Wafer temperature control device, wafer temperature control method, and wafer temperature control program

Abstract

To provide a device for controlling the temperature of a wafer by adjusting the pressure or flow rate of a gas, in which the temperature of a first region where temperature measurement is possible or the temperature in the vicinity of the first region is measured, and the temperature of a second region where temperature measurement is difficult is controlled to a target temperature.SOLUTION: A wafer temperature control device 100 in which a wafer W is placed on a temperature-adjusted plate 2 and gas is supplied between the plate 2 and the wafer W to control the temperature of the wafer W, includes a gas regulator 43 that adjusts the pressure or flow rate of the gas, a temperature sensor 5 that measures the temperature of a measurement target region W2 or its vicinity on the wafer W, an observer 10 for estimating the temperature of a non-measurement target region W1 different from the measurement target region W2 of the wafer W based on the measured temperature of the temperature sensor 5 and a gas operation amount input to the gas regulator 43 or the pressure or flow rate adjusted by the gas regulator 43, and a gas control unit 11 that controls the gas operation amount input to the gas regulator 43 by model predictive control based on the estimated temperature of the non-measurement target region W1 estimated by the observer 10 and the target temperature of the wafer W.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a wafer temperature control device, a wafer temperature control method, and a wafer temperature control program. [Background technology]

[0002] Conventionally, in a semiconductor manufacturing process such as a film formation process, a wafer to be processed is placed on a plate such as an electrostatic chuck, and the temperature of the plate such as an electrostatic chuck is adjusted to control the temperature of the wafer to a predetermined target temperature.

[0003] Since the plate on which the wafer is placed is placed in a low-pressure environment, such as a vacuum, inside the process chamber, it has been considered to supply a heat transfer gas, such as helium gas, between the plate and the wafer in order to promote heat transfer from the temperature-regulated plate to the wafer, as shown in Patent Document 1.

[0004] Here, since the heat transfer coefficient varies depending on the pressure of the heat transfer gas supplied between the plate and the wafer, it is necessary to adjust the pressure of the heat transfer gas.

[0005] However, even if the pressure of the heat transfer gas is adjusted, it is difficult to control the temperature of the wafer placed on the plate to a predetermined target temperature due to various technical constraints.

[0006] Here, it is conceivable to measure the temperature of the peripheral part (e.g., edge part) of the wafer, where it is relatively easy to measure the temperature, and control the wafer to a predetermined target temperature using the measured temperature. However, since a temperature difference occurs between the central part and the peripheral part of the wafer, it is difficult to control the central part of the wafer to a predetermined target temperature.

[0007] It is also possible to measure and control the temperatures of the central and peripheral parts of the wafer, but in practice it is difficult to provide a process chamber with a temperature sensor that measures the temperature of the central part of the wafer and a temperature sensor that measures the temperature of the peripheral part of the wafer. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Patent No. 4034344 Summary of the Invention [Problem to be solved by the invention]

[0009] Therefore, the present invention has been made to solve the above-mentioned problems, and has an object to control the temperature of a wafer by adjusting the gas pressure or flow rate, for example, by measuring the temperature of a measurement target area or its vicinity, where temperature measurement is relatively easy, and controlling the temperature of a non-measurement area, where temperature measurement is difficult, to a target temperature. [Means for solving the problem]

[0010] That is, the wafer temperature control device of the present invention is a wafer temperature control device in which a wafer is placed on a temperature-regulated plate and gas is supplied between the plate and the wafer to control the temperature of the wafer, and is characterized in that it comprises a gas regulator that adjusts the pressure or flow rate of the gas, a temperature sensor that measures the temperature of a specified measurement target area of ​​the wafer or its vicinity, an observer that estimates the temperature of a non-measurement target area different from the measurement target area of ​​the wafer based on the temperature measured by the temperature sensor and a gas manipulation amount input to the gas regulator or the pressure or flow rate adjusted by the gas regulator, and a gas control unit that controls the gas manipulation amount input to the gas regulator by model predictive control based on the estimated temperature of the non-measurement target area estimated by the observer and a target temperature of the wafer.

[0011] Such a wafer temperature control device estimates the temperature of the non-measurement area of ​​the wafer using an observer that uses the measured temperature of the measurement area of ​​the wafer or its vicinity and the gas pressure or flow rate as input variables, so that the temperature of the non-measurement area of ​​the wafer can be estimated with sufficient accuracy. Also, the gas manipulated variable input to the gas regulator is controlled by model predictive control based on the estimated temperature of the non-measurement area estimated by the observer and the target temperature of the wafer, so that it is easy to incorporate the non-linear behavior of the heat transfer coefficient from the plate to the wafer, and the temperature of the non-measurement area of ​​the wafer can be accurately controlled to the target temperature. By combining the observer and model predictive control in this way, nonlinear behavior can be incorporated in the model predictive control, and it is not necessary to consider nonlinear behavior in the observer. Therefore, complex modeling for incorporating nonlinear behavior in the observer is not required, and modeling of the state equation in the observer can be simplified. Furthermore, by combining the observer and model predictive control, the temperature of the non-measurement target area of ​​the wafer can be precisely controlled by simply measuring the temperature of the measurement target area of ​​the wafer. In other words, by simply measuring the temperature of one point on the wafer, the temperature of the other points can be precisely controlled, improving practicality. In addition, by combining the observer and model predictive control, it is possible to achieve robust control against disturbances from plasma, etc., which injects heat into the wafer.

