Calculated by equation (12), sinθ_ep = Ycross ² / {2 · Rcross · (Rcross · Xcross)} (12) Further, the projection vector of the flux onto the cross section of the shape of the re-sputtered particles is Fresp, In the opposite direction, the vector starting from the shape point located at the intersection of the shape section and the horizontal plane containing the intersection of the adhered section and the re-sputtered particle is defined as the movement amount vector M by the re-sputtered particle. X and Z components of the Spread Fresp
_X and Fresp_z, the absolute value | M |
11 is calculated by the following equation (13): | M | = {Fresp_z ² + Fresp_x ² · sin ² θ_ep} (13) The method of simulating a sputter shape according to claim 10, wherein: 12. A computer-readable recording medium storing a program for causing a computer to execute a simulation of a sputter shape of a sputter device used in a contact hole forming step of a semiconductor device manufacturing process. A sputter rate preparing step of storing data of a sputter rate corresponding to an angle and an incident energy in a storage area in advance, a sputter particle incident step of injecting the sputter particles, and A re-sputtering particle generating step of retrieving a sputter rate corresponding to the incident angle and incident energy of the detected sputter particles from the storage area and generating a number of re-sputtered particles corresponding to the retrieved sputter rate; When calculating the shape of the Trajectory determining step of determining the trajectory of the re-sputtered particles corresponding to the incident angle and the incident energy of the re-sputtered particles using random numbers or pseudo-random numbers, and that the film growth by the re-sputtered particles is axially symmetric. Assuming that the shape cut surface (X
A computer-readable recording medium having recorded thereon a program for causing a computer to execute a film shape calculation step of performing data processing for film shape calculation only on the (Z plane).