JP2006329869A - Temperature estimation device, temperature control device, temperature estimation method, temperature control method, temperature estimation program, and temperature control program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a temperature estimation device, a temperature control device, a temperature estimation method, a temperature control method, a temperature estimation program, and a temperature control program capable of estimating the temperature of an object with high accuracy.
[Solution]
A reference point temperature acquisition unit that acquires the temperature of the reference point of the substrate, a first temperature calculation unit that estimates the temperature of the object according to the thermal parameter and the temperature of the reference point, and an estimated value of the thermal parameter and the temperature of the object And a thermal parameter correcting unit that corrects the thermal parameter based on the reference point temperature and the estimated value. Each time the thermal parameter is corrected by the parameter correction unit, the estimated temperature of the object and the estimated temperature of the reference point are recalculated using the corrected thermal parameter, and the estimated temperature of the reference point is calculated. Modify the thermal parameters each time it is redone.
[Selection] Figure 6

Description

  The present invention relates to a temperature estimation device, a temperature estimation method, a temperature estimation program, and a temperature control device, a temperature control method, and a temperature control program for controlling the temperature of an object.

  In a semiconductor manufacturing process, there are many heat treatment steps for placing a wafer on a hot plate and heating the wafer. In this heat treatment step, it is preferable to adjust the output heat amount of the hot plate according to the temperature of the wafer and control the wafer temperature with high accuracy, but since a thermometer cannot be directly attached to the surface of the wafer, In practice, a temperature sensor is provided around the wafer, the wafer temperature is estimated from the measured temperature value, and the output heat amount of the hot plate is adjusted based on the estimated wafer temperature.

  However, the wafer is slightly warped, and the warpage is different for each wafer. For this reason, the thermal parameter represented by the thermal resistance differs for each wafer process, and also for each part of the wafer. Therefore, if an attempt is made to estimate the wafer temperature by applying the same thermal parameter to all the wafers, the estimated wafer temperature may be greatly deviated from the actual surface temperature of the wafer.

Regarding such a problem, Patent Document 1 uses a heat transfer model in which a heated object and a heated object heated by the heated object interact with each other, and a temperature sensor is provided near the plate. The cooking device calculates the amount of warping of the bottom of the pan placed on the plate based on the second-order differential value of the plate temperature, which is the object to be heated, measured by the temperature sensor. By calculating the warpage amount of the wafer using the warpage calculation method described in Patent Document 1, it is possible to acquire the thermal parameter suitable for each wafer and estimate the wafer temperature.
Japanese Patent Laid-Open No. 2001-351717

  Here, in the semiconductor manufacturing process, considerable accuracy is required for the temperature control of the wafer, and the warpage of the wafer is smaller than the warpage of a pan or the like. The effect of the included error appears greatly. However, in the warp calculation method described in Patent Document 1, when a substantial thermal parameter is estimated, a warp determination graph or table obtained in advance is referred to based on the second-order differential value of the measured temperature. Then, the warpage determination is performed only once for one warpage determination target. Therefore, when an error occurs in the warpage determination, there is no means for confirming the error, and there is no means for correcting the error, so that there is a problem that the reliability of the accuracy for the warpage determination is lowered. In other words, since the error included in the calculated value of warpage is largely allowed, there is a problem that the accuracy is too low to be applied to wafer temperature control.

  The above-described problem is not limited to a semiconductor manufacturing process in which a wafer is heated by a hot plate, and is a problem that generally occurs in a temperature control process in which the temperature of an object is controlled with high accuracy by heat generated from a heat source.

  In view of the above circumstances, the present invention provides a temperature estimation device, a temperature control device, a temperature estimation method, a temperature control method, a temperature estimation program, and a temperature control program that can estimate the temperature of an object with high accuracy. With the goal.

The temperature estimation device of the present invention that achieves the above object includes a reference point temperature acquisition unit that acquires the temperature of a reference point that refers to the temperature of a substrate that is in thermal contact with an object,
A first temperature calculation unit that calculates an estimated value of the temperature of the object according to the thermal parameter related to the object and the temperature of the reference point acquired by the reference point temperature acquisition unit;
A second temperature calculating unit that calculates an estimated value of the temperature of the reference point according to the thermal parameter and the estimated value of the temperature of the object calculated by the first temperature calculating unit;
A thermal parameter correction unit that corrects the thermal parameter based on the temperature of the reference point acquired by the reference point temperature acquisition unit and the estimated value of the temperature of the reference point calculated by the second temperature calculation unit;
Each time the first temperature calculation unit and the second temperature calculation unit correct the thermal parameter in the thermal parameter correction unit, the estimated temperature of the object and the temperature of the reference point are calculated using the corrected thermal parameter. The thermal parameter correction unit corrects the thermal parameter each time the second temperature calculation unit recalculates the estimated temperature of the reference point. To do.

  Here, the “thermal parameter relating to the object” referred to in the present invention represents, for example, the heat capacity, heat conductivity, emissivity, heat transfer coefficient, and heat resistance of the object, and represents the thermal characteristics of the object itself. In addition to the above, parameters representing thermal characteristics between the object and the surrounding environment are also included. In addition, the “reference point for referring to the temperature of the substrate” is preferably a point on the substrate when the temperature of the substrate can be directly measured, but when the temperature of the substrate cannot be directly measured, The point which can measure temperature may be sufficient.

  According to the temperature estimation device of the present invention, according to a heat transfer model that “a substrate such as a heat source and an object that is in thermal contact with the substrate thermally affect each other”, An estimate of the temperature of the object is calculated according to the temperature of the reference point and the thermal parameter, and an estimate of the temperature of the reference point is calculated according to the estimate of the temperature of the object and the thermal parameter. The thermal parameter is modified based on the estimated value and the actual reference point temperature. Since such correction of the heat parameter is repeated, a more accurate heat parameter can be acquired, and the temperature of the object can be estimated with high accuracy.

  In the temperature estimation device of the present invention, it is preferable that the reference point temperature acquisition unit reacquires the temperature of the reference point every time the thermal parameter is corrected by the thermal parameter correction unit.

  According to the preferred embodiment of the temperature estimation apparatus of the present invention, the temperature of the reference point is reacquired every time, so that the temperature of the object can be stably estimated with high accuracy.

  In the temperature estimation device of the present invention, it is preferable that the thermal parameter is a thermal resistance between the object and the substrate.

  The thermal resistance between the object and the substrate can be used to estimate the temperature of the object.

  Moreover, in the temperature estimation apparatus of the present invention, it is preferable that the thermal parameter correction unit calculates a correction value of the thermal parameter by PID calculation.

