JPH10284483A - Oxidation simulation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an oxidation simulation method by which stable calculated results can be obtained even when time steps are narrowed and the calculating time can be shortened by performing oxidation simulation by using an elastic constant found from the stress of an oxide film after the stress of the film in a transition region is relieved as the elastic constant of the transition area. SOLUTION: In an oxidation simulation method, the concentration distribution of an oxidation species 4, such as H2 , O2 , etc., is calculated by solving a steady state diffusion equation and the oxidizing velocity of a silicon substrate 1 at the silicon/silicon oxide interface between the substrate 1 and a silicon oxide film 2 is found from the concentration of the species 4 at the interface, because the 4 is diffused in the silicon oxide film 2 and reaches the surface of the substrate 1. Then a new transition region 5 in which the substrate 1 changes to the silicon oxide film 2 is set between the oxide film 2 and substrate 1 in accordance with the found oxidizing velocity. In the transition region 5, a Young's modulus assumed for the same oxidizing condition is selected from a table of Young's moduli found by calculating actually measured Young's moduli under various oxidizing conditions is used.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an oxidation simulation method in a semiconductor manufacturing process, and more particularly to an oxidation simulation method for determining a stress distribution and an oxide film shape generated in an oxidation step.

[0002]

2. Description of the Related Art A thermal oxide film of silicon is used to electrically isolate active elements on an LSI.
In an oxidation process such as a LOCOS process widely used in SI manufacturing, an oxidation reaction proceeds at an uneven silicon / silicon oxide film interface, so that high stress is generated due to volume expansion when silicon is changed to a silicon oxide film. . Such stress causes a crystal defect in the silicon substrate, and D
Since it is considered to be a cause of deterioration of the data retention time of the RAM, it is indispensable in the development of DRAM to accurately evaluate the stress generated in the oxidation process. The stress generated in the oxidation process is evaluated using an oxidation simulation system based on the simulation.

FIG. 5 shows a flow chart of a conventional oxidation simulation based on a viscoelastic model, and Table 1 shows an example of an elastic constant table showing the Young's modulus and Poisson's ratio of each material used in the simulation. .

[Table 1] Such a conventional oxidation simulation step will be described with reference to a schematic two-dimensional cross-sectional view of the LOCOS step shown in FIG. 6. First, as shown in FIG.
_{Since the} oxidizing species 4 such as ₂ O or O ₂ diffuses and reaches the surface of the silicon substrate 1, the concentration distribution of the oxidizing species 4 is calculated by solving a steady state diffusion equation, and the silicon / silicon oxide film interface is calculated. From the concentration of the oxidizing species 4 in (1), the local oxidation rate of the silicon 1 at the interface is determined (calculation of the oxidizing species). Here, 3 indicates a SiN film. Next, as shown in FIG. 6B, a transition region 5 where the silicon substrate 1 is changed to the oxide film 2 is newly set between the oxide film 2 and the silicon 1 according to the calculated oxidation rate. . Next, after selecting a Young's modulus and a Poisson's ratio specific to the material constituting each region (silicon, silicon oxide film, silicon nitride film, and the like) from Table 1 above, an initial strain due to volume expansion is given to the transition region 5. . Table 1 does not include temperature as a parameter, but a table may be created for each temperature. Subsequently, the stress generated in the oxide film is obtained by using the finite element method. At this time, in the finite element method, the following equation (I) derived from the principle of virtual work

(Equation 1) Solve. Where △ am is the nodal displacement increment at the m-th time step, which is unknown, B is the strain-displacement matrix,
D is the elastic matrix, Dtm, △ fm are the time increment and nodal load increment at the mth time step. As described above, by setting the transition region 5, giving the volume expansion to the transition region 5, and repeating the above-described simulation process of calculating the stress of the oxide film by the finite element method,
Finally, the stress distribution of the oxidized silicon substrate can be obtained.

