JP5786557B2 - Prediction method of dislocations generated from oxygen precipitates generated during laser spike annealing by simulation - Google Patents

Description

  In the present invention, a laser spike annealing (Laser Spike Annealing; hereinafter referred to as LSA) process is computer-simulated to accurately calculate the temperature distribution and stress distribution generated in the silicon substrate during the LSA process. The present invention relates to a method of predicting physical phenomena that occur during the LSA process using the stress distribution and, more specifically, dislocations generated from oxygen precipitates (Bulk Micro Defect; hereinafter referred to as BMD) contained in a silicon substrate.

  In order to achieve higher speed and higher performance of semiconductor elements, each semiconductor device manufacturer has successively introduced means for realizing further miniaturization of devices. In particular, after the 65 nm generation, in order to form USJ (Ultra Shallow Junction), which is essential for high speed and high performance, Flash Lamp Annealing (FLA) technology (see, for example, Patent Documents 1 to 3). So-called millisecond annealing technology such as LSA technology has been introduced.

  Among them, LSA uses a laser as a heat source and enables annealing in a very short time, so it has excellent performance in USJ formation and attracts attention as a technology that can be applied in various fields in the future. (For example, refer to Patent Document 4).

As shown in FIG. 20, the LSA places a silicon substrate 2 to be heat-treated on a stage 1 and irradiates the surface of the silicon substrate 2 with a laser beam 4 from a laser 3 fixed above the silicon substrate 2 to produce a laser beam. This is performed by moving the stage 1 while the beam is irradiated and scanning the irradiation position of the laser beam. The laser currently used in LSA is a CO ₂ laser (wavelength 10.6 μm).

  However, LSA has a rapid temperature distribution in the depth direction of the laser-irradiated silicon substrate because LSA heats only the surface of a very small area at high temperatures up to about 1350 ° C. It will be. Due to this rapid temperature distribution, a high thermal stress of 100 MPa or more is generated, and there are problems such as cracks in the silicon substrate and slip dislocations causing warpage in the silicon substrate. The warpage of the silicon substrate due to the occurrence of slip causes inconsistency in the pattern between the upper and lower sides in the subsequent exposure and other processes, which causes an error due to this so-called overlay alignment error problem. Has been reported.

JP 2006-261192 A (Claims 1 to 3, paragraphs [0022] to [0023], FIG. 1) JP 2007-305968 A (paragraphs [0006] to [0007]) JP 2009-231652 (paragraphs [0004] to [0008]) JP 2008-235495 A (paragraphs [0002] to [0004])

  In order to deal with such a problem, it is necessary to grasp what physical phenomenon is occurring in the silicon substrate during the LSA process and understand the mechanism. Since the actual phenomenon during the LSA process is local and instantaneous, it is almost impossible to obtain experimental data such as temperature distribution and stress distribution due to measurement problems.

  From this point of view, it is important to develop a model that can be simulated on a computer in the same way as the LSA process that is actually performed, and to reproduce the model so as to grasp the phenomenon that occurs in the model. However, no technology that can simulate the LSA process has been known so far.

  An object of the present invention is to provide a method for predicting generated dislocations from BMD that occurs when performing LSA by simulation, which can accurately predict a physical phenomenon occurring in a silicon substrate in an LSA process.

As shown in FIG. 1, the first aspect of the present invention is a first step of subdividing a silicon substrate having a main surface (100) subjected to laser beam scanning of laser spike annealing into a plurality of mesh elements to be meshed. A second step of calculating a temporal change in energy of the mesh element irradiated with the laser beam from the scanning speed of the laser beam, the size of the laser beam, the energy of the laser beam, and the scanning path, and coordinate data of each mesh element, The third step of inputting the physical property value, the initial temperature of the substrate, and the time change of the energy calculated in the second step to the computer, and the incident energy of the laser beam based on the initial temperature of the substrate and the thermal conductivity as a load A fourth step for obtaining a temporal change in the temperature distribution of the substrate, and the fourth step A stress calculation is performed using the temperature distribution obtained in step (5), a fifth step for determining a temporal change in the thermal stress distribution generated in the substrate, an arbitrary position A of the meshed substrate is set, and the first step A sixth step of selecting, in each time, a temperature distribution and a thermal stress distribution in the depth direction at an arbitrary set position A from the temperature distribution obtained in four steps and the thermal stress distribution generated in the substrate in the fifth step; As shown in FIG. 2, from the temperature distribution selected in the sixth step and the BMD size and residual oxygen concentration contained in the substrate, the seventh step for obtaining the critical stress of dislocation generated from the BMD, and the sixth step An eighth step of calculating a shear stress component in the [110] direction of the (111) plane, which is the main slip surface of the silicon single crystal, from the selected stress components σ _xx , σ _yy , τ _{xy of} the thermal stress distribution; In the ninth step, the shear stress in the eighth step and the critical stress in the seventh step are compared for each depth position, and the dislocation length at each depth position is obtained from the comparison result. This is a method for predicting dislocations generated from BMD generated when laser spike annealing is performed by simulation using a computer including a tenth step of calculating the depth of occurrence of slip from the obtained dislocation length.