  According to the preferred embodiment of the temperature estimation apparatus of the present invention, it is possible to efficiently calculate a precise thermal parameter, and to accurately estimate the temperature of the object.

In the temperature estimation device of the present invention, the object is a semiconductor wafer,
The base is preferably a hot plate for heating the semiconductor wafer.

  In the heat treatment for heating the semiconductor wafer, a thermometer cannot be directly attached to the semiconductor wafer. Therefore, it is preferable to estimate the temperature of the semiconductor wafer with high accuracy by applying the temperature estimation device of the present invention.

In addition, the temperature control device of the present invention that achieves the above object includes a reference point temperature acquisition unit that acquires the temperature of a reference point that refers to the temperature of a substrate that is in thermal contact with an object,
A first temperature calculation unit that calculates an estimated value of the temperature of the object according to the thermal parameter related to the object and the temperature of the reference point acquired by the reference point temperature acquisition unit;
A second temperature calculating unit that calculates an estimated value of the temperature of the reference point according to the thermal parameter and the estimated value of the temperature of the object calculated by the first temperature calculating unit;
A thermal parameter correction unit that corrects the thermal parameter based on the temperature of the reference point acquired by the reference point temperature acquisition unit and the estimated value of the temperature of the reference point calculated by the second temperature calculation unit;
Each time the first temperature calculation unit and the second temperature calculation unit correct the thermal parameter in the thermal parameter correction unit, the estimated temperature of the object and the temperature of the reference point are calculated using the corrected thermal parameter. The thermal parameter correction unit corrects the thermal parameter every time the second temperature calculation unit recalculates the estimated value of the reference point temperature,
The present invention is characterized in that a base body control section is provided for controlling the heat generation amount or the heat absorption amount of the base body so that the estimated temperature value of the object calculated by the first temperature calculation section approaches the target temperature.

  According to the temperature control device of the present invention, the temperature of the object can be estimated with high accuracy, and the temperature of the object can be brought closer to the target temperature more accurately.

  Note that the temperature control device is only shown in its basic form here, but this is only for avoiding duplication, and the temperature control device according to the present invention is not limited to the above basic form. Various forms corresponding to the respective forms of the temperature estimation device are included.

Further, the temperature estimation method of the present invention that achieves the above object includes a reference point temperature acquisition step of acquiring the temperature of a reference point that refers to the temperature of a substrate that is in thermal contact with an object,
A first temperature calculation process for calculating an estimated value of the temperature of the object according to the thermal parameter related to the object and the temperature of the reference point acquired in the reference point temperature acquisition process;
A second temperature calculating step of calculating an estimated value of the temperature of the reference point according to the thermal parameter and the estimated value of the temperature of the object calculated in the first temperature calculating step;
A thermal parameter correction process for correcting a thermal parameter based on the reference point temperature acquired in the reference point temperature acquisition process and the estimated temperature of the reference point calculated in the second temperature calculation process. ,
The first temperature calculation process and the second temperature calculation process each time the thermal parameter is corrected in the thermal parameter correction process, using the corrected thermal parameter, the estimated temperature of the object and the temperature of the reference point The thermal parameter correction process corrects the thermal parameter every time the estimated temperature of the reference point is recalculated in the second temperature calculation process. To do.

  According to the temperature estimation method of the present invention, even if the temperature of the object cannot be directly measured, the temperature can be estimated with high accuracy.

  Note that the temperature estimation method is only shown in its basic form here, but this is only for avoiding duplication, and the temperature estimation method referred to in the present invention is not limited to the above basic form. Various forms corresponding to the respective forms of the temperature estimation device are included.

Further, the temperature control method of the present invention that achieves the above object includes a reference point temperature acquisition step of acquiring the temperature of a reference point that refers to the temperature of a substrate that is in thermal contact with an object,
A first temperature calculation process for calculating an estimated value of the temperature of the object according to the thermal parameter related to the object and the temperature of the reference point acquired in the reference point temperature acquisition process;
A second temperature calculating step of calculating an estimated value of the temperature of the reference point according to the thermal parameter and the estimated value of the temperature of the object calculated in the first temperature calculating step;
A thermal parameter correction process for correcting a thermal parameter based on the reference point temperature acquired in the reference point temperature acquisition process and the estimated temperature of the reference point calculated in the second temperature calculation process. ,
The first temperature calculation process and the second temperature calculation process each time the thermal parameter is corrected in the thermal parameter correction process, using the corrected thermal parameter, the estimated temperature of the object and the temperature of the reference point The thermal parameter correction process corrects the thermal parameter each time the estimated temperature value of the reference point is recalculated in the second temperature calculation process.
It has a base body control process which controls the calorific value or endothermic quantity of a base so that the presumed value of the temperature of an object computed in the 1st temperature calculation process may approach target temperature.

  According to the temperature control method of the present invention, the temperature of the object can be brought close to the target temperature with high accuracy.

  Note that the temperature control method is only shown in its basic form here, but this is merely to avoid duplication, and the temperature control method referred to in the present invention is not limited to the basic form described above. Various forms corresponding to the respective forms of the temperature estimation device are included.

Moreover, the temperature estimation program of the present invention that achieves the above object is executed in a computer, and on the computer,
A reference point temperature acquisition unit that acquires a temperature of a reference point that refers to a temperature of a substrate that is in thermal contact with the object;
A first temperature calculation unit that calculates an estimated value of the temperature of the object according to the thermal parameter related to the object and the temperature of the reference point acquired by the reference point temperature acquisition unit;
A second temperature calculating unit that calculates an estimated value of the temperature of the reference point according to the thermal parameter and the estimated value of the temperature of the object calculated by the first temperature calculating unit;
A thermal parameter correcting unit configured to correct the thermal parameter based on the reference point temperature acquired by the reference point temperature acquiring unit and the estimated temperature of the reference point calculated by the second temperature calculating unit; ,
Each time the first temperature calculation unit and the second temperature calculation unit correct the thermal parameter in the thermal parameter correction unit, the estimated temperature of the object and the temperature of the reference point are calculated using the corrected thermal parameter. The thermal parameter correction unit corrects the thermal parameter each time the second temperature calculation unit recalculates the estimated temperature of the reference point. To do.

  Note that the components such as the first temperature calculation unit constructed by the temperature estimation program of the present invention may be constructed by one program component, or a plurality of one component. The program component may be constructed, or a plurality of components may be constructed by one program component. In addition, these components may execute such actions themselves, or may be executed by giving instructions to other programs and program components incorporated in the computer. Also good.

  Note that only the basic form of the temperature estimation program is shown here, but this is merely to avoid duplication, and the temperature estimation program referred to in the present invention is not limited to the above basic form. Various forms corresponding to the respective forms of the temperature estimation device are included.