[0012] Here, the nearby temperature is, for example, the temperature of a member or space within a predetermined distance from the measurement target area of ​​the wafer, and includes a temperature for which a temperature model can be constructed that shows the relationship between the temperature of the measurement target area and the nearby temperature. The nearby temperature also includes the temperature of a member that is in direct contact with the measurement target area of ​​the wafer, the temperature of the space or gas where the interface with the wafer exists, or the temperature of a member that exists with respect to the wafer via a gap of several μm. Furthermore, the nearby temperature may include the temperature of a member through which heat may be conducted or transferred between the measurement target area of ​​the wafer and the measurement target area by at least one of conduction, convection, and radiation.

[0013] Since the measurement target area and the non-measurement target area of ​​the wafer mutually affect each other by heat, it is necessary to estimate the temperature of the measurement target area with sufficient accuracy in order to accurately predict the future temperature of the non-measurement target area and accurately control the temperature of the non-measurement target area. Therefore, it is preferable that the observer estimates not only the temperature of the non-measurement target area but also the temperature of the measurement target area, and the gas control unit includes a gas control unit that controls the gas manipulated variable input to the gas regulator by model predictive control based on the estimated temperature of the measurement target area, the estimated temperature of the non-measurement target area, and the target temperature of the wafer.

[0014] In order to accurately control the temperatures of the measurement area and non-measurement area of ​​the wafer, it is desirable that the gas regulator has a first gas regulator that adjusts the gas pressure or flow rate between the plate and the non-measurement area of ​​the wafer, and a second gas regulator that adjusts the gas pressure or flow rate between the plate and the measurement area of ​​the wafer, and that the gas adjustment unit controls a first gas manipulation amount input to the first gas regulator by model predictive control based on the estimated temperature of the measurement area, the estimated temperature of the non-measurement area, and a target temperature of the non-measurement area, and controls a second gas manipulation amount input to the second gas regulator by model predictive control based on the estimated temperature of the measurement area, the estimated temperature of the non-measurement area, and the target temperature of the measurement area.

[0015] In order to accurately estimate the temperature of the non-measurement area and accurately control the temperature of the non-measurement area to a target temperature, it is desirable for the observer to use a state space model in which the heat transfer coefficient between the plate and the wafer is a variable determined from the gas pressure.

[0016] Here, in order to simplify the model and reduce the calculation load, it is possible to use constants calculated from physical property values ​​for the coefficient matrix of the state vector (matrix A) and the coefficient matrix of the input vector (matrix B) in the state equation of model predictive control. However, because the heat transfer coefficient varies depending on the pressure of the gas supplied between the plate and the wafer, in a model in which the thermal conductivity changes over time, if a constant (fixed thermal conductivity) is used in the coefficient matrix (A matrix) of the state vector, it becomes difficult to accurately control the wafer temperature to the target temperature. For this reason, it is desirable that the gas control unit uses, as a predictive model for the model predictive control, a model in which the heat transfer coefficient between the plate and the wafer is a variable determined from the gas pressure. With this configuration, the future temperature of the non-measurement area can be predicted with high accuracy, and the temperature of the non-measurement area can be controlled to the target temperature with high accuracy.

[0017] It is relatively easy to measure the temperature of the peripheral portion (e.g., edge portion) of the wafer, but it is difficult to measure the temperature of the central portion of the wafer, so it is desirable that the measurement target area is the peripheral portion of the wafer, and the non-measurement target area is the central portion of the wafer.

[0018] In order to measure the temperature of the measurement target area with a simple configuration, it is desirable that the temperature sensor be a radiation temperature sensor.

[0019] It is preferable that the observer estimates the amount of heat supplied to the wafer from outside. By estimating the amount of heat supplied from outside in this manner, the temperature of the measurement target area or non-measurement target area of ​​the wafer can be controlled with high precision.

[0020] In addition, a wafer temperature control method of the present invention is a wafer temperature control method in which a wafer is placed on a temperature-regulated plate and gas is supplied between the plate and the wafer to control the temperature of the wafer, the method comprising: regulating the pressure or flow rate of the gas using a gas regulator; measuring the temperature of a predetermined measurement target area of ​​the wafer or its vicinity using a temperature sensor; estimating the temperature of a non-measurement target area of ​​the wafer different from the measurement target area using an observer based on the measured temperature of the temperature sensor and a gas manipulation amount input to the gas regulator or the pressure or flow rate adjusted by the gas regulator; and controlling the gas manipulation amount input to the gas regulator by model predictive control based on the estimated temperature of the non-measurement target area estimated by the temperature estimation observer and a target temperature of the wafer.

