Patent Publication Number: US-9411914-B2

Title: Simulator, processing system, damage evaluation method and damage evaluation program

Description:
BACKGROUND 
     The present disclosure relates to a simulator for evaluating the damage sustained by a workpiece when a given process is performed on the workpiece, a processing system having the same, damage evaluation method and damage evaluation program. 
     If a process such as etching, PVD (Physical Vapor Deposition) or ion implantation is performed on a film to be processed in the device manufacturing process, the processed film is damaged (e.g., crystal defects in the processed film) by ion injection. It has been indicated that this damage significantly affects the electrical characteristics of the device. As a result, it has become an important challenge for the device manufacturers to solve this problem immediately. 
     However, it is difficult to directly measure a real pattern of damage distribution with measuring devices available today. In order to consider in detail the relation between the condition of ion injection during the process and the electrical characteristics of the device, countermeasures against the above problem and other factors, and improve the electrical characteristics of the device, therefore, it is necessary to develop a damage distribution prediction technique (evaluation technique) using simulation. 
     In related art, therefore, a variety of simulation techniques have been proposed that can evaluate the condition when ions are injected into a target film (refer, for example, to Japanese Patent Laid-Open Nos. Hei 7-115071 and 2010-232594 (hereinafter referred to as Patent Documents 1 and 2, respectively), J. F. Ziegler, J. P. Biersack and U. Littmark: “The Stopping and Range of Ions in Solids,” Pergamon Press, New York, 1985 (Non-Patent Document 1, hereinafter) and Kawase and Hamaguchi: Dry Process Symposium 2005 (Non-Patent Document 2, hereinafter)). 
     Patent Document 1 proposes an ion implantation simulation technique, and Non-Patent Document 1 an SRIM (Stopping and Range of Ions in Matter) simulation technique. These simulation techniques allow, for example, for prediction of the ion penetration depth in a target film having an amorphous structure. However, it is difficult for these techniques to quantitatively express crystal defects (e.g., crystal lattice disorder in polysilicon or silicon oxide) that occur as a result of ion penetration in consideration of the crystal structure of the target film. 
     Non-Patent Document 2 proposes a simulation technique using a molecular dynamics simulator. This simulation technique can predict a crystal lattice disorder in atomic or molecular level, for example, according to the incident ion energy, incidence angle, target film type and so on in consideration of interaction between incident ions and atoms making up the target film. 
     With the simulation technique proposed in Non-Patent Document 2, however, the amount of calculations is enormous, resulting in an extremely long calculation time. For example, if the damage distribution is calculated by applying this simulation technique to a real pattern, it is only possible to calculate the damage distribution of an extremely limited area sized about several nm by several nm in a practical calculation time (e.g., within about several weeks). Further, this simulation technique leads to an even longer calculation time if the incident ion mass is small (e.g., hydrogen ion) because of a long flying distance of the incident ions in the film. In practically calculating the damage distribution of a target film using a molecular dynamics simulator, therefore, the damage distribution of the target film is calculated by ignoring the processing pattern and assuming that the target film is flat due to these calculation time restrictions. 
     On the other hand, Patent Document 2 proposes a technique as an extension of the simulation technique described in Non-Patent Document 2. More specifically, the damage distribution of a workpiece is found in advance under a variety of conditions by calculating the behavior of incident particles (ion particles) in the film based on molecular dynamics, followed by preparation of a database in which the found damage distribution data is stored. In practically predicting a real pattern of damage distribution by simulation, the position of collision of the incident particles onto the workpiece and the incidence angle are calculated first using the Monte Carlo method in consideration of the transportation route in the real pattern of the incident particles. Next, the database is searched based on the calculated position of collision of the incident particles and the incidence angle to find the corresponding damage distribution. This technique eliminates the need to perform molecular dynamics calculations every simulation run, thus contributing to reduced calculation time. 
     SUMMARY 
     As described above, the simulation technique proposed in Patent Document 2 provides, for example, faster damage distribution calculation than the technique using a molecular dynamics simulator proposed in Non-Patent Document 2 and so on. 
     It should be noted, however, that a database necessary for the calculations is prepared by molecular dynamics calculations. As a result, it takes time to prepare the database. In particular, if incident particles are, for example, light particles such as hydrogen, and if their energy is high, their flying distance is long in the film, thus resulting in longer time to prepare the database. 
     In the technique described in Patent Document 2, on the other hand, the transportation route in a real pattern of incident particles is calculated using the Monte Carlo method. As a result, a number of particles are necessary to calculate, with high accuracy, the distribution of incidence angles of incident particles to the pattern opening and the collision position distribution on the side walls and bottom of the pattern. In this case, the actual calculation time per calculation step is long in time evolution calculations. 
     As described above, the various simulation techniques in the past have significant restrictions in terms of their calculation times, thus making it difficult to calculate the damage sustained by a workpiece as a result of ion injection in a short period of time. At present, therefore, the development of a new damage calculation technique is sought after to solve the above problems. 
     In light of the foregoing, it is desirable to provide a simulator, processing system, damage evaluation method and damage evaluation program using a calculation technique that can calculate, in a short period of time, the damage sustained by a workpiece in a process such as ion injection. 
     According to an embodiment of the present disclosure, there is provided a simulator that includes an input section and damage calculation section. The input section acquires processing conditions for a given process performed on a workpiece. The damage calculation section acquires the damage of the workpiece based on the processing conditions. It should be noted that the damage of the workpiece acquired at this time is acquired by calculating, using the Flux method, the relationship between the amount of a first substance externally injected onto a given evaluation point on the workpiece during a given process and the amount of a second substance released from the given evaluation point on the workpiece as a result of the injection of the first substance. 
     Further, a processing system according to another embodiment of the present disclosure includes a processing section, the simulator according to the present disclosure and a control section. The processing section performs a given process on a workpiece. The control section corrects processing conditions for the given process based on the damage of the workpiece acquired from the simulator. 
     Still further, in a damage evaluation method and damage evaluation program according to further embodiment of the present disclosure, processing conditions for a given process performed on a workpiece are acquired. Next, the damage of the workpiece is acquired based on the acquired processing conditions. It should be noted that, at this time, the damage of the workpiece is acquired that can be acquired by calculating, using the Flux method, the relationship between the amount of a first substance externally injected onto a given evaluation point on the workpiece during a given process and the amount of a second substance released from the given evaluation point on the workpiece as a result of the injection of the first substance. 
     As described above, the present disclosure evaluates (predicts) the damage distribution during a given process performed on a workpiece using the damage calculated by the Flux method. The Flux method provides a significantly reduced amount of calculations as compared to the calculation methods used in related art including the molecular dynamics calculation method. Therefore, the present disclosure allows for calculation of the damage sustained by a workpiece in a given process such as ion injection in a shorter period of time. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic block configuration diagram of a simulator according to a first embodiment of the present disclosure; 
         FIG. 2  is an outline diagram of a reaction model of a workpiece used in the first embodiment; 
         FIGS. 3A and 3B  are model configuration diagrams of a reactive layer; 
         FIGS. 4A and 4B  are diagrams for describing a reactive layer redivision method; 
         FIGS. 5A and 5B  are model configuration diagrams of the reactive layer after redivision; 
         FIG. 6  is a flowchart illustrating the procedure for calculating the damage distribution of a workpiece in the first embodiment; 
         FIG. 7  is a diagram illustrating the results of evaluation example 1; 
         FIG. 8  is a diagram illustrating the results of evaluation example 1; 
         FIG. 9  is a diagram illustrating the results of evaluation example 2; 
         FIGS. 10A and 10B  are diagrams illustrating the results of evaluation example 3; 
         FIG. 11  is a diagram illustrating the results of evaluation example 4; 
         FIGS. 12A and 12B  are diagrams for describing the solid angle effect considered in the simulator according to a second embodiment of the present disclosure; 
         FIGS. 13A and 13B  are diagrams for describing the solid angle effect considered in the simulator according to the second embodiment; 
         FIG. 14  is a diagram illustrating an example of characteristics of the solid angle effect; 
         FIGS. 15A to 15D  are diagrams illustrating the results of evaluation example 5; 
         FIGS. 16A to 16D  are diagrams illustrating the results of evaluation example 5; 
         FIGS. 17A to 17D  are diagrams illustrating the results of evaluation example 5; 
         FIGS. 18A to 18D  are diagrams illustrating the results of evaluation example 5; 
         FIGS. 19A to 19D  are diagrams illustrating the results of evaluation example 6; 
         FIGS. 20A to 20D  are diagrams illustrating the results of evaluation example 6; 
         FIGS. 21A to 21D  are diagrams illustrating the results of evaluation example 6; 
         FIGS. 22A to 22D  are diagrams illustrating the results of evaluation example 6; 
         FIG. 23  is a diagram illustrating the outline of a combined model combining a damage calculation model and shape evolution model used in a simulation system according to a third embodiment of the present disclosure; 
         FIG. 24  is a schematic block configuration diagram of the simulation system according to the third embodiment; 
         FIG. 25  is a flowchart illustrating the procedure for calculating the damage distribution of a workpiece in the third embodiment; 
         FIG. 26  is a flowchart illustrating the procedure for setting a mask pattern in a mask pattern layout prediction tool according to a fourth embodiment of the present disclosure; 
         FIG. 27  is a schematic block configuration diagram of a dry etcher according to a fifth embodiment of the present disclosure; and 
         FIG. 28  is a flowchart for describing the etching control method of the dry etcher according to the fifth embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A description will be given below of simulators according to the preferred embodiments of the present disclosure, various systems (tools) having the same, and a damage evaluation method in the following order with reference to the accompanying drawings. It should be noted that the present disclosure is not limited to the following embodiments. 
     1. First embodiment: Basic configuration example of the simulator 
     2. Second embodiment: Configuration example of the simulator considering the solid angle effect 
     3. Third embodiment: Configuration example of a simulation system connecting a damage calculation model and shape evolution model 
     4. Fourth embodiment: Configuration example of a mask pattern layout prediction tool 
     5. Fifth embodiment: Configuration example of a dry etcher 
     6. Sixth embodiment: Configuration example of a simulator with a database storing damage data calculated in advance by the Flux method 
     &lt;1. First Embodiment&gt; 
     [Configuration of the Simulator] 
       FIG. 1  illustrates the schematic block configuration of a simulator according to a first embodiment. A simulator  10  includes an input section  11 , a damage calculation section  12 , a database section  13  (database) and an output section  14 . 
     The input section  11  acquires various processing conditions supplied externally. Further, the input section  11  is connected to the damage calculation section  12  and outputs thus obtained processing conditions to the damage calculation section  12 . It should be noted that the input section  11  can include desired means so long as this means can serve the above function. 
     The damage calculation section  12  calculates the damage sustained by a workpiece when the workpiece is subjected to a given process such as etching for a given amount of time. 
     More specifically, the damage calculation section  12  acquires various processing conditions externally via the input section  11  and searches the database section  13  based on the processing conditions, thus acquiring various parameters necessary for calculations. Then, the damage calculation section  12  calculates the damage sustained by the workpiece after the given period of the given process by the Flux method using the acquired processing conditions and various parameters. It should be noted that the processing conditions and parameters used during damage calculation and the damage calculation method by the Flux method will be described in detail later. Further, the damage calculation section  12  is connected to the output section  14  and outputs a calculated damage prediction (evaluation) result to the output section  14 . 
     It should be noted that, in the present embodiment, the damage calculation section  12  may include hardware to perform various calculations for the damage distribution of a workpiece which will be described later. Alternatively, these various calculations which will be described later may be performed using a given program (software). In this case, the damage calculation section  12  includes a CPU (Central Processing Unit) or other processor that loads a damage distribution calculation program (damage evaluation program) externally and executes the program to calculate the damage distribution of a workpiece. 
     On the other hand, the damage evaluation program may be stored, for example, in the database section  13  or a separate storage section such as ROM (Read Only Memory). At this time, the damage evaluation program may be, for example, installed in advance in the database section  13  or separate storage section. Alternatively, the program may be, for example, installed into the database section  13  or separate storage section externally. It should be noted that if the damage evaluation program is acquired externally, the program may be distributed in a medium such as optical disk or semiconductor memory. Alternatively, the program may be downloaded via transmission means such as the Internet. 
     The database section  13  stores various parameters necessary for damage calculations of a workpiece. It should be noted that although a description will be given, in the present embodiment, of an example in which the simulator  10  includes the database section  13 , the present disclosure is not limited thereto. Instead, the database section  13  may be provided externally to the simulator  10 . Further, if various parameters necessary for damage calculations of a workpiece are supplied externally every simulation run, there is no need to provide the database section  13 . 
     The output section  14  outputs a damage calculation result output from the damage calculation section  12 . It should be noted that, at this time, the output section  14  may output information including the processing conditions and parameters used for calculations together with the damage calculation result. The output section  14  includes, for example, one of a display device adapted to display a damage calculation result and a printer adapted to print a calculation result and output the printed result, or a combination of both as appropriate. It should be noted that although a description will be given, in the present embodiment, of an example in which the simulator  10  includes the output section  14 , the present disclosure is not limited thereto. Instead, the output section  14  may be provided externally to the simulator  10 . 
     [Simulation Model] 
     The simulator  10  according to the present embodiment finds, by the Flux method, the distribution of damage sustained by a workpiece during a given process performed on the workpiece. More specifically, the simulator  10  calculates the relationship between the amount of various particles (first substance) externally injected onto a workpiece and the amount of various particles (second substance) released from the workpiece as a result of the injection of the various particles, thus calculating the damage sustained by the workpiece. 
     (1) Reaction Model of a Workpiece 
     In finding the relational formula between the amount of various particles injected from the ambient gas (externally) onto a workpiece and the amount of various particles released from the workpiece on the workpiece surface (surface to be processed) by the Flux method, a reaction model between the workpiece and gas is established first. In the present embodiment, a description will be given by taking, as an example, a reaction model for dry-etching a SiO 2  film (workpiece) using a CF-based gas and a gas including oxygen (O). 
       FIG. 2  illustrates the outline of a reaction model near the interface between the SiO 2  film and ambient gas (plasma). When a SiO 2  film  21  is dry-etched in the atmosphere of a CF-based gas plasma  20 , an etching reactive layer  21   a  (hereinafter simply referred to as the reactive layer  21   a ) is formed near the surface of the SiO 2  film  21 . Further, if a CF-based gas is used as an etching gas, a polymer layer  22  including carbon (C) is formed (builds up) on the surface of the SiO 2  film  21 . That is, a two-layer model made up of the polymer layer  22  and reactive layer  21   a  is considered in this reaction model. 
     In the reaction model shown in  FIG. 2 , the reactions considered for the reactive layer  21   a  are as follows. 
     When the SiO 2  film  21  is etched as a result of an ion particle  23  being injected (arrow A 1  shown in  FIG. 2 ) onto the SiO 2  film  21  from the plasma  20  (gas), the bond between silicon (Si) and oxygen (O) is broken in the reactive layer  21   a  (refer to the area enclosed by a dashed line). At this time, the ratio at which the bond between the silicon (Si) and oxygen (O) is broken (dangling bond ratio) is expressed here by a reaction area ratio θ (0&lt;θ&lt;1). In the reactive layer  21   a , therefore, the ratio at which the silicon (Si) and oxygen (O) remain bonded together is 1−θ. 
     The silicon (Si) whose bond with the oxygen (O) has been broken in the reactive layer  21   a  reacts with fluorine (F) in the CF-based gas injected via the polymer layer  22  (arrow A 2  in  FIG. 2 ), turning into SiF 2  and/or SiF 4 . The produced SiF 2  and/or SiF 4  are released externally from the SiO 2  film  21  (arrow A 3  in  FIG. 2 ). 
     On the other hand, the oxygen (O) whose bond with the silicon (Si) has been broken in the reactive layer  21   a  reacts with carbon (C) in the polymer layer  22  (arrow A 4  in  FIG. 2 ), turning into CO. Then, the produced CO is released externally (arrow A 5  in  FIG. 2 ). 
     On the other hand, in the reaction model shown in  FIG. 2 , the reactions considered for the polymer layer  22  are as follows. 
     The carbon (C) in the polymer layer  22  reacts, of all the fluorine (F) in the CF-based gas injected from the plasma  20  (arrow A 2  in  FIG. 2 ), that which remains unconsumed (unreacted) in the SiO 2  film  21 , turning into CF 2 . Then, the produced CF 2  is released externally (arrow A 6  in  FIG. 2 ). 
     Further, the carbon (C) in the polymer layer  22  reacts with the oxygen (O) injected from the plasma  20  (arrow A 7  in  FIG. 2 ), turning into CO. Then, the produced CO is released externally (arrow A 8  in  FIG. 2 ). 
     In the present embodiment, the relationship between the amount of various injected particles and the amount of various released particles (products) (hereinafter collectively referred to as the reaction particle flux) in the above various reactions is resolved by using the Flux method, thus predicting and evaluating the damage sustained by the SiO 2  film  21 . 
     (2) Reactive Layer Model 
     In order to evaluate the damage sustained by the SiO 2  film  21  along the depth, in the present embodiment, the reactive layer  21   a  is divided along the depth (along the thickness) into a plurality of thin film slabs (hereinafter simply referred to as the slabs). Then, the relational formula between the various reaction particles in terms of flux acquired from the above reaction model in each slab is found by the Flux method, thus calculating the etching contribution rate and the reaction area ratio θ of each slab. 
       FIGS. 3A and 3B  illustrate the model configuration of the reactive layer  21   a . It should be noted that  FIG. 3A  illustrates the overall configuration of the reaction model shown in  FIG. 2 , and that  FIG. 3B  illustrates the reactive layer  21   a  and polymer layer  22  in an enlarged fashion. 
       FIGS. 3A and 3B  illustrate a configuration example in which the reactive layer  21   a  is divided into ‘n’ slabs  21   b  along the thickness. It should be noted that the slabs  21   b  are equally thick with a thickness L. That is, in this example, the reactive layer  21   a  is divided equally into the ‘n’ slabs  21   b  each having the thickness L. Further, in this example, as for the area subject to calculation (thickness including the reactive layer  21   a  and polymer layer  22 ), the maximum penetration depth of the ion particle  23  is Dp, the thickness of the polymer layer  22  (hereinafter referred to as the polymer film thickness) T, and the thickness of the reactive layer  21   a  Dp−T. 
     In the present embodiment, an etching contribution rate ER k  (where k is the index of the slabs  21   b : k=1, 2, . . . , n) and the reaction area ratio θ k  in each of the slabs  21   b  are found using the relational formula between the various reaction particles in terms of flux at the interface between the adjacent slabs  21   b . The specific calculation method of (calculation formula for) the contribution rate ER k  and reaction area ratio θ k  of each of the slabs  21   b  will be described in detail later. It should be noted that the total sum of the etching contribution rates ER k  of all the slabs  21   b  is the etching rate of the reactive layer  21   a  (hereinafter simply referred to as the etch rate ER). 
     Further, in the present embodiment, the damage sustained by each of the slabs  21   b  is calculated based on the etching contribution rate ER k  and reaction area ratio θ k  calculated for each of the slabs  21   b , thus finding the damage distribution in the reactive layer  21   a . At this time, in the present embodiment, in order to find the damage distribution along the depth caused by etching, the thickness L of each of the slabs  21   b  is converted into a thickness L k * which is weighted with the linear ratio of the contribution rate ER k . That is, in the present embodiment, in order to calculate the damage, the reactive layer  21   a  is redivided into the slabs  21   b  each having the thickness L k * in consideration of the etching contribution rate ER k  of each of the slabs  21   b.    
       FIGS. 4A and 4B  illustrate how the reactive layer  21   a  is redivided. It should be noted that  FIG. 4A  is a diagram illustrating how the reactive layer  21   a  is divided before the redivision, and that  FIG. 4B  is a diagram illustrating how the reactive layer  21   a  is divided after the redivision. 
     The thickness L k * of each of the slabs  21   b  varies depending on the etching contribution rate ER k  of the associated slab  21   b . Therefore, the thickness L k * is no longer constant as illustrated in  FIG. 4B  and changes along the thickness of the reactive layer  21   a . More specifically, the farther the slab  21   b  is from the surface of the reactive layer  21   a  along the thickness of the reactive layer  21   a , the smaller the etching contribution rate ER k  of the slab  21   b . Therefore, the farther the slab  21   b  is from the surface of the reactive layer  21   a , the smaller the thickness L k * of the slab  21   b  after the redivision. 
     Further,  FIGS. 5A and 5B  illustrate the model configuration of the reactive layer  21   a  after the above redivision. It should be noted that  FIG. 5A  illustrates the overall configuration of the reaction model shown in  FIG. 2 , and that  FIG. 5B  illustrates the reactive layer  21   a  and polymer layer  22  after the redivision in an enlarged fashion. In the model of the reactive layer  21   a  shown in  FIGS. 5A and 5B , on the other hand, the same elements as those in  FIGS. 3A and 3B  are denoted by the same reference numerals. 
     As is obvious from the comparison between  FIGS. 5A and 5B  and  FIGS. 3A and 3B , the model of the reactive layer  21   a  and polymer layer  22  after the redivision is identical to that before the redivision except that the thicknesses of the slabs  21   b  in the reactive layer  21   a  are different. It should be noted that the calculation method of the thickness L k * of each of the slabs  21   b  after the redivision will be described in detail later. 
     [Calculation Principle of the Damage Distribution] 
     A description will be given below of the principle behind the technique for calculating, by the Flux method, the damage sustained by the SiO 2  film  21  when the same film  21  is dry-etched. 
     In the simulator  10  according to the present embodiment, the damage calculation section  12  calculates the damage distribution of the SiO 2  film  21  based on the processing conditions supplied externally via the input section  11 . To briefly describe the calculation process at this time, the damage calculation section  12  calculates a reaction area ratio θ k (t), etch rate ER(t) and polymer film thickness T(t) of each of the slabs  21   b  in this order every calculation step Δt (where Δt&lt;etching time t 0 ). Next, the same section  12  repeats this calculation process until a given etching time t 0  is reached. Then, the damage calculation section  12  redivides the reactive layer  21   a  based on the reaction area ratio θ k (t) of each of the slabs  21   b  and etch rate ER(t) at the given etching time t 0 , thus calculating the damage distribution. 
     A detailed description will be given below of the calculation principle of various evaluation parameters (reaction area ratio θ k (t), etch rate ER(t), polymer film thickness T(t), thickness L k * of each of the slabs  21   b  after redivision and damage level) found at the time of damage calculation. 
     (1) Calculation Principle of the Reaction Area Ratio θ k (t) 
     The reaction area ratio θ k (t) of each of the slabs  21   b  at the given time t (≦etching time t 0 ) during etching is found by solving the ordinary differential equation of the reaction area ratio θ k (t) with respect to time t shown below in Formula (1). 
     
