Process simulation method, process simulator and chemical vapor deposition system employing the same

A process simulation method and a process simulator are disclosed wherein a simulation for optimum process conditions for formation of a dielectric film for a capacitor by a chemical vapor deposition method is executed using a non-empirical reaction model. The process simulator comprises an inputting apparatus for inputting parameters required to determine optimum process conditions, which provide the best step coverage for a dielectric film of a capacitor to be formed, as values defining given variation ranges, a storage apparatus for storing vapor phase reactions and film surface reactions individually corresponding to process condition sets each of which is a combination of a plurality of parameters as models obtained by a non-empirical method in advance, a simulation condition setting apparatus for setting process condition sets, a reaction model setting apparatus for recalling models from the storage apparatus in response to the thus set process condition sets, and a simulation execution apparatus for executing simulations in accordance with the thus recalled models and comparing results of the simulations with each other to select optimum process conditions.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to a process simulation method, a process simulator 
and a chemical vapor deposition system employing the same, and more 
particularly to a process simulation method, a process simulator and a 
chemical vapor deposition system employing the same wherein process 
conditions upon formation of a dielectric film for a capacitor by a 
chemical vapor deposition (hereinafter referred to simply as CVD) method 
can be set automatically and non-artificially. 
2. Description of the Related Art 
In recent years, as the degree in integration of semiconductor devices goes 
up, increases in number of steps and cost in a manufacturing process and 
increases in time and cost required for development of the process make 
problems. For example, in a dynamic random access memory (DRAM), in order 
to obtain a large capacity, a dielectric film with a uniform thickness 
must be formed on a capacitor having a complicated electrode structure of 
such type as the trench type or the hemispherical grain (HSG) type. For 
the formation of a dielectric film on the above mentioned electrodes, the 
CVD method is principally employed since it is advantageous in that it 
gives a good step coverage of the dielectric film which is evaluated in 
terms of a ratio between the film thickness on the uppermost surface of a 
step and that on the side wall of the step (hereinafter referred to as 
coverage ratio) and that it can easily achieve selective deposition upon 
formation of a film. In order to reduce the time and the cost required for 
development of such process technique, a process simulator wherein optimum 
conditions for achieving a desired process are automatically set to a CVD 
apparatus has been proposed. 
Here, how to set optimum CVD condition which gives the best step coverage 
of a dielectric film is considered. It is known that improvement in step 
coverage, where the theoretical value for the best step coverage is 1, can 
be achieved qualitatively by reducing the amount in material gases which 
arrive at the film surface and contribute to formation of the film, and by 
reducing the surface reaction coefficient of the species which will be 
hereinafter described. Accordingly, when the optimum CVD condition is 
automatically determined by a process simulator using certain parameters 
and the obtained optimum condition is required to be simultaneously set to 
the CVD system, it is necessary that, in the process simulator, the vapor 
phase reactions and the film surface reactions be treated without 
depending on any experimental results, that is, those reactions are 
non-empirically described. 
One of the documents which describe a representative process simulator in 
which a step coverage of a thin film formed by a conventional CVD process 
is calculated by computer simulation is disclosed in M. Ikegawa and J. 
Kobayashi, Journal of Electrochemical Society, Vol. 136, No. 10, 1989, pp. 
2,982-2,986. According to the simulator of the document, the procedure of 
growth of the film is simulated using such a model as shown in FIG. 9. 
In the model shown in FIG. 9, it is assumed that a process region in which 
a film 103 is formed on a substrate surface 102 is constituted roughly 
from a vapor phase and a surface/solid phase. First, in the vapor phase, 
material gases are decomposed by heat, light or plasma so that a molecule 
which is liable to react, that is, a reactant 101, is produced. The 
reactant 101 arrives at the substrate after colliding with other 
molecules, and it is absorbed on the substrate surface 102. Meanwhile, in 
the surface/solid phase, the reactant 101 arriving at the substrate 
surface 102 follows either procedure; one is that the reactant causes the 
reaction on the substrate surface 102 to form a film 103, and the other is 
that it is reflected by the substrate surface 102 without causing any 
reaction with the substrate surface 102 and moves to a different position 
on the substrate surface 102. Such procedures are calculated for a large 
number of individual molecules and the results of the calculations are 
accumulated to simulate the growth of the film 103 in such a manner as 
illustrated in FIG. 10. 