  The second aspect of the present invention is based on the prediction result obtained by the prediction method based on the simulation based on the first aspect, and the laser spike annealing treatment is performed under conditions that can minimize the occurrence of dislocations generated from the BMD. This is a method for selecting laser spike annealing treatment conditions, characterized by being selected as conditions.

  According to a third aspect of the present invention, based on a prediction result obtained by a prediction method based on a simulation based on the first aspect, an oxygen precipitation nucleus density and an oxygen concentration in a range where dislocations generated from BMD do not reach the substrate surface are determined. A silicon substrate selection method is characterized in that a silicon substrate having a substrate is selected as a laser spike annealing target substrate.

  According to a fourth aspect of the present invention, the density of oxygen precipitation nuclei in a range where the density reaching the substrate surface of dislocations generated from BMD is small, based on the prediction result obtained by the prediction method by simulation based on the first aspect, and oxygen A silicon substrate selection method, wherein a silicon substrate having a concentration is selected as a laser spike annealing target substrate.

  In the method for predicting generated dislocations from oxygen precipitates generated when LSA is performed according to the simulation of the present invention, the temperature distribution generated in the silicon substrate during the LSA process is obtained through the steps from the first step to the tenth step. Accurately calculate the stress distribution and use the calculated temperature distribution and stress distribution to accurately predict the physical phenomenon that occurs in the silicon substrate during the LSA process, that is, the length of dislocations generated from the BMD contained in the silicon substrate. can do.

  Based on this prediction result, it is possible to deal with problems such as silicon substrate warpage due to silicon substrate cracking during the LSA process and dislocations generated from BMD.

  Specifically, based on the prediction result obtained by using this simulation, by selecting a condition capable of minimizing the occurrence of dislocations generated from BMD as the LSA processing condition, the occurrence of dislocations due to LSA Can be suppressed.

  Further, based on the prediction results obtained using this simulation, by selecting a silicon substrate having a BMD nucleus density in a range where dislocations generated from BMD do not reach the substrate surface, and an oxygen concentration as the LSA processing target substrate, Generation of dislocations due to LSA can be suppressed.

  Furthermore, based on the prediction result obtained by using this simulation, a silicon substrate having a BMD nucleus density and an oxygen concentration in a range where the density reaching the substrate surface of dislocations generated from BMD is small is selected as the LSA processing target substrate. Thus, the occurrence of dislocations due to LSA can be suppressed.

The flowchart which shows the 1st step | paragraph of embodiment of this invention. The flowchart which shows the 2nd step | paragraph of embodiment of this invention. The flowchart which shows the comparison method of a 9th step. Sectional drawing of the silicon substrate subdivided into the some mesh element of the 1st step and meshed. The figure which shows the relationship between the several mesh element and laser beam size of a 1st step. The figure which shows the time change degree in the laser scan of a 2nd step. The figure expressing the laser scanning speed of the 2nd step. The figure which shows the thermal conductivity (temperature dependence) of the silicon | silicone of a 3rd step. The figure which shows the specific heat (temperature dependence) of the silicon | silicone of a 3rd step. The figure which shows the thermal expansion coefficient (temperature dependence) of the silicon | silicone of a 3rd step. The figure which shows the time change of the temperature distribution of the board | substrate of a 4th step. The figure which shows the temperature distribution of the meshed board | substrate after the energy conditions 2 of a 4th step, and 11 milliseconds. Stress condition 2 of the fifth step, stress distribution of the meshed substrate after 11 milliseconds ((a): X direction tensile stress component σxx, (b): X direction or Y direction shear stress component τxy, (c): The figure which shows Y direction tensile-stress component (sigma) yy). The figure which shows the arbitrary positions A and temperature distribution which the 6th step set. The figure which shows the temperature distribution of the depth direction selected for every time in the arbitrary positions A of a 6th step. FIG. 10 is a calculation diagram of the fitting equation of the seventh step. The figure which shows the critical stress of the dislocation | rearrangement generate | occur | produced from BMD of a 7th step. The figure which piled up the shear stress and critical stress in each depth position of the 9th step. The figure which shows the relationship between the depth from the substrate surface of 10th step, and a dislocation length. Explanatory drawing of general laser spike annealing.