[0021] Furthermore, the wafer temperature control program of the present invention is a wafer temperature control program used in a wafer temperature control device that has a gas regulator that adjusts the pressure or flow rate of the gas and a temperature sensor that measures the temperature of a specified measurement target area of ​​the wafer or its vicinity, in which a wafer is placed on a temperature-adjusted plate and gas is supplied between the plate and the wafer to control the temperature of the wafer, and is characterized in that the program has a function as an observer that estimates the temperature of a non-measurement target area different from the measurement target area of ​​the wafer based on the temperature measured by the temperature sensor and the gas manipulation amount input to the gas regulator or the pressure or flow rate adjusted by the gas regulator, and a function as a gas control unit that controls the gas manipulation amount input to the gas regulator by model predictive control based on the estimated temperature of the non-measurement target area estimated by the temperature estimation observer and the target temperature of the wafer.

[0022] The wafer temperature control program may be distributed electronically, or may be recorded on a program recording medium such as a CD, a DVD, or a flash memory. Effect of the Invention

[0023] Thus, according to the present invention, in a device for controlling the temperature of a wafer by adjusting the gas pressure or flow rate, it is possible to measure the temperature of a measurement target area or its vicinity where temperature measurement is possible, and control the temperature of a non-measurement area where it is difficult to measure the temperature, to a target temperature. [Brief description of the drawings]

[0024] [Figure 1] 1 is a perspective view showing a schematic configuration of a wafer temperature control apparatus according to an embodiment of the present invention; [Diagram 2] 2 is a schematic diagram showing the configuration of a gas supply mechanism and a control device CTL of the embodiment. FIG. [Diagram 3] 11 is a diagram showing the relationship between the pressure of the heat transfer gas supplied between the wafer and the suction plate and the heat transfer coefficient between the wafer and the suction plate. FIG. [Figure 4] FIG. 2 is a diagram showing a schematic diagram of a wafer temperature control system in the embodiment. [Diagram 5] FIG. 2 is a functional block diagram of a wafer control device in the embodiment. [Figure 6] FIG. 2 is a diagram illustrating a mechanism of model predictive control in the embodiment. [Figure 7] FIG. 2 is a diagram showing a control object model used in model predictive control in the embodiment. [Figure 8] 4 is a diagram showing a reference trajectory and a predicted trajectory in which two different regions are not distinguished from each other in the model predictive control of the embodiment. FIG. [Figure 9] FIG. 2 is a diagram illustrating a state equation and a reference trajectory of the model predictive control according to the embodiment. [Figure 10] 4A to 4C are diagrams illustrating predicted values ​​based on a free response, predicted values ​​based on a step response, and predicted trajectories of the model predictive control of the embodiment. [Figure 11] FIG. 4 is a diagram illustrating an evaluation function of the model predictive control according to the embodiment. [Figure 12] 11A and 11B are diagrams showing experimental results and simulation results in the case where the wafer temperature is controlled using the wafer temperature control device of the embodiment. [Figure 13]11A and 11B are diagrams showing simulation results when disturbances are generated in the case where the wafer temperature is controlled using the wafer temperature control device of the embodiment; DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] <One embodiment of the present invention> DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a wafer temperature control device according to the present invention will be described below with reference to the drawings. In addition, in any of the drawings shown below, for the purpose of easy understanding, some parts are omitted or exaggerated in schematic form as appropriate. The same components are denoted by the same reference numerals and the description thereof is omitted as appropriate.

[0026] <1. Basic configuration of wafer temperature control device> The wafer temperature control device 100 of this embodiment is used in a semiconductor manufacturing device that performs a semiconductor manufacturing process such as a film formation process, and is configured to electrostatically chuck the back surface of a wafer W in a vacuum chamber, for example.

[0027] Specifically, the wafer temperature control device 100 includes an adsorption plate 2 on the upper surface of which a wafer W is placed, and a temperature regulator 3 that adjusts the temperature of the adsorption plate 2, as shown in FIG.

[0028] The suction plate 2 constitutes a so-called electrostatic chuck that holds the wafer W by electrostatic suction force. The suction plate 2 in this embodiment is a ceramic plate having a substantially circular shape, and the upper surface thereof serves as an suction surface 2a that suctions the wafer W. An electrostatic electrode (not shown) for generating an electrostatic force between the suction plate 2 and the wafer W is provided inside the suction plate 2.

[0029] The temperature regulator 3 regulates the temperature of the suction plate 2 to a preset temperature, and includes a cooler 31 that cools the suction plate 2. The temperature regulator 3 may also include a heater that heats the suction plate 2.

[0030] The cooler 31 is provided in contact with the lower surface of the suction plate 2, and includes a substantially disk-shaped base plate 31a and a cooling passage 31b formed within the base plate 31a.

[0031] The cooling flow passage 31b is formed in a spiral shape in a plan view inside the base plate 31a. An inlet flow passage 31c and an outlet flow passage 31d, which are connected to a cooling source (not shown) such as a chiller, are connected to the cooling flow passage 31b. A control valve 31e for controlling the flow rate of the refrigerant is provided in the flow passage connected to the cooling flow passage 31b, and the valve opening of the control valve 31e is controlled by a cooling control unit (not shown) of the control device CTL.