[0004]

When the oxide film is treated as a viscoelastic body as described above, the calculated value of the stress is about two orders of magnitude larger than the actual value, so that there is a stress generated in the oxide film. In order to lower the viscosity coefficient when the stress is exceeded and to reduce the generated stress, introduction of a model in which the viscosity coefficient has stress dependency is studied. However, in such a model, since stress relaxation occurs in the transition region at a very high speed immediately after the volume expansion of the transition region, the simulation tends to be unstable due to calculation. That is, FIG. 7 shows a simulation result of the relationship between the oxidation time and the generated stress in the transition region when the oxidation simulation method based on the viscoelastic model considering the stress dependence of the viscosity coefficient is used. White circle (oxidation time about 25
The calculated value is extremely unstable, as can be seen in the range up to 2 seconds). In order to avoid such instability and obtain a stable solution, it is necessary to perform an oxidation simulation with a small time step, but on the other hand, there is a problem that the calculation time becomes long and the calculation cost becomes extremely large. Will occur. Accordingly, an object of the present invention is to provide a simulation method capable of obtaining a stable simulation result without reducing a time step in an oxidation simulation using a viscoelastic model considering the stress dependence of a viscosity coefficient. And

[0005]

The inventors of the present invention have conducted intensive studies and have found that the elastic constant of the silicon oxide film is not used as the elastic constant of the transition region used in the oxidation simulation. By using the measured elastic constant obtained from the measured stress of the silicon oxide film formed by oxidizing the silicon substrate, it was found that a stable simulation result could be obtained without reducing the time step, and completed the present invention. .

That is, according to the present invention, a silicon oxide film is treated as a viscoelastic body whose viscosity coefficient has stress dependence, and a region where silicon is oxidized to a silicon oxide film at a silicon / silicon oxide film interface is a transition region. Elastic constants are set for the transition region and necessary regions other than the transition region, and an initial strain is given to the transition region based on volume expansion caused by oxidation of the transition region. In an oxidation simulation method for calculating a stress distribution generated in a transition region and a peripheral region thereof under a set oxidation condition and a shape of an oxide film corresponding to the stress distribution, the oxidation condition is set as an elastic constant of the transition region. Measured elastic constants obtained from measured values of residual stress of silicon oxide film formed by oxidizing silicon substrate with In this case, the calculated elastic constant obtained from the residual stress of the silicon oxide film obtained by performing the oxidation simulation of the silicon substrate is set, and the elastic constant of the necessary region other than the above-mentioned transition region is defined as the elastic constant of the material constituting the region The oxidation simulation method is characterized in that the elastic constants are set respectively.

As can be seen from the graph of the dependence of the stress generated in the transition region on the oxidation time shown in FIG. 3, in the conventional simulation method using the elastic constant inherent to the oxide film as the elastic constant of the oxide film in the transition region, Since the viscosity coefficient η of the silicon oxide film has a stress dependency, a rapid stress relaxation (rapid decrease in stress) occurs in the transition region at the beginning of the oxidation simulation, and the time step must be reduced accordingly. In contrast to the case where a stable simulation result cannot be obtained, in the simulation method according to the present invention, the measured elastic constant of the silicon oxide film obtained by oxidizing the silicon substrate under the oxidation conditions of the oxidation simulation is used as the elastic constant of the transition region. Or calculated elasticity obtained from simulation results of oxidation of silicon substrate under the above oxidation conditions By using the number, the simulation can be started from the state after the stress in the transition region is relaxed, and the simulation for the rapid stress relaxation phenomenon in the transition region immediately after the start of oxidation of silicon can be saved. Therefore, a stable numerical calculation result can be obtained without reducing the time step. As a result, the calculation time required for the oxidation simulation can be reduced, that is, the calculation cost can be reduced. Note that the elastic constant includes four constants of Young's modulus, Poisson's ratio, bulk modulus, and shear modulus.

The elastic constant of the transition region is selected from a group of a plurality of measured elastic constants tabulated by calculating based on each measured value of the residual stress of the silicon oxide film on the silicon substrate oxidized under a plurality of oxidation conditions. Is preferably performed. In this way, from the measured values of the residual stress of the silicon oxide film formed by oxidizing the silicon substrate under a plurality of oxidation conditions in advance, the measured elastic constants under the respective oxidation conditions are calculated and tabulated, and the table is prepared for each oxidation simulation. Oxidation simulation can be quickly performed by selecting and using a necessary elastic constant from a table as appropriate.