  Next, an embodiment for carrying out the present invention will be described with reference to the drawings.

  The present invention accurately calculates the temperature distribution and stress distribution generated in the silicon substrate in the LSA process by computer simulation of the LSA process, which is one of the semiconductor device manufacturing processes, and calculates the calculated temperature distribution and stress. Dislocations generated from BMD contained in the silicon substrate generated during the LSA process are predicted using the distribution.

  Until now, a specific calculation method of annealing using a laser beam that can simulate the LSA process has not been realized. Further, until now, the optical constant at room temperature has been usually used in the simulation of the process of irradiating the silicon substrate with light.

At 10.6 μm, which is the wavelength of the CO ₂ laser used in the LSA process, light absorption by silicon is due to free carrier absorption, so it passes through the silicon substrate at room temperature. Due to free carriers (electrons and holes) generated thermally, the penetration depth of light becomes shorter as the temperature increases. For this reason, accurate calculation cannot be performed unless this phenomenon is taken into account and applied.

  In the present invention, a more physically reasonable calculation is possible by taking into account the concentration of carriers generated by temperature changes, calculating the penetration depth of the laser beam, and applying energy corresponding to the laser beam in the depth direction. It was.

  Hereinafter, each step will be described in detail. The simulation model of the present invention is performed by a commonly used computer simulation such as general-purpose structural analysis software using a finite element method or the like. Specific examples of general-purpose structural analysis software using the finite element method include ABAQUS (ABAQUS), ANSYS (ANSYS), GENESIS (Vanderplats Research & Development), JMAG (JMAG), etc., which are general-purpose finite element method simulators. Illustrated.

(a) First Step First, as shown in FIG. 1, a silicon substrate having (100) as a main surface that receives an LSA laser beam scan is subdivided into a plurality of mesh elements and meshed. The height and width of the calculation range of the silicon substrate to be meshed are determined in consideration of the thickness of the silicon substrate, the laser beam size, the scan speed, the simulation time, the calculation capability of the computer, and the like. The smaller the mesh element to be subdivided, the more accurate calculation can be performed that is closer to the phenomenon that actually occurs in the LSA process. On the other hand, if the number of mesh elements to be calculated increases, the computer processing becomes slower. It is necessary to determine the size so that accurate results can be obtained efficiently. The X-axis direction and the Y-axis direction of the calculation range subdivided into a plurality of mesh elements are arbitrary and can be set in any direction. In FIG. 4, as an example, it is assumed that the X-axis direction of the calculation range is a plane that coincides with the [110] direction and the Y-axis direction coincides with the [100] direction. The reason why the Y-axis direction is assumed to be a plane coinciding with the [100] direction is that the (100) substrate is a general silicon substrate. The X axis direction is assumed to be a plane coinciding with the [110] direction for convenience. Generally, when a (100) substrate is used, the [110] notch is at the bottom. 110] direction scanning.

  In order to simulate the operation of irradiating the surface of the substrate with the laser beam, it is convenient to maintain a constant spacing in the horizontal direction, so the width of each mesh element is constant and the surface area is calculated in more detail. In order to do so, it is preferable to reduce the height of the mesh element as it approaches the surface. Meshing is preferably performed so that the width of each mesh element is sufficiently smaller than the laser beam width. The width of each mesh element is preferably adjusted so that it is a reciprocal of a multiple of the laser beam width. For example, as shown in FIG. 5, when the beam size of the laser beam 4 is 120 μm, the width of one mesh element is set to 15 μm so that the width of eight mesh elements corresponds to the beam size. In order to obtain an accurate result, it is preferable to set the width of the mesh element so that the width of at least five mesh elements corresponds to the beam width.