[0032] <2. Gas supply mechanism 4> Furthermore, as shown in FIGS. 1 and 2, the wafer temperature control device 100 of this embodiment is equipped with a gas supply mechanism 4 that supplies a gas that transfers heat (hereinafter referred to as a heat transfer gas), such as helium gas or argon gas, between the suction plate 2 and the wafer W.

[0033] The gas supply mechanism 4 supplies a heat transfer gas at a predetermined pressure between the suction surface 2a of the suction plate 2 and the rear surface of the wafer W that is suctioned.

[0034] 1, the gas supply mechanism 4 has a gas circulation groove 41 formed on the suction surface 2a of the suction plate 2, a gas supply path 42 for supplying a heat transfer gas to the gas circulation groove 41, and a pressure regulator 43 which is a gas regulator for adjusting the pressure of the heat transfer gas supplied to the gas circulation groove 41. The heat transfer gas supplied to the gas circulation groove 41 flows from the gas circulation groove 41 into the gap between the suction surface 2a of the suction plate 2 and the back surface of the wafer W being suctioned.

[0035] The gas flow grooves 41 include, for example, a plurality of linear grooves formed radially from the central axis of the suction plate 2 and a plurality of circular grooves formed circularly from the central axis of the suction plate 2.

[0036] 2, the gas supply path 42 has a first gas supply path 421 for supplying a heat transfer gas to the center of the adsorption surface 2a of the adsorption plate 2, and a second gas supply path 422 for supplying a heat transfer gas to the peripheral portion of the adsorption surface 2a of the adsorption plate 2. The center of the adsorption surface 2a (corresponding to the center portion W1 which is a non-measurement target area of ​​the wafer W) is a circular portion, and the peripheral portion of the adsorption surface 2a (corresponding to the peripheral portion W2 which is a measurement target area of ​​the wafer W) is an annular portion. The first gas supply path 421 and the second gas supply path 422 are connected to a heat transfer gas source (not shown).

[0037] As shown in FIG. 2, the pressure regulator 43 includes a first pressure regulator 431 which is a first gas regulator provided in the first gas supply path 421 and which adjusts the pressure of the heat transfer gas supplied to the central portion of the adsorption surface 2a, and a second pressure regulator 432 which is a second gas regulator provided in the second gas supply path 422 and which adjusts the pressure of the heat transfer gas supplied to the peripheral portion of the adsorption surface 2a.

[0038] The first pressure regulator 431 adjusts the pressure of the gas supplied to the center of the adsorption surface 2a, thereby adjusting the pressure of the heat transfer gas between the adsorption plate 2 and the central portion W1 which is a non-measurement target area of ​​the wafer W. The second pressure regulator 432 adjusts the pressure of the heat transfer gas between the adsorption plate 2 and the peripheral portion W2 which is a measurement target area of ​​the wafer W, by adjusting the pressure of the heat transfer gas supplied to the peripheral portion of the adsorption surface 2a.

[0039] Furthermore, each of the pressure regulators 431, 432 can adjust the pressure of the heat transfer gas to change the heat transfer rate from the suction plate 2 to the wafer W (the heat transfer coefficient between the wafer W and the suction plate 2). Fig. 3 shows the relationship between the pressure of the heat transfer gas supplied between the wafer W and the suction plate 2 and the heat transfer coefficient between the wafer W and the suction plate 2. The heat transfer coefficient in this embodiment has a nonlinear relationship depending on the pressure of the heat transfer gas, but may have a linear relationship.

[0040] Specifically, each pressure regulator 43 has a pressure sensor and a pressure control valve, and the valve opening degree of the pressure control valve is controlled by a pressure control unit 12 which is a gas control unit of the control device CTL, which will be described later.

[0041] 2, the wafer temperature control device 100 includes a temperature sensor 5 for measuring the temperature of the peripheral portion W2, which is a predetermined measurement target region of the wafer W, or the vicinity thereof. The temperature sensor 5 in this embodiment is an infrared sensor such as a radiation thermometer that measures the temperature of the peripheral portion W2 of the wafer W. When a radiation thermometer is used as the temperature sensor 5, it is considered that the temperature of the peripheral portion W2 of the wafer W is measured through an optical window provided in a side wall of the vacuum chamber. The temperature sensor 5 may be provided on the base plate 31a or the suction plate 2 and may measure the temperature of the base plate 31a or the suction plate 2 as the temperature in the vicinity of the wafer W.

[0042] <3. Wafer temperature control system> Furthermore, the wafer temperature control apparatus 100 includes a control device CTL that controls the operations of at least the temperature regulator 3 and the pressure regulators 431 and 432 .

[0043] The control device CTL is a so-called computer equipped with a CPU, a memory, an A / D converter, a D / A converter, and various input / output devices. A wafer temperature control program stored in the memory is executed, and various devices cooperate to configure a wafer temperature control system as shown in Figs. 4 and 5.

[0044] First, the wafer temperature control system of this embodiment will be outlined with reference to FIGS.