The elastic constants of the transition region are calculated based on the calculated values of the residual stress of the silicon oxide film obtained by the oxidation simulation of the silicon substrate under a plurality of oxidation conditions, and are tabulated as a plurality of calculated elastic constants. Is preferably selected from the group of As described above, the oxidation simulation of the silicon substrate is performed in advance under a plurality of oxidation conditions, the calculated elastic constants of the silicon oxide film under the respective oxidation conditions are obtained and tabulated, and the elastic constants necessary for performing the actual oxidation simulation are appropriately determined. Is selected from the above table, and the oxidation simulation can be quickly performed.

[0010]

BEST MODE FOR CARRYING OUT THE INVENTION

Embodiment 1 FIG. FIG. 1 is a flowchart of an oxidation simulation according to the first embodiment of the present invention.
Is an example of a general oxidation simulation system used for oxidation simulation. As shown in FIG. 2, the central part of the oxidation simulation system is E
The computer 11 is a computer 11, such as a WS, a personal computer, or a large computer, and a user of the system instructs the computer 11 on oxidation conditions such as an oxidation temperature, an oxidation time, an oxidation atmosphere, and an initial shape. As a method of giving these conditions, there are a method of creating conditions in a file using a keyboard and a method of giving an initial shape using a graphical user interface built on the computer 11.
The calculator 11 calculates the oxide film shape and the stress distribution by a calculation method described below, and displays the calculation result on the display. The user of the system looks at the calculation results and adjusts the oxidation conditions to obtain the optimal shape (for example, the separation interval can be shortened) and the stress distribution (less stress generation and less silicon damage). Make changes and repeat calculations. The scanner 12 captures an actually measured shape such as an SEM photograph on a computer and compares it with the actually measured shape. The hard copy machine 13 is used to print the oxide film shape and stress distribution on the screen on paper.

[0011] In such an oxidation simulation method according to the present embodiment, as in the oxidation simulation method based on the conventional viscoelastic model, first, as shown in FIG. 6 (a), a middle oxide film 2, H ₂ O Ya Since the oxidizing species 4 such as O ₂ diffuses and reaches the surface of the silicon substrate 1, the concentration distribution of the oxidizing species 4 is calculated by solving the steady-state diffusion equation, and the oxidizing species at the silicon / silicon oxide film interface is calculated. From the concentration of 4, the local oxidation rate of silicon 1 at the interface is determined (calculation of oxidizing species). Next, as shown in FIG. 6B, a transition region 5 where the silicon substrate 1 is changed to the oxide film 2 is newly set between the oxide film 2 and the silicon 1 according to the calculated oxidation rate. . Next, for regions other than the transition region 5 (silicon, silicon oxide film, silicon nitride film, etc.), the same as in the conventional method, the following Table 2 (a)
, The Young's modulus and Poisson's ratio specific to the material constituting each region are selected. On the other hand, for the transition region 5, the Poisson's ratio is selected from the following Table 2 (a). For the Young's modulus, instead of using the Young's modulus inherent to the oxide film as in the conventional method, the following Table 2 (b) is used. ), A residual stress of a silicon oxide film formed by oxidizing a silicon substrate under a plurality of oxidation conditions in advance from an actual measurement value measured from the warpage of the substrate,
From the table of the Young's modulus obtained by calculating the virtual Young's modulus (actually measured Young's modulus) under each oxidation condition, a virtual Young's modulus when the same oxidation condition is used is selected and used.

