Apparatus and method for controlling temperature uniformity of substrate
An apparatus for controlling temperature uniformity of the disclosure includes a heater to supply a heat source to a substrate, a temperature sensor to generate temperature data of the substrate, a heating controller to present a distribution of a heat source based on the temperature data, and a heat source-electricity converter to calculate an amount of electricity to generate a heat source based on the distribution of a heat source and to supply the calculated amount of electricity to the heater. Since a method and an apparatus of the disclosure for controlling temperature uniformity uses a heat source and electricity having a linear relationship, problems of high costs and deterioration of an apparatus may be overcome that a typical method has to control an amount of electricity in a heater by temperature information.
1. An apparatus for controlling temperature uniformity, comprising:
a heater to supply a heat source to a substrate;
a temperature sensor to generate temperature data of the substrate;
a heating controller to present a distribution of a heat source based on the temperature data; and
a heat source-electricity converter to calculate an amount of electricity to generate a heat source based on the distribution of a heat source and to supply the calculated amount of electricity to the heater,
wherein the heat source-electricity converter calculates the amount of electricity based on a loss of a thermal energy occurring in a heat transfer process from the heater to the substrate and the distribution of a heat source from the heating controller.
2. The apparatus for controlling temperature uniformity of claim 1 ,
wherein the heating controller presents the distribution of a heat source by using a numerical model below.
Δ t=t i+1 −t i
Δ q i+1 [( X i+1 ) T ( X i+1 )+α I ] −1 ( X i+1 ) T ( V i+1 − Y i+1 )
q i+1 =q i +Δq i+1
Ŷ i+1 =Y i +X i+1 Δq i+1
(t i : present time, t i+1 : future time, Δt: interval of measurement, q i+1 : future heat source vector for controlling, V i+1 : target temperature vector, Y i : measured temperature vector, Ŷ i+1 : estimated temperature vector for future, Y i+1 : virtual temperature vector when Y i is constantly heated by q i , α: parameter for adjusting stability against noises of measured temperature, X i+1 : sensitivity coefficient matrix).
3. The apparatus for controlling temperature uniformity of claim 2 ,
wherein the heat source-electricity converter calculates the amount of electricity by inputting data of a distribution of a heat source input from the heating controller in a linear model below.
[
A
1
q
1
i
+
1
A
2
q
2
i
+
1
⋮
A
M
q
M
i
+
1
]
=
[
λ
1
Q
1
i
+
1
λ
2
Q
2
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λ
M
Q
M
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(M: the number of heaters, A i (i=1, . . . , M): heated area of each heater, Q i (i=1, . . . , M): an amount of electricity input in a heater, λ i (i=1, . . . , M): a compensation coefficient).
4. The apparatus for controlling temperature uniformity of claim 3 ,
wherein the heat source-electricity converter accumulates data of the measured temperature vector and the estimated temperature vector and corrects the compensation coefficient when a least squares error that is calculated by accumulated data exceeds a predetermined range.
5. The apparatus for controlling temperature uniformity of claim 1 ,
wherein the heating controller estimates an entire temperature distribution based on the temperature data and presents the distribution of a heat source based on the entire temperature distribution.
6. A method for controlling temperature uniformity, comprising:
a generating operation to generate temperature data of a substrate;
a presenting operation to present a distribution of a heat source based on the temperature data;
a calculating operation to calculate an amount of electricity to generate a heat source based on the distribution of a heat source; and
a supplying operation to supply the calculated amount of electricity to a heater generating the heat source,
wherein the calculating operation calculates the amount of electricity based on a loss of a thermal energy occurring in a heat transfer process from the heater to the substrate and the distribution of a heat source from the heating controller.
7. The method for controlling temperature uniformity of claim 6 ,
wherein the distribution of a heat source is generated by using a numerical model below.
Δ t=t i+1 −t i
Δ q i+1 [( X i+1 ) T ( X i+1 )+α I ] −1 ( X i+1 ) T ( V i+1 − Y i+1 )
q i+1 =q i +Δq i+1
Ŷ i+1 =Y i +X i+1 Δq i+1
(t i : present time, t i+1 : future time, Δt: interval of measurement, q i+1 : future heat source vector for controlling, V i+1 : target temperature vector, Y i : measured temperature vector, Ŷ i+1 : estimated temperature vector for future, Y i+1 : virtual temperature vector when Y i is constantly heated by q i , α: parameter for adjusting stability against noises of measured temperature, X i+1 : sensitivity coefficient matrix).
8. The method for controlling temperature uniformity of claim 7 ,
wherein the amount of electricity is calculated by inputting data of the distribution of a heat source in a linear model below.
[
A
1
q
1
i
+
1
A
2
q
2
i
+
1
⋮
A
M
q
M
i
+
1
]
=
[
λ
1
Q
1
i
+
1
λ
2
Q
2
i
+
1
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λ
M
Q
M
i
+
1
]
(M: the number of heaters, A i (i=1, . . . , M): heated area of each heater, Q i (i=1, . . . , M): an amount of electricity input in a heater, λ i (i=1, . . . , M): a compensation coefficient).
9. The method for controlling temperature uniformity of claim 8 , further comprising:
an accumulating operation to accumulate data of the measured temperature vector and the estimated temperature vector; and
a correcting operation to correct the compensation coefficient when a least squares error calculated by accumulated data exceeds a predetermined range.
10. The method for controlling temperature uniformity of claim 6 , further comprising:
an estimating operation to estimate an entire temperature distribution of the substrate based on the temperature data,
wherein the presenting operation to present the distribution of a heat source generates the distribution of a heat source based on the estimated and entire temperature distribution.
11. The method for controlling temperature uniformity of claim 10 ,
wherein the estimating operation comprises,
a building operation to build a numerical model for a form and a thermal behavior of the substrate;
a setting operation to set a regularization parameter to adjust a measured temperature of the substrate;
a generating operation to generate a sensitivity coefficient matrix that estimates a heat source received by the substrate from a plurality of heaters;
a condensing operation to condense the sensitivity coefficient matrix based on a power ratio input in the heaters respectively; and
an estimating operation to estimate an entire temperature distribution of the substrate based on the numerical model, the regularization parameter, and the condensed sensitivity coefficient matrix, when predetermined temperature data are input.