       
         
           
             
               
                 
                   
                     
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     The first term on the right side of the formula represents the flux of the ion particle  23  that can react with SiO 2  in each of the slabs  21   b . The second term on the right side represents the CO flux released as a result of the reaction of oxygen (O) in each of the slabs  21   b  with carbon (C) in the polymer layer  22 . Further, “σ SiO2 ” in Formula (1) is the surface density of the SiO 2  film  21 . Further, “Γ i ” in Formula (1) is the total flux of the ion particle  23  injected into the SiO 2  film from the plasma  20 . 
     “Y iSiO2 (T′)” in Formula (1) is the reaction probability between a CF-based ion and the SiO 2  film  21  in the slab  21   b  having the index k. The reaction probability Y iSiO2 (T′) is a function of a depth T′ from the surface of the polymer layer  22  to the slab  21   b  having the index k. That is, the reaction probability Y iSiO2 (T′) is a parameter that varies depending on the polymer film thickness T(t) and the position of the slab  21   b.    
     It should be noted that the polymer film thickness T(t) is a function of time t. Therefore, the reaction probability Y iSiO2 (T′) is also a function of time t. Hence, the value at time t−Δt which is earlier than the current time t by one calculation step or a given initial value is used as the reaction probability Y iSiO2 (T′) in Formula (1). It should be noted that the reaction probability Y iSiO2 (T′) is calculated by using Formula (2) shown below.
 
 Y   iSiO2 ( T ′)= K{α 1×exp[α2×( E−ΔE )]}
 
Δ E=α 3+α4 ×T′   (2)
 
     In Formula (2), “E” is the incident ion energy, and “ΔE” is the attenuation of the incident ion energy E. Further, “K” and “α 1 ” to “α 4 ” in Formula (2) are given constants. The values of these parameters are set as appropriate, for example, according to the processing conditions including the process conditions, material of the workpiece, and gas type. 
     On the other hand, “Γ O   ER (k,t)” in Formula (1) is expressed as the product of the total flux of oxygen (O) produced in the slab  21   b  having the index k during etching of the SiO 2  film  21  and a reaction probability Y OC2  between carbon (C) and oxygen (O) in the polymer layer  22 . More specifically, “Γ O   ER (k,t)” is calculated by using Formula (3) shown below.
 
Γ O   ER ( k,t )= ER   k ( t− 1)×2ρ SiO2   ×Y   OC2   (3)
 
     “ER k (t−1)” in Formula (3) is the etching contribution rate of the slab  21   b  having the index k at time t−Δt which is earlier by one calculation step (or in the initial condition). Further, “ρ SiO2 ” in Formula (3) is the number density of the SiO 2  film  21 . 
     Normally, the surface reaction speed during etching (change of the reaction area ratio θ k (t) over time) is considered to be sufficiently faster (smaller) than the one calculation step Δt. In order to calculate the reaction area ratio θ k (t) using Formulas (1) to (3), therefore, the reaction area ratio θ k (t) of each of the slabs  21   b  at the given time t is calculated by assuming dθ k (t)/dt in Formula (1) to be 0. More specifically, the reaction area ratio θ k (t) of each of the slabs  21   b  is calculated by using Formula (4) shown below. 
                       θ   k     ⁡     (   t   )       =           Y     iSiO   ⁢           ⁢   2       ⁡     (     T   ′     )       ⁢     Γ   i               Y     SiO   ⁢           ⁢   2       ⁡     (     T   ′     )       ⁢     Γ   i       +       Γ   O   ER     ⁡     (     k   ,   t     )                   (   4   )               
(2) Calculation Principle of the Etch Rate ER(t)
 
     The etch rate ER(t) of the reactive layer  21   a  at the given time t is calculated by using the reaction area ratio θ k (t) of each of the slabs  21   b  calculated in “(1) Calculation principle of the reaction area ratio θ k (t).” More specifically, the etch rate ER(t) is calculated as follows. 
     First, the etching contribution rate ER k (t) of each of the slabs  21   b  at the given time t is calculated using the reaction area ratio θ k (t) of each of the slabs  21   b  and Formula (5) shown below. 
     
       
         
           
             
               
                 
                   
                     
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                       ⁢ 
                       
                         
                           Γ 
                           F 
                         
                         / 
                         β 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     
                       ρ 
                       
                         SiO 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     In Formula (5), “β 1 ” is a parameter relating to a detached substance (SiF 2  and/or SiF 4  in the example of the reaction model shown in  FIG. 2 ) produced during etching of the SiO 2  film  21 . Further, “Y FSiO2 (T′)” in Formula (5) is the reaction probability between the SiO 2  film  21  and fluorine (F) in the slab  21   b . It should be noted that the polymer film thickness T(t) is a function of time t. Therefore, the reaction probability Y FSiO2 (T′) is also a function of time t. Hence, the value calculated at time t−Δt which is earlier than the current time t by one calculation step or a given initial value is used as the reaction probability Y FSiO2 (T′) in Formula (5). It should be noted that the reaction probability Y FSiO2 (T′) is calculated by using Formula (6) shown below.
 