[0045] In this embodiment, the estimated temperatures T W1_est , T W2_est , and the measured temperature T of the peripheral portion W2 measured by the temperature sensor 5 W2_measRegardless of the temperature, the valve opening degree of the control valve 31e of the cooler 31 is controlled to be constant. That is, the cooling operation amount is fixed during operation, and the temperature adjustment amount per unit time by the temperature regulator 3 is controlled to be constant.

[0046] In contrast, the pressure regulators 431 and 432 adjust the estimated temperatures T W1_est , T W2_est , and the measured temperature T of the peripheral portion W2 measured by the temperature sensor 5 W2_meas The input pressure manipulation amount is successively changed based on the above.

[0047] Specifically, the control device CTL uses the observer 10 to measure the temperature T W2_meas Based on this, the temperatures T W1_est , T W2_est Then, the control device CTL estimates the estimated temperatures T W1_est , T W2_est By feeding back each estimated temperature T W1_est , T W2_est is each target temperature T W1_SET , T W2_SET The pressure regulators 431 and 432 are controlled to follow the pressures.

[0048] More specifically, the control device CTL controls the temperature T W1_est , T W2_est and a target temperature T W1_SET , T W2_SET and the estimated temperatures T W1_est , T W2_est and a pressure control section 11 that feedback-controls the pressure regulators 431 and 432 based on the above.

[0049] <3-1.Observer 10> The observer 10 simulates at least the thermal behavior of the system and measures the temperature T W1_est , T W2_est This is an estimate of the following.

[0050] Specifically, the observer 10 detects the measured temperature T W2_meas and the pressures P output by the pressure regulators 431 and 432. W1_OUT , P W2_OUT Based on this, the estimated temperature T W1_est and the estimated temperature T W2_est and

[0051] Specifically, the observer 10 detects the temperature T W1 and the temperature T of the peripheral area W2 W2 A temperature estimation model 10a is a linear or nonlinear state space model having an output variable, and an estimated temperature T of the central part W1 estimated based on the temperature estimation model 10a. W1_est The first temperature output unit 10b outputs the estimated temperature T W2_est and an observer gain 10d.

[0052] The observer 10 then outputs the estimated temperature T W2_est and the measured temperature T of the peripheral portion W2 measured by the temperature sensor 5. W2_meas The deviation from the temperature estimating model 10a is multiplied by an observer gain 10d, and the result is fed back to the temperature estimating model 10a.

[0053] The temperature estimation model 10a is a model of, for example, the heat conduction regarding the suction plate 2 and the wafer W themselves, and the heat transfer between the suction plate 2 and the wafer W.

[0054] This temperature estimation model 10a estimates at least the temperature TW and the pressure of the heat transfer gas P HG In this embodiment, the state space model of the temperature estimation model 10a is a nonlinear model that is the same as a prediction model (controlled object model) of the pressure control unit 11 described later, as shown in FIG. 7. The input variables of the temperature estimation model 10a in this embodiment are each pressure P W1_OUT , P W2_OUT (P1, P2 in FIG. 7) as well as the amount of cooling by the cooler 31 (the temperature T p ) or the amount of heat (q in FIG. 7) supplied to the wafer W from an external source (for example, plasma).

[0055] Specifically, the temperature estimation model 10a estimates the pressures P W1_OUT , P W2_OUTT The input variable vector including the above is input, and the estimated temperature T W1_est and the estimated temperature T of the surrounding area W2 W2_est The output is a state variable vector containing

[0056] The first temperature output unit 10b estimates the estimated temperature T W1_est and outputs it to the pressure control unit 11.

[0057] The second temperature output unit 10c estimates the temperature T W2_est The estimated temperature T of the outputted peripheral area W2 is W2_est and the measured temperature T of the peripheral area W2 measured by the temperature sensor 5. W2_meas The deviation from this is calculated and input to the observer gain 10d.

[0058] <3-2. Pressure control unit 11> The pressure control unit 11 controls the target temperature T SET and the estimated temperature T estimated by observer 10. W1_est , T W2_estBased on this, the pressure of the heat transfer gas P is calculated by model predictive control. HG The pressure regulator 431, 432 is used to control the pressure regulators 431, 432 that adjust the pressure.

[0059] Here, model predictive control is a control method for performing optimization while predicting future responses at each time, as shown in FIG. 6, and by having a prediction model (controlled object model) inside the pressure control unit 11, it predicts the future behavior of the controlled object over a finite interval from the current time.

[0060] In FIG. 6, the target command r(t) is the target temperature of each of the central portion W1 and the peripheral portion W2 of the wafer W, the control input u(t) is a pressure control amount which is a gas control amount input to each of the pressure regulators 431 and 432, and the control output y(t) is the estimated temperature T W1_est , T W2_est The estimated temperature T W1_est , T W2_est is applied to a prediction model inside the pressure control unit 12, and a new control input u(t) is determined in an optimizer so as to minimize the tracking error from the current time to a specified time.