Further, the temperature control program of the present invention that achieves the above object is executed in a computer, and on the computer,
A reference point temperature acquisition unit that acquires a temperature of a reference point that refers to a temperature of a substrate that is in thermal contact with the object;
A first temperature calculation unit that calculates an estimated value of the temperature of the object according to the thermal parameter related to the object and the temperature of the reference point acquired by the reference point temperature acquisition unit;
A second temperature calculating unit that calculates an estimated value of the temperature of the reference point according to the thermal parameter and the estimated value of the temperature of the object calculated by the first temperature calculating unit;
A thermal parameter correcting unit configured to correct the thermal parameter based on the reference point temperature acquired by the reference point temperature acquiring unit and the estimated temperature of the reference point calculated by the second temperature calculating unit; ,
Each time the first temperature calculation unit and the second temperature calculation unit correct the thermal parameter in the thermal parameter correction unit, the estimated temperature of the object and the temperature of the reference point are calculated using the corrected thermal parameter. The thermal parameter correction unit corrects the thermal parameter every time the second temperature calculation unit recalculates the estimated value of the reference point temperature,
The substrate control unit is configured to control the heat generation amount or the heat absorption amount of the substrate so that the estimated value of the temperature of the object calculated by the first temperature calculation unit approaches the target temperature.

  Note that the constituent elements such as the first temperature calculation unit constructed by the temperature control program of the present invention may be one constituent element constructed by one program part, and a plurality of one constituent element. The program component may be constructed, or a plurality of components may be constructed by one program component. In addition, these components may execute such actions themselves, or may be executed by giving instructions to other programs and program components incorporated in the computer. Also good.

  Note that only the basic form of the temperature control program is shown here, but this is merely to avoid duplication, and the temperature control program referred to in the present invention is not limited to the above basic form. Various forms corresponding to the respective forms of the temperature estimation device are included.

  As described above, according to the present invention, when there is an error in the estimation of the thermal parameter, the thermal parameter correction unit that checks the error and corrects the error is provided. A temperature estimation device, a temperature control device, a temperature estimation method, a temperature control method, a temperature estimation program, and a temperature control program can be provided.

  Embodiments of the present invention will be described below with reference to the drawings.

  FIG. 1 is a schematic view of a wafer heating system to which an embodiment of the present invention is applied.

  The wafer heating system shown in FIG. 1 has a chill plate 10 that keeps the temperature of the wafer 30 at a normal temperature when the wafer 30 is placed thereon, a chamber 20 that heats the wafer 30 carried from the chill plate 10, And a computer 40 for adjusting the temperature. The chamber 20 includes a hot plate 22 for heating the wafer 30 and a lid 21 that is closed after the wafer 30 is placed on the hot plate 22. The hot plate 22 includes a plurality of heaters 22 b, a plurality of temperature sensors 22 a that measure temperatures at positions corresponding to the respective heaters 22 b of the hot plate 22, and a stopper 22 c that supports the wafer 30. A temperature sensor 21 a that measures the temperature of the lid 21 at a position corresponding to each of the plurality of heaters 22 b is provided on the inner side of the lid 21 (the side facing the hot plate 22).

  Here, the wafer 30 is placed on the stopper 22 c of the hot plate 22 with the back side of the front and back sides facing the hot plate 22. In order to determine whether or not the temperature of the wafer 30 has been heated to the set temperature, it is preferable to determine whether or not the temperature of the surface of the wafer 30 not facing the hot plate 22 has reached the set temperature. However, the temperature sensor cannot be directly mounted on the surface of the wafer 30. In this embodiment, the heater 22b and the temperature sensors 21a and 22a are connected to the computer 40. In the computer 40, the measurement result of the temperature sensor 21a provided inside the lid 21 and the hot plate 22 are provided. The surface temperature of the wafer 30 is estimated based on the measurement result of the temperature sensor 22a, and the amount of heat output from the heater 22b is controlled so that the surface temperature becomes the set temperature.

  The computer 40 has a main body device 41, a display device 42 that displays characters and images on a display screen 42a in response to an instruction from the main body device 41, and various types of information corresponding to key operations on the main body device 41 in terms of external configuration. And a mouse 44 for inputting an instruction corresponding to, for example, an icon or the like displayed at that position by designating an arbitrary position on the display screen 42a. The main unit 41 has an FD loading port 41a for loading a flexible disk (hereinafter abbreviated as FD) and a CD-ROM loading port 41b for loading a CD-ROM.

  FIG. 2 is a hardware configuration diagram of the computer shown in FIG.

  As shown in FIG. 2, the main unit 41 includes a CPU 411 that executes various programs, a main memory 412 that is read out from the programs stored in the hard disk device 413 and developed for execution by the CPU 411, and various programs. 1 and the hard disk device 413 in which data and the like are stored, the FD 100 is loaded, the FD drive 414 that accesses the loaded FD 100, the CD-ROM drive 415 that accesses the CD-ROM 110, and the temperature sensors 21a and 22a shown in FIG. An input interface 416 connected to receive measurement values from the temperature sensors 21a and 22a and an output interface 417 connected to the heater 22b shown in FIG. 1 and sending a heater control signal to the heater 22b are built-in. Further, the display device shown in FIG. 2, keyboard 43, and mouse 44 are connected to each other via a bus 45.

  Here, the CD-ROM 110 stores a temperature control program to which one embodiment of each of the temperature estimation program and the temperature control program of the present invention is applied. The CD-ROM 110 is loaded into the CD-ROM drive 415, and the temperature control program stored in the CD-ROM 110 is uploaded to the computer 40 and stored in the hard disk device 413. When the temperature control program is started and executed, a temperature control device 50 (see FIG. 4), which is an embodiment of each of the temperature estimation device and the temperature control device of the present invention, is constructed in the computer 40. The

  Next, a temperature control program executed in the computer 40 will be described.

  FIG. 3 is a conceptual diagram showing the CD-ROM 110 in which the temperature control program is stored.

  The temperature control program 420 includes a heater temperature acquisition unit 421, a temperature estimation unit 422, a model formula update unit 423, a target temperature setting unit 424, a heater control unit 425, and a signal output unit 426. The details of each part of the temperature control program 420 will be described together with the operation of each part of the temperature control device 50 (see FIG. 4).

  In FIG. 3, the CD-ROM 110 is illustrated as a storage medium for storing the temperature control program. However, the storage medium for storing the temperature estimation program and the temperature control program of the present invention is not limited to the CD-ROM. Other storage media such as an optical disk, MO, FD, and magnetic tape may be used. Further, the temperature estimation program and temperature control program of the present invention may be directly supplied to a computer via a communication network, not via a storage medium.

