JP2011047828A - Creation method of calibration curve of light scattering type particle size measuring device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a creation method of a calibration curve enabling a light scattering type particle size measuring device to measure simply the accurate particle size even in the case of particles having a small particle size. <P>SOLUTION: In this creation method of the calibration curve of the light scattering type particle size measuring device, each scattering intensity of particles having two kinds of known particle sizes D<SB>1</SB>, D<SB>2</SB>(D<SB>1</SB><D<SB>2</SB>≤105 nm) is measured respectively by the light scattering type particle size measuring device, and α, β and γ are determined, which satisfy expressions: I<SB>1</SB>=α×(D<SB>1</SB>)<SP>γ</SP>, I<SB>2</SB>=α×(D<SB>2</SB>)<SP>γ</SP>, and I<SB>1</SB>=β×(D<SB>1</SB>)<SP>6</SP>, by using the scattering intensity I<SB>1</SB>of the particle having the particle size D<SB>1</SB>, and the scattering intensity I<SB>2</SB>of the particle having the particle size D<SB>2</SB>, and the calibration curve is created, wherein the particle size D and the scattering intensity I satisfy the expression: D=ä(I/α)<SP>-γ</SP>+(I/β)<SP>-6</SP>}/2 in a domain of the particle size D<D<SB>1</SB>. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a method for creating a calibration curve of a light scattering type particle size measuring device (hereinafter referred to as “light scattering type particle size measuring device”), and in particular, a light scattering type particle size measuring device, for example, having a particle size of The present invention relates to a method for creating a calibration curve that can be suitably used when measuring the particle diameter of fine particles of less than 40 nm.

  Conventionally, a light-scattering particle size measuring device is known as a device for measuring the particle size of particles by measuring and analyzing the intensity (scattering intensity) of scattered light generated when the particles are irradiated with laser light. .

  In the particle size measurement using the light scattering particle size measuring device, standard particles having different particle sizes are used for the range of particle sizes in which standard particles with known particle sizes (polystyrene latex (PSL) particles, etc.) are present. Then, a calibration curve (a calibration curve created by connecting the measured values of the scattering intensity of each standard particle) showing the relationship between the particle diameter and the scattering intensity is created in advance, and the scattering intensity of a sample with an unknown particle diameter is measured. Thus, it is generally performed to easily determine the particle diameter of a sample.

  Here, especially for free particles present in gas and liquid, the scattering intensity is proportional to the sixth power of the particle diameter at the so-called Rayleigh limit (the limit region where the particle diameter of the particle is sufficiently small with respect to the wavelength of the incident light). However, if the particle size is not negligible with respect to the wavelength of the incident light (however, the size is sufficiently smaller than the wavelength of the incident light), the particle diameter of the scattering intensity is used. It is known that the dependence on becomes weaker (smaller) than the sixth power. For this reason, with respect to a particle size range (for example, a range of less than 40 nm) that has a small particle size, no standard particles, and that is currently traceable for ensuring the tolerance of particle size industrially (for example, a range of less than 40 nm) Using a calibration curve proportional to the sixth power of the diameter, the particle diameter of the sample is obtained from the value of the scattering intensity when the sample having an unknown particle diameter is measured (for example, see Non-Patent Document 2). . For particles existing on a solid surface such as a substrate, depending on the incident angle of incident light (laser, etc.) used to the substrate and the configuration of the detector, the scattering intensity at the Rayleigh limit is not less than the sixth power of the particle diameter. Although it may be proportional to the size, the dependence of the scattering intensity on the particle diameter is weak in the range where the particle diameter is not negligible with respect to the wavelength of the incident light (laser light). .

S. Stokowski, Vaez-Iravani, “Characterization and Metrology for ULSI Technology”, page 405, 1998 Semiconductor Equipment and Materials International, “SEMI Draft Document 4583”, page 4, May 14, 2008

  However, as a result of investigation by the present inventor, the scattering intensity of a particle having a small particle diameter between the range of the particle diameter in which known standard particles exist and the Rayleigh limit is proportional to the sixth power of the particle diameter. It was revealed that there was a problem that the scattering intensity calculated by using the calibration curve in FIG.