[Table 2] Table 2 (b) shows the measured residual stress of the silicon oxide film when the silicon substrate was oxidized under each oxidation condition.
The following formula (II)

(Equation 2) _Is a table of the virtual Young's modulus E _trans obtained using Here, σ _film is the measured stress value of the oxide film, and e ^T is the volume expansion coefficient when silicon is changed to an oxide film, which is usually 1.25. ν is a Poisson's ratio, which is the same value as the oxide film here, but may be another value. As described above, setting an elastic coefficient smaller than that of a normal oxide film means that a stress generated as an elastic response (a stress at time 0 immediately after expansion) is considered in consideration of a stress relaxation mechanism other than viscous flow. ) Is adjusted to reduce the parameter. Next, as in the conventional method, an initial strain due to volume expansion is applied to the transition region 5 in the transition region, and the stress generated in the oxide film is obtained using the finite element method. At this time, in the finite element method, the following equation (I) derived from the principle of virtual work

(Equation 3) Solve. Next, the transition region 5 obtained in this way is considered as an oxide film, and a new transition region is provided thereon (updating the shape), and a similar oxidation simulation is performed to form a new oxide film. It is possible to perform an oxidation simulation of the stress distribution corresponding to. Finally, a suitable oxidation time,
By repeating the oxidation simulation, it is possible to obtain the distribution of stress generated in the substrate after a given oxidation time and the shape of the oxide film corresponding to this.

FIG. 3 shows a case where a conventional oxidation simulation using a Young's modulus inherent to an oxide film constituting a transition region is used as a transition region Young's modulus, and a case where a virtual Young's modulus selected from the above table is used. 4 shows the relationship between the oxidation time and the stress in the transition region when using the oxidation simulation of the present invention. As is apparent from FIG. 3, by using the virtual Young's modulus selected from the above table, the stress value generated in the transition region at the start of the oxidation simulation is:
From the point A to the point B in the conventional case, the stress becomes smaller, so that the stress relaxation immediately after the start of oxidation, which occurs in the conventional method, does not occur. That is, in the oxidation simulation according to the present embodiment, the virtual Young's modulus obtained from the actually measured value of the stress of the oxide film corresponding to the stress in the transition region after the stress relaxation is used as the transition region's Young's modulus. It is possible to obtain the stress distribution after oxidation without performing the simulation of the stress relaxation process performed in the oxidation simulation.

Here, it is known by optical measurement that a high-density layer having a thickness of about 5 ° exists at the silicon / silicon oxide film interface. This indicates that the volume expansion of the transition region as large as 125% caused by the oxidation of the region is alleviated in a very short time (between thin layers) by a mechanism different from ordinary viscous flow. In other words, in the conventional simulation method, it is necessary to handle extremely fast stress relaxation because it is intended to handle the normal viscous flow including the stress relaxation phenomenon having a different mechanism from the stress relaxation due to the normal viscous flow. As a result, calculation instability is caused, and it is indispensable to reduce the time step, and the calculation time is lengthened. Therefore,
In the oxidation simulation method according to the present embodiment,
As described above, by performing an oxidation simulation using the virtual Young's modulus obtained from the stress of the oxide film after the stress relaxation in the transition region as the Young's modulus in the transition region, the rapid stress relaxation phenomena different in the above mechanism is performed. Need not be handled in the oxidation simulation, and as a result, a stable calculation result can be obtained without reducing the time step.

Embodiment 2 FIG. In the first embodiment, a virtual transition region calculated using equation (II) is calculated from the measured value of the residual stress after stress relaxation obtained by measuring the warpage of a silicon substrate previously oxidized under a plurality of oxidation conditions. Young modulus
Although the (calculated Young's modulus) is tabulated, in the second embodiment, first, the Young's modulus of the transition region in the oxidation simulation in which the viscosity coefficient has the stress-dependent viscosity, In the conventional oxidation simulation method using the rate, the time step is made small (that is, over a long time), the stress in the transition region after the stress relaxation under a plurality of oxidation conditions is obtained in advance, and the equation (II) is used from the obtained stress. The virtual Young's modulus obtained in this way is tabulated. For example, FIG. 4 shows each oxidation condition (oxidation temperature: 800, 900, 100) simulated by such preliminary oxidation simulation (numerical analysis).
5 is a graph showing stress values in a transition region at (0, 1100 ° C.), and based on the results, respective virtual Young's moduli are obtained using Expression (II).