 Y   FSiO2 ( T ′)=α1×exp[α2×( E−ΔE )]  (6)
 
     On the other hand, “Γ F ” is the product of the total flux of fluorine (F) injected from the plasma  20  onto the SiO 2  film  21  and the reaction probability between the CF-based gas and polymer layer  22 . More specifically, “Γ F ” is expressed by Formula (7) shown below. 
     
       
         
           
             
               
                 
                   
                     Γ 
                     F 
                   
                   = 
                   
                     
                       ∑ 
                       m 
                     
                     ⁢ 
                     
                       
                         Γ 
                         CFm 
                       
                       ⁢ 
                       
                         Y 
                         CFm 
                       
                       ⁢ 
                       
                         R 
                         Fm 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     It should be noted that “Γ CFm ” in Formula (7) is the total flux of the CF-based gas injected from the plasma  20 . “Y CFm ” in Formula (7) is the reaction probability between the CF-based gas and polymer layer  22 . “R Fm ” in Formula (7) is the ratio of fluorine (F) in the CF-based gas. Further, an index m in Formula (7) represents the type of the reaction gas CF. 
     Then, the etching contribution rates ER k (t), calculated by using Formula (5), are summed up to calculate the etch rate ER(t) of the reactive layer  21   a  at the given time t. More specifically, the etch rate ER(t) at the given time t is calculated by using Formula (8) shown below. 
                     ER   ⁡     (   t   )       =       ∑   k     ⁢       ER   k     ⁡     (   t   )                 (   8   )               
(3) Calculation Principle of the Polymer Film Thickness T(t)
 
     The polymer film thickness T(t) at the given time t is calculated by using the reaction area ratio θ k (t) and etch rate ER(t) calculated respectively based on the calculation principles described in Sections (1) and (2). 
     More specifically, the polymer film thickness T(t) is found by solving the ordinary differential equation of the polymer film thickness T(t) with respect to time t shown below in Formula (9). At this time, the polymer film thickness T(t) is calculated, for example, by substituting dT(t)/dt in Formula (9) by a difference formula such as [T(t)−T(t−Δt)]/Δt. 
     
       
         
           
             
               
                 
                   
                     
                       ρ 
                       P 
                     
                     ⁢ 
                     
                       
                         ⅆ 
                         
                           T 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                       
                         ⅆ 
                         t 
                       
                     
                   
                   = 
                   
                     
                       Γ 
                       C 
                     
                     - 
                     
                       Γ 
                       O 
                     
                     - 
                     
                       Γ 
                       F 
                       * 
                     
                     - 
                     
                       
                         ∑ 
                         k 
                       
                       ⁢ 
                       
                         
                           
                             θ 
                             k 
                           
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             Γ 
                             O 
                             ER 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               , 
                               t 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     The first term on the right side of Formula (9) represents the flux of carbon (C) injected onto the SiO 2  film  21  from the plasma  20 . The second term on the right side of Formula (9) represents the CO flux released as a result of the reaction of oxygen (O) in the plasma  20  with carbon (C) in the polymer layer  22 . The third term on the right side of Formula (9) represents the flux of CF 2  released as a result of the reaction between fluorine (F) which remains unconsumed (unreacted) in the SiO 2  film  21  of all the fluorine (F) injected onto the SiO 2  film  21  from the plasma  20  and carbon (C) in the polymer layer  22 . Further, the fourth term on the right side of Formula (9) represents the total flux of CO released as a result of the reaction between oxygen (O) in each of the slabs  21   b  and carbon (C) in the polymer layer  22 . 
     “ρ P ” in Formula (9) is the number density of the polymer layer  22 . Further, “Γ C ” in Formula (9) is the product of the total flux of carbon (C) injected from the plasma  20  and the reaction probability between the CF-based gas and polymer layer  22 . More specifically, “Γ C ” is expressed by Formula (10) shown below. It should be noted that “R Cm ” in Formula (10) is the ratio of carbon (C) in the CF-based gas. 
     
       
         
           
             
               
                 
                   
                     Γ 
                     C 
                   
                   = 
                   
                     
                       ∑ 
                       m 
                     
                     ⁢ 
                     
                       
                         Γ 
                         CFm 
                       
                       ⁢ 
                       
                         Y 
                         CFm 
                       
                       ⁢ 
                       
                         R 
                         Cm 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     On the other hand, “Γ O ” in Formula (9) is the product of the total flux of oxygen (O) injected from the plasma  20  and the reaction probability between oxygen (O) and the polymer layer  22 . More specifically, “Γ O ” is expressed by Formula (11) shown below.
 
Γ O   =Y   OC1 Γ O   P   (11)
 
     It should be noted that “Y OC1 ” in Formula (11) is the reaction probability between oxygen (O) and carbon (C) in the polymer layer  22 . Further, “Γ O   P ” in Formula (11) is the total flux of oxygen (O) injected from the plasma  20 . 
     Further, “Γ F *” in Formula (9) is the product of the flux of fluorine (F) which remains unconsumed (unreacted) in the SiO 2  film  21  of all the fluorine (F) injected onto the SiO 2  film  21  from the plasma  20  and the reaction probability between fluorine (F) and the polymer layer  22 . More specifically, “Γ F *” is expressed by Formula (12) shown below.
 
Γ F *=(1 −Y   FSiO2 ( T ′)β1)Γ F   R   d /β2  (12)
 
     It should be noted that “β 2 ” in Formula (12) is a parameter relating to a detached substance (CF 2  in the example of the reaction model shown in  FIG. 2 ) produced during etching of the polymer layer  22 . On the other hand, “R d ” in Formula (12) is the reaction probability between fluorine (F) and carbon (C) in the polymer layer  22 . 
     (4) Recalculation Principle of the Slab Thickness 
     In the present embodiment, in order to calculate the damage distribution, the thickness of each of the slabs  21   b  is reset (recalculated) in consideration of the ratio (weight) of the contribution rate ER k  of each of the slabs  21   b  in the etch rate ER as described above. Then, the reactive layer  21   a  is redivided into the plurality of slabs  21   b  each having the reset thickness. 
     In this example, a linear ratio is used as the weight of the contribution rate ER k  of each of the slabs  21   b  in the etch rate ER so as to reset the thickness of each of the slabs  21   b  to L k * using Formula (13) shown below. It should be noted that the etch rate ER, contribution rate ER k  and polymer film thickness T in Formula (13) are those at the time of the end of etching (t=t 0 ). 
     
       
         
           
             
               
                 
                   
                     L 
                     k 
                     * 
                   
                   = 
                   
                     
                       
                         ER 
                         k 
                       
                       ER 
                     
                     × 
                     
                       ( 
                       
                         Dp 
                         - 
                         T 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     If the thickness of each of the slabs  21   b  is reset by using Formula (13), the overall thickness (Dp−T) of the reactive layer  21   a  after the redivision remains unchanged. However, the farther each of the slabs  21   b  is from the surface of the reactive layer  21   a , the smaller the thickness L k * of each of the slabs  21   b  (refer to  FIG. 4B ). As a result, the thicknesses L k * of the slabs  21   b  near the surface of the reactive layer  21   a  whose contribution rates ER k  are greater are greater than before the redivision. On the other hand, the thicknesses L k * of the slabs  21   b  near the bottom of the reactive layer  21   a  whose contribution rates ER k  are smaller are smaller than before the redivision. 
     By resetting the thickness of each of the slabs  21   b  as described above, it is possible to reflect the impact of the contribution rates ER k  of each of the slabs  21   b  in the etch rate ER in the reset thicknesses L k * of the slabs  21   b . That is, by resetting the thickness of each of the slabs  21   b  to the value weighted with the corresponding contribution rate ER k , it is possible to reflect information about damage along the depth in the thickness L k * of each of the slabs  21   b.    
     (5) Calculation Principle of the Damage Level 
     In the present embodiment, the number of dangling bonds of silicon (Si) taking place during etching is used as an indicator of damage caused by etching. In the present embodiment, therefore, a damage level damage(k) of each of the slabs  21   b  caused by etching is defined as the product of the thickness L k * of each of the slabs  21   b  after redivision and the reaction area ratio θ k  at the end of etching. That is, the damage level damage(k) of each of the slabs  21   b  is defined by using Formula (14) shown below.
 
damage( k )≡ L   k *×θ k   (14)
 