The flow chart of the process simulation is described by referring to FIG. 
10. First initial conditions for the simulation, such as kinds of material 
gases and a process temperature are determined or chosen (step P1). 
Behavior of reactants 101 in the vapor phase is calculated by a Monte 
Carlo method (step P2) until they arrive at the substrate surface 102 or 
the film 103 from positions where they have been generated. From the 
results of the calculation, the positions of the reactants arriving on the 
substrate surface and the number of the reactants 101 arriving at a 
position on the substrate surface are obtained (step P3). Then, it is 
determined whether or not the thus arriving reactants 101 react with the 
surface of the film 103 at the individual positions of the surface (step 
P4). The thickness of the film 103 is increased as the amount of the 
reactants 101 which have reacted with the surface of the film 103. Whether 
or not reaction actually occurs is determined from the value of a surface 
reaction coefficient set in advance. For example, where the reaction 
coefficient is 1.0, all of the reactants 101 arriving at the surface of 
the film 103 react with the surface of the film 103, but where the 
reaction coefficient is 0.5, half of the reactants 101 arriving at the 
surface react with the surface. The operations at steps P1 to P4 are 
repeated until the thickness of the film 103 becomes equal to a 
predetermined thickness tfs (step P5). 
A most significant factor in the calculation described above is a reaction 
coefficient which indicates the probability of the reactant causing the 
reaction, and the reaction coefficient is determined by the energy which 
is need for the reactant causing the reaction. Particularly, the step 
coverage is influenced significantly by the reaction coefficient at the 
surface of the film. For example, when the reaction coefficient becomes 
low, since the ratio in surface reflection becomes high, reactants can 
reach a deep portion or the bottom of a groove, that is, a trench, of a 
substrate. Consequently, the coverage ratio approaches unity. 
As mentioned above, the reaction coefficient is an important parameter 
which has a significant influence on the step coverage of the film in CVD 
process. According to the conventional simulation, however, the value of 
the reaction coefficient is set to be an empirical value, or is so 
determined as to fit the simulation results, in which the reaction 
coefficient is set as an artificial parameter, to the experimental 
results. Therefore, in the conventional simulation, the optimum condition 
for causing the coverage ratio to approach unity is a semi-experimental 
condition determined only from a large number of results of experiments, 
and this does not satisfy the requirement for a non-empirical value 
described above. Further, a process wherein the step coverage is improved 
using such a result of the simulation as described above is insufficient 
for supporting the development of the CVD process described above since 
the dominant factor of step coverage is indefinite. 
In short, the conventional process simulator described above is 
disadvantageous in that, since an empirically estimated value or an 
artificial or experiential corrected value with which a result of the 
simulation and the result of the experiment coincide with each other is 
used as a value of the reaction coefficient, a process optimum condition 
for improving the step coverage is a semi-experiential value based on a 
large number of experimental results and the requirement for a 
non-empirical value for automatically setting a result of a simulation on 
the real time basis as a process condition for a CVD process apparatus is 
not satisfied. Further, since the dominant factor of step coverage is 
indefinite, the conventional process simulator is further disadvantageous 
in that it is insufficient as a process simulator for supporting the 
development of a CVD process which optimizes the step coverage of a 
dielectric film. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide a process simulation 
method and a process simulator in which dominant factors of step coverage 
are definite over all of steps of a process and by which the simulation 
time and the cost for development can be reduced remarkably comparing with 
those of a conventional process simulation method and a conventional 
process simulator in which a result of an experiment is used, and a 
chemical vapor deposition system in which the process simulation method 
and the process simulator are employed. 