  FIG. 4 is a functional block diagram of the temperature control device 50 constructed in the computer 40 when the temperature control program 420 is installed in the computer 40 shown in FIGS. 1 and 2.

  A temperature control device 50 shown in FIG. 4 includes a heater temperature acquisition unit 51, a temperature estimation unit 52, a model formula update unit 53, a target temperature setting unit 54, a heater control unit 55, and a signal output unit 56. When the temperature control program 420 shown in FIG. 3 is installed in the computer 40 shown in FIG. 1, the heater temperature acquisition unit 421 of the temperature control program 420 constitutes the heater temperature acquisition unit 51 of FIG. Constitutes the temperature estimation unit 52, the model formula updating unit 423 constitutes the model formula updating unit 53, the target temperature setting unit 424 constitutes the target temperature setting unit 54, and the heater control unit 425 constitutes the heater control unit 55. The signal output unit 426 constitutes the signal output unit 56.

Here, when the wafer 30 is placed on the hot plate 22 shown in FIG. 1, the wafer 30 is heated by the heater 22 b and the temperature rises. Conversely, the temperature of the heater 22 b is the heat of the hot plate 22. Decrease by being deprived of 30. And the temperature T _h of the heater, the temperature T _w of the wafer, the following heat transfer model type A, B holds.
Heat transfer model equation A when transferring heat from the hot plate 22 to the wafer 30:

Heat transfer model formula B when transferring heat from the wafer 30 to the hot plate 22:

Here, C _h : heat capacity of the hot plate 22, C _w : heat capacity of the wafer 30, R _hw : thermal resistance between the hot plate 22 and the wafer 30, R _we : wafer 30 and the outside (the lid 21 in FIG. 1) , Q: heat flux from the hot plate 22 toward the wafer 30, T _e : ambient temperature (the temperature of the lid 21 in FIG. 1), T _h : temperature of the heater 22 b, T _w : of the wafer 30 Temperature, ΔT _h : Temperature change rate of the heater 22 b, ΔT _w : Temperature change rate of the wafer 30 As shown in the heat transfer model equations A and B, the wafer 30 and the hot plate 22 have an influence on each other. . The temperature control device 50 estimates the temperature of the wafer 30 using the measurable temperature of the hot plate 22 based on the relationship between the wafer 30 and the hot plate 22.

The heater temperature acquisition unit 51 measures the measurement value of the temperature sensor 21 a provided inside the lid 21 (hereinafter, this measurement value is referred to as the baffle temperature T _b ) and the measurement of the temperature sensor 22 a provided on the hot plate 22. A value (heater temperature T _h ) is acquired. The heater temperature acquisition unit 51 corresponds to an example of a reference point temperature acquisition unit according to the present invention. The acquired baffle temperature T _b and heater temperature _Th are transmitted to the temperature estimation unit 52, and the heater temperature _Th is also transmitted to the model formula update unit 53.

Here, the wafer 30 is slightly warped, and the warpage is different for each wafer. That is, among the parameters used in the heat transfer model equations A and B, the thermal resistance R _hw between the hot plate 22 and the wafer 30 is unknown. In the temperature controller 50, a thermal parameter M representing the thermal resistance R _hw between the hot plate 22 and the wafer 30 is also calculated in the process of estimating the temperature T _w of the wafer 30.

If the wafer 30 is divided into a plurality of regions in the horizontal direction, the warpage of the wafer 30 can be regarded as a change in the thermal resistance between the hot plate 22 and the wafer 30 in each region. In the present embodiment, a plurality of sets of temperature sensors 21a and 22a are provided on the lid 21 and the hot plate 22, and the baffle temperature _Tb and the heater temperature _Th are acquired by each set of the temperature sensors 21a and 22a. The thermal resistance R _hw between the hot plate 22 and the wafer 30 in each of the plurality of regions is calculated. Therefore, by substituting each of the plurality of thermal resistances R _hw into the heat transfer model equations A and B, the wafer temperature T _w in each region when the wafer 30 is divided into a plurality of regions can be calculated in detail. In the following text, for simplification of description, description will be given focusing on only one area when the wafer 30 is divided into a plurality of areas.

Temperature estimating unit 52, first, the temporary estimated thermal parameters M', baffle temperature T _b, and the heater temperature T _h and the like substituted for the heat transfer model formula A, to obtain an estimate of the temperature of the wafer 30 (hereinafter, This estimated value is referred to as an estimated wafer temperature T _w ′). Further, the temperature estimation unit 52 substitutes the estimated wafer temperature T _w ′, the heat flux Q calculated from the control output value MV of the heater 22b, and the estimated heat parameter M ′ into the heat transfer model formula B, and the heater 22b. Is obtained (hereinafter, this estimated value is referred to as an estimated heater temperature T _h ′). The portion for obtaining the estimated value of the temperature of the wafer 30 in the temperature estimating unit 52 corresponds to an example of the first temperature calculating unit referred to in the present invention, and the portion for obtaining the estimated value of the temperature of the heater 22b is referred to in the present invention. It corresponds also to an example of 2 temperature calculation parts. The calculated estimated heater temperature T _h ′ is transmitted to the model formula update unit 53.

If it is correct estimated thermal parameters M', it should be equal in the heater temperature T _h obtained by the heater temperature acquiring unit 51, and the estimated heater temperature T _h 'estimated by the temperature estimation unit 52. Model expression update unit 53, the estimated heater temperature T _h 'and the heater temperature T to correct the estimated thermal parameters M'based on the _h, heat transfer model formula A with the estimated thermal parameters M'after correction, the B Update. The model formula update unit 53 corresponds to an example of a thermal parameter correction unit according to the present invention. The updated heat transfer model equations A and B are transmitted to the temperature estimation unit 52.

From the model equation updating portion 53, updated heat transfer model formula A, if B is transmitted, the temperature estimating unit 52, the heater temperature acquiring unit 51 acquires a new baffle temperature T _b and the heater temperature T _h, they Are applied to the updated heat transfer model equations A and B to calculate a new estimated wafer temperature T _w ′ and an estimated heater temperature T _h ′. The calculated estimated heater temperature T _h ′ is transmitted to the model formula update unit 53, and the estimated heat parameter M ′ is further corrected. Such estimated thermal parameters M'modifications, the estimated heater temperature T _h 'and the heater temperature T _h are repeated until the approaching predetermined degree.