     By defining the damage level damage(k) of each of the slabs  21   b  by using Formula (14) shown above, it is possible to express the damage level along the depth factoring in the etch rate ER. 
     On the other hand, “L k *” in Formula (14) is a parameter weighted with the etching contribution rate ER k  of each of the slabs  21   b  (factoring in the etching rate). Therefore, “L k *” is a parameter relating to the damage distribution along the depth of the reactive layer  21   a . On the other hand, “θ k (t)” is a parameter relating to the damage distribution in the in-plane direction of the etched surface. Hence, it is possible to evaluate the three-dimensional damage distribution by defining the damage damage(k) of each of the slabs  21   b  by using Formula (14) shown above. 
     [Calculation of the Damage Distribution] 
     A specific description will be given next of the calculation of damage sustained by the workpiece (SiO 2  film) performed by the simulator  10  according to the present embodiment with reference to  FIG. 6 . It should be noted that  FIG. 6  is a flowchart illustrating the procedure for calculating the damage distribution in the present embodiment. 
     First, the damage calculation section  12  acquires various processing conditions supplied to the simulator  10  externally via the input section  11  (step S 1 ). 
     Among the processing conditions acquired in step S 1  are gas type, gas flow rate, gas pressure, workpiece temperature (e.g., wafer temperature), material of the workpiece (e.g., film type), etching time and ion injection energy. Further, among the processing conditions are calculation parameters such as the initial thickness L of each of the slabs  21   b  (thickness before redivision), initial polymer film thickness T and maximum penetration depth Dp of the ion particle  23  (depth of the area subject to calculation). 
     Next, the damage calculation section  12  searches the database section  13  based on the acquired processing conditions (particularly, gas type, gas flow rate, gas pressure, material of the workpiece and so on), thus acquiring various parameters necessary for the simulation (step S 2 ). 
     Among the various parameters acquired in step S 2  are those relating to various reactions between the workpiece and gas such as the fluxes Γ of various reaction particles corresponding to the processing conditions (e.g., Γ i , Γ CF , Γ O   P ), various reaction probabilities and reaction product parameters. Further, among the various parameters acquired in step S 2  are parameters of the material of the workpiece such as the number density and surface density of the SiO 2  film  21 . 
     It should be noted, however, that if the fluxes Γ of various reaction particles corresponding to the processing conditions are not available in the database section  13  in step S 2 , the fluxes Γ of various reaction particles corresponding to the processing conditions may be calculated, for example, as described below. First, the damage calculation section  12  acquires data of the fluxes Γ of various reaction particles corresponding to conditions close to the processing conditions. Next, the same section  12  interpolates the acquired data, thus calculating the fluxes Γ of various reaction particles corresponding to the processing conditions. 
     It should be noted that the acquisition method of the fluxes Γ of various reaction particles corresponding to the processing conditions in step S 2  is not limited to that adapted to acquire the fluxes Γ from the database section  13 . Alternatively, for example, the damage calculation section  12  may calculate the fluxes Γ of various reaction particles based on the acquired processing conditions (particularly, gas type, gas flow rate, gas pressure, material of the workpiece and so on). 
     On the other hand, for example, if the measured values of the fluxes Γ of various reaction particles can be acquired externally, the damage calculation section  12  may acquire the fluxes Γ of various reaction particles in step S 2  externally via the input section  11 . It should be noted that not only the fluxes Γ of various reaction particles but also various parameters to be acquired in step S 2  may be directly entered externally. In this case, the process step in step S 2  may be omitted, and these various parameters necessary for the damage calculations may be acquired in step S 1 . 
     Next, the damage calculation section  12  divides the reactive layer  21   a  into the plurality of slabs  21   b  based on the initial thickness L of the slabs  21   b , initial thickness T of the polymer layer  22  and the maximum penetration depth Dp of the ion particle  23  acquired in step S 1  (step S 3 ). More specifically, the reactive layer  21   a  having the initial depth Dp−T (initial value) is equally divided into the plurality of slabs  21   b  each having the initial thickness L. 
     Next, the damage calculation section  12  calculates the reaction area ratio θ k (t) of each of the slabs  21   b  at the given time t (≦etching time t 0 ) using the acquired processing conditions and various parameters corresponding to these conditions (step S 4 ). More specifically, the damage calculation section  12  calculates the reaction area ratio θ k (t) of each of the slabs  21   b  using Formulas (1) to (4) shown above. 
     Next, the damage calculation section  12  calculates the etch rate ER(t) at the given time t using the reaction area ratio θ k (t) of each of the slabs  21   b  calculated in step S 4  (step S 5 ). More specifically, the damage calculation section  12  calculates the etch rate ER(t) using Formulas (5) to (8) shown above. 
     Next, the damage calculation section  12  calculates the polymer film thickness T(t) at the given time t using the reaction area ratio θ k (t) of each of the slabs  21   b  and the etch rate ER(t) calculated in steps S 4  and S 5 , respectively (step S 6 ). More specifically, the damage calculation section  12  calculates the polymer film thickness T(t) using Formulas (9) to (12) shown above. 
     Next, the damage calculation section  12  determines whether the current time t has reached the etching end time (step S 7 ). More specifically, the damage calculation section  12  determines whether the elapsed time from the beginning of the calculation has reached the etching time t 0  set in advance. 
     If the current time t has yet to reach the etching end time in step S 7 , the determination in step S 7  is No. In this case, the damage calculation section  12  performs time evolution, that is, updates the calculation time (t=t+Δt) (step S 8 ) and then returns to the process step in step S 4 . Then, the damage calculation section  12  repeats steps S 4  to S 8  until the time t reaches the etching time t 0 . 
     On the other hand, when the current time t has reached the etching end time in step S 7 , the determination in step S 7  is Yes. In this case, the damage calculation section  12  redivides the reactive layer  21   a  into the plurality of slabs  21   b  in consideration of the ratio (weight) of the contribution rate ER k  of each of the slabs  21   b  in the etch rate ER at the etching end time (t=t 0 ) (step S 9 ). More specifically, the damage calculation section  12  resets the thickness L k * of each of the slabs  21   b  using Formula (13) shown above, thus redividing the reactive layer  21   a  into the plurality of slabs  21   b  each having the reset thickness. 
     Then, after having redivided the reactive layer  21   a  into the plurality of slabs  21   b , the damage calculation section  12  calculates the damage level damage(k) of each of the slabs  21   b  caused by etching (step S 10 ). More specifically, the damage calculation section  12  calculates the damage level damage(k) of each of the slabs  21   b  by using Formula (14) shown above. 
     In the present embodiment, the damage level damage(k) of each of the slabs  21   b  during etching is calculated as described above, thus predicting (evaluating) the damage distribution of the workpiece. 
     The present embodiment is an approach using the Flux method as described above, thus contributing to a significantly reduced amount of calculations as compared to the past approaches (particle method) based on molecular dynamics. Therefore, the simulator  10  according to the present embodiment allows for calculation of the damage distribution of a workpiece more quickly. 
     More specifically, if a database is created using the damage distribution calculated using various processing conditions as in a sixth embodiment which will be described later, the Flux method can, for example, reduce the time it takes to create a database from about a month with the particle method to several minutes or so. That is, the present embodiment can calculate the damage distribution in an exceptionally shorter amount of time than the past particle method. This makes it possible for the present embodiment to predict the damage distribution over a wide area such as across the chip or wafer surface. 
     It should be noted that a case has been described in the present embodiment in which the SiO 2  film  21  is dry-etched using a CF-based gas as a reaction model, the present disclosure is not limited thereto. Even if the workpiece is, for example, an Si, SiN or organic film, it is possible to predict (evaluate) the damage distribution with the same algorithm. Further, even if the gas type is changed, it is possible to predict (evaluate) the damage distribution with the same algorithm. 
     It should be noted, however, that if the material of the workpiece and/or the gas type is changed, the reaction model also changes. Therefore, the relational formula between the fluxes Γ of various reaction particles is set as appropriate according to the reaction model to be considered. Further, in this case, various parameters necessary for the damage calculations are changed as appropriate according to the reaction model to be considered. It should be noted that if the gas type is changed, the film that builds up on the reactive layer  21   a  is also changed as appropriate according to the gas type (e.g., changed to an oxide film). 
     [Various Evaluation Examples] 
     A description will be given next of various evaluation examples using the simulator  10  according to the present embodiment described above. 
     (1) Evaluation Example 1 
     In evaluation example 1, the reproducibility of the etch rate ER and polymer film thickness T was evaluated by using the simulator  10  according to the present embodiment. More specifically, the measured values of the etch rate ER and polymer film thickness T at the time of dry-etching of the SiO 2  film  21  using the plasma  20  of a CF-based gas were compared against the predicted values calculated by the above simulation. 
     The process conditions in evaluation example 1 are as follows. The C 4 F 8  gas was used as a CF-based gas. A mixture gas of argon (Ar) and oxygen (O 2 ) was circulated in the chamber of the etcher. The flow rates of argon (Ar) and oxygen (O 2 ) were maintained constant respectively at 400 sccm and 8 sccm. Further, the flow rate of the C 4 F 8  gas was varied to compare the measured values of the etch rate ER and polymer film thickness T against the predicted values at each flow rate. Still further, the gas pressure in the chamber was set at 30 mT, and the incident ion energy E of the ion particle  23  was 1450 V. 
     As for the fluxes Γ of various reaction particles used for simulation calculations, the measured values monitored in the chamber of the etcher were used. On the other hand, the initial values of various parameters used for simulation calculations were set as appropriate according to the process conditions and other factors. Further, the initial values of the various evaluation parameters (polymer film thickness T, etch rate ER and contribution rate ER k  of each of the slabs  21   b ) were all set to zero. 
       FIGS. 7 and 8  illustrate the results of evaluation example 1.  FIG. 7  illustrates the characteristic of change in the etch rate ER with change in the flow rate of C 4 F 8 , with the horizontal axis representing the flow rate of C 4 F 8  and the vertical axis representing the etch rate ER. On the other hand,  FIG. 8  illustrates the characteristic of change in the polymer film thickness T with change in the flow rate of C 4 F 8 , with the horizontal axis representing the flow rate of C 4 F 8  and the vertical axis representing the polymer film thickness T. It should be noted that characteristics  31  and  33  shown by solid lines in  FIGS. 7 and 8  are characteristics of the predicted values obtained by the simulation, and that characteristics  32  and  34  shown by dashed lines in  FIGS. 7 and 8  are characteristics of the measured values. 
     As is obvious from the evaluation results shown in  FIGS. 7 and 8 , the distinctive changes of the characteristics  32  and  34  of the measured values and the absolute values of the etch rate ER and polymer film thickness T are reproduced with high accuracy by the characteristics  31  and  33  obtained from the simulation. That is, it is clear from these results that the simulation technique according to the present embodiment can predict, with high accuracy, the etch rate ER and polymer film thickness T of a workpiece. 
     (2) Evaluation Example 2 
     In evaluation example 2, the Si film is dry-etched under the same process conditions as in evaluation example 1 to find the measured values and the predicted values calculated by the above simulation in the same manner as in evaluation example 1, of the etch rate ER of the Si film at various flow rates of C 4 F 8 . Then, in evaluation example 2, the measured and predicted values of the etch rate selection ratio between the SiO 2  and Si films (=SiO 2  film etch rate/Si film etch rate) were calculated together with the evaluation result of evaluation example 1 for comparison between the two. It should be noted that the etch rate selection ratio between the SiO 2  and Si films is an important parameter for etching the SiO 2  film into a desired pattern in a multilayer film made up of a SiO 2  film formed on a Si film. 
       FIG. 9  illustrates the result of evaluation example 2. It should be note that  FIG. 9  illustrates the characteristic of change in the etch rate selection ratio with change in the flow rate of C 4 F 8 , with the horizontal axis representing the flow rate of C 4 F 8  and the vertical axis representing the etch rate selection ratio. Further, a characteristic  35  shown by a solid line in  FIG. 9  is a characteristic of the predicted value obtained by the simulation, and that a characteristic  36  shown by a dashed line in  FIG. 9  is a characteristic of the measured value. 
     As is obvious from the evaluation result shown in  FIG. 9 , the distinctive change of the characteristic  36  of the measured value and the absolute value of the etch rate selection ratio between the SiO 2  and Si films are reproduced with high accuracy by the characteristic  35  obtained from the simulation. 
     (3) Evaluation Example 3 
     In evaluation example 3, the reproducibility of the damage distribution of a workpiece by the simulator  10  according to the present embodiment was evaluated. 
     It should be noted that, in the present embodiment, a TEM (Transmission Electron Microscope) image of the workpiece was used to find the measured value of the damage distribution of the workpiece. However, if a SiO 2  film is used as a workpiece, the workpiece is oxidized. Therefore, it is difficult to clearly identify the thickness of the damaged layer (hereinafter referred to as the etching-damaged layer) in a TEM image. 
     For this reason, in evaluation example 3, the measured value of the damage distribution and the predicted value thereof obtained by the simulation were compared for evaluation in the Si film in which the thickness of the etching-damaged layer was clearly identifiable. 
     It should be noted that a Si film was used as a workpiece in evaluation example 3. Therefore, the reaction model was changed to one corresponding to dry etching of a Si film. Various parameters used for damage calculations (e.g., surface density and number density of the workpiece, reaction probability) were also changed as appropriate. Therefore, the relational formula between the fluxes Γ of various reaction particles was also changed as appropriate because of the change in reaction model. For dry etching of a Si film, for example, the term of “θΓ O   ER ” is omitted in Formulas (1) and (9). 
     In evaluation example 3, a Si film was dry-etched with a CF-based gas using a CCP (Capacitively Coupled Plasma) etcher, thus measuring the damage distribution of the Si film. It should be noted that, in evaluation example 3, the flow rate of C 4 F 8  was maintained constant at 11 sccm and all other process conditions were the same as in evaluation example 2. Further, in evaluation example 3, the thickness of the etching-damage layer was measured not only with a TES image but also by using XPS (X-ray Photoelectron Spectroscopy). 
     Further, in the simulation calculations for evaluation example 3, the initial thickness L of each of the slabs  21   b  was 0.5 nm, and the maximum penetration depth Dp of the ion particle  23  was 7 nm. It should be noted that, in evaluation example 3, an etcher was used that was equipped with various devices adapted to monitor the fluxes Γ of various reaction particles and the incident ion energy E in its chamber. Therefore, the monitored (measured) values were used for the parameters for simulation calculations. 
       FIGS. 10A and 10B  illustrate the results of evaluation example 3. It should be noted that  FIG. 10A  illustrates a TEM image showing the cross-sectional structure of the Si film near its surface.  FIG. 10B  is a characteristic diagram of the damage distribution calculated by the simulator  10  along the depth of the reactive layer  21   a.    
     In the TEM image, the thickness of the etching-damaged layer was approximately 1.4 nm. Further, a similar result was obtained from XPS. 
     In the simulation result, on the other hand, the damage level was 0.2 to 0.4 in the area 1.5 nm in depth from the surface of the Si film. The damage level was 0.0 to 0.2 in the area deeper than 1.5 nm. That is, in the simulation result (predicted value), the thickness of the etching-damaged layer was approximately 1.5 nm which is roughly the same as the measured value. 
     It is clear from the evaluation result of evaluation example 3 described above that the damage distribution along the depth of the workpiece can be reproduced by the simulator  10  according to the present embodiment with high accuracy. 
     (4) Evaluation Example 4 
     In evaluation example 4, the change in damage distribution of a SiO 2  film with change in flow rate of a CF-based gas was calculated by the simulator  10  according to the present embodiment for evaluation. 
     More specifically, using C 4 F 8  as a CF-based gas, the damage distribution along the depth of a SiO 2  film was calculated (predicted) with the simulator  10  with the flow rate of C 4 F 8  at 11 sccm or 33 sccm. That is, the damage distribution along the depth of the SiO 2  film was calculated in the condition (11 sccm) in which the etch rate ER was large and the polymer film thickness T was small or the condition (33 sccm) in which the etch rate ER was small and the polymer film thickness T was large. 
     It should be noted that, in the simulation calculations for evaluation example 4, the calculation conditions (initial values of various calculation parameters and process conditions) were the same as in evaluation example 3 except that a SiO 2  film was use as a workpiece, and that the flow rate of C 4 F 8  was changed. 
       FIGS. 11A and 11B  illustrate the simulation result of evaluation example 4. As is obvious from  FIG. 11 , the damage level was maximal in the area near the surface of the SiO 2  film and decreased with increasing depth away from the surface, irrespective of the gas flow rate. 
     Further, as is obvious from the result shown in  FIGS. 11A and 11B , when the gas flow rate was 11 sccm, the damage level was 0.2 to 0.4 or more in the area down to about 7 nm in depth from the surface of the SiO 2  film. On the other hand, when the gas flow rate was 33 sccm, the damage level was 0.2 to 0.4 or more in the area down to about 3.5 nm in depth from the surface of the SiO 2  film. Further, as a result of comparison of the damage levels near the surface, the damage level was found to be greater when the flow rate was 11 sccm than when the flow rate was 33 sccm. 
     It is clear from the evaluation result of evaluation example 4 described above that the damage level of the workpiece was greater and the workpiece was damaged deeper in the condition (11 sccm) in which the etch rate ER was large and the polymer film thickness T was small. That is, it has been discovered from this evaluation result that the simulator  10  according to the present embodiment can quantitatively evaluate the characteristic of probable change in damage distribution resulting from the change in flow rate of C 4 F 8  during etching of a SiO 2  film with a CF-based gas. 
     It is clear from the results of evaluation examples 1 to 4 described above that the simulator  10  according to the present embodiment can predict and evaluate, with high accuracy, the damage distribution of a workpiece that takes place as a result of ion injection. 
     &lt;2. Second Embodiment&gt; 
     A description has been given in the first embodiment of a case in which no structure (e.g., side walls) is formed around the damage evaluation point that is designed to prevent the injection of various reaction particles from the plasma (gas) onto the workpiece. In a practical device pattern, however, the surface to be processed, i.e., an area to be evaluated, often has a shape with projections and depressions (three-dimensional shape). In this case, of various reaction particles injected onto the workpiece from the plasma, the fluxes of those particles reaching the bottom surface of the depressed portion of the surface to be processed vary depending on the shape of the depressed portion (e.g., width, depth and aspect ratio therebetween). 
     In the second embodiment, for this reason, a description will be given below of a configuration example of a simulator capable of calculating the damage distribution even if there is a structure around the damage evaluation point that prevents the injection of various reaction particles onto the workpiece from the plasma. 
     If the fluxes of various reaction particles injected onto the evaluation point on the bottom of the depressed portion vary (decrease) because of the impact of the structure such as side walls formed around the evaluation point, this variation depends on the field-of-view region there is a line of sight from the evaluation point to the plasma. In the present embodiment, the field-of-view region in which there is a line of sight from the evaluation point to the plasma is expressed by a three-dimensional angle (hereinafter referred to as a solid angle), and the impact of the surrounding structure on the damage distribution at the evaluation point is reflected in the solid angle. 
     [Calculation Principle of the Solid Angle Effect] 
     A specific description will be given first of the method of reflecting the impact of the surrounding structure on the damage distribution at the evaluation point in the solid angle at the evaluation point (hereinafter referred to as the solid angle effect calculation method) with reference to the accompanying drawings. It should be noted that a workpiece with a groove portion formed on its surface (workpiece having a trench structure) will be taken as an example to describe the solid angle effect calculation method at the evaluation point. 
       FIGS. 12A and 12B  schematically illustrate the configuration of a workpiece with a groove portion formed on its surface. It should be noted that  FIG. 12A  is a schematic perspective view of a workpiece  40  and  FIG. 12B  is a side view of the workpiece  40  as seen from the direction of extension of a groove portion  41 . 
     A given evaluation point on a bottom surface  41   a  (surface to be processed) of the groove portion  41  of the workpiece  40  in  FIGS. 12A and 12B  is denoted by ‘P.’ Further, the intersection between a line segment on the bottom surface  41   a  passing through the evaluation point P and extending in the direction orthogonal to the direction of extension of the groove portion  41  and a side wall surface  41   b  is denoted by ‘S.’ The intersection between this line segment and another side wall surface  41   c  is denoted by ‘Q.’ The line segment connecting the points S and Q is denoted by ‘XP.’ 
     In the present embodiment, the solid angle at the given evaluation point P on the bottom surface  41   a  of the groove portion  41  is calculated as follows. It should be noted that, in the present embodiment, the solid angle at the given evaluation point P is obtained by subtracting the field-of-view region (solid angle) obstructed by the surrounding structure from the overall solid angle (2π) at the evaluation point P. That is, a solid angle dΩ 0  at the evaluation point P is obtained by subtracting, from the overall solid angle (2π), a solid angle dΩ 1  of the field-of-view region obstructed by the side wall surface  41   b  and a solid angle dΩ 2  of the field-of-view region obstructed by the other side wall surface  41   c.    
     It should be noted, however, that the field-of-view regions obstructed by the side wall surfaces  41   b  and  41   c  at the evaluation point P are rectangular. In the present embodiment, the rectangular field-of-view regions are converted, in a simplified manner, into circles having the same areas, thus calculating the solid angles (dΩ 1 ′ and dΩ 2 ′) obstructed by the side wall surfaces  41   b  and  41   c.    
       FIGS. 13A and 13B  illustrate the outline of the solid angle conversion method.  FIG. 13A  is a diagram illustrating a solid angle dΩ at the evaluation point P when a plane  45  of the field-of-view region is rectangular (before the conversion). On the other hand,  FIG. 13B  is a diagram illustrating a solid angle dΩ′ at the evaluation point P when the rectangular plane  45  of the field-of-view region is converted into a circular plane  46  having the same area (after the conversion). 
     Here, in  FIG. 13A , we assume the distance from the evaluation point P to the center of the rectangular plane  45  to be denoted by ‘h 1 ’ and the angle between the direction from the evaluation point P to the center of the plane  45  and the direction of the normal of the plane  45  (normal vector N) to be denoted by ‘δ.’ Further, we assume the distance from the evaluation point P to the center of the circular plane  46  to be denoted by ‘h 1 ′’ and the distance from the evaluation point P to the outer periphery of the plane  46  to be denoted by ‘h 2 .’ Still further, we assume the radius of the circular plane  46  in  FIG. 13B  to be denoted by ‘r.’ 
     If the geometric conditions shown in  FIGS. 13A and 13B  hold between the rectangular plane  45  and circular plane  46  serving as field-of-view regions and the evaluation point P, the solid angle dΩ′ at the evaluation point P after the conversion is expressed by Formula (15) shown below. 
     