In order to attain the object described above, according to an aspect of 
the present invention, there is provided a process simulation method 
wherein a plurality of parameters required to determine optimum process 
conditions which provide a maximum step coverage of a dielectric film to 
be formed on an electrode of a capacitor by a chemical vapor deposition 
method by supplying a plurality of raw material gases to the electrode of 
a capacitor are inputted as values defining predetermined variation ranges 
and the thus inputted parameters are individually varied to select optimum 
process conditions, comprising the steps of setting a plurality of process 
condition sets of different combinations from the plurality of inputted 
parameters, recalling, from a data base in which vapor phase reactions and 
film surface reactions individually corresponding to a plurality of 
process condition sets are stored as models obtained by a non-empirical 
method in advance, those of the vapor phase reaction models and the film 
surface reaction models which correspond to the individual process 
condition sets, and executing simulations of a vapor phase reaction and a 
film surface reaction in accordance with the thus recalled vapor phase 
reaction step models and film surface reaction step models and comparing 
results of the simulations with each other to select optimum process 
conditions. 
According to another aspect of the present invention, there is provided a 
process simulator, which comprises an inputting apparatus for inputting a 
plurality of parameters required to determine optimum process conditions, 
which provide a maximum step coverage of a dielectric film to be formed on 
an electrode of a capacitor by a chemical vapor deposition method by 
supplying a plurality of raw material gases to the electrode of a 
capacitor, as values defining predetermined variation ranges, a simulator 
section for individually varying the parameters inputted from the 
inputting apparatus to select optimum process conditions, and a storage 
apparatus for storing vapor phase reactions and film surface reactions 
individually corresponding to a plurality of condition sets, which have 
been obtained by a non-empirical method in advance, the simulator section 
including a simulation condition setting apparatus for setting a plurality 
of process condition sets which are each a combination of a plurality of 
parameters inputted from the inputting apparatus, a reaction model setting 
apparatus for recalling vapor phase reaction models and film surface 
reaction models from the storage apparatus in response to the process 
condition sets supplied from the simulation condition setting apparatus, 
and a simulation execution apparatus for performing simulations of vapor 
phase reactions and film surface reactions using the vapor phase reaction 
models and the film formation reaction step models supplied from the 
reaction model setting apparatus and comparing results of the simulations 
with each other to determine optimum process conditions. 
The non-empirical method for obtaining the reactions for both vapor phase 
and film surface may be an ab-initio molecular orbital method which is 
based on a principle of the quantum chemistry by which individual molecule 
orbitals of raw material gas are obtained. 
The plurality of raw material gases may include SiH.sub.2 Cl.sub.2 or 
SiH.sub.4 and NH.sub.3. 
The parameters to be inputted may include kinds of the raw material gases, 
pressures of the individual raw material gases, and flow rates of the raw 
material gases. 
The process simulator may further comprise a reaction model determination 
section having a molecular orbital calculation program for developing a 
reaction model using the data stored in the storage apparatus. 
According to a further aspect of the present invention, there is provided a 
chemical vapor deposition system, comprising a process simulator described 
above, and a chemical vapor deposition apparatus for receiving optimum 
process conditions from the process simulator and performing a process of 
a chemical vapor deposition method under the optimum process conditions. 
The chemical vapor deposition apparatus may include a control apparatus for 
CVD condition including a gas flow control section, a temperature control 
section and a time control section, a process condition setting section 
for setting the optimum process conditions to the CVD condition control 
apparatus, and a process execution section for performing a chemical vapor 
deposition process under the optimum process conditions set by the process 
condition setting section. 
With the process simulation method, the process simulator and the chemical 
vapor deposition system of the present invention, a non-empirical 
simulation in which dominant factors of a step coverage are made definite 
over the entire process can be executed. Accordingly, the simulation time 
and the cost for developing CVD process which provides the best step 
coverage can be reduced remarkably comparing with those of the prior art 
in which a result of an experiment is employed. 
The above and other objects, features and advantages of the present 
invention will become apparent from the following description and the 
appended claims, taken in conjunction with the accompanying drawings in 
which like parts or elements are denoted by like reference characters.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
A simulation for optimization of a step coverage in a CVD process is 
required to simulate vapor phase reactions and film surface reactions 
non-empirically as described hereinabove in connection with the prior art. 
