JPH04219388A - Control of diameter of silicon single crystal and apparatus therefor - Google Patents

Abstract

PURPOSE:To save PID parameter adjustment operation at the job site by improving the calculation method of PID operation performed under direct control, adding dead time compensation control and improving the ability for following up a set point. CONSTITUTION:In controlling the diameter of a drawn-up silicon single crystal rotating correlatively to a crucible by the draw up rate, a measured diameter value by a video measure 5 as an optical means is processed by a crystal diameter input part 10 of a unit 20 for controlling the diameter by non-exact differentiation PID process. The above-processed diameter is compared with a target diameter by a non-exact differentiation PID operation part 11 to calculate the draw up rate. The resultant draw up rate is sent through a part 12 for sending out the draw up rate to a motor controller 8 to give a command and a drawn-up single crystal 1 is drawn up at a controlled draw up rate, thus giving the objective silicon single crystal 1.

Description

[Detailed description of the invention]

0001

[Industrial Application Field] The present invention relates to a method and apparatus for controlling the diameter of a silicon single crystal, and more particularly, to controlling the diameter of a pulled single crystal during crystal pulling in which silicon single crystals are continuously produced while rotating relative to a crucible. The present invention relates to a method and apparatus for controlling the diameter of a silicon single crystal.

0002

2. Description of the Related Art FIG. 2 is a schematic explanatory diagram showing a single crystal manufacturing apparatus using the Czochralski method, which is well known as a method for manufacturing semiconductor single crystals such as silicon. Note that the Czochralski method is widely referred to as the CZ method, and is also generally referred to as the crystal pulling method.

In the figure, when producing a silicon single crystal, a crucible 2 contains a silicon melt 3 heated and melted by a heater 4, and a silicon single crystal 1 is rotated from there by a rotating mechanism (not shown) in the crucible 2. While rotating in the opposite direction, it is gradually pulled up by a pulling device 7 to cause crystal growth in the interface region between the silicon melt 3 and the silicon single crystal 1. This silicon single crystal 1 is grown by crystal growth from a seed crystal 1a, and the seed crystal 1a is supported by a seed crystal holder 6 connected to a pulling device 7. In the following explanation, such growing silicon single crystal 1 will be referred to as a pulled single crystal. In addition, the pulling device 7
is equipped with a mechanism for raising and lowering the silicon single crystal 1 and a mechanism for rotating it, and is composed of a motor controller 8, a pulling motor 9, and others, but since it is a well-known device, a detailed explanation of its structure will be omitted. do. In addition to the above-mentioned rotation mechanism, the crucible 2 is supported by an up-and-down mechanism (not shown), and this up-and-down mechanism keeps the melt level constant without lowering even if a crystal grows, for example. Efforts have been made to not change the temperature distribution near the liquid surface.

[0004] Since the pulled single crystal 1 produced by the CZ method is later finished into a cylindrical silicon single crystal ingot, the pulled single crystal 1 is required to be pulled with approximately the same diameter over the entire body portion. Therefore, the single crystal 1 is pulled by optical means such as video measure 5.
The diameter of the material is directly measured during the pulling process, and the diameter of the material is controlled while adjusting the pulling speed to maintain the diameter at the target value. In this case, the optical means is fixed to the crystal pulling device, and measures the fusion ring seen at the boundary between the pulled single crystal 1 and the melt surface with a single measurement line from diagonally above, directly pulling the pulled single crystal 1. Measuring the diameter of.

[0005] The diameter of the pulled single crystal is controlled by adjusting the pulling speed as described above, by comparing the actual diameter value measured by optical means with the target diameter value and using the well-known PID control to calculate the deviation as a manipulated variable. This is performed by calculating the pulling speed, inputting the calculated value to the motor controller 8, and controlling the pulling speed.