       
         
           
             
               
                 
                   
                     
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                             ⁢ 
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                       = 
                       
                         
                           h 
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                           ⁢ 
                           
                               
                           
                           ⁢ 
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                             ( 
                             
                               
                                 r 
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                           0.5 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
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     In the present embodiment, the solid angle dΩ 1  of the rectangular field-of-view region obstructed by the one side wall surface  41   b  as seen from the evaluation point P is converted into the solid angle dΩ 1 &#39; of the circular field-of-view region having the same area as the rectangular field-of-view region by using Formula (15) shown above. Similarly, the solid angle dΩ 2  of the rectangular field-of-view region obstructed by the other side wall surface  41   c  as seen from the evaluation point P is converted into the solid angle dΩ 2 ′ of the circular field-of-view region having the same area as the rectangular field-of-view region. 
     Next, the solid angle dΩ 0 ′ at the evaluation point P used for the simulation is calculated by using Formula (16) shown below and the solid angles dΩ 1 ′ and dΩ 2 ′ calculated by using Formula (15) shown above.
 
 dΩ 0′=2 π−dΩ 1 ′−dΩ 2′  (16)
 
     Then, in the present embodiment, the flux Γ′ of each of the reaction particles reaching the evaluation point P from the plasma are calculated by using Formula (17) shown below and the solid angle dΩ 0 ′ at the evaluation point P calculated by using Formula (16). 
     
       
         
           
             
               
                 
                   
                     Γ 
                     ′ 
                   
                   = 
                   
                     
                       
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Ω0 
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                         2 
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     Γ 
                   
                 
               
               
                 