An object of the present invention is to advantageously solve the above-described problems, and a method for creating a calibration curve for a light scattering particle size measuring device of the present invention is a light scattering particle size measuring device, which is divided into two types. known particle diameter _D 1, _{D 2 (where, D 1 <D 2 ≦ 105nm} ) was measured scattering intensity of the particles respectively, the scattering intensity _{I 1} of the particles having a particle diameter _{D 1,} the particle diameter _{D 2} of the particles by using the scattering intensity _{I 2,} the following formula (I) ~ (III):
I ₁ = α × (D ₁ ) ^γ (I)
I ₂ = α × (D ₂ ) ^γ (II)
I ₁ = β × (D ₁ ) ⁶ (III)
Α, β, and γ satisfying the above conditions are determined, and the particle diameter D and the scattering intensity I are expressed by the following formula (IV) in the region where the particle diameter D <D ₁
D = {(I / α) ^−γ + (I / β) ⁻⁶ } / 2 (IV)
Generating a calibration curve that satisfies:

Here, how to create a calibration curve of the light scattering particle diameter measurement device of the present invention, the particle diameter _{D 1} is 40 to 50 nm, it is preferable that the particle diameter _{D 2} is 50～105Nm.

Furthermore, in the method for creating a calibration curve of the light scattering particle size measuring apparatus of the present invention, the difference (D ₂ −D ₁ ) between the particle size D ₁ and the particle size D ₂ is preferably 20 nm or less. .

  And as for the preparation method of the calibration curve of the light-scattering type particle diameter measuring apparatus of this invention, it is preferable that the said particle diameter D is less than 40 nm. In particular, when the particle diameter is less than 40 nm, there is a problem with the size accuracy of the standard particles, and since the traceability for guaranteeing the tolerance of the particle diameter is not sufficient industrially, it is preferable to use the calibration curve prepared according to the preparation method of the present invention. It is.

  According to the present invention, a light-scattering particle size measuring device that makes it possible to easily measure an accurate particle size with a light-scattering particle size measuring device even for fine particles having a small particle size, particularly less than 40 nm. A calibration curve generation method can be provided.

It is a graph explaining the preparation method of the calibration curve of the light-scattering type particle diameter measuring device concerning the present invention.

  Hereinafter, embodiments of the present invention will be described in detail. Here, the method for creating a calibration curve of the light scattering particle size measuring device of the present invention is for creating a calibration curve used when measuring the particle size of a sample whose particle size is unknown with the light scattering particle size measuring device. Is the method. The light scattering particle size measuring device includes a device that measures both the particle size and the particle size distribution. In addition, the light scattering particle size measuring device is not particularly limited, and particles existing on a solid surface (for example, a flatly processed surface such as a silicon wafer or a glass substrate) in a gas, a liquid, or the like. It can be used for the particle size measurement.

Here, the calibration curve creation method of the present invention uses particles having a particle diameter of D ₁ and D ₂ (where D ₁ <D ₂ ≦ 105 nm) and particles having a particle diameter of D <D ₁ . This is to create a calibration curve to be applied to the measurement. Incidentally, when measuring the particle diameter of the sample particles径未knowledge using a light scattering particle diameter measuring apparatus is also required calibration curve to be applied to the measurement of the particle diameter D ≧ D _1, the particle size The calibration curve applied to the measurement of the particle of D ≧ D ₁ can be performed according to a known method. Specifically, particles having different particle sizes are measured with a light scattering type particle size measuring device, and the measured values of the scattering intensity of each particle are connected to obtain particles in a range of D ≧ D _1. A calibration curve showing the relationship between the diameter and the scattering intensity can be created.