In the present invention, those reaction processes are modeled by an 
ab-initio molecular orbital calculation, and simulation of a CVD process 
is performed based on the model thereby to allow non-empirical simulation. 
FIG. 1 shows a process simulator and a system including a CVD apparatus 
which employs the process simulator according to a preferred embodiment of 
the present invention. Referring to FIG. 1, the system shown includes an 
inputting apparatus 1 for inputting therethrough a desired CVD condition, 
an acceptable range of the simulation and so forth, a process simulator 2 
for carrying out a simulation for the CVD process, and a CVD apparatus 8 
for receiving the result of simulation from the process simulator 2 and 
performing the CVD process. 
The process simulator 2 includes a simulator section 21 including two 
engineering work stations (EWSs) for carrying out a plurality of 
simulations for a desired process in parallel, a reaction model developing 
section 22 including EWSs similar to those of the simulator section 21 and 
having an ab-initio molecular orbital calculation program for executing, 
when a reaction model which is not included in a data base is required, a 
calculation newly to determine such reaction model, a storage apparatus 23 
for storing results of simulation, and another storage apparatus 24 
connected to the reaction model developing section 22 and serving as a 
data base in which CVD reaction models of various gases obtained as 
results of molecular orbital calculations of reaction procedures are 
stored. 
The simulator section 21 includes a simulation condition setting section 
211 for setting a condition for a simulation, a reaction model setting 
section 212 serving as a program section for determining a reaction model 
corresponding to a given process condition using data of the storage 
apparatus 24, and a simulation section 213 having a CVD process simulation 
program. The simulation condition setting section 211 includes a 
determination section 214 for determining whether or not there is a 
simulation result corresponding to an inputted set of process conditions. 
The CVD apparatus 3 includes a CVD condition control apparatus 32 including 
a gas control section 321, a temperature control section 322 and a time 
control section 323, a process condition setting section 31 for setting 
the conditions of a CVD process for the CVD condition control apparatus 32 
to optimum process conditions determined from the CVD process simulation, 
and a CVD process execution section 33 for executing a CVD process under 
the conditions set by the process condition setting section 31. 
One of the two EWSs of the simulator section 21 carries out a simulation 
regarding vapor phase reactions of the CVD process to obtain arrival 
distributions of reactants at the surface of a substrate under given 
process conditions including gas pressures, gas flow rates and a 
processing temperature. Meanwhile, the other engineering work station 
carries out a simulation for growth of a film by the CVD based on the 
obtained arrival distributions of the reactants. 
The way of automatically setting process conditions in the process 
simulator of the present embodiment will be described below with reference 
to FIG. 1. First, ranges for process conditions corresponding to a 
required CVD process, ranges peculiar to the process apparatus, ranges of 
variation of the process conditions corresponding to a quality standard or 
the like, and so forth are inputted from the inputting apparatus 1. The 
simulation condition setting section 211 determines a set of process 
conditions such as a temperature, kinds of gases, gas pressures, gas flow 
rates and a processing time to be sent to the simulation section 213 
within the process condition ranges mentioned above. Further, the 
simulation condition setting section 211 examines presence or absence of 
simulation result corresponding to the set of process conditions by means 
of the determination section 214, and if presence of the required result 
is confirmed, then the result is stored as it is, but on the contrary, if 
absence of such result is confirmed, then the simulation condition setting 
section 211 supplies the set of process conditions to the simulation 
section 213. In this instance, the process condition set is simultaneously 
sent to the reaction model setting section 212. The reaction model setting 
section 212 determines a reaction model corresponding to the given process 
condition set and supplies the model to the simulation section 213. But 
when such required reaction model is not found out in the storage 
apparatus 24, a calculation is carried out in the reaction model 
developing section 22 using an ab-initio molecular orbital calculation 
program to obtain a new reaction model, and the obtained new reaction 
model is supplied to the reaction model setting section 212. After the 
simulation is completed, the result of the simulation is stored into the 
storage apparatus 23. After all simulations are completed, optimum process 
conditions with which, for example, the coverage ratio exhibits its best 
value are deduced from the results of simulations. The optimum process 
conditions thus determined are supplied to the process condition setting 
section 31. The above described procedure are executed by the process 
simulator 2. 