Next, when actually performing an oxidation simulation, an oxidation simulation is performed by appropriately selecting a virtual Young's modulus suitable for the oxidation conditions used in the simulation from the above table. As described above, the virtual Young's modulus of the transition region under a plurality of oxidation conditions is tabulated in advance using the conventional simulation method, and the oxidation conditions used for the simulation are used in the actual oxidation simulation as in the first embodiment. By selecting a virtual Young's modulus according to the above table from such a table, it is not necessary to deal with rapid stress relaxation phenomena with different mechanisms described above in the oxidation simulation. As a result, stable calculations can be performed without reducing the time step. The result can be obtained.

In the first and second embodiments, the Young's modulus is tabulated as an elastic constant. Of the four elastic constants of Young's modulus, Poisson's ratio, bulk modulus and shear modulus, the independent parameter is 2 Other parameters can be calculated using these parameters alone, so that even if one or two of these parameters are tabulated, the same effect can be obtained.

[0017]

As is apparent from the above description, in the oxidation simulation method according to the present invention, the oxidation simulation is performed by using the elastic constant obtained from the stress of the oxide film after the stress relaxation in the transition region as the elastic constant of the transition region. By doing so, it is no longer necessary to handle the rapid stress relaxation phenomenon used in the conventional oxidation simulation in the oxidation simulation, and as a result, a stable calculation result can be obtained without reducing the time step. . Therefore, it is possible to reduce the calculation time and the calculation cost required for the oxidation simulation.

[Brief description of the drawings]

FIG. 1 is a flowchart of an oxidation simulation according to the present invention.

FIG. 2 is a system configuration diagram of an oxidation simulation system according to the present invention.

FIG. 3 is an oxidation simulation result of a relationship between an oxidation time and a stress in a transition region.

FIG. 4 shows the relationship between the oxidation temperature and the stress in the transition region calculated by a preliminary analysis.

FIG. 5 is a flowchart of a conventional oxidation simulation.

FIG. 6 shows a method of setting a transition region in an oxidation simulation.

FIG. 7 shows a relationship between an oxidation time and a stress in a transition region obtained by using a conventional oxidation simulation method.

[Explanation of symbols]

1 silicon substrate, 2 oxide film (LOCOS oxide film),
3 SiN film, 4 oxidized species (H ₂ O or O ₂ ), 5
Transition area, 11 computers, 12 scanners, and 13 hard copy output machines.

Continued on the front page (51) Int.Cl. ⁶ Identification code FI H01L 21/31 H01L 21/94 A

Claims (3)

[Claims] The silicon oxide film is treated as a viscoelastic body whose viscosity coefficient has stress dependence, and a region where silicon is oxidized to the silicon oxide film at a silicon / silicon oxide film interface is a transition region. An elastic constant is set for each of the necessary regions other than the region and the transition region, and an initial strain is given to the transition region based on volume expansion caused by oxidization of the transition region, and is set based on the initial strain. In the oxidation simulation method for calculating the stress distribution generated in the transition region and its peripheral region under the oxidizing condition and the shape of the oxide film corresponding to the stress distribution, the silicon substrate is subjected to the oxidizing condition as the elastic constant of the transition region. The measured elastic constant obtained from the measured residual stress of the silicon oxide film formed by oxidation The calculated elastic constant obtained from the residual stress of the silicon oxide film obtained by performing the oxidation simulation of the substrate is set, and the elastic constant specific to the material constituting the region is set as the elastic constant of the necessary region other than the transition region. The oxidation simulation method characterized in that: 2. A group of a plurality of measured elastic constants calculated from the measured values of the residual stress of a silicon oxide film on a silicon substrate oxidized under a plurality of oxidation conditions and tabulated. The oxidation simulation method according to claim 1, wherein the oxidation simulation method is selected from the following. 3. A plurality of calculations in which the elastic constant of the transition region is calculated and tabulated based on each calculated value of the residual stress of the silicon oxide film obtained by an oxidation simulation of a silicon substrate performed under a plurality of oxidation conditions. The oxidation simulation method according to claim 1, wherein the oxidation simulation method is selected from a group of elastic constants.