[0006]

[Problems to be Solved by the Invention] In the conventional silicon single crystal diameter control method or diameter control device as described above, for example, the response of the silicon single crystal when the pulling speed of the crystal pulling device is changed, that is, the pulled single crystal It generally takes a long time for a change in the diameter to take effect (long dead time), and the rate of change is small (change or response speed is small). Therefore, when performing PID control by comparing with the target diameter value, it is necessary to timely manipulate the pulling speed to accurately capture changes in the diameter of the pulled single crystal. Advance control is required. However, since there is a lot of noise in the actual measured diameter of a pulled single crystal measured by optical means, there is a risk that the pulling speed may fluctuate excessively due to this influence, and control with a large differential term cannot be performed. There wasn't. For this reason, there is a limit to suppressing variations in crystal diameter, and the yield tends to be poor.

[0007] Furthermore, since on-site PID parameter adjustment was essential, silicon single crystals had to be pulled up in order to adjust the PID parameters.

The present invention has been made to solve the above-mentioned problems, and improves the algorithm of PID calculation performed in diameter control, and furthermore adds dead time compensation control to improve target value tracking. It is an object of the present invention to provide a method and apparatus for controlling the diameter of a silicon single crystal that is excellent and eliminates the need for on-site PID parameter adjustment work.

[0009]

[Means for Solving the Problems] A first method for controlling the diameter of a silicon single crystal according to the present invention is performed during the process of manufacturing a silicon single crystal by pulling the silicon single crystal while rotating it relative to a crucible. , compare the actual diameter value of the pulled single crystal measured by optical means with the target diameter value, calculate the pulling speed by performing PID processing using incomplete differentiation based on this deviation, and adjust the pulling speed to the crystal pulling speed. The diameter of the pulled single crystal is controlled by outputting it to the motor controller of the device and manipulating the pulling speed.

[0010] Furthermore, in the second method for controlling the diameter of a silicon single crystal according to the present invention, instead of the PID process using incomplete differentiation in the first diameter control method, processing is performed using the Smith method to calculate the pulling rate. This is how it was done.

[0011] Next, the first silicon single crystal diameter control device according to the present invention includes an input section that receives an actual measured diameter value of the pulled single crystal measured by optical means, and an input section that receives the actual measured diameter value of the pulled single crystal. It is composed of an incomplete differential PID calculation section that calculates the pulling speed by comparing target diameter values, and an output section that outputs the pulling speed to the motor controller of the crystal pulling apparatus.

Further, the second silicon single crystal diameter control device according to the present invention has an incomplete differential P of the first diameter control device.
It is constructed using a Smith method calculation section instead of the ID calculation section.

Furthermore, in the method for determining model parameters of a silicon single crystal according to the present invention, the response characteristic of the diameter value of the pulled single crystal to the pulling rate is modeled using a transfer function shown in the following equation, and the pulling rate is changed in steps. Two model parameters, response speed V and dead time L in the transfer function, are determined by a step response test that examines the response of the diameter value when

Transfer function: Gp(s)=V/s2・e−Ls Also,
The PID parameter determination method according to the present invention calculates optimal parameters by performing a computer simulation using the silicon single crystal model described above.

[0015]

[Operation] In the present invention, in the first silicon single crystal diameter control method and apparatus, an effective differential effect can be exerted by suppressing the influence of noise on the actual measured diameter value by incomplete differential PID control. The diameter value of the single crystal can be brought as close as possible to the target value.

Furthermore, in the second silicon single crystal diameter control method and device, the diameter is controlled by the Smith method, not just the incomplete differential PID control, so that in addition to the operation of the first diameter control method and device, the diameter is controlled by the Smith method. , Gp(s)・(1−
By inserting a dead time compensation model called e−Ls ) into the minor loop, the transfer function Gp (
s) can be controlled, and diameter control with excellent target value followability is performed. Moreover, the PID parameters and Smith method parameters applied to the calculation means of the diameter control method and apparatus described above are not determined by actually pulling a silicon single crystal, but the optimum parameters are determined by computer simulation.

[0017]

[Examples] Examples according to the present invention will be described below. Embodiment 1 mainly describes a method and apparatus for controlling the diameter of a silicon single crystal using incomplete differential PID calculation, and Example 2 mainly describes a method and apparatus for controlling diameter of a silicon single crystal using Smith method calculation.