(b) Second Step Next, returning to FIG. 1, the time change of the energy of the mesh element irradiated with the laser beam is calculated from the scanning speed of the laser beam, the size of the laser beam, the energy of the laser beam, and the scanning path. . In order to simulate the operation of irradiating the substrate surface with the laser beam, energy is given locally in a small region (beam size region) that is a characteristic of the laser beam, and the laser beam is incident and converted to heat. It is necessary to express In the present invention, it is applied to the surface or to a certain depth in the form of an energy flow rate. Specifically, when it is given to the surface of the region, it is given by the surface heat flow rate (J / cm ² s), and when given to the whole region, it is given by the object heat flow rate (J / cm ³ s). Then, if a surface thermal flow velocity (J / cm ² s) is given as a load only to the surface portions of a plurality of mesh elements corresponding to the width of the laser beam as shown in FIG. 5, the effect of the laser beam hitting that portion can be realized. . In the case of giving the object heat flow rate (J / cm ³ s), the effect of the laser beam hitting the portion can be realized by applying energy to the volume of the mesh element as a heat source. Depending on the situation, a surface heat flow rate or an object heat flow rate is applied to the surface portion.

  Next, in order to realize the scanning operation of the laser beam, it is necessary to change the time of the energy at each position in accordance with the scanning operation. In the present invention, the time change of the load on each mesh element is obtained using the degree of time change as shown in FIG. Specifically, when the surface heat flow rate is a and the time variation is b, the product of the surface heat flow rate a and the time variation b, that is, the surface heat flow rate a × time variation b, The time change of the load on the mesh element is obtained. Thereby, the time change of the energy of the mesh element irradiated with the laser beam as shown in FIG. 7 can be expressed.

(c) Third Step Next, returning to FIG. 1, the coordinate data of each mesh element, the physical property value, the initial temperature of the substrate, and the time change of the energy calculated in the second step are respectively input to the computer. As the physical property values, silicon density (2.3 g / cm ³ ), Young's modulus (1.7 GPa), Poisson's ratio (0.26), thermal conductivity, specific heat, and thermal expansion coefficient are input. In the present invention, as described above, the temperature dependency data shown in FIGS. 8 to 10 are used for the thermal conductivity, the specific heat, and the thermal expansion coefficient in order to consider the concentration of the carrier generated by the temperature change.

(d) Fourth Step Next, returning to FIG. 1, the time change of the temperature distribution of the substrate is obtained by using the incident energy of the laser beam based on the initial temperature and thermal conductivity of the substrate as a load. The time change of the temperature distribution of the substrate is obtained by solving the heat conduction equation for the two dimensions (x, y) shown in the following equation (1). For example, the time of the temperature distribution as shown in FIG. The change and the temperature distribution of the meshed substrate as shown in FIG. 12 are obtained.

In the above formula (1), ρ is the density of silicon, c is the specific heat of silicon, kx and ky are x and y components of thermal conductivity, T is the temperature at each mesh element, and t is time.

(e) Fifth Step Next, returning to FIG. 1, the stress calculation is performed using the temperature distribution obtained in the fourth step, and the time change of the thermal stress distribution generated in the substrate is obtained. In this fifth step, first, the thermal strain ε ^th in each mesh element is obtained by the following equation (2). And the stress (sigma) in each mesh element is calculated | required from the product of thermal strain (epsilon) ^th and Young's modulus E (T) shown to following Formula (3). From this stress σ, an X direction tensile stress component σxx, a Y direction tensile stress component σyy, and an X direction or Y direction shear stress component τxy are calculated. By solving the above relational expression, for example, the stress distribution of the meshed substrate as shown in FIGS. 13A to 13C is obtained.

In the above formula (2), α (T) is a thermal expansion coefficient, T is a current temperature, T ^I is an initial temperature, T ⁰ is a reference temperature for the thermal expansion coefficient, and thermal expansion at this reference temperature is zero. Assumed.

(f) Sixth Step Next, returning to FIG. 1, the arbitrary position A of the meshed substrate is set, the temperature distribution obtained in the fourth step and the heat generated in the fifth step substrate. From the stress distribution, the distribution in the depth direction at the set arbitrary position A is selected at each time. In this sixth step, for example, as shown in FIG. 14, an arbitrary position A with the meshed substrate is set. Then, the distribution in the depth direction at the set arbitrary position A is selected at each time. By selecting the distribution in the depth direction at the arbitrary position A in this way, for example, a temperature distribution as shown in FIG. 15 can be obtained. The selected temperature distribution is used to calculate the critical stress (dislocation from BMD). The selected stress distribution is used for comparison with the critical stress.