The process condition setting section 31 gives the values of the optimum 
process conditions to the CVD condition control apparatus 32 provided for 
the CVD process execution section 33 in order to set the process executing 
conditions of the CVD process execution section 33 to the optimum process 
conditions obtained by the simulations described above. The optimum 
process conditions obtained by the simulation section 213 are 
automatically set to the CVD process execution section 33 in this manner. 
The construction of the simulation section 213 which is an important 
feature in the present invention is shown in FIG. 2. Referring to FIG. 2, 
the simulation section 213 shown includes a vapor phase reaction 
simulation section 131 for simulating reactions or movement of reactants 
in a vapor phase and calculating the arrival distribution of reactants at 
the surface of a substrate under the conditions of a gas pressure, a gas 
flow rate and a temperature condition given as a result of the simulation, 
a film growth simulation section 132 for simulating film deposition using 
the arrival distribution obtained by the vapor phase reaction simulation 
section 131 in order to calculate step coverage, and an optimum condition 
determination section 133 for determining optimum process conditions from 
a result of calculation for step coverage. 
In operation of the simulation section 213, reactions and transportation of 
reactants in a vapor phase are calculated solving a diffusion equation. 
First, as for reactions in vapor phase, a reaction model set by the 
reaction model setting section 212 is employed. An example of such 
reaction model is illustrated in FIG. 3. The reaction model shown in FIG. 
3 shows an example of a calculated result of densities D of reactants, 
SiCl.sub.2 and HCl, in dichlorosilane (SiH.sub.2 Cl.sub.2) and ammonia 
(NH.sub.3) mixture where the range of the temperature T was set to 
550.degree. C. to 950.degree. C. 
Using the density of the reactants calculated by the vapor phase reaction 
simulation section 131, film growth is simulated by a Monte Carlo method 
in the film deposition reaction simulation section 132. For a simulation 
of the film growth, first, the arriving positions of reactants on the film 
surface; second, the kinds of the arriving reactants; third, the 
frequencies of occurrences of reactions of the reactants on the film 
surface; and fourth, the frequencies of occurrences of desorption reaction 
on the film surface, are required. The frequencies of the occurrences of 
the reactions or desorption are determined using a random number as 
described below in order to perform the simulation described above. It is 
noted that, in the present embodiment, a trench structure is assumed as an 
electrode structure. 
1. Determination of Arriving Positions of Reactants 
If speeds of reactants in vapor are isotropic, then the arriving flux of 
reactants at individual points of the surface of a trench increase in 
proportion to angles of elevation indicated by solid angles from the 
individual points. If, for example, the arriving flux .GAMMA..sub.total of 
reactants at a point A on the uppermost surface of a trench from the 
points of the angle of elevation .theta..sub.A is 1, then the arriving 
flux at another point B on the side wall of the trench from the points of 
the angle of elevation .theta..sub.B is given by .theta..sub.B 
/.theta..sub.A. The arriving flux .GAMMA..sub.total is given by the 
following formula: 
EQU .GAMMA..sub.total =(1/4)nV.sub.ther [cm.sup.-1 s.sup.-1 ] 
where n is the concentration of the reactant, V.sub.ther is a thermal 
velocity of the reactant=[8kT/.pi.M].sup.-1/2, k is a Boltzmann constant, 
and T is a temperature of the system. 
2. Determination of Kind of Arriving Reactant 
A reactant is determined by comparing the ratio in concentration of the 
reactant in a vapor phase with a random number .xi..sub.1. For example, 
where three kinds of reactants X, Y and Z exist and the concentration 
ratio of each of of them is X=0.5, Y=0.3 and Z=0.2, if the random number 
.xi..sub.1 is 0.7, then the reaction species Y is selected. 