Embodiment 1: FIG. 1 is a schematic diagram showing an embodiment of a diameter control device used in a diameter control method using incomplete differential PID calculation. In the figure, numerals 1 to 9 indicate the same or equivalent parts as those used in the explanation of the conventional silicon single crystal manufacturing apparatus in FIG. 2, and the explanation thereof will be omitted. Further, FIG. 3 is a block diagram illustrating the functions of the diameter control device of FIG. 1.

Reference numeral 20 in FIG. 1 is a block diagram of a diameter control device using incomplete differential PID processing. The controlled object data in this device is basically the actual diameter value measured by the video measure 5 used as an optical means. As shown in the figure, the diameter control device includes a crystal diameter input section 10 that processes the actual measured diameter value, and an incomplete differential PID calculation section 11 that calculates the pulling speed by comparing the processed actual measured diameter value and the target diameter. and a pulling speed output section 12 that instructs a silicon single crystal manufacturing apparatus (crystal pulling apparatus) to perform a pulling speed. Note that 13 indicates a PID parameter that stores parameters used during calculation.

Next, an embodiment of a diameter control method using incomplete differential PID will be explained based on FIGS. 1 and 2. The actual diameter measurement value obtained from the video measure 5 (in FIG. 3, the output from the silicon single crystal production apparatus 30, in FIG. 1, the output from the crystal input section 10) is added to the target diameter stored in a memory (not shown) at the addition point 31. Compare and incomplete differential PID calculation unit 1
1, a PID calculation 11a using incomplete differentiation is performed to calculate the rate of increase in the operation output. A command is issued by outputting this pulling speed to the motor controller 8 via the pulling speed output section 12, and the pulled single crystal 1 is pulled at the controlled pulling speed to produce the silicon single crystal 1. Such a control operation is performed several times during one rotation of the pulled single crystal 1, for example, and this operation is performed over the entire body part pulling.

By carrying out the diameter control method as described above, it is possible to produce silicon single crystal 1 with little variation in diameter and having a diameter value close to the target diameter. In this control method, since the best parameters for the PID parameters 13 have already been determined by computer simulation using a silicon single crystal model, there is no need to adjust the PID parameters on site.

[0022] Here, the algorithm of incomplete differential PID calculation and the method of determining model parameters will be explained.

Operation output Go by normal PID operation only
(s) is the deviation between the actual measured diameter value and the target diameter E(s)
, it becomes as shown in equation [2].

[0024]

[Math 2]

Go(s)=K*{1+1/(Ti*s)+
Td *s}E(s)...[2] Here,
K is a proportional gain, Ti is an integral time, Td is a differential time, and s is a Laplace variable (complex number).

On the other hand, the operation output G(s) of the incomplete differential PID operation used in the diameter control of the present invention can be expressed by equation [3].

[0027]

[Math 3]

G(s)=K*{1+1/(Ti*s)
+Td *s/(1+α*Td *s}*E(s)
...[3] Here, 1/α
is called differential gain. The difference between formula [2] and formula [3] lies in the calculation of the manipulated variable using the differential term, but in the case of formula [3], a first-order lag filter is applied to the normal differential term output Td *s of formula [2]. It is worth the price. FIG. 4 is a comparative waveform diagram of the response characteristics to a step change in the deviation E(s). (a) in FIG. 4 shows the value of deviation versus time on the horizontal axis, (b) in FIG. ) is the response characteristic of the manipulated output amount M of the differential operation part in the incomplete differential PID calculation. As is clear from Figure 4, in the case of incomplete differential PID, for example, the output for noise deviation is suppressed by a gain of 1/α (M/α in the figure), which suppresses the sensitive response to noise and is effective. It is possible to obtain a differential effect.

