JPH02128106A - Measurement of refractive index, absorption coefficient and thickness for thin film - Google Patents

Abstract

PURPOSE:To enable highly accurate and handy measurement of a refractive index, absorption coefficient and thickness of an uppermost layer thin film in a non-destructive and non-contact manner by arranging a measuring process of an energy reflection factor, a specified process of a function for computation and an arithmetic process. CONSTITUTION:One layer or more of thin films are formed on a substrate with a refractive index and an absorption coefficient known and a refractive index, an absorption coefficient and a thickness of a thin film other than the uppermost layer are known. When one or more of a refractive index n1, an absorption coefficient K1 and a thickness d1 of the upper layer are unknown values, these unknown values are measured as follows: First, when the number of known values is (i) (i<=3), monochromatic light P polarized and S polarized with a wavelength lambda is made incident at angles theta01... and theta0j of the number (j) (j>=i) of multi-layer films and an energy reflection factor RP (theta0k) and RS (theta0k) (wherein K=1... and j) are measured. Then, based on the refractive index, the refractive index and absorption coefficient of the substrate and the absorption coefficient, the thickness, the reflection factor HP (theta0k), RS (theta0k) and the angles theta0k (K=1... and j), (j) specified equations are specified according to a Fresnel formula. Subsequently, these equations are computed to determine unknown values.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a method for measuring the refractive index, absorption coefficient, and film thickness of a thin film, and more specifically, a method for measuring the refractive index, absorption coefficient, and film thickness of the uppermost thin film of a multilayer film.
This invention relates to a method for measuring film thickness.

[Prior Art] Ellipsometry has been known as a method for non-contact, non-destructive measurement of the refractive index of a thin film, but it requires a complicated and large-scale device to carry out.

[Problem to be solved by the invention] The inventor first applied S-polarized light and P-polarized light to a thin film whose refractive index was to be measured.
We proposed a refractive index measurement method in which polarized monochromatic light is incident, its energy reflectance is measured, and the refractive index is determined computationally based on the results (for example, Japanese Patent Laid-Open No. 63-1
40940).

However, these methods can only be applied to films that are transparent to the wavelength used.

The present invention has been made in view of the above-mentioned circumstances, and its purpose is to measure the refractive index, absorption coefficient, and film thickness of the top layer thin film of not only a single layer film but also a multilayer film. The object of the present invention is to provide a new method for measuring refractive index.

[Means to solve the problem] One aspect of the present invention will be explained below.

The present invention is characterized in that ``one or more thin films are formed on a substrate whose refractive index and absorption coefficient are known, and the refractive index, absorption coefficient, and film thickness of the thin films other than the topmost layer are known; When one or more of the refractive index (nl), absorption coefficient (kl), and film thickness (d+) of the upper layer are unknown quantities, this is a method for measuring the unknown quantities of the uppermost thin film. If it is formed as a film, it goes without saying that this thin film is the top layer film, and in this case it is sufficient that the refractive index and absorption coefficient of the substrate are known.

The method of the present invention is realized by performing the following steps. That is, a measurement process of measuring energy reflectance, and a specification process of specifying a function for calculation.

This is a calculation process.

In the measurement process, when the number of unknown quantities is j (i≦3), j (j≧i) different incident angles of 0°1. θ. l＋＋＋＋θ. , let P-polarized light and S-polarized monochromatic light whose wavelength is λ enter, and calculate the energy reflectance Rρ(OoJ, Rs(Ooh)(k”) for each incident light.
x, 2. , , j).

The specific step is to determine the refractive index and absorption coefficient of the substrate.

Refractive index, absorption coefficient, and film thickness of thin films other than the top layer.

The above energy reflectance Rρ(θok)tR3(θok)
and the angle of incidence θ. g(k:1tz-+j), i.e., j equations based on known quantities and measured quantities, according to Fresnel's formula, with only the above nl+kl and di as variables%
).