3. Determination of Reaction Frequency 
It is assumed that all of the reactions are of Arrhenius type. In this 
instance, the reaction frequency is in proportion to A.sub..theta. 
exp(-.epsilon..sub.a /kT), where A.sub..theta. is a frequency factor, and 
.epsilon..sub.a is an activation energy of the reaction. 
In this instance, whether or not the reaction occurs is determined by 
comparison between the value of the expression A.sub..theta. 
exp(-.epsilon..sub.a /kT) and a uniform random number .xi..sub.2 of 0.1. 
In other words, it is determined that the reaction occurs when the 
following equation is satisfied: 
EQU -1n.xi..sub.2 .gtoreq.(-.epsilon..sub.a /kT) 
4. Also the desorption reaction frequency from the surface of a film can be 
determined in a similar manner as in (3) above. 
The reactions of individual reactants arriving at the film surface from a 
vapor phase are traced in accordance with the obtained model to simulate a 
CVD process. 
The reaction or activation energy used in the present simulation is 
obtained by an ab-initio molecular orbital calculation. The determination 
of a reaction model by such an ab-initio molecular orbital calculation 
will be described subsequently. In particular, in low pressure chemical 
vapor deposition (LPCVD) for a silicon nitride film, reaction steps such 
as (1) thermal decomposition of mother gas, (2) surface absorption of the 
reactants and Si--N bonds formation and (3) desorption of the absorbed 
species and desorption of the species from the film surface are involved. 
When the material gas is SiH.sub.2 Cl.sub.2 /NH.sub.3, the following 
thermal decomposition reactions of the gas may be involved: 
EQU SiH.sub.2 Cl.sub.2 .fwdarw.SiCl.sub.2 +H.sub.2 (1) 
EQU SiH.sub.2 Cl.sub.2 .fwdarw.SiHCl+HCl (2) 
EQU NH.sub.3 .fwdarw.NH.sub.2 +H (3) 
EQU NH.sub.3 .fwdarw.NH+H.sub.2 (4) 
The reaction energies of the above described reaction systems are 
calculated by am ab-initio molecular orbital calculation method. In the 
present example, the reaction energies of the equations (1) and (2) are 
obtained to be much lower than those of the equations (3) and (4). 
Accordingly, it can be determined that the reactants in a vapor phase are 
principally SiCl.sub.2 and SiHCl which are produced by thermal 
decomposition of SiH.sub.2 Cl.sub.2. 
Subsequently, as regards reactions on the film surface, considering a 
molecule of a certain size as a local portion of the film, a reaction of 
the molecule with reactants produced in the vapor phase is determined from 
an ab-initio molecular orbital calculation based on a principle of the 
quantum chemistry. For example, formation of Si--N bonds is calculated in 
accordance with the following reaction: 
EQU SiCl.sub.2 +NH.sub.3 .fwdarw.SiHCl.sub.2 NH.sub.2 (5) 
In order to simulate the growth of a silicon nitride film, the formation of 
Si--N bonds must successively occur. The successive formation of Si--N 
bonds is modeled as follows. SiCl.sub.2 NH.sub.2 produced by the reaction 
described above changes to SiClNH.sub.2 by desorption of HCl from 
SiCl.sub.2 NH.sub.2 as given by the following expression: 
EQU SiClNH.sub.2 .fwdarw.SiClNH.sub.2 +HCl (6) 
Since SiCl.sub.2 NH.sub.2 has dangling bonds and is in the form of 
SiX.sub.2 (X=Cl, NH.sub.2), it can react with NH.sub.3 in the same manner 
as SiCl.sub.2 and form new Si--N bond. 