Regarding the silicon single crystal model used in the computer simulation to determine the PID parameter 13, the second-order integral system shown in equation [4] takes into account the dead time L that can faithfully reproduce the actual response. It was approximated by

[0030]

[Math 4]

Gp(s)=V/s2・e−Ls
…
[4] However, V: The dead time L and reaction rate V, which are reaction rate model parameters, are determined by the following procedure. First, in a silicon single crystal manufacturing apparatus, the pulling speed is changed stepwise, and response data of the silicon single crystal diameter at that time is collected. Next, assuming dead time L and reaction rate V, the step response test is reproduced by computer simulation. Then, V and L are determined to minimize the error between the simulation result and the actual response waveform data.

[0032] Here, the results of an example in which a silicon single crystal was actually manufactured using the incomplete differential PID control method and apparatus as described above will be explained.

In this embodiment, the series of operations of comparing the moving average value of diameter measurement data every 0.1 seconds with the target diameter value, calculating the pulling speed, and outputting to the motor controller 8 are performed once per second. In other words, it was performed three times during one rotation of the silicon single crystal. (The rotational speed of the pulled single crystal is 20.0 rpm.) This control period will become shorter if the pulling speed and rotational speed increase, or if there are large operational disturbances such as temperature fluctuations inside the crucible. This is considered to be effective in controlling the diameter. The target diameter of the body part is 16
It is 0.0 mm. The manufactured silicon single crystal is 0.0, 50.0, 100.0,
The results of measuring the diameter at 150.0, 200.0, and 250.0 mm are shown in the schematic diagram of FIG. As shown in FIG. 5, the maximum and minimum deviations from the target diameter of 160.0 mm were within ±0.5 mm, and it was possible to manufacture silicon single crystals with uniform diameters in each part.

[0034] Furthermore, this data is based on the PI obtained by computer simulation using a silicon single crystal model.
This was the first production performed using the D parameter, and from the first attempt we were able to produce a silicon single crystal that accurately followed the target diameter.

Embodiment 2: FIG. 6 is a schematic diagram showing an embodiment of a diameter control device used in a diameter control method using Smith method calculation. In the figure, 1 to 13 excluding 11 indicate the same or corresponding parts as the partial symbols used in the explanation of the embodiment device of FIG. Further, FIG. 7 is a block diagram illustrating the functions of the diameter control device shown in FIG. 6.

Reference numeral 21 in FIG. 6 is a block diagram showing a diameter control device using Smith method processing, and 14 is a Smith method calculation section. This is the incomplete differential PID of the example in Figure 1.
The configuration is simply that the calculation unit 11 is replaced with the Smith method calculation unit 14, but as shown in FIG. 7, the main adjustment function in Smith method control is the calculation of the incomplete differential PID11a, but The diameter control of the single crystal 1 is further characterized in that the silicon single crystal model shown in equation [4] is used to determine the control deviation. That is, the transfer function V/s2 (1-e-Ls)14 based on the dead time compensation model obtained from equation [4] is added to the main feedback loop of the incomplete differential PID11a.
a is inserted into the minor loop and fed back to addition point 2 to obtain the control deviation. This enables control that compensates for dead time, and achieves diameter control with excellent target followability.

FIG. 8 is a diagram showing the results obtained by computer simulation of diameter control by Smith method control in the production of silicon single crystals. In the figure, the horizontal axis is the control time, and the vertical axis is the diameter of the pulled single crystal. The solid line is the control characteristic by the Smith method, and for reference, the conventional PI
The simulation results using D control are also shown by dotted lines. In all simulations, the initial diameter was 162.0 mm,
The target diameter is 160.0 mm. As is clear from the figure, in PID control, it takes about 2 times to match the target value.
Although it takes time, the Smith method takes about 1 hour, and the Smith method allows control with good follow-up of the target value while compensating for dead time.

[0038]

[Effects of the Invention] As described above, according to the method and apparatus for controlling the diameter of a silicon single crystal according to the present invention, firstly, the diameter can be controlled during crystal pulling while suppressing the influence of noise by PID control using incomplete differentiation. , it is possible to improve the control performance, which not only makes the crystal quality uniform, but also allows control using a differential term to bring the diameter as close as possible to the target value, thereby improving yield. effective.

Next, in control using the Smith method, not only can effects similar to those of incomplete differential PID control be obtained, but also control can be performed that compensates for dead time, resulting in excellent target value tracking performance. Diameter control is achieved and yields are further improved.