The calculation step is a step of calculating the unknown quantity by solving the above equation group for the unknown quantity among the above nl+klydl.

[Made for use] The present invention will be described in detail with reference to FIG.

In FIG. 1(A), the reference numeral 13 indicates a substrate, and the reference numerals u, iz
As shown in Figure 0, which shows thin films stacked on a substrate 13, the thin film 11 is the topmost thin film, and the case where the refractive index, absorption coefficient, and film thickness of this thin film are to be measured will be described as an example. That is, it is assumed that the refractive index, absorption coefficient, and film thickness of the uppermost thin film 11 are unknown quantities.

As shown in the figure, the interface between the incident medium and the thin film 11 is 50. .

The interface between the thin films 11 and 12 is S, 2. Thin film 12 and substrate 13
Let the boundary surface be S23.

The refractive index is that of the incident medium n. , thin film 11. Thin film 12
, the refractive index of the substrate 13 is 'Flt'n+-IJ, 'nz'nz-1kl, 7, respectively.
1g"nl-iks.The imaginary part on the right side of these equations is the absorption coefficient. Normally, 1 can be used as the refractive index of air.

In addition, the film thickness of the thin film If, 12 is set as <d+, d2 as shown in the figure,
The incident angle of light to the thin film 11 is θ. , interface So1 and 5
The refraction angle at LitS23 was set to 01. θ1. θ Treasure.

Among the quantities shown above, the known quantities are n,,'n2. 3, d2. and the angle of incidence θ. and laser light source LS
The wavelength λ of the incident light from can be uniquely determined as a measurement condition.

Now, FIG. 1(B) shows a thin film 1 formed on a substrate 13.
2 shows a state in which light enters an incident medium with a refractive index of 6I at an incident angle θ1, that is, a state in which the thin film 11 in the state shown in FIG. 1(A) is replaced by an incident medium with a refractive index of 61. There is.

As shown in FIG. 1(B), when monochromatic light is incident from a laser light source S, its amplitude reflectance is as follows.

rs, p” [r+ta, p+rz, s, pexp(2i
β1) ko/[1+rtzs, przss, pexp(2
iβ01 (1) The subscripts S and P indicate whether the incident light is S-polarized light or P-polarized light, and r□2+r! 3 is the boundary surface 512r
This is the Fresnel reflection coefficient at SN3.

These reflection coefficients are determined by the angle of incidence θ1. Refraction angle θ1. It can be expressed as follows using θ1.

rlzp"cnxcosθT-n2cosθpaper)/(r
izcosθ7+F+xcosθH(2-1)r+z@
”(Fi+cosθY-n2cosθnote)/(n2co
sθ paper”6zCO9θi) (2-2) r2sp
:crJcO9θm-n2cosθpaper)/CE5cos
θi+nzcosθ:) (2-3)rzxs”
(n2cO9θff-n5co!l01)/(W, co
s8:+n1cos e:) (2-4
) Also, 2β1 in equation (1) means that the light travels to the boundary surface S+Z
and 523, the wavelength λ, film thickness d2, refraction angle θ1, and refractive index 6. Using.

2β:”4 x axdx (cosθ1)/λ
It is expressed as (3).

Returning to FIG. 1(A) again, the amplitude reflectance rs when two thin films 11 and 12 are laminated as shown in the same figure,
Since the amplitude reflectance at the boundary surface SXZ is equivalent to ra and t in the above equation (1),
obs, p”rs,,exp(2jβ↑)ko/[Dro
++s, pra, pexp(2i β'r)]
It can be expressed as (4). However, rot is the boundary surface S. I
The Fresnel reflection coefficient at
)/(n, cosθo+nocO5θ1) (
4-1) rQlfi: (nQcO8θo4rcO8θτ
)/(nocos θ o+n+cos θ t)
(4-2) and the light is the boundary surface S. l
The phase change 2β1 that occurs during one round trip between and S+Z
is 2βτ=4πn, d, (cosθ1)/λ
(5).