Here, if the heat output of the heater 22b is constant below and places the wafer 30 on the hot plate 22, the heat is deprived heater temperature T _h of the hot plate 22 by the wafer 30 is lowered (transient state), When the wafer 30 is warmed and the heat transfer between the wafer 30 and the hot plate 22 is stabilized, the heater temperature _Th is restored (steady state). In the transient state in which the wafer 30 is heated by the heater 22b and the temperature rises, the above-described heat transfer model equations A and B hold, but the heat exchange between the hot plate 22 and the wafer 30 is stable, In the steady state where the temperature change of the wafer 30 is settled, the following equation is established.
Heat transfer model equation C in steady state:

In the steady state, and the heat transfer model equation C is (R _hw + R _we) claim became constant, the heater temperature T _h, the correlation between the thermal resistance R _hw between the hot plate 22 and the wafer 30 is lost End up. For this reason, the estimation of the estimated thermal parameter M ′ is repeated only in the transient state. Model expression update section 53, when the estimated heater temperature T _h 'and the heater temperature T _h is sufficiently close to (i.e., when the thermal parameters M'approaches a sufficiently accurate value), or the heater temperature T _h When the heating is continued for a predetermined time or longer (that is, when the calculation of the thermal parameter M ′ is continued due to the approach to the steady state, the correction of the estimated thermal parameter M ′ is stopped).

When the correction of the estimated thermal parameter M ′ is stopped in the model formula update unit 53, the temperature estimation unit 52 causes the estimated wafer temperature T _w ′ (hereinafter referred to as the estimated wafer temperature T _w ′) estimated based on the final estimated thermal parameter M ′ This estimated wafer temperature T _w ′ is referred to as a determined wafer temperature T _w ) and is transmitted to the heater controller 55.

The heater control unit 55, the target temperature of the wafer 30 that has been set in the decision wafer temperature T _w target temperature setting unit 54 conveyed from the temperature estimating unit 52 (hereinafter, referred to as the target temperature and the target wafer temperature P_T _w) The output value MV of the heater 22b for approaching to is calculated. The calculated heater output value MV is transmitted to the signal output unit 56, and a heater control signal is transmitted from the signal output unit 56 to the heater 22b. A combination of the heater control unit 55 and the signal output unit 56 corresponds to an example of a substrate control unit according to the present invention.

The heater 22b to which the heater control signal is transmitted outputs with a heat generation amount corresponding to the heater control signal. Thus, the output value MV of the heater 22b is controlled, the temperature T _w of the wafer 30 is adjusted.

  The temperature control device 50 is basically configured as described above.

FIG. 5 is a flowchart showing a flow of a series of processes performed by the temperature control device 50. Hereinafter, along the flowchart, the heat treatment will be described for adjusting the temperature of the wafer 30 in the target wafer temperature P_T _w.

First, a target temperature (target wafer temperature P_T _w ) of the wafer 30 is designated by the operator of the temperature control device 50 using the mouse 44 shown in FIG. Specified target wafer temperature P_T _w is transferred from the target temperature setting unit 54 shown in FIG. 4 to the heater control unit 55.

When the target wafer temperature P_T _w is set, the wafer 30 is placed on the chill plate 10, the temperature of the wafer 30 is maintained at room temperature, the heater control unit 55 and the signal output section 56, shown in FIG. 4 The output heat amount of the heater 22b is controlled to the control output (step S1 in FIG. 5). If the output of the heater 22b is too large, the temperature of the hot plate 22 is influenced only by the heater output, and it becomes difficult to be affected by the wafer temperature and the hot plate-to-wafer thermal resistance, and the accuracy of temperature estimation of the wafer 30 deteriorates. For this reason, in this embodiment, the output of the heater 22b is controlled to about 30% of the maximum output at the beginning of the temperature control process.

When the wafer 30 is moved on the hot plate 22, the hot plate 22 is heat taken away by the wafer 30, (enters a transient state) heater temperature T _h is reduced. Heater temperature acquiring unit 51 acquires the heater temperature T _h which is measured by the temperature sensor 22a provided in the hot plate 22 at each predetermined timing, the heater temperature T _h (n) is the previous (n at a point in time n -1), which is lower than the heater temperature _Th (n-1) (step S2 in FIG. 5: Yes), and it is detected that the wafer 30 is placed on the hot plate 22, the heater temperature _Th The baffle temperature T _b is transmitted to the temperature estimation unit 52. When the heater temperature _Th and the baffle temperature _Tb are transmitted to the temperature estimation unit 52, the thermal parameter estimation process is started (step S3 in FIG. 5).

  FIG. 6 is a flowchart showing the flow of the thermal parameter estimation process shown in step S3 of FIG. In the following, the description of FIG. 5 is temporarily interrupted, and the thermal parameter estimation processing is described with reference to FIG.

When the thermal parameter estimation process is started, the heater temperature T _h (n) and the baffle temperature T _b (n) newly acquired by the heater temperature acquisition unit 51 are transmitted to the temperature estimation unit 52 (step of FIG. 6). S31), the heater temperature T _h (n) is also transmitted to the model formula update unit 53. The process in which the heater temperature T _h (n) is acquired in step S31 corresponds to an example of the reference point temperature acquisition process in the present invention.

In the temperature estimation unit 52, first, the temperature of the wafer 30 is estimated (step S32 in FIG. 6). The heat transfer model equations A and B described above are modified as follows.
Modified formula A ′ of heat transfer model formula A:

Modified formula B ′ of heat transfer model formula B:

However, in the modified formulas A ′ and B ′, T _h (n): temperature of the heater 22b at time n, T _w (n): temperature of the wafer 30 at time n, Δt: sampling time, m: hot Change coefficient of thermal resistance R _hw (thermal parameter M) between the plate 22 and the wafer 30 (value “1” at the time of system identification. Inversely proportional to the distance between the hot plate 22 and the wafer 30), a, b , C, d: model coefficients (coefficients obtained in advance at the time of system identification, that is, coefficients obtained by performing a model identification experiment in advance using a test wafer capable of measuring temperature and using a parametric identification method such as ARX modeling), MV (n): Control output value of heater 22b at time point n The variable m of the above conversion formula A ′ is added to the estimated change coefficient in the previous step (n−1) (hereinafter, the estimated change coefficient m ′ (n−1)). Express , T _h (n-1) the previous step (n-1) the heater temperature T _h (n-1) in the baffle temperature in the preceding step to _{T b (n-1) (} n-1) T b (n- 1) 'by substituting (n-1), the temperature T _w of the wafer 30 at the current step n' where T _w (n-1) the previous step (n-1) estimated in the estimated wafer temperature T _w ( n) is estimated. In step 1, as an initial state, heater temperature T _h (0): heater temperature at the start of thermal parameter estimation processing, T _w (0): temperature of chill plate 10 and m ′ (0) = 1 are substituted. Thus, the temperature T _w ′ (1) of the wafer 30 in step 1 is estimated. The process of estimating the temperature T _w ′ (n) of the wafer 30 in step S32 corresponds to an example of a first temperature calculation process according to the present invention.

