DESCRIPTION
TEMPERATURE MEASURING METHOD AND APPARATUS AND SEMICONDUCTOR HEAT TREATMENT APPARATUS
TECHNICAL FIELD
The present invention relates to a temperature measurement technique using a radiation thermometer and, more particularly, to a temperature measuring method and apparatus for measuring a temperature of a measuring object by a non-contact method.
BACKGROUND ART
In a heat treatment of a semiconductor wafer and the like, it is necessary to accurately measure a temperature of the heated semiconductor wafer. A temperature measuring apparatus using a contact method such as a thermocouple cannot be used for measuring a temperature of a semiconductor wafer on which semiconductor circuits are actually formed. Therefore, in a heat treatment apparatus for semiconductor wafers, a radiation thermometer is normally used to measure a temperature of a semiconductor wafer.
A radiation thermometer measures an intensity of an infrared light radiated from a surface of a measuring object, and estimates the temperature of the measuring object from the measured intensity. An intensity of infrared light emitted from a semiconductor wafer changes with the emissivity of the radiation surface of the semiconductor wafer. For example, an oxide film is formed on the radiation surface of the semiconductor wafer, and such an oxide film has an emissivity different from the emissivity of the surface of the semiconductor wafer at an
initial stage of heating.
Therefore, a measuring method which is independent of emissivity of a radiation surface and a measuring method which corrects emissivity have been suggested, as mentioned below.
1) Irradiate a reference light having a predetermined intensity onto a measuring object (semiconductor wafer) , and measure an intensity of the reference light reflected by the measuring object so as to obtain an actual emissivity. That is, an actual emissivity is obtained according to the relationship (emissivity = reflection factor - 1) so as to obtain a temperature of the measuring object using the thus- obtained emissivity. 2) Establish more than two states of effective emissivity, and obtain an emissivity by calculating a solution of simultaneous equations containing the emissivity representing different states. A temperature of a measuring object can be obtained by calculation using the thus-obtained emissivity. United States Patent No. 5,660,472 discloses this approach.
3) Form a multiple reflection structure with a measuring object so as to bring an effective emissivity close to 1. For example, a semiconductor wafer as a measuring object is arranged so that a light radiated from the semiconductor wafer is reflected between the semiconductor wafer and a placement stage multiple times , and obtain a temperature of the measuring object by calculation based on an intensity of the multiple- reflected radiation light. Namely, temperature is calculated by assuming a measuring object as a pseudo blackboby (emissivity = 1) . Examples of this approach are disclosed in United States Patents No. 6,174,080 and No.
6,293,696.
The above-mentioned temperature measuring method for a radiation thermometer has a problem in that a structure of the measuring apparatus is complicated and a manufacturing cost of the measuring apparatus is high. Moreover, there is a problem that the accuracy of the measured temperature cannot be high since reproducibility is low due to changes in the environment near the temperature measuring point and changes in the measurement system with passage of time, etc.
For example, the above-mentioned approach 1) , which irradiates a reference light having a predetermined intensity onto a ^{"}measuring object, requires an accurate control of a wavelength and an intensity of the reference light, but an apparatus for irradiating such an accurate reference light is expensive.
Additionally, although the above-mentioned approach 2) , which establishes more than two states of effective emissivity, can achieve a predetermined state of effective emissivity by maintaining an environment near the temperature measuring point, it is difficult to maintain the environment near the temperature measuring point always unchanged. Moreover, if there is a change in the measurement system with passage of time, it is difficult to maintain an accurate temperature measurement due to an influence of the change with passage of time.
Further, although the approach 3) , which forms a multiple reflection structure with a measuring object, requires multiple reflection between a body having a reflectance equal to 1 and the measuring object, there is not such a body having a reflectance equal to 1 in practice. Accordingly, calculation must be carried out by assuming a body having a reflectance not equal to 1 as a
body having a reflectance equal to 1 , which causes an inevitable error being included in a temperature obtained by the calculation.
DISCLOSURE OF INVENTION
It is an object of the present invention to provide an improved and useful temperature measuring method and apparatus in which the above-mentioned problems are eliminated. A more specific object of the present invention is to provide a temperature measuring method and apparatus that can accurately measure a temperature of a measuring object according to a non-contact manner without using a complicated hardware structure, and to provide a semiconductor heat treatment apparatus using such a temperature measuring method.
In order to achieve the above-mentioned objects, there is provided according to one aspect of the present invention a temperature measuring method for measuring a temperature of a measuring object according to a non- contact manner, comprising the steps of: measuring a radiation light radiated from the measuring object; obtaining a state variable according to estimate algorithm calculation based on a result of measurement of the radiation light, the state variable including an effective emissivity as an unknown variable; and calculating the temperature of the measuring object based on the calculated state variable.