[0061] The controlled object model used in this model predictive control is shown in FIG. 7. The controlled object model in this embodiment has two concentric heating zones, a circular heating zone (Zone 1) located in the central part W1 and an annular heating zone (Zone 2) located in the peripheral part (outer periphery) W2. As described above, the controlled object model used in the model predictive control is a nonlinear model similar to the temperature estimation model 10a of the observer 10. In this suction plate 2, the target temperature of the heating zone in the central part W1 is T W1_SET The target temperature of the heating area of ​​the peripheral part W2 is T W2_SET In addition, in Fig. 8, the reference trajectory and the predicted trajectory are shown without distinguishing between the two different regions.

[0062] In the control model shown in Fig. 7, the wafer temperature TW1 and the wafer temperature T in Zone 2 W2 The change over time in can be expressed by the heat radiation to the outside, the heat transfer between zones, the heat transfer between layers, and the heat supply from the outside. Note that the heat radiation is proportional to the fourth power of the temperature, but this term itself is a small value, so here it is expediently expressed as the first power to simplify the calculation.

[0063] Specifically, as described above, the pressure control unit 12 calculates the heat transfer coefficient between the suction plate 2 and the wafer W as a prediction model (control target model) of the model predictive control using the pressure P HG More specifically, the pressure control unit 12 uses a model in which the variables are calculated from the estimated temperatures T W1_est , T W2_est and the target temperature T W1_SET , T W2_SET Based on this, the pressure manipulation amount input to each of the pressure regulators 431, 432 is controlled by model predictive control.

[0064] Here, the pressure control unit 12 controls the pressure manipulation amount using a state equation in which the coefficient matrix (A matrix) of the state vector includes the pressures P1 and P2 of the heat transfer gas as parameters in the model predictive control. Here, the reason why the coefficient matrix (A matrix) of the state vector includes the pressures P1 and P2 of the heat transfer gas is that the heat transfer coefficients α1 (P1) and α2 (P2) between the wafer and the chucking plate change depending on the pressures P1 and P2 of the heat transfer gas.

[0065] Specifically, the pressure control unit 12 uses the state equation shown in FIG. In this state equation, the coefficient matrix (A matrix) multiplied by the state vector is a matrix indicating the thermal conductivity and heat capacity of each divided area (zone), and includes the heat transfer coefficients α1 (P1) and α2 (P2) between the wafer W and the suction plate 2, which are determined from the pressures P1 and P2 of the heat transfer gas. In addition, the coefficient matrix (B matrix) multiplied by the input vector in the state equation is a matrix indicating the coefficients for converting the heat transfer coefficients α1 (P1) and α2 (P2) between the wafer and the suction plate, and the amounts of heat (power) q1 and q2 injected from the plasma into temperature changes. Furthermore, the reference trajectory in the model predictive control indicates an ideal trajectory that exponentially approaches the set temperature from the current temperature, as shown in Figure 8.

[0066] Then, the pressure control unit 12 calculates a coefficient matrix (A matrix) every time a predicted trajectory regarding the temperature of the wafer W is calculated in the model predictive control, and calculates the next predicted trajectory using the coefficient matrix (A matrix) updated by the calculation.

[0067] Specifically, the pressure control unit 12 calculates a predicted trajectory obtained from a state equation as shown in Figures 9 and 10, and more specifically, calculates the predicted trajectory using a predicted value based on a free response and a predicted value based on a step response.

[0068] The predicted value based on the free response indicates the trajectory for the next Np steps if the current (time k) inputs P1(k) and P2(k) remain unchanged.

[0069] The predicted value by the step response is the trajectory for the future Np steps and the current temperature T W1 (k), T W2 This shows the difference (change) from (k).

[0070] Here, since the inputs P1(k) and P2(k) are updated sequentially, they must be calculated every hour. The inputs P1(k) and P2(k) used for the predicted values ​​based on this step response are the pressure manipulation amounts input to the pressure regulators 431 and 432 or the pressures adjusted by the pressure regulators 431 and 432.

[0071] Then, as shown in Fig. 11, the pressure control unit 12 determines the pressure manipulation amount so as to minimize the evaluation function using the weighted least squares method regarding the deviation between the reference trajectory regarding the temperature of the wafer W and the predicted trajectory regarding the temperature of the wafer W in the model predictive control. In addition, in order to prevent the occurrence of hunting in the evaluation function, terms r1 and r2 that reduce the pressure are added, and these terms r1 and r2 are made as small as possible. By using the weighted least squares method as the evaluation function in this way, iterative calculation is not required, and the amount of calculation can be reduced. In addition, when the evaluation function cannot be analytically solved due to constraints such as constraint conditions, a method for exploratory solution such as the shooting method, gradient descent method, or Newton's method may be used.

[0072] <4. Experimental and Simulation Results> 12 shows experimental results and simulation results when the temperature of the wafer W is controlled using the wafer temperature control device 100 of this embodiment. In the experiment, the amount of heat supplied to the wafer W from the outside was reproduced using a halogen lamp.