Subsequently, the temperature estimation unit 52 substitutes the control output value MV (n−1) of the heater 22b in the previous step (n−1) for MV (n−1) of the conversion formula B ′, thereby the current step. The temperature T _h ′ (n) of the heater 22b at n is estimated (step S33 in FIG. 6). In Step 1, the estimated heater temperature T _h ′ (1) is calculated by substituting the control output value MV (0) = 30% of the heater 22b in the initial state into the conversion equation B ′. The process of estimating the temperature T _h ′ (n) of the heater 22b in step S33 corresponds to an example of a second temperature calculation process according to the present invention.

The estimated heater temperature T _h ′ (n) thus estimated is transmitted to the model formula update unit 53.

In the model formula update unit 53, first, a difference D between the heater temperature T _h (n) transmitted from the heater temperature acquisition unit 51 and the estimated heater temperature T _h ′ (n) estimated by the temperature estimation unit 52 is It is determined whether or not the value is equal to or less than a predetermined value set over a predetermined period N (step S34 in FIG. 6). That the difference D is less than or equal to a predetermined value over a predetermined period N means that the estimated change coefficient m ′ (n−1) is almost accurate, and this estimated change coefficient m ′ (n−1) is used. This indicates that the estimated wafer temperature T _w ′ (n) estimated in the above is calculated with high accuracy. When the difference D is equal to or less than the predetermined value over a predetermined period N (step S34 in FIG. 6: Yes), the thermal parameter estimation process is ended.

Further, when the difference D has not converged below the predetermined value (step S34 in FIG. 6: No), it indicates that the accuracy of the estimated change coefficient m ′ (n−1) is insufficient. At this time, it is further determined whether or not the heat transfer between the wafer 30 and the hot plate 22 is in a transient state (step S35 in FIG. 6). When a predetermined time elapses after the wafer 30 is placed on the hot plate 22 and the temperature of the heater 22b approaches a steady state (step S35: No in FIG. 6), the thermal parameter estimation process is ended. Further, when the heater temperature T _h (n) of the current step is smaller than the heater temperature T _h (n−1) of the previous step and the temperature of the wafer 30 is rising (step S35 in FIG. 6: Yes). In the model formula update unit 53, the thermal parameter estimation process is continued.

In the model formula update unit 53, the estimated change coefficient m ′ (n−1) is corrected so that the estimated heater temperature T _h ′ (n) and the heater temperature T _h (n) approach each other (step S36 in FIG. 6). ). In the present embodiment, the heater temperature T _h (n) at the time point n is SP (target value) and the estimated heater temperature T _h ′ (n) is PV (estimated value), so that PV approaches SP by PID calculation. PID output u (n) is acquired (provided that −100 ≦ output u (n) ≦ 100). Since the PID calculation is a calculation method that has been widely known in the past, the description thereof is omitted in this specification. The PID output u (n) is subjected to the following calculation to calculate the estimated change coefficient m ′ (n) at time n.

  In the model formula update unit 53, the estimated change coefficient m ′ (n) estimated is substituted into the conversion formulas A ′ and B ′, and the conversion formulas A ′ and B ′ are updated. The process of correcting the estimated change coefficient m ′ (n) in step S36 corresponds to an example of a thermal parameter correction process according to the present invention. The updated conversion formulas A ′ and B ′ are transmitted to the temperature estimation unit 52.

The temperature estimation unit 52, the heater temperature acquisition unit 51, newly heater temperature T _h (n), the baffle temperature T _b (n) is acquired, the estimated wafer estimated before one period in step S32 in FIG. 6 The estimated heater temperature T _h ′ (n) in the new step is estimated using the temperature T _w ′ as the estimated wafer temperature T _w ′ (n−1) in the previous step. Further, the model formula update unit 53 estimates a new estimated change coefficient m ′ (n) using the new estimated heater temperature T _h ′ (n). A series of processes from step S31 to step S35 as described above are repeated until the thermal parameter estimation process is stopped in the model formula update unit 53. The estimated change coefficient m ′ may be calculated using an adaptive algorithm such as a sequential least square method or an LMS method instead of the PID calculation.

  Returning to the flowchart of FIG.

When the thermal parameter estimation process is completed (step S3 in FIG. 5), the temperature estimation unit 52 uses the estimated change coefficient m ′ (finally estimated by the model formula update unit 53) as the variable m in the conversion formula A ′. n) is substituted, and the temperature of the wafer 30 in the current step is re-estimated in the same manner as in step S32 shown in FIG. 6 (step S4 in FIG. 5). By this process, an error caused by assuming that the estimated change coefficient m ′ (0) = 1 is corrected, and the wafer temperature T _w is estimated with higher accuracy. The estimated wafer temperature T _w re-estimated is transmitted to the heater controller 55.

The heater control unit 55, a decision wafer temperature T _w which is transmitted from the temperature estimating unit 52, the control output value MV of a heater 22b to approximate set target wafer temperature P_T _w at the target temperature setting unit 54 is calculated (Step S5 in FIG. 5). In this process, after the thermal parameter is determined, the temperature is continuously estimated based on the obtained m, and the determined wafer temperature _Tw is updated. In the present embodiment, the target wafer temperature P_T _w SP (target value), the decision wafer temperature T _w as PV (estimated value), the PID operation, the control output value MV to approximate PV to SP is obtained. The acquired control output value MV is transmitted to the signal output unit 56, and a heater control signal is output from the signal output unit 56 to the heater 22b. The process of controlling the output of the heater 22b in step S5 corresponds to an example of the substrate control process according to the present invention.

  As described above, according to the temperature control device 50 of the present embodiment, the wafer temperature can be estimated with high accuracy, and the temperature of the wafer can be adjusted accurately.

  Below, the result of the demonstration experiment which actually performed the temperature control of the wafer mentioned above is demonstrated. In this demonstration experiment, in the wafer heating system shown in FIG. 1, two or one polyimide tape is pasted on the stopper 22c of the hot plate 22, and the distance between the wafer 30 and the hot plate 22 is changed. The thermal resistance Rhw between the wafer 30 and the hot plate 22 was changed into two types of large and small.

FIG. 7 is a graph showing the relationship between the actual measured value _Th of the heater temperature and the estimated value Th _h ′ of the heater temperature. In FIG. 7, time (s) is associated with the horizontal axis and temperature (° C.) is associated with the vertical axis, the actual measurement value is indicated by a solid line, and the estimated value is indicated by a broken line.

