Plasma electron temperature measuring method and device
View Patent ↗A laser beam with a wavelength capable of exciting atoms of helium in the metastable state is directed to a generated plasma, and atoms in the metastable state are excited. Absorption amount information representing the amount of laser beam absorbed is acquired, and the density of atoms of helium in the metastable state in the plasma is computed from the absorption amount. The emissions of light from helium gas in the plasma caused by transition from two different excited states to the lower level are measured, and the ratio between the intensities of the emissions is determined. The electron temperature of the produced plasma is computed from the computed density of the atoms of helium gas in the metastable state and the computed emission intensity ratio. With this, the plasma electron temperature can be computed with a relatively high accuracy irrespective of the condition of the plasma atmosphere.
1. A method of measuring electron temperature of generated plasma, comprising the steps of:
providing at least helium gas to a predetermined container to generate plasma in the predetermined container;
irradiating laser light, by using a laser irradiation device, to the generated plasma, the laser light having wavelength which is capable of exciting atoms of the helium gas in a metastable state, to excite the atoms in the metastable state;
obtaining absorption amount information, by using a laser irradiation device, representing an amount of the laser light absorbed by the atoms in the metastable state;
computing density of the atoms of the helium gas in the metastable state in an irradiation area of the laser light in the plasma based on the absorption amount information by using a computer;
measuring each of light emissions, by using a camera, due to level transition processes from two different excited states of the helium gas in the plasma to a state having an energy level lower than an energy level of the excited states and computing an emission intensity ratio between the light emissions; and
computing electron temperature of the generated plasma based on the emission intensity ratio and the computed density of the atoms of the helium gas in the metastable state by using the computer.
2. The method of measuring plasma electron temperature according to claim 1 , further comprising the steps of:
irradiating laser light to the generated plasma, by using the laser irradiation device, the laser light having wavelength which is capable of exciting the atoms of the helium gas in the metastable state, to excite the atoms in the metastable state; and
obtaining information of a distribution of induced fluorescence intensity, by the camera in the irradiation area along a path of the laser light, the induced fluorescence intensity representing intensity of induced fluorescence from the atoms in the metastable state, the induced fluorescence being caused by irradiation of the laser light, and
wherein, in the step of computing density of the atoms in the metastable state, a distribution of density of the atoms in the metastable state in the irradiation area along the path of the laser light is at least computed based on the absorption amount information and the information of the distribution of the induced fluorescence intensity.
3. The method of measuring plasma electron temperature according to claim 1 , wherein,
in the step of computing density of the atoms of the helium gas in the metastable state, density of the atoms in each of states 2 1 S 0 and 2 3 S 1 is computed as the density of the atoms in the metastable states, and
in the step of computing the emission intensity ratio, the emission intensity ratio is computed by measuring a light emission due to level transition processes from a state 4 3 D to a state 2 3 P 0 , corresponding to a wavelength of 447 nm and a light emission due to a level transition process from a state 3 3 D to the state 2 3 P 0 , corresponding to a wavelength of 588 nm.
4. The method of measuring plasma electron temperature according to claim 1 , wherein,
in the step of the computing density of the atoms in the metastable state, density of the atoms in each of states 2 1 S 0 and 2 3 S 1 is computed as the density of the atoms in the metastable state, and
in the step of computing the emission intensity ratio, the emission intensity ratio is computed by measuring a light emission due to a level transition process from a state 4 3 S to a state 2 3 P 0 , corresponding to a wavelength of 471.6 nm, and a light emission due to a lower level transition process from a state 3 3 S to the state 2 3 P 0 , corresponding to a wavelength of 706. 5nm.