                   ( 
                   17 
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     In Formula (17), “Γ” is the total flux of each of the reaction particles injected from the plasma onto the workpiece  40 . That is, in the present embodiment, the total flux Γ of the reaction particle injected from the plasma onto the workpiece  40  is multiplied by the ratio of the solid angle dΩ 0 ′ to the overall solid angle (2π) at the evaluation point P, thus calculating the flux Γ′ of the reaction particle reaching the evaluation point P. The solid angle effect at the evaluation point P is calculated as described above in the present embodiment. 
     Here,  FIG. 14  illustrates the relationship between the position of the evaluation point P on the bottom surface  41   a  of the groove portion  41  and the ratio of the solid angle dΩ 0 ′ to the overall solid angle (2π) at the evaluation point P (dΩ 0 ′/2π: hereinafter referred to as the solid angle effect value). The characteristics shown in  FIG. 14  are those of the change in solid angle effect value on the line segment XP (between the points S and Q) in  FIG. 12A , with the horizontal axis representing the position on the line segment XP and the vertical axis representing the solid angle effect value. 
     Further, the characteristics shown in  FIG. 14  are those obtained when the width of the groove portion  41  (length of the line segment XP) is 200 nm and the length of extension of the groove portion  41  is 1000 nm (refer to  FIG. 12A ). Still further,  FIG. 14  illustrates the characteristics when the depth of the groove portion  41  is varied, that is, when the aspect ratio (depth/width) of the groove portion  41  is varied. 
     As is obvious from  FIG. 14 , the greater the depth (aspect ratio) of the groove portion  41 , the smaller the solid angle effect value (dΩ 0 ′/2π). That is, the greater the depth (aspect ratio) of the groove portion  41 , the less the flux Γ′ of each of the reaction particles reaching the evaluation point P from the plasma. 
     It should be noted that the workpiece  40  having the groove portion  41  formed on its surface has been taken as an example in the present embodiment, the present disclosure is not limited thereto. The present disclosure is applicable to a workpiece having an arbitrary pattern of projections and depressions formed on its surface. In this case, it is only necessary to calculate, as appropriate, the solid angle effect at the evaluation point for each of the patterns of the region to be evaluated in the same manner as the principles described above. 
     [Simulator Configuration and Damage Calculation Method] 
     The simulator according to the present embodiment can be configured in the same manner as the simulator  10  according to the first embodiment shown in  FIG. 1 . It should be noted, however, that the calculation of the fluxes Γ′ of various reaction particles factoring in the solid angle effect described above is handled by the damage calculation section  12 . On the other hand, information about the structure surrounding the evaluation point, i.e., information about the surface shape of the region to be evaluated, is supplied externally as with the processing conditions. 
     It should be noted that the solid angle effect value dΩ 0 ′/2π may be calculated by the damage calculation section  12  every simulation run based on the supplied information about the surface shape of the region to be evaluated. Alternatively, characteristic data (characteristics shown in  FIG. 14 ) of the solid angle effect values associated with the surface shapes of various regions to be evaluated may be calculated and stored in advance in the database section  13 . In this case, the damage calculation section  12  searches the database section  13  every simulation run, thus acquiring solid angle effect data for the supplied information about the surface shape of the region to be evaluated. 
     Further, the present embodiment allows for calculation of the damage distribution at an arbitrary evaluation point in the same manner as the calculation method (calculation principle) described in the first embodiment except that the fluxes Γ′ of various reaction particles reflecting the solid angle effect are used to calculate the damage distribution. It should be noted that the solid angle effect may be calculated, for example, prior to step S 3  (process step adapted to divide the reactive layer into a plurality of slabs) in the flowchart of the damage calculation in the first embodiment shown in  FIG. 6 . 
     [Various Examples of Evaluation] 
     A description will be given next of various examples of evaluation performed using the simulator according to the present embodiment. It should be noted here that a description will be given below of evaluation examples of the workpiece  40  shown in  FIGS. 12A and 12B , i.e., the workpiece  40  that is 200 nm in width (length of the line segment XP) and that has the groove portion  41  with a length of extension of 1000 nm formed on its surface. 
     In the various evaluation examples described below, the etch rate ER, polymer film thickness T and damage distribution at the time of dry-etching of the groove portion  41  of the workpiece  40  using a CF-based gas were calculated by using the simulation method described above. At this time, the various evaluation parameters (etch rate ER, polymer film thickness T and damage distribution) were calculated by varying the aspect ratio of the groove portion  41  to four different levels, namely, 0.0, 0.1, 0.5 and 1.0. Further, in the various evaluation examples described below, the various evaluation parameters were calculated at the evaluation points located at various positions on the line segment XP of the bottom surface  41   a  of the groove portion  41 . Then, the characteristics of change in these evaluation parameters on the line segment XP were found. 
     (1) Evaluation Example 5 
     In evaluation example 5, a description will be given below of a case in which a Si film was formed on the bottom surface  41   a  of the groove portion  41 , and the Si film was dry-etched in a mixture gas of C 4 F 8  (CF-based gas), argon (Ar) and oxygen (O 2 ). 
     It should be noted that the process conditions in evaluation example 5 are as follows. The flow rates of argon (Ar) and oxygen (O 2 ) were maintained constant respectively at 400 sccm and 8 sccm. The gas pressure in the chamber was set at 30 mT, and the incident ion energy E of the ion particle  23  was 1450 V. Further, the etching time t 0  was 30 seconds. 
     The initial thickness L of each of the slabs  21   b  of the reactive layer under the bottom surface  41   a  was 0.5 nm, and the maximum penetration depth Dp of the ion particle  23  was 7 nm. It should be noted that the measured values obtained in the same manner as in evaluation example 1 described above were, for example, used as the fluxes Γ of various reaction particles used for simulation calculations. 
     First, in evaluation example 5, various evaluation parameters of the groove portion  41  and the characteristics of change in these evaluation parameters on the line segment XP were calculated under the above simulation conditions, and additionally with the flow rate of C 4 F 8  set at 11 sccm. That is, various evaluation parameters of the groove portion  41  and the characteristics of change in these evaluation parameters were calculated under conditions of a high etch rate and the small polymer film thickness T (low deposition conditions).  FIGS. 15A to 15D  and  FIGS. 16A to 16D  illustrate the calculation results. 
       FIGS. 15A to 15D  illustrate the characteristics of change in the etch rate ER and polymer film thickness T on the bottom surface  41   a  of the groove portion  41  (on the line segment XP), with the horizontal axis representing the position on the line segment XP and the vertical axes representing the etch rate ER and polymer film thickness T. It should be noted that the characteristics shown in  FIGS. 15A to 15D  are those obtained when the aspect ratio of the groove portion  41  was set to four different levels, namely, 0.0, 0.1, 0.5 and 1.0. Further, the characteristic shown by a solid line in each of  FIGS. 15A to 15D  is that of the etch rate ER, and the characteristic shown by a dashed line is that of the polymer film thickness T. Still further, position  1  (×20 nm) on the horizontal axis in each of  FIGS. 15A to 15D  is the point S at one end of the line segment XP, and position  11  (×20 nm) on the horizontal axis is the point Q at the other end of the line segment XP. 
     As is obvious from  FIGS. 15A to 15D , the larger the aspect ratio of the groove portion  41 , the smaller the etch rate ER and polymer film thickness T became near the center of the bottom surface  41   a . Further, in the results shown in  FIGS. 15B and 15C , the etch rate ER and polymer film thickness T near the wall surfaces on the bottom surface  41   a  were smaller than those near the center of the bottom surface  41   a.    
     On the other hand,  FIGS. 16A to 16D  are damage distribution diagrams on the bottom surface  41   a  of the groove portion  41  (on the line segment XP). It should be noted that  FIGS. 16A to 16D  illustrate, respectively, the characteristics when the aspect ratio of the groove portion  41  was set to 0.0, 0.1, 0.5 and 1.0. 
     As is obvious from  FIGS. 16A to 16D , it has been discovered that the damage distribution in the reactive layer  42  under the bottom surface  41   a  changes with change in the etch rate ER and polymer film thickness T relative to the aspect ratio of the groove portion  41 . 
     Next, in evaluation example 5, various evaluation parameters of the groove portion  41  and the characteristics of change in these evaluation parameters on the line segment XP were calculated under the above simulation conditions, and additionally with the flow rate of C 4 F 8  set at 33 sccm. That is, various evaluation parameters of the groove portion  41  and the characteristics of change in these evaluation parameters on the line segment XP were calculated under conditions of a low etch rate and the large polymer film thickness T (high deposition conditions).  FIGS. 17A to 17D  and  FIGS. 18A to 18D  illustrate the calculation results. 
       FIGS. 17A to 17D  illustrate the characteristics of change in the etch rate ER and polymer film thickness T on the bottom surface  41   a  of the groove portion  41  (on the line segment XP), with the horizontal axis representing the position on the line segment XP and the vertical axes representing the etch rate ER and polymer film thickness T. It should be noted that the characteristics shown in  FIGS. 17A to 17D  are those obtained when the aspect ratio of the groove portion  41  was set to four different levels, namely, 0.0, 0.1, 0.5 and 1.0. Further, the characteristic shown by a solid line in each of  FIGS. 17A to 17D  is that of the etch rate ER, and the characteristic shown by a dashed line is that of the polymer film thickness T. Still further, position  1  (×20 nm) on the horizontal axis in each of  FIGS. 17A  to  17 D is the point S at one end of the line segment XP, and position  11  (×20 nm) on the horizontal axis is the point Q at the other end of the line segment XP. 
     As is obvious from  FIGS. 17A to 17D , the larger the aspect ratio of the groove portion  41 , the smaller the etch rate ER and polymer film thickness T became near the center of the bottom surface  41   a  also under the high deposition conditions as with the results shown in  FIGS. 15A to 15D . Further, in the results shown in  FIGS. 17B to 17D , the etch rate ER and polymer film thickness T near the wall surfaces on the bottom surface  41   a  were smaller than those near the center of the bottom surface  41   a.    
     On the other hand,  FIGS. 18A to 18D  are damage distribution diagrams on the bottom surface  41   a  of the groove portion  41  (on the line segment XP). It should be noted that  FIGS. 18A to 18D  illustrate, respectively, the characteristics when the aspect ratio of the groove portion  41  was set to 0.0, 0.1, 0.5 and 1.0. 
     As is obvious from  FIGS. 18A to 18D , it has been discovered that the damage distribution in the reactive layer  42  under the bottom surface  41   a  also changes under the high deposition conditions with change in the etch rate ER and polymer film thickness T relative to the aspect ratio of the groove portion  41 . 
     It is clear from the results of evaluation example 5 shown above that the simulator according to the present embodiment can quantitatively predict the change in damage distribution that is likely to take place with increase in the aspect ratio of the groove portion  41  during etching of the groove portion  41  having a Si film formed on the bottom surface  41   a.    
     (2) Evaluation Example 6 
     A description will be given below of a case in which a SiO 2  film was formed on the bottom surface  41   a  of the groove portion  41 , and the SiO 2  film was dry-etched in a mixture gas of C 4 F 8  (CF-based gas), argon (Ar) and oxygen (O 2 ). 
     It should be noted that the various simulation conditions (process conditions and initial conditions of the calculation parameters) were the same as those in evaluation example 5 described above except that the type of film formed on the bottom surface  41   a  of the groove portion  41  was changed. Further, the measured values were used as the fluxes Γ of various reaction particles used for simulation calculations as in evaluation example 5. 
     First, in evaluation example 6, various evaluation parameters of the groove portion  41  and the characteristics of change in these evaluation parameters on the line segment XP were calculated under the above simulation conditions, and additionally with the flow rate of C 4 F 8  set at 11 sccm.  FIGS. 19A to 19D  and  FIGS. 20A to 20D  illustrate the calculation results. 
       FIGS. 19A to 19D  illustrate the characteristics of change in the etch rate ER and polymer film thickness T on the bottom surface  41   a  of the groove portion  41  (on the line segment XP), with the horizontal axis representing the position on the line segment XP and the vertical axes representing the etch rate ER and polymer film thickness T. It should be noted that the characteristics shown in  FIGS. 19A to 19D  are those obtained when the aspect ratio of the groove portion  41  was set to four different levels, namely, 0.0, 0.1, 0.5 and 1.0. Further, the characteristic shown by a solid line in each of  FIGS. 19A to 19D  is that of the etch rate ER, and the characteristic shown by a dashed line is that of the polymer film thickness T. Still further, position  1  (×20 nm) on the horizontal axis in each of  FIGS. 19A to 19D  is the point S at one end of the line segment XP, and position  11  (×20 nm) on the horizontal axis is the point Q at the other end of the line segment XP. 
     As is obvious from  FIGS. 19A to 19D , the larger the aspect ratio of the groove portion  41 , the smaller the etch rate ER and polymer film thickness T became near the center of the bottom surface  41   a . Further, in the results shown in  FIGS. 19B to 19D , the etch rate ER and polymer film thickness T near the wall surfaces on the bottom surface  41   a  were smaller than those near the center of the bottom surface  41   a.    
     On the other hand,  FIGS. 20A to 20D  are damage distribution diagrams on the bottom surface  41   a  of the groove portion  41  (on the line segment XP). It should be noted that  FIGS. 20A to 20D  illustrate, respectively, the characteristics when the aspect ratio of the groove portion  41  was set to 0.0, 0.1, 0.5 and 1.0. 
     As is obvious from  FIGS. 20A to 20D , it has been discovered that the damage distribution in the reactive layer  42  under the bottom surface  41   a  changes with change in the etch rate ER and polymer film thickness T relative to the aspect ratio of the groove portion  41 . 
     Next, in evaluation example 6, various evaluation parameters of the groove portion  41  and the characteristics of change in these evaluation parameters on the line segment XP were calculated under the above simulation conditions, and additionally with the flow rate of C 4 F 8  set at 33 sccm (high deposition conditions).  FIGS. 21A to 21D  and  FIGS. 22A to 22D  illustrate the calculation results. 
       FIGS. 21A to 21D  illustrate the characteristics of change in the etch rate ER and polymer film thickness T on the bottom surface  41   a  of the groove portion  41  (on the line segment XP), with the horizontal axis representing the position on the line segment XP and the vertical axes representing the etch rate ER and polymer film thickness T. It should be noted that the characteristics shown in  FIGS. 21A to 21D  are those obtained when the aspect ratio of the groove portion  41  was set to four different levels, namely, 0.0, 0.1, 0.5 and 1.0. Further, the characteristic shown by a solid line in each of  FIGS. 21A to 21D  is that of the etch rate ER, and the characteristic shown by a dashed line is that of the polymer film thickness T. Still further, position  1  (×20 nm) on the horizontal axis in each of  FIGS. 21A to 21D  is the point S at one end of the line segment XP, and position  11  (×20 nm) on the horizontal axis is the point Q at the other end of the line segment XP. 
     As is obvious from  FIGS. 21A to 21D , the larger the aspect ratio of the groove portion  41 , the smaller the etch rate ER and polymer film thickness T became near the center of the bottom surface  41   a  also under the high deposition conditions as with the results shown in FIGS.  19 A to  19 D. Further, in the results shown in  FIGS. 21A to 21D , the etch rate ER and polymer film thickness T near the wall surfaces on the bottom surface  41   a  were smaller than those near the center of the bottom surface  41   a.    
     On the other hand,  FIGS. 22A to 22D  are damage distribution diagrams on the bottom surface  41   a  of the groove portion  41  (on the line segment XP). It should be noted that  FIGS. 22A to 22D  illustrate, respectively, the characteristics when the aspect ratio of the groove portion  41  was set to 0.0, 0.1, 0.5 and 1.0. 
     As is obvious from  FIGS. 22A to 22D , it has been discovered that the damage distribution in the reactive layer  42  under the bottom surface  41   a  also changes under the high deposition conditions with change in the etch rate ER and polymer film thickness T relative to the aspect ratio of the groove portion  41 . 
     It is clear from the results of evaluation example 6 shown above that the simulator according to the present embodiment can quantitatively predict the change in damage distribution that is likely to take place with increase in the aspect ratio of the groove portion  41  during etching of the groove portion  41  having a SiO 2  film formed on the bottom surface  41   a.    
     Further, it is clear from the evaluation results of damage distribution shown in evaluation examples 5 and 6 described above that the damage sustained by a SiO 2  film etched with a CF-based gas is several-fold greater than that sustained by a Si film etched with a CF-based gas. This result is also a probable characteristic obtained when a SiO 2  film is etched with a CF-based gas, and it has been discovered that this characteristic can also be expressed quantitatively by the simulator according to the present embodiment. 
     As described above, the simulator and damage evaluation method according to the present embodiment allow for prediction (evaluation) of the damage distribution for each pattern even if the region of the workpiece to be evaluated for damage has a pattern of projections and depressions. Therefore, the present embodiment allows for theoretical prediction, in a shorter period of time and with higher accuracy, of the damage distribution of an extremely small pattern region that is difficult to observe with ordinary methods using cross-sectional SEM (Scanning Electron Microscope) and TEM. 
     Further, the present embodiment can predict (evaluate) the pattern dependence of damage, thus contributing to reduced variations in device characteristics and providing improved reliability. Still further, the simulator and damage evaluation method according to the present embodiment contributes to shorter development TAT (Turn-around Time) and reduced prototype wafers, thus providing reduced cost. 
     Still further, the simulator and damage evaluation method according to the present embodiment calculate the damage distribution of a workpiece using the Flux method as in the first embodiment, thus providing the same advantageous effect as in the first embodiment. 
     From the above, the simulator according to the present embodiment is extremely effective as a tool for accurately predicting the process dependence and pattern dependence of damage in designing devices that will become even smaller. 
     &lt;3. Third Embodiment&gt; 
     Normally, if the surface of a workpiece is subjected to a process such as etching, the surface shape of the workpiece changes with the processing time. In order to calculate the change in the surface shape of the workpiece, shape evolution models have been proposed, for example, using the string method, level set method and cell removal method. In order to evaluate, in detail, the damage sustained by a workpiece when the workpiece is subjected to a process such as etching, it is preferred to build an evaluation system that includes a damage distribution calculation model and shape evolution model combined (connected) together. 
     However, the damage distribution calculation models using the particle method (e.g., molecular dynamics calculation method) in related art lead to an enormous amount of calculations, thus making it difficult to use these models in combination with a shape evolution model. In contrast, the damage distribution calculation model according to the embodiments described above use the Flux method, thus contributing to a significantly smaller amount of calculations than those using the particle method. This makes it easier to use the damage distribution calculation model according to the above embodiments in combination with a shape evolution model. 
     In the third embodiment, a description will be given below of a simulation system (simulator) that includes the damage distribution calculation model according to the embodiments described above and a shape evolution model connected together, and an example of the damage evaluation method. 
     [Outline of the Combined Model] 
       FIG. 23  illustrates the schematic outline of a combined model combining the damage distribution calculation model according to the above embodiments and a shape evolution model. In the present embodiment, a description will be given of an example in which a shape evolution model based on the string method is used. It should be noted that the present disclosure is not limited thereto. Instead, an arbitrary shape evolution model based, for example, on the level set method or cell removal method may be used. 
     In the shape evolution model based on the string method, lattice points are arranged at a given spacing of 1 nm or so in the initial shape of a surface to be processed  51  of a workpiece  50 . Alternatively, the initial shape is divided into cells each having a given spatial resolution of 1 nm or so. In the example shown in  FIG. 23 , lattice points  52  are arranged (set) at a given spacing on the surface to be processed  51  of the workpiece  50 . Then, in the combined model according to the present embodiment, the damage distribution calculation model according to the above embodiments is applied at each of the lattice points  52  (each of the evaluation points). That is, the polymer layer  22  and the reactive layer  21   a , divided into the plurality of slabs  21   b , are set at each of the lattice points  52  as illustrated in  FIG. 23 . 
     It should be noted that, in the shape evolution model based on the string method, the coordinates of each of the lattice points  52  (or cells) that move on the surface to be processed  51  with time as a result of etching or other process are calculated, thus calculating the change in shape of the surface to be processed  51 . For example, the movement of the coordinates of the lattice point  52  having an index j in  FIG. 23  is calculated by using Formula (18) shown below.
 
 x   j ( t )= x   j ( t− 1)+ ER   jx ( t− 1)× dt  
 
 y   j ( t )= y   j ( t− 1)+ ER   jy ( t− 1)× dt   (18)
 