The growth of a silicon nitride film is modeled with repetition of 
insertion reaction of SiCl.sub.2 into N--H or Si--H bonds on the film 
surface and desorption of HCl from the film surface which is terminated by 
H or Cl. Referring to FIGS. 4(A) to 4(G) which schematically illustrate 
the growth model of a silicon nitride film, SiCl.sub.2 produced by thermal 
decomposition of SiH.sub.2 Cl.sub.2 by a reaction of (1) is first inserted 
into N--H bonds on the film surface (FIG. 4(A)) so that N--SiHCl.sub.2 
bonds are produced (FIG. 4(B)) of the surface. Then, HCl is desorbed from 
this N--SiHCl.sub.2 of the surface while a Si--Cl bond remains on the 
surface (FIG. 4(C)). Since the Si--Cl bond (Si--Cl site) is in the form of 
SiX.sub.2 which has two dangling bonds, it reacts with the N--H bond of 
NH.sub.3 from the vapor phase (FIG. 4(D)) so that new Si--N bond is formed 
(FIG. 4(E)). SiCl.sub.2 can insert also into the Si--H(Cl) bond on the 
film surface so that a Si--Si bond is also formed (FIGS. 4(F) and 4(G)). 
The reaction energy of this Si--Si bond formation is of the Si--N 
formation shown in FIG. 4(A). The growth of the film proceeds by 
repetition of the steps described above. 
As described above, reaction energies of all of possible reaction systems 
are calculated, and reaction paths having small reaction energies 
sufficient to cause the reactions to occur under a given process 
temperature are selected. The reaction paths and reaction energies are 
determined for each reaction step including (1) the thermal decomposition 
of the material gases, (2) surface absorption of the reactants, and the 
formation of Si--N bonds and (3) desorption of the absorbed species and 
desorption of the species from the film surface. The reaction model 
developing section 22 executes the calculation for the reaction energies 
described above for the species of gases supplied thereto, and stores the 
thus produced reaction model into the storage apparatus 24. 
FIG. 5 shows a flow chart of procedures of the film growth simulation 
section 132 by a Monte Carlo method based on the reaction model produced 
in such a manner as described above. Referring to FIG. 5, the film growth 
simulation section 132 first sets initial conditions such as kinds of 
gases to be supplied, a processing temperature, and so on (step T1). Then, 
reactions of desorption of H.sub.2 and HCl of (1) and (2) are calculated 
(steps T2 and T3). Next, a species to arrive at the film surface and the 
arriving position are determined (step T4). Then, it is determined whether 
or not the species is HCl (step T5). If the reactant is HCl, the control 
sequence advances to step T6, at which it is determined whether or not the 
species is absorbed. If the determination is in the affirmative, 
calculation of absorption of HCl is executed at step T7, whereafter the 
control sequence advances to step T10. On the other hand, if the 
determination at step T6 is in the negative, that is, the HCl species is 
not absorbed, the control sequence advances directly to step T10. On the 
other hand, if the determination at step T5 is in the negative, that is, 
the arriving species is not HCl, the control sequence advances to step T8, 
at which it is determined whether or not the species reacts with the bonds 
or dangling bonds of the film surface. If the determination is in the 
affirmative, the control sequence advances to step T9, at which a new 
Si--N or Si--Si bond formation is calculated, the thickness of the film is 
increased, and the species of the bonds of the film surface is changed, 
whereafter the control sequence advances to step T10. On the contrary, if 
the determination at step T8 is in the negative, that is, the species does 
not react, then the control sequence directly advances to step T10. At 
step T10, it is determined whether or not all reactions required are 
completed. If the determination is in the negative, the control sequence 
returns to step to repeat the operations at steps T2 to T9. If the 
determination at step T10 is in the affirmative, the control sequence 
advances to step T11, at which step coverage, a deposition rate of the 
film and so forth are calculated and outputted, thereby ending the 
simulation procedure. 
FIG. 6 illustrates determination of an optimum CVD condition executed by 
the optimum condition determination section 133. Referring to FIG. 6, a 
simulation is first executed with a single process condition (step U1), 
and parameters such as a coverage ratio, a film composition and a process 
time corresponding to the set condition are determined based on a result 
of the simulation as described above (step U2). The parameters are 
compared with individual optimum values which have been applicable under 
the set condition within given ranges to successively determine whether or 
not the process conditions are optimum, that is, whether or not the 
process time is within the given range (step U3), whether or not the 
coverage ratio is optimum (step U4) and whether or not the film 
composition is optimum (step U5). If the determinations at all of steps U3 
to U5 are in the affirmative, then the set conditions are stored as a set 
of optimum process conditions (step U6). Then, it is determined whether or 
not such determination has been performed for all of the set conditions 
(step U7), and then the sets of optimum process candidates are outputted 
(step U8). 