(g) Seventh Step Next, as shown in FIG. 2, the critical stress of dislocations generated from the BMD is obtained from the temperature distribution selected in the sixth step, the BMD size and the residual oxygen concentration contained in the substrate. In the seventh step, the temperature distribution selected in the sixth step, the BMD size of the substrate, and the residual oxygen concentration are input to the fitting equation to obtain the critical stress τ _{BMD of} dislocations generated from the BMD. The critical stress is a stress at which dislocation starts to occur from a certain BMD. The following equation (4) is a related fitting equation obtained for the plate-like oxygen precipitates based on the experimental results shown in FIG. 16 conducted by the present applicant, and is a heat treatment assumed in the present invention. From this situation, it is appropriate to use the fitting equation for the plate-like oxygen precipitate shown in the following equation (4). By inputting the temperature distribution selected in the sixth step, the BMD size of the substrate and the residual oxygen concentration into this related fitting equation, for example, the critical stress τ _{BMD of} dislocations generated from the BMD as shown in FIG. Can be sought.

In the above formula (4), Co is the residual oxygen concentration and is assumed to be 1.1 × 10 ¹⁸ cm ⁻³ (old ASTM). L is the BMD size and is assumed to be 100 nm. k is a Boltzmann constant, T is a temperature distribution, and the absolute temperature (K) is used as a unit.

(h) Eighth Step Next, returning to FIG. 2, the main slip surface of the silicon single crystal is obtained from the stress components σ _xx , σ _yy , τ _{xy of} the thermal stress distribution selected in the sixth step (111). The [110] direction shear stress component τ ″ _{xy of the surface} is calculated. In this eighth step, the (111) surface is calculated from the stress components σ _xx , σ _xy , τ _xy calculated in two dimensions (x, y). [110] direction shear stress τ ″ _xy is calculated. The calculation method is as follows. The shear stress component on the _xy plane is τ _xy, but if the x direction is [110] and the y direction is the [100] direction, the angle formed by this plane and the (111) plane is 54.7 degrees. The relationship shown in equation (5) is derived. In this plane, since the (110) direction is further 30 °, the relationship shown in the following equation (6) is derived. Accordingly, the shear stress in the [110] direction of the (111) plane is τ ″ _xy . Therefore, from the stress components σ _xx , σ _yy , τ _{xy of} the thermal stress distribution selected in the sixth step, the equation (5) And based on the relational expression shown in Expression (6), the shear stress τ ″ _xy can be obtained.

(i) Ninth Step Next, returning to FIG. 2, the shear stress τ ″ _{xy in} the eighth step and the critical stress τ _{BMD in} the seventh step are compared for each depth position. In this ninth step, for example, as shown in Fig. 18, the shear stress τ " _xy and the critical stress τ _BMD at each depth position are compared for each time, and the comparison result is obtained. For example, the dislocation length at each depth position as shown in FIG. 19 is obtained. The growth of the dislocation, the shear stress tau "dislocation and _xy is greater than the critical stress tau _BMD occurs, the shear stress tau" _xy movement of dislocations long as greater than the critical stress tau _BMD (proliferation) is followed by a shear stress tau " It is assumed that the dislocation stops when _xy becomes smaller than the critical stress τ _BMD .

Specifically, the comparison method is performed by the following method. As shown in FIG. 3, first, the shear stress τ ″ _xy and the critical stress τ _BMD at a certain depth are compared with time, and the result does not satisfy the relationship of shear stress τ ″ _xy > critical stress τ _BMD. In this case, the time is advanced as t ₀ = t ₀ + Δt, and the shear stress τ ″ _xy and the critical stress τ _{BMD at} the advanced time are compared. On the other hand, when the relationship of shear stress τ ″ _xy > critical stress τ _BMD is satisfied, ΔL calculated from the dislocation speed equation shown in the following equation (7) is added to the dislocation length Ld. Note that the dislocation movement distance ΔL per time is obtained from the product of the dislocation velocity V and Δt obtained from the dislocation velocity equation shown in equation (7).

Next, when the relationship of t ₀ > scan time is not satisfied, the time is advanced as t ₀ = t ₀ + Δt, and the shear stress τ ″ _xy and the critical stress τ _{BMD at} the advanced time are compared. Then, t ₀ > When the relationship of the scan time is satisfied, the comparison of a certain depth position is terminated, and the calculated dislocation length Ld up to this point is set as the dislocation length at a certain depth position, and the remaining depth positions are determined. This comparison is also performed in the same manner as in the above comparison method, and the dislocation lengths at the remaining depth positions are obtained.