     “ER jy (t)” in Formula (18) shown above is the etch rate component in the direction of depth (y direction in  FIG. 23 ) of the workpiece  50  of the etch rate ER(t) at the lattice point j. On the other hand, “ER jx (t)” is the etch rate component in the direction orthogonal to the direction of depth (x direction in  FIG. 23 : hereinafter referred to as the horizontal direction) of the etch rate ER(t) at the lattice point j. 
     The etch rate ER(t) at the lattice point  52  having the index j is calculated using the damage distribution calculation model described in the above embodiments. On the other hand, the etching direction (bold solid line arrow in  FIG. 23 ) at the lattice point  52  having the index j can be calculated by the change in the coordinates of the lattice point  52  over time (displacement) calculated by using Formula (18). Therefore, “ER jy (t)” and “ER jx (t)” in Formula (18) shown above can be calculated from the etch rate ER (t) calculated using the damage distribution calculation model and displacement of the coordinates of each of the lattice points  52 . 
     [Configuration of the Simulation System] 
     A description will be given next of a configuration example of the simulation system for implementing the above combined model.  FIG. 24  illustrates a schematic block configuration of the simulation system (simulator) according to the present embodiment. It should be noted that the input section  11  is not shown in a second simulator  62  in  FIG. 24  to facilitate the description. 
     A simulation system  60  includes a first simulator  61  and the second simulator  62 . The first simulator  61  calculates the change in shape of the surface to be processed  51  with time (hereinafter referred to as the shape evolution). The second simulator  62  calculates the damage distribution at each of the lattice points  52  (or cells) set on the surface to be processed  51 . 
     The first simulator  61  includes a shape evolution calculation section  63  and a database section  64  that is connected to the shape evolution calculation section  63 . 
     The shape evolution calculation section  63  calculates the shape evolution of the surface to be processed  51  based on Formula (18) shown above. Further, the shape evolution calculation section  63  acquires the etch rate ER(t) at each of the lattice points  52  calculated by the second simulator  62 . Then, the shape evolution calculation section  63  calculates the etch rate component ER jy  (t) in the direction of depth of the workpiece  50  and the etch rate component ER jx (t) in the horizontal direction at each of the lattice points  52  based on the etch rate ER(t) and the calculation results of shape evolution (coordinate displacement). 
     Still further, the shape evolution calculation section  63  outputs the calculation results of the shape evolution of the surface to be processed  51  and the etch rate components at each of the lattice points  52  to the database section  64 . These various pieces of data are used when the shape evolution is calculated the next time. It should be noted that, at this time, the shape evolution calculation section  63  may output the calculation results of the shape evolution of the surface to be processed  51  to the second simulator  62  so that the manner in which the shape of the surface to be processed  51  changes is displayed on the output section  14  of the second simulator  62 . 
     In order to calculate the shape evolution of the surface to be processed  51 , the shape evolution calculation section  63  externally acquires the initial conditions such as the initial shape of the surface to be processed  51 , the spacing between the lattice points  52  (cells) and calculation step Δt via the second simulator  62  or directly therefrom. Further, at this time, the shape evolution calculation section  63  acquires the past calculation result data such as the coordinates of each of the lattice points  52  and etch rate from the database section  64 . 
     It should be noted that, in the present embodiment, the shape evolution calculation section  63  may include hardware to perform various calculations for the shape evolution of the surface to be processed  51 . Alternatively, however, a given program (software) may be used to perform various calculations for the shape evolution. In this case, the shape evolution calculation section  63  includes a CPU (Central Processing Unit) or other processor that externally loads a shape evolution calculation program (shape evolution program) and executes the program to perform various shape evolution calculations. 
     On the other hand, the shape evolution program may be stored, for example, in the database section  64  or a separate storage section such as ROM. At this time, the shape evolution program may be, for example, installed in advance in the database section  64  or separate storage section. Alternatively, the program may be, for example, externally installed into the database section  64  or separate storage section. It should be noted that if the shape evolution program is externally acquired, the program may be distributed in a media such as optical disk or semiconductor memory. Alternatively, the program may be downloaded via a transmission section such as the Internet. 
     The database section  64  stores data such as various parameters necessary for shape evolution calculations. For example, the database section  64  stores shape evolution data of the surface to be processed  51  calculated by the shape evolution calculation section  63 , the etch rate of each of the lattice points  52  and various etch rate components. 
     The second simulator  62  includes the input section  11  (not shown in  FIG. 24 ), damage calculation section  12 , database section  13  and output section  14 . The second simulator  62  according to the present embodiment is configured in the same manner as the simulator  10  described in the first embodiment ( FIG. 1 ). Therefore, the description of each of the sections of the second simulator  62  will be omitted. 
     [Damage Distribution Calculation] 
     A description will be given next of the method used by the simulation system  60  according to the present embodiment to evaluate (calculate) the damage distribution of the workpiece  50  with reference to  FIG. 25 . It should be noted that  FIG. 25  is a flowchart illustrating the procedure for calculating the damage distribution in the present embodiment. 
     First, the simulation system  60  acquires various processing conditions (process conditions and initial conditions of the calculation parameters) supplied externally (step S 11 ). At this time, the first and second simulators  61  and  62  can both externally acquire the processing conditions directly. Alternatively, at this time, one of the first and second simulators  61  and  62  may externally acquire the processing conditions directly so that the other simulator acquires the processing conditions from the one simulator. 
     It should be noted that, of the processing conditions acquired in step S 11 , the process conditions are, for example, gas type, gas flow rate, gas pressure, temperature of the workpiece  50 , film type of the surface to be processed  51 , etching time t 0  and incident ion energy E of the ion particle  23 . On the other hand, the calculation parameters acquired in step S 11  are, for example, the initial thickness L of each of the slabs  21   b , the initial value of the polymer film thickness T, the reactive layer  21   a  and the maximum penetration depth Dp of the ion particle  23 . 
     Next, the damage calculation section  12  of the second simulator  62  searches the database section  13  based on the acquired processing conditions (particularly, gas type, gas flow rate and gas pressure), thus acquiring various parameters necessary for the damage calculations (step S 12 ). Among the various parameters acquired in step S 12  are the fluxes Γ of various reaction particles corresponding to the processing conditions, various reaction probabilities and ratios of the components in the gas (e.g., carbon (C)). Further, various parameters such as reaction product parameters during etching and number density and surface density of the film formed on the surface to be processed  51  are acquired in step S 12 . 
     It should be noted that if, for example, the measured values of the fluxes Γ of various reaction particles can be acquired externally, the damage calculation section  12  may externally acquire the fluxes Γ of various reaction particles in step S 12 . On the other hand, not only the fluxes Γ of various reaction particles but also various parameters acquired in step S 12  may be directly entered externally. In this case, the process step in step S 12  may be omitted so that the various parameters necessary for the damage calculations are acquired in step S 11 . 
     Next, the simulation system  60  sets the initial shape of the surface to be processed  51  of the workpiece  50  (step S 13 ). More specifically, the simulation system  60  sets the spacing for arranging the lattice points  52  (or cells) and parameters such as the initial coordinates of each of the lattice points  52 . 
     Next, the simulation system  60  selects the given lattice point  52 . Then, the damage calculation section  12  divides the reactive layer  21   a  into the plurality of slabs  21   b  at the selected lattice point  52  based on the initial thickness L of the slab  21   b , the initial polymer film thickness T and the maximum penetration depth Dp of the ion particle  23  (step S 14 ). More specifically, the damage calculation section  12  equally divides the reactive layer  21   a  having the depth Dp−T into the plurality of slabs  21   b  each having the initial thickness L at the selected lattice point  52  as in the first embodiment. 
     Next, the damage calculation section  12  calculates the reaction area ratio θ k (t) of each of the slabs  21   b  at the given time t at the selected lattice point  52  using the processing conditions and various parameters corresponding to the processing conditions (step S 15 ). More specifically, the damage calculation section  12  calculates the reaction area ratio θ k (t) of each of the slabs  21   b  at the selected lattice point  52  by using Formulas (1) to (4) shown above described in the first embodiment. 
     Next, the damage calculation section  12  calculates the etch rate ER(t) at time t at the selected lattice point  52  using the reaction area ratio θ k (t) of each of the slabs  21   b  calculated in step S 15  (step S 16 ). More specifically, the damage calculation section  12  calculates the etch rate ER(t) at the selected lattice point  52  by using Formulas (5) to (8) shown above described in the first embodiment. 
     Next, the damage calculation section  12  calculates the polymer film thickness T(t) at time t at the selected lattice point  52  (step S 17 ). More specifically, the damage calculation section  12  calculates the polymer film thickness T(t) using the reaction area ratio θ k (t) of each of the slabs  21   b  and the etch rate ER(t) calculated in steps S 15  and S 16  and by using Formulas (9) to (12) shown above described in the first embodiment. 
     Next, the damage calculation section  12  determines whether the current time t has reached the etching end time (step  18 ). More specifically, the damage calculation section  12  determines whether the elapsed time from the beginning of the calculation has reached the etching time to set in advance. 
     If time t has yet to reach the etching end time in step S 18 , the determination in step S 18  is No. 
     In this case, the shape evolution calculation section  63  of the first simulator  61  calculates the coordinates of the selected lattice point  52  (shape evolution of the lattice point  52 ) (step S 19 ). 
     More specifically, in step S 19 , the shape evolution calculation section  63  acquires first the shape evolution calculation results (coordinates [x(t−1), y(t−1)]) at the selected lattice point  52  which is earlier by one calculation step from the database section  64 . Further, the shape evolution calculation section  63  acquires the data of the etch rate component ER jy (t−1) in the direction of depth and the etch rate component ER jx (t−1) in the horizontal direction at the lattice point  52  which are earlier by one calculation step from the database section  64 . Next, the shape evolution calculation section  63  calculates coordinates [x(t), y(t)] at time t at the selected lattice point  52  by using the acquired data and Formula (18) shown above. 
     Then, after calculating the coordinates at time t at the selected lattice point  52 , the damage calculation section  12  performs time evolution, that is, updates the calculation time (t=t+Δt) (step S 20 ) and then returns to the process step in step S 15 . Then, the damage calculation section  12  repeats steps S 15  to S 20  until the time t reaches the etching end time t 0 . 
     On the other hand, when the current time t has reached the etching end time in step S 18 , the determination in step S 18  is Yes. 
     In this case, the damage calculation section  12  redivides the reactive layer  21   a  into the plurality of slabs  21   b  at the selected lattice point  52  in consideration of the ratio (weight) of the contribution rate ER k  of each of the slabs  21   b  in the etch rate ER at the etching end time (step S 21 ). At this time, the thickness L k * of each of the slabs  21   b  after the redivision is calculated by using Formula (13) described in the first embodiment. 
     Next, the damage calculation section  12  calculates the damage level of each of the slabs  21   b  at the selected lattice point  52  (step S 22 ). More specifically, the damage calculation section  12  calculates the damage level damage(k) of each of the slabs  21   b  by using Formula (14) shown above described in the first embodiment. 
     Next, the damage calculation section  12  determines whether the damage calculation is over at all the lattice points  52  (or cells) (step S 23 ). 
     If the damage calculation has yet to be over at all the lattice points  52  (or cells) in step S 23 , the determination in step S 23  is No. In this case, the simulation system  60  changes the selected lattice point  52  (step S 24 ). More specifically, the simulation system  60  updates the index j of the lattice point  52  used for the above series of damage calculations (j=j+1). Then, the simulation system  60  returns to step S 14  to repeat steps S 14  to S 24  until the damage calculation is over at all the lattice points  52 . 
     On the other hand, when the damage calculation is over at all the lattice points  52  (or cells) in step S 23 , the determination in step S 23  is Yes. In this case, the simulation system  60  terminates the damage distribution calculations. In the present embodiment, the damage distribution of the surface to be processed  51  is calculated while at the same time calculating the change in shape of the surface to be processed  51  as described above. 
     As described above, the simulation system  60  and damage evaluation method according to the present embodiment can predict (evaluate) the damage distribution of a workpiece in consideration of the shape of the workpiece and the change in shape thereof, thus providing the same advantageous effect as in the second embodiment. 
     Further, in the present embodiment, the damage distribution of a workpiece is calculated by using the Flux method as in the first embodiment, thus providing the same advantageous effect as in the first embodiment. 
     It should be noted that the solid angle effect calculation described in the second embodiment may be added to the damage evaluation method according to the present embodiment. In this case, the pattern dependence of workpiece damage can be calculated in more detail. In this case, however, the solid angle effect need only be calculated, for example, prior to step S 14  (process step adapted to divide the reactive layer into a plurality of slabs) in the flowchart of the damage calculation in the present embodiment shown in  FIG. 25 . 
     &lt;4. Fourth Embodiment&gt; 
     The simulators (or simulation systems) and damage evaluation methods described in the second and third embodiments can predict the damage distribution of a workpiece for each pattern. Therefore, the simulators according to the second and third embodiments can be used as a mask (resist mask) pattern layout setting (prediction) tool that is used to bring the pattern damage down to a given level or less and optimize the damage uniformity in the pattern. 
     In the fourth embodiment, a description will be given of an example of a process performed when the simulator (simulation system) according to the second or third embodiment is used as a mask pattern layout setting tool. It should be noted that the configuration of the simulator according to the present embodiment is the same as that shown in  FIG. 1 or 24 . Therefore, the description of the configuration will be omitted here, and only the optimization of the mask pattern layout will be described. 
     A description will be given below of the optimization of the mask pattern layout in the present embodiment with reference to  FIG. 26 . It should be noted that  FIG. 26  is a flowchart illustrating the procedure for optimizing the mask pattern layout. 
     First, the simulator acquires the GDS (Graphic Design System) file (mask information) of the mask, film thickness information (initial value) and processing conditions of the workpiece (step S 31 ). 
     Next, the simulator determines a desired evaluation pattern region (pattern region of interest) (step S 32 ). It should be noted that this pattern region of interest is determined as appropriate, for example, according to the preference of the user. Further, at this time, the simulator sets at least one evaluation point (lattice point or cell) in the pattern region of interest. 
     Next, the simulator calculates the reaction area ratio θ k (t) of each of the slabs  21   b  at each of the evaluation points in the pattern region of interest of the workpiece, the etch rate ER(t) of the reactive layer and the polymer film thickness T (step S 33 ). 
     At this time, if the simulator according to the second embodiment is used as a simulator, an assumption is made as to the mask shape (processing depth and taper angles of the side wall surfaces) after a simplified process in the pattern region of interest. Then, the damage calculation section calculates, based on the assumed conditions, the solid angle distribution (distribution characteristic of the solid angle effect) at each of the evaluation points in the pattern region of interest. Next, the damage calculation section calculates the reaction area ratio θ k (t), etch rate ER and polymer film thickness T at each of the evaluation points using the fluxes Γ′ of various reaction particles factoring in the calculated solid angle effect in the same manner as in the second embodiment. 
     On the other hand, when the simulation system according to the third embodiment is used as a simulator, the reaction area ratio θ k (t), etch rate ER and polymer film thickness T at each of the evaluation points are calculated while at the same time calculating the shape evolution of the pattern region of interest in the same manner as in the third embodiment. 