If other thin films are formed on the substrate 13 in addition to the thin films 11 and 12 (assuming that the other thin films are sequentially provided between the thin film 12 and the substrate 13), the above By repeating the procedure, the amplitude reflectance ra, p at the topmost N thin film of a multilayer film formed on a substrate can be calculated by changing the amplitude reflectance ra,p at the interface between the top layer and the incident medium to r0□2
1. If the above-mentioned top layer thin film is replaced with an incident medium (refractive index) having the same refractive index as that of the top layer thin film, and the amplitude reflectance when monochromatic light is directly incident on the thin film directly below is rs, P, then
The above equation (4) can be applied as is.

rotal prrl Since P is generally a complex quantity.

These are defined as robs, p=/)ops, peXP(j φ .xa
, P) (8-1) ra, p=ρs, peXP
(jδ l, P) (6-2) Since 2βt is also a complex quantity, we can write this as 2βτ=
γ(ut+iv+) (6-3) where γ=4πdt/λ.

Also, 11. V is given as follows.

2ut=ni-kj-ngsin"θ.+nI-to+-
nosln θ. ÷nmJ (6-4)2u4=
−(nf−ki−ngsin”θ.)÷nl−+−n
os111 θo +4nxkn (6-5)
When formulas (8-1), (6-2), and (8-3) are substituted into formula (4), the amplitude reflectance r=, p becomes as follows.

rsrp: [p ota, pexp(iφoss, p
)” ρ !L peXP(-Vt γ)axp(i(
δs+p”utγ)]/[Dpoxm, ppts, p
eXPC-v1γ)exp(i(φ oss, p+δ
a, plum 'f))] (7) This (7)
If we set eXP(-V□7)=f' yu+γ=θ in the equation, the energy reflectance will be as follows.

Rp=I rp I ” [ρRI?+ρ ρ2+2ρOIPρpρcos(δP
−φ. rp+ o )]/[l+ρjlPρj p 2
+2p orpp pp cos(φOIP+δ, θ)
]R5=1r312=[ρ island, +ρヱρ2+2ρG+8ρ, pcos(δ3−
φ018”θ)]/[1+ρ island 3ρヱρ2+2ρ018
ρ3ρcos (φ01a+68+θ)] (8-1)
, (8-2) can be transformed as follows.

Apcosθ−Bpsjnθ”CP
(9-1)^acosθ−B, sinθ=Ca
(El-1) However.

As, P = R,, cos(φ611!1.P÷δa, P)-
CO5(δs, p-φ01B, P)8B, P''Ra, psin(φoss, p+δa, p)-s
in (δs, p-φ61111P) CM, p = [ρR+s, p-Ra, p÷ρ2ρ! ,F(1-R8
, Pρo, , P)]/2ρO1a, Pρs, pρ.

Solving the above (9-1) and (9-2) for sin θ and cos θ, sin θ = (C, A, -A, C,)/(A
, BS-BPA8) cos θ: (CpBs-BpCs)
/ (AJs-BpAs). Therefore, the identity s
If we use in"θ÷eO9"θ=1.

Cj(AM+Bri)CM(Ai!+[j)-2CpC+
+(ApAs"BpBg)"(ApBs-BpAs)"
(10) is obtained.

If we write this (10) in addition to ρ, we get a(θ)+
o”+b(θ)p+c((j) (
11) becomes a quadratic equation.

however.