5. The method of measuring plasma electron temperature according to claim 1 , wherein,
in the step of computing the electron temperature, the plasma electron temperature is computed using the following formula (1),
k
ex
0
A
n
0
+
∑
m
=
1
k
exm
A
n
m
k
ex
0
B
n
0
+
∑
m
=
1
k
exm
B
n
m
=
A
A
A
B
·
n
A
*
n
B
*
I
A
I
B
=
g
A
g
B
·
λ
B
λ
A
·
A
i
A
·
n
A
*
A
i
B
·
n
B
*
}
(
1
)
and wherein, in the formula (1),
each of numerals relates to the atoms of the helium gas in the plasma;
“I A ” represents a measured value of intensity of the light emission due to a lower level transition process from a first excited state A to a state having an energy level lower than an energy level of the first excited state A, whereas “I B ” represents a measured value of intensity of the light emission due to a level transition process from a second excited state B to a state having an energy level lower than an energy level of the second excited state B;
“A i A ” represents an Einstein A-coefficient of the light emission due to the level transition process from the first excited state A to a state having an energy level lower than an energy level of the first excited state A, whereas “A i B ” represents an Einstein A-coefficient of the light emission due to the level transition process from the second excited state B to a state having an energy level lower than an energy level of the second excited state B;
“A A ” represents an inverse of a radiative lifetime of the atoms in the first excited state A to a state having an energy level lower than an energy level of the first excited state A, which is represented by the sum of Einstein A-coefficients in a plurality of natural transition processes from the first excited state A, whereas “A B ” represents an inverse of a radiative lifetime of the atoms in the second excited state B, which is represented by the sum of Einstein A-coefficients in a plurality of natural transition processes from the second excited state B;
“n m ” represent the computed density of the atoms in the m-th metastable state; “n 0 ” represents density of the atoms in a ground state;
“n A * ” represents density of the atoms in the first excited state A; and “n B * ” represents density of the atoms in the second excited state B;
“k A ex0 ” represents an electron impact excitation rate constant from the ground state to the first excited state A, whereas “k A eXm ” represents an electron impact excitation rate constant from the m-th metastable state to the first excited state A;
“k B ex0 ” represents an electron impact excitation rate constant from the ground state to the second excited state B, whereas “k B exm ” represents an electron impact excitation rate constant from the m-th metastable state to the second excited state B, and “k A ex0 ,” “k A exm ,” “k B ex0 ” and “k B exm ” are functions of the plasma electron temperature;
“g A , g B ” are functions of wavelengths λ A and λ B , each representing solid angle and quantum efficiency of an observation system in each of the excited states A and B, and “λ A , λ B ” are wavelengths of light to be measured in the excited states A and B.
6. The method of measuring plasma electron temperature according to claim 5 , wherein the rate constant k a exb to be used in the step of computing the electron temperature is represented by the following formula (2) and the plasma electron temperature is computed using the formula (1),
k exb a =∫vσ exb ( v ) f ( v ) dv (2)
and wherein, in the formula (2),
“a” represents “A” or “B”, whereas “b” represents “0” or “m”; and
“σ a exb ” represents cross section in each of the excitation processes; “v” represents electron velocity; and “f(v)” represents an electron velocity distribution function.
7. The method of measuring plasma electron temperature according to claim 1 , wherein,
in the step of obtaining the absorption amount information, transmittance of the laser light irradiated to the plasma is obtained as the absorption amount information representing the amount of absorption of the laser light.
8. The method of measuring plasma electron temperature according to claim 7 , wherein,
in the step of obtaining the absorption amount information, transmittance I t /I 0(m) of the laser light is computed by obtaining intensity I 0 of laser light to be irradiated to the plasma for exciting the atoms in the m-th metastable state and intensity I t of the laser light which has transmitted through the plasma,
in the step of computing the density of the atoms of the helium gas in the metastable state, density n m of the atoms of the helium gas in the metastable state in the plasma is computed based on the transmittance I t /I 0(m) of the laser light and the following formula (3),
I t /I 0(m) =exp {−σ exm ( v ) n cl I} (3)
and wherein, in the formula (3),
“σ exm ” represents absorption cross section of the atoms in the m-th metastable state;
“I” represents length of a transmitting path of the laser light through the plasma; and
“n m ,” represents density of the atoms in the m-th metastable state.