(j) Tenth Step Next, returning to FIG. 2, the slip generation depth is calculated from the dislocation length obtained in the ninth step. A dislocation length curve as shown in FIG. 19 is obtained from the dislocation length at each depth position obtained in the ninth step. From this dislocation length curve, it is possible to predict the length of dislocation generated from this BMD when BMD is present at a certain depth. From the relationship of dislocation length Ld> depth D, the depth of occurrence of slip can be calculated. Specifically, when the depth from the substrate surface is compared with the dislocation length at the depth position and the relationship of dislocation length Ld> depth D is satisfied, if BMD exists at a depth that satisfies the relationship, This shows the possibility that dislocations generated from BMD extend to the substrate surface and cause slip.

  For example, in the dislocation length curve in energy condition 2 shown in FIG. 19, when the depth from the substrate surface is 5 μm, the dislocation length is about 6.5 μm, and the relationship of dislocation length Ld> depth D is satisfied. Therefore, it can be seen that if the BMD exists at a depth of 5 μm from the substrate surface, the possibility that the generated dislocations reach the substrate surface is very high.

  In the dislocation prediction method of the present invention configured as described above, the length of dislocations generated from the BMD included in the silicon substrate in the LSA process can be accurately predicted through the above steps. This makes it possible to find an LSA processing condition that can minimize dislocations generated from the BMD. Further, it is possible to find out the BMD nucleus density and oxygen concentration in a range where dislocations generated from BMD do not reach the substrate surface or in a range where the density reaching the substrate surface is small.

  Therefore, based on the prediction result obtained using this simulation, by selecting the conditions that can minimize the dislocations generated from the BMD as the LSA processing conditions, the occurrence of dislocations due to LSA can be suppressed. it can.

  Based on the prediction results obtained using this simulation, a silicon substrate having a BMD nucleus density and an oxygen concentration in a range in which dislocations generated from BMD do not reach the substrate surface is selected as a substrate subject to LSA processing. The occurrence of dislocation can be suppressed.

  Based on the prediction results obtained using this simulation, a silicon substrate having a BMD nucleus density and an oxygen concentration in a range where the density reaching the substrate surface of dislocations generated from BMD is small is selected as the LSA processing target substrate. , Generation of dislocations due to LSA can be suppressed.

  Next, embodiments of the present invention will be described in detail.

<Example 1>
(a) First Step First, as shown in FIG. 4, a calculation range having a structure in which a part of a cross section of a silicon substrate, a width (X direction) is 4.5 mm, and a height (Y direction) is 775 μm is divided into a plurality of mesh elements. It was subdivided into meshes. The height (Y direction) calculation region corresponds to the general thickness of a 300 mm silicon substrate. At this time, it was assumed that the direction of the X axis coincides with the [110] direction and the direction of the Y axis coincides with the [100] direction. Moreover, the width of each mesh element was made constant, and in order to calculate the surface portion in more detail, the height of the mesh element was made smaller toward the surface. The minimum mesh element size on the surface was about 1.2 μm high × 15 μm wide. With this size, the laser beam with a width of 120 μm coincides with eight mesh elements with a width of 15 μm. The number of mesh elements in the horizontal direction in the calculation range of the meshed silicon substrate is 300, the number of mesh elements in the depth direction is 100, and the total number of mesh elements is 30000.

(b) Second Step Next, the time change of the energy of the mesh element irradiated with the laser beam was calculated from the scanning speed of the laser beam, the size of the laser beam, the energy of the laser beam, and the scanning path. As laser beam conditions, the laser beam size was set to a width of 120 μm, and the scan speed was set to 200 mm / second. From this size condition, the element size width described in the simulation model structure in the first step is determined. Further, the laser beam power is determined by energy condition 1 (2.4 × 10 ⁴ J / cm ² s), energy condition 2 (2.6 × 10 ⁴ J / cm ² s) and energy condition 3 (2 .8 × 10 ⁴ J / cm ² s) were selected. This energy level is selected from various tests so as to be 1100 to 1300 ° C., which is the annealing temperature actually performed in the LSA process. Further, the scan time corresponding to the actual LSA process time is set to 11 milliseconds in consideration of the time for roughly changing to a constant temperature.