a(θ)”/) As3/) M”ρ5(1-RpρL
p)"(AM+8ri"J)alpP f'/)a(1
−R8/)Ls)”(Ai+Bi)−2ρ., 8ρλρ
. , Pρ 滲(1-RpρgIP)(1-Rsp Lm)
(AJa×BPBII)b(θ)=l) gsslJ
MP! (, o Lp-RP) (1-RPρLr) (Ai
+Bwa+27) LplJ 寥ρM(1) Lm-R8
) (1-Rsp island s) (AM+Bri+2ρLa/) a
ρg, pl) p((1) Lp-RP) 9 M(1
−RspLs)+(ρLs−Rs)ρi (1−Rp+
o j IF)) (APA8+BPBII)-4ρ(
i Isρ蟲ρglPρ1(ApBs”ApBa)”C
(θ): ρgISρho(ρLp−Rp)”(Ai+Bi
)”/) Lpρi(, o Ls-R5)”(Af+
÷Bt)-2ρ018ρSρo+pρ de(ρg 1p
−Rp) (ρLa−Rs) (ApAs+BJs) Solving the above equation (11) for ρ, we get ρ = (−b(θ)± −aθbθ )/2a(θ)
(12), by the way, ρ=exp(-v, γ)
Therefore, by solving (12) roughly for γ, we get γ = −(1/2v+)In[−b(θ)± −a
c/2a(θ)] (13) This fact Y can be expressed as follows.

γ=γ(λ, θ0tnOtnl, +*+tns, 1.
2. , , ,kwtdl+dz+--td+++t
na, ka, RP+R5) (”) i.e. γ
are the wavelength λ of monochromatic light and the angle of incidence θ. , refractive index n of the incident medium
0 (usually n, , = 1), the refractive index and absorption coefficient of the substrate n8. ks, the refractive index and absorption coefficient n1~nmtkl~ of the thin film laminated in m layers on the substrate. Film thickness d.

~d at is determined as a function of the energy reflectance Rp, Rs.

By definition, γ is 4πd+/λ.

In the above equation (14), among the arguments that determine γ, the above λ
, θ. , no+ n1lyB, n2~+)@yk2~+a+ d2~d m are known quantities, and the energy reflectances Rp and Rs are obtained by measurement. Therefore, Rp,
After measuring Rs, the unknown quantity nI t k l +
The following equation for d H is obtained:

4zd+/λ=y (nxtks)
(15) The form of the function γ is not necessarily simple, but basically, each element of the defining equation is replaced by the basic variables λ and θ. It can be calculated by sequentially reducing it as a function, and this process can be done by programming the calculation process in a computer.

Since the number of unknown quantities in equation (15) is three, in order to specify these, the same equation as (15) must be written as three.
If there are any of the above, these unknown quantities can be identified by solving them as simultaneous equations regarding the unknown quantities. (1,5
) can be obtained by measuring the energy reflectance by varying the incident angle.

That is, if the incident angle changes, the energy reflectance generally changes, so the parameter 〇 in equation (14). , Rp
, Rs changes, and an equation equivalent to (15) is obtained.

Therefore, if the number of unknown quantities in the refractive index nt, absorption coefficient, and film thickness d of the top layer thin film is generally one (i≦3), then the number of required equations is i. Because of the above, there are j (j≧i) different incident angles θ on the multilayer film on the substrate.
. 1. θ. 2*++to. , , P-polarized light and S-polarized monochromatic light having a wavelength of λ are input, and the energy reflectances Rp(θok) and Rs(θ, , )(k=i) for each incident light are made incident.

2, , j) were measured, and the refractive index and absorption coefficient of the above-mentioned substrate, the refractive index and absorption coefficient of the thin film other than the top layer, and the film thickness were measured.

Based on the energy reflectance Rp (θokLRs (θok)) and the incident angle θox (k: 1t2., j),
j equations with only 1ykl+dl as a variable 4πd+/λ=γx (+ for nt+) (k: 1 to .0 is specified, and these equations are calculated computationally for the unknown quantity in n1ykl*dl above. The desired measurement can be achieved by solving the equation and finding the unknown quantity.

It should be noted that various methods have already been programmed to solve the above-mentioned equation group computationally by numerical calculation as simultaneous equations, so these can be used as appropriate.

[Example] Hereinafter, description will be given based on specific examples.

FIG. 2 shows an example of an apparatus for carrying out the invention.