Part (A) of FIG. 7 shows a graph when two sheets of polyimide tape are attached to the stopper 22c and the thermal resistance R _hw between the wafer 30 and the hot plate 22 is increased. Part (B) of FIG. 7 shows a graph when one sheet of polyimide tape is applied to increase the thermal resistance R _hw between the wafer 30 and the hot plate 22. In both the case of part (A) and part (B), the wafer 30 is placed on the stopper 22c and within the predetermined time (3 seconds for part (A) and 4 seconds for part (B)) as described above. The estimated change coefficient m ′ was estimated, and then the heater temperature estimated value T _h ′ and the wafer temperature estimated value T _w ′ were calculated using the determined estimated change coefficient m ′. When two sheets of polyimide tape are applied, the thermal resistance R _hw is increased more than when one piece of polyimide tape is applied. Even if the thermal resistance R _hw is large, the heater estimate T _h temperature 'is to follow accurately the actual measurement value T _h of the heater temperature, as a result, as shown in part (a) of FIG. 9 to be described later, the wafer temperature can be accurately estimated.

  FIG. 8 is a graph showing changes in the estimated change coefficient m ′ during the thermal parameter estimation process.

  In FIG. 8, time (s) is associated with the horizontal axis, and the estimated change coefficient m ′ is associated with the vertical axis, which corresponds to part (A) of FIG. 7 (polyimide tape is interposed between the wafer 30 and the stopper 22c. The graph (with two sheets attached) is indicated by a solid line, and the graph corresponding to part (B) of FIG. 7 (with one polyimide tape attached) is indicated by a broken line. In both the solid line and the broken line, the estimated change coefficient m ′ converges almost uniformly after a certain period of time.

  As described above, according to the present invention, the estimated change coefficient m ′ is estimated with high accuracy.

FIG. 9 is a graph showing the relationship between the measured value T _w of the wafer temperature and the estimated value T _w ′ of the wafer temperature. In FIG. 9, time (s) is associated with the horizontal axis, and temperature (° C.) is associated with the vertical axis.

The solid line in FIG. 9 shows the actually measured value T _w when the measuring the temperature of the wafer 30 directly, dashed lines indicate the estimated value T _{w'_1} the temperature of the wafer 30, which is estimated by the present invention, the dashed line, An estimated value T _{w —} 2 when the estimated change coefficient m ′ is maintained at the initial value (1) and the temperature of the wafer 30 is estimated is shown. The estimated value T _{w '} _1 indicated by the broken line is sufficiently close to the actual measured value T _w indicated by the solid line over time, but the estimated value T _w' _2 indicated by the alternate long and short dash line is separated from the actual measured value T _w over time. It has been.

  Thus, according to the present invention, the wafer temperature can be estimated more accurately.

Here, in the above, it is configured so as to acquire the baffle temperature T _b by the heater temperature acquisition unit 51, if the change in the baffle temperature less regarded as substantially constant, or may be set in advance constant value . Further, when the influence of the baffle temperature T _b is small, the temperature of the object may be estimated by ignoring the baffle temperature T _b .

  In the above description, the example in which the thermal parameter is mainly corrected using the PID calculation using the difference between the estimated value and the measured value of the heater temperature has been described. However, as described above, the sequential minimum based on the difference is described. A square method, an LMS method, or the like may be used.

  Further, in the above, the thermal resistance of the object is applied as an example of the thermal parameter referred to in the present invention. However, the thermal parameter referred to in the present invention is a heat capacity, a thermal conductivity, an emissivity, and a heat transfer coefficient. There may be.

  In the above description, the example in which the present invention is applied to a semiconductor manufacturing process in which a wafer is heated by a hot plate has been described. However, the present invention is not limited to a semiconductor manufacturing process as long as the temperature of an object is estimated. You may apply.

1 is a schematic view of a wafer heating system to which an embodiment of the present invention is applied. It is a hardware block diagram of the computer shown in FIG. It is a conceptual diagram which shows CD-ROM in which the temperature control program was memorize | stored. It is a functional block diagram of the temperature control apparatus constructed | assembled in a computer when a temperature control program is installed in the computer shown in FIG. 1 and FIG. FIG. 4 is a flowchart showing a flow of a series of processes performed by the temperature control device 50. It is a flowchart figure which shows the flow of the thermal parameter estimation process shown to step S3 of FIG. And the measured values T _h of the heater temperature is a graph showing the relationship between the estimated value T _h of the heater temperature '. It is a graph which shows the change of the estimation change coefficient m 'in a thermal parameter estimation process. It is a graph which shows the relationship between the actual value _Tw of wafer temperature, and the estimated value _Tw 'of wafer temperature.

Explanation of symbols

10 Chill Plate 20 Chamber 21 Lid 21a Temperature Sensor 22 Hot Plate 22a Temperature Sensor 22b Heater 30 Wafer 40 Computer 41 Main Unit 41a FD Loading Port 41b CD-ROM Loading Port 42 Display Device 42a Display Screen 43 Keyboard 44 Mouse 45 Bus 411 CPU
412 Main memory 413 Hard disk device 414 FD drive 415 CD-ROM drive 416 Input interface 417 Output interface 420 Temperature control program 421 Heater temperature acquisition unit 422 Temperature estimation unit 423 Model formula update unit 424 Target temperature setting unit 425 Heater control unit 426 Signal output Unit 50 Temperature control device 51 Heater temperature acquisition unit 52 Temperature estimation unit 53 Model formula update unit 54 Target temperature setting unit 55 Heater control unit 56 Signal output unit

Claims (10)