(c) Third Step Next, the coordinate data of each mesh element, the physical property value, the initial temperature of the substrate, and the time change of the energy calculated in the second step were input to the computer. Physical property values are silicon density (2.3 g / cm ³ ), Young's modulus (1.7 GPa), Poisson's ratio (0.26), and thermal conductivity, specific heat, and thermal expansion coefficient are shown in FIGS. The temperature dependence data shown was used as input data. The initial temperature of the substrate was 400 ° C., which was set as an initial condition for heat transfer calculation.

(d) Fourth Step Next, the time change of the temperature distribution of the substrate was obtained using the incident energy of the laser beam based on the initial temperature and thermal conductivity of the substrate as a load. FIG. 11 shows energy condition 1 (2.4 × 10 ⁴ J / cm ² s) given as laser energy, energy condition 2 (2.6 × 10 ⁴ J / cm ² s), and energy condition 3 (2.8). The time change of the temperature of the substrate at × 10 ⁴ J / cm ² s) is shown. As is apparent from FIG. 11, the final temperature is about 1140 ° C. under energy condition 1 (2.4 × 10 ⁴ J / cm ² s), and under energy condition 2 (2.6 × 10 ⁴ J / cm ² s). It can be seen that up to about 1230 ° C., energy condition 3 (2.8 × 10 ⁴ J / cm ² s) reaches about 1300 ° C. FIG. 12 shows the temperature distribution of the meshed substrate after energy condition 2 (2.6 × 10 ⁴ J / cm ² s) and a scan time of 11 milliseconds. The temperature distribution shown in FIG. 12 shows that the portion of the substrate surface irradiated with the laser beam rises to about 1230 ° C., and the elevated high temperature region diffuses in the depth direction.

(e) Fifth Step Next, stress calculation was performed using the temperature distribution obtained in the fourth step, and the time change of the thermal stress distribution generated in the substrate was obtained. FIG. 13 shows the stress distribution of the meshed substrate after energy condition 2 (2.6 × 10 ⁴ J / cm ² s) and a scan time of 11 milliseconds. With the tensile stress component σxx in the X direction shown in FIG. 13A, a compressive stress of about 241.7 MPa at maximum is applied on the substrate surface side. On the other hand, a tensile stress of about 37.06 MPa at maximum, which is smaller than the compressive stress, is applied to the back side of the substrate. The X-direction or Y-direction shear stress component τxy shown in FIG. 13B is about 0.1 times larger than the stress of the σxx component, and the compressive stress is in front of the beam. It can be seen that a tensile stress is applied behind the beam, and that the beam is reversed when the beam passes. Here, since the X and Y directions are assumed to be isotropic, the same results are obtained in the X and Y directions. In the tensile stress component σyy in the Y direction shown in FIG. 13C, it can be seen that the Y direction tensile component having a maximum value of about 21.5 MPa is distributed in the cross-sectional direction. From these results, it can be seen that the generation of large stress exceeding 100 MPa exists only in the surface portion, and if this generated stress reaches the BMD existing by the depth distribution, it may lead to dislocation. Yes.

(f) Sixth step Next, an arbitrary position A of the meshed substrate is set, and set from the temperature distribution obtained in the fourth step and the thermal stress distribution generated in the fifth step substrate. The distribution in the depth direction at an arbitrary position A was selected at each time. FIG. 14 shows an arbitrary position A set on the meshed substrate. FIG. 15 shows a temperature distribution in the depth direction selected for each time at an arbitrary position A under energy condition 2 (2.6 × 10 ⁴ J / cm ² s).

(g) Seventh Step Next, the critical stress of dislocations generated from BMD was determined from the temperature distribution selected in the sixth step, the BMD size contained in the substrate, and the residual oxygen concentration. As the fitting formula, the related fitting formula for the plate-like precipitate shown in the above formula (4) derived based on the experimental result shown in FIG. 16 was used. The concentration of residual oxygen was assumed to be 1.1 × 10 ¹⁸ / cm ³ , and the precipitate size was assumed to be 100 nm. FIG. 17 shows critical stress τ _BMD of dislocations generated from BMD under energy condition 2 (2.6 × 10 ⁴ J / cm ² s). As apparent from FIG. 17, the calculation region selected at the arbitrary position A passes through the laser beam in about 6 milliseconds. At that time, the critical stress on the surface side becomes low and gradually increases in the depth direction. I understand. From the change in critical stress over time, the temperature rises and the critical stress decreases accordingly during the time the beam passes, but the temperature also decreases before or after the beam passes, It can be seen that it increases rapidly. This indicates that the critical stress decreases as the temperature rises when passing through the beam. Therefore, it is possible that dislocations may occur if the BMD is subjected to a stress larger than the critical stress.