Standard particles such as polystyrene latex (PSL) particles can be used as the particles with known particle sizes of D ₁ and D ₂ . A more in view to create the appropriate calibration curve, the particle diameter of the particles used is preferably _{D 2} is _{D 1} is 40~50nm is 50～105Nm _(where, D 1 _{<D 2)} . Also, _{D 1} and the difference between _{D 2 (D 2} -D ₁₎ is preferably 20nm or less. If the difference between D ₁ and D ₂ is 20 nm or less, the error when measuring the particle diameter using the created calibration curve can be reduced to, for example, 1% or less. This is because a (high) calibration curve can be created.

  In the calibration curve creation method of the present invention, the calibration curve is created, for example, in the following manner using the above-described standard particles and a known light scattering particle size measuring apparatus.

First, with a light scattering particle size measuring device that will use the created calibration curve, the scattering intensity of particles with known particle diameters D ₁ and D ₂ (where D ₁ <D ₂ ≦ 105 nm) is measured, a scattering intensity _{I 1} of the particles having a particle diameter _{D 1,} obtaining a scattering intensity _{I 2} of the particle diameter _{D 2} particles.

Next, α, β and γ satisfying the following formulas (I) to (III) are obtained.
I ₁ = α × (D ₁ ) ^γ (I)
I ₂ = α × (D ₂ ) ^γ (II)
I ₁ = β × (D ₁ ) ⁶ (III)
Note that γ is, for example, the following formula (V) obtained by dividing both sides of the formula (I) by both sides of the formula (II):
I ₁ / I ₂ = (D ₁ / D ₂ ) ^γ (V)
The logarithm of both sides of the formula (V) is taken as the following formula (VI), and the formula (VI) is rearranged into the formula (VII).
log (I ₁ / I ₂ ) = γlog (D ₁ / D ₂ ) (VI)
γ = log (I ₁ / I ₂ ) / log (D ₁ / D ₂ ) (VII)
Further, α can be obtained, for example, by rearranging the formula (I) into the following formula (VIII) and substituting γ obtained as described above.
α = I ₁ / (D ₁ ) ^γ (VIII)
Furthermore, β can be obtained by rearranging the formula (III) into the following formula (IX).
β = I ₁ / (D ₁ ) ⁶ (IX)

Finally, the region of the particle diameter D <D _1, to create a calibration curve and the particle diameter D, and a scattering intensity I satisfies the following formula (IV).
D = {(I / α) ^−γ + (I / β) ⁻⁶ } / 2 (IV)
In addition, it is preferable that the range of the particle diameter to which this calibration curve is applied is particularly an area of less than 40 nm.

Here, an example of a calibration curve created using the method described above is shown in FIG. Here, the measured line of FIG. 1 were prepared based on the results of actual measurement of the scattering intensity versus the different standard particles particle diameter D ₁ or more particle diameter, the measured values of the scattering intensity of each standard particles It is a connected line. Also, extrapolation of the formula (X): a line represented by I = α × D ^γ, theoretical line has the formula (XI): is a line expressed by I = β × ^{D 6.} Furthermore, the calibration curve of the present invention is an x-axis between an extrapolated line and a theoretical line represented by the formula (IV): D = {(I / α) ^−γ + (I / β) ⁻⁶ } / 2 (Axis of particle diameter D) is a line passing through the intermediate point in the direction. Α, β and γ can be obtained as described above.

In FIG. 1, particles measured with a light scattering particle size measurement apparatus using the calibration curve of the present invention in the range of particle size D <D _{1 and} the actual measurement line in the range of particle size D ≧ D _1. The particle diameter can be obtained from the scattering intensity of a sample with an unknown diameter. Here, in the so-called Rayleigh limit in the limit region where the particle diameter of the particles is sufficiently small with respect to the wavelength of the incident light, the scattering intensity is proportional to the sixth power of the particle diameter. In the non-negligible range, the dependence of the scattering intensity on the particle diameter gradually becomes weaker than the sixth power. Therefore, if a calibration curve created by the method according to the present invention and taking the middle between the extrapolated line and the theoretical line is used. Compared to the case where an extrapolation line or a theoretical line is used as a calibration curve, an accurate particle diameter can be obtained.