A reference point temperature acquisition unit that acquires a temperature of a reference point that refers to a temperature of a substrate that is in thermal contact with the object;
A first temperature calculation unit that calculates an estimated value of the temperature of the object according to a thermal parameter related to the object and the temperature of the reference point acquired by the reference point temperature acquisition unit;
A second temperature calculating unit that calculates an estimated value of the temperature of the reference point according to the thermal parameter and an estimated value of the temperature of the object calculated by the first temperature calculating unit;
A thermal parameter correction unit that corrects the thermal parameter based on the temperature of the reference point acquired by the reference point temperature acquisition unit and the estimated value of the temperature of the reference point calculated by the second temperature calculation unit; With
The first temperature calculation unit and the second temperature calculation unit use the corrected thermal parameter each time the thermal parameter is corrected by the thermal parameter correction unit, and the estimated value of the temperature of the object and Recalculating the estimated value of the temperature of the reference point, and the thermal parameter correcting unit calculates the thermal parameter each time the estimated value of the temperature of the reference point is recalculated by the second temperature calculating unit. A temperature estimation device which is to be corrected.   2. The temperature estimation device according to claim 1, wherein the reference point temperature acquisition unit acquires the temperature of the reference point each time the thermal parameter is corrected by the thermal parameter correction unit.   The temperature estimation apparatus according to claim 1, wherein the thermal parameter is a thermal resistance between the object and the base.   The temperature estimation device according to claim 1, wherein the thermal parameter correction unit calculates a correction value of the thermal parameter by a PID calculation. The object is a semiconductor wafer;
The temperature estimation apparatus according to claim 1, wherein the base is a hot plate for heating the semiconductor wafer. A reference point temperature acquisition unit that acquires a temperature of a reference point that refers to a temperature of a substrate that is in thermal contact with the object;
A first temperature calculation unit that calculates an estimated value of the temperature of the object according to a thermal parameter related to the object and the temperature of the reference point acquired by the reference point temperature acquisition unit;
A second temperature calculating unit that calculates an estimated value of the temperature of the reference point according to the thermal parameter and an estimated value of the temperature of the object calculated by the first temperature calculating unit;
A thermal parameter correction unit that corrects the thermal parameter based on the temperature of the reference point acquired by the reference point temperature acquisition unit and the estimated value of the temperature of the reference point calculated by the second temperature calculation unit; With
The first temperature calculation unit and the second temperature calculation unit use the corrected thermal parameter each time the thermal parameter is corrected by the thermal parameter correction unit, and the estimated value of the temperature of the object and Recalculating the estimated value of the temperature of the reference point, and the thermal parameter correcting unit calculates the thermal parameter each time the estimated value of the temperature of the reference point is recalculated by the second temperature calculating unit. To correct,
A temperature comprising a base body control unit that controls the amount of heat generated or absorbed by the base body so that an estimated value of the temperature of the object calculated by the first temperature calculation unit approaches a target temperature. Control device. A reference point temperature acquisition process for acquiring a reference point temperature referring to a temperature of a substrate in thermal contact with an object;
A first temperature calculation process for calculating an estimated value of the temperature of the object according to a thermal parameter related to the object and a reference point temperature acquired in the reference point temperature acquisition process;
A second temperature calculating step of calculating an estimated value of the temperature of the reference point according to the thermal parameter and the estimated value of the temperature of the object calculated in the first temperature calculating step;
A thermal parameter correction process for correcting the thermal parameter based on the reference point temperature acquired in the reference point temperature acquisition process and the estimated temperature of the reference point calculated in the second temperature calculation process; Have
In each of the first temperature calculation process and the second temperature calculation process, when the thermal parameter is corrected in the thermal parameter correction process, an estimated value of the temperature of the object is obtained using the corrected thermal parameter and Recalculating the estimated value of the temperature of the reference point, and the thermal parameter correction process changes the thermal parameter every time the estimated value of the temperature of the reference point is recalculated in the second temperature calculation process. A temperature estimation method characterized by correction. A reference point temperature acquisition process for acquiring a reference point temperature referring to a temperature of a substrate in thermal contact with an object;
A first temperature calculation process for calculating an estimated value of the temperature of the object according to a thermal parameter related to the object and a reference point temperature acquired in the reference point temperature acquisition process;
A second temperature calculating step of calculating an estimated value of the temperature of the reference point according to the thermal parameter and the estimated value of the temperature of the object calculated in the first temperature calculating step;
A thermal parameter correction process for correcting the thermal parameter based on the reference point temperature acquired in the reference point temperature acquisition process and the estimated temperature of the reference point calculated in the second temperature calculation process; Have
In each of the first temperature calculation process and the second temperature calculation process, when the thermal parameter is corrected in the thermal parameter correction process, an estimated value of the temperature of the object is obtained using the corrected thermal parameter and Recalculating the estimated value of the temperature of the reference point, and the thermal parameter correction process changes the thermal parameter every time the estimated value of the temperature of the reference point is recalculated in the second temperature calculation process. To correct,
A temperature control comprising: a base body control process for controlling a heat generation amount or a heat absorption amount of the base body so that an estimated value of the temperature of the object calculated in the first temperature calculation process approaches a target temperature. Method. Executed in a computer, on the computer,
A reference point temperature acquisition unit that acquires a temperature of a reference point that refers to a temperature of a substrate that is in thermal contact with the object;
A first temperature calculation unit that calculates an estimated value of the temperature of the object according to a thermal parameter related to the object and the temperature of the reference point acquired by the reference point temperature acquisition unit;
A second temperature calculating unit that calculates an estimated value of the temperature of the reference point according to the thermal parameter and an estimated value of the temperature of the object calculated by the first temperature calculating unit;
A thermal parameter correction unit that corrects the thermal parameter based on the temperature of the reference point acquired by the reference point temperature acquisition unit and the estimated value of the temperature of the reference point calculated by the second temperature calculation unit; Configure
The first temperature calculation unit and the second temperature calculation unit use the corrected thermal parameter each time the thermal parameter is corrected by the thermal parameter correction unit, and the estimated value of the temperature of the object and Recalculating the estimated value of the temperature of the reference point, and the thermal parameter correcting unit calculates the thermal parameter each time the estimated value of the temperature of the reference point is recalculated by the second temperature calculating unit. A temperature estimation program which is to be corrected. Executed in a computer, on the computer,
A reference point temperature acquisition unit that acquires a temperature of a reference point that refers to a temperature of a substrate that is in thermal contact with the object;
A first temperature calculation unit that calculates an estimated value of the temperature of the object according to a thermal parameter related to the object and the temperature of the reference point acquired by the reference point temperature acquisition unit;
A second temperature calculating unit that calculates an estimated value of the temperature of the reference point according to the thermal parameter and an estimated value of the temperature of the object calculated by the first temperature calculating unit;
A thermal parameter correction unit that corrects the thermal parameter based on the temperature of the reference point acquired by the reference point temperature acquisition unit and the estimated value of the temperature of the reference point calculated by the second temperature calculation unit; Configure
The first temperature calculation unit and the second temperature calculation unit use the corrected thermal parameter each time the thermal parameter is corrected by the thermal parameter correction unit, and the estimated value of the temperature of the object and Recalculating the estimated value of the temperature of the reference point, and the thermal parameter correcting unit calculates the thermal parameter each time the estimated value of the temperature of the reference point is recalculated by the second temperature calculating unit. To correct,
A temperature that constitutes a substrate control unit that controls the amount of heat generated or absorbed by the substrate so that the estimated value of the temperature of the object calculated by the first temperature calculation unit approaches a target temperature. Control program.

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