In the temperature measuring method according to the present invention, the step of obtaining the state variable may include a step of inputting an energy value used for heating the measuring object so as to calculate the state variable based on a heat balance model having an
input as the energy value and an output as the result of measurement of the radiation light, the state variable further including the temperature of the measuring object as an unknown variable. The estimate algorithm calculation may be an extended Kalman filter algorithm obtained by extending a Kalman filter into a nonlinear system.
Additionally, there is provided according to another aspect of the present invention a temperature measuring apparatus for measuring a temperature of a measuring object according to a non-contact manner, comprising: measuring means for measuring a radiation light radiated from the measuring object; state value obtaining means for obtaining a state variable according to estimate algorithm- calculation based on a result of measurement of the radiation light, the state variable including an effective emissivity as an unknown variable; and temperature calculating means for calculating the temperature of the measuring object based on the calculated state variable.
In the temperature measuring apparatus according to the present invention, said state value obtaining means may include inputting means for inputting an energy value used for heating the measuring object so as to calculate the state variable based on a heat balance model having an input as the energy value and an output as the result of measurement of the radiation light, the state variable further including the temperature of the measuring object as an unknown variable. The estimate algorithm calculation may be an extended Kalman filter algorithm obtained by extending a Kalman filter into a nonlinear system.
Further, there is provided according to another
aspect of the present invention a semiconductor heat treatment apparatus for applying a heat treatment to a semiconductor substrate, comprising; heating means for heating the semiconductor substrate; a radiation thermometer for measuring a temperature of the semiconductor substrate, the radiation thermometer comprising measuring means for measuring a radiation light radiated from the heated semiconductor substrate, state variable obtaining means for obtaining a state variable according to estimate algorithm calculation based on a result of measurement of the radiation light, the state variable including an effective emissivity as an unknown variable, and temperature calculating means for calculating the temperature of the measuring object based on the calculated state variable; and control means for controlling the energy supplied to said heating means based on the temperature calculated by said temperature calculating means .
In the semiconductor heat treatment apparatus according to the present invention, said state variable obtaining means may include inputting means for inputting an energy value used for heating the measuring object so as to calculate the state variable based on a heat balance model having an input as the energy value and an output as the result of measurement of the radiation light, the state variable further including the temperature of the measuring object as an unknown variable. The estimate algorithm calculation may be an extended Kalman filter algorithm obtained by extending a Kalman filter into a nonlinear system.
According to the above-mentioned invention, a temperature of the measuring object is obtained by estimating an effective emissivity by calculation, and,
therefore, there is no need to take an actual measurement of the effective emissivity. That is, the temperature of the measuring object can be obtained by merely measuring an intensity of radiation of the measuring object. For this reason, a hardware structure for measuring an effective emissivity is unnecessary, and a corresponding manufacturing cost can be reduced.
An estimation of the effective emissivity and a calculation of the temperature of the measuring object are carried out in accordance with the estimation algorithm calculation of a state variable including the effective emissivity and the temperature of the measuring object as unknown variables based on a heat balance model . Such an algorithm can be easily established. Moreover, calculation means can be easily attained by performing the estimation algorithm with an extended Kalman filter.
Other objects , features and advantages of the present invention will become more apparent from the following detailed description when read in conjunction with the accompanying drawings.
BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 is a cross-sectional view of a semiconductor heat treatment apparatus according to an embodiment of the present invention;
FIG. 2 is a functional block diagram of a radiation thermometer shown in FIG. 1 ;
FIG. 3 is a schematic diagram of a heat balance model used as a base of a calculation performed by the radiation thermometer; and
FIG. 4 is a block diagram showing a process of estimating a temperature and an effective emissivity of a semiconductor wafer.
BEST MODE FOR CARRYING OUT THE INVENTION
A description will now be given, with reference to FIG. 1, of a semiconductor heat treatment apparatus according to an embodiment of the present invention. FIG. 1 is a cross-sectional view of the semiconductor heat treatment apparatus according to the embodiment of the present invention. The heat treatment apparatus shown in FIG. 1 is a rapid thermal processing (RTP) apparatus that applies a rapid thermal process to a semiconductor wafer placed in an RTP chamber.
The heat treatment apparatus 1 shown in FIG. 1 is an apparatus that applies a heat treatment to a semiconductor wafer 3 by carrying out rapid heating of the semiconductor wafer 3 with a heat ray from halogen lamps 2 at 1000 °C. The halogen lamps 2 are attached to a halogen lamp house 4. The halogen lamp house 4 is provided with an electric-power adjustment circuit (not shown) that attach adjusts an electric power supplied to the halogen lamp 2.