  The calibration curve creation method of the present invention can be modified as appropriate. Specifically, when creating a calibration curve used to measure the particle size of particles on a substrate, simulation is performed according to the incident angle of the incident light (laser) used to the substrate and the detector configuration, and the Rayleigh limit. The size dependence (the slope of the theoretical line in FIG. 1) is obtained, and a line passing through the intermediate point between the theoretical line and the extrapolated line in the x-axis (particle diameter D) direction may be used as the calibration curve.

  EXAMPLES Hereinafter, although an Example demonstrates this invention further in detail, this invention is not limited to the following Example at all.

The scattering intensity of PSL particles (manufactured by Duke) having particle diameters of 60 nm (D ₁ ) and 83 nm (D ₂ ) was measured using a light scattering particle size measuring apparatus. As a result, the scattering intensity (I ₁ ) of PSL particles having a particle diameter of 60 nm was 0.5814 (arbitrary unit), and the scattering intensity (I ₂ ) of PSL particles having a particle diameter of 83 nm was 3.1960 (arbitrary unit). It was. Then, α, β and γ were calculated from the values of D ₁ , D ₂ , I ₁ and I ₂ as described above. As a result, α = 1.568025 × 10 ⁻¹⁰ , β = 5.2519, and γ = 7.333025 × 10 ⁻¹² .

  Moreover, the scattering intensity of PSL particles (manufactured by Duke) having a particle diameter of 50 nm and 40 nm was measured using the same apparatus. As a result, the scattering intensity of PSL particles having a particle diameter of 50 nm was 0.2142 (arbitrary unit), and the scattering intensity of PSL particles having a particle diameter of 40 nm was 0.0570 (arbitrary unit).

(Example 1, Comparative Examples 1-2)
The calculated α, β, and γ were substituted into the formula (IV), the formula (X), and the formula (XI). Then, by substituting the measured value (0.2142) of the scattering intensity of PSL particles with a particle diameter of 50 nm into I (scattering intensity) of each formula obtained by substituting α, β, and γ, and calculating based on each formula The particle diameter D (D ₅₀ ) to be obtained was determined. Similarly, the measured value (0.0570) of the scattering intensity of PSL particles having a particle size of 40 nm was substituted to determine the particle size D (D ₄₀ ) calculated based on each formula. The results are shown in Table 1.

  From Example 1 and Comparative Examples 1 and 2 in Table 1, it became clear that a more accurate particle diameter can be obtained according to the calibration curve created according to the calibration curve creation method of the present invention.

  According to the present invention, it is possible to easily measure an accurate particle size of a fine particle having a small particle size with a light scattering particle size measuring apparatus.

Claims (4)

With a light scattering particle size measuring device, the scattering intensity of each of two types of known particle sizes D ₁ and D ₂ (where D ₁ <D ₂ ≦ 105 nm) is measured,
A scattering intensity I ₁ of the particles having a particle diameter D _1, by using the scattering intensity I ₂ of the particle diameter D ₂ particles, the following formula:
I ₁ = α × (D ₁ ) ^γ
I ₂ = α × (D ₂ ) ^γ
I ₁ = β × (D ₁ ) ⁶
Determine α, β and γ that satisfy
The region of the particle diameter D _{<D 1,} and the particle diameter D, a scattering intensity I D = {(I / α) -γ + (I / β) -6} / 2
A method for creating a calibration curve for a light scattering particle size measuring apparatus, comprising creating a calibration curve that satisfies the following conditions. Wherein a particle diameter _{D 1} is 40 to 50 nm, the particle diameter _{D 2} is 50～105Nm, how to create a calibration curve of the light scattering type particle size measuring apparatus according to claim 1. The difference between the particle diameter _{D 1} and the particle diameter _{D 2 (D} 2 -D ₁₎ is at 20nm or less, how to create a calibration curve of the light scattering type particle size measuring apparatus according to claim 1 or 2.   The method for creating a calibration curve for a light scattering particle size measuring apparatus according to any one of claims 1 to 3, wherein the particle size D is less than 40 nm.

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