Thermal imaging for semiconductor process monitoring
First Claim
1. A method for determining the temperature T at at least one location on the surface of a sample, comprising the steps:
- (a) measuring, at an oblique take-off angle and at at least one wavelength v, radiance at at least two linearly independent polarizations p1 and p2;
(b) computing a polarized radiance ratio Rp1(v)/Rp2(v) of said measured radiances Rp1(v), Rp2(v) to determine the associated polarized emissivity ratio ε
p1(v)/ε
p2(v), in accordance with the relationship Rp1(v)/Rp2(v)=ε
p1(v)ε
p2(v);
(c) applying at least one additional constraint to compute the value of at least one of the emissivities, ε
p1(v), ε
p2(v), constituting said polarized emissivity ratio;
(d) determining the temperature T at said one location by solving the equation;
Rp1(v,T)=ε
p1(vT)×
P(v,T),wherein P(v,T) is the Planck function;
(e) irradiating said surface with radiation including said wavelength v, and measuring reflectance ρ
from said surface at said wavelength v and said polarizations p1 and p2 to thereby determine the reflectance-derived ratio 1−
ε
p1(v)/1−
ε
p2(v); and
(f) applying said reflectance-derived ratio as said at least one additional constraint in said step (c) for computing said at least one emissivity value.
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Abstract
The method measures the temperature, emissivity, and other properties of relatively smooth surfaces radiating thermal energy, and is especially adapted for monitoring semiconductor fabrication processes. Temperature is determined by relating measured radiance to the predictions of the Planck radiation law, using knowledge of the emissivity determined from an analysis of the polarization of the thermally emitted radiance. Additional information regarding the properties of thin films, such as thickness and composition, can be computed from the emissivity or the ratio of the emissivities measured at two independent polarizations. Because the data are obtained from the intrinsic thermal radiance, rather than from an extrinsic light source, the measurement can be performed when it is inconvenient or impossible to provide a light source for reflectance measurements.
19 Citations
19 Claims
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1. A method for determining the temperature T at at least one location on the surface of a sample, comprising the steps:
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(a) measuring, at an oblique take-off angle and at at least one wavelength v, radiance at at least two linearly independent polarizations p1 and p2; (b) computing a polarized radiance ratio Rp1(v)/Rp2(v) of said measured radiances Rp1(v), Rp2(v) to determine the associated polarized emissivity ratio ε
p1(v)/ε
p2(v), in accordance with the relationship Rp1(v)/Rp2(v)=ε
p1(v)ε
p2(v);(c) applying at least one additional constraint to compute the value of at least one of the emissivities, ε
p1(v), ε
p2(v), constituting said polarized emissivity ratio;(d) determining the temperature T at said one location by solving the equation;
Rp1(v,T)=ε
p1(vT)×
P(v,T),wherein P(v,T) is the Planck function; (e) irradiating said surface with radiation including said wavelength v, and measuring reflectance ρ
from said surface at said wavelength v and said polarizations p1 and p2 to thereby determine the reflectance-derived ratio 1−
ε
p1(v)/1−
ε
p2(v); and(f) applying said reflectance-derived ratio as said at least one additional constraint in said step (c) for computing said at least one emissivity value. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A method for determining the emissivity ε
- at at least one location on the surface of a sample, comprising the steps;
(a) measuring, at an oblique take-off angle and at at least one wavelength v, radiance at at least two linearly independent polarizations p1 and p2; (b) computing a polarized radiance ratio Rp1(v)/Rp2(v) of said measured radiances Rp1(v), Rp2(v) to determine the associated polarized emissivity ratio ε
p1(v)/ε
p2(v), in accordance with the relationship Rp1(v)/Rp2(v)=ε
p1(v)/ε
p2(v);(c) applying at least one additional constraint to compute the value of at least one of the emissivities, ε
p1(v), ε
p2(P), constituting said polarized emissivity ratio;(d) irradiating said surface with radiation including said wavelength v, and measuring reflectance ρ
from said surface at said wavelength v and said polarizations p1 and p2 to thereby determine the reflectance-derived ratio 1−
ε
p1(v)/1−
ε
p2(v); and(e) applying said reflectance-derived ratio as said at least one additional constraint in said step (c) for computing said at least one emissivity value. - View Dependent Claims (9, 10)
- at at least one location on the surface of a sample, comprising the steps;
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11. Apparatus for determining at least one emissivity value ε
- from a surface of a sample, comprising a radiance sensor including a radiation detector, polarization selective means, wavelength selective means, and electronic data processing means, said sensor being configured for carrying out the following steps;
(a) measuring, at an oblique take-off angle and at at least one wavelength v, radiance at at least two linearly independent polarizations p1 and p2; (b) computing a polarized radiance ratio Rp2(v)/Rp2(v) of said measured radiances Rp1(v), Rp2(v) to determine the associated polarized emissivity ratio ε
p1(v)/ε
p2(v), in accordance with the relationship Rp1(v)/Rp2(v)=ε
p1(v)/ε
p2(v);(c) applying at least one additional constraint to compute the value of at least one of the emissivities, ε
p1(v), ε
p2(v), constituting said polarized emissivity ratio;(d) measuring reflectance ρ
from said surface at said wavelength v and said polarizations p1 and p2 to thereby determine the reflectance-derived ratio 1−
ε
p1(v)/1−
ε
p2(v); and(e) applying said reflectance-derived ratio as said at least one additional constraint in said step (c) for computing said at least one emissivity value. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19)
- from a surface of a sample, comprising a radiance sensor including a radiation detector, polarization selective means, wavelength selective means, and electronic data processing means, said sensor being configured for carrying out the following steps;
Specification