The semiconductor wafer 3 is accommodated in a chamber 5, and is subjected to a heat treatment. A quartz support ring 6 is arranged inside the chamber 5, and a guard ring 7 is attached on the quartz support ring 6. The semiconductor wafer 3 is placed on the guard ring 6 in a state in which a peripheral part of the semiconductor wafer 3 is supported by the guard ring 6. Therefore, a back surface of the semiconductor wafer 3 other than the peripheral part faces a bottom plate 8 with a small gap therebetween.
The bottom plate 8 is formed of a material having a high reflectance so as to reflect a radiation light from the heated semiconductor wafer 3 and return the
radiation light to the semiconductor wafer 3 so that the semiconductor wafer 3 is heated efficiently. A quartz rod 11 connected to a radiation thermometer 10 through an optical fiber 9 is embedded in a predetermined position of the bottom plate 8. The quartz rod 11 receives a radiation light from the semiconductor wafer 3 , and the radiation light received by the quartz rod 11 is supplied to the radiation thermometer 10 through the optical fiber 9. The radiation thermometer 10 measures an intensity of the radiation light of the semiconductor wafer 3 in accordance with the radiation light supplied through the optical fiber 9 , and obtains a temperature of the semiconductor wafer 3 by calculation based on a result of the measurement. That is, the radiation thermometer 10 calculates the temperature of the semiconductor wafer 3 based on the result of measurement of the radiation light of the semiconductor wafer 3.
The radiation thermometer 10 supplies the temperature of the semiconductor wafer 3 obtained by the calculation to a control unit 13 via a connection line 12. The control unit 13 serves as control means for controlling an operation of the heat treatment apparatus 1 , and is connected to the electric-power adjustment circuit provided in the halogen lamp house 4. The electric-power adjustment circuit controls an electric power supplied to the halogen lamp 2 according to a control signal from the control unit 13. Thereby, heating of the semiconductor wafer 3 by the halogen lamps 2 is controlled, and the semiconductor wafer 3 is heated or maintained at a predetermined temperature .
A description will now be given, with reference to FIG. 2, of the radiation thermometer 10 shown in FIG. 1.
FIG. 2 is a functional block diagram of the radiation thermometer 10 shown in FIG. 1. The radiation thermometer 10 has a radiation light measuring part 20 and a calculating part 22. The optical fiber 9 is connected to the radiation light measuring part 20, and the radiation light from the semiconductor wafer 3 is supplied to radiation light measuring part 20 through the optical fiber 9. The radiation light measuring part 20 measures . various items containing an intensity of the radiation light supplied through the optical fiber 9, and supplies the result of measurement to the calculating part 22.
The calculating part 22 obtains the temperature of the semiconductor wafer 3 by calculation based on the result of measurement supplied from the radiation light measuring part 20. The temperature of the semiconductor wafer 3 is supplied to the control part 13 through the connection line 12. Moreover, the value of the electric power to be supplied to the lamps 2 is supplied from the control part 13 to the calculating part 22 through the connection line 12.
Next, a description will be given of a temperature estimating method, which is a base of a calculation of the temperature performed by the calculating part 22. The temperature estimating method is performed based on an apparatus model with respect to heat balance of the semiconductor wafer 3 as a measuring object.
FIG. 3 is a schematic diagram of a heat balance model used as a base of the calculation performed by the calculating part 22 of the radiation thermometer 10. In the heat balance model shown in FIG. 3, an amount of heat transfer with respect to the wafer is represented by the following equation (1) , where Δ is a discrete time interval.
Δ^{Q} = * A_{l}{-(β_{i}θ_{1} +εβ_{2})σT?(t)
-k_{ϊ}(T_{i}(t) -T_{i}__{1}(t)) ~k_{2}(T_{i}(t) -T_{i+l}(t))
In equation (1) , the subscript i indicates the i-th element of the semiconductor wafer 3 when the semiconductor wafer 3 is divided into a plurality of concentric rings, and Ai represents an area of the i-th element. ki and k_{2} represent coefficients relate to heat transfer, and σ is a Stefan-Boltzmann constant. Additionally, ε_{x} represents an emissivity of the reflector 4a of the halogen lamp house 4, and ε_{2} represents an emissivity of the surface of the bottom surface 8, which faces the semiconductor wafer 3. θi is an effective emissivity in consideration of the multiple reflection of the surface of the simiconductor wafer 3, which faces the lamps 2 , and θ_{2} is an effective emissivity in consideration of the multiple reflection of the surface of the semiconductor wafer 3, which faces the bottom plate 8.