Procedures of a process simulation in the present embodiment will be 
described in more detail with reference to FIG. 7 which illustrates the 
procedures beginning with a simulation by the simulation condition setting 
section 211 and the simulation section 213 and ending with determination 
of optimum process conditions. First, variation ranges of aimed parameters 
such as a film deposition rate and a film composition ratio in addition to 
a coverage for a film of an object for formation are inputted (step S1). 
Then, fixed parameter values of process conditions to be fixed are 
inputted (step S2). Further, variation ranges for the parameters of 
process conditions are inputted(step S3). The process condition variation 
ranges are set within a control range peculiar to the CVD process 
execution section 33 and so forth. Next, the parameters of the process 
conditions are varied within the individually given ranges to determine a 
set of process conditions which make candidates for an optimum process, 
that is, an optimum process condition set (step S4). Then, it is detected 
whether or not a result of a simulation corresponding to the optimum 
process condition set exists on the data base (step S5). If such result 
exists already, it is determined that the simulation is completed, 
whereafter the control sequence advances to step S7. If such result is not 
found at step S5, a simulation is condition under the conditions of the 
optimum process candidate set (step S6). A result of the simulation is 
stored into the data base of the storage apparatus 23 (step S7). Then, it 
is determined whether or not simulations have been completed for optimum 
process condition sets which satisfy all of the conditions within the 
given ranges (step S8). Thereafter, that one of all of the optimum process 
condition sets which provide the best coverage is selected (step S9). 
Then, it is determined whether or not the parameters other than the 
coverage remain within the control ranges under the conditions of the 
selected optimum process condition set. If the determination is in the 
negative, the determination is performed for that one of the optimum 
process candidate sets which exhibits the second best coverage. The 
operations are repeated to select a single optimum process condition set 
from within the plurality of optimum process candidate sets (steps S10 and 
S11). Then, the parameters of the optimum process condition set thus 
selected are outputted (step S12). 
Where the simulation described above is applied to formation of a silicon 
nitride Si.sub.3 N.sub.4 film for a dielectric film of a capacitor from 
gases of dichlorosilane (SiH.sub.2 Cl.sub.2) and ammonia (NH.sub.3) by a 
low pressure chemical vapor deposition (LPCVD) method, when the process 
temperature T as a desired process condition is varied with the step of 
50.degree. C. within the range from 700.degree. C. to 900.degree. C. while 
the pressures of the gasses are all fixed to 0.4 Tort and the ratio of gas 
flow rates of SiH.sub.2 Cl.sub.2 and NH.sub.3 is varied to three values of 
1/2, 1/5 and 1/10, a total of 15 process condition sets are given in order 
to obtain the coverage c, the film deposition rate a and the film 
composition ratio b for each of the temperatures. 
An example of a result of the simulation described above is illustrated in 
FIG. 8. Referring to FIG. 8, where the pressures of the gasses and the 
ratio of the gas flow rates are fixed, the result of the simulation 
indicates that the process temperature of 750.degree. C. is an optimum 
temperature which provides the best coverage ratio. The optimum process 
conditions obtained by the simulation are sent to the CVD process 
execution section 33 so that a film having a good step coverage is formed 
in the CVD process execution section 33. 
The time required for simulating the growth of a silicon nitride film of 
100 angstroms thick using the present embodiment is about 5 minutes for 
one process condition for the vapor phase reaction step and about 3 
minutes for one process condition for the film deposition step. 
Consequently, the total time required for the entire simulation to obtain 
the result illustrated in FIG. 8 is about 30 minutes including setting of 
conditions. 
Having now fully described the invention, it will be apparent to one of 
ordinary skill in the art that many changes and modifications can be made 
thereto without departing from the spirit and scope of the invention as 
set forth herein.