Light sources 21 and 22 are He-Ne with a stable output of 6328 wavelengths.
It is a laser, and S-polarized light and P-polarized light can be extracted by polarizers 25 and 26, respectively. S,
Selection of P-polarized light is performed by opening and closing shutters 23 and 24. Reference numeral 27 denotes a polarizing beam splitter with a high extinction ratio, which guides the S and P side lights to the measurement sample 0.

The measurement sample O and the photodetector 28 are set in the θ-2θ system as shown in the figure. That is, the measurement sample O is.

Installed on the turntable 29, the photodetector 2
8 is fixed to the tip of the arm 30. arm 49
When the turntable 29 is rotated by 20, the turntable 29 is rotated by θ in the same direction. Therefore, the angle of incidence on the measurement sample O is set to 0~
It can be set arbitrarily within a 90 degree range.

The output of the photodetector 28 is input to a data processing system 38. The data processing system 38 is composed of a photoelectric conversion system 38A and an arithmetic circuit 38B (specifically, a computer) that performs arithmetic processing on the output of the photoelectric conversion system 38A. is output to.

As a measurement sample, a refractive index of 3.858-0.018i,
A SiN film formed on a Si substrate by plasma CVD was prepared.

Refractive index n1w absorption coefficient kl + film thickness d of this SiN thin film
1 is the measurement target.

This measurement sample was set in the apparatus shown in Fig. 2, and the incident angle θ was set. θ. ,=30° θ. 2 = 45°, θ, 3 = 60°, and for each of these three incident angles, S-polarized monochromatic light,
Energy reflectances Rp and Rs for P-polarized monochromatic light were determined.

These values are Rp(θ.1=30°)=0.03432. Rp(θ.

,=45″″)=0.01430°Rp(θ.,=60
°)=0.00318Rs(θot"30")=0.
08119. R3(θa*”45’)=0.1359
9°Rs(θoi=60')"0.25276.

Using these, the above equation (%) is obtained, but for the true value of n1yk+, γl: γ2
=γ3 should hold true.

Therefore, for example, assuming an appropriate value of nl and changing the value of kl as a parameter, check whether there is a value of □ for the above γ1 = γ, = γ to hold, and if there is no 1 in the above, then The same operation is repeated by changing the value of nl to another value. This calculation process can be performed by a computer by programming, and nl that satisfies the above γ1 = γ = γ3,
If 1 is found, the film thickness d can be obtained by substituting these values into the right-hand side of the above equation.

In this example, first, assuming that the value of is 0.400,
By changing the value of nl from 1.800 to 2.200, γ
l, γ2°γ3 were calculated. At this time, γl2 γ2 = γ3
There was no value of nl that satisfied. Therefore, next, the value of kl is slightly shifted from 0.400 and the same calculation as above is performed.While repeating the calculation in this way, the value of k□ is changed to 0.400.
500, as nl changes, γ, γ2 . γ,
changes as shown in Figure 3, and when n1=2.000, γ1=γ
, =γ, =0.9929 was satisfied.

From this, the refractive index of the SiN thin film nx = 2.000
, the absorption coefficient can be specified as = 0.5006 and the film thickness d
, can be specified as d+=5oo people by setting the right side of the above equation 4zd+/λ''7x(n++kt) as 0.9929 and using 6328 people as λ.

FIG. 4 shows another example of an apparatus for carrying out the invention. To avoid confusion, the same reference numerals as in FIG. 2 are used for items that are unlikely to be confused.

The laser light from the He-Ne laser 21 with a wavelength of 6328 is split into two by the beam splitter 42.

One of the lights is received by the photodetector 44, photoelectrically converted by the photoelectric conversion system 38G, and input to the data processing system 38B.

On the other hand, the other of the two divided laser beams is made into S or P polarized light by the polarizer 43 and enters the measurement sample O.