     Further, when a simulator combining the simulator according to the third embodiment and the solid angle effect calculation described in the second embodiment is used, the various evaluation parameters at the evaluation points are calculated as follows. First, the simulator calculates the solid angle distribution (distribution characteristic of the solid angle effect) at each of the evaluation points in the pattern region of interest in the same manner as in the second embodiment. Next, the simulator calculates the various evaluation parameters at each of the evaluation points in the pattern region of interest by using the fluxes Γ′ of various reaction particles factoring in the solid angle effect while at the same time calculating the shape evolution of the pattern region of interest in the same manner as in the third embodiment. 
     As described above, after calculating the various evaluation parameters at each of the evaluation points in the pattern region of interest, the damage calculation section redivides the reactive layer into a plurality of slabs at each of the evaluation points in the same manner as in the first embodiment (step S 34 ). At this time, the thickness L k * of each of the slabs after the redivision is calculated by using Formula (13) shown above described in the first embodiment. 
     Next, the damage calculation section calculates the damage level of each of the slabs at each of the evaluation points in the pattern region of interest, thus finding the damage distribution at each of the evaluation points (step S 35 ). At this time, the damage calculation section calculates the damage level (damage(k)) of each of the slabs by using Formula (14) shown above described in the first embodiment. 
     Next, the damage calculation section determines whether the damage level of the pattern region of interest calculated in step S 35  is equal to or less than the desired damage level (step S 36 ). It should be noted that the desired damage level serving as a threshold in step S 36  is set as appropriate, for example, according to the application. Further, this desired damage level information is set in advance and stored, for example, in the database section of the simulator. 
     If the damage level of the pattern region of interest calculated in step S 35  is greater than the desired damage level in step S 36 , the determination in step S 36  is No. In this case, the simulator changes (corrects) the layout pattern shape of the mask (e.g., film thickness, taper angles and pattern-to-pattern spacing) (step S 37 ). 
     It should be noted that, at this time, the range of pattern change per layout change (e.g., ±50% of the film thickness, ±5% of the taper angles and ±100% of the pattern-to-pattern spacing) may be set in advance so that the mask layout pattern is changed gradually according to this range of change. Alternatively, the mask layout pattern may be changed to a desired extent every layout change. 
     Then, after changing the mask layout pattern in step S 37 , the simulator returns to step S 33 . Then, the simulator performs steps S 33  to S 35  again to calculate the damage level of the pattern region of interest using the changed layout pattern. The process steps from steps S 33  to S 37  are repeated until the damage level of the pattern region of interest falls to the desired damage level or less. 
     On the other hand, when the damage level of the pattern region of interest calculated in step S 35  is equal to or less than the desired damage level in step S 36 , the determination in step S 36  is Yes. In this case, the output section of the simulator visualizes the calculated damage distribution of the pattern region of interest (step S 38 ). At this time, the output section may display the evaluation results, for example, on a display device or print the displayed evaluation results. After the visualization of the damage distribution of the pattern region of interest, the simulator terminates the optimization of the mask layout pattern. 
     By setting a mask pattern layout as described above, it is possible to automatically extract a pattern layout that can bring the damage level of the evaluated pattern down to a given level or less and suppress the spatial variation in damage level (provide improved damage uniformity). 
     Further, in the present embodiment, the damage distribution is evaluated (predicted) while at the same time changing the shape of the resist formed around the evaluation points of the workpiece. As a result, the present embodiment ensures optimal OPC (Optical Proximity Correction) in consideration of both the resist shape and damage reduction. 
     Still further, in the present embodiment, the damage distribution of a workpiece is calculated using the Flux method as in the first embodiment, thus providing quick setting of a mask pattern layout. 
     &lt;5. Fifth Embodiment&gt; 
     The simulators (simulation systems) according to the first to third embodiments calculate the damage distribution of a workpiece using the Flux method, thus allowing for quicker calculation of the damage distribution of a workpiece. Therefore, if the simulator (simulation system) according to one of the first to third embodiments is incorporated, for example, in an etcher or other processing system, it is possible to evaluate (predict) and control the damage distribution of the workpiece at any time during the process. 
     For this reason, in the fifth embodiment, a description will be given of an example in which a dry etcher is used as a processing system and the simulation system described in the third embodiment is incorporated in the dry etcher. 
     [Configuration of the Dry Etcher] 
       FIG. 27  illustrates the schematic block configuration of the dry etcher according to the present embodiment. A dry etcher  100  (processing system) includes an etching chamber  101  (processing section), control system  102  (control section) and the simulation system  60  (simulator). It should be noted that the input section  11  is not shown in the second simulator  62  in  FIG. 27  to facilitate the description. 
     The etching chamber  101  can include, for example, a CCP, ICP (Inductive Coupled Plasma) or ECR (Electron Cyclotron Resonance) chamber. On the other hand, an optical emission spectrometer OES, mass spectrometer QMS and energy spectrum analyzer are installed in the etching chamber  101 . 
     It should be noted that the optical emission spectrometer OES and mass spectrometer QMS monitor the fluxes Γ of various reaction particles (reaction gases) that vary depending on the condition in the etching chamber  101 . On the other hand, the energy spectrum analyzer measures the incident ion energy E. 
     Further, the condition in the etching chamber  101  is monitored by the optical emission spectrometer OES, mass spectrometer QMS and energy spectrum analyzer at given time intervals (e.g., every second) while the workpiece is processed. It should be noted that these monitoring time intervals should preferably be equal to the calculation step Δt used by the simulation system  60  to calculate the damage distribution or less. 
     Still further, the etching chamber  101  is electrically connected to the simulation system  60 , outputting various pieces of information (e.g., fluxes and incident ion energy) indicating the monitored condition in the chamber to the simulation system  60 . 
     The control system  102  corrects the various process parameters (e.g., gas flow rate, gas pressure, wafer temperature, etching time) of the etching chamber  101  based on the damage distribution calculation results supplied from the simulation system  60 . Further, the control system  102  is electrically connected to the etching chamber  101 , outputting the various corrected process parameters to the etching chamber  101  and controlling the etching conditions. 
     The simulation system  60  is configured in the same manner as the simulation system described in the third embodiment ( FIG. 24 ). Therefore, the description of each of the sections of the simulation system  60  will be omitted. 
     The simulation system  60  calculates the shape evolution and damage distribution of the workpiece by using the various pieces of monitoring information from the etching chamber  101  in the same manner as in the third embodiment. Further, the simulation system  60  is electrically connected to the control system  102 , outputting the calculated damage distribution to the control system  102 . 
     It should be noted that, in the present embodiment, the acquisition method of the fluxes Γ of various reaction particles is not limited to that described above (acquisition of monitored values). For example, only various process conditions (e.g., gas flow rate, gas pressure, wafer temperature, etching time) may be acquired from the etching chamber  101  so that the damage calculation section  12  calculates, based on these pieces of information, the fluxes Γ of various reaction particles. 
     Alternatively, the fluxes Γ of various reaction particles corresponding to various process conditions may be stored in advance in the database section  13  so that the damage calculation section  12  acquires the corresponding fluxes Γ by searching the database section  13  based on the supplied process conditions. It should be noted, however, that if the fluxes Γ corresponding to the supplied process conditions are not available in the database section  13 , the damage calculation section  12  may calculate the corresponding fluxes Γ of various reaction particles by interpolating the data obtained under the conditions close to the supplied process conditions. 
     If the fluxes Γ of various reaction particles are acquired in the manner as described above, it is not necessary to provide any device adapted to monitor the fluxes Γ of various reaction particles in the etching chamber  101 . 
     [Etching Control Method] 
     A description will be given next of the etching control method of the dry etcher  100  according to the present embodiment with reference to  FIG. 28 . It should be noted that  FIG. 28  is a flowchart illustrating the procedure for controlling etching according to the present embodiment. 
     First, the dry etcher  100  acquires various externally supplied processing conditions (process conditions and initial conditions of various calculation parameters) (step S 41 ). At this time, the process conditions such as gas type, gas flow rate, gas pressure, wafer temperature and etching time are supplied to the etching chamber  101 . On the other hand, the calculation parameters necessary for the damage calculations such as the material of the workpiece, initial shape of the surface to be processed, initial thickness L of the slabs, initial polymer film thickness T and maximum penetration depth Dp of the ion particle are supplied to the simulation system  60 . 
     Next, the etching chamber  101  performs etching based on the process conditions acquired in step S 41  or the process parameters corrected by the control system  102  (step S 42 ). At this time, the etching chamber  101  monitors information indicating the condition in the chamber such as the fluxes Γ of various reaction particles (reaction gases) and the incident ion energy at given time intervals (e.g., every second), outputting the various pieces of monitoring information to the simulation system  60 . 
     Next, the dry etcher  100  determines whether to terminate the etching (step S 43 ). More specifically, the dry etcher  100  determines whether the elapsed time from the beginning of the etching has reached the etching time. 
     If the elapsed time from the beginning of the etching has yet to reach the etching time in step S 43 , the determination in step S 43  is No. In this case, the dry etcher  100  continues with the etching in step S 42 . On the other hand, when the elapsed time from the beginning of the etching has reached the etching time in step S 43 , the determination in step S 43  is Yes. In this case, the dry etcher  100  terminates the etching. 
     A description will be given here of the etching process control performed during etching in step S 42  (part of the flowchart enclosed by a long dashed short dashed line in  FIG. 28 ). 
     First, the simulation system  60  calculates the shape evolution and damage distribution of the workpiece based on the various calculation parameters acquired in step S 41  and the various pieces of monitoring information supplied from the etching chamber  101  (step S 44 ). 
     At this time, the simulation system  60  calculates the shape evolution (change in shape of the surface to be processed) and damage distribution of the workpiece in the same manner as in the third embodiment. Then, the simulation system  60  outputs the simulation results to the control system  102 . 
     Next, the control system  102  determines whether the damage level of the workpiece calculated by the simulation system  60  is equal to or less than the desired damage level (step S 45 ). 
     When the damage level of the workpiece calculated by the simulation system  60  is equal to or less than the desired damage level in step S 45 , the determination in step S 45  is Yes. In this case, the control system  102  outputs a signal to the etching chamber  101  to inform that the various process parameters will not be corrected. 
     On the other hand, if the damage level of the workpiece calculated by the simulation system  60  is not equal to or less than the desired damage level in step S 45 , the determination in step S 45  is No. In this case, the control system  102  calculates the correction of the various process parameters in such a manner as to reduce the damage level of the workpiece (step S 46 ). 
     Next, the control system  102  outputs the various corrected process parameters to the etching chamber  101 , thus controlling the etching conditions (step S 47 ). In the present embodiment, the etching is controlled based on the calculation results of the simulation system  60 . 
     As described above, in the present embodiment, the simulation system  60  adapted to calculate the damage distribution of the workpiece by using the Flux method is incorporated in the dry etcher  100 , thus making it possible to evaluate (predict) and control the damage distribution of the workpiece at any time during the process. This contributes to improved yield of the workpiece in the production line. 
     It should be noted that, in the present embodiment, the dry etcher  100  may have, for example, an alarm system such as an FDC (Fault Detection and Classification)/EES (Equipment Engineering System) system. This makes it possible to sound an alarm and stop the dry etcher  100  if the damage level calculated by the simulation system  60  at given time intervals (e.g., every second) exceeds the specification level set by the FDC. 
     Further, although an example was described in the present embodiment in which the simulation system  60  described in the third embodiment is incorporated in the dry etcher  100 , the present disclosure is not limited thereto. For example, the simulator described in the first or second embodiment can also be incorporated in the dry etcher  100 , thus providing the same advantageous effect. 
     6. &lt;Sixth Embodiment&gt; 
     Although examples were described in the above embodiments in which the damage calculation section  12  directly calculates the damage distribution of the workpiece based on the supplied processing conditions, the present disclosure is not limited thereto. Damage data calculated by the simulator according to any one of the embodiments under various processing conditions may be stored in advance in the database section  13  so that the damage is evaluated by using the stored damage data. 
     That is, damage data calculated by using the Flux method under various processing conditions may be archived in the form of a database so as to predict (evaluate) the damage sustained by the workpiece using the data in the database. A description will be given in the sixth embodiment of a configuration example thereof. 
     The simulator (simulation system) according to the sixth embodiment is configured in the same manner as the simulator according to any one of the above embodiments (refer, for example, to  FIG. 1 or 24 ). It should be noted, however, that the damage calculation section  12  according to the present embodiment acquires (calculates) the damage as follows unlike the counterpart according to any one of the above embodiments. 
     First, the damage calculation section  12  acquires the various processing conditions (e.g., the material of the workpiece, gas type, gas pressure, gas flow rate, temperature of the workpiece and processing time) supplied via the input section  11 . Next, the damage calculation section  12  searches the database section  13  based on the acquired processing conditions, thus acquiring the damage data corresponding to the processing conditions. Then, the damage calculation section  12  outputs the acquired damage data to the output section  14 . 
     It should be noted that if the damage data corresponding to the processing conditions is not available in the database section  13 , the damage calculation section  12  can, for example, calculate the damage data corresponding to the processing conditions as follows. In this case, the damage calculation section  12  acquires the damage data obtained under the conditions close to the supplied process conditions from the database section  13 . Then, the damage calculation section  12  interpolates the acquired data, thus calculating the damage data corresponding to the supplied processing conditions. 
     As described above, the simulator according to the present embodiment predicts (evaluates) the damage sustained by the workpiece using a damage database prepared in advance, thus providing even faster prediction (evaluation) of the damage sustained by the workpiece. It should be noted that the simulator according to the present embodiment can be used alone as with the simulators described in the first to fourth embodiments. However, the simulator according to the present embodiment can be incorporated in an etcher or other processing system as in the fifth embodiment. 
     In the above embodiments, a description was given of the simulators (simulation systems) and damage evaluation methods for evaluating the damage sustained by a workpiece subjected to dry etching. However, the present disclosure is not limited thereto. 
     The simulators and damage evaluation methods according to the above embodiments are applicable to any process achieved as a result of the injection of ion particles or other reaction particles (e.g., PVD, ion implantation or other process), thus providing the same advantageous effect. Further, the processing system incorporating the simulator according to one of the above embodiments is not limited to a dry etcher. Instead, the simulator according to one of the above embodiments can be incorporated in any processing system designed to perform a process as a result of injection of reaction particles, thus providing the same advantageous effect. 
     It should be noted that if the process to which the simulator and damage evaluation method according to one of the above embodiments are applied changes, the reaction model of the surface to be processed also changes. In this case, therefore, it is necessary to change the reaction model as appropriate according to the new process. In this case, however, the damage calculation algorithm described in the above embodiments can be used as-is. 
     The present disclosure contains subject matter related to that disclosed in Japanese Priority Patent Application JP 2010-284130 filed in the Japan Patent Office on Dec. 21, 2010, the entire content of which is hereby incorporated by reference. 
     It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and alternations may occur depending on design requirements and other factors insofar as they are within the scope of the appended claims or the equivalent thereof.