In addition, since silicon single crystal manufacturing using the best PID parameters can be carried out from the beginning through computer simulation, there is no need to actually pull the silicon single crystal and carry out unnecessary crystal pulling to obtain the parameters as in the conventional method. Redundant work in silicon single crystal manufacturing can be eliminated.

[Brief explanation of the drawing]

FIG. 1 is a schematic configuration diagram showing an embodiment of a diameter control device used in a method for controlling the diameter of a silicon single crystal using incomplete differential PID calculation according to the present invention.

FIG. 2 is a schematic explanatory diagram showing a conventional silicon single crystal manufacturing apparatus using the Czochralski method.

FIG. 3 is a block diagram illustrating the functions of the embodiment device of FIG. 1;

FIG. 4 is a comparative waveform diagram showing response characteristics of incomplete differentiation with respect to step-like changes in deviation.

FIG. 5 is a schematic diagram showing measured diameter values of manufactured silicon single crystals.

FIG. 6 is a schematic configuration diagram showing an embodiment of a diameter control device used in a diameter control method using Smith method calculation.

FIG. 7 is a block diagram illustrating the functions of the embodiment device of FIG. 6;

FIG. 8 is a diagram showing the results of computer simulation of diameter control using the Smith method.

[Explanation of symbols]

1 Silicon single crystal (pulled single crystal) 2 Crucible 3 Silicon melt 4 Heater 5 Video measure 6 Seed crystal holder 7 Pulling device 8 Motor controller 9 Pulling motor 10 Crystal diameter input section 11 Incomplete differential PID calculation section 12 Pulling speed output section 13 PID parameter 14 Smith method calculation unit 20 Diameter control device 21 using incomplete differential PID processing
Diameter control device 30 using Smith method processing Silicon single crystal manufacturing device

Claims (6)

[Claims] Claim 1. A diameter control method for a silicon single crystal in which the diameter of a pulled single crystal rotating relative to a crucible is controlled by a crystal pulling speed, wherein the diameter of the pulled single crystal measured by optical means is Compare with the target diameter value to find the deviation, and based on this deviation, calculate P by incomplete differentiation.
A method for controlling the diameter of a silicon single crystal, characterized in that the diameter of the pulled single crystal is controlled to a target diameter by calculating a single crystal pulling speed by performing ID processing, and instructing a pulling means to use the single crystal pulling speed. 2. The method for controlling the diameter of a silicon single crystal according to claim 1, characterized in that the deviation is processed by the Smith method instead of being processed by PID using incomplete differentiation. 3. In a silicon single crystal diameter control device that controls the diameter of a pulled single crystal that rotates relative to a crucible by a crystal pulling speed, an actual measured value of the diameter of the pulled single crystal measured by optical means. a crystal diameter input section that takes in the crystal diameter, an incomplete differential PID calculation section that compares the actual measured diameter value with the target diameter value and calculates the single crystal pulling speed from the deviation, and instructs the crystal pulling speed to the pulling means. 1. A diameter control device for a silicon single crystal, comprising a pulling speed output section. 4. The silicon single crystal diameter control device according to claim 3, wherein a Smith method calculation unit is used in place of the incomplete differential PID calculation unit. 5. A step response test in which the response characteristic of the diameter value of the pulled single crystal to the crystal pulling rate is defined by a transfer function shown in equation [1], and the response of the diameter value to a stepwise change in the crystal pulling rate is determined. A method for determining model parameters, characterized in that two types of model parameters, V and L, in the transfer function are determined by performing the following steps. [Equation 1] Gp(s)=V/s2 ・e−Ls
… [1
] However, V: Response speed L: Dead time
s: Laplace variable 6. The PID parameters used in the calculation by the incomplete differential PID processing according to claims 1 and 3 and the Smith method parameters used in the calculation by the Smith method processing according to claims 2 and 4 are obtained by using the silicon unit according to claim 5. A method for determining PID parameters, characterized in that the PID parameters are determined by computer simulation using a crystal model.