[0073] In both results, the estimated temperatures T W1_est , T W2_est and the target temperature T W1_SET , T W2_SET Based on this, the pressure control amount input to each pressure regulator 431, 432 is controlled by model predictive control, thereby enabling the temperatures of the central portion W1 and the peripheral portion W2 of the wafer W to be accurately controlled to the target temperature. It can also be seen that the observer 10 is able to estimate the amount of heat injected into the wafer W (injected power). In FIG. 12, q is a fixed amount of heat (set value), and q estis the estimated heat quantity.

[0074] 13 shows a simulation result in the above experiment or simulation in which a disturbance is generated on the wafer W. The disturbance on the wafer W is reproduced by changing the amount of heat supplied from the outside to the wafer W (power shift).

[0075] In the results of this simulation, even if a disturbance occurs, the estimated temperature T W1_est , T W2_est and the target temperature T W1_SET , T W2_SET Based on this, the pressure manipulation amount input to each of the pressure regulators 431, 432 is controlled by model predictive control, thereby enabling the temperatures of the central portion W1 and the peripheral portion W2 of the wafer W to be accurately controlled to the target temperature. In other words, the wafer temperature control device 100 of this embodiment is capable of robust control even against disturbances from plasma or the like that injects heat into the wafer.

[0076] <5. Effects of this embodiment> As described above, according to the wafer temperature control device 100 of the present embodiment, the temperature of the non-measurement area (center area W1) of the wafer W is estimated using the observer 10, which uses the measured temperature of the measurement area (periphery area W2) of the wafer W and the pressure of the heat transfer gas as input variables, so that the temperature of the non-measurement area (center area W1) of the wafer W can be estimated with sufficient accuracy. Also, based on the estimated temperature of the non-measurement area (center area W1) estimated by the observer 10 and the target temperature of the wafer W, the pressure manipulation amount input to each pressure regulator 431, 432 is controlled by model predictive control, so that it becomes easy to incorporate the non-linear behavior of the heat transfer coefficient from the suction plate 2 to the wafer W, and the temperature of the non-measurement area (center area W1) of the wafer W can be accurately controlled to the target temperature.

[0077] In this way, by combining the observer 10 and model predictive control (MPC control), it is possible to precisely control the temperature of the non-measurement target area (center area W1) of the wafer W simply by measuring the temperature of the measurement target area (peripheral area W2) of the wafer W. In other words, by merely measuring the temperature of one location on the wafer, it is possible to precisely control the temperatures of other locations, improving practicality. In addition, by combining the observer 10 and model predictive control (MPC control), it is possible to achieve robust control even against disturbances from plasma or the like that inject heat into the wafer W.

[0078] <6. Other embodiments> For example, in the above embodiment, the temperature sensor 5 measures the temperature of the peripheral portion W2 of the wafer W, but it may measure the temperature in the vicinity of the peripheral portion W2 of the wafer W. In this case, the observer 10 calculates the temperature measured by the temperature sensor (proximal temperature) and the pressure manipulated variable input to the pressure regulators 431 and 432 or the pressure P W1_OUT , P W2_OUT Based on this, the temperatures of the central portion W1 and the peripheral portion W2 of the wafer W are estimated.

[0079] In addition, the pressure control unit 11 of the embodiment estimates the temperature T W1_est , T W2_est The pressure regulators 431 and 432 are controlled by MPC using the estimated temperature T W1_est and the measured temperature T of the surrounding area W2 W2_meas Each pressure regulator 431, 432 may be MPC controlled using the above.

[0080] Furthermore, in the above embodiment, the area to be measured is the peripheral portion W2 and the area to be non-measured is the central portion W1, but the opposite may also be true, or the area to be measured may be any location on the wafer and the area to be non-measured may be any location other than the area to be measured.

[0081] In the above embodiment, the suction plate 2 has multiple regions with different target temperatures for the wafer W set by varying the pressure of the heat transfer gas across the surface of the suction plate 2. However, it is also possible to set a single target temperature across the entire suction plate 2 without varying the pressure of the heat transfer gas across the surface of the suction plate 2.

[0082] The temperature adjustment region of the wafer W and the suction plate 2 is not limited to being divided into two regions (a central region and a peripheral region), and may be divided into a larger number of regions.

[0083] Furthermore, the suction plate 2 may not have a suction function and may simply be a plate on which the wafer W is placed.

[0084] The wafer temperature control device 100 of the above embodiment controls the temperature of the wafer W by adjusting the pressure of the heat transfer gas using the pressure regulators 431 and 432, but the temperature of the wafer W can also be controlled by adjusting the flow rate of the heat transfer gas. For this reason, the wafer temperature control device 100 includes a flow rate regulator, which is a gas regulator that adjusts the flow rate of the heat transfer gas, a temperature sensor 5 that measures the temperature of a predetermined measurement target area W2 of the wafer W or its vicinity, an observer 10 that estimates the temperature of a non-measurement target area W1 different from the measurement target area W2 of the wafer W based on the measured temperature of the temperature sensor 5 and a flow rate manipulated variable that is a gas manipulated variable input to the flow rate regulator or a flow rate adjusted by the flow rate regulator, and a flow rate control unit, which is a gas control unit that controls the flow rate manipulated variable input to the flow rate regulator by model predictive control based on the estimated temperature of the non-measurement target area W1 estimated by the observer 10 and the target temperature of the wafer W.