First, the ratio of the amount of incident light after passing through the beam splitter 42 and the polarizer 43 to the amount of light incident on the photodetector 44 is measured in advance and input to the data processing system 38B.

The measurement sample O has a refractive index of 3.858-0.018i
A film of SiO□ (with a refractive index of 1.
460. A SiN film with a thickness of 5,000 mm) was formed, and a SiN film was further formed thereon by plasma CVD. The present invention was carried out as follows, assuming that the absorption coefficient x, =o, soo of this top layer thin film is known, and the refractive index n3 and film thickness d1 are unknown quantities.

That is, θ is the angle of incidence. ,=30° θ. z"80@
year.

For S, P polarized light. The energy reflectance measured at each angle of incidence.

Rp(θ.,=30°)=0.22609. Rp(0,
2=60@), 0.00313°Rs(θo+”30°
)=0.33770. Rs(0012"60°)=0.
It became 30120. Using these, the equation %) can be obtained, but since k is known, the right-hand side should hold γ, = γ2 for the true value of enl, which is a function of only n.

In this example, the value of n is changed from 1.800 to 2.200, and γ1. γ2 was calculated. At this time, γ1. γ
The changes in No. 2 were as shown in Figure 5. As shown in the figure,
2.000, γ1 = γ, =t, 9858.

Therefore, the relationship 4πd, /λ = 1.9858, 1.6
Using 328 people, we can get d,=IO00 people.

In this way, we were able to identify a SiN thin film with a refractive index of 2.0 and a film thickness of 1,000 mm.

[Effects of the Invention] As described above, according to the present invention, a novel method for measuring refractive index, absorption coefficient, and film thickness can be provided. Since this method has the above-mentioned configuration, the refractive index of the topmost thin film of a single-layer film or multi-layer film
Non-destructive absorption coefficient and film thickness.

Can be measured easily and accurately without contact.

[BRIEF DESCRIPTION OF THE DRAWINGS] Fig. 1 is a diagram for explaining the present invention in detail, Fig. 2 is a diagram schematically illustrating only the main parts of an example of an apparatus used for carrying out the present invention, and Fig. 3 is a diagram for explaining the present invention in detail. , FIG. 4 is a diagram schematically illustrating only the main parts of another example of the apparatus used for carrying out the present invention, and FIG. 5 is a diagram for explaining an embodiment using the apparatus shown in FIG. FIG. 3 is a diagram for explaining an example using the device. 110. Top layer thin film, 12. , , thin film, 13. ,, Board, 0° diagram (A') CB> Dust haze momme f Horse υ diagram

Claims (1)

[Claims] One or more thin films are formed on a substrate whose refractive index and absorption coefficient are known, and the refractive index, absorption coefficient, and film thickness of the thin films other than the top layer are known, and the above-mentioned When one or more of the refractive index n_1, absorption coefficient k_1, and film thickness d_1 of the top layer is an unknown quantity, this is a method for measuring the unknown quantities of the thin film of the top layer. When i (i≦3), there are j (j≧i) different incident angles θ_0_ on the multilayer film on the substrate.
2, θ_0_2, . ．． , θ_0_j, P-polarized light and S-polarized monochromatic light with wavelength λ are incident, and the energy reflectances Rp(θ_o_k) and Rs(θ_o_
k) (k = 1, 2..., j), the refractive index and absorption coefficient of the substrate, the refractive index and absorption coefficient of the thin film other than the top layer, the film thickness, and the energy reflectance Rp (
θ_o_k), Rs(θ_o_k) and incident angle θ_o_
Based on K (k=1, 2.., j), j equations with only the above n_1, k_1, d_1 as variables according to Fresnel's formula 4πd_1/λ=γ_K(n_1, k_1) (
refractive index/absorption of a thin film, which includes a step of specifying k=1 to j), and a step of calculating the unknown amounts by computationally solving the above equation group for the unknown quantities among the above n_1, k_1, and d_1. Coefficient/film thickness measurement method.