Determining the temperature of silicon at high temperatures
View Patent ↗The temperature of an object such as a semiconductor wafer that includes silicon can be determined based on the variation of the optical absorption coefficient of silicon with temperature. Temperatures above about 850° C., can be found by measuring phenomena that are affected by the magnitude of the optical absorption coefficient, especially at wavelengths >˜1 μm. Phenomena could include measuring light reflected, transmitted, emitted, absorbed, or scattered by the wafer and deriving the absorption coefficient from the measurements and then deriving temperature from the absorption coefficient. Temperature could be determined from a model relating phenomena directly to temperature, the model constructed based on absorption behavior and techniques discussed herein. The resulting temperature could be used to calibrate or control a rapid thermal processing chamber or other apparatus.
1. A method for estimating the temperature of a wafer, the method comprising:
placing a wafer comprising silicon proximate at least one measurement device;
performing a measurement that can be used to determine an absorption coefficient, α, of said silicon comprising the wafer at a first wavelength, λ;
determining a value for said absorption coefficient, α, of said silicon at said wavelength, λ; and
calculating an estimate of the wafer temperature, wherein said estimate takes a value that lies between a lower limit, T−δT and an upper limit T+δT;
wherein δT is less than or equal to 30 K, and
T =(−1210.8+1863.6λ−506.84λ 2 )α 0.46449−0.38607λ+0.10584λ 2 ,
when the value of T is in degrees Centigrade, the value of said wavelength, λ, is in units of microns, and the value of said absorption coefficient, α, is in units of cm −1 .
2. The method set forth in claim 1 , wherein:
performing a measurement comprises measuring a transmittance of the wafer at the first wavelength; and
the value of the absorption coefficient of the silicon is determined from the transmittance.
3. The method set forth in claim 1 , wherein:
performing a measurement comprises measuring a reflectance of the wafer at the first wavelength; and
the value of the absorption coefficient of the silicon is determined from the reflectance.
4. The method set forth in claim 1 , wherein:
performing a measurement comprises measuring an emittance of the wafer at the first wavelength; and
the value of the absorption coefficient of the silicon is determined from the emittance.
5. The method set forth in claim 1 , wherein:
performing a measurement comprises measuring an absorptance of the wafer at the first wavelength; and
the value of the absorption coefficient of the silicon is determined from the absorptance.
6. The method set forth in claim 1 , wherein the value of said absorption coefficient, α, is greater than about 300 cm −1 .
7. The method set forth in claim 1 , wherein the first wavelength lies between about 1.2 and about 2.4 μm.
8. The method set forth in claim 1 , wherein the first wavelength lies within 0.1 μm of one of the following wavelengths: 1.31, 1.54, and 2.3 μm.
9. The method set forth in claim 1 , wherein the estimate of wafer temperature is greater than 850° C.
10. The method set forth in claim 1 , wherein placing a wafer comprising silicon proximate at least one measurement device comprises placing the wafer into a thermal processing chamber, the at least one measurement device configured to perform measurements of one or more properties of objects in the chamber.
11. The method set forth in claim 10 , wherein:
the thermal processing chamber comprises a second measurement device configured to perform measurements of one or more properties of objects in the chamber; and
the method further comprises calibrating the at least one second measurement device based on the calculated estimate of wafer temperature.
12. The method set forth in claim 11 , wherein the second measurement device comprises a pyrometer.
13. The method set forth in claim 1 , wherein δT is less than or equal to 5 K.
14. The method set forth in claim 1 , wherein calculating an estimate of the wafer temperature comprises evaluating an expression substantially in the form of:
T =(−1210.8+1863.6λ−506.84λ 2 )α 0.46449−0.38607λ+0.10584λ 2
wherein T represents the value of the estimated temperature in degrees Centigrade, the value of said wavelength, λ, is in units of microns, and the value of said absorption coefficient, α, is in units of cm −1 .
15. A method for estimating the temperature of a wafer, the method comprising:
placing a wafer comprising silicon proximate at least one measurement device;
performing a measurement that can be used to determine an absorption coefficient, α, of said silicon comprising the wafer at a first wavelength, λ;
determining a value for said absorption coefficient, α, of said silicon at said wavelength, λ; and
calculating an estimate of the wafer temperature, T;
wherein the calculated value of T is in degrees centigrade and is such that the value of the determined absorption coefficient, α, in units of cm −1 , differs from that of a value of α calc by no more than 30% when λ calc is determined by an expression having the following form when the value of said wavelength, λ, is in units of microns:
α
calc
=
[
135
(
1.24
λ
)
+
0.07
T
-
168
]
2
+
8.2869
×
10
-
6
λ
1.5
(
T
+
273
)
3.1867
exp
(
-
7000
T
+
273
)
.
16. The method set forth in claim 15 , wherein calculating an estimate of the wafer temperature T is based on providing said absorption coefficient into an expression of temperature as a function of α, the expression of temperature as a function of a representing a solution of the following equation for T:
α
=
[
135
(
1.24
λ
)
+
0.07
T
-
168
]
2
+
8.2869
×
10
-
6
λ
1.5
(
T
+
273
)
3.1867
exp
(
-
7000
T
+
273
)
.
17. The method set forth in claim 15 , wherein:
performing a measurement comprises measuring a transmittance of the wafer at the first wavelength; and
the value of the absorption coefficient of the silicon is determined from the transmittance.
18. The method set forth in claim 15 , wherein:
performing a measurement comprises measuring a reflectance of the wafer at the first wavelength; and
the value of the absorption coefficient of the silicon is determined from the reflectance.
19. The method set forth in claim 15 , wherein:
performing a measurement comprises measuring an emittance of the wafer at the first wavelength; and
the value of the absorption coefficient of the silicon is determined from the emittance.
20. The method set forth in claim 15 , wherein:
performing a measurement comprises measuring an absorptance of the wafer at the first wavelength; and
the value of the absorption coefficient of the silicon is determined from the absorptance.
21. The method set forth in claim 15 , wherein the value of said absorption coefficient, α, is greater than about 300 cm −1 .
22. The method set forth in claim 15 , wherein the first wavelength lies between about 1.2 and about 2.4 μm.
23. The method set forth in claim 15 , wherein the first wavelength lies within 0.1 μm of one of the following wavelengths: 1.31, 1.54, and 2.3 μm.
24. The method set forth in claim 15 , wherein the estimate of wafer temperature is greater than 850° C.
25. The method set forth in claim 15 , wherein placing a wafer comprising silicon proximate at least one measurement device comprises placing the wafer into a thermal processing chamber, the at least one measurement device configured to perform measurements of one or more properties of objects in the chamber.
26. The method set forth in claim 25 , wherein:
the thermal processing chamber comprises a second measurement device configured to perform measurements of one or more properties of objects in the chamber; and
the method further comprises calibrating the at least one second measurement device based on the calculated estimate of wafer temperature.
27. The method set forth in claim 26 , wherein the second measurement device comprises a pyrometer.