(h) Eighth Step Next, from the stress components σ _xx , σ _yy , τ _{xy of} the thermal stress distribution selected in the sixth step, the [110] direction of the (111) plane that is the main slip surface of the silicon single crystal The shear stress component τ ″ _{xy of} was calculated.

(i) Ninth Step Next, the shear stress τ ″ _{xy in} the eighth step and the critical stress τ _{BMD in} the seventh step are compared for each depth position, and the dislocation length at each depth position is determined from the comparison result. 18 shows a diagram in which the shear stress τ ″ _xy and the critical stress τ _BMD at each depth position are superimposed.

(j) Tenth Step Next, the depth of occurrence of slip was calculated from the dislocation length obtained in the ninth step. FIG. 19 shows the length of dislocation in energy conditions 1 to 3 calculated by the simulation method of the present invention. As can be seen from FIG. 19, the dislocation length increases as the temperature increases. Specifically, under energy condition 1 (2.4 × 10 ⁴ J / cm ² s), if BMD exists at a depth of about 3 μm from the substrate surface, dislocations may extend to the substrate surface and slip may occur. Is shown. Further, under energy condition 2 (2.6 × 10 ⁴ J / cm ² s), the depth is about 6 μm from the substrate surface, and under energy condition 3 (2.8 × 10 ⁴ J / cm ² s), it is approximately from the substrate surface. If each BMD exists at a depth of 9 μm, it can lead to slipping and cause an overlay alignment error problem.

Claims (4)

A first step of subdividing a silicon substrate having a main surface (100) subjected to laser beam scanning of laser spike annealing into a plurality of mesh elements to form a mesh;
A second step of calculating a temporal change in energy of a mesh element irradiated with the laser beam from a scanning speed of the laser beam, a size of the laser beam, an energy of the laser beam, and a scanning path;
A third step of inputting the coordinate data of each mesh element, the physical property value, the initial temperature of the substrate and the time change of the energy calculated in the second step, respectively, to a computer;
A fourth step of obtaining a time change of the temperature distribution of the substrate with the incident energy of the laser beam based on the initial temperature and thermal conductivity of the substrate as a load;
Performing a stress calculation using the temperature distribution obtained in the fourth step, and obtaining a time change of the thermal stress distribution generated in the substrate;
An arbitrary position A of the meshed substrate is set, and the depth direction at the set arbitrary position A is determined from the temperature distribution obtained in the fourth step and the thermal stress distribution generated on the substrate in the fifth step. A sixth step of selecting the temperature distribution and thermal stress distribution of each at each time;
A seventh step for obtaining a critical stress of dislocations generated from the oxygen precipitates from the temperature distribution selected in the sixth step and the oxygen precipitate size and residual oxygen concentration contained in the substrate;
A shear stress component in the [110] direction of the (111) plane that is the main slip surface of the silicon single crystal is calculated from the stress components σ _xx , σ _yy , τ _{xy of} the thermal stress distribution selected in the sixth step. Steps,
A ninth step of comparing the shear stress of the eighth step and the critical stress of the seventh step for each depth position, and determining the dislocation length at each depth position from the comparison result;
From the dislocation length obtained in the ninth step, a dislocation generated from oxygen precipitates generated when laser spike annealing is performed is predicted by simulation using a computer including a tenth step for calculating the depth of occurrence of slip. Method.   Based on a prediction result obtained by the prediction method by simulation according to claim 1, a condition capable of minimizing the occurrence of dislocations generated from oxygen precipitates is selected as a laser spike annealing treatment condition. How to select laser spike annealing treatment conditions.   A laser spike annealing treatment of a silicon substrate having an oxygen precipitation nucleus density and an oxygen concentration in a range in which dislocations generated from oxygen precipitates do not reach the substrate surface based on a prediction result obtained by the simulation prediction method according to claim 1 A method for selecting a silicon substrate, comprising selecting the target substrate.   A silicon substrate having a density of oxygen precipitation nuclei in a range where the density of dislocations generated from oxygen precipitates reaching the substrate surface is small, and a silicon substrate having an oxygen concentration based on the prediction result obtained by the simulation prediction method according to claim 1. A method for selecting a silicon substrate, wherein the substrate is selected as an annealing target substrate.