[0085] The configuration of the cooler or heater is not limited to those described above. For example, the cooler may be configured using a Peltier element, and the heater is not limited to a heater electrode, but may be configured to heat the wafer by light irradiation, or may be configured to heat the wafer by plasma.

[0086] In addition, various modifications and combinations of the embodiments may be made without departing from the spirit of the present invention. [Explanation of symbols]

[0087] 100 Wafer temperature control device W: Wafer W1: Center (non-measurement area) W2: Periphery (measurement area) 2. Adsorption plate (plate) 3...Temperature regulator 43 Pressure regulator (gas regulator) 431 First pressure regulator (first gas regulator) 432 Second pressure regulator (second gas regulator) 5. Temperature Sensor 10. Observer 11 Pressure control section (gas control section)

Claims

1. A wafer temperature control device is provided, wherein a wafer is placed on a temperature-controlled plate, and a gas is supplied between the plate and the wafer to control the temperature of the wafer, A gas regulator for adjusting the pressure or flow rate of the aforementioned gas, A temperature sensor that measures the temperature of a predetermined measurement target area or its vicinity on the wafer, An observer that estimates the temperature of a non-measurement target region of the wafer, which is different from the measurement target region, based on the temperature measured by the temperature sensor and the gas operation amount input to the gas regulator or the pressure or flow rate adjusted by the gas regulator, A wafer temperature control device comprising a gas control unit that controls the amount of gas input to the gas regulator by model predictive control based on the estimated temperature of the non-measurement target area estimated by the observer and the target temperature of the wafer.

2. The observer estimates not only the temperature of the non-measured area but also the temperature of the measured area. The wafer temperature control device according to claim 1, wherein the gas control unit controls the amount of gas operation input to the gas regulator by model predictive control based on the estimated temperature of the measurement target area, the estimated temperature of the non-measurement target area and the target temperature of the wafer.

3. The aforementioned gas regulator is It includes a first gas regulator for adjusting the gas pressure or flow rate between the plate and the non-measurement target region of the wafer, A second gas regulator for adjusting the gas pressure or flow rate between the plate and the measurement target region of the wafer, The gas control unit, Based on the estimated temperature of the measurement target area, the estimated temperature of the non-measurement target area, and the target temperature of the non-measurement target area, the first gas operation amount input to the first gas regulator is controlled by model predictive control. The wafer temperature control device according to claim 2, wherein the second gas operation amount input to the second gas regulator is controlled by model predictive control based on the estimated temperature of the measurement target area, the estimated temperature of the non-measurement target area and the target temperature of the measurement target area.

4. The wafer temperature control device according to any one of claims 1 to 3, wherein the observer uses a state-space model in which the heat transfer coefficient between the plate and the wafer is a variable determined from the gas pressure.

5. The wafer temperature control device according to any one of claims 1 to 3, wherein the gas control unit uses a model in which the heat transfer coefficient between the plate and the wafer is a variable obtained from the gas pressure as the prediction model for the model prediction control.

6. The measurement target area is the peripheral part of the wafer, The wafer temperature control device according to any one of claims 1 to 3, wherein the non-measurement target region is the central part of the wafer.

7. The wafer temperature control device according to any one of claims 1 to 3, wherein the temperature sensor is a radiation temperature sensor.

8. The wafer temperature control device according to any one of claims 1 to 3, wherein the observer estimates the amount of heat supplied to the wafer from the outside.

9. A wafer temperature control method comprising placing a wafer on a temperature-controlled plate and supplying gas between the plate and the wafer to control the temperature of the wafer, The pressure or flow rate of the aforementioned gas is adjusted by a gas regulator. The temperature of a predetermined area of ​​the wafer or its vicinity is measured using a temperature sensor. Based on the temperature measured by the temperature sensor and the amount of gas input to the gas regulator or the pressure or flow rate adjusted by the gas regulator, the observer is used to estimate the temperature of a non-measurement target area of ​​the wafer that is different from the measurement target area. A wafer temperature control method that controls the amount of gas input to the gas regulator by model predictive control based on the estimated temperature of the non-measurement target region estimated by the observer and the target temperature of the wafer.

10. A wafer temperature control program used in a wafer temperature control device, which controls the temperature of a wafer by placing the wafer on a temperature-controlled plate and supplying gas between the plate and the wafer, and which includes a gas regulator for adjusting the pressure or flow rate of the gas and a temperature sensor for measuring the temperature of a predetermined measurement target area of ​​the wafer or its vicinity, Based on the temperature measured by the temperature sensor and the amount of gas manipulated input to the gas regulator or the pressure or flow rate adjusted by the gas regulator, the observer functions to estimate the temperature of a non-measurement target area of ​​the wafer that is different from the measurement target area. A wafer temperature control program that provides a computer with the function of a gas control unit that controls the amount of gas input to the gas regulator by model predictive control based on the estimated temperature of the non-measurement target area estimated by the observer and the target temperature of the wafer.

Images