Moreover, in equation (1) , u is an input (for example, a current supplied to the lamp) to a halogen lamp, and an energy of the radiation light travels from the halogen lamp 2 to the semiconductor wafer 3 is represented by a function g(u) . The first term in equation (1) expresses a heat which escapes by radiation from both the front and back sides of the semiconductor wafer, the second term expresses an amount of heat transferred between the element i-1 and the element i+1 , and the third term expresses an amount of heat input from a halogen lamp.
Additionally, a temperature of the i-th element is represented by the following equation (2) , where Mci is
a heat capacity of the i-th element.
Ti(t+1) = Ti(t)+ΔQ/MCi (2)
Furthermore, the intensity of the radiation light measured by the radiation thermometer is expressed by the following equation (3) using the Planck's law, where h is a Planck's constant, c is a velocity of light, k_{B} is a Boltzmann constant and λ is a measured wave length.
According to the above-mentioned equations (1) ,
(2) and (3) , the extended Kalman filter, which calculates a temperature of a semiconductor wafer while estimating an effective emissivity, can be designed by setting effective emissivities θi and θ_{2} of the front and back sides of the semiconductor wafer as unknown values and setting the temperature of the semiconductor wafer as a state variable. FIG. 4 is a block diagram showing a process of estimating the effective emissivity and the temperature of the semiconductor wafer in practice. The Kalman .filter is an on-line data algorithm which gives sequentially a least squares estimate value of a state of a system in accordance with 1) a dynamic characteristic of a system producing a signal, 2) a statistical characteristic of noise, and 3) priori information with respect to an initial value and observation data given according to passage of ime.
Suppose that a difference equation of a linear system can be expressed by the following equation (4)
using an input u , an output y, and a state x .
y_{t} = C_{t}x_{t} + v_{t} 'A)
An estimated value ^{Λ} of the state x according the Kalman filter is given by the following equation (5) .
^{x}»υt = A^{χ}u_{t} +^{B}t^{u}t +^{κ} _{t}(y_{t} - c_{t} ^{χ}ut ^{( 5 )}
Where, t is a time in a discrete time system, and Kt is a value referred to as a Kalman gain. The Kalman gain Kt is represented by the following equation (6) by using a covariance analysis matrix P_{/t} - ι = E{ [x_{t}- x t/t-ιI [ ~x /-ι]^{T}} of an error (x_{t}-x^{Λ}t/t -I) of an estimated value and a covariance analysis matrix Rt of noise entering an output.
^{K}ι = ^{P}tlt-\^{C}t C^{T}P C^{1} + «r (6
The Kalman filter is designed based on a linear system like a formula (4) . An extended Kalman filter is linearized near an operating point so as to extend the Kalman filter to a non-linear system. That is, the Kalman filter can be designed for a system having a known operating characteristic. However, when an unknown constant is contained, the unknown value is reselected as a variable so as to establish a difference equation of the system, and, thereby, an adaptive filter using the algorithm of the extended Kalman filter can be designed. When a system can be expressed by the following equation containing an unknown value θ, a state variable x in the difference equation (7) of the system is
substituted by z as represented by equation (8) so as to obtain equation (9) .
x_{t+l} = A(θ )x_{t} + B(θ)u_{[} + w_{l}
(7) y_{t} = C(θ)x_{t} + V_{t}
= f(x_{t},θ) + w_{t} = f(z_{t}) + w_{t}
Then, the state value x (e.g., a temperature of the semiconductor wafer) can be obtained by calculation while estimating the unknown value θ by applying equation (9) to the algorithm of an extended Kalman filter.
It should be noted that coefficients A, B and C in the above-mentioned formula (4) are determined based on comparison of results of various experiments using a blackbody furnace .
As mentioned above, in the present embodiment, a temperature of the semiconductor wafer 3 can be obtained while estimating an emissivity of the semiconductor wafer 3, by using an extended Kalman filter for the calculating part 22 of the radiation thermometer 10.
When a temperature of a bare wafer, which was heated to about 600°C at a heating rate of 10 °C/sec, was measured using the radiation thermometer according to the present embodiment, an error with respect to a temperature measured by a thermocouple was about ±10°C.
As mentioned above, the radiation thermometer according to the present embodiment can obtain a
temperature very close to an actual temperature, by merely measuring an intensity of a radiation light. For this reason, a hardware structure of the radiation thermometer is simplified, and the radiation thermometer can be manufactured at a cost of about 1/4 of a manufacturing cost of the conventional radiation thermometer that actually measures an emissivity.
The present invention is not limited to the specifically disclosed embodiment, and variations and modifications may be made without departing from the scope of the present invention.