Non-contact temperature measurement of a film growing on a substrate

Claim 1

Apparatus for controlling the temperature of a surface of a film-substrate composite while the film is undergoing a change in thickness, comprising: heater apparatus for heating the film-substrate composite; detector apparatus for detecting radiance from the surface of the film-substrate composite and generating an electronic radiance signal corresponding to the detected radiance; computing apparatus including means for generating an electronic temperature signal which corresponds to the temperature of the surface of the film-substrate composite, said generating means converting the electronic radiance signal to the electronic temperature signal by use of a radiance/temperature relation comprising: ##EQU5## where: S(t) is the electronic radiance signal at time t, ε(λ,t) is the emissivity function at wavelength λ and time t and depends on the film thickness d 1 , where d 1 changes with time, T(t) is the real temperature of the film-substrate composite, T b is the equivalent blackbody temperature of the film-substrate composite, e b is the blackbody hemispherical emissive power, λ 1 and λ 2 are the lower and upper wavelength limits, R(λ) is the spectral responsivity, where R(λ)=R d (λ)τ o (λ), R d (λ) is the electronic radiance signal of the detector apparatus per unit energy, where R d (λ)=dS/dΦ, τ o (λ) is the spectral transmittance of all optical elements, Φ is the radiance energy arriving at the detector apparatus per unit time, t is time, λ is the wavelength of the radiance, and C is a geometric constant based on the detector apparatus and is independent of wavelength; and control apparatus responsive to the electronic temperature signal for controlling the output of the heater apparatus to cause the temperature of the surface of the film-substrate composite to approach a predetermined value.

Claim 3

A method for controlling the temperature of a surface of a film-substrate composite while the film is undergoing a change in thickness, comprising: providing a substrate; heating the substrate with a heater apparatus; applying a film to a surface of the substrate to obtain a film-substrate composite; detecting radiance from the surface of the film-substrate composite and generating an electronic radiance signal corresponding to the detected radiance; generating an electronic temperature signal, which corresponds to the temperature of the surface of the film-substrate composite, from the electronic radiance signal, wherein a radiance/temperature relation comprises: ##EQU6## where: S(t) is the electronic radiance signal at time t, ε(λ,t) is the emissivity function at wavelength λ and time t and depends on the film thickness d 1 , where d 1 changes with time, T(t) is the real temperature of the film substrate composite, T b is the equivalent blackbody temperature of the film-substrate composite, e b is the blackbody hemispherical emissive power, λ 1 and λ 2 are the lower and upper wavelength limits, R(λ) is the spectral responsivity, where R(λ)=R d (λ)τ o (λ), R d (λ) is the electronic radiance signal of the detector apparatus per unit energy, where R d (λ)=dS/dΦ, τ o (λ) is the spectral transmittance of all optical elements, Φ is the radiance energy arriving at the detector apparatus per unit time, t is time, λ is the wavelength of the radiance, and C is a geometric constant based on the detector apparatus and is independent of wavelength; and controlling the output of the heater apparatus with the electronic temperature signal to cause the temperature of the surface of the film-substrate composite to approach a predetermined value.

Claim 4

A method for controlling the temperature of a surface of a film-substrate composite while the film is undergoing a change in thickness, comprising: providing a substrate; heating the substrate with a heater apparatus; applying a film to a surface of the substrate to obtain a film-substrate composite; detecting radiance from the surface of the film-substrate composite and generating an electronic radiance signal corresponding to the detected radiance; generating an electronic temperature signal, which corresponds to the temperature of the surface of the film-substrate composite, from the electronic radiance signal, wherein a radiance/temperature relation comprises: ##EQU6## where: S(t) is the electronic radiance signal at time t, ε(λ,t) is the emissivity function at wavelength λ and time t and depends on the film thickness d 1 , where d 1 changes with time, T(t) is the real temperature of the film substrate composite, T b is the equivalent blackbody temperature of the film-substrate composite, e b is the blackbody hemispherical emissive power, λ 1 and λ 2 are the lower and upper wavelength limits, R(λ) is the spectral responsivity, where R(λ)=R d (λ)τ o (λ), R d (λ) is the electronic radiance signal of the detector apparatus per unit energy, where R d (λ)=dS/dΦ, τ o (λ) is the spectral transmittance of all optical elements, Φ is the radiance energy arriving at the detector apparatus per unit time, t is time, λ is the wavelength of the radiance, and C is a geometric constant based on the detector apparatus and is independent of wavelength; and controlling the output of the heater apparatus with the electronic temperature signal to cause the temperature of the surface of the film-substrate composite to approach a predetermined value.

Claim 7

A method for controlling the temperature of a surface of a film-substrate composite while the film is undergoing a change in thickness, comprising: providing a substrate; heating the substrate with a heater apparatus; applying a film to a surface of the substrate to obtain a film-substrate composite; detecting radiance from the surface of the film-substrate composite and generating an electronic radiance signal corresponding to the detected radiance; generating an electronic temperature signal, which corresponds to the temperature of the surface of the film-substrate composite, from the electronic radiance signal, wherein a radiance/temperature relation is used which includes an emissivity function ε which varies with the wavelength of the radiance and the film thickness and depends on the reflectance R of the film-substrate composite, the emissivity function ε comprising: ##EQU8## and where: n 1 is the complex refractive index of the film defined by n 1 =n 1 -ik 1 , n 2 is the complex refractive index of the substrate defined by n 2 =n 2 -ik 2 , d 1 is the film thickness which varies over time t, k 1 is the extinction coefficient of the film, k 2 is the extinction coefficient of the substrate, r 1 is the Fresnel coefficient of a film-vacuum interface, r 2 is the Fresnel coefficient of the film-substrate interface, δ 1 is the phase change across the thickness of the film, and λ is the wavelength of the detected radiance; and controlling the output of the heater apparatus with the electronic temperature signal to cause the temperature of the surface of the film-substrate composite to approach a predetermined value.

Claim 8

A method for controlling the temperature of a surface of a film-substrate composite while the film is undergoing a change in thickness, comprising: providing a substrate; heating the substrate with a heater apparatus; applying a film to a surface of the substrate to obtain a film-substrate composite; detecting radiance from the surface of the film-substrate composite and generating an electronic radiance signal corresponding to the detected radiance; generating an electronic temperature signal, which corresponds to the temperature of the surface of the film-substrate composite, from the electronic radiance signal, wherein a radiance/temperature relation is used which includes an emissivity function ε which varies with the wavelength of the radiance and the film thickness and depends on the reflectance R of the film-substrate composite, the emissivity function ε comprising: ##EQU8## and where: n 1 is the complex refractive index of the film defined by n 1 =n 1 -ik 1 , n 2 is the complex refractive index of the substrate defined by n 2 =n 2 -ik 2 , d 1 is the film thickness which varies over time t, k 1 is the extinction coefficient of the film, k 2 is the extinction coefficient of the substrate, r 1 is the Fresnel coefficient of a film-vacuum interface, r 2 is the Fresnel coefficient of the film-substrate interface, δ 1 is the phase change across the thickness of the film, and λ is the wavelength of the detected radiance; and controlling the output of the heater apparatus with the electronic temperature signal to cause the temperature of the surface of the film-substrate composite to approach a predetermined value.